Department of Condensed Matter Physics

Department of Condensed Matter Physics

Novel Developments and Applications ofBimodal Atomic Force Microscopy and 3D-AFM

A thesis submitted to the Universidad Autónoma de Madridin accordance with the requirements of the degree of

Doctor in Philosophy by

Simone Benaglia

Director:Prof. Ricardo García García

Instituto de Ciencia de Materiales de MadridConsejo Superior de Investigaciones Científicas

May 2021

Acknowledgments

During these years as PhD student, I had the chance to meet many people that helpedme to grow during my research and personal path. I honestly consider the presence ofall the people listed hereafter (in alphabetical order) fundamental for my scientific andpersonal accomplishment other than the success of this PhD thesis.

First, I want to acknowledge Ricardo Garcia to have given me the possibility to bepart of an international and important group such as the ForceTool group. I thank himto have shared his view of the scientific world with me. I believe his supervision andguidance has pushed me to improve more and more my professional and research skills.

Second, I am grateful to Fabio Biscarini whose mentoring activities towards me havenever stopped since our first scientific discussion. I consider his continuous support fun-damental for my academic achievements.

Third, I want to thank all the members of the ForceTool lab that have worked withme during these years: Alma, Arancha, Carlos A., Carlos G., Cate, David, Fran, Juan,Manu, Pablo, Ruben, Ryu, Stefano and Victor. I learned so much and enjoyed my timehere because of you, guys. Thanks for all the scientific (and less scientific) discussions.The time spent with all of you makes me thinking about the importance of sharing scien-tific achievements and failures (to be considered achievements anyway), and how muchI have learned from that. In particular, I thank the colleagues that have been workingcloser to me, Alma, Carlos A., Manu, and Victor. Finally, thanks to Manu, Victor andFran who revised and helped to improve the manuscript of this thesis.

Being part of a Marie Curie ITN network, I had the possibility to meet many peoplearound Europe, to discuss with them and learn from them. I thank all the SPM 2.0fellows and supervisors that shared this experience with me, and made me understand-ing the importance of European research and international collaborations. Since Europehas given me so much, I hope to bring back to the European Union added values in thefuture. I want to thank Jonas Hafner for the good collaboration and nice time spenttogether. A special thank goes to Sofia Drakopoulou, for her partnership and friendship.We shared a good part of our PhD (in Madrid, Modena, Ferrara, and virtual chats), andI consider this extremely important for the outcome of my work.The reader will see that a great part of this work was realized together with severalcollaborators; all of them are thanked and their contribution acknowledged at the be-ginning of each chapter.

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I am grateful to the members of the PhD committee, Agustina Asenjo, EnriqueChacón, Fabio Biscarini, Gabriel Gomila, Pedro Tarazona, Roger Proksch, and RubénPérez.I want to thank my tutor, Celia Polop, for helping me with all the university paper-

work.

Voglio ringraziare la mia famiglia per il loro supporto durante questi anni lontano dacasa. Grazie a mia madre e mio padre, Susi e Gianluca, a mio fratello, Riccardo; grazie amia zia e mio zio, Amedea e Rino, e a tutto il resto della famiglia Rota, Mati, Vale, Cris,Barbara, Rubes e Mariella. Grazie per avermi sostenuto nel mio cammino personale eaccademico.

Voglio ringraziare i miei amici piú cari, che mi sono mancati duranti questi anni anchese la loro presenza si è sempre fatta sentire. Grazie Richi, Luca, Dero, Gio, Lambru,Pier e Matte.

Infine voglio ringraziare Lisa: la tua presenza è stata fondamentale e necessaria perraggiungere questo traguardo. Grazie del tuo sostegno e quello della tua famiglia. Grazieper avermi supportato durante questi anni. Non vedo l’ora di vivere nuove avventure altuo fianco.

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Contents

Abstract 13

Resumen 15

1. Introduction 171.1. AFM historical background . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2. AFM working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3. Tip-sample forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3.1. Contact mechanics forces . . . . . . . . . . . . . . . . . . . . . . . 221.3.2. Solvation forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.4. Dynamic modes AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.4.1. Amplitude Modulation AFM . . . . . . . . . . . . . . . . . . . . . 271.4.2. Frequency Modulation AFM . . . . . . . . . . . . . . . . . . . . . 291.4.3. Multifrequency AFM . . . . . . . . . . . . . . . . . . . . . . . . . . 301.4.4. 3D-AFM on solid-liquid interfaces . . . . . . . . . . . . . . . . . . 31

2. Bimodal Atomic Force Microscopy for the study of soft matter mechanicalproperties 332.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2. Set-up and Theoretical framework of bimodal AFM viscoelastic mapping 34

2.2.1. Consideration about the Kelvin-Voigt model and true topographyreconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.1. Bimodal AFM on PS, LDPE and PS-b-PMMA . . . . . . . . . . . 40

2.3.1.1. Preparation of the samples . . . . . . . . . . . . . . . . . 402.3.1.2. Bimodal AFM experimental set-up . . . . . . . . . . . . . 402.3.1.3. Cantilever calibration . . . . . . . . . . . . . . . . . . . . 422.3.1.4. Numerical simulations . . . . . . . . . . . . . . . . . . . . 43

2.3.2. Bimodal AFM on P(VDF-TrFE) . . . . . . . . . . . . . . . . . . . 432.4. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.4.1. Bimodal AFM mapping on PS and LDPE . . . . . . . . . . . . . . 442.4.2. Bimodal AFM on PS-b-PMMA . . . . . . . . . . . . . . . . . . . . 482.4.3. Accuracy of bimodal AFM to determine viscoelastic parameters . . 502.4.4. Reliability of bimodal AFM true topography reconstruction . . . . 522.4.5. Bimodal AFM on P(VDF-TrFE) . . . . . . . . . . . . . . . . . . . 53

2.4.5.1. Temperature dependent mechanical behavior . . . . . . . 552.4.5.2. Polymer reorganization above Tc . . . . . . . . . . . . . . 56

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2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3. Bimodal and high resolution AFM for the study of organic electronic semi-conductors 613.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.2. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.2. Device fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.3. Electrical stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2.4. Bimodal AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.2.5. Amplitude Modulation AFM high resolution imaging . . . . . . . . 67

3.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.3.1. Bimodal AFM and high resolution AM-AFM . . . . . . . . . . . . 673.3.2. In operando bimodal AFM nanomechanical mapping . . . . . . . . 69

3.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4. Solid-liquid interface characterization of hydrophobic surfaces 774.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2. Set-up and theory of 3D-AFM . . . . . . . . . . . . . . . . . . . . . . . . . 784.3. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.3.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.3.2. 3D-AFM and 2D-AFM . . . . . . . . . . . . . . . . . . . . . . . . 834.3.3. Electrochemical Impedance spectroscopy . . . . . . . . . . . . . . . 844.3.4. Molecular dynamic simulation . . . . . . . . . . . . . . . . . . . . . 84

4.4. 2D-AFM Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.5. 3D-AFM Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.5.1. Comparison with hydrophilic surfaces . . . . . . . . . . . . . . . . 914.5.2. Consideration about the ripples and solvation layers on hydropho-

bic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.5.3. Experiments in alkanes and degassed water . . . . . . . . . . . . . 944.5.4. Comparison with MD simulations . . . . . . . . . . . . . . . . . . 95


5. 3D-AFM visualization of alkane-solid interfaces 1035.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.2.2. 3D-AFM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

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6. 3D-AFM mapping of high molarity electrolyte solutions 1136.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.2.1. 3D-AFM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2.2. AFM Tip functionalization . . . . . . . . . . . . . . . . . . . . . . 1166.2.3. DFT simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.3.1. 3D-AFM results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.3.2. Comparison with DFT simulations . . . . . . . . . . . . . . . . . . 123


General Conclusions 129

Conclusiones Generales 132

List of Publications 135

Appendix 137

A. Supporting Information Chapter 3 138

B. Supporting Information Chapter 4 144

C. Supporting Information Chapter 5 150

D. Supporting Information Chapter 6 152

References 155

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Abstract

Understanding surface and interfacial properties of materials is fundamental to employthem for novel applications. The Atomic Force Microscope is one of the most versatiletools for that purpose. It can be applied in vacuum, air or liquid solution, for the study ofmaterials of very different nature, and with the purpose of unraveling intrinsic propertiesother than resolving morphological features with sub-nm resolution. All together, theseare characteristics that make the AFM unique.Among the different AFM techniques developed so far, dynamic modes stand out for

their flexibility. Dynamic AFM methods consist of an oscillatory excitation of the AFMcantilever. The two main dynamic AFM techniques are called Amplitude Modulation(AM) and Frequency Modulation (FM), which differ for the mechanism exerted by theelectronic controllers. Their use has reached a widespread popularity in academia andindustry. Recently, novel advanced dynamic AFM techniques have been developed withthree general purposes: (i) higher sensitivity, (ii) faster acquisition time, (iii) abilityto analyze material properties not accessible before. In this thesis, bimodal AFM and3D-AFM are the advanced dynamic methods of interest. Bimodal AFM is a multifre-quency AFM technique based on the simultaneous excitation of two eigenmodes of theAFM cantilever. It can be applied to unravel different types of material properties, e.g.mechanical and magnetic characteristics. For that purpose, proper force models have tobe combined with a theoretical description of the cantilever movement, and corroboratethrough simulations and experiments. 3D-AFM is a novel AFM technique which allowsto map with high resolution a three-dimensional volume. It has been applied to studyforces happening at solid-liquid interfaces, and it has unraveled how liquid moleculesarrange at the surface of a variety of materials.This thesis comprises six chapters with two main focuses, being the first the further

development and improvement of bimodal AFM and 3D-AFM, and the second to showtheir feasibility to be applied for the study of nanoscale phenomena otherwise difficult toprobe with other techniques. The details of the chapters are briefly listed in the following.

Chapter 1. A basic introduction of the Atomic Force Microscope and its compo-nents is given. Different operating modes, with a focus on dynamic AFM methods, areexplained, together with the types of forces involved in the tip-sample contact. A shortdescription of recent applications of advanced dynamic AFM techniques is finally given.

Chapter 2. Bimodal AM-FM AFM is combined with a new theoretical model whichaccounts for viscolelastic forces. It is demonstrated being valid for the study of poly-meric samples in air environment. Its feasibility is proved through experiments on testsamples and comparison with numerical simulations. Bimodal AFM is then applied to

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the study of the mechanical properties of a ferroelectric polymer (P(VDF-TrFE)) andin particular their temperature-dependence.

Chapter 3. PEDOT:PSS, an organic electronic material, is studied by means of bi-modal AFM and AM-AFM. A full compositional understanding of morphological andmechanical characteristics of the polymer is given. Finally, in operando bimodal AFMis applied to map the mechanical behavior of PEDOT:PSS upon ion insertion.

Chapter 4. The solid-liquid interface of layered hydrophobic materials (HOPG andhBN) with water is studied through 3D-AFM and AM-AFM. In particular, it is charac-terized the dependence of the interfacial properties on the air-exposure time. Air-agedsurfaces show a singular behavior, different to the one expected from literature simu-lations. AFM data are then compared to Molecular Dynamics simulations to betterunderstand the origin of the new interface.

Chapter 5. 3D-AFM is applied to study the solid-liquid interface formed by two alkanespecies, n-hexane and n-octane, and solid crystalline materials (mica and HOPG). Itis demonstrated that a very small amount of water found in nonpolar liquids forms anunexpected organization of the solid-liquid interface of hydrophilic surfaces.

Chapter 6. The solid-liquid interface of highly concentrated electrolyte solutions ismapped through 3D-AFM. In particular, AFM tips exposing a negative, positive andneutral charge are used to perform 3D-AFM experiments. They are obtained througha combination of chemical functionalizations and a fine tuning of the pH of the elec-trolyte solution. The interfacial structures change depending on the tip charge. Densityfunctional theory simulations are used to explain the 3D-AFM imaging mechanism.

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Resumen

Para comprender las propiedades superficiales e interfaciales de los materiales es fun-damental desarrollar nuevas tecnologías. El microscopio de fuerza atómica es una delas herramientas más versátiles para esa finalidad. Se puede utilizar en vacío, en aireo en líquido, para medir materiales de distinta naturaleza y para estraer propiedadesintrínsecas. Además se puede resolver características morfológicas con una resoluciónpor debajo del nanometro. Todas estas particularidades hacen que el AFM sea único.Entre las diferentes técnicas de AFM desarrolladas hasta ahora, los modos dinámicos

destacan por sus flexibilidades, donde una excitación oscilatoria es aplicada a la mi-cropalanca. Las dos principales técnicas de AFM dinámico se denominan Modulaciónde Amplitud (AM) y Modulación de Frecuencia (FM). Se diferencian por el mecanismode control electrónico. Su uso ha alcanzado una gran popularidad en el mundo académicoy en la industria. Recientemente, se desarrollaron nuevas técnicas dinámicas avanzadasde AFM, con tres finalidades: (i) mayor sensibilidad, (ii) mayor rapidez del tiempo deadquisición y (iii) capacidad de analizar propiedades de los materiales todavía no accesi-bles. En esta tesis, se utilizan principalmente dos métodos dinámicos avanzados: el AFMbimodal y el 3D-AFM. El AFM bimodal es una de las técnicas de AFM multifrecuenciaque se basa en la excitación simultánea de dos modos de oscilación de la micropalanca.Se puede aplicar para medir diferentes tipos de propiedades de los materiales, como porejemplo características mecánicas y magnéticas. Para obtener informaciones cuantita-tivas, los modelos de fuerza adecuados son combinados con una descripción teórica delmovimiento de la micropalanca, y son corroborados mediante simulaciones y experimen-tos. 3D-AFM es una nueva técnica de AFM que permite mapear con alta resoluciónun volumen tridimensional. Se puede emplear para estudiar las fuerzas que se producenen las interfaces sólido-líquido y para visualizar cómo se organizan las moléculas de loslíquidos en la superficie de distintos materiales diferentes.Esta tesis consta de seis capítulos con dos objetivos principales: el primero es el desar-

rollo y la mejora del AFM bimodal y 3D-AFM y el segundo es utilizarlos para estudiarfenómenos en la nanoescala que serían difícil de investigar con técnicas diferentes. Acontinuación, los detalles de los capítulos se enumeran brevemente.

Capítulo 1. Introducción básica del microscopio de fuerza atómica y sus componentes.Se explican los diferentes modos de funcionamiento, centrándose en los métodos dinámi-cos de AFM y los tipos de fuerzas fundamentales en el contacto punta-muestra. Fi-nalmente, se ofrece una breve descripción de las aplicaciones recientes de las técnicasavanzadas de AFM dinámico.

Chapter 2. El AFM bimodal es combinado con un nuevo modelo teórico que tiene

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en cuenta las fuerzas viscoelásticas. Se demuestra que el método es válido para medirmuestras poliméricas en aire. Se corrobora su potencialidad con los experimentos sobremuestras con un modulo elástico conocido y por medio de comparaciónes con las simu-laciones numéricas. Además, se aplica el AFM bimodal para determinar las propiedadesmecánicas de un polímero ferroeléctrico (P(VDF-TrFE)) y, en particular, la dependenciacon respecto a la temperatura.

Chapter 3. El polímero PEDOT:PSS es un material electrónico orgánico que se vaa estudiar mediante AFM bimodal y AFM en alta resolución. Se determinan las carac-terísticas morfológicas y mecánicas del polímero. Por último, se aplica el AFM bimodalpara entender el comportamiento mecánico del PEDOT:PSS tras la inserción de ionescuando un voltage es aplicado.

Chapter 4. Se estudia la interfase sólido-líquido de materiales 2D hidrofóbicos (HOPGy hBN) con agua por medio de 3D-AFM y AM-AFM. En particular, se caracteriza ladependencia de las propiedades interfaciales con el tiempo de exposición al aire. Lassuperficies expuestas al aire muestran un comportamiento singular. Además, los datosde AFM se comparan con las simulaciones de dinámica molecular para entender el origende la nueva interfase.

Chapter 5. Se aplica 3D-AFM para estudiar la interfase sólido-líquido formada pordos especies de alcanos (n-hexano y n-octano) y materiales sólidos cristalinos (mica yHOPG). Se demuestra que una cantidad muy pequeña de agua presente en los hidrocar-buros líquidos se organiza en la interfase de superficies hidrofílicas.

Chapter 6. La interfase sólido-líquido de soluciones electrolíticas altamente concen-tradas se visualiza mediante 3D-AFM. Para realizar experimentos de 3D-AFM se utilizanpuntas de AFM que exponen una carga negativa, positiva y neutra. Se obtienen medi-ante una combinación de funcionalizaciones químicas y un ajuste del pH de la soluciónelectrolítica. Las estructuras interfaciales cambian en función de la carga de la punta.El mecanismo de interacción punta-liquido es explicado por medio de simulaciones deteoría del funcional de la densidad (DFT).

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1. Introduction

1.1. AFM historical backgroundThe purpose of the Atomic Force Microscope (AFM) is to measure forces and to studyprocesses happening at the nanoscale. The AFM was developed between Stanford Uni-versity (USA) and IBM Zürich in 1986 by Gerd Binnig, Calvin Quate and ChristophGerber [1], and the very first prototype is now displayed at the Science Museum ofLondon (UK) (Fig. 1.1).The AFM was honored with the Kavli prize in Nanoscience in 2016 [2]. Since its

early days the Atomic Force Microscope has been employed to fill the gap left by othermicroscopic techniques, and especially by the Scanning Tunnelling Microscope (STM, itspredecessor, for whose invention Binning and Roher received the Nobel Prize in Physicsin the same 1986 [3]). In fact, despite its great potential, the STM can work onlyon conductive samples (since its feedback mechanism consists in the tunneling currentflowing between the tip and the sample). The AFM is not limited on measuring the(tunneling) current but it senses all kinds of forces due to the probe-sample interaction.With the introduction of the AFM, non-conductive samples [4], such as polymers [5–9],or samples in liquid environment, as biomolecules and cells [10–12] could be imaged.Interestingly, the first AFM detection system was based on a STM (Fig. 1.1b). Themovement of the cantilever rastering the sample was detected thanks to the change inthe tunneling current felt by an STM tip sitting just above the AFM cantilever, somehowunderlying the role of the AFM as natural evolution of the STM.In this manuscript, we focus on a particular class of AFM techniques which have been

the core of the development of the AFM in the last 20 years, called AFM dynamicmodes [11, 13–15]. This name derives from the fact that a sinusoidal wave is used tooscillate the cantilever (in particular at its resonances). It is worth mentioning that theconcept of dynamic mode was already linked to the first AFM: two of the three possiblemodes proposed by Binnig, Quate and Gerber resemble the nowadays dynamic AFM,driving the lever at its first eigenfrequency and using a feedback related to the changein amplitude or phase of its oscillation.The objective of this thesis is the optimization of some advanced dynamic AFM tech-

niques for unraveling and understanding surface properties and interfacial phenomena.

1.2. AFM working principleThe AFM is a mechanical system which uses a probe as detector. The AFM set-upconsists of:

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Figure 1.1.: Picture of the first AFM. (a) The prototype of the first AFM, or “touch-ing microscope”, is exhibited at the Science Museum of London (UK). (b)Scheme of the first AFM. The feedback mechanism is based on a STM set-uppositioned at the back of the AFM cantilever. Adapted from [1].

• a cantilever, usually made of silicon or Si3N4, whose backside is reflective, andat which apex a tip is located. The radius of the tip has dimensions of fewnanometer and its aspect ratio have a crucial role to determine the lateral resolutionof the imaging mechanism. The cantilever can be rectangular or V-shaped. Inthis framework, rectangular cantilevers were used. Relevant parameters of thecantilever are its stiffness or spring constant (k), resonance frequency (ω = 2πf)and Q-factor. The determination of these parameters requires the use of specificmethodologies which have been proposed during the last 30 years. In particular, therelevant ones for this thesis are: (i) the Thermal Noise Method [16,17], based on theequipartition theorem; the latter states for a free cantilever at equilibrium with theenvironment, that the kinetic energy (Ek) is equal to 1

2k⟨z2⟩ = 1

2kBT , where⟨z2⟩

is the mean deflection caused by thermal vibrations, kB is the Boltzmann constantand T is the temperature. A fitting of the single harmonic oscillator (SHO) modelto⟨z2⟩, obtained from the power spectral density (PSD) amplitude, allows to get

unknown cantilever parameters (Fig. 1.2). (ii) A more recent development ofSader’s theory, i.e. the so-called Qf1.3 scaling method (more details are given inChapter 2) [18, 19]. (iii) An empirical formula proposed by Labuda et al. for thedetermination of higher eigenmodes of the cantilever (more details are given inChapter 2) [20];

• a tip-sample motion system. This is a set of piezoelectric actuators (x,y,z)which allows to move the tip orthogonal to the sample (z movement) and to rasterthe sample (x,y movement) with high accuracy. The piezo scanners can be placedeither underneath the sample surface or above it;

• a feedback controller. The feedback system is chosen depending on the AFMmode. In the simplest working mode, called contact mode, the cantilever is scannedin x,y directions with respect to the sample. The presence of nanoscale features

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Figure 1.2.: AFM probes and calibration. (a) Optical pictures of microcantilevers madeof Si3N4 (top-left side) and silicon (top-right side). Scanning electron mi-croscopy image of a silicon cantilever with a nanometric tip at its apex(bottom part). Adapted from [15, 21]. (b) Power spectral density (PSD)of a microcantilever (BL-AC40TS) exposed to thermal noise in liquid. Thefirst four resonances are clearly observed. The insets show the fitting of thePSD of the first two modes to the function of the single harmonic oscillator.Adapted from [21].

with different dimension and physico-chemical properties is probed by the tipthrough the bending of the cantilever. The latter is sensed by the detection systemthat feeds the feedback controller. In contact mode, the feedback is based on aset-point of the force applied to the sample by the cantilever. In the followingparagraphs, a description of dynamic mode feedback mechanisms will be provided;

• a detection system. The most common system is optical-based [22, 23]. Alaser (wavelength of around λ = 650 nm) is directed at the back of the cantilever,which in turn reflects the laser towards a photodiode. The latter, by convertingthe light into current, feeds the electronic feedback and produces the output; it iscommon to use four segmented photodiodes, enabling the detection of both normaland lateral forces. Moreover, with the optical-based method the deflection of thecantilever z (vertical displacement) is not directly measured but its change in slopedz/dx. Anyway, it is possible to deduce a relationship between changes in slopeand changes in deflection, such as z(L) = 2L

3dz(L)dx , where L is the length of the

cantilever. Finally, the output current of the photodiode detector is eventuallytransformed in an output voltage. To measure the deflection, this voltage has tobe converted in nm. This is done thanks to a factor, called sensitivity, which can beobtained moving the cantilever towards the sample and recording the photodiodeoutput voltage with respect to the z piezo displacement, σs = ∆V

∆Z . σs is the staticsensitivity, i.e. obtained when no excitation is applied to the cantilever. Thereare factors which allow to convert the static sensitivity to dynamic ones. In this

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thesis, the inverse of the optical sensitivity (InvOLS, σ−1n where n indicates the

nth eigenmode) will be used.

• an excitation system. This component allows to apply a sinusoidal excitationto the cantilever. This is the fundamental feature for dynamic AFM modes. Themost used excitation is mechanical-based. A piezo-actuator is connected at thebottom of the cantilever and its vibration produces the oscillation of the cantileveritself. The main drawback is that in liquid environment it also excites the fluid,causing the so-called “forest of peaks” [24], which makes the work of the feedbackcontroller for dynamic modes particularly difficult. To avoid this issue, a magneticexcitation, based on a magnetized cantilever and a coiled-generated magnetic fieldhas been used. Another method to excite the cantilever is based on a photothermalexcitation [25], where a sinusoidal beam generated by a laser diode points to theback of the cantilever: this set-up will be the one used in this thesis when workingin a liquid fluid.

A typical AFM set-up is shown in Fig. 1.3. In particular, it illustrates an AM scheme(more details are given in the next paragraphs).In general, there are two different types of functionalities: imaging and force spec-

troscopy. During the imaging, the cantilever moves with an x,y movement over thesample where the x and y are called fast and slow movements, respectively. The outputis an image in two dimension (2D) where each pixel contains information regarding thetip-sample interaction. A feedback mechanism, depending on the chosen mode (con-tact, AM, FM etc.), acts on the cantilever keeping a certain set-point. The spectroscopymechanism works in a considerable different way: the cantilever is displaced in z, record-ing a curve (force, amplitude, phase etc. depending on the feedback mechanism). It ispossible to record different force curves in a x,y matrix in order to obtain a map whereeach pixel contains a single curve. The difference between the two methods is the speedof the image acquisition, which is much higher in the scanning with respect to the spec-troscopy. In the recent history of AFM, there have been improvements on the speedof the spectroscopy techniques [26]; still, most of the commercial instruments generallysuffers of this limitation. On the other end, spectroscopies, and especially the ones wherethe force is used as the main feedback, give a direct connection to the tip-sample forcewhich is not the case for imaging methods. There has been a big effort to transformobservables of scanning methods into the tip-sample force. These are called parametricmethods and they are mainly referred to dynamic AFM techniques [27]. In the following,the mechanism of different parametric methods will be summarized.

20

Figure 1.3.: AFM scheme of an amplitude modulation set-up. The system is composedof: an AFM cantilever driven at a certain oscillation that performs an xymovement with respect to the sample surface (actually, here x and y scan-ners move the sample). A laser diode pointing at the back of the cantileveris reflected towards a detector, whose read-out goes through a lock-in ampli-fier. The latter records the phase shift of the oscillation and the oscillationamplitude with respect to a reference signal (due to the driving oscillationof the cantilever). The amplitude is kept at certain set-point by the activ-ity of a feedback controller which acts on the z piezo and determines thetopographical image.

1.3. Tip-sample forcesIn general, the forces probed by an atomic force microscope can be split in short andlong range forces. They depend on different factors, especially the medium where themeasurement takes place. In air, the relevant forces are van der Waals interactions, shortrange repulsive interactions, adhesion and capillary forces. In liquid, an electric doublelayer is built up and solvation forces become important. Thus, electrostatic interactionsare of particular relevance in liquid and their intensity is controlled by the ionic strength.In the following, a brief discussion regarding contact mechanics and solvation forces aredone.

21

1.3.1. Contact mechanics forcesThese are forces happening when the tip is in close vicinity with the substrate. Usually,they comprise elastic, viscous and adhesion forces. In the following description, we ne-glect adhesion forces and consider forces due to the tip-sample repulsive contact. Whenthe latter occurs, the surfaces of two objects are deformed, and this deformation dependson the applied force, and on their mechanical characteristics. Even at the nanoscale,continuum models are widely used. They assume the contact of a tip with a semi-infiniteplane. Commonly, the tip is modeled as spherical, conical or cylindrical; in our descrip-tion, the tip will be modeled as a sphere. The choice of a particular contact mechanicsmodel depends on the characteristics of the tip-sample interaction. To describe a pureelastic interaction, the most common model to use is the Hertz model. It was developedand published in 1882 by Hertz [28], and it describes the deformation of two elasticspheres without any type of dissipative processes. Sneddon generalized the Hertz modelfor any type of tip shape [29] and the resulting force can be written as [30]

F = αδβ (1.1)

where α is a coefficient that depends on the tip geometry and size and β is a coefficientwhich depends on the tip geometry. δ is the sample deformation (tip indentation). Theeffective Young’s modulus, Eeff , is expressed as

E−1eff =

(1− ν2

t

Et+ 1− ν2

s

Es

)(1.2)

where Et and Es are the Young’s modulus of the tip and the sample; νt and νs arethe Poisson coefficient of the tip and the sample. Usually, when the measurements areperformed on soft materials (such as polymers or biological matters) Et Es, eq. 1.2becomes

Eeff ≈Es

1− ν2s

(1.3)

From now on, we will make use of the sphere model (α = 4Eeff

√R

3(1−ν2s ) and β = 3/2 [27],

with R being the tip radius); eq. 1.1 then simplifies in

F = 43Eeffδa (1.4)

where a =√Rδ is defined as the contact radius between the sphere and the sample.

The sample elasticity can be represented with a spring whose stiffness is easily derivedas

ks = ∂F

∂δ= 2Eeffa (1.5)

Sneddon contact mechanics has been widely used to fit AFM data for different kindsof samples, from hard materials to biostructures, with either contact and dynamic AFM

22

techniques [31, 32]. Interestingly, especially in the case of soft samples (i.e. polymersand cells), considering them simple elastic structures neglects important characteristics,such as dissipative properties. In fact, when the tip is in contact with the sample, itcan experience not only conservative forces but also dissipative ones [33]. Those forces,such as adhesion hysteresis and viscosity, are of particular interest for this thesis. Wewill focus our discussion on viscoelasticity, in particular of polymer thin films. If theelasticity of the sample can be represented with a spring, viscous components can bepictured as dashpots.

Figure 1.4.: Modelling viscoelasticity with AFM. (a) Kelvin-Voigt, on the left, andMaxwell model, on the right. The spring represent the elastic component,while the dashpot the viscous one. (b) Simulated force behavior of a vis-coelastic material modeled as a Kelvin-Voigt material [34]. The Young’smodulus, E, is kept constant, while the viscous coefficient, η, is varied. Amore viscous behavior is marked by an increased separation between thetrace and the retrace.

The two simplest linear viscoelastic models are the Maxwell and Kelvin-Voigt mod-els, where a spring and a dashpot are in series and in parallel (Fig. 1.4a), respec-tively [35]. Nowadays, these models are widely implemented to quantify mechanicalproperties through AFM spectroscopic methods [30, 32, 36–38]. Though, their applica-tion in dynamic mode techniques is not straightforward and it has been mainly theoret-ical [39, 40] or requires a relevant computational effort [41, 42]. In an AFM force curvetaken over a viscoelastic material, the behavior of the approach and retraction curve ofthe cantilever changes. In particular for a Kelvin-Voigt material, the distance betweenthe two curves tends to increase the higher is the viscosity of the material (Fig. 1.4b).Mathematically speaking, the elastic force and the viscous force are simply added on.In particular, the viscous contribution can be approximated as [30,43]

23

Fvis = −2η√Rδ

dδ

dt(1.6)

where η is the viscous coefficient. It is worth to note that Fvis depends on the deforma-tion and on its derivative, i.e. the speed of the deformation. Additional considerationsabout the Kelvin-Voigt model applied to AFM will be done in Chapter 2.

1.3.2. Solvation forcesWhen speaking about solid-liquid interfaces [44], the liquid density distribution changesdepending on the distance from the solid surface: in fact, it oscillates with the distanceand these oscillations are about few molecular diameters. Their periodicity is close tothe dimension of the size of the liquid molecules. These particular forces are calledsolvation forces or hydration forces when the liquid is water. Solvation forces werefirst described by Israelachvili’s group with the use of the Surface Force Apparatus(SFA), which measures the force between two surfaces (usually mica surfaces) when oneapproaches the other [45]. Oscillations, with periodicity equals to the van der Waalsdiameter of the liquid molecules, were shown taking place in organic liquid and in purewater, overall underling that liquids of different nature behave in a similar manner [46–49]. The presence of solvation structures was initially attributed to two contributions, thefirst being the attractive interaction between the surface and the liquid, and the secondthe confinement induced by pressing together two surfaces. However, disentangling oneelement to the other was a hard duty for the SFA, due to the large extension of themica surfaces. Other spectroscopic techniques, such as X-ray reflectometry [50] and X-ray absorption spectroscopy [51], allowed to visualize the organization of liquid at theinterface.Interestingly, when the AFM started to be applied to study solid-liquid interfaces,

similar results were accomplished [52,53]. Contact and dynamic AFM modes have beenused to unravel the organization of a variety of liquids (i.e. water, aqueous ionic solutions,ionic liquids, organic liquids) [53–66] on surfaces of different nature (i.e. hydrophilic andhydrophobic crystalline layered materials, biomolecules and lipids) [67–74]. Theoreticalapproaches have been developed and nowadays a better understanding of the solvationstructures has been achieved. In particular, the radius of the tip is assumed to berelated to the solvation layer that is formed around the tip (solvent-tip approximation,STA) [75], thus close to the dimension of the liquid molecules. Moreover, the STAmodel establishes a one-to-one correlation between peaks in the force distance curvesand peaks in the liquid density. Further theoretical works showed that the solvationstructures would not be possible if attractive forces were not formed between the solidand the liquid, underling the intrinsic nature of solvation structures [76].

1.4. Dynamic modes AFMThese modes are named dynamic because the cantilever is oscillated, usually at itsresonance frequency, and a specific feedback system is implemented to control the move-

24

ment of the cantilever. In particular, we recognize two fundamental dynamic modes [14],called Amplitude Modulation (AM) and Frequency Modulation (FM), and a third classof derived modes which is of fundamental interest in this thesis, called MultifrequencyAFM [15,77,78].The cantilever motion can be described with the mathematical framework of the har-

monic oscillator, using the point-mass approximation [15, 77]. The simplest idea of theharmonic oscillator comes from a mass acting on a spring. In case no oscillation isapplied to the system, the force acting on the mass is given by Hooke’s law as

F = −kx (1.7)

where k and x are the stiffness and the deflection of the cantilever. When an oscillationis applied at the cantilever base, z = A cos(2πf0t−φ) where A is the amplitude and φ isthe phase shift of oscillation. In an actual AFM experiment, two important terms have tobe considered. This is formulated as the driven and damped harmonic oscillator [15]. Themotion of the cantilever can be described with the well known second order differentialequation,

k

ω02 z +(

k

ω0Q

)z + kz = F cos (ωt) + Fts (t) (1.8)

where ω (= 2πf), ω0 (= 2πf0), Q, k and F are, respectively, the driving frequency,the free resonant frequency, the quality factor, the stiffness and the driving force of thecantilever, and Fts is the tip-sample interaction force. In the left side of eq. 1.8, thesecond term is related to the damping (Q = m∗ω0/γ, with m∗ and γ as the effectivemass and the damping coefficient), while the first term of the right side is related to thedriving. A characteristic of the harmonic oscillator is the relation between the frequency,the mass and the force constant of the oscillator. In fact,

ωo =

√k

m(1.9)

The harmonic oscillator main observables are the amplitude and the phase of the oscil-lation. A mathematical solution for both of them can be derived,

A (ω) = F0/m[(ω2

0 − ω2)2 + (ω0ω/Q)2]1/2 (1.10)

tanφ (ω) = ω0ω/Q

ω20 − ω2 (1.11)

A fundamental property of dynamic AFM is the possibility to experience attractiveand repulsive interactions with the sample [15, 77, 79]. In a first approximation, let’simagine that the cantilever is brought towards the sample for small amplitudes withrespect to the resting position (z = 0); naming D = d+ z the tip-sample distance, withd being the average tip-sample distance during an oscillation cycle and z the spatialcoordinate, the tip-sample interaction force can be expressed as

25

Fts (D) = Fts (d) +(∂Fts∂z

)z=0

z + ... (1.12)

The tip-sample interaction can be represented as a small spring constant k∗

k∗ = −(∂Fts∂z

)z=0

(1.13)

In this way, two springs in series add up and we obtain keff = k + k∗. We can thenrewrite eq. 1.9 as

ω∗o =

√keffm

=

√k + k∗

m=√k

m

(1 + k∗

k

)= ω0

√1 + k∗

k(1.14)

Assuming k∗ k, for small x we can use the approximation√

1 + x ≈ 1 + 12x. The new

resonance frequency is written as

ω∗o = ω0

(1 + k∗

2k

)(1.15)

Then, we can finally write the frequency shift as,

∆ω = ω∗0 − ω0 = ω0k∗

2k = −ω02k

(δFtsδz

)(1.16)

As stated before, this concept is useful to explain the attractive and repulsive regimeexperienced by the cantilever, and how the resonance frequency, amplitude and phasechange accordingly to the type of force. Assuming a Lennard-Jones potential behavior,it is clear, that when the force is attractive, i.e. with a positive force gradient, a negativefrequency shift is obtained; while when the force is repulsive, i.e. with a negative forcegradient, ∆ω is positive. This is represented in Fig. 1.5a,b. The amplitude alwaysdecreases independently of the gradient of the force, while the phase shifts to valueshigher than 90° when an attractive force is experienced, and smaller than 90° when arepulsive force is detected. In reality, the mechanism of interaction between the tip andthe sample is rather more complex, usually non-linear [80, 81]. Moreover, it is not truethat attractive (repulsive) forces always correspond to a negative (positive) frequencyshift and positive (negative) force gradient: as it is illustrated in Fig. 1.5c, there is anarea in the attractive regime where the frequency shift is positive. Nevertheless, thisexplanation is useful in a first approximation to understand the tip-sample interactionin dynamic AFM.

26

Figure 1.5.: Amplitude modulation working principle. (a) Amplitude and (b) phasebehavior depending on the gradient of the force of interaction between thetip and the sample. In blue and in red, the shift of the resonance frequencyand consequently of the amplitude and phase curves is highlighted due toa repulsive and an attractive force, respectively. The black dots mark thenew values of the amplitude and phase when a repulsive and an attractiveforce are felt. The amplitude decreases in both cases, while the phase getsa smaller or higher value (than 90°) if the force is repulsive or attractive,respectively. (c) Potential (U(d)), force (F (d)) and negative gradient of theforce (−F ′(d)) for a Lennard-Jones model as a function of the average tip-sample distance, d. Repulsive and attractive regimes are marked in grayand in blue, respectively.

1.4.1. Amplitude Modulation AFMIn AM-AFM, commercially also named tapping or intermittent contact mode, the can-tilever is driven to a certain free amplitude (A0) by an external excitation at a drivingfrequency (ω), usually one of its resonances; a lock-in amplifier is used to track theamplitude of oscillation [82]. A set point for the amplitude (Asp) is chosen and keptconstant during the imaging. This is achieved by changing the distance z between thetip and the sample (Fig. 1.3). More recently, other demodulation methods have beenused to speed up the electronic performance and to achieve faster speed in amplitudemodulation, such as peak hold and peak detector method [82, 83]. The observables arethe topography, due to the motion of the z-piezo to keep the amplitude constant, theamplitude, and the phase of the oscillation, which changes depending on the type ofinteraction between the tip and the sample, as previously illustrated. The shift of theoscillation amplitude and phase can be due to a change of topography and/or compo-sitional properties of the sample. The amplitude change happens after a typical time,

27

called transient of the oscillation, τAM , dependent on the Q-factor and on ω0 as

τAM = 2Qω0

(1.17)

This makes AM not feasible in ultra-high vacuum (UHV), where the Q-factor is inthe order of 100000.When performing an image in AM, the shift of the resonance frequency (and con-

sequently of the phase and amplitude) is connected to the type of the interaction be-tween the tip and the sample. Conservative and dissipative processes happening at thenanoscale can be distinguished using a theoretical framework based on the virial andenergy dissipation theorem [84–91]. Firstly, it is important to underline that in the caseof high Q (i.e. air environment), the phase contrast is insensitive to variations of sampleelastic properties while changes with differences in energy dissipation. This was demon-strated being an intrinsic mechanism of the AM feedback [89–91]. More recently, Ramanet al. demonstrated that the same mechanism couldn’t be considered valid for imagingin low Q condition, such as in liquid environment, where the phase shift is actually linkedto the stiffness of the sample [92]. These two mechanisms are illustrated in Fig. 1.6.Anyway, it is possible to use the virial V and energy dissipation Edis theorem to linkthe amplitude and phase shift to properties related to the tip-sample interaction. For asinusoidal oscillation z = A cos(2πf0t− φ) we obtain

V = f

1/f

0Fts(t)z(t)dt = −

(kAA0

2Q

)cosφ (1.18)

Edis = - 1/f

0Fts(t)z1(t)dt = πkAA0

Q

(sinφ− A

A0

)(1.19)

where the free amplitude A0 = F0Q/k.

28

Figure 1.6.: Phase behavior in AM atomic force microscopy. (a) Simulation of the phaseshift dependence on elastic and dissipative properties. The graph showshow for a pure elastic interaction, there is no phase shift depending on thechange of Young’s modulus of the sample. When dissipative contributionsare included (viscosity or adhesion hysteresis) a phase shift is detected, es-pecially for compliant samples. Adapted from [89]. (b) Simulations of thephase shift for a cantilver tapping (A0 = 10 nm) on a hypothetical hetero-geneous sample. The upper schematic illustrates a heterogeneous samplewhere simulations are performed. The latter is composed by three regionswith different elastic and dissipative properties: region I and II share thesame elastic modulus (EI = EII = 100 MPa) while differ in the viscous coef-ficient (ηI = 10 Pa s, ηII = 0 Pa s); region II and III share the same viscouscoefficient (ηII = ηIII = 0 Pa s) while differ in elastic properties (EII = 100MPa, EIII = 1 GPa). For a stiff cantilever in air, bottom left graph, thephase contrast behaves as stated in (a), i.e. φI 6= φII and φII = φIII ; whilefor a soft cantilever in liquid, bottom right graph, φI = φII and φII 6= φIII .Adapted from [92].

1.4.2. Frequency Modulation AFMIn FM-AFM [77], the cantilever oscillation frequency is tracked. The cantilever is notoscillated at a fixed frequency, such as in AM, but it is excited always at the resonance.When the cantilever is in contact with the sample there is a shift of the resonance fre-quency and the feedback, which usually is a Phase Lock Loop (PLL) controller, movesthe driving to that frequency, following the shift and keeping the phase at 90°. More-over, the amplitude of oscillation is controlled and kept to a fixed value by adjustingthe excitation amplitude, through an Automatic Gain Controller (AGC). If the energyis dissipated, the amplitude of oscillation decreases and then, it is increased directlyadjusting the driving power, keeping the chosen set-point. In conventional FM, a refer-

29

ence frequency is set and the output signal is proportional to the difference between thedetected frequency and the reference frequency. This signal, ∆f , is used as the imaginginformation in FM-AFM: the images are acquired at a fixed frequency shift (set-pointfrequency shift control), kept constant by changing the z-distance.

In FM, the change in eigenfrequency happens within a single oscillation cycle as τFM ≈ω−1

0 [77, 93]. Thus, it doesn’t depend on the Q-factor: this is the reason why FM hasbeen extensively applied in UHV [94–97]. In FM there is a direct way to connect ∆fto the tip-sample force, as illustrated in eq. 1.16 [98]. Moreover, the virial for a FMconfiguration is defined as

V = −kA2Δf

f0(1.20)

1.4.3. Multifrequency AFMIn the last 15 years, a new branch of AFM techniques, named multifrequency meth-ods [78, 99] has been developed and improved, allowing the fast diffusion of some ofthese methodologies as commercial instruments [100]. They are all based on the excita-tion and/or tracking of the cantilever at several eigenfrequencies. Examples are bimodalAFM [101–109], torsional mapping [110–113], multi-harmonic AFM [114–117], inter-modulation AFM [118,119] and others [120,121]. The schemes of some of these methodsare shown in Fig. 1.7. As a matter of fact, multifrequency methods have allowed toachieve compositional and, in some cases, quantitative mapping of different types ofsurface properties at the nanoscale, spanning from soft to hard materials, with highresolution and higher speed with respect to spectroscopic techniques. In multi-harmonicAFM, for example, higher harmonic components generated while scanning in dynamicmode are recorded and linked to elastic and dissipative processes at the nanoscale (Fig.1.7b). In intermodulation AFM, two frequencies in the vicinity of the resonance areexcited and a new set of frequencies generated by the nonlinear tip-sample interaction,called intermodulation products, can be translated to sample properties (Fig. 1.7c). Intorsional AFM, the tip-sample force is obtained from higher harmonic components ofthe torsional signal (Fig. 1.7d). Bimodal AFM is the multifrequency method that isused in this thesis. Bimodal AFM consists in the simultaneous excitation of two eigen-modes of the cantilever, usually the first and the second (Fig. 1.7a). These modes canbe controlled in an AM, FM or PM (phase modulation) fashion [107]. Bimodal AFMhas been used to detect long and short range forces. Examples of extracted propertiesare of magnetic [122–124] and electrical [125] origin, and of mechanical type: for in-stance, viscoelastic properties of polymers [106, 126–129], organic semiconductors [130]lipids [131, 132], proteins [105, 108, 133–137], DNA [138, 139] and cells [140]. Moreover,it allowed to achieve high resolution imaging in UHV [141–146] and in liquid environ-ment [73,147], other than subsurface imaging [121,148]. In order to extract quantitativeinformation, theoretical approaches have been developed, able to link AFM observablesto the tip-sample interaction [104, 107, 149–152]. Mathematically speaking, bimodalAFM enables the description of the dynamics of the AFM cantilever (and the properties

30

of the sample) by matching the number of unknowns and theoretical equations. In thisthesis, we will focus on the use of bimodal AFM for the study of mechanical propertiesof soft materials, such as polymers and proteins. To accomplish this purpose, a newtheoretical approach to probe viscoelastic interactions is introduced.

Figure 1.7.: Multifrequency AFM methods. (a) Bimodal AFM scheme. Two of thecantilever modes are excited simultaneously. Each oscillation mode has acharacteristic shape. (b) Multi-harmonic AFM scheme: the excitation ofhigher harmonics is due to nonlinear interaction forces. The cantilever re-sponse at its harmonics is a reflection of the interaction with the sample.Adapted from [115]. (c) Intermodulation product given by the excitation oftwo frequencies around one of the cantilever eigenmodes. Top and bottompanels show the linear and nonlinear response of the cantilever, respectively.Adapted from [118]. (d) Torsional harmonic scheme. Blue and orange curvesin the oscilloscope indicate respectively the flexural and the torsional oscil-lations. Adapted from [110].

1.4.4. 3D-AFM on solid-liquid interfacesAs mentioned above, force spectroscopy consists in measuring the tip-sample interactionas a function of the vertical coordinate z. Thus, the basic mechanism comprises a onedimensional (1D) measurement. Nevertheless, it is possible to perform several 1D curveson a 2D matrix obtaining then a 3D information. The cantilever can be modulated instatic [153–155] or dynamic mode [156].One of the most promising application of such techniques is to image the interface

between liquids and solid surfaces. The first measurements realized for this purpose wereperformed by Fukuma et al. [54,157]; in particular, FM was used to control the oscillation

31

of the cantilever, and the hydration structures of water molecules on mica were resolved(Fig. 1.8a). The AFM technique was named 3D-AFM or 3D-SFM (Scanning ForceMicroscopy), due to its ability to acquire a three dimensional information. 3D-AFMgave access to new possibilities to map the solid-liquid interface with a three-dimensionaldepth of different materials at the nanoscale and in contact with liquids of differentnature. This novel technique has allowed to visualize how solvents, solutes, ions andmolecules are organized at solid-liquid interfaces. For instance, new volumetric imagesof the organization of water [54, 58, 59, 70, 71, 158], organic solvents [57], ionic liquids[155, 159] and even polymers [160] have been generated. Moreover, the distribution ofwater on a variety of surfaces has been analyzed: for instance, the interface betweenwater molecules and crystalline surfaces other than mica, such as calcite [161–163],bohemite [164], graphite [69,70,76,165] and other 2D-materials [71], and the one formedwith biomolecules, such as proteins [73], lipids [72] and DNA [74].In this thesis, 3D-AFM is run in an AM fashion [59,71,161,166]. Its working principle

lies in an additional sinusoidal z-modulation that is fast enough not to be influencedby the feedback distance regulation (AM feedback) which controls the z-movement (Fig.1.8b). Moreover, the possibility of using other types of excitation schemes in combinationwith 3D-AFM, such as bimodal AFM, has been shown [73].When the cantilever is driven in one of its modes, there is a need to convert the dynamic

observables in the tip-surface properties. Thus, different algorithms to reconstruct theinteraction force between the tip and sample for AM experiments have been developedand used in 3D-AFM experiments [86,167,168]. A thorough description of the techniqueand of the force reconstruction is provided in Chapter 4.

Figure 1.8.: Illustration of the 3D-AFM. (a) 3D-AFM image obtained at the solid-liquidinterface between mica and a PBS solution. The map shows the presenceof ordered layers of water molecules in the vicinity of the mica surface.Adapted from [157]. (b) 3D-AFM scheme: a series of z-curves is applied asa sinusoidal wave over the sample in order to obtain the 3D image. This isthe 3D-AFM scheme used in this thesis.

32

2. Bimodal Atomic Force Microscopy forthe study of soft matter mechanicalproperties

2.1. IntroductionAs discussed in the previous chapter, the AFM operation is based on the force sensed bythe tip with a defined sample. This force can be of different nature, i.e. long and shortrange. Short range forces are the type of interest in this chapter. The mechanical char-acteristics of a material are derived analyzing the repulsive contact between the tip andthe sample [27]. Mechanical properties at the nanoscale have important consequences onthe behavior of different kinds of materials. Polymers, with intrinsic spatial diversities,or multicomponent systems, show a complex bulk mechanical behavior. Therefore, beingable to connect the nanoscale morphology with their mechanical properties provides away to link nanoscale structures to intrinsic properties of the material [169]. Further-more, concerning biological samples such as cells, their viscoelastic behavior has beenlinked to their life cycle and health condition [30,32,36,37]. The AFM is one of the mostsuitable tools to provide a connection between mechanical information with features atthe nanoscale. AFM methods that aim to this purpose should be quantitative (withthe quantification independent of the probe properties or feedback parameters), able toachieve a resolution in the nanometer or sub-nanometer scale, possibly easy to implementin conventional microscopes and compatible with fast or high-data acquisition, able toprovide compositional information without cross-talks with morphological features.We can distinguish between two types of AFM approaches: force-distance curves

(FDCs) and parametric methods. Force-distance curve-based methods consist in themeasurement of the dependence of the force on the tip-sample distance [170]. Then, theYoung’s modulus is obtained by fitting the repulsive section of the force-distance curvewith a certain contact mechanics model. In FDC methods the surface is divided in amatrix of points, at each of which a FDC is recorded. Thus, these methodologies areintrinsically quite slow. Parametric nanomechanical methods consist in performing ax, y scan over the sample surface recording the cantilever response while scanning [171].The observables associated with that response are directly connected (parameterized)to certain mechanical properties. In these methods, the cantilever is usually excited ata resonant frequency or multiple eigenfrequencies [78]. Such approaches require the useof a theoretical framework, but they are intrinsically faster with respect to FDC-basedmethods (only one point per pixel is needed to obtain mechanical information). BimodalAFM is one of the most promising parametric methods developed so far.

33

In this section, the theoretical framework of bimodal AM-FM is exploited. BimodalAM-FM is a multifrequency technique where the cantilever is excited at two of its res-onant frequencies, usually the first and the second flexural mode. The use of torsionalmodes was also described [128]. Different bimodal AFM configurations have been devel-oped, where a combination of the standard dynamic AFM methods (AM, FM and PM)has been chosen. In this thesis, we will focus on the AM-FM setup. This is justified es-sentially by experimental reasons, while the theoretical derivation shown in this chaptercan be applied for all the bimodal configurations. Thus, from now on when speakingabout bimodal AFM, we refer to bimodal AM-FM. The novelty of the theory describedbelow consists in the development of a viscoelastic theory for the application of bimodalAFM.Bimodal viscoelastic characterization was applied to study the properties of thin poly-

meric films. In particular, in the first section, experiments on single polymers andpolymer composites are used to test the theoretical framework. In the second section,the technique is applied to a ferroelectric polymer to better understand the connectionbetween nano and macroscale mechanical properties.The theoretical framework is part of the PhD thesis of Carlos A. Amo [172]. The

experimental work is the result of discussions and experiments performed with VictorG. Gisbert. Prof. Francesc Perez-Murano and Steven Gottlieb (Instituto de Microelec-trónica de Barcelona) are thanked for providing the protocol about the preparation ofthe block copolymer (PS-b-PMMA). The work regarding the P(VDF-TrFE) ferroelectricpolymer is part of a collaboration with Prof. Ulrich Smith and Jonas Hafner (Technis-che Universität Wien, TUW). The following results were published in three scientificarticles [21,173,174].

2.2. Set-up and Theoretical framework of bimodal AFMviscoelastic mapping

From the elastic beam equation of a rectangular cantilever, it was demonstrated thatthe motion of individual excited modes can be approximated by eq. 1.8. We can rewritethis equation in terms of the i-th mode as

ki(2πf0i) 2 zi + ki

2πf0iQizi + kizi = Fi cos (2πfit) + Fts (t) (2.1)

where fi, f0i, Qi, ki and Fi are, respectively, the driving frequency, the free resonantfrequency, the quality factor, the stiffness and the driving force of the i-th mode. Thedeflection of the tip is split in two components oscillating at the resonant frequencies

z (t) = z0 + zi (t) + z(i+n) (t) ≈Ai cos (2πfit− φi) +A(i+n) cos(2πf(i+n)t− π/2

)(2.2)

And assuming to use the first and the second mode

z (t) = z0 + z1 (t) + z2 (t) ≈A1 cos (2πf1t− φ1) +A2 cos (2πf2t− π/2) (2.3)

34

where z0, z1 and z2 are the static, the first and the second mode deflections. In the AM-FM configuration, the first mode is controlled with an AM feedback while the secondmode in FM. While scanning, the amplitude of the first mode is set to the set-pointamplitude (from now on called A1), which is smaller than the free-oscillation amplitudeA01. The second mode amplitude, A2, is kept constant by changing the driving forceF2; φ2 is kept at π

2 by means of shifting f2 at the resonance (∆f2). The analyticalexpressions were derived assuming that the value of A2 is much smaller than A1; finally,z0 is considered negligible with respect to both A1 and A2 (see below for a furtherdiscussion about z0). Fig. 2.1 illustrates the detection and excitation system appliedin bimodal AFM. In particular, it shows the excitation and detection schemes used inbimodal AM-FM along with the main observables, A1, φ1, f1 and the driving force ofthe second mode F2. To relate the observables with the tip-sample force, the virial Viand energy dissipation Edisi equations are applied to the excited modes

V1 = f1

1/f1

0Fts (t) z1 (t) dt (2.4)

V2 = f2

1/f2

0Fts (t) z2 (t) dt ≈ A2

24π

1/f1

0F ′ts (t) dt (2.5)

Edis1 = − 1/f1

0Fts (t) z1 (t) dt (2.6)

The above equations can be expressed in terms of the observables without knowingthe interaction force by integrating the equation of motion (eq. 2.1) over a period

V1 = −(k1A1A01

2Q1

)cosφ1 (2.7)

V2 = −k2A22Δf2f02

(2.8)

Edis1 = −πk1A1Q1

(A1 −A01 sinφ1) (2.9)

It is worth to note that all the parameters and observables included in eq. 2.7-2.9but φ1 and ∆f2 are set at the beginning of each experiment. The next step is tosolve eq. 2.4-2.6 in terms of the parameters of a specific tip-surface force Fts. In thenew approach shown here, a viscoelastic force which considers elastic and dissipativeinteractions is exploited. In the literature, equations 2.4-2.6 were solved for a pureelastic force [21,107–109]

Fts = αδβ (2.10)

where δ is the deformation, α is a coefficient that depends on the tip geometry, thesample Young’s modulus and Poisson coefficient, and β is a coefficient that depends onthe tip geometry. The deformation is expressed as

35

Figure 2.1.: Scheme of bimodal AM-FM for mapping viscoelastic properties. The mi-crocantilever is driven simultaneously at the first two flexural resonances.An amplitude modulation feedback (AM) acting on the first mode is used totrack the sample topography. A frequency modulation feedback (FM) actingon the second mode provides spatial variations of the frequency shift ∆f2.A theoretical model transforms observables into viscoelastic parameters ofthe tip-sample interaction force.

δ (zc) =

0 , z1 < zc

z1 − zc , z1 ≥ zc(2.11)

In the following, we demonstrate that equations 2.4-2.6 can be solved analytically fora force of the type

Fts = αδβ + λδµdδ/dt (2.12)

where λ is a coefficient that depends on the geometry of the tip and on the viscosityof the sample and µ is a coefficient that depends on the geometry of the tip. For a

36

paraboloid tip λ = 2ηR1/2ω1 and µ = 1/2 [172]. Specifically, V1, V2 and Edis1 (forA1 A2) can be expressed as

V1 = − 1π

δ

0kts (δ)

√2A1

√δmax − δdδ (2.13)

V2 = −A22

2π

δ

0

kts (δ)√2A1√δmax − δ

dδ (2.14)

Edis1 = −2 δ

0gts (δ)

√2A1

√δmax − δdδ (2.15)

where kts = dFts/dδ = αβδβ−1 is the interaction stiffness and gts = λω1δµ is an

effective damping coefficient (with ω1 = 2πf1). δmax is the maximum deformation.Let’s assume that the tip-surface force for a parabolic tip of radius R takes the form of

Fts(δ, δ) = 43Eeff

√Rδ3 + 2ηcom

√Rδδ (2.16)

and Eeff can be expressed as in eq. 1.2

E−1eff =

(1− ν2

t

Et+ 1− ν2

s

Es

)(2.17)

ηcom is the compressive viscosity coefficient which can be easily converted in the morecommon rheological parameter, shear viscosity coefficient η (ηcom = 3η) [30]. The com-bination of Hertz contact mechanics and the mechanical system formed by a spring inparallel with a dashpot is called 3D Kelvin-Voigt (3D K-V) model (eq. 2.16) [30]. Solvingthe integrals included in the equations 2.13-2.15 for the 3D K-V model, we obtain

V1 = −14Eeff

√2A1Rδ2

max (2.18)

V2 = −Eeff

√R

8A1A2

2δmax (2.19)

Edis1 = −π2√2A1Rηcomω1δ

2max (2.20)

Now, using eq. 2.7-2.9 in combination with eq. 2.18-2.20, the maximum deformation,the effective Young’s modulus and the viscosity coefficient are expressed in terms of thevirial and energy dissipation

δmax =(A2

2A1

)(V1V2

)(2.21)

Eeff =

√8A1R

V 22V1

A1A4

2(2.22)

37

ηcom = (2πω1)−1EeffEdis1V1

(2.23)

When Edis1 is assumed to be negligible, for whatever source of dissipation, the rela-tionship derived above (eq. 2.9) is equal to 0. This happens when a purely elastic forcemodel is considered. In particular, for a Sneddon model with a paraboloid tip (i.e. Hertzmodel, eq. 1.4), we can rewrite the deformation and the Young’s modulus as [108,175]

δmax =(

k12Q2k2

) (A2

01 −A21)1/2

∆f⁄f02(2.24)

Eeff =(

4√

2k1Q1√R

)(k2k1

)2 A3/21 (∆f2⁄f02)2

A201 −A2

1(2.25)

In the experiments shown hereafter, Edis1 is considered not negligible, but directlylinked to the viscosity of the sample.

2.2.1. Consideration about the Kelvin-Voigt model and true topographyreconstruction

The expressions derived above enable bimodal AM-FM to generate images of the true to-pography of the surface at the same time that it generates maps of the Young’s modulus,the viscosity coefficient and the loss tangent. The use of the loss tangent is particularlyrelevant because, as the Young’s modulus, is a well characterized material property, thusmaking possible to compare bimodal results with literature values. In Fig. 2.2 typicalvalues for soft and hard materials are given. In particular, the correlation between theYoung’s modulus and the loss tangent for bulk materials is shown [176]. The use of theloss tangent derived for amplitude modulated atomic force microscope applications wasrecently introduced by Proksch et al. [177, 178]. It has been shown how the value ofthe loss tangent obtained from AFM measurements can be improved depending on theAFM parameters. Upon following a precise protocol, which consists in setting a properfree amplitude and a correct value of the amplitude ratio (A/A0, as the ratio betweenthe set point amplitude and the free amplitude), reliable loss tangent measurements canbe obtained. The theoretical derivation connects the AM variables (φ and A) to thematerial property. For a cantilever modulated at the resonant frequency

tan ρ = sinφ−A/A0cosφ (2.26)

And in our particular case, the greater part of the dissipative interaction is assumedto be related to the first mode (φ1, A1, A01). Thus, the quantity Edis1

V1can be connected

to the definition of the loss tangent

tan ρ = Edis12πV1

= ω1ηcomEeff

= ω1τ (2.27)

38

where τ is the retardation time of the Kelvin-Voigt model. This time is describedas the time needed to build up a strain in the material after a stress has been applied.A higher τ means a more dissipative and viscous material. The derivation of the losstangent allows to reconstruct the viscous coefficient from the bimodal characterization.

Figure 2.2.: Viscoelasticity and energy dissipation processes of materials. (a) Loss tan-gent vs Young’s modulus for bulk measurements. The circle in blue containsthe polymeric samples of interest. Adapted from [176]. (b) Energy dissipa-tion in AM-AFM. Different processes are characterized by a different shapeof Edis vs A/A0 curves. The first derivative helps to recognize the energydissipation mechanism. From left to right, non-contact interaction with aSi substrate, adhesion hysteresis on a Si substrate and viscoelasticity takenover the polystyrene phase of a polystyrene/polybutadiene blend. Adaptedfrom [33].

Nevertheless, the Kelvin-Voigt model cannot be applied without any restriction andto any kind of sample. First of all, it is hard to compare local and bulk viscoelasticproperties because the properties of polymer regions probed by AFM could be affectedby surface relaxation processes and interphase interactions [179,180]. These effects couldbe negligible in bulk measurements. For instance, it has been demonstrated the glasstransition temperature Tg lowers at the polymer surface, due to the presence of liquid-likemolecular layers. This was explained assuming an increase in the surface mobility [181].Second of all, other dissipative processes can take place, especially in air environment. Itis clear the Kelvin-Voigt model doesn’t take into account other dissipative interactionswith the exception of the viscosity. Thus, if for instance adhesion forces are relevant, thismodel cannot be used. This was recently illustrated by Raman’s group [41]. Anyway, itis possible to distinguish the main source of dissipation comparing experimental resultswith theoretical or simulated values. Finally, the shape of the energy dissipation vs

39

the amplitude ratio (A/A0) curve is a marker of the type of dissipative contribution indynamic AFM, as shown in Fig. 2.2 [33].Due to the high deformability of soft materials (i.e polymers and biomaterials), we

cannot consider the topographical image coming directly from the first mode feedbackas real (apparent topography, ha). The force exerted by the tip on the surface producesa deformation not considered in the apparent topography [182–185]. Usually in tappingmode AFM this effect is ignored because the derivation of the deformation of the sampleis not straightforward: as a matter of fact, the latter is entangled in the deflectionsignal associated with the topography. Nonetheless, in bimodal AFM, it is possibleto reconstruct the true topography (htrue) of the sample by taking into account thereconstructed deformation (δmax) as [106]

htrue(x, y) = ha(x, y) + δmax(x, y) (2.28)

2.3. Materials and Methods2.3.1. Bimodal AFM on PS, LDPE and PS-b-PMMA2.3.1.1. Preparation of the samples

The polystyrene (PS) sample and the polyolefin elastomer (ethylene-octene copolymer,LDPE) sample were provided by Bruker (USA). The PS has a nominal Young’s modulusvalue of 2.7 GPa. The LDPE has an estimated Young’s modulus value of around 0.1GPa. The block copolymer is a poly(styrene-block-methyl-methacrylate) (PS-b-PMMA)synthesized as a thin film by self-assembling over a layer of poly(styrene-random-methyl-methacrylate) (PS-r-PMMA). The protocol used to make the block copolymer thin filmwas previously described and tested [186]. This procedure can be actually used to preparedifferent possible geometries (e.g., lamellar, cylindrical), depending on the characteristicsof the random and block copolymers that are used. Block copolymer thin films with alamellar geometry and a 23.4-nm pitch were fabricated as follows: the PS-r-PMMA andPS-b-PMMA were dissolved in propylene glycol monomethyl ether acetate (PGMEA,Sigma-Aldrich) to a concentration of 1.5% (wt/wt) each. Then, ∼50 µl of the PS-r-PMMA solution were deposited over a oxygen plasma treated Si wafer. Next, it wasspin-coated at 5000 r.p.m. for 30 s. The resulting film was left to anneal for 10 minat ∼200 °C. The sample was rinsed with PGMEA to remove the first polymer layers.The PS-b-PMMA solution was then deposited over the surface and spin-coated at 2500r.p.m. for 30 s. Then, the resulting film was left to anneal for 10 min at ∼200 °C.

2.3.1.2. Bimodal AFM experimental set-up

Experiments were performed on a Cypher ES/VRS platform (Asylum Research, OxfordInstruments, USA). Bimodal AFM requires to perform the measurement in the tip-sample repulsive regime in order to extract mechanical information [81]. To meet thiscondition, φ1 must always stay below 90°; this is obtained by setting correctly A01 andA1, and choosing the proper cantilever (appropriate k). In bimodal AFM, A2 is chosen

40

to be at least one order of magnitude less than A1, and the deflection of the cantilevermust respect the condition z0 < A2. This was checked taking a force curve prior to theexperiments (Fig. 2.3).It has been shown that the adsorption of water on a polymer thin-film surface could

influence AFM experiments and in particular the value of some nanomechanical prop-erties, such as the loss tangent [187]. This observation was confirmed by measuring thenanomechanical parameters of PS-b-PMMA with and without N2 flow. The results areshown in Table 2.1. The viscosity coefficient and loss tangent show higher values in pres-ence of ambient Relative Humidity (RH= 22%). To avoid this effect, the experimentswere performed in a dry N2 atmosphere, with a gas pressure of 0.5 bar, thus reducingthe RH (3%).

Figure 2.3.: Deflection (z0) in bimodal AFM experiments. The left (a) and the right (b)panels show the deflection and A1 recorded for a PPP-NCH and a PPP-FM-AuD cantilever over the LDPE and PS sample. A2 is 0.5 nm and 1.3nm respectively for the PPP-NCH and the PPP-FM-AuD.

Measurementcondition

PS-b-PMMAphase

Eeff (GPa) tanρ τ (µs) ηcom (Pa s)

RH= 22% PS 2.1 ± 0.25 0.11 ± 0.02 0.22 ± 0.03 460 ± 65PMMA 2.6 ± 0.30 0.07 ± 0.02 0.15 ± 0.03 350 ± 65

RH= 3% PS 2.1 ± 0.10 0.09 ± 0.02 0.19 ± 0.04 418 ± 100PMMA 2.6 ± 0.10 0.03 ± 0.01 0.08 ± 0.03 186 ± 81

Table 2.1.: PS-b-PMMA viscoelastic properties at two RH.

When running bimodal AFM, it is important to define the offset needed to calculateA01 and the frequency shift ∆f2. In Fig. 2.4, a typical behavior of amplitude, phase

41

Figure 2.4.: Amplitude, phase and frequency distance curves in bimodal AFM. (a) Firstmode amplitude vs cantilever-sample separation. (b) First mode phase vscantilever-sample separation. (c) Second mode frequency vs cantilever-sample separation. In the yellow region, the tip is out of contact anddoesn’t have any interaction with the sample. The area where the tip startsprobing a phase and a frequency shift provides the value of A01 and f2s(∆f2 = f2 − f2s). The blue region represents the attractive regime of theinteraction. In the gray area the tip is in repulsive contact with the sample.This is the area of choice for bimodal nanomechanical measurements. Datataken with a PPP-NCH cantilever over a PS sample.

and frequency distance (APFD) curves is shown. The x axis correspond to the z-piezodistance as measured from the microscope (cantilever-sample separation). The APFDcurve was taken over a PS sample. In the first area marked in yellow, the tip is out ofcontact and it is approaching the sample. The light blue area corresponds to an increasein φ1 (>90°), and the tip turns out to be in the attractive regime. f2 tends to decrease inthis area. Upon approaching the sample, the tip enters in a third region, named repulsiveregime (gray area), dominated by a drop of φ1 and a sudden increase of f2. The firstmode amplitude, decreases independently of the regime. Going into the repulsive region,the first mode amplitude, after an abrupt increase, decreases monotonically. This shift tohigher values is due to the transition from the attractive to the repulsive regime [81,85].In bimodal AFM the working region, for stable imaging conditions, is the repulsiveregion. A01 and ∆f2 are then determined in the area before the tip-sample interactionstarts. This definition is applied to all the measurements shown in this thesis.

2.3.1.3. Cantilever calibration

PPP-NCH (NanoAndMore, Germany) microcantilevers with f01 = 331.434 kHz, k1 =54.8 N m−1, Q1 = 596, f02 = 2050 kHz, k2 = 2857 N m−1 and f01 = 324.783 kHz,k1 = 43.2 N m−1, Q1 = 532, f02 = 2009 kHz, k2 = 2269 N m−1 were used to imagethe LDPE (Fig. 2.6-2.7 and Fig. 2.8, respectively). PPP-FM-AuD (NanoAndMore,Germany) cantilevers with f01 = 77.250 kHz, k1 = 3.2 N m−1, Q1 = 206, f02 = 490.283

42

kHz, k2 = 166 N m−1 and with f01 = 68.070 kHz, k1 = 2.77 N m−1, Q1 = 208,f02 = 432.333 kHz, k2 = 142 N m−1 were used to characterize the block copolymerand the polystyrene samples, respectively. The experimental data were processed byassuming a paraboloid tip. For the LDPE and PS polymers, radii of 11 nm (PPP-NCH)and 12 nm (PPP-NCH) were assumed, while for the block copolymer R =2 nm (PPP-FM-AuD). The spring constant of the first mode was calibrated by using the multiplereference calibration method already mentioned in Chapter 1 [18,19]. This method avoidsthe mechanical contact with the sample during the calibration. It is implemented in thesoftware of the Cypher S/VRS as GetReal™ tool. First, the thermal noise spectrum(power spectral density, PSD) is recorded and the Q-factor and resonance frequency ofthe lever are determined. The so-called Qf1.3 scaling method consists in deriving thestiffness k of the cantilever using reference values for the Q-factor Qref , frequency frefand stiffness kref as follow

k1 = kref

(Q1Qref

)(f1fref

)1.3

(2.29)

Reference values were extracted in factory on a set of cantilevers of the same type usinga laser Doppler vibrometer (in air). Bimodal AM-FM requires the calibration of the forceconstant of the second mode. In order to achieve reliable mechanical reconstructions,this becomes a critical step. The second mode of the cantilevers was calibrated throughthe stiffness-frequency power law relationship developed by Labuda et. al [20],

k2 = k1(f2/f1)ζ2 (2.30)where ζ2 is an experimental calibration parameter, which is equal to 2.17 and 2.13 for

PPP-NCH and PPP-FM cantilevers, respectively.

2.3.1.4. Numerical simulations

Numerical simulations were performed with dForce, a program developed in the group ofR. Garcia (https://wp.icmm.csic.es/forcetool/dforce/) which allows to simulate dynamicforce microscopy experiments [34]. The code is written in Python/SciPy, and it isopen source. The parameters used to perform the simulations were A01 = 54 nm,f01 = 331.434 kHz, k1 = 54.8 N m−1, Q1 = 596, f02 = 2050 kHz, k2 = 2857 N m−1

and A2 = 0.5 nm which are the same ones used in the actual experiments on the LDPE.A force model of the Kelvin-Voigt type was used to model the tip-sample interaction(Young’s modulus and viscous coefficient were the ones extracted from the bimodal AFMmeasurements).

2.3.2. Bimodal AFM on P(VDF-TrFE)Polymer thin films of P(VDF-TrFE) were fabricated under clean room conditions by J.Hafner in TUW. The description of the fabrication protocol can be found somewhere else[188]. The random copolymer P(VDF70-TrFE30) used in the experiments was realizedwith a ratio VDF:TrFE of 70:30 mol%. The layer thickness obtained was 1.0 ± 0.1 μm.

43

Bimodal AFM measurements were performed using the Cypher S AFM (Asylum Re-search, Oxford Instruments, Ca, USA). Experiments were performed at ambient condi-tion in a dry nitrogen atmosphere. A custom-built heating system (built and optimizedby Marco Teuschel in TUW) was used to realize measurements at different tempera-tures. The heating system was implemented inside the microscope. The temperaturewas finely tuned with a relative error with respect to the set-point temperature of ± 0.1°C. This ensures a good stability of AFM measurements. The bimodal nanomechanicalcharacterization was performed at four different temperatures (27 °C, 60 °C, 102 °C,122 °C). The focus of the experiment was to understand the mechanical behavior of thematerial below and above the Curie temperature (Tc = 101°C). The line scan rate wasfixed at 2-3 Hz.PPP-FM-AuD and PPP-FM cantilevers (NanoAndMore, Germany) have been used

throughout all the experiments. The experimental parameters are: A01 = 110 nm, A1 =74 nm, f01 = 56.454 kHz, k1 = 1.75 N m−1, Q1 = 170.1, A2 = 0.5 nm, f02 = 356.427kHz, k2 = 69.76 N m−1 (for Fig. 2.14, Fig. 2.15 a,b,d and Fig. 2.16); A01 = 71nm, A1 = 54 nm, f01 = 79.753 kHz, k1 = 3.45 N m−1, Q1 = 209.3, A2 = 1.4 nm,f02 = 505.248 kHz, k2 = 176 N m−1 (for Fig. 2.13 and Fig. 2.15c). The cantilevers werecalibrated as described in the previous section. The radius of the tip was estimated byusing a test sample made of PS-b-PMMA (poly(styrene-block-methyl methacrylate)).The radius of the tip lies in the range of 6 nm to 12 nm, and remained constant during asingle experiment. The experiments were repeated with different cantilevers and differentsamples to confirm the reproducibility of the data. In addition, sequential experimentswith the same tip were performed to verify the stability of the measurement.Finally, the nanomechanical properties were compared with bulk mechanical prop-

erties. The macroscopic Young’s modulus was measured using Dynamic MechanicalAnalysis (DMA) measurements on a 10 µm-thick freestanding polymer film with a rateof 100 Hz (measurement performed by J. Hafner in TUW with a TA Instruments DMAQ800).

2.4. Results and Discussion2.4.1. Bimodal AFM mapping on PS and LDPEBimodal AFM viscoelastic mapping was performed on standardized samples in orderto test the reliability of the technique. Fig. 2.5 shows the viscoelastic reconstructionon a polystyrene thin film. The calibrated polystyrene sample has a Young’s modulusnominal value of 2.7 GPa. Using bimodal AFM, the estimated modulus equals 2.75 ±0.16 GPa, thus giving similar value with respect to the nominal one. Let’s now focus onthe viscous characteristics. The reconstructed loss tangent value is 0.028 ± 0.009 whichis in the order of magnitude of literature values (as shown in Fig. 2.2a). The retardationtime in 0.06 ± 0.02 µs and the viscous coefficient is 204 ± 73 Pa s.

44

Figure 2.5.: Viscoelastic mapping of a polysterene test sample. (a) Young’s modulus, (b)viscous coefficient, (c) loss tangent and (d) retardation time on a PS sampleof nominal elastic modulus value of 2.7 GPa. The Young’s modulus hasbeen calculated considering a νs = 0.34. (e) The extracted nanomechanicalvalues are shown. The measurement parameters are A01 = 81 nm, A1 = 65nm, A2 = 1.2 nm. Adapted from [173].

The second test sample measured was LDPE. On this sample, the reliability of thenanomechanical reconstruction was tested. As a matter of fact, an important feature ofa nanomechanical method is its independence of the operational parameters (the mainoperational parameter is A1 as feedback for the topography). To test this hypothesis, theimages shown in Fig. 2.6 and Fig. 2.7 were realized by reducing the set-point amplitudeA1 approximately 3 nm every 100 nm of the slow scanning direction. This generatesa stripe-like structure. These stripes are observed in other observables such as φ1 and∆f2, the virial V1 and the energy dissipation E1. It is clear that the dependence of theobservables, virial and energy dissipation on the feedback parameters is justified by thefact that these parameters or calculated quantities are not intrinsic properties of thematerial.

45

Figure 2.6.: Bimodal AM-FM observables (LDPE). (a) Map of the first mode amplitude.A1 was changed 3 nm approximately every 100 nm in the slow scanningdirection. (b) Map of ∆f2. The variations in ∆f2 reflect the elastic responseof the LDPE and the changes of the main feedback. (c) Map of φ1. Themap shows the changes due to the change in A1. (d) Map of the virial ofthe first mode. The cross-section shows a step-like trend associated with thechanges in A1. The bimodal AFM parameters are A01 = 54 nm, A2 = 0.5nm. Adapted from [173].

However, the nanomechanical parameters should be independent. After applying thebimodal AFM theory, the Young’s modulus, viscosity coefficient, loss tangent, and re-tardation time were reconstructed. The parameters are unaffected by the change in A1(Fig. 2.7). More precisely, the value of the nanomechanical reconstructed parameterstends to stabilize at certain value of A1. This behavior is in agreement with previoussimulation [108] and shown by other nanomechanical methods [42, 106]. This result isan indication of the absence of artifacts in the measurements. It is also clear that, whenperforming bimodal AFM experiments, an appropriate amplitude ratio has to be chosento ensure a good quantitative reconstruction. Furthermore, good care has to be taken inthe choice of A01: previous results showed a dependence of its value on the loss tangentreconstruction [178]. This was justified by the presence of water layers on the samplecausing adhesion with contribution to Edis1. By carefully tuning the amplitude, it ispossible to approach a better viscoelastic contact, avoiding this capillary effect [178].The Young’s modulus map (Fig. 2.7c) shows a homogeneous material characterized by0.11 ± 0.02 GPa. This value approaches closely the nominal value of the LDPE (0.1GPa). The viscosity coefficient map (Fig. 2.7d) remains almost constant at 37–40 Pas across the sample. Finally, bimodal AM-FM provided spatially-resolved maps of theretardation times and the loss tangent (Fig. 2.7a,b). The loss tangent value is in theorder of magnitude of the expected one for LDPE (Fig. 2.2).

46

Figure 2.7.: Bimodal AM-FM viscoelastic reconstruction (LDPE). (a) Loss tangent. (b)Retardation time. (c) Young’s modulus. (d) Viscosity coefficient. Bottompanels show cross-sections obtained across the dashed lines marked in thenanomechanical maps. Blue regions show values that lie within a 5% windowfrom the average value obtained through the bimodal AFM reconstruction.The above images were obtained with the parameters listed in Fig. 2.5. Atip radius of 12 nm was used to fit the data. Adapted from [173].

Additional experiments were performed in order to recover the true topography of thesample. Fig. 2.8 shows the reconstruction of the true topography from the apparenttopography and deformation of the polymer. The topographic image (Fig. 2.8a) shows aflat sample with height variations of 1–3 nm. The deformation is quite uniform across theimage, ∼9.5 nm taken with an applied force of 30 nN (Fig. 2.8b): the near constant valueof the deformation across the surface indicates a homogeneous mechanical response. InFig. 2.8c the true topography of the polymer surface is displayed after processing thedata with eq. 2.28.

47

Figure 2.8.: Apparent, deformation and true topography of a polymer blend. (a) Ap-parent topography. (b) Deformation. (c) True topography. Bottom panelsshow the cross-sections across the lines marked in the top panel. The bi-modal AFM parameters are A01 = 87 nm, A1 = 51 nm, A2 = 0.5 nm.Adapted from [173].

2.4.2. Bimodal AFM on PS-b-PMMATo demonstrate the capability of bimodal AFM to perform high resolution nanome-chanical mapping, measurements on a block copolymer with a lamellar geometry wererealized. The sample used here was a poly(styrene-block-methylmethacrylate) (PS-b-PMMA) thin film, a diblock copolymer that arranges in an ordered lamellar structurealternating PS and PMMA domains with a pitch of about 25 nm [189].First of all, the apparent topography, deformation and true topography are shown

in Fig. 2.9. The thickness of one domain with respect to the other is about 0.3 nm.From the deformation map, we can already identify which domain corresponds to thePS and to the PMMA: in fact, the latter is the stiffest between the two polymers andthus it is indented less than the other component. This is confirmed by the Young’smodulus map (Fig. 2.10). Thus, raised features correspond to the PMMA while lowerfeatures are associated with PS. Then, the true height was reconstructed: as alreadymentioned the apparent topography does not correspond to the true height difference ofthe unperturbed polymer surface. Both PMMA and PS domains are deformed by theforce exerted by the tip, respectively, 12.2 nN (for the PMMA) and 12.9 nN (for thePS). The deformation measured on PS is 1.9 nm while on PMMA is 1.6 nm (Fig. 2.9b).The true topography of the block copolymer is shown in Fig. 2.9c.

48

Figure 2.9.: Apparent, deformation and true topography of a PS-b-PMMA block copoly-mer. (a) Apparent topography. (b) Deformation. (c) True topography. Inbottom panels, cross-sections corresponding to the dashed lines marked intop panels are shown. Bimodal AFM parameters are A01 = 90 nm, A1 = 55nm, A2 = 1.3 nm. Adapted from [173].

The bimodal AFM viscoelastic maps are shown in Fig. 2.10. The viscoelastic parame-ters provide a comprehensive compositional understanding of the block copolymer. Thealternating PS and PMMA domains generate an oscillation in the value of the Young’smodulus, viscosity coefficient and retardation time. For the PS domains, the Young’smodulus, viscosity coefficient and retardation time are, respectively, 2.1 ± 0.1 GPa, 418± 100 Pa s and 0.19 ± 0.04 µs while for the PMMA domains the values are 2.6 ± 0.1GPa, 186 ± 81 Pa s and 0.08 ± 0.03 µs. In particular, the retardation time shows anoscillatory behaviour alternating PS (190 ns) and PMMA (80 ns) domains. Those valuesare linked to the loss tangent (as shown in eq. 2.27). The loss tangent value is 0.09 ±0.02 for the PS and 0.03 ± 0.01 PMMA, which again is in the range of expected values.

49

Figure 2.10.: Bimodal AFM nanomechanical maps of a PS-b-PMMA block copolymer.(a) Young’s modulus. (b) Viscosity coefficient. (c) Retardation time. Fromthe nanomechanical reconstruction it is possible to assign features to thePMMA and PS: PMMA is stiffer and has a lower viscosity coefficient anda faster response time. Bottom panels show cross-sections across the linesmarked in top panels. The above images have been obtained simultaneouslywith those of Fig. 2.9. Adapted from [173].

2.4.3. Accuracy of bimodal AFM to determine viscoelastic parametersThe accuracy of a new method to determine viscoelastic parameters lies in (i) the validityof the AFM theoretical background (i.e. the virial and energy dissipation theorem) and(ii) the choice of the proper mechanical model (i.e. the 3D Kelvin-Voigt model).

The virial and energy dissipation theorem have already been proven being valid inthe description of an AFM cantilever tapping on a defined sample: different numericalsimulations and experiments were used to validate it [33, 34, 190, 191]. It is relevant tounderline that the experimental determination of the virial and the energy dissipated bythe tip in contact with the sample is valid as long as the oscillation remains sinusoidal.With respect to the nanomechanical model it is well known that the Kelvin-Voigt

model does not describe properly the stress relaxation of a viscoelastic material un-der a fixed strain. In a bimodal AFM experiment a time-dependent force is applied,which causes a time-dependent deformation. Thus, a bimodal, or more in general a dy-namic AFM experiment, is quite different with respect to a stress relaxation experimentperformed at a fixed strain (i.e. constant deformation). Another issue is related to thecontact area, which in the case of the Kelvin-Voigt model was defined as in Hertz contactmechanics (paraboloid approximation). Let’s assume the oscillation of the cantilever asmultiple approach and retraction curves at high frequency (excitation frequency). Fi-nite element simulations show that for a paraboloid tip the contact area has a near

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Figure 2.11.: Comparison between the energy dissipation derived from numerical simula-tions and experiments on a LDPE polymer sample. (a) Energy dissipationmap of LDPE recorded simultaneously with the maps of Fig. 2.6 and 2.7.(b) Average values of (a) are plotted together with simulated values. Thenumerical simulation was performed for a 3D K–V with parameters de-rived from bimodal AFM experiments: ELDPE = 0.11 GPa, ηLDPE = 38Pa s. The blue shaded region shows values for the dissipated energy ifthe viscosity coefficient is determined with a 10% relative error. The insetin (b) shows the derivative of Edis1 vs the amplitude ratio A1/A01. Theshape of Edis1 and its derivative are comparable with literature data for aviscoelastic material (for reference see Fig. 2.2). Adapted from [173].

Hertzian dependence on the indentation, during the approach of the oscillation [43]. Fora viscoelastic material, the actual problem comes when the tip is moving away fromthe sample: in this case, the contact area disagrees with Hertz theory. Furthermore,the difference between contact areas increases by increasing the indentation. Thus, thesource of error associated with the contact area could be reduced by using relativelysmall indentations. This is easily achieved in bimodal AFM. The AM feedback of thefirst mode ensures a gentle tapping to the surface. For instance, in the experimentsshown here, the indentation is 10 nm on LDPE, 1.9 nm on PS and 1.6 nm on PMMA.These deformations can be considered relatively small for a viscoelastic material. Fi-nally, as mentioned above, the K-V model does not take into account any other form ofenergy dissipation (such as adhesion hysteresis and capillary effect) which could play animportant role in the tip-sample contact.To test the accuracy of bimodal AM-FM to determine viscoelastic parameters, numer-

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ical simulations were performed through dForce, a dynamic AFM simulator developedin R. Garcia’s group [34]. The idea is to compare the actual energy dissipated by the tipmeasured on the LDPE for different amplitude ratios (A1/A01) with values computedthrough the simulator by using the nanomechanical parameters reconstructed from thebimodal AM-FM theory (ELDPE = 0.11 GPa, ηLDPE = 38 Pa s) and assuming a forcemodel of the Kelvin-Voigt type. Fig. 2.11a shows the Edis1 related to the experimentsof Fig. 2.6 and Fig. 2.7. The average value of Edis1 for each stripe is plotted in Fig.2.11b, and compared with the simulated value. The Edis1 has a typical shape with aninflection point, as already shown in Fig. 2.2. It was demonstrated that the maximum ofthe curve happens for the value of amplitude ratio that maximizes the product betweenthe indentation and its rate. At high and low value of the amplitude ratio, the Edis1 isminimized due to the small deformation at these points [33]. Fig. 2.11b shows a goodagreement between experimental values and the theory. The relative error in the deter-mination of the energy dissipated with the simulation is below 3%. To understand theinfluence of the viscous component to the energy dissipation, let’s plot energy dissipatedcurves obtained by using two different viscosity coefficients, one 10% higher and one 10%lower than the one deduced from the experiments (blue area in Fig. 2.11b). This clearlyshows that the agreement between experimental data and simulations is not fortuitous.

2.4.4. Reliability of bimodal AFM true topography reconstructionAn additional experiment was performed to prove the reliability of the true topographyreconstruction. To that purpose a particular sample was chosen, composed by tworegions: the first made of silicon and the second of LDPE. Silicon is an extremely stiffmaterial and the indentation obtained on this region is almost negligible. Multiplemeasurements over the same area were performed by changing the applied force, thusincreasing the deformation into the LDPE region. Fig. 2.12 shows three cross-sectionsat three different applied forces (15 nN, 32 nN and 51 nN). The apparent topography,recorded on the LDPE region, changes when the applied force is increased. In particular,a height difference of about 11 nm was obtained between the image at lower forces andthe one at higher forces. When the deformation, calculated from the bimodal AFMtheory, is taken into account, the true topography of the sample can be reconstructed.The result is plotted in Fig. 2.12b. For the three measurements, the true height of thesample has a value of about 61 nm. It is remarkable the overlap of the three cross-sections, meaning that independently of the applied force, the same actual topographyis obtained.

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Figure 2.12.: True Topography reconstruction at different applied forces. (a) Topogra-phy map of the area plotted in (b) and (c). Pink and blue regions cor-respond to the silicon and LDPE, respectively. (b) Apparent topographyplotted as obtained from the AFM feedback of the first mode. (b) Truetopography reconstructed by adding the apparent topography to the defor-mation (obtained from the bimodal AFM theory). The data shows threecross sections of the same area scanned with increasing forces. The bimodalAFM reconstruction provides the same true topography independently ofthe applied force. The data were obtained with a PPP-NCH-AuD with thefollowing parameters: A01 = 230 nm, f01 = 285.139 kHz, k1 = 37.54 Nm−1, Q1 = 551.5, A2 = 1.2 nm, f02 = 1807 kHz, k2 = 2603 N m−1, R = 10nm.

2.4.5. Bimodal AFM on P(VDF-TrFE)The random copolymer P(VDF-TrFE) was analyzed in order to understand its me-chanical properties at the nanoscale and compare them with its macroscopic behavior.P(VDF-TrFE) is a semi-crystalline polymer, consisting of amorphous (disordered) andcrystalline (ordered) regions [192] as shown in Fig. 2.13a. It is a random copolymer ofpoly(vinylidene fluoride) (P(VDF)) and trifluorethylene (TrFE). P(VDF-TrFE) shows aferroelectric and piezoelectric behavior. Materials are considered ferrolectric when theirdipoles undergo a reversible alignment in the direction of an applied electrical field [193].A material shows piezoelectricity, when due to the application of an external mechanicalstress, an increase of the electrical potential in the material is recorded [194]. The fab-ricated thin-film is in the β-phase, which is highly polarizable. Ferroelectric materialshave a temperature above which they do not show ferroelectricity (paraelectric phase),

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that is called Curie Temperature (Tc). For P(VDF-TrFE), Tc is 101°C.

Figure 2.13.: Bimodal AFM images of P(VDF-TrFE). (a) Graphical design of a semi-crystalline polymer. Highly ordered structures, where lamellae are located,are crystalline regions (darker color). Around them, molecules assume aless ordered conformation (amorphous regions). Adapted from [195]. (b)Real topographical image and (c) second mode frequency shift of the poly-mer obtained through bimodal AFM. In the frequency shift map, lamellarstructures are clearly visible. (d) Loss tangent map. Crystalline regionshave a lower loss tangent value with respect to amorphous regions. Crosssections taken along the white dotted lines are shown below the maps. Thedata were obtained with the following parameters: A01 = 71 nm, A1 = 54nm, A2 = 1.4 nm. Adapted from [174].

The morphology of (P(VDF-TrFE)) is characterized by small needle-like (rice-like)

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grains where the lamellae assume an edge-on conformation, i.e. with the chain’s axisparallel to the sample surface [196]; around them a matrix mostly composed of amor-phous material is found [197–200]. Polymer chains go in and out through the same ordifferent lamellae, having as a consequence the formation of a complex morphology wherecrystalline and amorphous parts are highly interconnected. The nanoscale morphologyof P(VDF-TrFE) is shown in Fig. 2.13, where the characteristic rice-like domains ofthe semi-crystalline polymer are visualized. From the real topography, it is difficult todistinguish the lamellar structures of the polymer (Fig. 2.13b). In order to obtain highresolution images, the second mode was activated. The map of the frequency shift ofthe second mode is shown in Fig. 2.13c. Here, lamellae are clearly visible. They havea width of 5-8 nm and a periodicity of about 10 nm, which is comparable with liter-ature values [201, 202]. As previously shown, the ∆f2 signal is linked to the elasticityof the sample, thus black regions in Fig. 2.13c represent softer components, related toa higher amount of amorphous material. Remarkably, crystalline grains (high ∆f2) fillthe majority of the frequency map.

2.4.5.1. Temperature dependent mechanical behavior

Using the bimodal AFM theory described in the previous section, nanomechanical pa-rameters were reconstructed. The AFM characterization was performed at four differenttemperatures, two below (27 °C, 60 °C), one around (102 °C) and one above (122 °C)the Tc. Fig. 2.14a shows Young’s modulus maps of the polymer P(VDF-TrFE) at thefour temperatures. The average value of the Young’s modulus decreased when the tem-perature was increased: starting from 1.7 ± 0.5 GPa at 27 °C, it arrived to an averagevalue of about 0.5 ± 0.2 GPa above the Tc. Bimodal AFM measurements were com-pared with a bulk DMA characterization. Fig. 2.14b shows the comparison betweenthe data obtained through DMA and bimodal AFM. The two curves show the sametrend. The absolute values obtained by the two techniques are similar but not the same,though. The difference is due to different factors. First of all, the two techniques probethe sample at different frequencies (bimodal AFM works at much higher frequencies,∼60 kHz, than DMA, ∼100 Hz). This is just a qualitative comparison, since here thetime-temperature superposition was not taken into account [35]. Second of all, the AFMcharacterization is performed at the surface of the polymer, where surface phenomenacan happen (i.e. capillary effect), while DMA is realized by applying a sinusoidal stressto a large area of the polymer. Finally, while in a DMA experiment we are limited toprobe bulk mechanical properties, in bimodal AFM, nanoscale morphological featuresare linked to their mechanical characteristics.Accordingly, it is possible to notice that at high temperatures, the mean value of the

elastic modulus in inter-grain regions remained approximately constant with respect tothe room temperature measurement (0.2-0.3 GPa in regions 1 and 4 of Fig. 2.15c), whilethe Young’s modulus and the topography on the grains changed (cross sections of regions2 and 3 in Fig. 2.15a,b,c). The latter observation seems to be linked to a modificationof the inter-grain regions upon the increase of the temperature. Moreover, lamellarstructures observed at room temperature, tended to disappear above Tc, although some

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Figure 2.14.: Temperature-dependance of P(VDF-TrFE) mechanical properties obtainedthrough bimodal AFM and DMA. (a) Young’s modulus maps at the fourtemperatures 27 °C, 60 °C, 102 °C and 122 °C. Comparison between bi-modal AFM and DMA measurements. Error bars in red are standarddeviation averages of the distribution of different maps. The data wereobtained with the following parameters: A01 = 110 nm, A1 = 74 nm,A2 = 0.5 nm. Adapted from [174].

of them were still visualized at 122 °C (Fig. 2.15). This indicates that crystallinedomains were preserved even when the paraelectric phase was induced. The thicknessof the lamellae tended to increase from ∼6 nm to ∼10 nm, as already reported for othersemi-crystalline polymer [203]. Furthermore, not only the thickness but also the spacingbetween the lamellae tended to increase from lower to higher temperature measurements.In particular, a lamellar spacing of about 13 nm and 35 nm was measured for the 27 °Cand 122 °C measurement, respectively (cross sections in Fig. 2.15d,e,f). This structuralchange was previously reported through spectroscopic measurement (wide-angle andsmall-angle X-ray scattering experiments) by Tashiro and coworkers [204]. They showeda lamellar spacing average increase from 10 to 35 nm, when probing the sample at 20°C and 130 °C, which is in good agreement with the AFM measurements.

2.4.5.2. Polymer reorganization above Tc

A statistical analysis was performed to characterize the reorganization of the polymeras a function of the temperature (Fig. 2.16). This helps to make the above observationquantitative. Let’s focus on the data recorded at 27 °C and 122 °C. First, the Young’s

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Figure 2.15.: High resolution bimodal AFM nanomechanical mapping of P(VDF-TrFE).(a), (d) Young’s modulus maps of a P(VDF-TrFE) thin film recorded at27 °C and (b), (e) recorded at 122 °C. (c) and (f) show cross-sections alongthe white lines in (a),(b) and (d),(e), respectively. Lamellar structures areobserved below and above the Curie temperature. (a), (b), (e) were takenwith A01 = 110 nm, A1 = 74 nm, A2 = 0.5 nm and (d) was obtained withA01 = 71 nm, A1 = 54 nm, A2 = 1.4 nm. Adapted from [174].

modulus threshold value of the grains was determined. This was done analyzing imagesat 122 °C. The Young’s modulus distributions were collected for each map: a typicalresult is shown in Fig. 2.16c where a double peak distribution was extracted and fittedwith a double Gaussian function. The peak with higher value was assigned to crystallinegrains. The threshold was obtained by subtracting the standard deviation to the meanvalue of these regions. Then, a mask with the defined threshold was applied on eachimage collected at 27 °C and 122 °C (Fig. 2.16a,b). Regions of the polymer witha Young’s modulus value lower than the threshold for the grains, were considered ashighly amorphous (inter-grain matrix). The number of pixels assigned to the inter-grainmatrix were normalized to the total number of pixels of each image. The analysis wasperformed on 8 images taken on different samples with different cantilevers (multipleimages for three independent experiments). The result indicates that at 27 °C thepercentage of pixels assigned to inter-grain regions was 2.5% ± 0.9%, while at 122 °Cthis was significantly higher (37.7% ± 3.8%).Thus, below the Curie transition crystalline grains are tightly packed and are the main

contributor to the Young’s modulus. Above the Curie transition, crystalline domains

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are no longer densely packed. A much softer matrix expands and separates the rice-likedomains from each other. At the bulk level (DMA measurement), the softer componentseems to dominate in the determination of the Young’s modulus, and a value of about0.2 GPa is reached. This value is comparable to the one obtained on the inter-grainmatrix extracted through bimodal AFM (0.3 ± 0.1 GPa).

Figure 2.16.: Statistical analysis of the Young’s modulus maps of the polymer at 27and 122 °C. (a) Young’s modulus map after the application of a thresholdmask (sample at 27 °C). (b) Young’s modulus map after the application ofa threshold mask (sample at 122 °C). (c). Young’s modulus distributionat 122°C. The distribution is fitted with a double Gaussian function (anexample of the function and extracted parameters is shown in the table).Adapted from [174].

2.5. ConclusionIn this chapter, bimodal AFM was introduced to unravel viscoelastic properties of softmaterials. The method is based on a double excitation of the AFM cantilever (bimodal

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AM-FM). Different experiments were performed to test the quality of the approach.First, two polymer samples (PS and LDPE) with known mechanical characteristics

were analyzed. In particular, in the experiment performed on the LDPE, the inde-pendence of the recovered nanomechanical values with respect to the main feedbackparameter (A1) was confirmed. Then, the ability of bimodal AFM to perform highresolution nanomechanical mapping was shown on a PS-b-PMMA thin polymer film.Second, a way to test the accuracy of the bimodal AFM reconstruction was proposed.

This method compares experimental values of the energy dissipation (directly linked toviscous properties) with results obtained by numerical simulations, using viscoelasticparameters determined by bimodal AFM theory as inputs. In this way, it was concludedthat the use of the 3D Kelvin-Voigt model explains the nanoscale viscoelastic propertiesof some polymers, considered as purely viscoelastic.Finally, in the last part of the chapter, a bimodal AFM analysis of the ferroelectric

polymer P(VDF-TrFE) was shown. A direct comparison with DMAmeasurements in thedetermination of the Young’s modulus gave some hints on how to combine the mechanicalreconstruction provided by the two techniques. While DMA determines bulk propertiesof the material, bimodal AFM provides morphological and mechanical information of itsnanostructures. Temperature-dependent mechanical properties were studied with bothtechniques. The extracted values show a similar trend with the temperature. Maps ofa phase transition of the polymer were generated: the softer amorphous region tendedto expand at higher temperatures becoming dominant in the determination of the bulkmodulus with respect to the crystalline part. High resolution bimodal AFM maps wereobtained to unravel the presence of lamellar structures below and above the Curie tran-sition temperature.

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3. Bimodal and high resolution AFM forthe study of organic electronicsemiconductors

3.1. IntroductionOrganic electronics makes use of organic materials to transport the electronic current.Organic semiconductors can be small molecules or polymeric materials [205–207]. Ingeneral, molecular organic semiconductors and polymers are p-type or n-type, if theytransport holes or electrons, respectively. The main feature of organic semiconductivematerials is that their electronic structure is characterized by a delocalized π-conjugatedsystem, where the charge transport proceeds via a hopping process. Nowadays, organicsemiconductors (OSCs) are used for several applications, even though the three maintechnological operations are OPV (Organic photovoltaic cell), OLED (Organic Light-Emitting Diode) and OFET (Organic Field-Effect Transistor) [208–215]. The latter isof particular interest in this chapter, thus we describe here its working mechanism.An OFET is a three-terminal device (Source, Drain and Gate), with a semiconductive

material placed between the source and the drain, and a dielectric material (e.g. SiOx)separating the organic semiconductor from the gate electrode. The relevant current isthe one passing from the source to the drain electrode through the semiconductor. Togenerate carriers inside the semiconductor, the dielectric material works as a capacitor,i.e. by means of a difference of potential between the gate and the source, holes/electronsare injected in the semiconductor. The sign of the gate-source and drain-source bias ischosen based on the type (p-n) of material used as semiconductor. EGOTs (ElectrolyteGated Organic Transistor) are OFETs that work in aqueous environment and wherethe dielectric materials is substituted by an electrolyte solution in contact with theOSC [216–220]. When the bias between the gate and the source is applied, ions (dis-solved in the electrolyte solution) accumulate at the interface with the OSC or penetrateinside the organic film. In the first case, the device is called electrolyte-gated field ef-fect transistor (EGOFET) while the second is named organic electrochemical transistor(OECT). Nevertheless, this is an old and controversial distinction, since there have beenreports of ion penetration in OSC commonly considered not penetrable by ions, i.e. usedin an EGOFET configuration [221–223]. These devices can work in accumulation or indepletion mode dependently if the charges (electrons or holes) are generated or removedfrom the semiconductor. In practical terms, OFETs and EGOTs are devices that amplifya small potential difference into high currents, thus are commonly used as sensors andbiosensors [224–234].

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Figure 3.1.: PEDOT:PSS morphological models proposed in the literature. (a) Chemicalstructure of PEDOT:PSS. Positive and negative charges of PEDOT and PSSare highlighted in red and blue, respectively. (b), (c), (d) PEDOT:PSS thinfilm morphology consists of PEDOT:PSS grains embedded in a PSS matrix.The nature of the structure is highly intermixed. (b) In blue and grey,PEDOT:PSS-rich and PSS-rich phase, respectively. Adapted from [235]. (c)In the PSS-rich area (in gray), PSS molecules form hydrogen bond amongthemselves. It was proposed that the outer shell of the grains is mainlycomposed of PSS molecules. Adapted from [236]. (d) When cations areinjected into the film, they compensate the negative charge of sulfonateanions. Adapted from [237].

We focused on the characterization of PEDOT:PSS. Poly(3,4-EthyleneDiOxyThiophene):Poly(Styrene-Sulfonate) (PEDOT:PSS) is a polyelectrolyte complex composed of PE-DOT, a positively charged conjugated polymer and PSS a poly-anion which acts as itscounter ion (Fig. 3.1a). The sulfonic group of PSS is a polar/hydrophilic and stronglyacid group, which ensures electroneutrality and stabilizes the doped PEDOT. Moreover,PEDOT has a poor water solubility and PSS provides a matrix to form an aqueousdispersion. Conjugated polymers have a chemical structure with a π-system along thepolymer backbone. Carbon atoms involved in the polymer backbone, form three σ-bondswith neighboring atoms and the remaining p orbitals are involved in the π-system. Thelatter allows the conduction of positive charges. In PEDOT:PSS, the semiconductor

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chain (PEDOT) is p-type doped due to the presence of uncompensated sulfonate anionsof the PSS chain. In electrolyte solution, the electronic modulation of PEDOT:PSS re-lies on the application of a positive bias (at the counter electrode) which drives cationsinto the film. Cations compensate for the negative PSS and the result is a de-doping ofthe conjugated polymer.PEDOT:PSS is the leading material when it comes to applications in liquid solutions.

This is due to its high conductivity and electrochemical stability [238]. In particular,PEDOT:PSS has been used as active layer for OECT-based biosensors, neuromorphicdevices and implantable electrodes [229, 230, 232, 234, 239–243]. Most of these deviceshas as final destination in vivo applications, where they can undergo different types ofmovements. In these cases, their mechanical properties become particularly relevant[232,244–246]. Though, very few studies have been realized on PEDOT:PSS mechanicalproperties [245,247], especially at the nanoscale.Morphological characteristics of organic semiconductors determine their electronic

properties [205,208,248–250]. The morphological model of PEDOT:PSS has been contin-uously revised during the last 15 years (Fig. 3.1b-d), though the common understandingis PEDOT:PSS grains with a hydrophobic and conductive core, made of PEDOT, with ashell of PSS and embedded in a hydrophilic and insulating matrix, made of PSS [235–237,251–254]. There have been a large number of reports trying to correlate the morpholog-ical and electrical properties of PEDOT:PSS [235–237,245,247,251,252,254–257]. AFMtechniques were applied for that purpose, though without much success. In fact, meth-ods used in those studies lack of the high resolution capability or the quantitative andcompositional ability to properly distinguish morphological features of PEDOT:PSS.Only recently, advanced AFM techniques (i.e. bimodal AFM, electrochemical strainmicroscopy, and photoinduced force microscopy) were used to study the effect of ionpenetration inside organic semiconductors [222,223,258].In this chapter, bimodal AFM is applied to characterize nanomechanical properties

of PEDOT:PSS. Through an accurate analysis of bimodal AFM maps, PEDOT:PSSgrains (with a PEDOT core) were discerned from PSS-rich areas. Measurements wereperformed in air and liquid solutions to understand the influence of water on morpholog-ical and mechanical properties. Moreover, amplitude modulation AFM was applied toresolve the molecular chains of the polymer with sub-nm resolution. Finally, in operandobimodal AFM was applied to understand the mechanical behavior of PEDOT:PSS uponion insertion (due to the application of a voltage bias). This experiment simulates areal application of PEDOT:PSS, i.e. as active layer of OECT or as electrode in aqueoussolution. It is shown that the penetration of ions have a non-reversible effect on theelastic properties of the film, which cannot be recover even upon ion removal.The experiments were realized in a collaboration with Prof. Fabio Biscarini’s group

(UNIMORE). In particular, Sofia Drakopoulou prepared the sample and was involvedin the realization of bimodal AFM measurements.

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3.2. Materials and Methods3.2.1. MaterialsEDOT (EthyleneDiOxyThiophene) and Na+PSS−(sodium poly(sterene-sulfonate)) werepurchased by Sigma-Aldrich. Test patterns made of gold electrodes on a quartz substratewere purchased by Fondazione Bruno Kessler (Italy). Ultrapure water (UPW) wasobtained before the experiments (ELGA Maxima, 18.2 MΩ cm−1). The pH of UPWhad a stable value of 5.6. Aqueous solutions of 50 mM KCl were prepared by dissolvingKCl (≥99 %, Sigma-Aldrich) in UPW.

3.2.2. Device fabricationPEDOT:PSS thin films were fabricated by means of electrodeposition on gold electrodes.A drop (50 µl) of a solution of EDOT (0.01 M) containing an excess of Na+PSS− (0.8% w/w) was deposited over the test pattern. A constant current (1 µA) was appliedbetween the two terminals of the device for a total time of 10 s. The thickness of thefilm (150 ± 60 nm) was measured through AFM. Since the purpose of the study wasto characterize mechanical properties of PEDOT:PSS, the use of 150 nm-thick films(Appendix Fig. A.1) allows to avoid any substrate effect (for relative small indentation,such as in bimodal AFM).

3.2.3. Electrical stageA home-made electrical set-up (Fig. 3.2a) was designed to perform in operando bimodalAFM nanomechanical mapping. It was implemented in the cantilever holder of a CypherS (Asylum Research, Oxford Instruments, Ca, USA). It consists of a thin Pt electrodeplaced in the vicinity of the AFM tip. A cable connects the Pt electrode to the electricalsource measure unit (SMU, Keithley 4200). Biases were applied between the Pt electrodeand the gold electrode below the PEDOT:PSS film (a scheme of the set-up is depictedin Fig. A.2a of the Appendix). The gold electrode was contacted through silver paint.Upon application of a positive bias (800 mV), electrochromic switching was noticed

happening at the film (Fig. 3.2b). This is a typical feature of PEDOT:PSS, as describedin the literature. The color of the PEDOT:PSS electrode tends to change due to the ionpenetration and consequent reduction of the electrode [259,260]. Every time we refer tovoltage biases, they are to be considered as applied at the Pt electrode with respect tothe gold/PEDOT:PSS electrode (VPt−Au).

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Figure 3.2.: Electrical AFM stage. (a) The AFM holder was modified by adding a flatPt electrode at the cantilever side. This is connected through a thin wire tothe SMU. The PEDOT:PSS film was contacted through the gold electrodeunderneath it. The left image shows the side view of the AFM set-up, whilethe bottom and right images show its bottom and top view. (b) Opticalimages of the PEDOT:PSS sample recorded with the internal optics of theAFM. Passing from 0 to 800 mV of VPt−Au (vs VOC), the PEDOT:PSS elec-trode changes color due to its reduction (effect known as electrochromism).

De-doping cycles were additionally tested on a thin film of PEDOT:PSS in an OECTfashion (in 50 mM KCl), using as gate electrode the one used for in operando bimodalAFM measurements (a scheme of the OECT set-up is depicted in Fig. A.2b of theAppendix). In this case, PEDOT:PSS (Clevios PH1000 water suspension, with 5%DMSO and 0.2% 3-glycidoxypropyltrimethoxylsilane (Silquest)) was spin coated over aquartz test pattern. Then, the current between the source and drain electrode (IDS) wasmeasured while a constant voltage (-600 mV) was applied between the source and drain(VDS) and a bias was switched from 0 to 800 mV between the source and gate (VGS).The negative voltage applied at the drain electrode moves positive carriers towards itand generates a negative current. The positive VGS de-dopes the film, and consequentlylowers the injected current IDS . This is well illustrated in Fig. 3.3 where consecutivecycles show the dependence of the current flowing in the PEDOT:PSS thin film on theapplied voltage VGS .

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Figure 3.3.: De-doping cycles for a PEDOT:PSS thin film in an OECT configuration.The upper panel shows the voltage bias applied between the source andgate electrode (VGS). The voltage between the source and the drain (VDS)is kept at a constant value of -600 mV. The lower panel shows the recordedsource-drain current IDS for the corresponding VGS .

3.2.4. Bimodal AFMBimodal AM-FM was used to characterize electrodeposited PEDOT:PSS thin films.The theoretical model used to derive mechanical properties is the same one illustratedin Chapter 2. For these particular measurements, the conservative part of the tip-sampleinteraction was analyzed, neglecting the contribution due to dissipative viscoelasticity.Thus, a Hertz model was chosen as mechanical model. Equations used to derive me-chanical parameters are eq. 2.24 and 2.25.Measurements were performed in air (RH=23%) and in electrolyte solution (50 mM

KCl). Measurements were performed in a Cypher S (Asylum Research, Oxford Instru-ments, Ca, USA). When working in liquid a photothermal excitation was used. Theacquisition time was 2-3 minutes for each image. Moreover, bimodal AFM mechanicalmapping was realized when a voltage bias was applied between a Pt electrode and thegold electrode below the PEDOT:PSS film (as described in the previous paragraph “Elec-trical stage”). We refer to this type of measurements as in operando bimodal AFM. Thetypes of cantilever used for the bimodal AFM mapping were PPP-NCH-AuD (NanoAnd-More, Germany) and HQ-150-AuD (Asylum Research, Oxford Instruments, Ca, USA)for air and liquid measurements, respectively. PPP-NCH-AuD microcantilevers withf01 = 346.595 kHz, k1 = 46 N m−1, Q1 = 589.9, f02 = 2135 kHz, k2 = 2376 N m−1,R = 15 nm and HQ-150-AuD with f01 = 90.742 kHz, k1 = 11.6 N m−1, Q1 = 6.7,f02 = 609.304 kHz, k2 = 560 N m−1, R = 13 nm were used to perform air and liquidmeasurements. The calibration of the first mode of the PPP-NCH-AuD was obtainedwith the method described in Chapter 2. For the HQ-150-AuD, the first mode wascalibrated by taking a force-distance curve towards a Si sample. From the slope of thedeflection (Volt)-piezo extension (nm) curve, it was possible to extract the static and

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first mode optical lever sensitivity σ0 and σ1 (σ1 = 1.09σ0 ). For the determination ofthe second mode, it was used the stiffness-frequency power law relationship developedby Labuda et. al [20] and already illustrated in the previous chapter (k2 = k1(f2/f1)ζ2 ,with ζ2 = 2.17 and 2.1 for PPP-NCH-AuD and HQ-150-AuD). The radii were calibratedthrough a test sample with known modulus (polysterene, with E = 2.7 GPa). The pois-son coefficient of PEDOT:PSS was assumed to be 0.35 [247]. For in operando bimodalAFM measurements the usual parameters were A01 = 16 nm, A1 = 0.5A01 , A2 = 0.2nm.

3.2.5. Amplitude Modulation AFM high resolution imagingHigh resolution AFM imaging was run in an AM mode [15]. To obtain high resolu-tion data, very small oscillation amplitudes (100-500 pm) were applied to the cantilever.Small and ultra-small amplitudes have allowed to obtain high resolution images of differ-ent materials in vacuum, air and liquid environment [73,138,145,261–264]. In particular,this technique was shown to be very efficient to resolve molecular structures of polymers,such as polythiophene [265]. In fact, the small amplitude operation enhances the sen-sitivity to short-range interaction forces and as a consequence allows to obtain a highspatial resolution. Experiments were performed in air (RH=23%) using PPP-NCH-AuDcantilevers (NanoAndMore, Germany) driven in the second flexural mode. Typical val-ues are f02 = 1800 kHz, k2 = 2000 N m−1 and Q2 = 600.

3.3. Results3.3.1. Bimodal AFM and high resolution AM-AFMBimodal AM-FM was applied to electrodeposited PEDOT:PSS thin films in air and inelectrolyte solution. Fig. 3.4 shows the two sets of measurements. First of all, uponaddition of the electrolyte solution, an increase in the thickness of about 66 nm wasrecorded, which corresponds to a swelling of 40 % (Appendix Fig. A.1). PEDOT:PSSshows a granular morphology where agglomerates of grains are formed over the granularfilm, as previously reported [236]. The grain size tended to increase from 29.5 ± 11.5nm to 86.9 ± 5.0 nm, going from the air to the wet state. When the second mode of thecantilever was activated, mechanical properties of the sample were obtained. Fig. 3.4shows Young’s modulus maps. In general, the modulus decreased from 2.9 ± 1.8 to 0.5± 0.2 GPa upon addition of the aqueous electrolyte.

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Figure 3.4.: Bimodal AFM of PEDOT:PSS thin films. (a) Real topography (top panel)and Young’s modulus (bottom panel) maps of PEDOT:PSS in air (RH =23%). (b) Real topography (top panel) and Young’s modulus (bottom panel)maps of PEDOT:PSS in aqueous solution. (c top panel) Cross sections ofthe topography map of two representative grains in air and liquid. Thegrain size tended to increase from 29.5 ± 11.5 nm to 86.9 ± 5.0 nm with theaddition of the water solution. (c bottom panel) Distribution (as densityfunction ρ(GPa−1)) of the Young’s modulus maps in air and liquid. TheYoung’s modulus decreased from 2.9 ± 1.8 to 0.5 ± 0.2 GPa. BimodalAFM parameters are: A01 = 33 nm, A1 = 18 nm, A2 = 0.8 nm for (a);A01 = 16 nm, A1 = 7 nm, A2 = 0.2 nm for (b).

These values are similar to previous reports [247]. It is worth noting the distributionof the modulus value is considerably large (especially for air measurements). This isrelated to the fact the material surface is not homogeneous but composed of features withdifferent mechanical properties, i.e. PEDOT and PSS regions (see discussion below).To complement the bimodal AFM nanomechanical study, high resolution AFM based

on small oscillation amplitudes was performed. Fig. 3.5 shows phase images with lamel-lar structures (additional images are shown in Fig. A.3 of the Appendix). The imageswere acquired using A0 = 0.4-0.5 nm and Asp = 0.5-0.7A0. Due to the rough nature ofthe polymer film, the visualization of molecular chains was not trivial. Though, somespots where it was possible to resolve the molecular structure with high resolution werefound. In particular, chains with a spacing of 1.25 nm and 0.79 nm were visualized.AFM high resolution data were further compared to literature values obtained throughX-ray diffraction (see discussion below).

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Figure 3.5.: High resolution AFM of PEDOT:PSS films. (a) Molecular chains showinga periodicity of about 0.79 nm, assigned to PSS molecules. (b) Molecularchains with a spacing of 1.25 nm, assigned to lamellar structures formedby PEDOT molecules. The imaging parameters were A0 = 0.45 nm andAsp = 0.25 nm. Graphs refer to cross-sections taken along dotted lines inphase images. (c) Scheme of PEDOT:PSS molecular organization with thecorresponding value of the lamellar stacking. (c) is adapted from [266].

3.3.2. In operando bimodal AFM nanomechanical mappingIn operando bimodal AFM nanomechanical characterization was performed while a con-stant potential was applied between the PEDOT:PSS electrode and a Pt electrode im-mersed in the solution (50 mM KCl). This was realized using a home-made electrical setup (as illustrated in Materials and Methods). The same region (Fig. 3.6a) was measuredconsecutive times and the Young’s modulus was reconstructed. The analyzed area in-cludes a PEDOT:PSS and a quartz part. Due to the possible variation of the tip radiusduring the measurement and assuming the modulus of the quartz independent of theapplied voltage, the tip radius was changed to keep the latter modulus constant and thechange in PEDOT:PSS modulus was normalized to the one of the quartz (Fig. 3.6b).Thus, the measurements do not provide an absolute value for the modulus: the analysiswas focused on the relative change (upon application of a bias) more than its actualvalue. Fig. 3.6b shows the (normalized) Young’s modulus distribution of the image inFig. 3.6a, at 0 mV and at 800 mV of applied bias. The application of the positive volt-age at the Pt electrode drives the anions (Cl−) towards the Pt and cations (K+) fromthe electrolyte solution into the PEDOT:PSS film; here, they combine with sulfonate

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Figure 3.6.: In operando bimodal AFM nanomechanical characterization. (a) Young’smodulus and (c) topography maps of a typical area measured with bimodalAFM. The region consists of a quartz and a PEDOT:PSS part. (b) Distri-bution of the modulus of the region in (a) before and after the applicationof a 800 mV bias (at the Pt electrode and vs VOC). The radius of the tip ischanged in order to keep the modulus of the quartz at the same value. (d)Upon the application of the bias, the Young’s modulus and the thickness ofthe sample shift to lower and higher values, respectively.

anions, thus de-doping the channel. Two biases (0 and 800 mV) were applied for 120s before starting the AFM measurements. The film was considered fully penetrated bycations after 120 s (K+ mobility is 2.2×10−3 cm2 V−1 s−1) [235, 259]. The variation ofthe thickness of the film was also analyzed. In general, the film tended to become softerand to swell after the de-doping voltage was applied (Fig. 3.6d).To quantify the mechanical behavior of the PEDOT:PSS film, measurements were

performed by switching the bias from 0 to 800 mV for five consecutive cycles. As forthe previous case, 120 s were left for the film to equilibrate before the bimodal AFMmapping. The swelling of the film and its mechanical properties were recorded simul-taneously. The results are shown in Fig. 3.7. In particular, the variation (in %) ofYoung’s modulus with respect to the initial value (Ein) and the thickness are plottedfor the corresponding applied voltage. The Young’s modulus tended to drop for thefirst two cycles independently of the applied voltage reaching a stable value of about30-40% of the initial one. Interestingly, after the first cycle, where a drop of 30% Einoccurred, the modulus only slightly decreased upon ion removal (0 mV). After that,the ion injection caused a similar effect with respect to the previous cycle, with a drop

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of 30% Ein. Starting from the third cycle, the modulus tended to decrease (30% Ein)when the positive bias was activated (i.e. cations in the film) while it increased whenzero voltage was applied (50% Ein). This trend was followed also for the fourth andfifth cycle. Additional experiments were realized to confirm the the dependence of theYoung’s modulus to the applied bias (Fig. A.5 of the Appendix).

Figure 3.7.: Influence of ion penetration to the mechanical properties of PEDOT:PSSthin films. Consecutive measurements were performed in a similar area asin (a) upon application of 0 mV and 800 mV (vs VOC). The system was leftto equilibrate for 120 s before each bimodal AFMmeasurement. The positivevoltage at the top electrode drove cations inside the film. When the voltagewas removed ions were free to return in solution. (b) Modulus variationand thickness behavior of PEDOT:PSS during 5 consecutive voltage cycles.Solid lines are guides to the eye. Error bars are standard deviations of 6maps.

The film swelled with a similar (but opposite) behavior with respect to the modulus.In general, for a decrease in modulus there is a corresponding increase in thickness andvice versa. For the first two cycles, the film continued to swell, independently of theapplied voltage. Starting from the third cycle, the thickness switched from ∼302 nm,at the rest state, to ∼310 nm, when the film was de-doped. In particular, a swellingof 20 nm was recorded (from the initial to the de-doped value). Let’s calculate roughlywhat could be the swelling due to the ion penetration. Here, we recall the simple modelpreviously illustrated in the literature [255, 267]. Let’s consider that at 800 mV all thePSS sites are coupled with K+ ions and that the average distance per site is about 1.8nm (calculated with a hole site density of about 1.9 × 1020 sites cm−3). From the firstbimodal AFM measurements, an initial swelling of 40% was measured, from the dryto the wet film. Thus, the number of possible occupied sites is around 115 (for a 207nm-thick sample in the dry state). Assuming that K+ ions carry inside the organic layer1-4 water molecules, the diameter of the K+-H2O system (hydrated cations, consideringthe first hydration shell) is approximately 0.66 nm [268]. Finally, the expected swellingwould be of 76 nm. This value is in the same order of magnitude but lower than the

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experimental value (the total swelling, from the dry film to the de-doped state is 103nm). This is not surprising since the estimation takes into account only the PSS sitesassociated with holes (h+/PSS− pairs). It was demonstrated that for relatively thickfilms (400 nm), many more cations can penetrate the film, together with additionalwater molecules [255]. This is related to an excess of PSS regions, not involved in thecharging/discharging of the polymer. From the bimodal AFM data, it seems that thiscan happen even for thinner films.

3.4. DiscussionBimodal AFMwas applied to unravel nanomechanical properties of PEDOT:PSS. Firstly,morphological and mechanical changes due to the addition of an electrolyte solution werecharacterized. A decrease of Young’s modulus was recorded along with an increase ofthe grain size.Let’s now focus on the details of the bimodal maps (Fig. 3.8). In the film, we notice

two areas: the first of circular shape of lower modulus which is surrounded by the secondof higher modulus (region 2 and 1 in Fig. 3.8). Additionally, the 1st mode phase andthe 2nd mode frequency shift maps were analyzed (Fig. 3.8b and Appendix Fig. A.4).It is well known how the phase signal, recorded with an AM feedback, correlates onlywith dissipative properties of the sample [89–91]. On the contrary, the frequency shiftof the second mode contains only the conservative part of the tip-sample interaction. Inbimodal AFM data, we visualize higher phase and frequency shift in the same areas ofthe sample (region 1). This means that those areas are stiffer (as pointed out from theYoung’s modulus map) but also have some dissipative characteristic. The interaction ofthe AFM tip with water forming capillaries is an important source of energy dissipationin AFM experiments [269, 270]. We recall that the PEDOT:PSS morphology has beendemonstrated consisting of PEDOT-rich cores surrounded by shells composed of PSSchains, as shown in the schematic of Fig. 3.8a. The part of the sample with higher phaseshift (more dissipative) and frequency shift (stiffer) are assigned to PSS-rich areas, whilethe part with lower phase and frequency shift consists of regions where the PEDOT coreis located (center of the grains). It is assumed hydrogen bonds are formed between HSO3groups of the PSS-rich outer shell of individual grains, promoting adhesion betweenindividual PEDOT:PSS grains, but also with water molecules from the air [236, 254].This is to say that a water layer is expected to form in the PSS matrix. Thus, the highphase shift, recorded in these regions, is interpreted due to capillary adhesive forces.Upon addition of electrolyte solution, PSS-rich shells take up water, causing a weakeningof hydrogen bonds, which leads to the (i) swelling of the film, (ii) increasing of the grainsize and (iii) decreasing of the Young’s modulus. This observation is a direct proof of themorphological model previously proposed and shown in Fig. 3.8a [235–237,251,252,254].Moreover, the presence of regions of lower modulus within the PEDOT core areas isclearly noticed (region 3 in Fig. 3.8b). These regions do not correlate with particularmorphological features, neither are recurrent in all the grains of the sample but onlyin few of them. They are preserved even upon addition of the aqueous solution. The

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PSS shell might not entirely cover the PEDOT core. Thus, the lower modulus regionscould correlate with partially uncovered PEDOT areas. This finding corroborates recentresults showing that PEDOT:PSS adopts a different composition of PEDOT and PSS-rich areas at the surface and in its bulk structure [255]. It can be argued that the contrast(phase shift, frequency shift and consequently Young’s modulus) of the features shownin Fig. 3.8 is due to topography artifacts [271]. Additional experiments were performedto verify that (i) PSS regions (region 1) and (ii) the variability between PEDOT regions(region 2 and 3) are not related to a particular morphology. The results are shown inFig. A.6 and Fig. A.7 of the Appendix. In particular, it is demonstrated that “valleys”(PSS regions) with the same height show different phase and frequency shift, and grainswith the same height have a different frequency shift value (and consequently a differentYoung’s modulus), confirming the variability within PEDOT regions.

Figure 3.8.: Compositional characterization of PEDOT:PSS. (a) Morphological schemeof PEDOT:PSS. PEDOT:PSS is composed of grains with a PEDOT coreand a PSS shell. PSS molecules form a matrix interconnecting the grains.Here, PSS molecules form hydrogen bonds through their HSO3 groups withother PSS molecules or with water molecules. (b) Topography, Young’smodulus, 1st mode phase shift, and 2nd mode frequency shift maps ob-tained simultaneously through bimodal AFM. Through the bimodal AFMcharacterization, we are able to recognize the presence of three regions (seemain text for further discussion).

The stacking of molecular chains with a periodicity of about 1.25 nm and 0.79 nm wasvisualized by analyzing PEDOT:PSS samples through high resolution AFM. A thoroughmorphological characterization of PEDOT:PSS was recently realized by means of X-raydiffraction (XRD) [266]. It was shown how PEDOT chains, separated by PSS molecules,

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stack with a spacing of about 1.1 nm, while lamellae formed by PSS molecules have aperiod of 0.79 nm (Fig. 3.5c). These two values resemble the ones obtained throughhigh resolution AFM. Moreover, these measurements confirmed the observation madewith bimodal AFM, i.e. the presence of PEDOT molecules exposed at the surface of thepolymer film.Finally, in operando bimodal AFM nanomechanical characterization was performed

during de-doping/doping cycles due to ion penetration. The film underwent two distinctresponses. For the first cycles, the Young’s modulus (thickness) decreased (increased)continuously, stabilizing after the third cycle. Starting from the latter, a change inmodulus and thickness was measured depending on the applied voltage, i.e. the mod-ulus increased/decreased when cations were removed/injected from/into the sample.PEDOT:PSS electrical properties (and especially high conductivity) have been alwayslinked to its volumetric capacitance. This is an empirical property firstly introduced byMalliaras’ group [267]. This concept was recently extended considering the electrode’selectroactive surface area: it was shown that morphological and electrical propertiesscale with the ratio of the volume and the electroactive surface area [257]. Ion injec-tion in PEDOT:PSS thin films was first studied recording the electrochromic changesassociated with the propagation of the de-doping front [235, 259, 260]. The data wererelated to spectroscopic measurements, finding that the moving leading front consistsof ions passing through regions of the PSS-rich matrix, while the lagging front is dueto ions penetrating inside PEDOT:PSS cores. Recently, the effect of ion penetration onthe structural properties of thin films of organic semiconductors was studied by meansof advanced AFM techniques and X-ray scattering. In particular, it was shown that aconjugated polymer with glycolated side chains could undergo a structural phase tran-sition (with two different crystalline structures) upon ion insertion [258]. The sameauthors linked the local stiffness of nanoscale regions of a poly(3-hexylthiophene) thinfilm with their ability to expand during ion penetration [222]. In the experiments per-formed here, the bimodal AFM data show that upon ion injection, neither the initialmodulus or thickness were restored when cations were driven out from the film. It wasreported that few de-doping/re-doping cycles are required to reach a reproducible andstable current behavior in order to use PEDOT:PSS as active material in organic elec-tronic applications. This was attributed to the formation of ion percolation channels andconsequent hydration of the polymer film during the first cycles [259]. The consequenceof this “hydration” is a drastic and non-reversible change of mechanical properties ofthe sample. Non-reversible behavior of PEDOT:PSS swelling upon ion insertion waspreviously shown by Savva et al. [255]. Through EQCM (electrochemical quartz crystalmicrobalance), they observed a substantial number of Na+ ions (and consequently watermolecules) remaining inside the film even at the doped state. This was explained withthe presence of a bulky hydrophilic PSS phase acting as sites for the accumulation ofions not involved in the de-doping process. Bimodal AFM was able not only to visualizethe same swelling trend but also to record its effect on the mechanical properties.

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3.5. ConclusionElectronic properties of organic conductive and semi-conductive materials are highly in-fluenced by their morphological and mechanical properties [235, 237, 244, 246, 255, 257].PEDOT:PSS is one of the most commonly used organic electronic materials. In thischapter, nanomechanical properties and morphological features of electrodeposited PE-DOT:PSS were investigated. For that purpose, bimodal AFM and amplitude modulationAFM were used. The combination of the two techniques allowed to map the mechani-cal properties of dry and hydrated polymer films and to visualize the molecular chainsorganization of the polymer. Finally, in operando bimodal AFM was performed duringde-doping/doping cycles. It was shown that in the first cycles, PEDOT:PSS undergoesa non-reversible Young’s modulus drop due to the penetration of cations and conse-quent formation of percolation channels. After that, de-doping/doping cycles have as aconsequence a decrease/increase of the elastic modulus. These data show how advancedhigh-resolution AFM methods could complement other spectroscopic and electrical tech-niques to obtain a comprehensive understanding of organic electronic materials.

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4. Solid-liquid interface characterization ofhydrophobic surfaces

4.1. IntroductionIn this section, 3D-AFM is used to study solid-liquid interfaces (SLIs), in particular theones formed by crystalline hydrophobic surfaces with water. HOPG and h-BN are thecrystalline hydrophobic materials under study.Interfacial properties of hydrophobic materials have been extensively analyzed through

force-probing instruments such as Surface Force Apparatus and AFM [272, 273]. Crys-talline hydrophobic materials are nowadays commonly employed in 2D material-baseddevices, and among them applications in water environment are particularly relevant,such as biosensors [274, 275], nanopores and nanocapillaries [276, 277], and electron mi-croscope grids [278]. Though, the SLI of hydrophobic crystalline materials is still notfully understood.As explained in Chapter 1, liquid solvation layers are commonly found forming at the

surface of solid materials. Since the interface is created with water, the predicted resultis hydration layers with a periodicity equal to the van der Waals diameter of the watermolecule [47,48,156]. Hydration layers were visualized on the graphene surface by meansof high resolution x-ray reflectivity [279]. When similar interfaces were probed by AFM,the hydrophobic material-water interface showed solvation structures with a periodicitylarger than the one assigned to water molecules [68–71,76,280–282].Furthermore, recent reports focused on peculiar electrical properties characterizing

the interface between crystalline hydrophobic materials and water: in particular, it wasshown that the dielectric constant of these interfaces has an anomalous drop, reaching avalue of about 2, which is a 40-fold decrease with respect to the one of bulk water. Thisresult was explained with the reorientation of water molecules at the interface, beingresponsible to the dielectric constant drop [283]. Even though, this peculiar behaviorof the water dielectric permittivity was already demonstrated happening on hydrophilicsurfaces [284], it is the first time that has been reported for hydrophobic materials.Moreover, researchers started noticing that if hydrophobic flat materials were left to

age in air (and in some cases in water), their surface properties were likely to change. Forinstance, their surface tension, work function and double layer capacitance have beenshown drastically changing with time [285–292]. The majority of these papers linkedthe observations to the presence of airborne contaminants, able to modify the surfacetension and electrical properties with respect to the pristine species. Furthermore, AFMexperiments recorded the presence of periodic features forming at the surface of thesematerials: in these reports, airborne contaminants are again considered as the most

77

probable cause of the structures [67,281,293,294]. Nevertheless, the origin and the typeof species characterizing airborne contaminants are still controversially discussed.The aim of this chapter is to bring together the aforementioned results and to illustrate

how they can be interpreted under the same phenomenon. In particular, the temporalevolution of the organization of water on hydrophobic materials and their surface prop-erties were investigated. For that purpose, 3D-AFM, a dynamic volume AFM techniquewhich can visualize the solid-liquid solvation structures with nanoscale resolution, andAM AFM were applied. Molecular Dynamic (MD) simulations were performed to betterunderstand the AFM characterization and to distinguish the possible species belongingto the solvation structures. A comprehensive understanding of the solid-liquid prop-erties of hydrophobic surfaces is of particular relevance to explain the origin of theirhydrophobicity, but also to optimize their operation in 2D material-based devices.The 3D-AFM technique was originally developed in our lab [295]. The software and

suite to analyze the 3D data were developed in our lab by Manuel R. Uhlig [296]. The2D and 3D-AFM measurements shown here were performed in collaboration with M. R.Uhlig. The electrochemical impedance spectroscopy experiments were realized in Prof.Fabio Biscarini’s lab (IIT-Ferrara and UNIMORE) with the support of Dr. Michele diLauro, Dr. Stefano Carli and Dr. Marcello Berto. The MD simulations were performedby Dr. Ravindra Thakkar and Prof. Jeffrey Comer from Kansas State University. Theresults are published in a scientific article [297].

4.2. Set-up and theory of 3D-AFMTo better appreciate the measurements performed in this chapter, a general explanationof 3D-AFM is here introduced. This thesis is focused on showing the feasibility of 3D-AFM for new applications, thus only an essential explanation of the technique is hereoffered. We refer to literature works for a detailed description [156,295–297].As already mentioned in the Chapter 1, 3D-AFM is a volume AFM technique which

allows to obtain atomic resolution of a three dimensional space. A typical 3D-AFM cubeis shown in Fig. 4.1c. The cube is composed of three sets of 2D panels: xy, xz and yz.Hereafter, xz panels are used to analyze 3D-AFM experiments. In the configuration usedhere, an AM controller is used to track one of the eigenmodes of the cantilever, while aslower sinusoidal movement is applied to the z-piezo. Finally, the x,y raster motion ofa typical 2D-AFM image is maintained. The 3D-AFM scheme and the characteristic zsinusoidal movement is graphically shown in Fig. 4.1a,b.

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Figure 4.1.: 3D-AFM scheme and movements. (a) 3D-AFM consists of three modula-tions: (i) an x,y movement, similar to the standard scanning motion of 2D-AFM imaging; (ii) a sinusoidal z-modulation, which allows the cantileverto perform a movement normal to the surface; (iii) an AM oscillation inone of the eigenmode of the cantilever, simultaneous to the z-modulation.The latter excitation is much faster and with a lower amplitude than thez-movement. (b) Illustration of the different distances involved in AM 3D-AFM spectroscopy. zc and z are the cantilever and the tip position, respec-tively. Being A the cantilever oscillation amplitude, the two extremes ofthe oscillation are z = zc − A (the minimum) and z + 2A = zc + A (themaximum). (c) 3D-AFM phase cube of a mica-aqueous solution interface.The 3D cube can be sliced in xy, xz and yz planes. The cube shows theorganization of the water molecules at the interface. High resolution of themica surface allows to visualize its crystal lattice. Adapted from [297].

The 3D-AFM feedback records any change of the amplitude and phase with respectto the z position. The main difference between 3D-AFM and common force volumetechniques is that the former controls the cantilever movement through a feedback whilein the latter a trigger mechanism is used. This allows 3D-AFM to be much more timeefficient, with a great reduction of the acquisition time [54]. Moreover, even if at firstglance the 3D-AFM feedback could resemble the classic 2D-AM mechanism, to a deeperlook they work in a quite different way. When AM is run in a 2D scan, a free amplitudeA0 and an amplitude set-point Asp are chosen at the beginning of the experiment. Therole of the feedback is to keep the amplitude, A, at the set-point value, acting on thedistance between the tip and the sample. So when A > Asp the distance between thetip and the sample will be reduced until A = Asp and when A < Asp the tip-sampledistance will be increased until A = Asp. Usually, A and Asp are extremely close anddifferences are related to the feedback response time. In 3D-AFM, A is greater than Asp

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Figure 4.2.: 3D-AFM observables in time and space. Left column (a): Phase and Ampli-tude panels displayed with respect to the time. Right column (b): Conver-sion of the observable’s panels in the space domain. In the phase map, theHOPG surface is marked with a black dotted line. Regions corresponding tothe first, second and third solvation layer are also highlighted. Data takenat the HOPG-n-pentadecane interface.

for most of the sinusoidal z oscillation. Moreover, a fast feedback compensation of A toreach Asp is not desired. For that purpose, the feedback is set at very low value and Aspis at 0.9-0.95 of A0, forcing a slow feedback response. This guarantees that the feedbackmechanism does not interfere with the z sinusoidal movement, and consequently A hasits lower value at the minimum tip-sample distance. Nevertheless, at each x, y pointan amplitude-phase distance curve is recorded and can be converted in entities whichprovide more intuitive physical meaning, such as the force or the dissipated energy. Atypical 3D-AFM image is shown in Fig. 4.2.It is possible to notice that in Fig. 4.2a, the vertical axis in the phase and amplitude

panel is time (ms). This means that the data have to be converted from the time to thedistance domain. In 2D amplitude modulation AFM, the feedback displacement wouldbe considered as topographic channel. As explained before, in 3D-AFM, an additionalz movement is added to the cantilever. The cantilever position, zc, is then calculatedby summing up two additional recorded channels: the feedback displacement and thedisplacement of the z sinusoidal movement (for a visual reference see Fig. 4.1b). More-over, the tip minimum position, z, can be calculated (considering a negligible cantileverdeflection) as

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z = zc −A(t) (4.1)The spatial range where the new data span is found by subtracting the minimum valueof z to its maximum value. In this way, the data are shown not in terms of the time butof the position. This allows to measure correct z distances.As mentioned before, the idea is to convert the observables in the actual force. This

is realized by using a force reconstruction algorithm developed for dynamic mode AFMtechniques [86,167,168,298]. In the following results, we will make use of Hölscher’s algo-rithm [86] to reconstruct force distance curves (FDCs), which is a similar approach withrespect to the virial and energy dissipation theorem already seen in Chapter 2. In par-ticular, the tip-sample contact is divided in Iodd and Ieven, linked to the non-conservativeand conservative part of the tip-sample interaction. To extract the conservative part ofthe force, we make use of the latter. It is reported that

f20 − f2

f20

= Ieven + A0QA

cosφ (4.2)

Ieven = 2 f

kA

1/f

0Fts [z(t), z(t)] cos (2πft+ φ) dt (4.3)

where f0 and f are the natural frequency and the driving frequency of the cantilever.Now, let’s consider the two extremes of the oscillation, z and z + 2A as in the schemein Fig. 4.1b. We can introduce in eq. 4.3 the steady-state solution of the equation ofmotion D(t) = z + A + A cos(2πft + φ) and write it in terms of the spatial coordinate(D) as

Ieven = 2πkA2

z+2A

zFts

D − z −A√A2 − (D − z −A)2dD (4.4)

We can expand the last term as D → z to D−z−A√A2−(D−z−A)2 ≈ −

√A

2(D−z) obtaining

Ieven ≈ −√

2πkA

3/20

z+2A

z

Fts√D − z

dD (4.5)

Let’s call κ(D) = π−1 z+2Az

Fts√D−zdD. Rewriting eq. 4.2 in terms of Ieven , and making

use of eq. 4.5 we obtain

κ = kA3/2√

2

[A0 cos(φ)QA

− f20 − f2

f20

](4.6)

which is simplified when driving the cantilever at the resonance (f0 = f). Finally,Hölscher inverted the integral equation extracting the tip-sample force

Fts(z) = − ∂

∂z

z+2A

z

κ(D)√D − z

dD (4.7)

The procedure is shown in Fig. 4.3. Once the amplitude and phase are obtained fromthe microscope, the tip-sample force is reconstructed.

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Figure 4.3.: Force reconstruction procedure through Hölscher’s algorithm. (a) Phase and(b) amplitude curves from a single panel extracted and plotted against thez-position. (c) Each curve is treated with Hölscher’s algorithm and the FDCis extracted. The data are referred to the panels of Fig. 4.2 and were takenat the HOPG-n-pentadecane interface.

4.3. Materials and methods4.3.1. MaterialsFlakes of hexagonal-boron nitride (h-BN, purchased from HQ Graphene, Netherlands),were mechanically exfoliated with adhesive tape and transferred onto clean Si/SiO2 sub-strates (275 nm thermally oxidized SiO2) using a polydimethylsiloxane (PDMS) stamp.Before deposition, the substrates were ultrasonicated in acetone (99.6 %, Acros Or-ganics), ethanol (≥ 99.8 %, Sigma-Aldrich), and ultrapure water. After drying thesubstrates with a flow of nitrogen gas, they were exposed to oxygen plasma for 15 min(Diener Electronic, Germany). Highly oriented pyrolytic graphite (HOPG, grade ZYB)was purchased from Bruker (USA) and cleaved with adhesive tape just before the ex-periment. Muscovite mica (Grade V-1) was purchased from SPI supplies (USA). Themica was freshly cleaved with adhesive tape and rinsed with ultrapure water before theAFM experiments.Ultrapure water (UPW) was obtained before the experiments (ELGA Maxima, 18.2

MΩ cm−1). Water’s pH values were recorded for 10 minutes with a pH meter (HannaInstruments HI 9024). The pH reached a value of 5.6, starting from 7.2, due to thedissolution of atmospheric CO2 into the water. The experiments on HOPG in n-hexane(>99 %, Scharlab), and n-pentadecane (>99 %, Sigma-Aldrich) were performed in thesealed cell of the Cypher ES/VRS to avoid the solvent evaporation.

For the measurements in degassed buffer, a glass beaker containing 50 mL of UPWwas inserted in a desiccator with connected a vacuum pump. The system was vacuumpumped with a dry diaphragm pump for∼2 h. This helps to reduce the gas concentrationof about 50 times.

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4.3.2. 3D-AFM and 2D-AFM3D-AFM and 2D-AFM were implemented here in a Cypher S and ES/VRS (AsylumResearch, Oxford Instruments, Ca, USA). For 3D-AFM experiments, typical oscilla-tion amplitudes were around 100 pm. The cantilevers used here were Arrow-UHF-AuD(NanoAndMore, Germany). These cantilevers were chosen because of their large fre-quency and sensitivity, already at the first resonance frequency. They were found thebest cantilever type for the visualization of the solvation structures on hydrophobic sur-faces. The sinusoidal signal applied to the z-piezo consisted of amplitudes (peak-to-peak)between 1 and 4 nm and a period (frequency) of 10 ms (100 Hz). The z-data were readout every 20 µs and stored in 512 pixels. Considering that a single xy-plane of the 3Dmap contains 80 × 64 pixels, the total time to record such a 3D-AFM image was 52 s.2D-AFM imaging was run in the AM mode. It is named 2D-AFM to distinguish

it from the 3D-AFM operation. To obtain high resolution data, very small oscillationamplitudes (100-500 pm) were applied to the cantilever. Small and ultra-small amplitudeAFM has allowed to obtain high resolution of different materials in vacuum, air andliquid environment [138, 145, 261–264]. In fact, the small-amplitude operation enhancesthe sensitivity to short-range interaction forces and as a consequence allows to obtain ahigh spatial resolution. Here, small amplitudes were used to highly resolve the crystallattice of hydrophobic materials and monitoring the formation of adsorbates on thosesurfaces. The cantilevers used for 2D imaging were PPP-NCH-AuD, PPP-FM-AuD(NanoAndMore, Germany) in their second eigenmode, FastScan-A (Bruker, USA) andArrow-UHF-AuD in their first resonance. In Tab. B.1, the cantilever parameters arereported.To avoid external contamination, the cantilevers were cleaned in a mixture (50:50

in volume) of isopropanol (99.6 %, Acros Organics) and ultrapure water, rinsed withultrapure water and finally treated in a UV-Ozone cleaner (PSD-UV3, Novascan Tech-nologies, USA) for ≈ 30-60 min. In all measurements, the cantilever was driven throughphotothermal drive, which in liquid avoids undesired spurious peaks. The cantileverswere calibrated with contactless methods reported in previous chapters [18–20].The experiments were realized on freshly cleaved or aged surfaces. In particular, after

the use of the adhesive tape to remove the superficial HOPG layer, the surface was(i) immediately immersed in UPW for freshly-cleaved experiments, (ii) left aging fora time > 1 h for air-aged experiments, (iii) left aging for several hours for water-agedexperiments.Mica was used as a reference for flat and hydrophilic materials. This is important for

the sake of comparison because mica is a well characterized material, and it is knownhow water arranges at its surface. In fact, hydration structures on mica were visualizedwith different techniques, e.g. Surface Force Apparatus and AFM, forming layers witha spacing of about the molecular size of water molecules (∼ 0.3 nm) [47,48,156].

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4.3.3. Electrochemical Impedance spectroscopyElectrochemical impedance spectroscopy (EIS) experiments were realized to record thechange in capacitance with time on a graphitic (HOPG) surface. Experiments wereperformed with an Agilent B2912A potentiostat (Agilent Technologies, US) using athree-electrode cell. The graphite was used as a working electrode (WE), while a Pt wireand an Ag/AgCl electrode were chosen as counter electrode (CE) and reference electrode(RE), respectively. The HOPG was cleaved and then 400 µl of an electrolyte solution(50 mM KCl) were placed over the sample. The WE area (0.385 cm2) was defined bya PDMS cell. The water used to make the solution was UPW with a resistivity of 18.2MΩ cm−1. EIS measurements were obtained by applying an AC voltage with a 100 mVamplitude over a frequency range from 0.5 Hz to 100 kHz in a DC potential (vs RE) of0 V. The data were analyzed following the protocol described by Zou et al. [289]. Theeffective capacitance Ceff of the WE was extracted

α =∣∣∣∣d (log |Zi|)d (logΦ)

∣∣∣∣ (4.8)

Ceff = −sin(απ

2

) 12πΦαZi

(4.9)

where α is a constant phase element exponent, Zi is the imaginary part of theimpedance and Φ is the sampling frequency. The capacitance value is then extracted byaveraging (over the most stable frequency range from 10 Hz to 1 kHz). The measure-ments were recorded every 10 min for a total amount of 90 min.

4.3.4. Molecular dynamic simulationMolecular Dynamic (MD) simulations were performed by the group of Prof. J. Comer(Kansas State University) and followed the protocol reported in [299,300]. The graphiteand mica systems included two rectangular graphene/mica sheets stacked one over theother and disposed perpendicular to the z-axis. Water or organic solvent molecules wereadded to create mica/graphite-water/organic molecules systems; 2000 steps of energyminimization time of 150 ps of equilibration were needed before performing each simula-tion. The pressure and the temperature were kept at 1.01325 bar and 295 K. To estimatethe force measured in the experiments, an AFM tip model was constructed. The modelwas assembled as a hydroxylated diamond structure. To reproduce the experimentaldata, the contact area between the tip apex and the surface has to be of few atoms. Theadaptive biasing force method [301] was used to calculate the average force as a functionof the distance for the analyzed interfaces.When comparing simulations and experimental data, a method to overlap the force

profiles was established. In fact, the precise coordinates of the surface atoms in thesimulations are known but not in the experiments. Thus, to align the data, the forceprofile from the simulations was shifted horizontally until the global minimum of thesimulated force coincided with the global minimum of the corresponding experimentalcurve.

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4.4. 2D-AFM ResultsWhen imaged in liquid, the surface of freshly cleaved 2D materials, such as HOPG (Fig.4.4), looked extremely flat and it was possible to obtain high resolution images of thecrystalline lattice. In Fig. 4.4b, the hexagonal structure of HOPG is shown, obtained ona freshly cleaved sample. Two-dimensional fast Fourier transforms (FFT) were appliedto the phase image to reconstruct the lattice vectors a and b, which are identical forHOPG (and h-BN), a = b. The lattice vectors obtained from the FFT have averagelengths of 0.24 nm for HOPG.When the surface was left to age in air, the formation of aggregates was noticed. Fig.

4.5 shows the surface of air-aged HOPG measured in UPW. The presence of rippleswith different orientations, as underlined by the arrows, confirms a free-of-artifact imagequality. The structures seem to cover the surface of HOPG entirely. The spacing betweenthe ripples is around 5 nm. During imaging, less stable and smaller patches of rippleswere also found.The aggregates were distinguished in two types. The first tended to dissolve upon

addition of UPW (disordered structures) while the second was stable in water (orderedstructures). The majority of the disordered structures were dissolved when UPW wasadded, while the ordered structures (ripples) were stable (Appendix Fig. B.1).

Figure 4.4.: AM-AFM images of fresh HOPG. (a) The surface of freshly-cleaved HOPGas imaged in UPW. The surface was free of adsorbates. (b) When a zoomwas taken on the HOPG, it was possible to image the crystal lattice (phasemap). The FFT with the lattice vector is shown. Adapted from [297].

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Figure 4.5.: AM-AFM images of HOPG exposed to air. (a) The surface of air-agedHOPG as imaged in UPW. White arrows are used to underline the differentorientations of the ripples. Arrows are parallel to ripple structures. (b)Zoom-in of the ripples. A cross section normal to their direction is shown.The pitch is about 5 nm. Adapted from [297].

Those ripples were imaged in air and water with small amplitudes as feedback pa-rameter. This allows to have good quality images, both in air and water. Interestingly,the formation of similar structures were also noticed when HOPG was freshly cleavedand left in water for several hours. This process seems to be slower with respect to theair-aging formation of ripples, though. This means that if water and air ripples had thesame origin, the water would slow down the process but not prevent it.It is important to emphasize that ripples were possible to image exclusively using

small amplitudes, and the use of larger amplitudes limited the possibility to visualizethem, eventually making it impossible. This is demonstrated in Fig. 4.6. When theoscillation amplitude was kept at 0.5 nm, the ripple structures were visible and highlyresolved. When A0 was increased to 1.5 nm, the ripples were difficult to visualize butstill resolved. Finally, when A0 was about 4 nm, no periodic structures were visible onthe HOPG surface. This demonstrates the need of keeping the amplitude as small aspossible to image this kind of structures. The small-amplitude operation enhances thesensitivity to short-range interaction forces and as a consequence allows to obtain a highspatial resolution [138,145,261–264]. Moreover, an additional and intuitive explanationis related to the features dimension with respect to the cantilever oscillation amplitude.As long as the amplitude is kept in the same order of magnitude of the sample roughness(hundreds of pm), the ripples are easily resolved. This is not the case when the amplitudeis increased to higher value.

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Figure 4.6.: Influence of the oscillation amplitude for high resolution imaging. Ripplestructures on a graphitic surface immersed in UPW measured with differentA0. (a) Topography at A0 = 540 pm. At small amplitudes, the ripplesare clearly seen on the surface. (b) Topography at A0 = 1500 pm. Atintermediate amplitudes, it is still possible to faintly see the ripples. (b)Topography at A0 = 4400 pm. At larger amplitudes, no periodic structuresare visible. Below each panel, cross-sections along the lines marked in (a),(b) and (c) are shown. Adapted from [297].

Figure 4.7.: High-resolution of air-aged h-BN. (a) Phase image on h-BN surface, showingripple structures similar to the ones imaged on HOPG. (b) When the set-point amplitude was decreased (lower phase value), high-resolution of thecrystal lattice of h-BN was obtained. The insets show the FFT with thelattice vector of h-BN. Adapted from [297].

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Figure 4.8.: High-resolution on ripples. (a) Small-amplitude AFM phase map obtainedon ripples. Smaller periodic structures are visible, perpendicular to thedirection of the ripples. (b) After applying a FFT filter, it is possible tobetter visualize internal features. The period is about 0.5 nm. Adaptedfrom [297].

The surface of h-BN was also analyzed (Fig. 4.7). h-BN is a structural isomorph ofgraphite. The use of this material helps to generalize the observation realized on HOPG.In fact, the presence of periodic ripples was confirmed at its surface, which resemble verymuch the ones found on HOPG. In the case of h-BN, due to technical reason, it wasmuch more difficult to control the time of air-exposure (preparation time > 40 min), thusthe analysis was considered on a air-aged h-BN. The set-point amplitude was decreased,consequently applying higher forces, and it was possible to resolve the crystal lattice ofh-BN (Fig. 4.7b). This means the ripples were removed and the material surface washit. FFT was also applied to the phase image of h-BN to reconstruct the lattice vectors.Their values are comparable to the ones of HOPG, being them isomorphs. The latticevectors obtained from the FFT transforms have average lengths of 0.26 nm.Furthermore, experiments to distinguish internal structures of the ripples were per-

formed. This is shown in Fig. 4.8. Within the 5 nm pitch of the ripples, a smallerperiodicity is found. Fig. 4.8b shows the FFT image of Fig. 4.8a. The spacing is about0.5 nm and their orientation is perpendicular to the one of the ripples. This value matchesrecent results where ripple structures were imaged with similar high resolution [281].

4.5. 3D-AFM Results3D-AFM was applied to perform the same time-dependent experiments as in 2D-AFM.As mentioned in the introduction, up to date AFM data taken on the hydrophobicmaterials-water interface have exhibited solvation structures with a dimension differentto the one expected for hydration layers [68–71, 76, 280–282]. 3D-AFM panels recordedon air-aged HOPG and h-BN are shown in Fig. 4.9. Already at first glance, we notice

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how the x,y panel recorded on air-aged HOPG and h-BN are very similar (Fig. 4.9a,b).After the 3D-AFM observables were recorded, it was possible to convert them in FDCs

(Fig. 4.9c,d). FDCs provide quantitative information on the tip-liquid interaction. Inparticular, FDCs show an oscillatory behavior with alternating attractive and repulsiveregions until the tip touches the surface, establishing a mechanical contact with it.After that, the force becomes increasingly repulsive. The maxima observed in FDCs canbe associated with maxima in the liquid density [75, 302]. This interpretation, namedsolvent-tip-approximation (STA), associates each oscillation in the force with a solvationlayer. In the STA the force on the AFM tip is related to the local liquid density by

F (z) = kBT

ρ(z)dρ(z)dz

(4.10)

with kB and T being the Boltzmann constant and the absolute temperature. Thisequation provides a conversion of the liquid density obtained from simulations into forcemaps, allowing a direct comparison with experimental 3D-AFM data.

Figure 4.9.: Solid-liquid interface of water on air-aged hydrophobic surfaces. (a) Air-agedHOPG-water interface xz map. (b) Air-aged h-BN-water interface xz map.(c) Force-distance curves (FDCs) corresponding to panel (a). (d) FDCscorresponding to panel (b). The average curve is highlighted. Adaptedfrom [297].

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Figure 4.10.: Solid-liquid interface of water on freshly-cleaved HOPG. (a) Freshly-cleavedHOPG-water interface xz map. (b) FDCs corresponding to panel (a). Theaverage curve is highlighted. Adapted from [297].

Moreover, distances between layers are related to the dimension of liquid molecules atthe interface. The position of the surface was assigned to the z value associated with therepulsive force whose slope has the highest value. In the STA model, the actual tip isconsidered formed by a water layer surrounding the tip itself. When the tip breaks in aliquid layer, a repulsive maximum in the force will appear followed by a consecutive deepminimum. The distance between the surface and the first layer is called d0, between thefirst and the second layer is named d1, between the second and the third d2, and betweenthe third and the fourth d3. Usually, a number of oscillation between 2 and 4 is found. Inthe 3D-AFM experiments shown here, the number of oscillations is not surface specific.Thus, we mainly focus on the interlayer distance to compare the solvation layers.The shape of FDCs measured on air-aged graphite and h-BN are quite similar, and

the measured interlayer separations as well (Fig. 4.9c,d). This distance on graphiteand h-BN is in the 0.43-0.52 nm range, which is in agreement with previous AFMmeasurements on hydrophobic flat materials [68–71, 76, 280–282]. It is important tounderline this interlayer distance does not reflect the water van der Waals diameter.When the surface of HOPG was freshly cleaved and suddenly immersed in UPW,

the result was quite different, though. This is shown in Fig. 4.10. The x,y panel ischaracterized by layers with smaller distance with respect to the air-aged case. Theinterlayer separation has a much smaller value, around 0.35 nm (Fig. 4.10b). This valueis similar to the one derived from high resolution x-ray reflectivity [279], and resemblesthe van der Waals diameter of water molecules.Every time the surface was aged in air, it led to the result plotted in Fig. 4.9. When

the surface was left to age in water, we obtained the same interlayer distance as for theair-aged surface only in 10% of the performed experiments. This means that somehowthe process of aging is slowed down, or the collective effect is smaller when the freshly-

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cleaved surface is immediately immersed in UPW.

4.5.1. Comparison with hydrophilic surfacesTo establish the generality of the observation on flat hydrophobic surfaces, additionalexperiments were performed on a flat hydrophilic surface, muscovite mica. The sametype of experiments (time-dependence), as the one on hydrophobic surfaces, was realized.When 3D-AFM was applied on mica, solvation layers were visualized, having a spacing

of around 0.3 nm (Fig. 4.11). The result was independent of the air-aging time. Thisvalue is in agreement with the van der Waals diameter of water molecules (0.28 nm).The same observation is found in the literature on a variety of hydrophilic materials[54, 58, 59, 156, 158]. The difference in dimension between the result obtained on air-aged hydrophobic material and the mica surface immersed in water is remarkable. Asa reference, let’s consider the FDCs of water on air-aged HOPG and h-BN in Fig.4.9. The interlayer distances differ of about 0.15-0.2 nm between the results obtainedon hydrophobic and hydrophilic surfaces. Interestingly, while the solid-liquid interfaceextends of 1 nm on mica, on the air-aged hydrophobic surfaces the result is quite different,with an extension of 2 nm from the surface.

Figure 4.11.: Solid-liquid interface of water on mica. (a) 3D-AFM xz force map of themica-H2O interface. (b) FDCs corresponding to panel (a). The averagecurve is highlighted. Adapted from [297].

The mica surface didn’t show any features that could resemble the ripple structuresvisualized on HOPG and h-BN. This means that this kind of adsorbates is to be con-sidered characteristic of hydrophobic surfaces. High resolution of the mica surface wasobtained from 3D-AFM experiments (Fig. 4.12). This was realized selecting the value ofthe phase at a certain z for all the phase curves forming a 3D-AFM cube. The result isa 2D image at a certain z value. The obtained image is compared with a high resolutionimage taken over mica in a 2D scan. Through the 3D image, it is not only possible to

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visualize the mica lattice (z = 0 nm) but also the arrangement of water molecules at thefirst hydration layer (z = 0.35 nm).

Figure 4.12.: 2D-AFM and 3D-AFM xy images of the mica-water interfaces. (a) 2D-AFM high resolution of the mica lattice. The FFT shows the lattice vectorsequal to 0.53 nm. (b) 3D-AFM xy image taken at z =0.00 nm showing themica surface. The resulting lattice is comparable with panel (a) showingthe ability of 3D-AFM to obtain high resolution data. The structure of themica is overlaid. Si is shown in yellow and oxygen in red. (c) At z =0.35nm, the image shows a honeycomb lattice of water molecules. A modelof water molecules is overlaid to help the visualization of the structure.Adapted from [297].

Furthermore, to have a general view of the time-evolution of the SLI, several exper-iments were performed on hydrophobic and hydrophilic surfaces. This is summarizedin the graph of Fig. 4.13 (a table, Tab. B.2, with the relevant statistical descriptors isshown in the Appendix). First of all, the interface between mica and water was charac-terized. It was found a well defined interface with interlayer distances not depending onthe time the mica surface was exposed to ambient air. All the values are centered around0.32 nm. The dispersion of the data is quite small, with a standard deviation STD < 0.03nm. On the other hand, as previously shown in Fig. 4.9, the interfacial water structureobserved on graphite showed a marked difference between fresh and air-exposed surfaces.On aged graphite surfaces, interlayer distances are centered at 0.45 (d1), 0.55 (d2) and0.51 nm (d3). As for the experiments on mica, a small data dispersion is obtained onair-aged surfaces (STD = 0.05 nm). On freshly-cleaved hydrophobic surfaces, a decreaseof the mean value is observed, in particular for what concerns the 1st solvation layer(0.37 nm). This value is close to the one obtained for hydration layers on hydrophilicsurfaces. Sometimes, larger interlayer distances were observed also on fresh surfaces (ad-ditional 3D-AFM panels and FDCs are shown in Appendix Fig. B.4 and Fig. B.5). Infact, a much higher dispersion of the data is obtained for experiments realized on freshly-cleaved HOPG (STD = 0.12 nm). In addition, the difference observed between the meanand median values indicates that the interfacial water structure on the fresh graphite

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surface was somehow unstable, with variations over different measurements. Overall, onaverage the interlayer distances increase of 0.10 nm for d1, 0.08 nm for d2 and 0.06 nmfor d3: these are larger values than the STD of the single interlayer distances recordedon air-aged HOPG. Summarizing, on the air-aged hydrophobic surface the solid-liquidinterface is somehow more stable and larger than the freshly-cleaved scenario.

Figure 4.13.: Time-evolution interfacial water on mica and graphite. Interlayer distancesof UPW on fresh (left pink area) and air-aged mica (left light blue area).Interlayer distances do not depend on the time the mica surface was exposedto ambient air. All the values are centered around 0.32 nm. Interlayerdistances of UPW on fresh (right pink area) and air-aged graphite (rightlight blue area). The data show a dependence on the aging time. Onexposed surfaces, interlayer distances are centered at 0.45 (d1), 0.55 (d2)and 0.51 nm (d3). A range of values (0.2-0.75 nm) are observed on freshly-cleaved graphite surfaces. The standard deviation is much larger than theone obtained in the other cases. Data are visualized through box plots (n≥ 9). The average value of each set of experiments is shown with an emptysquare. The median is shown as a black line. Black dots are consideredas outliers. Statistical parameters are calculated by taking into accountoutliers. Adapted from [297].

4.5.2. Consideration about the ripples and solvation layers on hydrophobicmaterials

Up to now, a description of the solid-liquid interface of water and hydrophobic materialshas been offered. A substantial difference with the SLI of hydrophilic surfaces wasreported. The main descriptors of the SLI formed by water with hydrophobic crystallinematerials are:

• The presence of periodic structures at the surface with a spacing of about 4-5 nm.Those ripples show internal periodic features with a periodicity of 0.5 nm.

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• The presence of solvation layers with an interlayer distance of about 0.5 nm. Thisdistance cannot be directly related to the van der Waals diameter of water.

• A time-dependent behavior of the SLI, especially when the surface was exposed toair-aging.

To provide an interpretation of the possible origin of the different SLI, we consider twopossibilities, already described in the literature and related to the adsorption of airbornespecies: adsorption of gases or hydrocarbon contaminants, named here gas and hydro-carbon hypothesis. This is a controversial topic in the literature, with reports in favorof one interpretation or the other. The gas adsorption hypothesis was initially describedby Hwang and coworkers [67]. Other groups considered this option, assuming the pres-ence of hydrated gas molecules (especially N2) to be the origin the 0.5 nm interlayerdistance and of the ripple structures [68–70, 282]. The gas molecules would graduallyaccumulate on hydrophobic surfaces immersed in water forming a new interface. Whilethis hypothesis could be considered in the formation of a new SLI in water, it does notexplain air-aging effects.On the other hand, several reports have considered the aging of graphitic surfaces (and

in general hydrophobic crystalline surfaces) due to the accumulation of hydrocarbonsfrom ambient air [281, 285–292, 294, 303–307] (see below for further discussion aboutliterature data). Interestingly, the thickness of (linear) hydrocarbon molecules stackedtogether would match the 0.5 nm periodicity found either forming the SLI and theripples.To understand which is the most plausible option between the two, further experiments

were performed other than a comparison with MD simulations.

4.5.3. Experiments in alkanes and degassed water3D-AFM experiments were performed in pure alkanes and in solution saturated withalkanes on freshly-cleaved HOPG. The results are shown in Fig. 4.14a,b. The FDCsobtained on pure n-hexane and n-hexane contaminated water resemble very much theones obtained on the air-aged surface. It is known that straight-chain hydrocarbonstend to stack parallel to the surface of graphitic materials, thus the interlayer distancesshould be similar independently of the molecular weight [61, 64]. This observation wasconfirmed by performing 3D-AFM on the HOPG-n-pentadecane interface (AppendixFig. B.2). The interlayer distances are similar to the ones obtained for n-hexane (d1=0.44 nm, d2= 0.50 nm, d3= 0.48 nm).Furthermore, to understand the influence of gases on the surface of hydrophobic ma-

terials, experiments in degassed water were realized. When degassed water was injectedon freshly-cleaved/air-aged HOPG and the interface was probed, it was not recordedany difference with the measurements performed using standard UPW (Appendix Fig.B.6). Thus, the presence/absence of gases in water did not determine any change in theexperiments, meaning the relevant contribution to the interface came from other factors.Interlayer distances obtained with liquid alkanes or alkane-water solution have basi-

cally the same values as the ones obtained on air-aged HOPG/h-BN. These experiments

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suggest the interface might be dominated by hydrocarbons more than gas molecules.

Figure 4.14.: 3D-AFM FDCs in alkanes. (a) FDCs obtained on freshly-cleaved HOPGimmersed in n-hexane. (b) FDCs obtained on freshly-cleaved HOPG im-mersed in water saturated with n-hexane. The average curves are plottedas thick and blue lines. Adapted from [297].

4.5.4. Comparison with MD simulationsMD simulations were used to test the above hypotheses and to understand the free energyfactors that drive the formation of this particular interfacial water structure. First of all,the force profile of water on mica and graphite was calculated and compared with theexperimental results. Fig. 4.15 shows that the interlayer spacing obtained on mica and onHOPG is similar (∼ 0.3 nm) and reflects the van der Waals diameter of water molecules.This result is comparable with values obtained from similar simulations in the literature[308–310]. When compared to the AFM experiments, the simulation obtained on micanicely fits the experimental data while this is not the case for the aged HOPG. Whilethe interlayer distance of the latter experiments is larger with respect to the simulationsof the same system, changing the interfacial liquid could give some more insights. MDsimulation for the alkane-HOPG interface was then performed. The interlayer distance isabout 0.44 nm. The result, which fits the alkanes-HOPG experiments, is also much morecomparable to the water-aged HOPG interface as well, with respect to the simulation ofthat specific case.

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Figure 4.15.: Molecular dynamics simulations compared to experimental FDCs. MDsnapshots of a model AFM tip asperity, MD and experimental FDCs ob-tained for a (a) mica-water, (b) graphite-water and (c) graphite-hexaneinterface. Atoms are shown as spheres (H, white; graphite C, gray; otherC, green; oxygen, red; K+, pink; Al black; Si, cyan). Adapted from [297].

To better understand the energy driving the process, the free-energy of adsorption ofalkanes, starting from an alkane aqueous solution on mica and graphite, was calculated.Fig. 4.16a,b shows the atomic model of the interface between mica/graphite and waterincluding a single hydrocarbon (n-hexane) molecule, as used in the simulation. Fig.4.16c represents the free energy as a function of the alkane-surface distance. It showsclearly that straight-chain alkanes adsorb to the graphite surface with an affinity thatincreases with the length (and eventually mass) of the alkane. Moreover, it is knownthat the high affinity of straight-chain hydrocarbons for graphite derives not only fromchemical interactions but also from an additional contribution due to the stacking of CH2

groups on top of the hexagon of the HOPG lattice [311]. The situation on mica is quitedifferent: the free-energy of adsorption of alkanes on the mica surface is positive. Thismeans that alkanes exhibit no affinity for the hydrophilic surface, and their adsorptionin a solution with water would be highly unfavorable.Finally, to better understand what would happen if N2 molecules stuck at the surface

of HOPG, MD simulations were performed including N2 (Fig. 4.17). The result showsthat if this interface were created, the interlayer distance would give a much differentresult with respect to the one obtained from the experimental data. In fact, a smallerinterlayer distance was obtained, not comparable with the 0.45-0.5 nm obtained on air-aged HOPG. This is another element against the gas hypothesis.

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Figure 4.16.: Free-energy calculations for adsorption of alkanes from aqueous solutionon mica and graphite surfaces. (a) Atomic model of an interface betweenmuscovite mica and water including a single hexane molecule. (b) Atomicmodel of hexane adsorbed to a graphite-water interface. Water moleculesare shown as a blue surface. Atoms are shown as spheres (H, white; graphiteC, gray; hexane C, green; oxygen, red; K+, pink; Al, black; Si, cyan). (c)Free energy as a function of the distance between the center of mass of thealkane molecule and surface plane. Adapted from [297].

Figure 4.17.: MD simulations of graphene-(contaminated) water interfaces. (a) MDsnapshots of a model AFM tip asperity near a mica-N2+ water interface.The nitrogen atoms are shown in blue. (b) MD force curves calculated forthe graphite-water, graphite-liquid hexane and graphite-N2+ water inter-face. The force curves are compared with an experimental FDC obtainedfor a aged graphite surface immersed in UPW. The MD simulation for aninterface including N2 neither matches the intermaxima distance nor theshape of the experimental data. Otherwise, a good agreement is obtainedfor a MD model including linear hydrocarbons. Adapted from [297].

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4.6. DiscussionThe experiments shown here indicate the formation of molecular-thick hydrophobic lay-ers composed of molecules in the ambient air and adsorbed to the surface of hydrophobiccrystalline materials directly through air or when dissolved in water. The experimentswere performed using purified water characterized by a resistivity of 18.2 MΩ cm−1.Nevertheless, it is known that purified water carries trace amounts of hydrocarbonmolecules (around 10 ppb) [287]. Thus, airborne or liquid-borne hydrocarbon moleculesmight accumulate on the graphite (h-BN)-liquid water interface. Their absence fromthe mica-water interface was clearly shown and motivated by experimental data andMD simulations.We found that there were aggregates on the surface of hydrophobic materials. Those

aggregates were distinguished in ordered structures or ripples (not water soluble) anddisordered structures (mainly water soluble). The presence of impurities at the surface ofcarbon based 2D materials and other 2D materials was already reported. In particular,ellipsometric measurements indicated that adsorption of a 0.55-0.6 nm-thick layer occurson exfoliated HOPG [288,312].Ripple structures were found and studied in air and in liquid with different techniques

over several layered materials, such as graphitic surfaces, MoS2 and WSe2. Some ofthe authors, ascribed the origin of these structures to contaminants (hydrocarbons orgases) found in the air or dissolved in the water which assemble over the surface of thelayered material [67,70,71,294,304,305,307,313]. Others assigned to catalytic processesthe formation of the ripples [293]. Finally, a recent report justified their presence tocontamination coming from the plastic pipettes used to inject the water onto the surfaceof the material [281]. All these observations seem to have in common the presence ofripples, but the source of contamination is controversial and open to discussion.Identifying the source of the ripple structures is a hard duty, since it would require

the ability to combine high resolution with chemical imaging. Up to now, the apparatusable to perform chemical imaging, based on recording chemical spectra at a specificfrequency (i.e. IR, Raman etc.), have a resolution of tens of nanometers (in the bestcase) when combined with atomic force microscopy [314–317]; moreover, their applicationin water environment has not been exploited yet. Nevertheless, the chemistry of thesurface, dependent on the air-exposure time, was recorded with microscale spectroscopy.This is justified, since ripple structures have been demonstrated extending over largeareas of the samples (several microns) [294]. To that purpose, ATR-FTIR (attenuatedtotal reflectance-Fourier transform infrared spectroscopy) and XPS (X-ray photoelectronspectroscopy) confirmed an increased amount of carbon species on graphitic surfaces andh-BN when the material was exposed to air aging [285, 290, 303]. To try to understandwhich is the origin of the contaminants, high resolution of the internal structures of theripples was obtianed (as shown in Fig. 4.8). Equivalent high resolution images werealso reported by Seibert et al. [281]. The 0.5 nm period was ascribed to hydrocarbonsstacked parallel to the graphitic surface. Similar features were already reported formingon the surface of hydrophobic crystalline materials by the adsorption of hydrocarbons[318]. In the experiments shown here, when higher scanning forces were applied, the

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crystal lattice of the material was resolved. Interestingly, as aforementioned, ripples werestudied not only by atomic force microscopy but also through optical measurements, suchas polarization-contrast microscopy [305], which ruled out the possibility of structuralrippling.When the interface of water with such contaminated (air-aged) hydrophobic materials

was studied with 3D-AFM, the same results reported in the literature for AFM exper-iments were found [68–71, 76, 280–282]. Interlayer distances of ∼0.5 nm were the onlyones recorded for aged surfaces. While when HOPG was freshly cleaved, the presenceof solvation layers with interlayer distances of about 0.35 nm (ascribed to the van derWaals diameter of water) could be visualized. This time-dependence suggests that watermolecules might form hydration layers on graphite whenever contaminants are not ad-sorbed on the surface. This phenomenon does not happen on the surface of hydrophilicmaterials, where the air-aging does not influence the interfacial water structure. More-over, the 0.5 nm interlayer distance resembles very much the periodicity of the internalstructure of the ripples.By comparing the experimental results to MD simulations, the possible source of con-

tamination was confirmed probably being straight chain hydrocarbons. While the timescale of simulations is very much different to the experimental one, it provided withinsights of the most plausible origin of the interfacial liquid. By comparing interlayerdistances obtained in simulation of water on HOPG and alkanes on HOPG, it was clearthat describing the solid-liquid interface of hydrophobic crystalline materials with MDsimulations that take into account the pure system was unfeasible. In fact, the result didnot fit the experimental observation. If liquid alkanes were introduced in the system,the result would lead to a nice overlap between simulations and experimental data (Fig.4.15). These simulations confirmed the experimental results obtained with liquid alkanesand alkane-contaminated water on freshly cleaved HOPG, as shown in Fig. 4.14. Someauthors claimed the origin of these solvation layers to be hydrated gases [68–70,282]. 3D-AFM experiments were performed using degassed UPW on HOPG. It was not recordedany difference with respect to the measurements realized with standard UPW, indicatingthat dissolved gases do not play the main contribution at the SLI. Additionally, MD sim-ulation of the graphite-N2+ water interface showed solvation structures with interlayerdistances not comparable to the ones obtained from the experimental data (Fig. 4.17).Overall, considering experimental data and simulations, the origin of the new interfacecannot be ascribed to gas molecules, while hydrocarbons stand out as the most plausiblehypothesis.The consequence of the formation of an adlayer of contaminants is broad and of a great

impact. It was shown how its presence modifies the surface tension and contact angle ofhydrophobic materials [285, 290, 312]. In those experiments the water contact angle ofgraphitic surfaces and h-BN increased from 64.4° to 80° after exposure to ambient air,leading to an higher hydrophobicity of the surface. Moreover, the friction properties ofthe material were noticed to change due to the presence of ripple structures at the surfaceof graphite [304]. Martinez-Martin et al. showed how the surface potential, recorded byKelvin Probe Force Microscopy, changed with the air-aging time [286].In liquid environment, the presence of a passivating layer was reported through the

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use of electrochemical impedance spectroscopy and scanning electrochemical microscopy[287,289,291]. This electrically dead layer was attributed to the accumulation of contam-inants on the material surface. In particular, the capacitance of graphite was measuredand it was noticed how either air-borne and liquid-borne contaminants could decreasethe double layer capacitance. To corroborate these observations, EIS experiments wererealized on the graphite surface immersed in electrolyte solution. The result is shown inFig. B.3 of the Appendix. It was obtained a general decrease of the capacitance withtime, confirming previous observations. Recently, the ζ potential of hydrophobic surfacesand its dependence on pH and salt concentration couldn’t be explained without takinginto account the presence of organic impurities contributing to its actual value [292].Moreover, the drop in the double layer capacitance might be reflected in other exper-imental results recently shown in the literature. In fact, the dielectric constant ε ofwater confined between two atomically flat hydrophobic surfaces (h-BN and graphite)was measured from large to few nm separations [283]. Electrostatic Force Microscopywas applied for that purpose. A value of ε = 2 was measured for very small separations(1-2 nm), which is far from the value expected for bulk water ε = 80. The results wereexplained by the presence of a constrained layer of water molecules which are unable toperform rotational movements of their dipole moments. However, the existence of a 1-2nm layer of hydrocarbon molecules provides a different explanation to the results. Infact, alkane molecules have a very low dielectric constant (ε = 2 at T =295 K) that issimilar to the value obtained in those results.

4.7. ConclusionHydration layers are commonly found on hydrophilic surfaces and are predicted fromsimulations as well for hydrophobic surfaces. When simulating solid-liquid interface, MDsimulations usually do not take into account the presence of trace amount of contam-inants. On mica, the interfacial water is formed by hydration layers. Though, whenAFM experiments are performed on crystalline hydrophobic materials, the result is dif-ferent from the predicted one. Ambient air and purified water contain trace amounts ofhydrocarbon molecules (≤10 ppb in water). These molecules might accumulate at thesurface of the material by direct adsorption from air or by diffusion through water. Inthe data shown here, every time the surface was exposed to air, a different type of in-terface was created, while on freshly-cleaved surfaces a dynamic interface was recorded.In the latter case, the formation of hydration layers was measured. In the first case, theinterfacial layers were never comparable to the ones formed by water. The origin of thesesolvation structures was ascribed to airborne hydrocarbon molecules. Other sources ofcontamination cannot be excluded (e.g. surface catalysis) but the result would lead tothe creation of the same interface.

These data clearly illustrate the complexity of the interface between hydrophobicmaterials and water. Through 3D-AFM, it was shown that hydration layers were onlyformed on hydrophobic flat materials when the surface was freshly cleaved. This resultreconciles some of the controversies of experimental data realized with AFM and x-ray

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reflectivity on the hydrophobic material-water interface. When the surface is aged, it isrelevant to consider components which are commonly neglected: as demonstrated theirpresence has a great relevance to determine the intrinsic properties of the interface. Agedsurfaces are the ones that are usually used in experiments and for device applications.This constitutes the importance and the broad significance of the finding.

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5. 3D-AFM visualization of alkane-solidinterfaces

5.1. IntroductionWhen water molecules meet an hydrophilic surface, hydration layers are formed, dueto strong attractive interactions between the liquid and the solid [44]. This is truealso for organic nonpolar liquids which form solvation layers at graphitic and otherhydrophobic surfaces. But when hydrophobic/hydrophilic surfaces are in contact withpolar/nonpolar liquids, the situation becomes less predictable (as also demonstrated inthe Chapter 4). In fact, the formation of solvation structures is more unfavorable dueto the weak interaction between the liquid and the surface; the interfacial structuresturn out to be sensitive to small changes of environmental conditions [319–321], or ofthe liquid composition [322,323].In the literature, we find different publications characterizing the influence of the water

content on the interface of hydrophilic surfaces with organic solvents. Surface ForceApparatus [319, 324, 325], contact angle goniometry [322, 326], infrared spectroscopy[327], ellipsometry [326], AFM [320,328] and Molecular Dynamics simulations [329] wereapplied to study those interfaces. It was shown that the presence of water in organicliquids can crucially change the interfacial properties and modify their functionality.This is relevant especially when the solid has a hydrophilic nature, and trace amounts ofwater can diffuse to the surface and condensate at the interface, having as a consequencethe formation of a nanometer-thick film [324,326].In this section, 3D-AFM is applied to study the solid-liquid interface formed by organic

liquids on hydrophilic/hydrophobic materials. Our interest is to broaden the significanceof the previous chapter, demonstrating that unexpected organized solid-liquid interfacesare formed by very small amounts of substances found in polar and nonpolar liquids.In particular, we focus on the solid-liquid interface formed by two alkane species, n-hexane and n-octane, and solid crystalline materials, mica (as hydrophilic surface) andHOPG (as hydrophobic surface). The influence of water molecules at those interfaces isstudied. The relevance of this study is intrinsic in the multiple applications that organicliquids have with hydrophilic surfaces such as nanotechnology, biotechnology, petroleumengineering and tribology. To mention few examples among them, processes involvingsurface functionalization [330], enzyme catalysis in organic media [330], boundary layerlubrication [64,331,332] and oil recovery [322,326] are influenced by the organization oftheir solid-liquid interface.Here, through 3D-AFM nanoscale images of the solid-liquid interfaces between organic

media and crystalline solid surfaces are provided. It is shown how the presence of trace

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amounts of water in alkane solvents have a relevant effect at the solid-liquid interfaceand that the interfacial structure is dominated by the interaction energies of the involvedmolecules.The 3D-AFM measurements shown here were performed in collaboration with Manuel

Uhlig.

5.2. Materials and Methods5.2.1. MaterialsMuscovite mica discs of grade V-1 and highly oriented pyrolytic graphite (HOPG) ofgrade ZYB were purchased from SPI supplies (USA) and from Bruker (USA), respec-tively. Both materials were freshly cleaved with adhesive tape before each experiment.Ultrapure water (UPW, 18.2 MΩ cm−1) was obtained from the machine (ELGA Max-

ima), with the water having a pH value of 5.6 (Hanna Instruments HI 9024). Aqueoussolutions of 200 mM KCl were prepared by dissolving KCl (≥99 %, Sigma-Aldrich) inUPW. For the experiments involving hydrocarbon solvents, n-octane (anhydrous, >99%, Sigma-Aldrich) and n-hexane (anhydrous, >99 %, Scharlab) were used. Both solventswere stored in sealed glass bottles in ambient conditions.

Experiments were performed both in standard (as-purchased) and dried hydrocarbonsolvents. Dried solvents were prepared before the experiments by molecular sieving withsilica gel (Sigma-Aldrich) for at least 2 h. For instance, treating n-octane with silicagel allows to decrease the estimated amount of water content (m/m) from 98 ppm to<6 ppm [325]. Experiments mixing octane in water were performed adding a drop ofn-octane to UPW. The mixture was then shaken and left resting for 1-2 days [333]. Thefinal concentration of n-octane was about 10 ppb (the solubility of n-octane in water is0.007 mg L−1).

5.2.2. 3D-AFM imaging3D-AFM was implemented on a Cypher VRS/ES (Asylum Research, Oxford Instru-ments) in a similar way with respect to what is shown in Chapter 4. Due to the fastevaporation of the organic liquid used here, AFM experiments were performed in a closedfluid cell. Before each experiment, the cantilever holder was cleaned using ethanol anddistilled water. Then, the sample discs, with either mica or HOPG glued on top, weremounted magnetically onto the microscope sample stage. The sample was cleaved andimmediately a small droplet of the aqueous solution/solvent was placed on top of thesurface. The cantilever, previously placed in the AFM holder, was immersed into theliquid and the liquid cell was then sealed. The temperature of the cell was kept constantat 28.0 ± 0.1 °C by using a thermal controller (ATC, Asylum Research, Oxford Instru-ments). The ambient relative humidity was measured being between 30 and 40% (testo605i, Testo GmbH).The 3D-AFM imaging was performed in amplitude modulation mode as it is described

in Chapter 4. The microcantilevers were excited at their 1st flexural eigenmode by using

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a photothermal excitation. The cantilevers used here were Arrow-UHF-AuD, Arrow-UHF-Al (NanoAndMore, Germany), and FS-1500AuD (Asylum Research, Oxford In-struments). The cantilever parameters are summarized in Appendix 5 Tab. C.1. Thefree amplitude values A0 were in the range of 70-100 pm. Set-point amplitudes of Asp≈ 0.35-0.60 A0 were used. The cantilevers were calibrated with the contactless methodreported in previous chapters. While the cantilever oscillates at its resonance frequency,an additional z sinusoidal movement is applied to control the relative distance betweenthe tip and the sample. The z-piezo sinusoidal motion had the following characteristics:peak-to-peak amplitude of 2.5 nm, period (frequency) of 10 ms (100 Hz). The z-datawere read out every 20 µs and stored in 512 pixels (256 pixels half cycle). Each xy-planeof the 3D map contains 80 × 64 pixels and the total time to acquire the entire image is52 s. It was not observed any reproducible feature in the liquid structure above 2 nm,thus we used z-range of 2.5 nm. The force was reconstructed using Hölscher’s algorithm,as explained in Chapter 4. Some of the force profiles reconstructed with 3D-AFM havea shape constituted by a long-range repulsive background with superimposed oscilla-tions (more details are given in Chapter 6) [58,65,334]. The background contribution isdetermined through an exponential function as

y = C1 + C2 exp(−xl

)(5.1)

where C1, C2, and l are fit parameters. The determination of the background forcegoes beyond the purpose of this chapter, and the focus is on the oscillatory part of theforce. Thus, the background contribution was subtracted from the force curves. Thefitting parameters are shown in Appendix Tab. C.2.

5.3. Results3D-AFM was applied to study the solid-liquid interface formed by mica and HOPG (usedas models for hydrophilic and hydrophobic surfaces) with unbranched octane as a modelfor nonpolar solvents. Experiments were performed with n-octane as-purchased (99%),as well as molecular sieved n-octane (from now on, named standard and dry n-octane,respectively). Experiments were repeated in n-hexane to confirm the observation madewith n-octane.

Fig. 5.1 shows the result obtained on mica in standard and dry n-octane. As a ref-erence, the interface between mica and water is also shown. All the three experimentsshow the presence of a stripe-like contrast in the space close to the mica surface, whichis assigned to solvation layers. Below each 3D-AFM panel, FDCs with their averagevalue are also plotted. Each panel consists of 80 individual force-distance curves. Evenif, qualitatively speaking, all FDCs have a similar appearance with oscillatory forcesapproaching the mica surface until contact with the solid surface is reached, quantita-tively FDCs are different for the solid-liquid interfaces investigated here. The interlayerdistances of the data obtained on standard n-octane and dry n-octane are clearly dif-ferent. In fact, while in the former the interlayer distance is 0.30 nm, the latter shows

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Figure 5.1.: Solid-liquid interface of water, standard and dry n-octane on mica. 3D-AFMxz force panel of (a) aqueous solution, (b) standard n-octane (>99 %) and(c) dry n-octane on mica. Below each panel, the corresponding FDCs areshown. Average curves are highlighted.

separations of 0.50 nm (d1) and 0.56 nm (d2) (see Chapter 4 for the precise definition ofd). As previously explained in Chapter 4, the interlayer distance is associated with thevan der Waals diameter of the molecule forming the solvation layer at the interface. Aninterlayer distance of 0.45-0.55 nm corresponds to n-octane molecules flatly lying on thesolid surface, as reported earlier for dry alkanes on mica [64,325].If the data obtained on the mica-water interface are compared to the ones relative

to the mica-standard n-octane interface, we can appreciate a neat similarity (d1 of themica-water interface is 0.32 nm). Measurements of the mica-standard n-octane interfacewere performed for 1-2 hours, scanning over several microns of the sample surface, andeither the presence of hydration layers (d ≈ 0.30 nm) or the absence of any solvationstructure was observed. Solvation layers with larger interlayer distances attributable ton-octane molecules were never recorded.If now we consider the mica-dry n-octane interface, the data show a different result.

A greater interlayer distance with respect to the previous case is recorded. Upon molec-ular sieving the estimated water content (m/m) was decreased more than an order ofmagnitude, from 98 ppm to <6 ppm [325]. In this scenario, removing (or reducing) theamount of water molecules inside the organic solvent allowed the formation of a differentinterface, explained by n-octane molecules parallel to the mica surface [64].It is important to underline that realizing experiments with conventional cantilevers

(such as PPP-NCH-AuD) provided a featureless interface between mica and standard n-

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Figure 5.2.: 3D-AFM of n-octane on mica with standard cantilevers. (a) 3D-AFM xzforce panel and (b) related FDCs of the mica-standard-n-octane interfacemeasured with a standard cantilever (PPP-NCH-AuD, 2nd eigenmode).

octane. This is shown in Fig. 5.2, where no solvation layers are visible. This observationconfirms recent works where molecular sieving was essential to visualize solvation layersof organic liquids on hydrophilic surfaces [64]. To obtain the high resolution needed toresolve features at this interface, smaller and softer cantilevers with higher sensitivitywere used (Arrow-UHF). It was demonstrated that reducing the AFM cantilever dimen-sion improves the minimum detectable force [335]. The use of this type of cantileverswas fundamental to realize the experiments shown in this chapter.To achieve a more general understanding of the system, the solid-liquid interface

formed by alkane molecules and graphite was investigated. HOPG symbolizes hydropho-bic crystalline surfaces. Fig. 5.3 shows representative xz panels of the force reconstructedfrom the 3D-AFM data. Below each panel the corresponding set of FDCs is also shown.Two experiments were performed, 3D-AFM on HOPG in contact with standard anddry n-octane, respectively. As for the previous set of experiments, solvation layers wereclearly visualized at the interface. The interlayer spacing for standard n-octane is d1=0.45 nm and d2= 0.52 nm. For dry n-octane similar values were obtained, d1= 0.45 nmand d2= 0.51 nm. Obviously, the interface is formed by the same molecular arrangementin both the experiments. These values indicate that octane molecules are oriented withtheir long axis parallel to the HOPG surface. The result is consistent with previousworks [56,57,60,64,168].Summarizing, in the case of an unbranched alkane onto a HOPG surface, the inter-

face was dominated by the hydrocarbon solvent, and independent with respect to thewater content. Interlayer distances and the formed interface were equivalent to the oneobtained for the mica-dry n-octane interface.

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Figure 5.3.: Solid-liquid interface of standard and dry n-octane on HOPG. 3D-AFMxz force panel of (a) standard n-octane (>99 %) and (b) dry n-octane onHOPG. Below each panel, the corresponding FDCs are shown. Averagecurves are highlighted. The results show similar features with respect toFig. 5.1c.

Furthermore, similar experiments were repeated on n-hexane. The data are reportedin Appendix Fig. C.1. The results obtained on mica and HOPG were similar to theones obtained for the n-octane. It is interesting to notice that when the organic liquidwas at the interface with mica (dry solvent) or with HOPG, the interlayer distance isindependent of the alkane chain length, once again confirming that organic moleculesdispose in a parallel fashion with respect to the material surface.

To better understand the energy driving the system to its equilibrium, the interfaceformed by muscovite mica and a water solution saturated with n-octane was studied.The estimated amount of n-octane molecules into the water was about 10 ppm (thesolubility of n-octane in water is 0.007 mg L−1). The results are shown in Fig. 5.4.The interlayer distances d1 and d2 are 0.28 nm and 0.31 nm, respectively. These valuescorrespond to the van der Waals diameter of water molecules, pointing out that theinterface was dominated by water (see below for a further discussion).

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Figure 5.4.: Solid-liquid interface of alkane-contaminated water on mica. (a) 3D-AFMxz force panel and (b) related FDCs of the mica-n-octane-saturated waterinterface on mica. The average curve is highlighted.

5.4. DiscussionAs aforementioned, solid-liquid interfaces formed by liquids and solids, with weak in-teractions between each other, are unstable and easily change when other molecules areadded to the solution or when environmental conditions are modified [319–323]. This isparticularly relevant in the context of organic liquids in contact with hydrophilic ma-terials; at their surface, trace amounts of water can diffuse and condensate, leading tothe formation of a nanometer-thick film [324,326]. Recently, Voïtchovsky’s group inves-tigated the influence of water on the lubricating properties of hexadecane, using micaas substrate [320]. In this experimental work, it was noticed how water condensates atthe surface of mica, displacing hexadecane at room temperature, while when the tem-perature was increased nucleation of water nanodroplets at the hydrophilic interface wasrecorded.Research works from Mugele’s group, focused on the influence of ion adsorption on the

wettability of hydrophilic surfaces immersed in organic solvents [322, 326]. The authorsshowed a dependence of the contact angle on the formation of a nanometer film of water,whose thickness is dependent on the type of cation and concentration in the solution. Thewater layer thickness can range from 0.5 to 10 nm. Interestingly, the presence of a film ofwater was recorded even when salt was not added to the system. The formation of thisnanometer-thick water film is determined by molecular interaction forces, summarizedin the effective interface potential. This potential is decomposed in contributions dueto van der Waals interactions, electrostatic interactions and chemical forces, such ashydration forces. While for the first two contributions, it is possible to calculate theirvalue (from DLVO theory), for the latter this is not true because a description of theatomic scale details of the system is in general difficult to provide.Up to now, the resolution of the techniques used in these studies did not allow to assess

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the molecular arrangement in the nanoscale water film. The finding shown here mightfill this gap, demonstrating the presence of organized water molecules at the solid-liquidinterface of such a system. Thus, understanding the atomic-scale details at the interfacemight contribute to a better formulation of current wetting theoretical models [336].The interpretation of the data shown here is analyzed considering the interaction

between liquids and surfaces. In a first approximation, the energy of the interfacialsystem is balanced. Let’s consider the work of adhesion (WAB) between the solid surface,the solvent and the solute. The work of adhesion of mica and water, WM−H2O, is in theorder of 150 mJ m−2, while the one between mica and n-octane, WM−C8, is about 50 mJm−2 [337]. To calculate the adhesion energy of the n-octane-water interface, WC8−H2O,it is assumed that dispersive forces are the main responsible for the interaction betweenthe two media [44]. Thus, we can write

WC8−H2O ≈√W dC8−C8W

dH2O−H2O

≈ 2√γdC8γ

dH2O

(5.2)

being

WAA ≈ 2γA (5.3)

where W dC8−C8 and W d

H2O−H2Oare the dispersive parts of the adhesion energy re-

lated to octane and water molecules, and γdC8 = 21.8 mJ m−2 and γdH2O= 20.0 mJ

m−2 the corresponding surface energy. Eq. 5.2 allows for an estimation of WC8−H2O ≈2√γdC8γ

dH2O

≈ 41.76 mJ m−2. Let’s now calculate the enthalpic gain due to the replace-ment of a layer of n-octane molecules in contact with the mica surface by water moleculesdissolved in octane. It is computed as follows: ∆WAds

H2O= WM−H2O − WC8−H2O −

WM−C8 = (150− 41.76− 50)mJ m−2 = 58.24 mJ m−2, which is a positive contributionmaking the adsorption of water favorable for the investigated conditions. This explainsthe experiments in Fig. 5.1.Let’s now consider the opposite situation, i.e. displacement of water adsorbed at the

mica surface by n-octane molecules dissolved in water; the following energy balance isderived: ∆WAds

C8 = WM−C8−WC8−C8−WM−H2O = (50− 42.6− 150)mJ m−2 = −142.6mJ m−2, which is a clear enthalpic penalty. The process of adsorption of n-octanemolecules from a water solution is unfavorable, which explains the result obtained inFig. 5.4.Summarizing, water molecules dissolved in alkane solvent diffuse to the hydrophilic

surface, forming a SL interface with mica, and obstructing the formation of the interfacebetween alkane molecules and the mica surface.Let’s now analyze what happens at the hydrophobic surface. Here, the interface

found in the experiments was formed by alkane molecules independently of the solvent’swater content (as shown in Fig. 5.3). Water molecules are much less attracted tothe nonpolar surface in comparison to n-octane molecules. We recall the simulationperformed in Chapter 4 for a better understanding (Fig. 4.16). From a solution ofalkanes and water, the adsorption of alkane molecules has always a negative free energyvalue (independently of the length of the alkane molecules). This energy component

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drives the formation of the hydrophobic surface-alkane interface. Moreover, in the caseof HOPG, an additional contribution to the adsorption energy is due to the stackingof CH2 groups on top of the hexagon centers within the HOPG lattice, as proposed byGroszek [311]. The consequence is that hydrocarbon chains can form several solvationlayers, adsorbing onto the graphite surface [56,57,64,168].

Figure 5.5.: Solvation layers at the interface with crystalline solid surfaces. Left column:in ultrapure water, (a) hydration layers are formed on a hydrophilic surface,while (b) trace hydrophobic species interact and promote their adsorptionat the interface on a hydrophobic surface. Middle column: in standardwet organic solvents, (c) hydration layers are formed due to dissolved wa-ter molecules which tend to segregate to the hydrophilic surface. (d) Incontrast, the organic solvent molecules form solvation layers unaffected bythe presence of water at the interface with an hydrophobic surface. Rightcolumn: in dried organic solvents, solvation layers are found either at theinterface with (e) hydrophilic and (f) hydrophobic surfaces. Reducing thewater content allows to the solvent not to be displaced by water moleculesat the interface with the mica surface.

Together with the experiments shown in Chapter 4, the 3D-AFM images displayedhere provide a better understanding of the SLI involving crystalline hydrophobic andhydrophilic materials (see schemes in Fig. 5.5). In particular, the SLI of hydrophobicsurfaces with water was shown to be characterized by the presence of a small amount ofairborne solutes [68–71, 76, 280–282] that was identified as hydrocarbon molecules. Hy-drophilic materials seemed to be unaffected by those contaminants, thus forming waterlayers. In the experiments performed in this chapter, another type of contamination wasconsidered, the one of water in organic solvents. This enables to further complete the

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nanoscale description of solid-liquid interfaces. When a standard organic solvent (∼98ppm of water content) was used, the hydrophilic surface turned out to be dominated byhydration structures. Using the same solvent on hydrophobic surfaces gave a differentresult, with molecular layers constituted by solvent molecules. When the water contentwas reduced upon molecular sieving (<6 ppm), the solid-liquid interface was governedby molecular layers of organic molecules, on either mica and HOPG. This demonstratesthat, even at an impurity level of <0.0098% (98 ppm), such as the case of water inn-alkanes, contaminants might give rise to appreciable additional forces (in the form ofhydration layers) on polar surfaces such as mica.

5.5. ConclusionIn this chapter, interfacial properties of alkane solvents at hydrophilic and hydrophobicsurfaces were studied. Muscovite mica and HOPG were used as hydrophilic and hy-drophobic model surfaces. In particular, it was shown how the presence of trace amountsof water (or supposedly other solutes) could dominate the interface. It becomes clear thatin those cases, the solute diffuses at the surface and locally expels solvent molecules, evenwhen its bulk concentration is several order of magnitude less. Furthermore, the actualnovelty of this work consists in showing how this water is structured at the nanoscale.Using 3D-AFM, the nanoscale features of the solid-liquid interface were resolved. Inparticular, it was demonstrated how the molecular-level interaction between mica andwater led to an ordering of water molecules. Through direct visualization of the wettingfilm, its inner structure was visualized, revealing up to three individual hydration layers.A simple explanation of the observations was then offered, by considering the adsorp-

tion energy of the solute and the solvent. If the interaction between the surface and thesolute is sufficiently higher than the one between the surface and the solvent, an orderedsolute prevails at the interface. In this way, in standard n-octane (and n-hexane), theinterfacial liquid on mica is formed by structured layers of water molecules. This is notthe case for dry n-octane (and n-hexane), where the solvent molecules do not have tocompete with water and adsorb flatly on mica, forming solvation layers. In contrast tothat, both mica-water and graphite-hydrocarbon interfaces are characterized by a highaffinity of the solid for the solvent. The consequence is that these solid-liquid interfacesare insensitive to trace amount of solutes despite of their presence in the bulk liquid.This allows the organization of solvent molecules through solvation layers.The described mechanism completes previous reports (and the results shown in Chap-

ter 4) on hydrophobic surfaces and provides a better understanding of the SLI at hy-drophilic and hydrophobic materials and, in particular, how liquids organize at theirsurfaces.

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6. 3D-AFM mapping of high molarityelectrolyte solutions

6.1. IntroductionWhen a solid is immersed in a fluid phase, a separation of the charges inside the fluidhappens. This is the common case of charged surfaces immersed in electrolyte solutions.Ions tend to segregate to neutralize the charge of the solid immersed in the solution.While doing that, a nm thick (1-100 nm) diffuse layer is formed at the interface, charac-terized by a monotonically decaying ionic profile. Ions are considered having a finite sizeand they tend to accumulate in the first nm from the surface (outer Helmholtz plane).The theoretical model that is usually used to describe this phenomenon is called Sternmodel (Fig. 6.1). The movement of the ions generates a potential decay, which is linearin the inner layer, and has an exponential shape in the diffuse layer [44,338].

Figure 6.1.: Stern model of the electrical double layer at a negatively charged surface.Anions tends to accumulate at the interface with the negative surface. Theouter Helmotz plane is where the diffusive layer begins. The potential φdrops in a linear (in the inner layer) and exponential (in the diffusive layer)way. Cations and anions are represented in red and blue, respectively.

The ability to visualize phenomena happening in the vicinity of the surface is nottrivial. The AFM provides new possible approaches for those studies. For instance,

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high spatial and temporal resolution AFM was applied to visualize the dynamics ofsingle metal ions on solid surfaces and their effect on the mechanical properties of softmaterials [132, 166, 339]. Moreover, as already mentioned in previous chapters, solva-tion structures of solid-liquid interfaces are nowadays accessible through advanced AFMtechniques, such as 3D-AFM [156]. Solvation structures formed by water molecules arecalled hydration layers. Hydration forces, happening at the solid-electrolyte interface,have extensively been characterized since the development of the surface force apparatus(SFA) by Israelachvili and Pashley, in the early 1980s [47,340–342]. Different techniqueshave been applied other than SFA, such as AFM [156] and x-ray reflectivity [279] aswell as Monte Carlo [76], molecular dynamics (MD) [65] and density functional the-ory (DFT) simulations [343]. In particular, at the solid-liquid interface of hydrophilicflat materials, such as muscovite mica, the interface is characterized by hydration lay-ers with an additional repulsive force, which changes depending on the type of liquidand dissolved salts (and their concentration) [59, 65]. Recently, through AM-AFM and3D-AFM spectroscopy, it was demonstrated that the trend of the force can be mathemat-ically described by a combination of two main components, being the first a monotonicexponential decay and the second a decaying oscillatory contribution. Two similar equa-tions were used to describe the behavior of (i) several electrolyte solutions (different ionicspecies) in contact with a mica surface [58, 65] and of (ii) two different liquids (an elec-trolyte solution and an organic solvent) on a mica surface [334]. The first is an empiricalequation which is not deduced from theoretical arguments, while the latter provides atheoretical interpretation of AFM experiments. In particular, it demonstrates that theperiodicity of the oscillation are due to the molecular packing of the liquid (entropiceffect), while its amplitude can be used to characterize the type of interactions betweenthe solid surface (substrate and tip) and the liquid. Moreover, the exponent of themonotonic exponential decay provides information related to the interactions betweenthe liquid molecules, while its amplitude describes the interaction between the liquidand the solid surface.Understanding the imaging mechanism of 3D-AFM is not trivial but needed for a

better interpretation of the data and to explore new possible applications of this noveltechnique. Interestingly, the imaging mechanism in 3D-AFM spectroscopy was recentlystudied by Fukuma’s group [162]. In particular, the influence of the chemistry of thetip on the visualization of solvation layers was analyzed by MD simulations and 3D-AFM experiments. The authors argued that the mechanical stability of the tip and thehydration structure formed at its apex are decisive in the imaging mechanism. Further-more, they pointed out the importance to exploit novel simulation approaches to betterinterpret experimental data.Recently, the interface of high molarity electrolyte solutions was studied by Martin-

Jimenez et al. [59]. It was demonstrated that the interface, at high concentrations,assumes an unexpected behavior. The solvation structures characterizing the interfaceare formed by alternating ions. They were explained considering a combination of bothliquid (water) and solid (crystalline salt) phases.The purpose of this chapter is to start from this last observation and provide a further

characterization of this type of solid-liquid interface. For that purpose, the high resolu-

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tion imaging capability of 3D-AFM is exploited. It is shown how at high molarity, theinterface is not only characterized by layers of alternating ions but that, through a finetuning of the tip chemistry, it is possible to assign cations and anions to positions of theforce distance curve. The imaging mechanism turns out to be based on the tip charge.On the contrary, when the charge of the tip is neutral, the solvation layers are due tothe total density profile of the system. The experimental results are finally comparedto DFT simulations, to gain a comprehensive understanding of the phenomenon understudy.The interpretation of the 3D-AFMmeasurements shown here was done in collaboration

with Manuel R. Uhlig from our group. The DFT simulations were performed by Dr. JoséHernández-Muñoz (Universidad Autónoma de Madrid), Dr. Enrique Chacón (Insitutode Ciencia de Materiales de Madrid-CSIC) and Prof. Pedro Tarazona (UniversidadAutónoma de Madrid).

6.2. Materials and MethodsMuscovite mica discs of grade V-1 were purchased from SPI supplies (USA). The micawas freshly cleaved with adhesive tape and flushed with ultrapure water prior eachexperiment.Ultrapure water (UPW, 18.2 MΩ cm−1) was obtained from the machine (ELGA Max-

ima), with the water reaching a pH value of 5.6 (Hanna Instruments HI 9024). Aqueoussolutions of 1 M NaCl were prepared by dissolving NaCl (≥99 %, Sigma-Aldrich) inUPW. The pH of the water was tuned depending on the experiment. To obtain acidicsolutions, HCl (Sigma-Aldrich) was added to the aqueous solution until a pH of 2.7 wasreached. To obtain basic solutions, NaOH (Sigma-Aldrich) was added to the aqueoussolution until a pH of 10 was reached. Electrolyte solutions were freshly prepared andthe pH was monitored with a pH meter (Hanna Instruments HI 9024) previous each ex-periment. Octadeciltriclorosilane (C18H37SiCl3, OTS), (3-aminopropyl)triethoxysilane(C9H23NO3Si, APTES), toluene (99.9%) and hydrogen peroxide were purchased fromSigma-Aldrich; Sulphuric Acid (1N) was purchased from Panreac Quimica SA (Spain).

6.2.1. 3D-AFM imaging3D-AFM was implemented on a Cypher S (Asylum Research, Oxford Instruments) in asimilar way with respect to what shown in previous chapters. To obtain a high molaritysystem (near saturation) the following protocol was adopted: (i) 3D-AFM measurementswere started from a relatively high concentrated solution of NaCl (1M) and (ii) the nearsaturated solution was obtained by waiting for the evaporation of the water. It wasnot possible to check the actual concentration of the solution. Though, it was noticedthat the change of the interfacial structure was obtained almost prior the completeevaporation of the water solution. Clearly at this point, the concentration of salt wasvery high, eventually approaching the saturation concentration (which is ∼ 6.1 M, sincethe solubility of NaCl is 357 g/L). The open cell of the Cypher S allows for an easy

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evaporation of the liquid. Thus, the evolution of the liquid structure at the interfacewas imaged in real time.Before each experiment, the cantilever holder was cleaned using ethanol and distilled

water. Then, the sample discs, with mica glued at the top, were magnetically mountedonto the microscope sample stage. The samples were cleaved and flushed with UPW,to remove the K+ ions attached to the mica surface after cleaving. Then, 50 µl of theelectrolyte solution were placed on top of the surface. The cantilever, previously insertedin the AFM holder, was immersed into the liquid and the imaging was started.The 3D-AFM imaging was performed in amplitude modulation mode as described

in previous chapters. Microcantilevers were excited at their 2nd flexural eigenmodeby using a photothermal excitation. AFM cantilevers of the type OMCL-AC160TS-R3(Olympus, Japan) were used throughout all the experiments. Carbon tips of the typeUSC-F5-k30 (NanoAndMore, Germany) were also used. Carbon tips were calibrated bytaking a force-distance curve towards the mica sample. OMCL-AC160TS-R3 cantileverswere calibrated with the contactless method reported in Chapter 2. Let’s remind thatfor the determination of the second mode, the stiffness-frequency power law relationshipdeveloped by Labuda et. al was used [20],

k2 = k1(f2/f1)ζ2 (6.1)

where ζ2 is equal to 1.67 for the OMCL-AC160TS-R3 cantilever. The parameters ofthe cantilevers used for each experiment are reported in Tab. D.1. The free amplitudevalues A0 were in the range of 50-70 pm. Set-point amplitudes of Asp ≈ 0.4-0.60 A0were used. While the cantilever oscillated at its resonance frequency, an additional zsinusoidal movement was applied to control the relative distance between the tip andthe sample. The z-piezo sinusoidal motion had the following characteristic: amplitudeof 2.5 nm, period (frequency) of 10 ms (100 Hz). The z-data were read out every 20 µsand stored in 512 pixels (256 pixels half cycle). Each xy-plane of the 3D map contains80 x 64 pixels and the total time to acquire the entire image is 52 s. The force wasreconstructed using Hölscher’s algorithm, as explained in Chapter 4.

6.2.2. AFM Tip functionalizationThe methods described here were combined with a specific electrolyte pH, to obtain tipswith a negative, positive and neutral charge. The three types of tip chemical function-alizations are shown in Fig. 6.2: a SiO−, a -NH+

3 and a -CH3 terminated tip.The first tip was a common AFM cantilever, being made of silicon oxide.The second type of tip was obtained by chemical modification with APTES: (i) the

cantilever was immersed in 4:1 (v/v) piranha solution (0.5 N sulphuric acid and 30% hydrogen peroxide) for 30 min; (ii) the cantilever was rinsed with UPW and driedthrough N2 flow; (iii) the cantilever was immediately transferred into a mixture (5:5:90in volume) of APTES : ultrapure water : ethanol to allow for the silanization of thetip and left functionalizing for 30 min. (iv) the cantilever was rinsed with ethanol andUPW and dried with N2 flow. The hydroxyl group of the tip reacts with the Si of the

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APTES. The APTES molecules condensate forming a stable layer. The tip turns out toexpose at its apex amino functional groups of the APTES molecules.The third type of tip was a SiOx cantilever chemically modified with OTS with the

following protocol: (i) the tip was treated with oxigen plasma (50 W and 0.4 mbar for30 s) and immediately immersed in toluene; (ii) the cantilever was then covered with asolution of OTS and toluene (0.06%, v/v) and then left functionalizing for 1 min; (iii)the cantilever was flushed with toluene to remove the OTS molecules in excess. The-SiCl3 group reacts with the hydroxyl group of the SiOx, rapidly forming a film over theAFM tip. The tip exposes at its apex -CH3 groups, thus making the tip hydrophobic.

Figure 6.2.: Tip functionalization for 3D-AFM. The figure shows the main types of tipsused in this study. From left to right, (a) silicon oxide tip with a negativecharge at pH 5.5, (b) APTES-functionalized tip exposing a positive chargeat pH 2.7, and (c) OTS-functionalized tip which is neutral at pH 2.7.

As mentioned before, the three tips were combined with a specific pH of the elec-trolyte solution to obtain the desired charge. The pKa of SiOx (bare tip) is in the 1-3range. Thus, a pH of 5.5 was chosen, making the cantilever negatively charged (effec-tive surface potential of -40 mV) [344]. For the second cantilever functionalized withAPTES, the working pH was 2.7. The pKa of the amino groups is 9.6, thus working atlow pH boosts the formation of -NH+

3 , making the cantilever positively charged (effec-tive surface potential of 55 mV) [342,344]. When immersed in electrolyte solutions, thefirst (negatively charged) and the second (positively charged) tips attract cations andanions, respectively. For the cantilever silanized with OTS, a pH of 2.7 was chosen. TheOTS functionalization creates a film of hydrophobic molecules covering the tip. It isknown that the neat water/OTS interface is not neutral, but basic. The reason for thisphenomenon is still under discussion. Some works indicated the adsorption of hydroxideions as a possible cause [345], while recently the origin of the negative charge was relatedto the presence at the hydrophobic surface of weak acidic impurities with an amphiphilic

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nature. The result is that at pH 5.5, the hydrophobic surface has a negative charge. Onthe contrary, a pH solution of 2.7 ensures an almost zero effective surface potential, thusproviding a neutral surface [292,346].

6.2.3. DFT simulationDFT simulations were performed in the group of Prof. P. Tarazona and Dr. E. Chacón.The system for the DFT simulation was composed of a planar substrate (i.e. neglectingthe roughness of the surface) and a sphero-cylindrical tip (Fig. 6.3). The movementof the AFM tip in the liquid followed the Newton equation of a forced oscillator. Theliquid was composed of spheres with a diameter σ of 0.3166 nm independently of thespecies (water, cations, anions). To study the dependence of the system on the saltconcentration, the total bulk density was fixed at ρb = 0.6, and the bulk densities ofeach component (water, cations and anions) was extracted as ρb;H2O = 0.6(1 − 2 χrel)and ρb;+ = ρb;− = 0.6 χrel. χrel is the relative concentration and it was set at 0.0583to reproduce the experimental condition considered near saturation. As reference, therelative concentration at which the simulated electrolyte crystallizes is χrel ∼ 0.1. Thepotential of the tip and the substrate over the liquid was modeled in a similar way as aLennard-Jones potential, except that the substrate was considered having a permanentnegative charge, while the charge of the tip was varied through an additional parameterto neutral, positive or negative. A Yukawa interaction was introduced to control theinteraction with the different species (water, anions and cations) [343].

Figure 6.3.: Definition of distances used for DFT simulations and 3D-AFM. x, y, z arethe spatial coordinates. Z is the tip-sample distance and s is the radialdistance from the tip.

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The density profile of the liquid was calculated with respect to the radial distancefrom the tip (s) and the normal to the substrate (z), as

ρt(z, s) = ρH2O(z, s) + ρ+(z, s) + ρ−(z, s) (6.2)

The grand-potential density function Ω was calculated including the packing entropyand screened interactions between ions. Then, the energy of the system E was derivedby minimizing Ω with respect to ρH2O, ρ+ and ρ−. Finally, the force acting on the AFMtip was calculated as the first derivative of the energy with respect to the tip-sampledistance

F (Z) = −∂E∂Z

(6.3)

The simulations were realized for tip-sample distances Z > 2.3σ for the negative tip, Z> 2.9σ for the positive tip, and Z > 1.2σ for the neutral tip. For smaller Z values, energyand force curves were then obtained by fitting the simulated results to the following twoformulas [334]

E (Z) ≈ Um exp (−κmZ)− U0 exp (−κ0 (Z − z0)) cos (q0 (Z − z0)) (6.4)

F (Z) = Umκm exp (−κmZ)−U0 exp (−κ0 (Z − z0)) (κ0 cos (q0 (Z − z0)) + q0 sin (q0 (Z − z0)))(6.5)

with Um, κm, U0, κ0, z0, q0 as fitting parameters describing the tip-sample and theliquid-sample interaction. It was proved that the behavior of the oscillatory force re-lated to hydration structure extracted from AFM data could be described by eq. 6.5.Additional details on the simulations can be found in [343].

6.3. Results6.3.1. 3D-AFM results3D-AFM experiments of 1 M NaCl and NaCl solutions near saturation (∼ 6.1 M) ona mica surface are here reported. Mica exhibits in aqueous solution a negative charge.As mentioned in the previous paragraph (“AFM Tip functionalization”), tips exposinga positive, negative or neutral charge were fabricated. In Fig. 6.4, 3D-AFM panelsrecorded at 1 M NaCl are shown. The three panels were performed with the threedifferent tips. Below each panel the corresponding force distance curve (FDC) is plotted.The panels are similar and the oscillations show interlayer distances of about 0.3 nm.Thus, independently of the tip charge, the same result was obtained below the solutionsaturation point.

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Figure 6.4.: 3D-AFM in electrolyte solution below saturation. 2D force panel with thecorresponding FDCs of 1 M NaCl on mica recorded with the (a) SiOxnegatively-charged tip, (b) APTES positively-charged tip and (c) hydropho-bic (neutral) tip. The average curve is highlighted. The three panels showthe same interfacial structure.

Near saturation, the interface changed and showed interlayer distances greater thanthe system below the saturation, as already shown in the literature [59]. 3D-AFMenabled to record in real time the evolution of the interface. The results obtained nearthe saturation are shown in Fig. 6.5. In particular, positively and negatively charged tipsmeasured interlayer distances of 0.40-0.55 nm. In contrast, interlayer distances recordedwith the neutral tip have smaller values (0.24-0.32 nm), which resemble the case oflower concentrated solutions. These experiments underline that the imaging mechanismsomehow changed when the tip had a different charge. The modification of the tipcreated a different interaction with the electrolyte solution which was reflected in theFDCs recorded with 3D-AFM. A statistical analysis of the interlayer distance is shownin Fig. D.1 of the Appendix. It is clearly shown that for a solution below saturation theaverage value of the interlayer distance does not depend on the tip charge and matchesthe one expected for hydration layers. On the other hand, for electrolyte solutions nearsaturation the interlayer distance does depend on the tip charge.Moreover, as marked by the red lines in Fig. 6.5a,b, the layers probed with the

negative tip are shifted with respect to the ones measured with the positive tip. Tobetter understand the latter observation, we can further compare the FDCs recordedwith positively and negatively charged tips near saturation (Fig. 6.6). As mentionedbefore, the two FDCs have similar and large interlayer distances (> 0.4 nm) but theydiffer because the two curves are shifted of about half a period. The shift is reflectedin the distance between the first peak and the surface (d0). Here, the position of thesurface was assigned to the z value associated with the repulsive force whose slope hasthe highest value.

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Figure 6.5.: 3D-AFM in electrolyte solution near saturation. 2D force panel with corre-sponding force curve of NaCl on mica near the concentration of saturationrecorded with the (a) negatively charged tip, (b) positively charged tip and(c) neutral tip. The average curve is highlighted. The three panels show adifferent interfacial structure with large periodicity for the charged tips andsmall for the neutral tip. The red dotted lines coincide with the maximain the force panel taken with the negative tip and with the minima in thepanel recorded with the positive tip.

The first peak of the FDC recorded through the negative tip is closer to the surface(0.24 nm) with respect to the one obtained with the positive tip (0.37 nm). To show thatthe shift of the FDCs is accurate, the data obtained with several positive and negativetips were compared. Fig. 6.6b shows the statistical analysis of d0 for the measurementsperformed with the two types of tips. The average values obtained for positive andnegative tip are 0.34 ± 0.11 nm and 0.20 ± 0.03 nm, respectively. This observationconfirms that the shift of the FDCs is not fortuitous.As mentioned before, the neutral tip measured always interlayer distances of about

0.3 nm, even near saturation conditions. To confirm the observation, the experimentswere repeated using other types of neutral tips. In particular, carbon tips (which areintrinsically hydrophobic) at pH 2.7 and amino-terminated (APTES) tips at basic pH(10) were used. This guarantees to have in both cases a neutrally-charged tip. Forhydrophobic carbon tips, the neutral charge was obtained keeping the pH at 2.7 as inthe case of OTS tips; for APTES functionalized tips, the use of a basic pH, above thepKa, allowed to deprotonate the amino group, making it neutral. The results are shownin Fig. 6.7. Interlayer distances are equal to 0.34 nm for the carbon tip and 0.27 (d1)and 0.33 (d2) for the amino-terminated tip at basic pH. These experiments corroboratethe data obtained with the OTS-functionalized tip.

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Figure 6.6.: Interfacial structures recorded with positive and negative tips near the sat-uration point. (a) Force curves (averages) corresponding to the experimentsin Fig. 6.5 realized with positive and negative tips. The two curves areout of phase. (b) Statistical analysis (n ≥ 10) of the distance between thesurface and the first peak in the force (d0). The average value of each set ofexperiments is shown with a circle. The median is shown as a white (positivetip) or black line (negative tip). The force curves recorded with the positivetip have a larger d0 (0.34 ± 0.11 nm) with respect to the ones obtained withthe negatively-charged tip (0.19 ± 0.03 nm).

Figure 6.7.: 3D-AFM in electrolyte solution near saturation performed with neutral tips.3D-AFM xy force panels (and FDCs) of the interface between NaCl solutionnear saturation and mica recorded with two neutral tips, (a) a carbon tip,and (b) an APTES functionalized tip at basic pH. The average curve ishighlighted. The two panels show the same interfacial structure, formed byhydration layers.

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6.3.2. Comparison with DFT simulationsDFT simulations were performed to understand the basic mechanism behind the ex-perimental data. The simulations reflected the experimental conditions, consisting ofa charged (+/-) or neutral tip inside a liquid. It was noticed that a concentration ofhalf the one needed for the crystallization of the system was sufficient to reproduce theexperimental data near saturation. It is remarked that in the experiments, it was notpossible to record the actual salt concentration, and it was assumed to be near saturationdue to the almost complete evaporation of the solution droplet.First of all, the density at the tip apex was simulated in the case of a negatively

charged and a neutral tip (Fig. 6.8). The x axis is here expressed in terms of σ (hardsphere diameter). The x axis includes the presence of the tip with a radius equals to1σ. The simulation shows the density of the species inside the liquid (water, cationsand anions) perpendicular to the tip. For a negatively charged tip near the saturatedsalt concentration, DFT simulations show that the density profile for cations and anionshas relevant oscillations as a function of the distance from the tip surface (Fig. 6.8a).In particular, a first strong peak related to the adsorption of cations is followed by asecond high density peak of anions. Contrariwise for the neutral tip, the water densityis dominant with respect to the density profiles of cations and anions.

Figure 6.8.: DFT density profile near the tip. Equilibrium density profile obtained for thecharged (a) and uncharged (b) tip near the saturation concentration. Thecurves show the density (number of particles per unit volume, normalizedto the dimension of σ) for water, anions and cations. The charged tip has anegative charge. The tip is simulated here with a radius of about 1σ.

Moreover, the energy and the force where calculated from the simulations. Fig. 6.9shows the energy and the force profiles, and the particle and charge density maps ob-tained for the negative, positive and neutral tip. The idea exploited here is to imaginethe 3D-AFM imaging mechanism as an interference (overlap) between the density profilearound the tip and the one of the substrate. The particle density reflects the entropiceffect of the molecular packing (in the simulation as spheres with the same diameter σ)which is basically the distribution of the total density of the system (considering both

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ions and water). Instead, the charge density maps consist in the difference in the distri-bution of anions and cations around the tip and the substrate (c (z) = ρ+ (z)− ρ− (z)).Here, the substrate is simulated as negatively charged (mica exposes negative chargesin water solution). The distribution of layers of cations or anions around the AFM tipis different depending on the tip charge (bright and dark colors in the charge densitymaps). When the tip has a negative/positive charge, it accumulates cations/anions inits immediate vicinity. From here, layers of counter ions subsequently distribute aroundthe previous one. Then, maxima and minima of the energy and the force can be relatedto the overlap between layers around the tip and the sample. The formation of layers ofions with alternate charge is due to the effect of the molecular packing in combinationwith the charge of the ions. This is the configuration corresponding to the optimum ofthe system in the calculation. When the tip approaches the sample, the overlap betweenions with the same charge is the configuration that resemble the most the optimum of thesystem: at this position, the energy has its minimum value (constructive interaction).On the contrary, the overlap between layers of different sign generates a maximum in theenergy, being the configuration that departs the most from the optimum (destructiveinteraction). Squares and circles in Fig. 6.9 mark z positions in the density maps relatedto minima and maxima of the energy curves, respectively.For example, let’s consider what happens with the negatively charged tip: at Z =

3.1σ, the anion/cation layers of the tip and the sample overlap on one another in thecharge density map (Fig. 6.9c first row, right panel); this situation corresponds to theenergy near one of its minimum (Fig. 6.9a, square symbol in the red curve) and toa zero value in the force with a negative slope (Fig. 6.9b, square symbol in the redcurve). The force has a negative slope due to the next incoming overlap: in fact, withthe tip further approaching the sample, anion/cation layers of the tip meet cation/anionlayers of the sample (Z = 2.3σ) (Fig. 6.9c first row, left panel). This corresponds to adestructive interaction (the yellow/black color around the tip overlap to the black/yellowcolor around the sample) and to a maximum in the energy (Fig. 6.9a, circle symbol inthe red curve) and a zero force with positive slope (Fig. 6.9b, circle symbol in the redcurve). The same type of reasoning can be applied for the positive tip. The final result isthat maxima and a minima in the energy profile for positive tips are located at positionswhere minima and maxima are for negative tips. Since, the force is the negative firstderivative of the energy, the same type of behavior is expected for the force profiles.If now, we consider the neutral tip, the scenario changes. Energy and force profiles are

determined by the overlap between the particle density around the tip and the sample.Minima in the energy are determined by constructive interactions (overlap of high/low-density layers of the tip and high/low-density layers of the substrate, as in Fig. 6.9c,third row, right panel), while maxima are determined by destructive interactions (overlapof high/low-density layers of the tip and low/high-density layers of the substrate, as inFig. 6.9c, third row, left panel).For the charged tip, the interaction created by the charge density decays with os-

cillations of the charged species, which have about twice the period of the oscillationsproduced by the overlap due to the total density of the system. For the neutral tip, theperiod of the oscillation is the one of the particle density (interlayer distance = σ).

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Figure 6.9.: Reconstruction of the force profile for charged and neutral tips. (a) Energyand (b) force profiles of the maps shown in (c). The value of the energy andthe force for the neutral tip were multiplied by 10 in order to graphicallycompare the profiles of the three tips. The x axis is expressed in terms of σ.(c) Particle density ρ (z) (particles per unit volume) and charge density c (z)(total charges per unit volume = positive charges per unit volume (ρ+ (z))- negative charges per unit volume (ρ− (z))) maps obtained for negative,positive and neutral tips show alternating layers relative to the tip and thesubstrate. Two Z positions (tip-sample distances) for each tip are shown.In the charge density map, bright and dark colors correspond to layers ofcations and anions, respectively. Circles and squares correspond to near-maximum and near-minimum positions in the energy profile.

6.4. DiscussionIn the experiments shown in this chapter, 3D-AFM was performed at high molar elec-trolyte solutions. By functionalization of the tip combined with a fine tuning of the pH,negative, positive and neutral tips were obtained.The aforementioned tips were used to perform 3D-AFM experiments in high molarity

solutions of NaCl in contact with mica. The interfaces created with electrolyte solutionsat two concentrations were mapped: below saturation (1 M NaCl) and near saturation (∼6.1 M NaCl). Below the saturation limit, the tip-sample interaction was independent ofthe type of tip and showed hydration layers. Near the saturation concentration, positiveand negative tips visualized large layers (interlayer distance of 0.40-0.55 nm) while theneutral tip probed hydration structures. The force curves recorded with positive andnegative tips turned out to be out of phase. This was confirmed by checking the distance

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between the first maximum in the force profile and the surface, which is greater for thedata recorded with the positive tip.From DFT simulations, it was demonstrated that when the electrolyte solution was

near saturation, the results depended on the interaction of the ions with the tip. In thecase of charged tips, DFT simulations showed forces following the charge density. Here,the tips and the sample form layers of alternating charges around themselves. Duringthe approach, the cantilever layers overlap with the layers of the surface. When thelayers have the same sign, the energy of interaction is minimized; if they have oppositecharge, the energy is maximized. This is reflected in the oscillation of the energy andforce profile reconstructed from the simulations and probed by 3D-AFM. Instead, whenneutral tips were used, the FDC shows a profile with smaller interlayer periodicity withrespect to the charged-tip scenario. When the tip did not have any affinity for the ionicspecies in the solution, the charge density was not dominant for the imaging mechanism.Thus, the force was of entropic origin, following the total density profile, dominated bywater molecules.To add further details to the discussion, let’s try to correlate simulated and experi-

mental force profiles. Fig. 6.10 shows the comparison of the force curves obtained from3D-AFM experiments and DFT simulations. Dotted lines help for the visualization ofthe position of maxima in the force. It was noticed that experimental and simulatedFDCs differ for an x offset (= 0.1175 nm), which was applied to the simulated curves.The origin of the offset is not known; it could be argued that (i) the radius of the exper-imental and simulated tips might be different, inducing a shift of the curves; however,this does not explain why the offset is unique for the three types of tips (the AFM tipsused in 3D-AFM experiments can be considered quite dissimilar due to the differenttypes of functionalization). (ii) The results from DFT simulations performed here wereobtained only for large tip-sample distances. On the contrary, experiments provided agood quality of data for small tip-sample distances. This means that the comparison isprobably realized with experimental layers which are not the exact same layers in thesimulations. Eventually, since the purpose of the comparison is to understand the originof maxima and minima in the experimental force profile, it is reasonable to fix a generaloffset which does not modify differences between the curves themselves.If we compare the two sets of curves, maxima of the DFT force profiles match quite well

the experimental ones. Small differences in the position of maxima are possibly due tothe fact that in the simulations, ions and water molecules were assumed having the samedimension σ = 0.3166 nm. In the experiments, the actual dimension of the ionic diameterof Na+ and Cl− is 0.204 nm and 0.362 nm [347]. Moreover, absolute values of maxima inthe experimental force differ to the simulated ones (of about two orders of magnitude).This can be due to three main reasons: (i) as already mentioned the tip in the simulations(Rt = 0.3166 nm) might have a different dimension with respect to the experiments. Itis reasonable to think that the experimental radius corresponds to several nm, thusincreasing the absolute value of the force. (ii) It is possible to notice that for small tip-sample distances, the experimental force profile increases approaching the sample. Thisbackground can be ascribed to short-range, repulsive forces as already illustrated byPashley and Israelachvili [340,341]. (iii) Finally, the force reconstruction algorithm used

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Figure 6.10.: Comparison between DFT and 3D-AFM force profiles near the satura-tion concentration. Force profiles corresponding to the measurements per-formed with positively and negatively-charged tip reconstructed from (a)DFT simulations and (b) 3D-AFM experiments. (c) Force profiles cor-responding to the measurements performed with the neutral tip recon-structed from (d) DFT simulations and (d) 3D-AFM experiments. An xoffset (= 0.1175 nm) was applied to simulated curves to allow for a bettercomparison. Dotted lines correspond to the maxima in FDCs.

to compute the experimental curve might carry some degree of uncertainty. Nevertheless,it is important to remark that the interest here is to compare interlayer distances andnot the value of the force itself.

As previously mentioned, the mechanical stability of the tip was demonstrated playinga role in the determination of the shape of FDCs on a hydrophilic substrate [162]. APTESand OTS films at the tip apex might have issues related to their flexibility or mechanicalstability. Even if it is not possible to rule out this option, it is considered negligible inthe experiments due to the following reasons: (i) the behavior of the tip functionalizedwith OTS (i.e. which shows hydration layers near saturation) was reproduced through aconventional carbon tip (without any functionalization) and through an APTES tip atbasic pH (which have different mechanical properties than OTS); (ii) at concentrationsbelow the saturation point, hydration layers characterized by the same periodicity werevisualized independently of the tip charge. To quantify the mechanical stability of thetips used in the experiments, the d0 distance was computed (as for Fig. 6.6) for all theexperiments performed below saturation. If the mechanical properties of the tip playa role in the position of maxima and minima of the force profile, we should be able tosee differences in the FDCs. Fig. D.2 of the Appendix shows that d0 assumes similar

127

values for the three types of tip (0.17 ± 0.04 nm, 0.16 ± 0.03 nm and 0.18 ± 0.02 nmfor positive, negative and neutral tips, respectively). Moreover, this value is comparablewith the one extracted for the neutral tip near saturation (0.15 ± 0.03 nm). Thus, it wasconcluded that the shift seen in the data for negative and positive tips near saturationwas determined by the charge and not from effect related to the mechanical stability ofthe tip. If there was any effect related to the latter, it would be collateral to the tipcharge.

6.5. ConclusionIn this chapter, it was shown how the imaging mechanism involved in 3D-AFM (andwe could argue in any other force spectroscopy measurement) is controlled by (i) theconcentration of the solute in the solution and by (ii) the charge of the probe. To demon-strate that, the AFM tip was chemically functionalized and the pH of the electrolytesolution was adjusted to obtain positive, negative and neutral charges. This is the firsttime that functionalized tips are applied to perform 3D-AFM. Near saturation, the in-terface was characterized by layers whose position and interlayer distance depended onthe tip charge. The interfacial structures obtained near saturation were reproduced overseveral experiments. To understand the phenomenon, DFT simulations were performedand compared with the 3D-AFM data. The result is unexpected but simply explained:when the probe/substrate is charged, ions form layers of alternating charges around thesurface. The imaging mechanism depends on constructive and destructive interactionsbetween the ionic layers of the tip and the substrate. When the tip is neutral, theforce profile recorded by 3D-AFM is dominated by the total density of the system, andreflects the van der Waals diameter of water. Here, it was demonstrate that 3D-AFMspectroscopy could be tuned to visualize the different components of a solution (solutesand solvent). Nevertheless, 3D-AFM and force spectroscopy users could use these find-ings to interpret their data and study novel (and highly concentrated) charged liquids,such as ionic liquid.

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General Conclusions

• A new theoretical approach (based on the 3D Kelvin-Voigt model) to unravel vis-coelastic properties through bimodal AM-FM AFM was proposed and verified byexperiments on test samples. In particular, the bimodal AFM viscoelastic re-construction was applied to PS, LDPE and PS-b-PMMA thin films. The Young’smodulus, the loss tangent, the retardation time and the viscous coefficient were ex-tracted. Soft materials, such as polymers, are likely to be deformed when analyzedwith AFM techniques. The method provides the true topography of the sampleby taking into account the deformation reconstructed through bimodal AFM. Amethod to verify the reliability of the viscoelastic reconstruction was proposed.The procedure consists in the comparison of the experimental energy dissipationwith the one derived from numerical simulations.

• The bimodal AFM approach was applied for the study of a ferrolectric polymer(P(VDF-TrFE)). Temperature-dependent mechanical properties were studied andreconstructed. P(VDF-TrFE) has the Curie transition at Tc = 101°C. Experimentsbelow and above Tc were performed. It was noticed an evolution of the morpholog-ical micro and nano-structures and mechanical properties: (i) the Young’s modulusoverall decreased from 1.7 ± 0.5 GPa at 27 °C to an average value of 0.5 ± 0.2GPa at 122 °C; (ii) the lamellar structures formed by the polymer chains were stillfound and visible even above the Tc; (iii) the inter-grain matrix expanded uponincreasing the temperature (from 2.5% ± 0.9% at 27 °C to 37.7% ± 3.8% at 122°C of the imaged area), becoming the main contributor of the bulk elastic modulusof the sample.

• Bimodal AFM was used to study morphological and mechanical properties of PE-DOT:PSS thin films in air and liquid environment. The Young’s modulus decreasedfrom 2.9 ± 1.8 GPa to 0.5 ± 0.2 GPa, and the grain size increased from 29.5 ±11.5 nm to 86.9 ± 5.0 nm, upon addition of the aqueous solution. Moreover, a40% swelling of the film was recorded. Through bimodal AFM, it was possible todistinguish among different phases of the polymer: PSS-rich matrix, PEDOT:PSSgrains and PEDOT-exposed regions. AM-AFM was applied to highly resolve themolecular organization of the polymer: chains with a spacing of 1.25 nm and 0.79nm were assigned to lamellae of PEDOT and PSS molecules, respectively. Finally,the polymer film was characterized while a constant (de-doping) potential wasapplied between the PEDOT:PSS electrode and a Pt electrode immersed in thesolution. The measurements unraveled that ion intercalation causes an hydration

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of the film along with a modulation of the mechanical properties of the polymer.

• The solid-liquid interface of layered hydrophobic crystalline materials, HOPG andh-BN, was studied by means of 3D-AFM and AM-AFM. The surfaces showed abehavior dependent on the air-exposure time. The freshly-cleaved material wascharacterized by a flat surface where the crystal lattice was easily resolved; how-ever, the presence of organized (4-5 nm periodicity) and disordered structures wasrecorded on the air-exposed surface (> 1 h). Disordered features were dissolvedupon addition of UPW, while organized ones (ripples) were stable in air and inwater. Internal features of the ripples were highly resolved, showing a periodicityof 0.5 nm. For a freshly-cleaved surface, 3D-AFM visualized a dynamic solid-liquidinterface, with the presence of structures ascribable to hydration layers (0.35 nm).Air-aged surfaces showed a much more stable interface, with layers having a pe-riodicity of about 0.5 nm. Additional experiments in alkanes, alkane-saturatedsolution, and degassed UPW were performed. It was noticed that the interfacecreated by alkane molecules with HOPG resembled the air-aged HOPG interface.MD simulations corroborated the finding, proving that a new interface is likely toform at the surface of 2D materials, due to the accumulation of airborne hydro-carbons.

• 3D-AFM was used to resolve the interfacial structure of n-alkanes on mica. Wa-ter and alkanes are highly immiscible: alkanes contain a few amount of watermolecules (98 ppm) in normal conditions. Molecular sieving allows to decrease thequantity of water to <6 ppm. It was shown that the interface of the standardorganic liquid with mica was characterized by hydration layers (interlayer distanceof 0.30 nm). On the contrary, when the organic liquid was dried, the interface wasformed by n-alkane molecules lying parallel to the mica surface (interlayer dis-tance of 0.45 nm). If the interface was created with an hydrophobic flat material,such as HOPG, organic molecules formed solvation layers, independently of thewater content. The energies involved in the process of formation of the interfaceswere derived. While condensation of water is expected happening at hydrophilicsurfaces, it is the first time that the organization of water molecules is reportedforming in such a thin nanometric capillary.

• The solid-liquid interface of high molar electrolyte solutions (NaCl) on a mica sur-face was visualized by means of 3D-AFM. For that purpose, SiOx tips were func-tionalized with APTES and OTS, to obtain AFM probes with a negative (baretip), positive and neutral charge. It was demonstrated that, for concentration be-low the solution saturation point, the interface was independent of the charge ofthe AFM tip, and formed by hydration layers. When the saturation concentra-tion was approached, the interface changed dependently on the charge of the tip:negatively and positively-charged tips visualized out-of-phase large solvation layers

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(0.4-0.5 nm), while the neutral probe displayed hydration structures. DFT simu-lations were performed to explain the observations: when the tip is charged, theimaging mechanism (and the position of maxima and minima in the force profile)depends on the charge density of the tip and the substrate; this is not the casefor the neutral tip, where the total density of the system defines the molecularoscillations in the interfacial force.

131

Conclusiones Generales

• Se propuso un nuevo enfoque teórico (basado en el modelo 3D Kelvin-Voigt) paradeterminar las propiedades viscoelásticas mediante AFM bimodal. En particu-lar, la reconstrucción viscoelástica bimodal por AFM se aplicó a muestras de PS,LDPE y PS-b-PMMA. Se extrajeron el módulo de Young, la tangente de pérdida,el tiempo de retardo y el coeficiente de viscosidad. Los materiales blandos, comolos polímeros, son susceptibles de deformarse. Se demostró que es posible recon-struir la topografía de la muestra teniendo en cuenta la deformación obtenida pormedio de AFM bimodal. Se propuso un método para verificar la fiabilidad dela reconstrucción viscoelástica. El procedimiento consiste en la comparación de ladisipación de energía experimental con la energía derivada a través de simulacionesnuméricas.

• El AFM bimodal se aplicó al estudio del polímero ferroeléctrico P(VDF-TrFE). Seestudió y reconstruyo la dependencia de las propiedades mecánicas con respectoa la temperatura. P(VDF-TrFE) tiene la transición de Curie a Tc = 101°C. Serealizaron experimentos por debajo y por encima de Tc. Se observó una evoluciónde la morfología de las micro y nanoestructuras y de las propiedades mecánicas:(i) el módulo de Young pasó de 1,7 ± 0.5 GPa (27 °C) a un valor medio de 0,5± 0.2 GPa (122 °C); (ii) las lamellae formadas por las cadenas de polímeros eranvisibles también por encima de la Tc; (ii) la matriz intergranular se expandía alaumentar de la temperatura, de 2,5% ± 0,9% (27 °C) a 37,7% ± 3,8% (122 °C)del área mapeada, convirtiéndose en el principal contribuyente del módulo elásticode la muestra.

• Se utilizó el AFM bimodal para estudiar las propiedades morfológicas y mecánicasdel polímero PEDOT:PSS en aire y en líquido. Al añadir la solución acuosa, el mó-dulo de Young disminuyó de 2,9 ± 1,8 GPa a 0,5 ± 0,2 GPa, y el tamaño de granoaumentó de 29,5 ± 11,5 nm a 86,9 ± 5,0 nm. Además, se registró un hinchamientodel 40% del polímero. Mediante AFM bimodal, fue posible distinguir entre lasdiferentes partes del polímero: matriz rica en PSS, granos de PEDOT:PSS y re-giones expuestas de PEDOT. El AFM AM se aplicó para resolver la organizaciónmolecular del polímero: se asignaron cadenas con un espaciado de 1,25 nm y 0,79nm a moléculas de PEDOT y PSS, respectivamente. Por último, se caracterizó elpolímero mientras se aplicaba un potencial constante (de dopaje) entre el electrodode PEDOT:PSS y un electrodo de Pt sumergido en la solución. Las medidas desve-laron que la intercalación de iones provoca una hidratación de la película junto con

132

una modulación de las propiedades mecánicas del polímero.

• La interfase sólido-líquido de materiales cristalinos hidrofóbicos, HOPG y h-BN,se estudió mediante 3D-AFM y AFM AM. Las superficies mostraron un compor-tamiento dependiente del tiempo de exposición al aire. El material recién exfo-liado se caracterizaba por una superficie plana en la cual se podría visualizar lared cristalina. En la superficie expuesta al aire (> 1 h) se registró la presenciade estructuras organizadas (con una periodicidad de 4-5 nm) y desordenadas; losrasgos desordenados se disolvían al añadir agua, mientras que los organizados eranestables en aire y en agua. Las estructuras organizadas se visualizaron con altaresolución, obteniendo características internas que mostraban un periodo de 0,5nm. Mediante 3D-AFM se visualizó una interfase dinámica sólido-líquido en elcaso de la superficie recién exfoliada, mostrando estructuras atribuibles a capasde hidratación (0,35 nm). Despues de una hora al aire, los datos mostraron unainterfase mucho más estable con capas que tenían una periodicidad de unos 0,5nm. Para entender el origen de esta observación, se realizaron experimentos enalcanos, solución saturada de alcanos y UPW desgasificado. Se observó que lainterfase creada por las moléculas de alcanos con el HOPG se asimilaba a la inter-fase del HOPG expuesto al aire. Las simulaciones MD corroboraron el hallazgo,demostrando que es probable que se forme una nueva interfase en la superficie delos materiales 2D, debida a la acumulación de hidrocarburos.

• Se utilizó 3D-AFM para resolver la estructura interfacial de los alcanos sobre mica.El agua y los alcanos son altamente inmiscibles: en condiciones normales, los al-canos contienen una pequeña cantidad de moléculas de agua (98 ppm). El tamizadomolecular permite disminuir la cantidad de agua a <6 ppm. Se demostró que lainterfase del líquido orgánico estándar con la mica se caracterizaba por capas dehidratación (distancia entre capas de 0,30 nm). Por el contrario, cuando el líquidoorgánico se secaba, la interfase estaba formada por moléculas de alcano paralelas ala superficie de la mica (distancia entre capas de 0,45 nm). Si la interfase se creabacon un material plano hidrofóbico, como el HOPG, las moléculas orgánicas forma-ban capas de solvatación, independientemente del contenido de agua. Se derivaronlas energías implicadas en el proceso de formación de las interfaces. Aunque seespera que la condensación del agua ocurra en superficies hidrofílicas, esta es laprimera vez que se demuestra la organización de las moléculas de agua formandoun capilar de tamaño nanométrico.

• Mediante 3D-AFM se visualizó la interfase sólido-líquido de soluciones electrolíti-cas de alta molaridad (NaCl) sobre una superficie de mica. Se funcionalizaronpuntas de SiOx con APTES y OTS, para obtener puntas de AFM con carga neg-ativa (punta desnuda), positiva y neutra respectivamente. Se demostró que, parauna concentración inferior al punto de saturación de la solución, la interfase era

133

independiente de la carga de la punta de AFM y estaba formada por capas dehidratación. Al acercarse al punto de saturación, la interfase cambiaba en funciónde la carga de la punta: las puntas con carga negativa y positiva visualizabangrandes capas de solvatación fuera de fase (0,4-0,5 nm), mientras que la sondaneutra mostraba estructuras de hidratación. Se realizaron simulaciones DFT paraexplicar las observaciones: cuando la punta está cargada, el mecanismo de forma-ción de imágenes (y la posición de los máximos y mínimos en el perfil de fuerza)depende de la densidad de carga de la punta y del sustrato; esto no es el casode la punta neutra, donde la densidad total del sistema define las oscilacionesmoleculares de la fuerza.

134

List of Publications

135

• S. Benaglia*, V. G. Gisbert*, A. P. Perrino, C. A. Amo, and R. Garcia, “Fast andhigh-resolution mapping of elastic properties of biomolecules and polymers withbimodal AFM”, Nature Protocols 13(12), pp. 2890–2907 (2018).

• S. Benaglia, C. A. Amo, and R. Garcia, “Fast, quantitative and high resolutionmapping of viscoelastic properties with bimodal AFM”, Nanoscale 11(32), pp.15289–15297 (2019).

• J. Hernández-Muñoz, M. R. Uhlig, S. Benaglia, E. Chacón, P. Tarazona, andR. Garcia, “Subnanometer Interfacial Forces in Three-Dimensional Atomic ForceMicroscopy: Water and Octane near a Mica Surface”, The Journal of PhysicalChemistry C 124(48), pp. 26296–26303 (2020).

• J. Hafner, S. Benaglia, F. Richheimer, M. Teuschel, F. J. Maier, A. Werner, S.Wood, D. Platz, M. Schneider, K. Hradil, F. A. Castro, R. Garcia, and U. Schmid,“Multi-scale characterisation of a ferroelectric polymer reveals the emergence of amorphological phase transition driven by temperature”, Nature Communications12(1), pp. 152 (2021).

• V. G. Gisbert, S. Benaglia, M. R. Uhlig, R. Proksch, and R. Garcia, “High-SpeedNanomechanical Mapping of the Early Stages of Collagen Growth by BimodalForce Microscopy”, ACS Nano 15(1), pp. 1850–1857 (2021).

• M. R. Uhlig*, S. Benaglia*, R. Thakkar, J. Comer, and R. Garcia, “Atomicallyresolved interfacial water structures on crystalline hydrophilic and hydrophobicsurfaces”, Nanoscale 13(10), pp. 5275–5283 (2021).

136

Appendix

137

A. Supporting Information Chapter 3

Figure A.1.: Swelling of PEDOT:PSS. (a) From top to bottom, topography images ofgold electrode, of the PEDOT:PSS film in air electrodeposited over the goldelectrode and of the same PEDOT:PSS film in liquid solution. (b) Crosssections taken over the dotted lines in (a).

138

Figure A.2.: Scheme of the electrical set-up used in Chapter 5. (a) Electrical configura-tion for in operando bimodal AFM measurements. A positive voltage ap-plied at the Pt electrode induces the insertion of cations in the PEDOT:PSSfilm and de-dopes the OSC. (b) Scheme of an OECT device. A bias voltagebetween the gate (G) and the source (S) electrode modulates the currentrecorded between the drain (D) and the source.

Figure A.3.: High resolution AFM on PEDOT:PSS. Phase maps show molecular chainson the PEDOT:PSS surface with a period of 1.35 nm (along the white line).

139

Figure A.4.: Bimodal AFM on PEDOT:PSS in air and aqueous solution. First modephase and second mode frequency maps of PEDOT:PSS in air (a,b) and inliquid solution (c,d). The images correspond to the maps of Fig. 3.4.

140

Figure A.5.: Dependence of PEDOT:PSS Young’s modulus on the applied voltage(Evariation = E/Ein, where Ein is the modulus recorded at the beginningof the experiment). (a) Upon application of a voltage bias, 0 mV and 800mV (vs VOC), the Young’s modulus was recorded by means of bimodalAFM. The positive voltage at the top electrode drove cations inside thefilm. When the voltage was removed (0 mV) ions were free to return in so-lution. (b) Modulus variation due to the applied bias performed on a devicepreviously cycled. The initial drop of Young’s modulus was not recordedfor this device. (c) Passive modulus variation with time (i.e. V = VOC).The time was chosen according to the time of the experiments performed in(a), (b) and 3.7. During the 80 min of measurements, it was not recordedany significant modulus variation.

141

Figure A.6.: Bimodal AFM compositional mapping of PEDOT:PSS: PSS regions. (a)Topography, (b) 1st mode phase shift, and (c) 2nd mode frequency shiftmaps with corresponding cross sections taken along the white dotted lines.Region 1 and 2 are “valleys” with the same height but showing a differentphase and frequency shift. This confirms that the higher phase shift valueof the PSS regions is not induced by a morphology artifact.

142

Figure A.7.: Bimodal AFM compositional mapping of PEDOT:PSS: PEDOT regions.(a) Topography and (b) 2nd mode frequency shift maps with correspondingcross sections taken along the white dotted lines. Region 1 and 2 are grainswith the same height but showing a different frequency shift value (andconsequently a different Young’s modulus). This confirms the variabilityamong PEDOT regions.

143

B. Supporting Information Chapter 4

Figure Type medium nmode

kn(N m−1) Qn fn(kHz) σ−1n (nmV−1)

4.4a PPP-NCST-AuD water 1 6.91 5.5 69 37.644.4b PPP-NCH-AuD water 2 2150 20 1025 84.5a FastScan-A water 1 15 6 424 104.5b ArrowUHF-AuD water 1 9.9 5.6 523 17.57B.1 PPP-NCH-AuD water 1 37.7 9.4 142 45.24.6 PPP-NCH-AuD water 1 37.7 9.4 142 45.24.7a PPP-FM-AuD water 2 183.7 6 192.1 6.64.7b PPP-NCH-AuD water 2 1908 17.1 910 7.34.8 ArrowUHF-AuD water 1 9.9 5.6 523 17.57

4.9a -4.10a

ArrowUHF-AuD water 1 9.63 4.7 525 8.81

4.9b,c -4.10b,c- 4.11


4.12a FastScan-A water 1 15 6 424 104.12b,c ArrowUHF-AuD water 1 8.13 4.8 492 15.84.14a ArrowUHF-AuD n-

hexane1 7.45 4.8 463 8.18

4.14b ArrowUHF-AuD n-hexane-saturatedwater

1 10.46 4.7 552 10.55

B.2 ArrowUHF-AuD n-pentadecane

1 7.03 3.0 547 12.62

B.4,B.5


B.6a ArrowUHF-AuD water 1 12.93 5.8 596 21.04B.6b ArrowUHF-AuD water 1 5.47 4.6 416 17.87

Table B.1.: Cantilever calibration in liquid solution. The table summarizes the parame-ters of the cantilevers used in Chapter 4.

144

Figure B.1.: Contaminants on a graphitic surface. (a) Air-aged surface measured inair. Two types of adsorbates were imaged, disordered structures, and ripplestructures. (b) Topography of the same area after addition of UPW. Thegreatest part of disordered structures disappeared upon addition of water.The ripples were stable and visible in UPW.

Mean (nm) Median(nm)

StandardDeviation

(nm)

MeanAbsoluteDeviation

(nm)

Mica

Freshd1 0.307 0.313 0.032 0.023d2 0.342 0.342 0.046 0.036d3 0.313 0.309 0.018 0.014

Agedd1 0.306 0.317 0.038 0.032d2 0.328 0.328 0.025 0.018d3 0.335 0.335 0.024 0.017

HOPG

Freshd1 0.379 0.350 0.123 0.084d2 0.487 0.470 0.145 0.111d3 0.470 0.450 0.099 0.057

Agedd1 0.449 0.456 0.061 0.046d2 0.537 0.550 0.050 0.034d3 0.510 0.510 0.042 0.030

Table B.2.: Statistical parameters extracted from 3D-AFM data recording the temporalevolution of solvation structures of hydrophobic and hydrophilic materials.The values refer to the box-plot of Fig. 4.13.

145

Figure B.2.: Solid-liquid interface of n-pentadecane on HOPG. (a) 3D-AFM xz forcemap of the n-pentadecane-HOPG interface. (b) FDCs corresponding topanel (a). The average curve is highlighted. Adapted from [297].

Figure B.3.: EIS measurements on HOPG. (a) Set-up of the electrochemical cell. HOPGwas used as working electrode (WE), a Pt sheet worked as counter electrode,and a standard Ag/AgCl was used as reference electrode. A PDMS cell witha defined diameter defined the electroactive area (0.385 cm2). (b) Capac-itance obtained through EIS measurement. The impedance was recordedevery 10 minutes, for a total time of 90 min. The capacitance decreasedwith time of about 0.7 µF cm−2.

146

Figure B.4.: 3D-AFM of freshly-cleaved HOPG-water interface. (a), (b) and (c) are 3D-AFM xz force maps of the interface characterizing a fresh HOPG surface.The interface shows solvation structures with different distances. FDCs areplotted below the corresponding 2D panel. The interlayer distance d1 is 0.34nm, 0.43 nm and 0.75 nm for panel (a), (b) and (c), respectively. Averagecurves are highlighted.

147

Figure B.5.: Sudden change of interlayer structures at the freshly-cleaved HOPG-waterinterface. (a) 3D-AFM xz map of the unstable interface characterizingfreshly-cleaved HOPG. 3D-AFM enables the visualization in real time ofinterfacial organizations; in (b) the force curves corresponding to the leftside of panel (a) and its right side are reported (average curves are high-lighted). The left and right side of panel (a) are divided by a white dottedline. The interface exhibits two different solvation structures, the first onthe left side of the panel with an interlayer distance of 0.52 nm and thesecond, on the right side, showing three peaks with interlayer distances of0.30 and 0.32 nm. The dotted lines in (b) help for the visualization of theposition of the peaks.


)Figure C1 (N) C2 (N) l (m)B.4a -3.32 ×10−11 2.49 ×10−10 2.98 ×10−10

B.4b -2.08 ×10−11 1.42 ×10−10 2.52 ×10−10

B.4c -1.36 ×10−12 7.87 ×10−11 6.54 ×10−10

B.5 -2.00 ×10−12 1.45 ×10−10 2.78 ×10−10

Table B.3.: Background subtraction. A fit to the force curves shown in Fig. B.4 andB.5 was obtained through the equation reported on the left side of the table.This is an exponential function with an offset. The function was subtractedfrom the force curves of Fig. B.4 and B.5 to allow the comparison of thesedata with the ones reported in Chapter 4.

148

Figure B.6.: 3D-AFM FDCs in degassed water. (a) FDCs obtained on air-aged HOPGimmersed in degassed water. (b) FDCs obtained on freshly-cleaved HOPGimmersed in degassed water. The results are comparable with FDCs ob-tained in standard UPW water. Average curves are plotted as thick andblue lines.

149

C. Supporting Information Chapter 5

Figure Type Medium nmode

kn(N m−1) Qn fn(kHz) σ−1n (nmV−1)

5.1a Arrow-UHF-AuD n-octane 1 8.13 4.8 492 15.85.1b,c Arrow-UHF-Al n-octane 1 10.79 5.8 940 10.55.3 FS-1500AuD n-octane 1 7.49 5.3 529 8.855.2 PPP-NCH-AuD n-octane 2 1602 19.52 952 10.2C.1a Arrow-UHF-AuD n-

hexane1 9.22 4.6 523 14.91

C.1b Arrow-UHF-AuD n-hexane

1 10.85 5 635 16.04

C.1c,d Arrow-UHF-AuD n-hexane

1 7.44 6.9 633 15.0

5.4 Arrow-UHF-AuD n-octane-saturatedwater

1 10.46 5.1 530 10.36

Table C.1.: Cantilever calibration. The table summarizes the parameters of the can-tilevers used in Chapter 5.


)Figure C1 (N) C2 (N) l (m)5.1b -1.40 ×10−12 23.5 ×10−12 8.69 ×10−11

5.1c -1.40 ×10−12 51.2 ×10−12 5.52 ×10−11

5.3a -6.35 ×10−12 19.7 ×10−12 2.01 ×10−12

C.1a -2.94 ×10−12 30.8 ×10−12 1.08 ×10−12

C.1b -7.16 ×10−12 6.35 ×10−11 9.70 ×10−10

5.4 -4.97 ×10−13 7.53 ×10−11 2.57 ×10−10

Table C.2.: Background subtraction. A fit to the force curves shown in Chapter 5 wasobtained through the equation reported on the left side of the table. Thisis an exponential function with an offset. The background was subtractedfrom the corresponding FDCs.

150

Figure C.1.: Solid-liquid interface of standard and dry n-hexane on mica and HOPG.3D-AFM xz force panel of (a) standard n-hexane (>99 %) and (b) dry n-hexane on mica. 3D-AFM xz force panel of (c) standard n-hexane (>99 %)and (d) dry n-hexane on HOPG. Below each panel, the corresponding FDCsare plotted. Average curves are highlighted. The results are equivalent tothe ones obtained for n-octane.

151

D. Supporting Information Chapter 6

Figure Type n mode kn(N m−1) Qn fn(kHz) σ−1n (nm V−1)

6.4a,6.5a OMCL-AC160-R3 2 674.5 7.9 872 9.66.4b,6.5b OMCL-AC160-R3 2 655.8 6.0 883 9.06.4c,6.5c OMCL-AC160-R3 2 656.9 10.8 849 10.96.7a USC-F5-k30 1 11.4 6.4 3264 14.96.7b OMCL-AC160-R3 2 508.4 13.1 816 14.3

Table D.1.: Cantilever calibration in aqueous solution. The table summarizes the pa-rameters of the cantilevers used in Chapter 6.

152

Figure D.1.: Statistical analysis (n ≥ 7) of the interlayer distance for experiments withNaCl solution below and near saturation obtained with neutrally, negativelyand positively charged tips. (a) The interlayer distance was derived byextracting q0 from the fit of the first two oscillations of the experimentalFDCs with eq. 6.5. The fit is shown in red. Then, the interlayer distancecan be calculated (2π/q0). (b) Box-plot of the extracted interlayer distancesfor the experiments below and near saturation. Below saturation (left andgray panel), the interlayer distance has an average value of 0.32 ± 0.03 nm,0.30 ± 0.06 nm and 0.28 ± 0.03 nm for neutral, negative and positive tips,respectively. Near the saturation concentration (right and red panel), theinterlayer distance has an average value of 0.31 ± 0.03 nm, 0.42 ± 0.02 nmand 0.55 ± 0.06 nm for neutral, negative and positive tips, respectively.The interface shows a clear change when the concentration is increased andwhen the tip has a net charge.

153

Figure D.2.: Statistical analysis (n ≥ 10) of the distance between the surface and thefirst peak in the force profile (d0). The data are relative to experimentsperformed with positive, negative and neutral tips below saturation (grayarea) and with neutral tips near saturation (green area). The average valueof each set of experiments is shown with an empty square. The median isshown as a black line. The average value of d0 is 0.17 ± 0.04 nm, 0.16 ±0.03 nm and 0.18 ± 0.02 nm for positive, negative and neutral tips belowsaturation, and 0.15 ± 0.03 nm for neutral tip near saturation. d0 is similarfor the four sets of experiments. When hydration layers are visualized, d0is independent of the tip charge and of the concentration of the solution.

154

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