Chapter 12 Single Molecule Force Spectroscopy of Supramolecular Complexes Authors: Tobias Schroeder (Bielefeld University, Faculty of

Chemistry) Volker Walhorn (Bielefeld University, Faculty of Physics) Jochen Mattay (Bielefeld University, Faculty of Chemistry) and Dario Anselmetti (Bielefeld University, Faculty of Physics)

Publisher Wiley-VCH , Weinheim, 2011 ISBN-10 3-527-32982-X

12.1 Introduction & Motivation

Supramolecular chemistry, which has been defined as “the chemistry beyond the molecule” [1]

deals with the chemistry and collective behavior of organized ensembles of molecules [2] where

the rational and synthetic fabrication of molecular structures of increasing size, complexity and

functionality is possible. The synthesis and (self) assembly of molecular architectures of higher

dimensionality is based on a subtle interplay of covalent and non-covalent interactions. Whereas

the individual building blocks or molecular constituents (templates) are predominantly stabilized

by strong covalent bonds, their assembly to supramolecular complexes or aggregates is mostly

directed and controlled by weak hydrogen, van-der-Waals, electrostatic or donor-acceptor

interactions. Due to the size and structural complexity of the supramolecules, several weak and

unspecific interactions contribute in such a way to this complex multibinding phenomenon that

novel binding properties like directionality, orientation, specificity and reversibility can be

coined and lead to new concepts and relevance. Since the very early concepts of key-lock-

principle [3] and coordination chemistry [4] the paradigm of molecular recognition is ubiquitous

in (bio)chemical and life sciences and is the conceptual basis for understanding the fundamental

processes in a biological cell as well as to develop new drugs and therapeutica.

As biological physicists, we are fascinated by the ability of the chemists to rationally design and

synthesize organic supramolecules that can mimic the function of naturally evolved

biomolecules. Moreover, in case they carry additional functionalities that can be controlled from

outside and/or exhibit robustness so that they can be transferred to a technical surface, this

reverse engineering approach of nature would allow developing artificial motors and synthetic

machines.

Supramolecular chemistry as a mesoscale science provides a new connection between the

molecular and the macroscopic world. While structural properties can already be analyzed in

great detail (mostly in molecular ensembles), it is important to establish a correlation between

other characteristic parameters of both dimensions. The understanding of the impact how (weak)

molecular forces act on and between (single) molecules, is highly relevant for understanding and

controlling the macroscopic properties and processes (for instance the structural integrity of

materials or adhesion phenomena). In the last decade, single molecule force spectroscopy

techniques have contributed a wealth of information on the impact of forces on the molecular

scale that go beyond the common knowledge of macroscopic force experiments and hitherto

have not been accessible. Upon stretching individual (bio)polymer strands [5] as well as

investigating and quantifying the interaction forces between macromolecules [6] a deep insight

into elapsed force and binding mechanisms, their associated reaction pathways and reaction

kinetics could be investigated. Furthermore, many experimental and theoretical verifications

allowed to establish a coherent framework where the stochastic, thermally driven reactions at the

single molecule level could be related to the macroscopic properties (observables) or

thermodynamic state variables of a molecular ensemble (ergodic principle).

Therefore, this book chapter is focused on the analysis of the interactions between non-

covalently linked supramolecular entities by AFM single-molecule force spectroscopy (AFM-

SMFS). After a material-oriented section where we discuss appropriate surface immobilization

strategies we will present and discuss selected examples reported in the literature in order to give

an idea about how to set up successful single-molecule force spectroscopy experiments, what

type of supramolecular architectures have already been investigated and what kind of

information could be accessed from theses studies. The main text of this book chapter is

supplemented by two tutorial sections where 1) the proper calibration of the AFM force sensors

and 2) the theoretical framework of single molecule force spectroscopy is presented which is

mandatory to analyze the data in a quantitative manner. The latter is fundamentally described by

the Kramers-Bell-Evans theory (KBE-theory) which provides a coherent bridge between the

nanoscopic force values determined in single-molecule experiments and the macroscopic

ensemble parameters of the analyzed system (e.g. dissociation rate constants). Generally, this

technique has proven to significantly contribute in molecular binding studies to quantitatively

determine:

forces required to disrupt inter- and intramolecular (non)covalent bonds

molecular elasticities

dissociation rate constants (average lifetime of the complex)

dimerization equilibrium constants

details of the binding energy landscape

entropic and enthalpic forces and energies required to stretch single molecules

binding properties of “insoluble” molecules in solvent environment

in and between surface-bound but “unlabelled” molecules in an affinity range of 10-4-10-15 M at

the sensitivity of single point mutations or structural variations. Although this book chapter does

not aim for a complete and therefore difficult to overview description of this fast growing field,

we will concentrate on somewhat historic and hallmark papers of AFM-SMFS on

supramolecular systems that might give you a balanced view of the field as well as may help to

plan and realize single-molecule force spectroscopy experiments, analyze and interpret force-

distance curves, providing a basis for further developments bridging dimensions and chemical

disciplines.

12.2 Functionally Immobilizing Supramolecules

A prerequisite to successful AFM experiments is the appropriate immobilization of the

components of the supramolecular complex. In this section, two well-proven methods for the

covalent attachment of functional groups to the surface of the AFM tip and the substrate are

presented followed by a discussion of the advantages of using polymeric linkers in SMFS. The

covalent attachment is recommended, since in AFM-SMFS the molecular components including

spacer and fixation molecules are mechanically and simultaneously probed in series and the

weakest bond should be designed as the one of interest. It is well known that covalent bonds are

in the nN range (Si-C: 2.0 nN at r = 10 nN·s-1 [7]) whereas (as we will see later) typical non-

covalent supramolecular bonds are within a force range of 30-200pN.

Several procedures are available to introduce functional groups at the surface of AFM cantilevers

[8-10]. We will present two of them but further examples are described together with results of

the corresponding AFM-SMFS experiments in details in the next section.

Because the sensitive AFM force sensors require careful handling, it can be advantageous to use

reliable benchtop reactions that proceed under mild conditions for the modification of the AFM

tip.

Fig. 12.1. Functionalization scheme for silicon nitride AFM-cantilevers with (3-aminopropyl)

triethoxysilane.

Fig. 12.1 shows a well established functionalization of silicon nitride tips [11]. The material of

the force probes is covered with a thin layer of SiO2. To clean the surface and generate a high

number of Si-OH groups at the surface, the tip is treated with concentrated oxidizing acid.

Thereafter, functional groups that can be employed in further coupling reactions are attached to

the cantilever. Introduction of amino groups employed frequently in immobilization strategies

can be realized by silanization with (3-aminopropyl) triethoxysilane (APTES) (Fig. 12.1). The

reaction can either be carried out in dry solvents or via gas phase reactions by evaporation of the

reagent under reduced pressure in a desiccator [12]. Because alkoxysilanes can oligomerize, gas

phase silanization might be advantageous in some cases since they deliver homogeneous and

nm-thin silane coatings at a reduced surface roughness. Here it is worth noting that upon

tailoring the density of functional group at the surface, the probability to detect a single molecule

reaction can be adjusted. In order to generate only a low number of amino groups at the surface,

a low concentration of the silane and short reaction times can be chosen. Alternatively,

incubating silicon nitride cantilevers with solutions of ethanolamine can be used to obtain low

functionalized cantilevers instead of the silanization process [13]. The amino groups at the

surface of the AFM cantilever can now be subjected to amidation reactions to couple the

supramolecular subunit to the surface.

Besides cantilevers with a SiO2-surface, gold coated AFM cantilever tips have been

functionalized and used for SMFS experiments. For that purpose, self-assembled monolayers

(SAMs) of thiols or disulfides are prepared that can be further reacted to attach the

supramolecular subunit [9,10,14]. The adsorption to gold results in the formation of

gold(I)thiolates on the surface (Fig. 12.2).

Fig. 12.2. Immobilization of thiols on gold coated silicon nitride cantilevers. (a) Reaction of the thiol during SAM formation. (b), (c) Schematic representation of a SAM obtained from alkylthiols or disulfides with terminal functional groups (FG) that can be used in further coupling reactions in homogeneous (b) and mixed monolayers (c).

Like the immobilization via silanes to silicon nitride cantilevers, thiol SAMs on gold-coated

AFM tips ensure a stable attachment for probing supramolecular interactions by SMFS.

Experimental values for the dissociation force of 1.4 nN have been determined for the desorption

of thiols from gold [7]. Details of the dissociation process have been investigated in theoretical

studies that predict removal of gold atoms as nanowire when the external forces act on thiolates

bound top stepped gold surfaces [15]. Therefore, the observed dissociation forces may be

attributed rather to Au-Au bond rupture instead of decay of the Au-S bond. However, thiol

SAMs on gold ensures a stable attachment for probing supramolecular interactions with SMFS.

Besides disulfides and thiols, molecules with several dialkylsulfide groups can be immobilized

as self-assembled monolayers on gold. Although the dative bonding between sulphur and gold is

weaker in these systems, van-der-Waals interactions between neighbouring alkyl chains

contribute favourably to the stability of the SAM substrates for force spectroscopy experiments

and are obtained using the same immobilization strategies as described for tip modification. In

order to detect interactions between single molecules, the concentration at the surface of the

AFM cantilever tip and the substrate should generally be low. Furthermore, the immobilization

strategy has to ensure that the building blocks are homogeneously distributed on the surface

without formation of highly aggregated areas due to homophilic interactions of the building

blocks. For single-molecule experiments with supramolecular building blocks preparation of

mixed SAMs of different sulfides or dialkylsulfides on gold surfaces has proven to be a valuable

strategy. By adjusting the ratio of the supramolecular building blocks with respect to the diluting

entities like sulfides or thiols, an optimized surface concentration can be obtained [16, 24a, 25a].

In AFM-SMFS, discrimination of specific binding events from unspecific ones is the key for

performing a reliable experiment and an associated quantitative binding study. Beyond the

commonly conducted control experiments, where the surface and tip immobilized binding

partners are specifically blocked by the addition of free ligands (see later), a dedicated surface

functionalization strategy that decouples the specific molecular recognition event from

concomitant surface interactions has been developed. Fig. 12.3 illustrates the exceptional

advantages for the analysis of the force-distance curves when flexible polymeric molecules are

used to tether the supramolecular building blocks to the cantilever surface and/ or the substrate

[17].

The two force curves presented in Fig. 12.3 clearly exhibit different force responses that are

characteristic for different functionalization of the cantilever and the substrates.

Fig. 12.3. Force-distance curves (retract part) obtained in AFM-FS experiments. Depending on the immobilization strategy of the building blocks without (a) and with (b) the use of a flexible polymeric linker, different force response can be measured.

If the interacting species are directly linked to the surface (Fig. 12.3a), a linearly descending

retract curve that directly passes from the repulsive to the attractive region towards the minimum

is obtained. The slope of the curve is solely determined by the spring constant of the cantilever.

When the force applied by the bend cantilever on the complex (depicted as red ball bound to the

blue box with a receptor cavity) overcomes the supramolecular interaction, the complex

dissociates and the cantilever immediately returns to the zero force position.

The only information accessible is the value of the adhesion of the cantilever to the surface,

corresponding to the minimum of the force-distance curve. Because short-range adhesion forces

acting between cantilever and substrate can be the result from various (unspecific) binding

phenomena, these force-distance curves only give limited information about their origin and it is

almost impossible to securely assign the measured force to the bonding in the supramolecular

complex. Possible unspecific interaction or adhesion can stem from electrostatic, van-der Waals,

or hydrophobic interactions, that can be related to the surface modification or organic

contamination.

These effects can be discriminated from the specific supramolecular interactions, if the building

blocks of the complex are immobilized via a flexible polymeric linker. Usually, poly(ethylene

glycol) (PEG) is used for this purpose. Fig. 12.3b shows a scheme of the immobilization (inset)

and a typical force curve resulting from the dissociation of the complex formed between the

substrate-bound component and the molecules attached to the cantilever via a PEG linker. When

the cantilever is retracted, a force-distance curve that is linearly descending from the repulsive to

the attractive region is observed. When the restoring force of the cantilever overcomes the

unspecific interaction, the zero-force position is reached. Further retraction of the force sensor

results in the extension of the polymeric linker, which initially does not require a significant

force. Finally, a non-linearly increasing force is acting on the complex resulting from the

combination of the simultaneous deflection of the cantilever and the stretching of the polymer

(red part of the curve). When the supramolecular complex dissociates under the external force,

the cantilever instantly snaps back to the zero-force position. Stretching experiments have shown

that the characteristic force signature observed in the force-distance curves upon extension of

polymers can adequately be described by polymer elasticity models like the modified freely-

jointed-chain model (FJC; eq. 12.1) [18] or the worm-like-chain model (WLC; eq. 12.2) [19].

Modified FJC-Model: Kuhn Bcontour

B Kuhn monomer

F l k T F Nx F Lk T F l k

= − +

( ) coth eq. 12.1

WLC-Model: ( )2

1 1( )44 1 /

B

p contourcontour

k T xF xLx L

= − +

−

eq. 12.2

where F, x, Lcontour, lp, lKuhn, kmonomer, kB, T, N denote force, molecular extension, overall contour

length, persistence length, segment Kuhn length, monomer elasticity, Boltzmann constant,

temperature and number of monomer segments.

Therefore, the non-linear regime in the curves can be used to make sure that single polymer

chains are stretched and consequently identify single-molecule interactions between the building

blocks of the supramolecular complex. Force-distance curves that do not match the expected

pattern can be discriminated and excluded from further analysis. In addition to the improved

possibilities in the interpretation of the data, flexible PEG linkers play an important role for the

recognition event. As the polymeric linker allows the attached supramolecular subunit to diffuse

in a certain volume, the steric freedom added to the system allows unconstrained formation of

the complex.

Therefore, the attachment of molecules via commercially available heterobifunctional PEG

linkers to the cantilever has become a standard procedure. Usually, one end of the polymer is

functionalized with a carboxyl group that can be reacted with amino groups at the cantilever

surface.

Fig. 12.4. Examples for heterobifunctional PEG linkers with maleimide, succinimide, carboxyl, mercapto and alkyne endgroups commercially available or reported in the literature.

Depending on the functional group that is used to couple the supramolecular building blocks to

the cantilever, the appropriate PEG linker bearing a second reactive group (for instance the thiol-

reactive maleimide group) can be chosen (Fig. 12.4). Alternatively, tailor-made

heterobifunctional PEGs can be synthesized in few steps by established procedures. The

sequence of the coupling reactions can be reversed, linking the supramolecular building block to

the heterobifunctional PEG linker before the conjugate is attached to the surfaces.

12.3 Supramolecular Interactions Investigated by AFM-SMFS

In the last decade, a number of supramolecular systems have been investigated using single-

molecule force spectroscopy. These studies have provided force regimes for different types of

interactions that can give orientation for researchers doing their first force spectroscopy

experiments. Besides presenting detailed force values and quantitative binding parameters

obtained for the supramolecular binding motifs, this section is intended to encourage

experimentalists to investigate new molecular architectures to examine their response to external

forces, properties at interfaces and their potential applications in material science and

nanoarchitectures. Although the first systems analyzed by AFM-SMFS have been complex

biomolecular structures, this method offers new impulses to solve fundamental questions using

simple model compounds and gain insights into processes that remained inaccessible so far.

From the various force spectroscopy experiments on the basic supramolecular interactions

(hydrogen bonds [20-23], host-guest binding [24,25], metal-ligand interactions [26-28],

hydrophobic interactions [29], π-π interactions [30], charge transfer [31]), only selected

examples are presented here.

However in this book chapter, a special emphasis is put on experiments where supramolecular

entities are connected via several hydrogen bonds, yielding structures that are well-defined, but

sometimes also rather dynamic due to the relatively weak nature of this interaction. On the other

hand, this parallel type of multiple - often cooperative - interaction at the mesoscale is realized in

biology in countless examples such as for stabilizing the DNA double helix as well as the

secondary structure of proteins, accounting for the remarkable stability and affinity of receptor-

ligand interactions like biotin-avidin or are responsible for the strength and discrimination of

nucleic acid base pairing. Therefore, supramolecular complex formation via hydrogen bonding

can be regarded as biomimetic model system where the character of the integral interaction can

be adjusted and tailored by controlling the size and spatial arrangement of the hydrogen bonding

network.

The leitmotif of this book chapter is therefore structured and developed along the historic AFM-

SMFS experiments on host-guest systems like the hydrogen-bridged cyclodextrins and

calixarenes, to structures of increasing complexity like metal-complexed ligand interactions as

well as supramolecular capsules and finally to supramolecular polymers illustrating the manifold

applications of AFM-SMFS in (supramolecular) chemistry.

12.3.1 Host-Guest Systems: Cyclodextrins The – to our best knowledge – historic first single molecule AFM study of supramolecular

complex formation was introduced by two colleagues Vancso and Reinhoudt from the University

of Twente in 2000, when they looked into the the binding of ferrocene and β-cyclodextrin (CD)

[24a-c]. In these studies, CD heptasulfide receptors were immobilized via thioether groups to

gold surfaces forming dense self-assembled monolayers. They were probed against ferrocene

ligands molecules immobilized as ferrocenyl-hexanethiol also via thiol chemistry on gold coated

AFM-tips (Fig. 12.5) in water and aqueous solution. Due to the dense surface coverage of

receptor and ligands, typical AFM force-distance experiments (Fig. 12.6a) were dominated by

multiple dissociation events and statistically analyzed in force histograms (Fig. 12.6b), where the

equidistant maxima of the force distribution were interpreted as the integer multiples of one

fundamental supramolecular decomplexation force which was determined to be around f* = 55-

60 pN. This statistical analysis procedure was well established at that time and related to the first

AFM-SMFS work on biotin-avidin in 1994 [6a].

Very interestingly, the measured single molecule decomplexation reaction was also probed at

different loading rates (see also Tutorial 12.1 on force spectroscopy theory), which means that

Fig. 12.5. AFM-SMFS setup for decomplexation studies between a ferrocene guest and a dense self-assembled monolayer of β-cyclodextrin. Both molecular systems were functionally immobilized on gold via thiol chemistry. Figure with courtesy from [24b].

the experimental AFM tip approach/withdraw velocity was varied over several orders of

magnitudes, and exhibited – in contrast to KBE-theory - no significant dependence (Fig. 12.6c).

This observation, which was also in contrast to experiments on biological receptors, [32, 33] was

interpreted by the fact that the probed supramolecular systems obey a very fast dissociation

kinetics (decomplexation rate constant of 10-5 – 10-6 s-1) with a relatively low complexation

affinity of Kd ~ 10-3 M, which is in contrast to the reported biological systems.

Fig. 12.6. (a) Typical AFM force-distance curve between a ferrocene-functionalized tip and a CD-SAM exhibiting multiple decomplexation events. (b) Force histogram of AFM decomplexation forces with statistical analysis with integer multiples of a fundamental dissociation force. (c) Dynamic force spectroscopy diagram with no distinct loading rate dependency of measured dissociation forces. Figures with courtesy adapted from [24b].

These fundamental and important insights on supramolecular host-guest interactions were

verified also in further investigations when the guest ligands where exchanged and probed

against surface immobilized CD in AFM-SMFS experiments [24c].

12.3.2 Host-Guest Systems: Calixarenes In addition to the previously described systems, calix[4]arenes, resorcin[4]arenes and cavitands

are versatile building blocks in supramolecular chemistry because of their three-dimensional

structure and the various functionalizations that can be introduced at different positions of the

molecular framework. Similarily to cyclodextrins, their ability to adopt chalice-like

conformation makes them ideally suited as the basis for molecular receptors (Fig. 12.7a,b).

Furthermore, well-defined self-assembled monolayers on gold can also be obtained if thioether

moieties are introduced at the part termed the “lower rim” of the molecule.

In 2005 at Bielefeld University, the first single molecule study of supramolecular complex

formation in a calixarene system was published, where the data could be quantitatively analyzed

in accordance with the theoretical KBE standard model – a result that was in contrast to the one

described above. Here, ammonium derivatives as the guest ligands were measured against

resorcin[4]arenes cavitands in ethanol at room temperature using commercial instrument that

was equipped with custom-made control and data acquisition system [25a,d]. The 2,8,14,20-

tetra-(10-(decylthio)decyl) cavitands were immobilized in diluted cavitand monolayers in a 1:40

mixture with didecylsulfide. The guest cations (ammonium (A), trimethyl ammonium (TMA)

and triethyl ammonium (TEA), carrying one chemically modified entity each) were covalently

attached to the AFM tip via a flexible polyethylene glycol (PEG) linker.

In AFM-SMFS experiments molecular dissociation events could be identified (Fig. 12.7c)

whereas their specificity could be verified in competition experiments (Fig. 12.8).

Fig. 12.7. Supramolecular host-guest complex structure with calixarene cavitand and (a) an ethyl ammonium ion and (b) an ethyl trimethyl ammonium ion. (c) Typical single molecule force-distance curve of complex a) exhibiting an unbinding or dissociation force of ~85 pN. Inset: experimental scheme. Figures adapted with courtesy from [25a].

Interestingly, only the two smallest guests A and TMA were able to specifically bind to the

cavitand, whereas the large TEA cation with a calculated diameter of 0.8 nm was sterically not

able to enter the 0.7 nm wide host cavity.

Loading rate dependent dynamic force spectroscopy experiments and quantitative binding

analysis according to the KBE-theory (see also tutorial) yielded koff = (0.99 ± 0.81) s-1 for A and

koff = (1.87 ± 0.75)×10-2 s-1 for the TMA residue, resulting in a bond lifetime of τ = 1.01 s and τ

= 53.5 s, respectively. This finding, together with the results of the competition experiments,

indicates that the TMA residue fits tighter into the receptor cavity, ensuring a rise in binding

affinity as compared to A. Upon assuming a diffusion limited association with a typical on-rate

constant of kon = 105 M-1s-1, equilibrium constants for these reactions of Kdiss = 0.99 s-1/105 M1s-1

= 10-5 M (corresponding to ∆G = -28 kJ mol-1) and of Kdiss = 2×10-2 s-1/105 M-1s-1 = 2×10-7 M

(corresponding to ∆G = -38 kJ mol-1) for A and TMA ions, respectively, can be deduced. From

the inverse slope of the loading rate dependency (Fig. 12.9) the molecular reaction length can be

extracted yielding xβ = (0.22 ± 0.04) nm for A, and xβ = (0.38 ± 0.06) nm for the TMA ions.

These estimated values qualitatively scale with calculated van-der-Waals diameters of 0.3 nm for

A and 0.6 nm for TMA, respectively. Therefore we can conclude that hydrogen bonds (not

present in the TMA cavitand interaction) and cation-π-interactions have to contribute

considerably to the molecular binding mechanism.

Fig. 12.8. Activity status of probed cavitand surfaces against the three different ligands. (a,d,g) Single molecule force histograms measured in ethanol; (b,e,h) Control experiment: Single molecule force histograms in ethanol saturated with free competitive ions; (c,f) Reactivating the surface: single molecule force histograms after washing with pure ethanol restored the original unbindig probability. (Whereas the ammonium and trimethyl ammonium ligands exhibited specific interaction, only unspecific binding could be verified with the triethylammonium ligand (g,h,i)). Figure adapted with courtesy from [25a].

Fig. 12.9. Dynamic force spectroscopy. The loading rate dependent dissociation forces are logarithmically plotted for the binding of the ammonium and trimethyl ammonium guest residues to the resorc[4]arene cavitand. Figure adapted with courtesy from [25a].

Especially, the TMA cavitand system may profit from the latter contribution due to its positive

charge distribution which is shown to reside on the hydrogen atoms of the methyl groups.

12.3.3 Host-Guest Systems: Photoswitchable Calixarene Systems The introduction of additional functionality and external control to mesoscopic systems is

fascinating by itself, however, also aims for the rational design and directed synthesis of

supramolecules that can mimic the function of biomolecules in distinct biomedical and technical

applications. With this reverse engineering approach artificial and robust molecular motors and

synthetic machines can be anticipated. Since future nanomachines rely on cyclic operation and

external control, repetitive transition between at least two different molecular states e.g. by the

conformational transition (switching) between two structural isomers is mandatory. As external

control mechanism and transition stimulus the interaction of molecules with light, electric,

chemical or mechanical potentials are known. External activation via electronic excitation,

energy transfer, and/or ionic transport by light harvesting complexes or energy up conversion in

photosynthesis is well known. Fundamental for all these processes is the ability to convert

electromagnetic energy into conformational changes where specific and noncovalent bonds can

be formed and released due to affinity changes. In order to investigate such phenomena in an

artificial model system, we have synthesized a bistable supramolecular host-guest system where

the supramolecular receptor cavity of the aforementioned resorcin[4]arene cavitand has been

combined with two photodimerizable anthracene moieties whose structures can externally

switched by UV-light and temperature [25b-d].

Fig. 12.10. Resorcin[4]arene photoswitch. (a) Pictogram visualizing the photoactive cavitand receptor that is affinity probed against its ammonium cation ligand by AFM-SMFS. The switching between the open (active) and closed (inactive) structure is externally controlled by UV-light and thermal energy and mimics biological regulation triggers. (b) Resorc[4]arene photoswitch UV absorption spectrum for the open and closed isomer. The observed peaks for the open isomer are characteristic for the anthryl groups. Figures adapted with courtesy from [25b].

Since the photodimerization process blocks the entrance of the cavitand, the affinity properties of

this photochemical macrocycle was investigated in AFM-SMFS experiments against guest cation

complexation. (For scheme see Fig. 12.10a). The transition from the open (active) to the closed

(inactive) structure of this photochemical single-molecule switch and vice versa was performed

by irradiation with a UV lamp at (368 ± 7) nm for 5 min and locally heating the sample to 60°C

for 2 h, respectively. Whereas the macroscopic switching properties were analyzed and verified

in UV absorption experiments (see Fig. 12.10b) the nanoscopic affinity modulation of this

optical switch was investigated by AFM-SMFS, where the photoactive cavitand was

immobilized on a gold surface in a SAM in a 1:40 dilution with di-n-decyl sulfide. The guest

molecule, an ammonium ion, was immobilized via a PEG-linker to the AFM tip.

Five series of AFM-SMFS experiments were performed in ethanol and presented as force

histograms in Fig. 12.11. As we have seen before, force histograms can be used as activity

monitor. Fig 11a-d summarize the consecutive single molecule activity of the photoactive

cavitand against ammonium complexation during the following stages: (a) open isomer after

heating, (b) closed configuration after UV exposure, (c) (re)opened isomer after heating, (d)

open isomer blocked with free ammonium and (e – image not shown) open isomer with full

activity after washing with ethanol. These experiments prove that the photoactive resorc[4]arene

cavitand can be reversibly switched between two different isomers that can be affinity probed by

AFM-SMFS. Whereas one of the two isomers shows a high affinity to ammonium, the other

exhibits almost none.

Interestingly, the transition between the two isomers and its change in complexation affinity is of

course related to a change in 3D structure of this supramolecular macrocycle.

Fig. 12.11. Single molecule force histograms of the resorcin[4]arene photoswitch. (a) Experimental series after heating the sample to 60°C for 2 h (open isomer and active state). (b) Series after irradiating the sample at 368 nm for 5 min (closed - inactive). (c) Series after renewed heating the sample for 2 h (open - active). (d) Series of competition experiments, performed in ethanol solution saturated with free ammonium (open/blocked - inactive). All experiments were performed with the same AFM tip and cavitand surface at a retract velocity of 1000 nm s-1. Figures with courtesy from [25b]. Additionally, we performed AFM (tapping mode) topography experiments under ambient

conditions with a commercial instrument (Multimode IIIa, Veeco, Bruker) in order to

complement the functional force spectroscopy experiments [34]. Therefore, a diluted monolayer

(1:200 in chloroform-ethanol) of the photoactive cavitands and di-n-decyl sulfide at mM

concentration was self-assembled on ultraflat gold substrates (roughness (RMS) < 0.2 nm) and

successively heated. In an overview AFM topography image (Fig. 12.12a) where individual

cavitands (visible as nm-sized hillocks protruding the molecular SAM background) could be

discerned, a region of interest (ROI) with only very few macrocycles was chosen. This ROI was

consecutively scanned several times with AFM before and after UV illumination (Fig. 12.12b).

Then identical AFM traces over the very same molecule were extracted and superimposed to

estimate a possible change of the apparent molecule height Δh caused by the isomeric transition.

Fig. 12.12. (a) AFM topography image of single immobilized anthracene modified resorcin[4]arenes cavitands on a flat gold substrate embedded in a SAM of di-n-decylsulfate. A region of interest (box) is cut out from successive scans to extract topography cross-sections of single cavitand molecules (see b) before (top row) and after (bottom row) UV-exposure (scalebar: 20 nm) (unpublished data). (unpublished data [34]).

Fig. 12.13. Cross-sections of the marked cavitand molecule in Figure 12b (arrows) are superimposed to estimate the apparent molecule height (blue before and red after UV exposure). A distinct difference of 0,18 nm can be discerned reflecting the bistable cavitand configuration in the open (active) and closed (inactive) isomer configuration (unpublished data). (unpublished data [34]). In Fig. 12.13, exemplarily, the statistical analysis is presented of the molecule that was marked

by an arrow in Fig. 12.12b yielding Δh = 0.18 nm. In total, we analyzed 18 molecules from

several samples and determined a mean increase of <Δh> = 0,22±0,043 nm. This difference in

the apparent molecule height of the isomers can be allocated to both the different molecular

topography as well as to the different contributions from the local nanometric force response

between AFM tip and cavitand. It is very likely that the photocyclized cavitand complex can

withstand the mechanical AFM probe impact much better than the macrocycle in the open

structure.

Although, much more interesting comments could be made and conclusions could be drawn

from this AFM imaging experiment, we would like to draw the reader´s attention to the

preceeding chapter written by Bianca A. Hermann and Regina Hoffman on general scanning

probe microscopy (SPM), where lots of more interesting issues will be presented and debated.

12.3.4. Hydrogen-Bonded Supramolecular Structures As mentioned above, H-bonded systems play a very important role in biological and

supramolecular chemistry. Interestingly, in a supramolecular system that was originally

introduced by Sibesma et al. the self-complementary aggregation of 2-ureido-4-pyrimidinone

(UPy) (Fig. 12.14a) that aggregate in apolar solvents like CHCl3 or hexadecane (HD) to dimers

with association constants of K > 106 M-1-109 M-1 [35] was investigated also in the light of the

SMFS loading rate dependence. The supramolecular system itself has due to its chemical and

structural homologies to pyrimidine nucleobases a close relationship to the fundamental Watson-

Crick DNA base pairing, and might be considered as a suprachemical model system to mimick

base pair recognition. As a consequence, Zou et al. investigated in 2005 the stability of this

effective H-bonded binding motif by AFM-SMFS [20]. Gold-coated AFM tips and gold-coated

substrates were functionalized with UPy moieties (Fig. 12.14b,c) via flexible PEG-linkers. After

formation of a SAM of the PEG disulfide at the surface, UPy isocyanate was immobilized by

reaction with the hydroxyl group of the PEG linker. AFM-SMFS experiments were carried out in

temperature dependent experiments at 301 K and 330 K in HD. Fig. 12.14d. shows a typical

force-distance curve at 301 K, where a characteristic non-linear molecular elasticity is observed.

A fit to a modified FJC polymer elasticity model (black line) demonstrates the excellent

agreement of the measured curve according the model of two serially attached PEG linker

molecules and proves the proposed single-molecule interaction. From the respective force

histogram (data not shown), a dissociation force of F = 148 pN at a loading rate of r = 5.7 nN·s-1

could be determined. The loading rate dependence of the dissociation forces was then evaluated

in AFM dynamic force spectroscopy experiments (Fig. 12.14e) at 301 K in HD. As the loading

rate increases from 5.7 nN·s-1 to 3.4·102 nN·s-1, the detected mean dissociation forces increased

from 148 pN to 269 pN. Analysis according to the KBE model yielded a UPy dimer lifetime τ of

5-7 s and a molecular reaction length of xβ= 0.22 nm at 301 K. These estimated values are in

good agreement with the results obtained in NMR experiments in toluene-d8, where a reaction

off-rate constant of koff0= 0.6 s-1 (corresponding to τ = (koff

0)-1 = 2 s) could be estimated.

Interestingly and in contrast to the distinct dependency of the loading rate at 301 K, a markedly

different behaviour is observed in measurements at 330 K in HD. For loading rates between

6.7 nN·s-1 to 1.9·102 nN·s-1, dissociation forces of ~145 pN – nearly independent of loading rates

- are obtained (Fig. 12.14f). This temperature-dependent complexation characteristics measured

on the same homodimeric (UPy)2 complex was attributed to the interplay of equilibrium

complexation constant, thermal energy and molecular lifetimes. Whereas at 301 K, the AFM-

SMFS experiments were conducted under thermodynamic nonequilibrium conditions, and

therefore obeying the law of KBE-theory, SMFS experiments at 330 K were carried out at quasi

equilibrium conditions. The authors succeded to formulate a model for a coherent molecular

time-temperature superposition that was able to account for the observed discrepancy in loading

rate dependency as it was also mentioned in the chapter describing the host-guest SMFS

experiments on cyclodextrins and calixarenes. In summary, these experiments impressively

demonstrate that the single molecule approach can generate deep mechanistic insights into the

binding or complexation of supramolecular mesoscale systems that will also have impact on the

inspection of related biological systems.

Fig. 12.14: (a) Quadruple H-bonded dimerization of UPy moieties. (b) Immobilization of the UPy groups to the AFM tip and the substrate. (c) Experimental scheme of the AFM-SMFS experiment. (d) Representative AFM force-distance curve of a (UPy)2 dimer complexation at 301K. (e-f) Plot of the dissociation forces vs ln(r) at 301 K (e) and 330 K (f). Figures adapted with courtesy from [20a].

12.3.5 π−π-Interactions in Supramolecular Chemistry Understanding π-π-interaction in bio- and supramolecular chemistry is another very important

aspect in order to design and taylor architectures of higher dimensions and complexity. π-π-

interaction (aromatic interactions) are ubiquitous in nature and it has been suggested that they are

an interplay of electrostatic, hydrophobic and van-der-Waals forces. It is well known that in

DNA π -stacking occurs between adjacent nucleotides adding to the stability of the molecular

structure. Since the nucleic acid bases of the nucleotides contain either aromatic purine or

pyrimidine rings, they interact via π- π-interaction with an orientational structure that is nearly

perpendicular to the main axis of the DNA strands. This phenomenon has also distinct

consequences for DNA binding agents like cancer chemotherapeutic drugs (daunorubicin,

doxorubicin, …) or fluorescent dyes (YOYO, TOTO, …) that are designed as planar

intercalators with aromatic ring systems.

Pyrene is an aromatic four-ring system that is known to bind to carbon nanotubes and graphite

through π-π-interactions. In 2007 Zhang et al. investigated the pyrene-graphite binding in

aequous solutions with AFM-SMFS [30a]. The pyrene derivative was attached to a flexible

carboxy-terminated PEG-linker and covalently attached to the tip of an AFM via APTES

silanization and 1-ethyl-3-[3-dimethylaminopropyl]carbodiimide (EDC) (Fig. 12.15a,b). The

experiments were either done in aequous solution or phosphate buffered saline (PBS) at 298 K.

They found distinct single-molecule force-distance curves that are governed by the non-linear

elasticity of the PEG-linker (Fig. 12.16a). In addition, they found in force histograms between

pyrene and graphite a clear dissociation force of f* = 55 pN at typical rupture lengths of around

47 nm (Fig. 12.16b). Whereas the latter could be related to the overall length of the PEG-linker,

the measured dissociation force f* could be located to the π-π-binding between pyrene and

graphite.

Fig. 12.15: (a) Scheme of the synthetic routes of Pyrene-PEG-COOH . (b) Setup of the AFM experiment to measure π-π-interaction between pryene and graphite. Figures adapted with courtesy from [30a].

Fig. 12.16: (a) Series of force-distance curves between pyrene and graphite taken in aeqous solution at a loading rate of 500 nm/s. (b) Force histogram of the measured force-distance curves at a loading rate of 4.0 nN/s exhibiting a dissociation force of f* = 55 pN. (c) Dynamic force spectroscopy plot exhibiting no distict loading rate dependence. Figures adapted with courtesy from [30a].

Detailed analysis within the framework of dynamic force spectroscopy yielded no significant

loading-rate dependence (Fig. 12.16c), similar to the results for cyclodextrin complexation or the

homophilic pyrimidine bonding. This finding would indicate that the time scale of the π-π-

interaction is much faster than the timescale of the SMFS experiment, therefore quasi-

equilibrium conditions apply.

12.3.6 Metal-Ligand Interactions It is worth to focus in this paragraph on metal-ligand interactions since this interaction facilitates

fascinating metallosupramolecular systems that can be very stable. As AFM-SMFS requires

robust and reliable immobilization of the molecular building building blocks, these experiments

are of fundamental as well as of preparative interest. In 2006 Craig and co-workers [26] studied

the interaction in square-planar Pd(II) pincer complexes (Fig. 12.17) that have been employed as

connecting units in supramolecular polymers. An interesting feature of such complexes between

Pd(II) pincer complexes and e.g. bipyridines is that they can exhibit very similar equilibrium

constants, while their ligand dissociation kinetics differs by two orders of magnitude. As a

consequence the kinetics of ligand exchange reactions on the metal centre can be controlled

while keeping the thermodynamics nearly constant by variations of the pyridine compound or the

steric requirements of substituents on the spectator ligand.

In order to realize SMFS experiments on this binding motif, pyridine ligands were attached to

Si3N4-cantilevers and SiO2-substrates functionalized with amino groups by silanization with

(3-aminopropyl) triethoxysilane (Fig. 12.18a). Therefore, the commercially heterobifunctional

PEG linker NHS-PEG-Fmoc with one protected amino group and one amino-reactive carboxyl

group was immobilized at the surface. After deprotection of the amine, coupling of the pyridyl

groups was finally realized by amidation reaction.

The AFM-SMFS experiment was carried out in DMSO containing 0.86 mM of the bis-Pd(II)-

complex (Fig. 12.18b). When the cantilever was in contact with the substrate, pyridyl groups

coordinated to the same bis(palladium(II)) complex.

Fig. 12.17. Metal ion mediated Pd2+ pincer complexes studied in SMFS experiments. Figure adapted with courtesy from [26].

Fig. 12.18. (a) Immobilization of the pyridyl ligands to the cantilever and the substrate. (b) Molecular structure of the bis-Pd(II)-complex.

Characteristic AFM-SMFS force-distance curves were obtained, containing a non-linear regime

due to the stretching of the two PEG linkers until the coordination bond dissociate at extensions

>40 nm (Fig. 12.19a). The specificity of the interaction was verified in two control experiments.

In the absence of bis-Pd(II)-complex, only non-specific interactions between pyridine

functionalized cantilever and substrate at tip-surface distances >25 nm due to the stretching of

single PEG chains were observed. In the second control experiment, 100 mM of

4-(dimethylamino)-pyridine added to the DMSO solution efficiently reduced the binding activity

by blocking the free coordination sites of the bis(Pd(II))-complex.

In dynamic force spectroscopy experiments, the loading rate dependence of the dissociation

forces was evaluated for coordination with the pyridyl ligand (PL) as well as its 4-amino-

substituted pyridyl ligand (4A-PL) to the bis(Pd(II))-complex (Fig. 12.19b). In both cases, the

dissociation forces increase with the loading rate in full consistency with thermally driven

dissociation KBE-theory. While the slope of the two f* vs. ln(r) plots is nearly identical (Fig.

12.19b), considerably larger (≈ + 50 pN) dissociation forces are observed for the 4-amino-

substituted pyridyl ligand. Analysis of the data according to KBE-theory yielded a molecular

reaction length of xβ= 0.19 nm and xβ= 0.17 nm for 4A-PL and PL, respectively.

Fig. 12.19. (a) Representative AFM-SMFS force-distance curve of Pd2+-pincer complexes. (b) Dynamic force spectroscopy plot of the measured dissociation forces vs ln(r) for 4A-PL (blue dots) and PL (red rhombs). (c) Suggested scheme of the complexation mechanism. Figures adapted with courtesy from [26].

The thermal off-rate constants were determined to be 1.4 s-1 and 40 s-1 for 4A-PL and PL,

respectively. Taking into account the proportional increase of the dissociation rate constant with

the number of consecutive bonds, dissociation rate constants of koff0 = 0.7 s-1 for 4A-PL and

koff0 = 20 s-1 for PL can be reasoned. These values are in excellent agreement with koff

0 = 1 s-1 for

4A-PL and koff0 = 17 s-1 for PL as determined in dynamic NMR experiments. In the absence of

external forces, the ligand exchange reaction in square planar Pd(II) complexes is assumed to

proceed via an associative mechanism including a five-coordinate transition state geometry (Fig.

12.19c). Although the exact reaction pathway is to date unknown, AFM force spectroscopy

experiments allow insights into the binding energy landscape. For this complexation reaction

differences between stress-free and mechanically activated reactions were considered to be low

due to agreement with the results of the ensemble measurements as well as almost identical

molecular reaction length. The latter statement is supported by the homologous substitution

reactions potential energy surface of the substitution reaction without an external force (upper

curve) and in the force spectroscopy experiment (lower curve) as presented in Fig. 12.19c.

12.3.7 Supramolecular Mesoscale Systems: Reversible Polymers In the following we would like to concentrate on supramolecular mesoscale systems whose size

and architectural complexity goes beyond the one of dimeric ligand-mediated systems. One of

the driving forces to synthesize and investigate (supramolecular) polymers is the possibility to

rationally design artificial and/or biomimetic polymers in order to develop meso- and macroscale

systems with dedicated mechanochemical properties with respect of flexibility, tensile strength,

fracture resistance, and elasticity.

Fig. 12.20. (a) Schematic Ig-multidomain structure of titin. (b) Supramolecular UPy-polymer mimicking the titin mechanochemistry. (c) UPy dimer modules (blue) with flexible PTMG-linker (green). Figures adapted with courtesy from [23].

In several studies, supramolecular non-covalent polymers (also called: reversible polymers)

based on the UPy motif were investigated in AFM-SMFS experiments by Guan et al [23] as well

as by the Vancso group at University of Twente (see also paragraph 3.4) [20b,c].

In the first experiment, a novel biomimetic modular polymer was designed in order to mimic the

immunoglobulin-like (Ig) multidomain mechanical unfolding pathway of the giant muscle

protein titin (Fig. 12.20a) [5]. This was achieved by connecting modular polymer domain where

the hydrogen-linked UPy motif was incorporated that was additionally stabilized by a PTMG

loop (Fig. 12.20b,c). AFM-SMFS stretching experiments in toluene at room temperature

revealed the sequential unfolding of the stabilizing loops during chain stretching where the

applied external mechanical force caused the UPy bonds to break, which manifests itself as a

saw-tooth force pattern (Fig. 12.21a). This behavior was previously known from AFM and

optical tweezers SMFS experiments on titin and marked an impressive development along the

framework of reverse engineering and biomimetics.

Fig. 12.21. (a) Single chain force-extension curves of UPy supramolecular polymer exhibiting a saw-tooth pattern of sequentially breaking loop domains very similar to titin unfolding. (b) Saw-tooth force-extension curve that was fitted with WLC polymer elasticity model. Figures with courtesy from [23].

It will be fascinating to pursue if and how the rational molecular design and synthesis of

multidomain polymer materials will allow to develop novel materials for particular applications

in biotechnology and biomedicine.

In the second series of experiments, the properties of noncovalently UPy linked supramolecular

polymers were quantitatively investigated in HD at room temperature with respect of the

measured length distribution of the reversibly aggregating system, the determination of the

corresponding equilibrium dimerization constant, and the dependence on external factors like

temperature, building block concentration and the role of further, stimuli-responsive additives in

solution.

Thus, bis-UPy end-functionalized PEG moieties were used as the polymeric building blocks for

the AFM-SMFS experiments. Gold coated AFM cantilever and substrate were functionalized as

shown in Fig. 12.22a. While the UPy group was immobilized at the substrate via a PEG linker,

the gold coated AFM tip was functionalized with UPy directly via disulfides. In AFM force-

distance curves obtained in HD in the absence of the bis-UPy PEG derivative, only dissociation

events expected for dimers composed of substrate- and cantilever-immobilized UPy groups were

observed (Fig. 12.22b). Upon fitting the measured molecular elasticity curve with a modified

FJC model, a Kuhn length of 0.65 nm, a segment elasticity of 6.2 nN·nm-1, as well as rupture

distances between 8 nm and 18 nm, corresponding to the length of the employed PEG linker

were determined. The formation of supramolecular polymers in solution was successfully

followed in situ, when 1·10-3 M of the bis-UPy PEG derivative X was added. Here, the

distribution of tip-substrate rupture distances significantly shifted due to formation of

supramolecular polymer chains towards larger values (Fig. 12.22c) ranging from 20 nm to

>150 nm. Upon considering the length of the single “monomer” bis-UPy PEG to be ~12 nm, a

degree of polymerization of up to 15 monomeric units was obtained. However, the “degree of

polymerization” determined in this AFM study was lower than the values obtained from

experiments in solution, probably due to surface effects.

Furthermore, for the supramolecular polymers several quantitative differences compared to the

results of the probed dimers apply and could be verified:

1) The mean value of the measured dissociation forces of the long supramolecular polymers (f*

= 119 pN) were slightly smaller than the ones for the dimers (f* = 104 pN) in full consistency

with the KBE-theory applied to longer polymers of that fail uncooperatively under load [36].

2) Whereas the rupture length probability distribution for dimers is rather short range and well

defined (8-18 nm), the corresponding length histogram for supramolecular polymers ranges up to

200 nm decaying exponentially with length.

Fig. 12.22. (a) Schematic representation of the single-molecule force spectroscopy experiment on the supramolecular polymer. (b) Representative force-distance curve measured at 301 K. (c), (d) Histogram of the rupture length observed in the presence of 1·10-3 M X in hexadecane (c) and in 15 % DMSO in 2-propanol (d). (e) Dependency of the dissociation force on the number of simultaneously loaded consecutive supramolecular bonds. Figures adapted with courtesy from [20b,c].

3) Considering 1) and 2), a graph combining measured rupture forces with rupture lengths can be

plotted where the length parameter can be downscaled to the number of involved monomers N

(Fig. 12.22c,d, insets). A relation of the measured supramolecular polymer dissociation forces

f*(N) with polymer length (under fixed loading rate rf) and therefore monomer number N can be

formulated as a consequence of a modified KBE-theory by Evans and Williams [36] and put into

correlation with the dissociation force f*sm of a single monomer (see also Tutorial 12.1):

sm*( ) ln( ) ln( ) * ln( )B Bf

k T k Tf N r N f Nx xβ β

= ⋅ − = − ⋅

eq. 12.3

From this analysis the following thermodynamic suprapolymer properties like kinetic off-rate

constant koff(0) = 0.25 s-1, dimerization equilibrium constant K = 1.3·109 M-1 and Gibbs´ free

energy ΔG = 52 kJ/mol could be derived at a fixed and constant loading rate (eq. 12.3).

4) The formation of longer suprapolymers was found to critically depend on the chosen solvent.

Whereas in apolar HD long polymers could be formed, polymerization in polar DMSO was

strongly suppressed (Fig. 12.22d) and proves that AFM-SMFS can distinctively give information

on the role of stimuli-responsive additives or the environment itself.

12.3.8 Supramolecular Mesoscale Systems: Capsules AFM-SMFS can also be applied to such complex structures as supramolecular capsules [21].

Tailor-made building blocks with a high degree of preorganization bearing functional groups at

defined positions are required to allow spontaneous self-assembly of these three-dimensional

aggregates. The heterodimeric aggregate introduced by Kobayashi et al. in the year 2003 [37] is

formed by the highly selective association of two cavitands: one bears four carboxylic acid

groups and the second is functionalized with four pyridyl groups (Fig. 12.23). The two halves of

the supramolecular capsule are connected by four hydrogen bonds between those.

Fig. 12.23. Formation of the hydrogen bonded supramolecular capsule based on tetra(carboxyl)cavitand (AFM-cantilever) and tetra(pyridyl)cavitand (surface). Figures adapted with courtesy from [21].

Fig. 12.24. Surface functionalization. (a) Immobilization of the tetra(carboxyl)cavitand to the AFM cantilever. (b), (c) Incorporation of the tetra(pyridyl)cavitand in a SAM (b) and in a mixed SAM (c) on gold. Figures adapted with courtesy from [21].

Guest ligands like 1,4-disubstituted benzenes are encapsulated and contribute significantly to the

stability of the aggregate. To analyze the capsule bonding by AFM-SMFS at room temperature

in p-xylene, modified building blocks have been immobilized on AFM Si3N4-cantilevers and

gold substrates. For this purpose, a tetra(carboxyl)cavitand (TCC) with acid-labile protected

carboxylic acid groups has been synthesized and coupled to a PEG linker with a free carboxylic

acid group (Fig. 12.24a). This cavitand was attached to the AFM cantilever functionalized with

(3-aminopropyl)-triethoxysilane via amidation reaction. Residual free amino groups were

blocked using N-hydroxysuccinimide acetoacetate. To cleave the protective groups and set free

the four carboxylic acid groups at the cavitand, the cantilevers were treated with formic acid. To

immobilize the tetra(pyridyl)cavitand (TPC), four dialkylsulfides were attached to the molecule

facilitating the formation of self-assembled monolayers on gold substrates (Fig. 12.24b,c). In

initial force spectroscopy experiments, multiple interactions between the TCC functionalized

AFM tip and the TPC functionalized surface were detected (Fig. 12.25a). In each force-distance

curve, strong adhesions were observed with several consecutive force steps indicating the

dissociation of more than one supramolecular capsules. In order to decrease the concentration of

the capsules´ building blocks on the surface, mixed self-assembled monolayers of didecylsulfide

and the TPC on gold were prepared. Because the binding activity can simply be adjusted by

finding the ideal fraction of the dialkylsulfide that essentially blocks the surface while keeping

the SAM intact, this is a rather general strategy that can be employed to realize single-molecule

force spectroscopy experiments. Fig. 12.25b,c shows two typical force-distance curve obtained

using a SAM containing a fraction of 1:100 of the TPC and didecylsulfide. In contrast to the

multiple dissociation events detected before, the results on the diluted SAM are markedly

different. The form of the typical force-distance curve (Fig. 12.25c) shows the features of a

single PEG chain being stretched until the supramolecular capsule formed by a TCC

immobilized at the cantilever and a TPC on the substrate dissociates. Plotting the dissociation

forces in a force histogram, a typical distribution that can be fitted with a Gaussian distribution

was obtained. The selectivity of the interaction was verified in control experiments, where excess

of free TCC in the solution efficiently blocked complex formation between cantilever-bound

TCC and TPC immobilized at the substrate (Fig. 12.25d,e).

Detailed information on the kinetics of heterodimeric capsule formation and the stability of the

aggregate for room temperature in p-xylene were obtained in dynamic force spectroscopy

experiments (Fig. 12.25f). Most probable dissociation forces ranging from 39 pN at 200 pN·s-1 to

71 pN at 12·103 pN·s-1 were observed. Evaluation of the data according to the KBE-model

yielded koff0 = 0.14 s-1, corresponding to an average complex lifetime of 7.3 s, and a reaction

length of xβ = 0.56 nm. In future experiments, the contribution and consequences of encapsuled

guest molecules and change of the solvent environment will be investigated in more details and

allow correlation of microscopic molecular architectures with meso- and macroscopic properties.

Fig. 12.25. (a), (b), (c) Typical force curves detected in force spectroscopy measurements on an undiluted (a) and a diluted (b, c) SAM of the TPC. (d) Dissociation force histogram and Gaussian fit to the distribution. (e) Control Experiment: Addition of free TCC results in a strongly reduced binding activity. (f) Dynamic force spectroscopy plot of the most probable dissociation forces vs ln(r). Figures adapted with courtesy from [21].

12.3.9 Supramolecular Mesoscale Systems: Calixarene-Catenane Polymers Last but not least, Janshoff and coworkers presented in 2009 a hallmark study of a sophisticated

architecture with so far the highest complexity at the supramolecular scale [22]. They

synthesized and investigated in AFM-SMFS experiments individual oligo calix[4]arene catenane

polymers containing hydrogen bonded tetra(urea)calix[4]arene dimers. In this supramolecular

oligomer, the halves of the calixarene nanocapsules are additionally connected and topologically

interlocked via flexible alkyl linkages in catenanic architecture. Thus, the individual building

blocks of the capsule can not be separated after dissociation, are held in place and permit the

reversible rupture and rejoining of the individual capsules. Thereby, the disruption and rejoining

of identical supramolecular bonds could be followed in stretching experiments on this Fig. 12.26

shows the elegantly designed structure.

Fig. 12.26. (a) Molecular structure and (b) schematic representation of the oligo calix[4]arene catenane – calix[4]arene capsules. (c) Functionalization strategy of the gold-coated cantilever and (d) the substrate. Figures adapted with courtesy from [22].

To investigate the rupture and rejoining of these hydrogen bonded nanocapsules in single chain

stretching experiments, gold coated cantilevers were functionalized with dithio bis(succinimidyl

undecanoate) (Fig. 12.26c). A SAM of trimethylammonium undecanethiol was used as a

positively charged substrate.

In the AFM measurements, immobilization of the supramolecular oligomer on the substrate was

realized by electrostatic interaction of the dissociated carboxylic acid group. A solution

containing 1 % triethylamine in mesitylene was used as medium. When the activated cantilever

was brought into contact with the substrate during the experiment, covalent anchoring of the

amino group of the supramolecular oligomer to the cantilever proceeds via amidation of the NHS

groups at the surface of the AFM tip. Upon retracting the cantilever, the oligomeric system was

stretched and the hydrogen bonded supramolecular capsules consecutively dissociate, while the

covalent linkages of the capsules halves stayed intact (Fig. 12.27a). In the corresponding force-

distance curves, characteristic sawtooth patterns were observed that were attributed to the

disruption of the hydrogen bonded capsules, similar to the results given in paragraph 3.7 (Fig.

12.27b).

A detailed investigation of the experimental data revealed, that a second process contributes to

the characteristic curve form. Molecular dynamics simulations were able to show, that the

extension of the covalent linkages can proceed via a sterically locked conformation. In Fig.

12.27d the calculated structures of three states during the force spectroscopy experiment is

shown. Whereas in the initial state the unstretched molecule contains the intact hydrogen bonded

capsule, in the second structure, the hydrogen bonds are already dissociated. Here, further

separation of the capsules´ halves is prevailed due to the sterically locked conformation.

Overcoming of this internal barrier results in distinct force steps in the force-distance curves

upon stretching the oligomeric system (Fig 12.27c, e, f). On the one hand, careful analysis of the

curves is required to identify forces that result purely on the dissociation of the hydrogen bonded

capsules and to extract quantitative information on the stability of the hydrogen bonded capsule.

On the other hand, these results impressively shows that single molecule experiments can

provide detailed information on energy landscapes not accessible by ensemble measurements.

One of the most intriguing facts of the force spectroscopy experiment on this complex system is

the behaviour of the expanded oligomer upon relaxation. During the approach of the AFM tip

towards the substrate, pronounced force plateaus are observed in the force-distance curves (green

line in Fig. 12.28a). This can be attributed to the rejoining of the hydrogen bonded capsules

disrupted when the cantilever was retracted from the surface. Fig. 12.28b summarizes the results

of dynamic force spectroscopy experiments.

Fig. 12.27. (a)Scheme of the AFM force spectroscopy experiment. (b) Force-distance curve recorded while stretching the oligo calix[4]arene catenane – calix[4]arene dimers. (c) Length increase ΔL with time obtained from molecular dynamics simulation of a single separation process. (d) Structures of one calix[4]arene dimer during extension obtained from molecular dynamics simulations. Hydrogen bonds in the intact capsule are highlighted by black lines, while the dotted lines indicate the dissociated hydrogen bonds. (e), (f) Histogram of length jumps ΔL during the stretching experiment (1500 pN/s) (e) and the simulations (f). Figures adapted with courtesy from [22].

With decreasing loading rates, the forces observed upon stretching and relaxing the oligomer

converge, indicating that the system reaches the quasi-equilibrium regime. When the retract

velocity is small enough, rebinding of the dimers can even be observed while stretching the

molecule. Therefore, the oligo calix[4]arene-calix[4]arene dimer is an excellent model system to

study barrier crossing ranging from quasi-equilibrium to non-equilibrium bond breakage upon

external force. These breathtaking results indicate that single-molecule force spectroscopy on

tailor-made supramolecular structures can be ground-breaking to study non-equilibrium and

equilibrium processes and verify modern theories of non-equilibrium statistical mechanics.

Fig. 12.28. (a) Force-distance curves of successive retract-approach cycles at r = 300 pN/s. Stretching curves are green, relaxation curves are coloured in green. (b) Results of loading rate-dependent experiments. Plot of the mean rupture (blue boxes) and rejoining (green dots) forces vs ln(r). Figures adapted with courtesy from [22].

12.4 Summary and Outlook The investigation of interactions between single molecules and the manipulation of structures on

the molecular scale is an interdisciplinary task. Although commercial atomic force microscopes

are readily available, exploiting the entire potential of these instruments requires detailed

knowledge and experience. On the other hand, a general understanding of chemical issues, the

synthesis of tailor-made molecules and the preparation of specifically functionalized surfaces are

just as important for successful experiments. But as diverse the requirements are, as multifaceted

are the topics that can be addressed with this technique. The presented examples show that the

binding in complexes with a wide range of affinities can be studied and dynamic processes as

optomechanical switching can be followed. Furthermore, stabilities of supramolecular binding

motifs can be investigated and structures composed of many subunits studied. With increasing

complexity of the analyzed structures, it is increasingly challenging to extract information from

the force distance curves and interpret the experimental data along the framework of

mechanochemistry and statistical mechanics. But the true power of following individual

molecules becomes obvious.

There are a multitude of research areas that might get essential progress by the information

accessible from single-molecule force spectroscopy experiments. Fundamental questions of

theoretical physics might be addressed in studies on sophisticated supramolecular structures.

SMFS experiments on simple model complexes can help to develop mathematical models for

macroscopic processes as adhesion, mechanical wear and (biological) recognition events. The

impact of forces on interactions between the building blocks of (large) non-covalently linked

aggregates, dynamic systems, chemical reactions and connections between surfaces mediated by

supramolecular interactions is already under investigation. In the general view, single molecule

force spectroscopy connects characteristic parameters of the macroscopic and the molecular

world. Thereby, this technique helps to diminish the borders between both – spatial and temporal

- dimensions and to develop a deeper understanding of processes on the molecular scale.

Supramolecular chemistry is closely linked to various research areas as macromolecular

chemistry, material science and the development of nanoarchitectures. In all of these disciplines,

AFM and related SPM methods presented by Bianca A. Herrmann and Regina Hoffmann in this

book provided fascinating results and major achievements. If single-molecule force spectroscopy

is used completely integrated in the set of these other techniques, rich information on

supramolecular principles and structures is accessible.

Acknowledgements The authors acknowledge support from the Collaborative Research Center SFB 613 from the

Deutsche Forschungsgemeinschaft (DFG) and valuable input and contributions from Rainer

Eckel, Björn Decker, Christian Schäfer, Robert Ros, Christoph Pelargus, Thomas Geisler, Björn

Schnatwinkel and Katja Tönsing.

12.5 References [1] J.-M. Lehn, Angew. Chem. Int. Ed., 1988, 27, 89-112. b) J.-M. Lehn, Science, 1993, 260,

1762-1763.

[2] S. B. T. Nguyen, D.L. Gin, J. T. Hupp, X. Zhang, Proc. Natl. Acad. Sci. USA, 2001, 98,

11849-11850.

[3] E. Fischer, Ber. Deutsch. Chem. Ges., 1894, 27, 2985-2993

[4] A. Werner, Zeitschr. Anorg. Chem., 1893, 3, 267-330

[5] M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez, H. E. Gaub, Science, 1997, 276, 1109-

1112

[6] E.-L. Florin, V. T. Moy, H. E. Gaub, Science, 1994, 264, 415-417. b) G. U Lee, L. A.

Chrisey, R. J. Colton, Science, 1994, 266, 771-775. c) U. Dammer, O. Popescu, P. Wagner,

M. Dreier, D. Anselmetti, H.-J. Güntherodt, G.N. Misevic, Science, 1995, 267, 1173-1175.

[7] M. Grandbois, M. Beyer, M. Rief, H. Clausen-Schaumann, H. E. Gaub, Science, 1999,

283, 1727-1730.

[8] S. Zou, H. Schönherr, G. J. Vancso, Atomic Force Microscopy-Based Single-Molecule

Force Spectroscopy of Synthetic Supramolecular Dimers and Polymers. In: P. Samorì (ed.)

Scanning Probe Microscopies Beyond Imaging: Manipulation of Molecules and

Nanostructures, Wiley-VCH, Weinheim 2006.

[9] R. Barratin, N. Voyer. Chem. Commun., 2008, 1513-1532.

[10] H. Takano, J. R. Kenseth, S.-S. Wong, J. C. O´Brien, M. D. Porter, Chem. Rev., 1999, 99,

2854-2890.

[11] R. Ros, F. Schwesinger, D. Anselmetti, M. Kubon, R. Schäfer, A. Plückthun, L.

Tiefenauer, Proc. Natl. Acad. Sci. USA, 1998, 95, 7402-7405.

[12] Y. Lyubchenko, L. Shlyakhtenko, R. Harrington, P. Oden and S. Lindsay, Proc. Natl.

Acad. Sci. USA, 1993, 90, 2137-2140.

[13] A. Ebner, P. Hinterdorfer, H. J. Gruber, Ultramicroscopy, 2007, 107, 922-927.

[14] a) C. D. Frisbie, L. F. Rozsnyai, A. Noy, M. S. Wrighton, C. L. Lieber, Science, 1994, 265,

2071-2074. b) R. C. Thomas, P. Tangyunyong, J. E. Houston, T. A. Michalske, R. M.

Crooks, J. Phys. Chem., 1994, 98, 4493-4494 .

[15] D. Krüger, H. Fuchs, R. Rousseau, D. Marx, M. Parinello, Phys. Rev. Lett., 2002, 89,

186402.

[16] a) L. Schmitt, M. Ludwig, H. E. Gaub, R. Tampé, Biophys. J., 2000, 78, 3275-3285.

[17] P. Hinterdorfer, W. Baumgartner, H. J. Gruber, K. Schilcher, H. Schindler, Proc. Natl.

Acad. Sci. USA, 1996, 93, 3477-3481.

[18] a) S. B., Smith, Y. Cui, C. Bustamante, Science, 1996, 271, 795-799. b) M. Rief, F.

Oesterhelt, B. Heymann, H. E. Gaub, Science, 1997, 275, 1295-1297.

[19] a) O. Kratky, G. Porod, Rec. Trav. Chim. Pays-Bas., 1949, 68, 1106-1123. b) M. Doi, S.F.

Edwards, The Theory of Polymer Dynamics. Oxford University Press 1999. c) C. Bouchiat,

M. D. Wang, J. F. Allemand, T. Strick, S. M. Block, V. Croquette, Biophys. J., 1999, 76,

409-413.

[20] a) S. Zou, H. Schönherr, G. J. Vancso, J. Am. Chem. Soc., 2005, 127, 11230-11231. b) S.

Zou, H. Schönherr, G. J. Vancso, Angew. Chem. Int. Ed., 2005, 44, 956-959; c) A.

Embrechts, H. Schönherr, G. J. Vancso, J. Phys. Chem. B, 2008, 112, 7359-7362.

[21] T. Schröder, T. Geisler, V. Walhorn, B. Schnatwinkel, D. Anselmetti, J. Mattay, Phys.

Chem. Chem. Phys., 2010, 12, 10981-10987.

[22] M. Janke, Y. Rudzevich, O. Molokanova, T. Metzroth, I. Mey, G. Diezemann, P. E.

Marszalek, J. Gauss, V. Böhmer, A. Janshoff, Nature Nanotech., 2009, 4, 225-229.

[23] Z. Guan, J. T. Roland, J. Z. Bai, S. X. Ma, T. M. McIntire, M. Nguyen, J. Am. Chem. Soc.,

2004, 126, 2058-2065.

[24] a) H. Schönherr, M. W. J. Beulen, J. Buegler, J. Huskens,F. C. J. M. van Veggel, D. N.

Reinhoudt, G. J. Vancso, J. Am. Chem. Soc., 2000, 122, 4963-4967: b) S. Zapotoczny, T.

Auletta, M. R. de Jong, H. Schönherr, J. Huskens, F. C. J. M. van Veggel, D. N.

Reinhoudt, G. J. Vancso, Langmuir, 2002, 18, 6988-6994: c) T. Auletta, M. R. de Jong, A.

Mulder, F. C. J. M. van Veggel, J. Huskens, D. N. Reinhoudt, S. Zou, S. Zapotoczny, H.

Schönherr, G. J. Vancso, L. Kuipers, J. Am. Chem. Soc., 2004, 126, 1577-1584.

[25] a) R. Eckel, R. Ros, B. Decker, J. Mattay, D. Anselmetti, Angew. Chem. Int. Ed., 2005, 44,

484-488. b) C. Schäfer, R. Eckel, R. Ros, J. Mattay, D. Anselmetti, J. Am. Chem. Soc.,

2007, 129, 1488-1489. c) C. Schäfer, B. Decker, M. Letzel, F. Novara, R. Eckel, R. Ros,

D. Anselmetti, and J. Mattay, Pure Appl. Chem., 2006, 78, 2247-2259. d) D. Anselmetti,

F.W. Bartels, A. Becker, B. Decker, R. Eckel, M. McIntosh, J. Mattay, P. Plattner, R. Ros,

C. Schäfer, and N. Sewald, Langmuir, 2008, 24, 1365-1370.

[26] F. R. Kersey, W. C. Yount, S. L. Craig, J. Am. Chem. Soc., 2006, 128, 3886-3887.

[27] F. Kienberger, G. Kada, H. J. Gruber, V. P. Pastushenko, C. Riener, M. Trieb, H.-G.

Knaus, H. Schindler, P. Hinterdorfer, Single Mol., 2000, 1, 59-65: b) M. Conti, G. Falini,

B. Samori, Angew. Chem. Int. Ed., 2000, 39, 215-218. c) C. Verbelen, H. J. Gruber, Y. F.

Dufrêne, J. Mol. Rec., 2007, 20, 490-494.

[28] M. Kudera, C. Eschbaumer, H. E. Gaub, U. S. Schubert, Adv. Funct. Mat., 2003, 13, 615-

620.

[29] a) C. Ray, J. R. Brown, B. B. Akhremitchev, J. Phys. Chem. B, 2006, 110 , 17578-17583.

b) C. Ray, J. R. Brown, A. Kirkpatrick, B. B. Akhremitchev, J. Am. Chem. Soc., 2008, 130,

10008-10018.

[30] a) Y. Zhang, C. Liu, W. Shi, Z. Wang, L. Dai, X. Zhang, Langmuir, 2007, 23, 7911-7915.

b) Y. Zhang, Y. Yu, Z. Jiang, H. Xu, Z. Wang, X Zhang, M. Oda, T. Ishizuka, D. Jiang, L.

Chi, H. Fuchs, Langmuir, 2009, 25, 6627-6632.

[31] a) H. Skulason, C. D. Frisbie, J. Am. Chem. Soc., 2002, 124, 15125-15130. b) R. Gil, M.-

G. Guillerez, J.-C. Poulin, E. Schulz, Langmuir, 2007, 23, 542-548.

[32] J. Fritz, A. Katopodis, F. Kolbinger and D. Anselmetti, Proc. Natl. Acad. Sci. USA, 1998,

95, 12283-12288.

[33] R. Merkel, P. Nassoy, A. Leung, K. Ritchie, E. Evans, Nature, 1999, 397, 50-53.

[34] V. Walhorn, T. Schröder, J. Mattay, and D. Anselmetti, in preparation (2011).

[35] R. P. Sijbesma, F. H. Beijer, L. Brunsveld, B. J. B. Folmer, J. J. K. K. Hirschberg, R. F. M.

Lange, J. K. L. Lowe and E. W. Meijer, Science, 1997, 278, 1601-1604.

[36] E. Evans, P. Williams, Dynamic force spectroscopy: I. single bonds, in: H. Flyvbjerg, F.

Jülicher, P. Ormos, F. David (eds.) Physics of Bio-Molecules and Cells. Springer 2002.

[37] K. Kobayashi, K. Ishii, S. Sakamoto, T. Shirasaka and K. Yamaguchi, J. Am. Chem. Soc.,

2003, 125, 10615–10624.

Tutorial 12.1 Single Molecule AFM Force Spectroscopy and Statistical Data Analysis

With single molecule AFM force spectroscopy (SMAFMFS) it is possible to detect and quantify

the specific dissociation forces between individual molecules under in vitro conditions.

Nowadays, AFM-SMFS is capable to render quantitative insights into intra- and intermolecular

binding phenomena in a very broad affinity range of 10-4 – 10-15 M at a sensitivity level of single

point mutations. Moreover, as a label-free technology AFM-SMFS is also capable of measuring

binding phenomena between rather small molecules (of low molecular mass) as well as

molecules with a considerable molecular mass difference.

Typical intermolecular dissociation forces (which can also be termed as recognition forces) are

within the range of 40-200 pN and can nicely be accessed and investigated with atomic force

spectroscopy using soft cantilevers. The two molecular binding partners have to be immobilized

and covalently bound to either the AFM tip and the surface. In order to first let the molecules

associate, AFM tip and surface will be approached and brought into contact. Upon withdrawing

the tip from the surface, a molecular binding event can be detected when the cantilever tip is

withheld at the surface. Approaching and withdrawing of the tip is investigated in a force-

distance curve (also termed as force cycle) as depicted in Fig. 1. There, the force acting on the

AFM tip is plotted against its vertical position (piezo extension), where a molecular dissociation

event can be identified by a sudden jump in the “attractive” force regime back to the curve at

zero force (F=0). In case a flexible polymer linker like PEG is used a typical nonlinear stretching

of the polymer chain that precedes the molecular dissociation can be discerned which reflects the

elasticity of the polymer chain and facilitates the detection and discrimination of a specific

dissociation event from unspecific binding. Unspecific tip-surface interactions occur closer to the

surface and can therefore be discriminated.

Since the process of molecular dissociation is of stochastic nature, many (typically hundreds)

individual force-distance curves have to be measured and combined in a force histogram (Fig. 2

Inset). The most probable dissociation force Fmax (maximum) is commonly referred to as

dissociation force and can be determined by fitting an appropriate distribution function (like a

Gaussian) to the measured force histogram.

The first theoretical description has been first published by Evans and Ritchie [1] who applied

the general picture of the Kramers-rate based Bell adhesion model to this nanobiological

dissociation problem with a ramped external force. Since the velocity of the tip in this active

force-induced dissociation process is relatively slow (compared to the Brownian motion of the

molecules) it can be described as a thermally activated decay with a force-dependent activation

energy. There, the theory predicted an increase of the observed dissociation forces with

increasing loading rate, as it could be verified in many single molecule experiments in the last

decade. Dissociation force Fmax, loading rate r, reaction length xβ, thermal energy kBT and off-

rate constant koff could be interrelated by the following equation:

BmaxoffB

k T x rF lnx k T k

β

β=

(1.1)

The dissociation force obviously depends logarithmically on the loading rate that is the product

of the experimental ramp speed v and the molecular elasticity keff (effective spring constant). The

latter can be estimated as a linear fit to the force-distance curve just before dissociation (Fig. 1).

The parameters xβ and koff can now be extracted by fitting the experimental Fmax – r data in a

semilogarithmic representation (Fig. 2). Whereas the reaction coordinate xβ represents the

distance between the minimum of the molecular binding potential and the transition state

(activation energy) and can therefore be interpreted as the depth of the binding pocket (energy

landscape), the off-rate constant is defined as a kinetic parameters in thermal equilibrium of a

molecular ensemble (mass action law). From a physical point of view, koff-1 = τ is the average

lifetime of the complex and gives information on the stability of the complex. Unfortunately, the

on-rate constant kon cannot simultaneously be accessed, which makes a determination of the

constant of equilibrium Kd = koff/kon or the binding energy Eb = kBT ln Kd difficult. However, in

the limit of a diffusion-controlled reaction, an estimate of kon = ksmol via the Smoluchowski

theory [2] is possible, allowing for a quantitative approach to determine Kd and therefore an

affinity ranking of the molecules involved. Here, ksmol = 4π R DSE NA , where R, DSE, NA denote

interaction distance, diffusion coefficient (Stokes-Einstein: DSE = kBT / 6 π η rprot) and Avogadro

number, respectively.

Ref:

[1] E. Evans and K. Ritchie, Biophys. J., 72, 1541-1555 (1997).

[2] M. Smoluchowski, Z. Phys. Chem. 92, 129 (1917)

Figure 1: Force response of a molecular guest host complex. After the cantilever is lifted from

the surface the flexible cross-linker is elongated. Further pulling increases the load on the bond

which is indicated by a typical force ramp. The dissociation of the bond is indicated by the snap

back of the cantilever. The dissociation Force F is estimated by the step height. The effective

elasticity keff the system (cantilever-crosslinker-molecular complex) can be evaluated by fitting

an appropriate function (here, second order polynomial, red plot) to force ramp and estimating

the slope at the point of dissociation. Inset: The dissociation forces of several unbinding events

are plotted in a histogram. The most probable unbinding force can be evaluated by an

appropriate fit (here, Gaussian distribution).

Figure 2: Force vs. loading-rate plots of two guest host systems with different affinity. The most

probable dissociation forces for several pulling velocities are plotted semi logarithmically versus

the loading-rate. The reaction length xβ and the off-rate constant koff are estimated by

approximation of equation (1.1) to the data.

Tutorial 12.2 Calibration of AFM Cantilever Force Sensors

The accuracy of single molecule force spectroscopy experiments highly depends upon the precise

knowledge of the force sensor’s elastic properties i.e. the spring constant k . Force sensors are

commonly made from silicon or silicon nitride in a series of lithography, etching and physical vapor

deposition (PVD) processes. Unfortunately inhomogeneities of the manufacturing process lead to slight

variations of the geometry or minute structural defects. Thus, the lever stiffness - even within the same

batch - can show significant deviations from the nominal spring constant [3, 4]. Moreover chemical

modification of the sensors prior to the experiment might have an unforeseeable influence on the

lever’s surface stress leading to a considerable shift of the force constant. Consequently, reliable, exact

and easy methods to evaluate k are needed.

Since the first nanomechanical experiments various procedures for estimating the cantilever stiffness

have been introduced. A straight forward approach is to calculate the spring constant from the levers

dimensions i.e. length l , width w , thickness t and the elastic properties of the material quantified by the

Young’s Modulus E . For a beam shaped lever with a rectangular cross section the spring constant can be

computed according to the following equation [1, 6].

3

3

E w tk4 l

= (1.1)

However, even for this very simple geometry this should only serve as a rough estimate. Actually many

soft levers are V-shaped with a wide variety of minute differences in detail (Fig. 1). Furthermore the

lever backsides are commonly coated with a reflection enhancing metal layer. Many simple models

neglect these details and should therefore merely provide as a rough validation for the calibration

routines. More elaborate approaches use finite element analysis (FEA) [8,9]. Nevertheless, the influence

of the lever’s chemical modification remains unrespected. Therefore it is inevitable to estimate the

spring constant of each lever prior to the experiment.

Here, we focus on the thermal fluctuation method that has been published in several variants 2, 4, 5, 6,

8, 9]. This approach bears several major advantages: The calibration procedure is non-destructive i.e.

the cantilever and the chemical modification are not spoiled while calibrating. No further equipment

than needed for force spectroscopy experiments is required. It is easy to implement in home-built AFM

setups. Besides it is also part of several commercial AFM control software packages.

In case of a small deflection x AFM cantilever force sensors show a spring like force response F as

depicted by Hooke’s Law in the following equation.

F k x= − (1.2)

Hence the cantilever can be described by the Hamiltonian of a harmonic oscillator.

2

20

p 1H m q2m 2

= + ω (1.3)

Where q and p are the displacement and the momentum respectively, m is the mass of the oscillator

and 0ω is the angular resonant frequency. Furthermore the resonant frequency can be expressed in

terms of k and m .

0km

ω = (1.4)

Cantilevers in ambient conditions or immersed in liquid are constantly bombarded by the thermally

driven molecules of the surrounding medium resulting in an oscillation of the lever. This fluctuation is

quantified by the mean square displacement noise 2q . In thermal equilibrium the equipartion

dissipation theorem states that the Energy of this thermally driven harmonic oscillator is equal to the

thermal Energy as stated in equation (1.5).

2 20 B

1 1m q k T2 2

ω = (1.5)

Where T is the temperature and Bk denotes the Boltzmann constant. Inserting equation (1.4) in (1.5)

and solving for the spring constant k leads to

B2

k Tkq

= (1.6)

In summary, apart from the temperature the only parameter that has to be measured is the mean

square displacement noise. This can be roughly estimated by solving equation (1.6) for 2q and using

the nominal spring constant: Given a cantilever with a force constant of Nm0.02 at room temperature (

294 K ) leads to a mean square displacement noise of 2 2q 0.2 nm= , which is equivalent to a root

mean square (RMS) deflection of approximately 0.45 nm . This thermal fluctuation is small; nevertheless

it can easily be estimated from the noise of the deflection signal of the free cantilever. However 2q is

hardly accessible from the time domain signal. For that reason it is transformed to the frequency

domain by Fourier transformation and 2q is estimated form the so called power spectral density

(PSD) or thermal power spectrum of the time domain signal q(t) . In brief: Due to the Nyquist Theorem

[7] q(t) is acquired with a sampling rate much higher than the expected lever resonant frequency. The

PSD of q(t) can be computed according to equation (1.7) by the squared absolute value of the Fourier

transformed time domain signal.

[ ]2

( i t )1PSD q(t) q(t) e dt2

∞− ω

−∞

=π ∫ (1.7)

The spectrum shows a pronounced peak at the Eigen or resonant frequency cω of the cantilever (Fig 2).

The area A under the resonant peak is proportional to 2q and can be estimated by a Lorentzian (Equ.

(1.8)) to the peak.

0 2 2c

2A wf ( ) y4( ) w

ω = +π ω − ω +

(1.8)

w and 0y are the peak’s width and offset respectively. Typically the cantilever amplitude is given in

Volts. Consequently, the unit of A is (Volt) 2. Hence a conversion factor often referred to as sensor

response or sensitivity zq

∂∂ has to be estimated. This is easily accomplished by evaluating the inverse

slope of a force distance plot in the contact regime (Fig 3). The mean square deflection of the cantilever

in meters is easily computed as follows:

( )22 zqq A ∂

∂= (1.9)

Finally the lever spring constant can be evaluated as given in equation (1.6).

Size Matters - The Choice of Cantilevers

SMFS experiments are performed in ambient condition, or most commonly in liquid media. Therefore

the force sensor is affected by the thermal motion of the surrounding molecules and the hydrodynamic

drag γ . lntroducing the friction in the equation of motion we get the Langevin equation:

q kq F(t)t

∂γ + =

∂ (1.10)

Where F(t) denotes the external random force caused by the thermal motion of the surrounding

medium. In the following section we will discuss the influence of γ on the force and temporal resolution

of the experiment. In addition we give a scheme of how to estimate and enhance the force and

temporal resolution of a SMFS assay.

As mentioned in the previous section, cantilevers experience a deflection due to the thermal motion of

the surrounding molecules. This fluctuation is quantified by the mean square displacement noise.

Therefore the evaluation of the force acting on the cantilever is subjected to an uncertainty that can be

quantified by the mean square force noise 2F :

2BF k k T= (1.11)

Hence, cantilevers with a low stiffness show a low force noise and should be therefore more sensitive,

resulting in a higher force resolution. However, the signal of the deflection sensor is proportional to the

cantilever displacement. According to equation (1.6) 2q can be estimated as follows

2 Bk Tqk

= (1.12)

Correspondingly the mean square deflection noise increases for low stiffness force sensors. This

apparent discrepancy solves when changing to the frequency representation. Expressing the PSD of the

deflection signal in terms of the angular resonant frequency cω and the hydrodynamic drag (c

kωγ =

(1.13) ) gives

( )2 B2 2c

2 k Tq( )

ω =γ ω + ω

(1.14)

The PSD quantifies the mean square deflection noise per unit frequency. lt occurs that these fluctuations

are not distributed homogeneously over all frequencies (Fig. 4). For low frequencies cω << ω the power

spectrum is approximately constant which is referred to as white noise. At high frequencies cω >> ω

the PSD falls off as 21

ω . Whereas the overall noise depends only on the spring constant, the spectral

distribution is governed by cω . The resonant frequency also defines the rate above which the force

sensor cannot respond to an external stimulus. lt is therefore an inherent limit for the speed at that

processes can be sensed and measured. For a beam shaped lever with rectangular cross section this can

be evaluated according the following equation:

c 2

1,02 E t2 l

ω =π ρ

(1.15)

Where E and t denote the Young's Modulus and the lever thickness respectively. ρ and l are the

lever's material density and length. For a given lever material cω depends only on the cantilever size.

As the resonant frequency is proportional to the inverse of the squared length, short cantilevers show a

preferable high resonant frequency. As the drag is intrinsically connected with the resonant frequency

(Equ. (1.13)), high cω levers show reduced viscous friction. When evaluating the spectral noise

distribution of two different cantilevers with the same spring constant but different resonant

frequencies significant differences in the spectral noise distribution can be found (Fig. 4) . For a

bandwidth well below the resonant frequency ( cB << ω ) the signal to noise ratio SN is evaluated by the

quotient of the measured force F and the square root of the spectral noise power times the bandwidth:

B

S FN 2 k T B

=γ

(1.16)

In a nutshell: Balancing the force and temporal resolution goes inherently along with the choice of the

appropriate force sensor. High cω levers in combination with narrow band low pass filtering allow the

observation of minute interactions due to low background noise. Using wide band low pass filters

alternatively very fast processes can be sensed. Typical resonant frequencies of commercial cantilevers

used in force spectroscopy applications are in the range of one to some ten kilohertz in air.

[1] BHUSHAN, B. (editor): Handbook of Nanotechnology. Springer, 2004

[2] BUTT, H.J., JASCHKE, M.: Calculation of thermal noise in atomic force microscopy. Nanotechnology 6

(1995), S. 1–7

[3] CLEVELAND, J.P., MANNE, S., BOCEK, Hansma, P. K. and Hansma H. D.: A nondestructive method for

determining the spring constant of cantilevers for scanning force microscopy. Rev Sci Instrum 64

(1993), S. 403–405

[4] HUTTER, J. L., BECHHOEFER, J.: Calibration of atomic-force microscope tips. Rev Sci Instrum 64 (1993),

S. 1868–1873

[5] LÉVY, R., MAALOUM, M.: Measuring the spring constant of atomic force microscope cantilevers:

thermal fluctuations and other methods. Nanotechnology 13 (2002), S. 33–37

[6] NEUMEISTER, J.M., DUCKER, W.A.: Lateral, normal and longitudinal spring constants of atomic force

microscopy cantilevers. Rev Sci Instrum 64 (1994), S. 2527–2531

[7] NYQUIST, H.; Certain topics in telegraph transmission theory. Trans. AIEE 47 (1928), S. 617

[8] SADER, J. E., LARSON, I., MULVANEY, P., WHITE, L.: Method for the calibration of atomic force

microscope cantilevers. Rev Sci Instrum 66 (1995), S. 3789

[9] STARK, R. W., DROBEK, T., HECKL, W. M.: Thermomechanical noise of a free v-shaped cantilever for

atomic-force microscopy. Ultramicroscopy 86 (2001), Jan, Nr. 1-2, S. 207–215

Figure 1: Commercial AFM force sensors.

Figure 2: PSD plot of a thermal fluctuating cantilever in ambient conditions (black dots). The plot is an

average of 200 spectra. The area under the peak A is evaluated by fitting a Lorentzian (red) to the data.

Figure 3: Force distance curve, showing the deflection of a force sensor as a function of the sample

movement (only retract plot shown). The slope of the contact regime qz

∂∂ is estimated by a linear fit.

Figure 4: Calculated noise power of two force sensors with a spring constant of N

m0.02 and resonant

frequencies of c1 1 kHzω = and c2 10 kHzω = respectively. The area under both curves is equal to

Bk Tk . B is the bandwidth of a low pass filter.