공학박사 학위논문

Control of Anisotropic Mechanical

Instabilities with Nanopatterned

Polymer Thin Films

나노패턴된 고분자 박막의

기계적 불안정성 조절에 관한 연구

2018년 2월

서울대학교 대학원

공과대학 화학생물공학부

권 도 경

Control of Anisotropic Mechanical Instabilities

with Nanopatterned Polymer Thin Films

나노패턴된 고분자 박막의 기계적 불안정성

조절에 관한 연구

지도 교수 차 국 헌

이 논문을 공학박사 학위논문으로 제출함

2018년 2월

서울대학교 대학원

공과대학 화학생물공학부

권 도 경

권도경의 공학박사 학위논문을 인준함

2017년 12월

위 원 장 (인)

부위원장 (인)

위 원 (인)

위 원 (인)

위 원 (인)

i

Abstract

Control of Anisotropic Mechanical

Instabilities with Nanopatterned

Polymer Thin Films

Dokyeong Kwon

School of Chemical and Biological Engineering

The Graduate School

Seoul National University

Mechanical instabilities in structured system arise when the structure is

subjected to various kinds of stresses which can make the structure lose integrity.

This aspect of engineering had been regarded as common failure in many systems,

and most of researches in the field had concentrated mainly on preventing

structural failures which can be catastrophic especially in many large-scale features.

However, when it comes to micro-and nano-engineering, there have been large

efforts to overcome or utilize mechanical instabilities. Particularly, after a few

pioneering studies to make simple mechanical instabilities useful, i.e. wrinkles,

folds, cracks, simple bilayer systems which are consisted of thin hard top film and

bottom soft elastomeric substrate have been spotlighted to a new method to

generate engineered patterns. Then the viewpoint for the mechanical instabilities to

make patterns have been widened to utilizing various top surfaces such as polymer

thin films, metal top coat, semiconducting material nanoribbons, etc. First efforts

ii

were concentrated on metallic top surfaces of which deposition is mainly done with

thermal deposition and also featured two dimensional wrinkles to form

herringbone-like or zig-zag structures which is due to isotropic nature of thermal

expansion/contraction. However, simple isotropic two-dimensional wrinkles were

difficult to provide useful features. To ensure functionality, researches on

anisotropic one-dimensional mechanical instabilities gained more interests.

Especially, wrinkled structures of metal nanoribbons or semiconductor nanoribbons

has gained keen interest because these structures opened a new possibility on

fabricating stretchable or bendable electronic devices. Furthermore, more various

applications utilizing wrinkling or buckling of bilayer systems were rigorously

studied to introduce optical gratings, microfluidic applications, anisotropic wetting,

dry adhesives and so on. Also, cracks emerging in bilayer systems with severe

stress gained attention for one method to make micropatterns. Efforts to utilize

these two-dimensional or one-dimensional mechanical instabilities for a new

micropatterning technique had been extended to simple mechanics of bilayer

systems.

In other sides, other than utilizing mechanical instabilities on patterning,

patterning on the top thin films can guide mechanical instabilities to form more

periodic or controlled structures. Particularly, the edge effect in buckling

mechanics is well known phenomenon and widely studied for various

micropatterns. The edge effect describes the importance of boundary condition on

the wrinkle formation of which size are comparable to the boundaries. Wrinkles

tend to form perpendicularly to the edge-cut boundaries, giving the ability to

engineer micropatterns with wrinkles. Also, researchers revealed that cracks can be

controlled in various systems. For example, making pre-cut or controlled notch can

iii

behave as seed for crack formation when tensile stress is applied to the system.

Other systems also can control formation of cracks, i.e. colloidal film systems, of

which formation can be tuned with heating rate, film thickness, etc. The key

criterion in the field of patterning with mechanical instabilities is to understand the

relationship between engineered patterns and patterns rising from mechanical

instabilities.

As the importance of patterning with mechanical instabilities increase with a

variety of applications, the structures of top surface have been of great importance.

For more sophisticated functionalities, manipulation with hierarchical structures

are usually considered as one powerful method. In case we develop hierarchical

structures with mechanical instabilities, the key criterion to control the system

should be the relationship between nanopatterns and mechanical instabilities.

However, this field of works lack systematic studies over various nanopatterns.

This is mainly due to the difficulty in formation of nanopattern-elastomeric

substrate bilayer system. Since our group have concentrated on control over

various hierarchical systems and their applications, we invented and developed a

few methods to form nanopattern-poly(dimethylsiloxane) (PDMS) bilayer systems.

This thesis demonstrates the systematic study on the formation and control of

hierarchical structures with nanopatterns and anisotropic microscale mechanical

instabilities. Various nanopatterns of line/space patterns, double prism patterns,

cylinder patterns are studied to investigate the relationship between nanopatterns

and wrinkles or cracks. Furthermore, anisotropic wetting application with

mechanical tuning is introduced to show functionality of hierarchical structure

based on anisotropic mechanical instabilities. More specifically, Chapter 1

introduces the concept and various applicable areas of mechanical instabilities in

iv

thin film-PDMS bilayer systems. Also, we introduce new transfer technique for the

transfer of nano or micropatterned polymer thin films onto PDMS substrate. And in

Chapter 2, we investigate wrinkling of films embedding anisotropic nanopatterned

surfaces prepared by nanoimprint lithography. We examine the anisotropic wrinkles

of well-defined nanolines with various widths, heights, and spacing ratios and

propose a model that considers only bending stiffness of the patterned film.

Chapter 3 describes wrinkled structures of other important nanopattern such as

hexagonal cylinder arrays or square cylinder arrays. The wrinkle micropatterns

with nanopatterned top surfaces behave totally differently from micropatterned top

surfaces and the two-dimensional stiffness parameters can be a way to describe the

phenomena. Finally, in Chapter 4 we present a mechanical method to manipulate

the anisotropy as well as the orientation of directional liquid flow by modulating

mechanical instabilities of UVO-treated PDMS system. Microscale wrinkles

resulted from compressive stress and cracks from tensile stress generate

hierarchical structures showing the change of the anisotropic liquid flow. We

demonstrate the mechanically responsive directional liquid flow and investigate the

behavior with the concept of critical contact angles to overcome ridges in step flow.

We believe this systematic study on mechanical instability-based hierarchical

structures can give a guide to the new strategies on manipulating patterns which

can be controlled with strains, and also widen the area of application using

mechanical instability driven structure based functionalities.

Keyword: Nanopattern, Mechanical Instability, PDMS, Wrinkle, Crack,

Hierarchical Structure

v

Student Number: 2011-22913

vi

Contents

Abstract.................................................................................................................. i

Contents....................................................................................................... v

List of Tables............................................................................................... ix

List of Figures.............................................................................................. x

Chapter 1. Introduction............................................................................. 1

1.1. Mechanical Instabilities with Thin Film......................................... 1

1.1.1. Definition and Classification of Mechanical Instabilities...... 1

1.1.2. Controlled Mechanical Instabilities for Micropattern

Fabrication........................................................................................ 5

1.1.3. Various Applications of Controlled Mechanical Instabilities..

7

1.1.4. Mechanical Instabilities with Micropatterned Top Films.......

7

1.2. Offset Polymer Film Printing...........................................................

9

1.2.1. Organosilicate Substrate with Sharp Interfaces for Polymer

Film Transfer................................................................................... 9

1.2.2. Polymer Offset Transfer Printing..........................................

12

vii

1.2.3. Offset Printing of Polymer Films onto Elastomeric Substrates

for Controlled Mechanical Instabilities.......................................... 14

1.3. References....................................................................................... 18

Chapter 2. Effect of the Orientation and Bending Stiffness of

Anisotropic Nanopatterned Films on

Wrinkles.......................................................... 26

2.1. Introduction...................................................................................

26

2.2. Experimental Section....................................................................

28

2.3. Results and Discussion.................................................................

30

2.3.1. Fabrication of Hierarchical Structure Based on Wrinkling of

Anisotropic Nanopatterned Polymer Film.....................................

30

2.3.2. Effect of Orientation and Structural Parameters of

Nanopatterns on Anisotropic

Wrinkle.................................................................. 36

2.3.3. Stiffness-Based Modeling of Anisotropic Nanopatterns in

Wrinkles......................................................................................... 38

2.4. Conclusions...................................................................................

45

viii

2.5. References.....................................................................................

46

Chapter 3. Anisotropic Wrinkling of Cylindrical Nanopatterned Films

.................................................................................................................... 49

3.1. Introduction...................................................................................

49

3.2. Experimental Section.....................................................................

51

3.3. Results and Discussion..................................................................

53

3.3.1. Formation of Anisotropic Wrinkles with Cylindrical Top

Patterns........................................................................................... 53

3.3.2. Effect of Strain Direction to Primitive Direction Vectors of

Cylindrical Arrays on Wrinkled Structures..................................... 57

3.3.3. Effect of Residual Layer Thickness of Cylindrically Patterned

Films on Wrinkled Structures.......................................................... 64

3.4. Conclusions.................................................................................... 66

3.5. References...................................................................................... 67

Chapter 4. Mechanoresponsive Anisotropic Wetting on Hierarchical

Patterns Based on Wrinkles and Cracks................................................ 70

4.1. Introduction....................................................................................

ix

70

4.2. Experimental Section.....................................................................

72

4.3. Results and Discussion.................................................................. 77

4.3.1. Flow Anisotropy Control on Hierarchical Patterns Based on

Wrinkles.......................................................................................... 77

4.3.2. Strain Dependent Critical Contact Angles of Hierarchical

Patterns Based on Wrinkles.............................................................

83

4.3.3. Flow Direction Control on Hierarchical Patterns Based on

Cracks.............................................................................................. 87

4.3.4. Strain Dependent Critical Contact Angles of Hierarchical

Patterns Based on Cracks................................................................

92

4.3.5. Simplified Model of Cracks and Wrinkles for Calculation of

Critical Angle Based on Height Profiles..........................................

95

4.3.6. Mechanoresponsive Tuning of Orientation and Anisotropy of

Water with Hierarchical Patterns...................................................

100

4.4. Conclusions.................................................................................. 106

4.5. References.....................................................................................

107

x

Chapter 5. Conclusions............................................................................

112

국문 초록.................................................................................................. 115

xi

List of Tables

Table 2.1. Geometric parameters of nanopatterned PS films and the

corresponding wavelengths of each vertical sample (��) and parallel sample

(��)............................................................................................................. 37

Table 3.1. Lists of modes in wrinkles with cylindrical top surfaces

according to the relationship between direction vector and external

strain................. 63

xii

List of Figures

Figure 1.1. Various mechanical instabilities can be found in everyday life

and in

nature........................................................................................................ 3

Figure 1.2. Some modes of mechanical instabilities of thin rigid top film-

elastomeric substrate bilayer system.............................................................

4

Figure 1.3. AFM height images of organosilicate substrate. After spin

coating on the silicon wafer, thermal curing of 360°C, 6hr in vacuum

condition was treated to ensure stability of the

substrate.................................................... 11

Figure 1.4. Offset polymer printing process to transfer polymer films

kinetically from organosilicate substrate to various target substrates.......... 13

Figure 1.5. Offset polymer printing process to transfer polymer films

kinetically from organosilicate substrate to various target substrates.......... 16

Figure 1.6. Hierarchical structure consisting of block copolymer

nanopatterns and wrinkle micropatterns. Mechanical strain of 7 % was

applied.......................................................................................................... 17

xiii

Figure 2.1. Schematics of the process forming hierarchical structure based

on buckling with nanopatterns from nanoimprint of polystyrene thin film.......

32

Figure 2.2. (a) Simple modeling of line / space patterns. h and t represents

thickness of top layer and residual layer respectively. x represents width of

line pattern while spacing ratio is termed f. (b-f) AFM height images and

SEM plan view images of imprinted PS thin films. (scale bar: 2 μm) Line

width and spacing ratio are varied while h and t are controlled by thickness

of PS thin films before

imprint..................................................................................... 33

Figure 2.3. Representative AFM images of (a) vertical (b) parallel buckled

samples. (scale bar: 10μm) Below are height profiles scanned along with the

red line. Image of vertical samples were taken with some negative scan

angle to ensure that the nanopatterns are presented on the

image......................... 35

Figure 2.4. (a) Schematic representation of in-plane stiffness and bending

stiffness in the beam theory. (b) Conventional modeling of patterned film

buckling consider both in-plane stiffness and bending stiffness of top film.

(c) When the patterns are significantly small compared to the buckling

xiv

patterns, we assume that the in-plane deformation almost does not appear to

take into

..................................................................................................................... 41

Figure 2.5. Defining unit cell of line/space nanopatterns........................... 42

Figure 2.6. Effect of aspect ratio (ℎ/�) of nanopatterns on the buckling

wavelength ratio of vertical and parallel samples (�� ��⁄ ). Considering only

bending stiffness, without in-plane stiffness, we can explain more precisely

when the pattern aspect ratio is high............................................................

43

Figure 2.7. Effect of spacing ratio (�) of nanopatterns on the buckling

wavelength ratio (�� ��⁄ ). Small numbers beside each point represents

corresponding h/t values. Considering both in-plane stiffness and bending

stiffness overestimates in high h/t region.....................................................

44

Figure 3.1. Schematic representation on the formation of wrinkled

structures with square/hexagonal cylinder array top surfaces. Transfer of

nanoimprinted PS patterns were conducted by utilizing offset polymer

transfer printing technique. According to the relationship between the

xv

cylindrical array direction vectors and the external strain, two different

systems can be obtained for each square and hexagonal array

pattern.................................. 55

Figure 3.2. (a) Schematic representation on the cylindrical array direction

vectors defined in this work. External compressive strain was applied along

the direction vectors defined above. (b) Representative SEM top view image

for square and hexagonal array each.............................................................

56

Figure 3.3. Wrinkled Structures of square cylinder arrays. As the residual

thickness of the pattern increases, wrinkles become perpendicular to the

strain. When the strain and the primitive direction vector lies parallel,

wrinkles with direction other than perpendicular to the strain exist. When

the strain and the primitive direction vector form 45° angle, wrinkles are

formed perpendicular to the

strain................................................................................................... 60

Figure 3.4. Wrinkled Structures of hexagonal cylinder arrays. As the

residual thickness of the pattern increases, wrinkles become perpendicular to

the strain. When the strain and the primitive direction vector lies parallel,

wrinkles with three different direction to the strain exist. When the strain

and the primitive direction vector form 90° angle, wrinkles are formed of

xvi

which direction shows two different

modes........................................................................... 61

Figure 3.5. Schematic representations on the cylindrical arrays both square

and hexagonal. Orange dots represent cylinder patterns and red dots

represent the sites with longest distance between cylinder patterns. Wrinkled

directions when external strain is applied are marked as modes. In all cases,

mode I shows the direction perpendicular to the external strain. In each case,

mode number are defined with increasing number when the mode across

more red dots in same

distance.................................................................................... 62

Figure 4.1. Schematic representation of fabricating hierarchical structures

based on wrinkles /cracks and hierarchical structures based on wrinkles and

cracks........................................................................................................... 75

Figure 4.2. A photograph on liquid flow experimental apparatus which can

apply tensile strain to the prestrained samples.............................................

76

Figure 4.3. Conceptual illustrations of anisotropic wetting on the

hierarchical structures originated from wrinkles and cracks. (a) Anisotropy

of water flow can be controlled by wrinkling in perpendicular direction of

xvii

line patterns. (b) Cracks on the line patterns can change the direction of

anisotropic water flow

...................................................................................................................... 78

Figure 4.4. (a) Atomic force microscopy (AFM) images and height profile

of line/space patterns (a) before and (b) after wrinkling...................................

81

Figure 4.5. Drop anisotropy can be controlled with varying prestrain on

wrinkled structures. The direction perpendicular to the line patterns is

defined as⊥, while the direction parallel to the line patterns is defined as∥.

Drop anisotropy was defined as [l(∥)-l(⊥)]∕[l(∥)+l(⊥)], where l(∥), l(⊥)

represent droplet length along ∥, ⊥ direction each. Scale bars represent

2mm each

...................................................................................................................... 82

Figure 4.6. Critical contact angle measurement in line patterns, wrinkle

patterns, crack patterns. Critical contact angles were taken as contact angles

at the moment just before the water droplet overcomes groove-like patterns

...................................................................................................................... 84

xviii

Figure 4.7. Critical contact angle measurement in line patterns, wrinkle

patterns, crack patterns. Critical contact angles were taken as contact angles

at the moment just before the water droplet overcomes groove-like patterns

...................................................................................................................... 85

Figure 4.8. (a) Effect of the prestrain on the critical contact angles of both

perpendicular and parallel directions to the line patterns. (b) The difference

in critical contact angles in each direction shows similar trends with the

drop

anisotropy..................................................................................................... 86

Figure 4.9. Atomic force microscopy (AFM) images and corresponding

height profiles of line/space patterns (a) before applying tensile strain, (b)

after applying 20% and (c) 40% tensile strains............................................

88

Figure 4.10. (a) Top view photographs on anisotropic water droplet along

the line patterns when the tensile strain is inexistent. (b), (c) Top view

photographs showing that the direction of water droplet has changed from

the original direction after applying 20% and 40% tensile strains each. Scale

bars represent 2mm

each..................................................................................... 89

xix

Figure 4.11. (a) Anisotropy of water droplets with varying drop volume in

wrinkled patterns with different compressive strain. (b) Anisotropy of water

droplets with varying drop volume in crack patterns with different tensile

strain. (Tensile strains are indicated with negative signs.)..........................

90

Figure 4.12. Adjacent crack-to-crack distance distribution in hierarchical

patterns based on cracks with applied tensile strain of (a) 0% (b) 10% (c) 20%

(d) 30% (e) 40%........................................................................................... 91

Figure 4.13. Optical images on critical contact angles on the hierarchical

structures (line patterns with microscale cracks in the perpendicular

direction) with varying tensile strain. The critical contact angles of the

direction parallel to the line patterns increases as the tensile strain increase,

while the critical contact angles of the direction perpendicular to the line

patterns remains almost the

same............................................................................................ 93

Figure 4.14. (a) Effect of the tensile strain on the critical contact angles of

both perpendicular and parallel directions to the line patterns. (b) The

difference in critical contact angles in each direction shows similar trends

with the drop anisotropy...............................................................................

94

xx

Figure 4.15. Characteristic height profiles from atomic force microscopy

for each (a) line patterns, (b) wrinkles, (c) cracks and corresponding

simplified groove angle (�)

each................................................................................... 96

Figure 4.16. Definition of critical angle (qcr) on patterned surfaces. Critical

angle is defined as the sum of intrinsic contact angle of the flat surface (q)

and pattern inclination (a)............................................................................

97

Figure 4.17. Intrinsic Contact Angle (q) of 1-hour-UVO treated PDMS.....

98

Figure 4.18. (a) (b) In both wrinkle and crack cases, calculated critical

angles from height profiles show the similar tendency over the measured

critical

angles........................................................................................................... 99

Figure 4.19. (a)-(c) AFM images on the hierarchical structures based on

wrinkles and cracks. As the strain increases, both closing of cracks and

emerging of wrinkles can be observed....................................................... 102

xxi

Figure 4.20. (a) A schematic illustration showing the mechanoresponsive

tuning of the direction of anisotropic water droplet with crack formation and

the anisotropy with wrinkle formation. (b) Top view photograph of

anisotropic water droplet when the tensile strain is larger than prestrain,

which leads to relatively large crack structures. (c) Top view photograph of

water droplet when the tensile strain is similar to the prestrain, where the

crack structures become negligible. (d) Top view photograph of anisotropic

water droplet when the prestrain is larger than the tensile strain, which is the

condition of wrinkle formation. Scale bars represent 2mm each............... 103

Figure 4.21. Critical contact angles on the hierarchical structures based on

wrinkles and cracks with varying strain.....................................................0 104

Figure 4.22. (a) Effect of the strain on the critical contact angles and the

drop anisotropy on hierarchical structures based on both wrinkles and cracks.

When applied strain is small, which leads to large crack features, critical

contact angles perpendicular to the strain are larger. With increasing strain,

close of cracks change the direction of wetting and the anisotropy of water

droplet can be controlled in the same way to the case where only wrinkles

exist. (b) The difference in critical contact angle in each direction and the

flow anisotropy shows similar trends with varying

strain. ................................. 105

1

Chapter 1. Introduction

1.1. Mechanical Instabilities with Thin Film

1.1.1. Definition and Classification of Mechanical Instabilities

Mechanical instabilities can be encountered daily in everyday life.1-4They are

phenomena commonly occurring in the natural world which means collapse of

structural integrity of mechanically defined structures. This phenomenon has

dominated tremendously from geological carving to the know-how of ancient

architectures. In real, representative examples of mechanical instabilities occurring

in the natural world include wrinkles,5-13 folds,14,15 creases,16-19 and cracks.20-25 In

case of wrinkles, it is common to see in nature such as wrinkles of leaves, wrinkles

of fruits, wrinkles of swollen finger in the water and so on. These mainly rise to

compensate for external stress when two materials with different elastic properties

are attached with good adhesion, leading to form a periodic and continuous

sinusoidal structure. Also, in the case of folds, structures emerge when there is

semi-discontinuous structure that appears in order to cancel out larger stresses in a

system resembling the case of wrinkles. These structures are commonly found in a

stratum subjected to a strong stress, or a very deep skin wrinkles. In the two cases

described above, they are phenomena naturally emerging in response to

compressive stress, while the following creasing and crack structures mainly

emerge naturally when tensile stress is applied to the system. Also, folds and

wrinkles are relatively reversible, while cracks and creases form irreversible

structures. Creasing is commonly found in used leathers especially with tannings

2

on it, and on the inside of fingers with frequent movements. It is a phenomenon

that a material is subjected to bending or tensile strains continuously and repeatedly,

the system is deformed in a microscale to make line shape structures commonly

with fibrils. In addition, cracks, the most common mechanical instability in nature,

can be found in everywhere. Typically, cracks can be found in mud cracks of

riverbeds when the rivers are dried, or in cracks in old paintings, or in breaks in

strata, or in cracks in building walls, and so on. Crack is the most extreme case of

mechanical instability and is described as a process that completely loses integrity

of the structure.

Previously, these mechanical instabilities were treated as an unwanted flaw,

and efforts were mainly concentrated to prevent their expression.26-30 In fact,

mechanical instabilities that break structural integrity can cause catastrophic

problems when expressed in unwanted areas. To show some examples to prevent

mechanical instabilities, enough moistures should be provided or wax coating

should be provided to prevent wrinkles with shrinking. Alternatively,

nanocomposite materials can be used to prevent creases, and steel rebar-concrete

systems which have similar thermal expansion coefficients are used to prevent

cracks. Especially, if these instabilities could not be prevented, the result could be

catastrophic in architectural engineering and mechanical engineering. As a result of

diligent efforts in these fields, there has been a through and general understanding

of many mechanical instabilities, but most have been studied with a focus on

understanding and preventing these phenomena.

3

Figure 1.1. Various mechanical instabilities can be found in everyday

life and in nature.

4

Figure 1.2. Some modes of mechanical instabilities of thin rigid top

film-elastomeric substrate bilayer system.

5

1.1.2. Controlled Mechanical Instabilities for Micropattern Fabrication

As mentioned above, former studies focused mainly on the prevention of

instability. In this regard, mechanical instability mechanics developed for systems

with various structures. Through these processes, researchers have found that

mechanical instability is formed not with random failure but with some degree of

regularity. For example, it came to be possible to predict the beam bending and

beam buckling structure in the construction area according to the applied stress.31-34

In addition, by using the composite material to increase the intrinsic integrity of

materials or to match thermal expansion coefficients of composing materials made

it possible to prevent cracks effectively.

Among these various efforts, the mechanical instability of the joint of two

materials, especially the bilayer systems, have been actively studied and the

mechanical instability of the system with one elastic layer material is called surface

elastic instability. This platform is a two-dimensional problem, so it had been less

focused than other systems. However, there was a critical discovery that the

periodic structure can be formed by controlling several factors in this platform.35,36

In this regard, there were some pioneering works to use the mechanical instability

as one kind of unconventional lithography to make some patterns.37,38 These studies

were mainly done through the wrinkle of thin film-elastomer bilayer which have

some properties in common with conventional lithography, periodicity and

predictability. A representative example of this is the work of Whitesides et al.,5 in

which a metal layer is thermally deposited on a PDMS to form a bilayer, and

boundary where wrinkles does not penetrate was arbitrarily given in controlled

manner, and applied stress through a difference in thermal expansion coefficient

during the thermal deposition process, eventually to control wrinkle formation

6

through the top metal surfaces. In addition, Crosby et al.39 formed a silicate on a

PDMS substrate and formed wrinkles with two-dimensional patterns using

swelling difference between silicate and PDMS layer in swelling/deswelling step

with chemical solvents. In the case of Stafford et al.,40 after the formation of

silicate-PDMS bilayer system, mechanical stress was applied to form periodic

patterns with wrinkles which have one dimensional patterns. In addition to

patterning studies using wrinkles, studies have also been made on making patterns

using creasing or cracking. A representative study by Suh et al.41 showed that

anisotropic cracks could be formed by bending the silicate-PDMS bilayer which

can give one dimensional tensile stress, and the spacing could be controlled

through the degree of bending.

The researches mentioned above suggest a new method to easily make

microstructures by using mechanical instabilities, especially for certain patterns

such as sinusoidal patterns or patterns with both continuous and discontinuous

features which is difficult to form by conventional lithography.

7

1.1.3. Various Applications with Controlled Mechanical Instabilities

As the interests in mechanical instabilities or surface elastic instabilities have

increased, attempts have been made to apply the mechanical instabilities to various

fields other than the patterning method as unconventional lithography. Many of

these applications take advantage of the intrinsic characteristics which is stimuli

responsive, for all of the mechanical instability driven structures. The most

commonly used stimuli are mechanical stimuli, thermal stimuli, and chemical

solvent stimuli. In each three cases, stress is applied through, giving mechanical

strain, or giving thermal expansion/contraction, giving swelling/deswelling with

chemical solvents. These stimuli responsive properties could be applied to various

applications such as micro/nanofluidics,42-45 organic photovoltaic devices,46-48 dry

adhesives,49-52 and wettability control systems53-58 because they can form a system

that regulates a wide variety of structure based properties by simple stimuli.

1.1.4. Mechanical Instabilities with Micropatterned Top Films

There also have been interests in applications other than functions using

mechanoresponsive features of the mechanical instabilities described above. For

this purpose, various studies have been carried out to construct dual structures

using mechanical instability driven patterns and patterns formed by using

conventional lithography or soft lithography techniques. In this way, researchers

were able to create much more complex and diverse applications than the former

simple structures. For example, in Char et al.'s work,59 pyramidal structures were

made through soft lithography technique and cracks were formed by drying out the

solvent, thereby improving optical integration efficiency of optical photovoltaics

through hierarchical structure. In addition, in Shu et al.'s work,60 micro pillar arrays

8

were formed through imprinting method and an oxide layer was formed on the

surface of the PDMS to form a wrinkle, thereby controlling the optical

transparency of the system according to the applied strain. Other than these, a study

of Rogers et al.61 dramatically used mechanoresponsive wrinkles to discover a

novel application. A flexible electronic device was realized by wringing the

constituent parts of an electronic devices such as metal films in the wrinkled state,

to form a bendable, flexible electronic device.

As shown in the above studies, especially in the case of the flexible electronics,

it is suggested that the micropatterning technique and the patterning technique with

mechanical instability can be used together to exploit a total new field. However, in

order to achieve better functionalities, hierarchical structures of a combination of

nanopatterns and mechanical instabilities are required other than the combination

of micropatterns and mechanical instabilities. But there have been many difficulties

in forming a bilayer system with nanopatterns and elastic substrates such as PDMS

to remain this part of the field barely known.

9

1.2. Offset Polymer Film Printing

1.2.1. Organosilicate Substrate with Sharp Interfaces for Polymer Film

Transfer

In order to form hierarchical structures with nanopatterns and mechanical

instabilities other than the above mentioned micropatterns and mechanical

instabilities, a method for successfully transferring the nanopatterns onto the

PDMS is needed. For this purpose, we developed the transfer method using the

previously developed organosilicate (OS) substrates in our group.

Organosilicate is a material similar to glass, with an organic moiety attached

to each Si atom. This material is one of the materials previously used in the

semiconductor engineering field of which dielectric constant is very low to make it

as insulating material. In our group, the sol-gel synthesis of this material was

rigorously studied, and the OS substrate was formed using the optimized OS

synthesis method.62-64 OS was synthesized with sol-gel reaction with

methyltrimethoxysilane (MTMS), 1,2-bis(trimethoxysilyl)ethane (BTMSE). Feed

ratio of MTMS:BTMSE was fixed to 7:2 by weight %. Sol-gel reaction was

consisted of two steps, first step is to conduct hydrolysis of MTMS and BTMSE

with hydrochloric acid catalyst and the second step is to polymerize to obtain gel-

like product. The product was purified with separatory funnel with excess diethyl

ether and water. Final powder form OS product was obtained by drying all diethyl

ether solvents. In order to form OS substrate, 1 wt% OS solution in methyl isobutyl

ketone (MIBK) was formed and spin coated on the piranha treated Si wafer. The

OS substrate thus prepared was subjected to a thermal curing step for the purpose

10

of ensuring stability. The thermal curing step can be also applied to control the

surface energy of the OS substrate as shown in the previous works in our group. In

addition, through the thermal curing step, the surface formulates very sharp surface

as shown in Figure 1.3. and this feature was previously demonstrated by others in

our group through neutron reflectivity experiments. Using these interesting

properties, a polymer transfer printing system was invented.

11

Figure 1.3. AFM height image of organosilicate substrate. After spin

coating on the silicon wafer, thermal curing of 360°C, 6hr in vacuum

condition was treated to ensure stability of the substrate.

12

1.2.2. Polymer Offset Transfer Printing

As described above, when the solid surface is sharp and the polymer is

deposited on the polymer by spin coating or some other methods, the adhesion

between the polymer film and the surface becomes extremely low. It is believed

that the penetration of the polymer to the interface is small and the interdiffusion is

very low as described in previous neutron reflectivity experiments. Using these

properties and referring to the previous molecular transfer printing technique of

Rogers' group, we developed a novel technique to transfer polymer thin film to

other target substrates.

Figure 1.4. shows the method of the polymer offset printing technique. PDMS

block which will act as a stamp is applied on top of the polymer film and let the

contact gets conformal. According to the previous works of Rogers' group,65-67 the

adhesion of the elastomeric materials such as PDMS at the interface depends

highly on the kinetic properties of the system. This property allows us to adjust the

film pick-up and printing step by varying the speed at which the stamp PDMS is

released. Specifically, when the PDMS is quickly removed after the conformal

contact with the polymer film, the film is released to the PDMS surface.

Afterwards, the film can be transferred to the target substrate by adjusting the

temperature or by slowly removing the stamp PDMS after the stamp was applied

on various target substrates. In principle, this technique shows an analogy to the

conventional offset printing method, so this can be called as the polymer offset

printing method.

13

Figure 1.4. Offset polymer printing process to transfer polymer films

kinetically from organosilicate substrate to various target substrates.

14

1.2.3. Offset Printing of Polymer Films onto Elastomeric Substrates for

Controlled Mechanical Instabilities

If a polymer thin film-PDMS bilayer is formed using the offset printing as

described above, a system for mechanical instability experiment can be constructed.

Although the polymer film-PDMS bilayer is formed during the first peel-off

process, however, when the polymer film is patterned the bilayer system remains

with the pattern upside down to make inappropriate system for the formation of

hierarchical structures of mechanical instability with patterned top surfaces. To

improve this, the target substrate set as also PDMS, but the adhesion between the

target substrate and the polymer film should be larger than the adhesion between

the stamp PDMS and the film. Thus, the intrinsic adhesion property was controlled

by changing the composition of target PDMS (precusor:crosslinker = 20:1) and

stamp PDMS (precusor:crosslinker = 15:1). As can be seen in Figure 1.5. the

patterned polymer film could be successfully transferred onto the target PDMS to

build a system for mechanical instability with nanopatterned top surface.

As a practical example, we have constructed a wrinkle system using a block

copolymer thin film nanopattern. A fingerprint like structure was prepared by

thermal annealing (190 °C, 24 h) after spin coating a lamellar-forming block

copolymer (PS-b-PMMA, 66k-63.5k) on a surface energy controlled OS substrate.

Then the PMMA block was selectively removed by oxygen plasma etching to

construct a fingerprint line/space nanopattern. Afterwards, the block copolymer

based nanopatterns were successfully transferred onto 20:1 target PDMS through

the offset printing method described above, leading to the hierarchical structure

with applying compressive mechanical strain, as shown in Figure 1.6. This

technique has been used for various patterns in subsequent Chapters to build a

15

mechanical instability system with a nanopatterned top surfaces.

16

Figure 1.5. Offset printing of fingerprint patterned block copolymer thin

film from organosilicate substrate to target PDMS.

17

Figure 1.6. Hierarchical structure consisting of block copolymer

nanopatterns and wrinkle micropatterns. Mechanical strain of 7 % was

applied.

18

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26

Chapter 2. Effect of the Orientation and Bending

Stiffness of Anisotropic Nanopatterned Films on

Wrinkles

2.1. Introduction

Wrinkling of thin films on elastomeric substrates such as

polydimethylsiloxane (PDMS) is well known and originates from the moduli

mismatch between a substrate and a thin film placed on the top surface.1-5 Recently,

many works based on the buckling of films made of metals, semiconductors, and

polymers have been reported for a wide range of applications, including strain

sensors,6-8 flexible devices,9-13 microchannels,14-17 and optical gratings.18 By

minimizing the energy of a system, i.e., the thin film bending energy and the

deformation energy of the elastic substrate, characteristic lengths, e.g., the

wavelength (λ), can be determined by λ = 2πt(Ef/3ES)1/3, where t is the film

thickness and Ef and Es are the moduli of the thin film and the substrate,

respectively.5 However, studies of flat thin films on elastomeric substrates have

shown that these systems have limited multi-functionalities; instead, the formation

of hierarchical structures with patterned thin films can expand their range of

applications. The formation of hierarchical structures by wrinkling consists of three

categories. 1) Hierarchical structure formations by sequential wrinkling or multi-

level layers. For example, Lee et al. reported a hierarchical polystyrene texture

achieved by multiple plasma treatments that exhibited superhydrophobicity.19

27

Although the wavelengths of the wrinkled structures can be controlled, the

structures are randomly oriented. 2) Wrinkling of thin film surfaces on

microstructures. In this system, buckling formation is perpendicular to the edges

and can be self-organized by boundary conditions.1,20 This method is typically used

to control the orientations and wavelengths of wrinkling. The wavelength is similar

to or greater than the microstructure. 3) Wrinkling of films decorated by structures.

For example, Jeong et al. demonstrated buckling of an elastomer surface containing

micropillars for reversible adhesion,21 and Lee showed optical transmittance

switching through the buckling of a surface with nanopillars.22 Although these

works focused on how to use mechanoresponsive wrinkling of elastomeric

substrates with micro- and nanostructures, the mechanism was not fully discussed.

Recently, Stafford et al.23 reported a method to fabricate anisotropic hierarchical

wrinkling that is controlled by the surface nanopatterns. The characteristic lengths

of the wrinkles, such as wavelengths and amplitudes, depended on the direction of

the nanopatterns, and the group developed a model to explain the experimental

results. However, the model for the bending modulus and the in-plane modulus did

not match well with the data. Here, we propose a model to predict the microscale

wrinkling of nanopatterns by neglecting in-plan stiffness in a thin residual layer

region. We fabricated nanoimprinted polystyrene patterns with different residual

thicknesses on organosilicate (OS) substrates and then transferred the

nanopatterned films to stretched PDMS elastomers. During release, the thin

polymer patterns are deformed into wavelengths and amplitudes according to the

design parameters of the nanoscale patterns. Our new model for analyzing systems

with large variations in feature sizes can explain the dependence of the bending and

in-plane moduli on the nanoscale patterns, and the results are in good agreement

28

with the experimental data.

28

2.2. Experimental Section

Materials

Organosilicate (OS), used as bottom substrate for polymer films, was

synthesized by the sol-gel reaction of methyltrimethoxysilane (MTMS, Aldrich)

and 1,2-bis(trimethoxysilyl)ethane (BTMSE, Aldrich). The detailed synthesis

process is described elsewhere.24-26 The feed ratio of MTMS to BTMSE was 7/2 by

weight %. The 20-nm thick OS films were prepared by spin coating with 1 wt% OS

solution dissolved in methylisobutyl ketone (MIBK) onto piranha-treated Si wafers.

The OS substrates were cured @ 360°C for 6 h under vacuum conditions to ensure

their robustness. The 75 kg/mol polystyrene (PS) with polydispersity index (PDI)

of 1.05 was purchased from Polymer Source Inc. and used without further

purification. PDMS (Sylgard 184, Dow Corning) sheets were prepared by mixing

the base and curing agent in a ratio of 15:1 or 20:1 by weight and pouring onto a

flat petri dish, followed by degassing and curing at 60°C for 6 h. The 15:1 PDMS

sheets were cut into 1.5 cm × 2.5 cm pieces and used for film transfer stamping,

whereas 20:1 PDMS sheets were into 1.5 cm × 4.5 cm pieces and used as

substrates for buckling.

Patterning of Polystyrene Thin Film

PS thin films were prepared by spin coating PS solutions dissolved in toluene

(Aldrich) onto organosilicate substrate, prepared as presented above. Film

thickness was controlled by changing the solution concentration (2-7 wt%) and the

spin speed (2000-4000 rpm). Silicon master patterns were used as a basic mold to

29

prepare a polyfluoropolyether (PFPE) pattern. The PFPE mold was prepared with a

mixture of PFPE prepolymers (5101X, Fluorolink) and initiator onto the master

pattern. After a short UV exposure (~40 s) through a backplane poly(ethylene

terephthalate) (PET) film, the PFPE replica was carefully detached from the master.

Further UV exposure was applied for 2-3 h to fully cure the PFPE mold, and the

patterned PFPE mold was applied to heated PS thin films to make conformal

contact. The temperature was maintained at 150°C, above the Tg of PS thin film.

The nanoimprint was performed for 15 min with a weight to apply constant force.

The film was cooled below the glass transition temperature, with the patterned

PFPE mold on top to lock in the structure formed by the nanoimprint. The PFPE

mold was carefully removed to obtain the patterned PS thin film.

Film Transfer and Wrinkle Formation

The patterned PS thin film was fixed onto a flat surface, and a 15:1 stamp

PDMS was applied to the film. The PDMS stamp was quickly peeled off to transfer

the film onto the PDMS. Target 20:1 PDMS was placed on a custom-made PDMS

pull/press machine, with which applied strain could be controlled. The patterned

film on the stamp was conformally contacted onto a 1-D prestrained target PDMS,

followed by slow lifting of the PDMS stamp to leave the patterned film on the

target PDMS. The strain was slowly relieved, and the vertical or parallel buckled

samples were obtained as the direction between the micropattern of wrinkle and the

nanopattern of the PS thin film varied. The buckling structure was analyzed by

observing the height profile obtained from AC-mode AFM images (Nanowizard 3,

JPK Instruments).

30

2.3. Results and Discussion

2.3.1. Fabrication of Hierarchical Structure Based on Wrinkling of

Anisotropic Nanopatterned Polymer Film

Figure 2.1. shows a schematic illustration of wrinkle formation of

nanopatterned films. First, topographical patterns were formed by an imprint on PS

film on OS substrates. Topographically patterned polymer films could be easily

transferred to PDMS due to low adhesion between the polymer film and OS

substrate. Rogers’ group reported a similar approach to transfer nanomaterials onto

a smooth target substrate using PDMS pads using only a kinetic variation of

interfacial adhesion.31-33 Polymer films can be detached from the OS substrate by

rapidly peeling off the PDMS pad after complete contact with the polymer film.

After rapid peeling, the patterned polymer film on the stamp PDMS film lies

upside down, and with one more similar transfer step to the prestrained target

PDMS, well-defined patterned top film-PDMS bilayer wrinkles are formed. In this

transfer technique, adhesion between polymer film and PDMS was controlled by

varying the crosslinker to precursor ratio (1:15 for stamp PDMS and 1:20 for target

PDMS).34

Figure 2.2. (a) presents schematics of a simplified model of a nanopatterned

top film used in this study. We defined the following structural parameters: high

pattern height h, low pattern height t, characteristic domain spacing x, and spacing

ratio f. For a more universal explanation, we further defined the pattern height ratio

h/t, controlled by varying the PS thin film thickness before the nanoimprint

procedure. In this study, line/space nanopatterns with varying domain spacing x

31

and spacing ratio f were used. Figure 2.2. (b)-(f) shows the geometric parameters of

the patterns used, AFM height images and SEM images.

32

Figure 2.1. Schematics of the process forming hierarchical structure

based on buckling with nanopatterns from nanoimprint of polystyrene

thin film.

33

Figure 2.2. (a) Simple modeling of line / space patterns. h and t

represents thickness of top layer and residual layer respectively. x

represents width of line pattern while spacing ratio is termed f. (b-f) AFM

height images and SEM plan view images of imprinted PS thin films.

(scale bar: 2 μm) Line width and spacing ratio are varied while h and t are

controlled by thickness of PS thin films before imprint.

34

As shown in Figure 2.3., a hierarchical structure based on buckling was

obtained through the transfer of a nanopatterned polymer film onto prestrained

PDMS to be buckled at the micron scale. As the directionality of nanopatterns and

1-D buckling structures can be aligned either vertically or in parallel, we prepared

both samples for every nanopattern. We define the vertical sample to refer to the

case in which the buckling pattern direction is vertical to the nanopattern direction

(2.3. (a)); the parallel sample refers to the case in which the buckling pattern

direction is parallel to the nanopattern direction (2.3. (b)).

35

Figure 2.3. Representative AFM images of (a) vertical (b) parallel

buckled samples. (scale bar: 10μm) Below are height profiles scanned

along with the red line. Image of vertical samples were taken with some

negative scan angle to ensure that the nanopatterns are presented on the

image.

36

2.3.2. Effect of Orientation and Structural Parameters of Nanopatterns on

Anisotropic Wrinkle

The buckling wavelength of vertical samples was always larger than that of

parallel samples with varying geometrical parameters of nanopatterns, and one

example is shown in the height profile of Figure 2.3. This result implies that the

directionality of the nanostructure from imprinted PS patterns affects the structural

parameters of hierarchical structures based on wrinkling. This type of directionality

effect between nanostructures and microstructures qualitatively agrees with a study

by C. Stafford et al.23 When using wrinkled structures in flexible or foldable

devices, it is more likely that patterned top films with feature sizes much smaller

than the wrinkle wavelengths are used instead of flat top films. In this regard, it is

necessary to anticipate final structures quantitatively with varying structural

parameters for the top patterns. In this study, various pattern parameters were

varied, such as the feature size of line/space patterns, spacing ratio and thickness of

top films.

In previous studies, our group introduced a nanoimprint system using a PFPE

mold for patterns with small feature sizes.35,36 Nanopatterned films were prepared

by imprinting with PFPE molds with small domain spacings of 130 nm to 600 nm.

Table 2.1. shows geometric parameters of imprinted PS films and the

corresponding wavelengths of buckled structures formed with patterned films. The

Buckled wavelengths of vertical samples are always larger than for parallel

samples, and the wavelength ratio between vertical samples and parallel samples

increases as the pattern height ratio h/t increases. This phenomenon corresponds

well to the results of previous studies and can be explained by introducing an

effective height concept.

37

Table 2.1. Geometric parameters of nanopatterned PS films and the

corresponding wavelengths of each vertical sample (��) and parallel

sample (��)

38

2.3.3. Stiffness-Based Modeling of Anisotropic Nanopatterns in Wrinkles

Figure 2.4. shows a scheme of our concept for the development of beam theory.

In conventional beam theory,23,27-30 we consider both in-plane stiffness and bending

stiffness to explain wrinkle formation, as shown in Figure 2.4. (a). When we

develop a model for the buckling of films with a texture, in-plane stiffness should

be included (Figure 2.4. (b)). However, in our experimental condition, the feature

size of nanopatterns after nanoimprint lithography is much smaller than the wrinkle

patterns. To match theory to the experimental data, we assume that in-plane

stiffness can be neglected, as shown in Figure 2.4. (c). In this work, the

experimental condition is an extreme case in Figure 2.4. (c).

Compared to previous models23, there is greater error in the experimental data

points, especially in the high h/t region. In addition, the previous analytic solution

significantly underestimates the wavelength change with varying f. Thus, we tried

to explain the phenomenon by carefully considering mechanical parameters,

especially the stiffness of the patterned top film. When the line pattern size and

wavelength of buckling are comparable, beam theory explains buckling behavior

with both bending stiffness (D) and in-plane stiffness (S). Bending stiffness refers

to the bending of each beam during deformation, and in-plane stiffness refers to

compression or extension of each beam. We assumed that in-plane stiffness should

be ignored when the characteristic beam size is much smaller than the buckling

wavelength, as in this study. We can thus redefine effective height with a second

moment of inertia that is directly related to bending stiffness.

Buckling of line/space nanopatterns can be easily presented as models using beam

theory or simplified plate theory. Figure 2.5. shows schematics on model line/space

nanopattern. We argue that if the characteristic size of nanopatterns are

39

significantly smaller than the characteristic size of buckling patterns, we should

ignore in-plane stiffness of the film thus explain only with bending stiffness as

shown in Figure 2.4. In this case, as bending stiffness is directly proportional to the

second moment of inertia (I), we can redefine effective height for each vertical and

parallel sample of unit cell by calculating accurate second moment of inertia.

� =ℎ���

�

12

ℎ��� = (12�)� �⁄

For the vertical case, second moment of inertia is given by

�� = ��

� + 1��

�� +1

� + 1����

�� ���

= ��

� + 1

12

��+

1

� + 1

12

(ℎ + �)��

��

For the parallel case, neutral axis is given by �� =∫ ���

∫ ��=

����(���)�

�(������)

Thus, the second moment of inertia of parallel case is

�� =∫(� − ��)���

�� + �

=�

� + 1�

1

3�� − ���� + ����� +

1

� + 1�1

3(� + ℎ)� − ��(� + ℎ)� + ���(� + ℎ)�

Eventually, the ratio of wavelength of buckling structure for each case can be

calculated with bending stiffness of each case.

��

��=

ℎ�

ℎ�= �

��

���

���

=

⎣⎢⎢⎢⎡ 1

(1 + �)�× �� + �1 +

ℎ

��

��

�

× �1 + � + 3 �ℎ

�� + �

3 + 6�

1 + �� �

ℎ

��

�

+ �1 + 2� + 4��

1 + 2� + ��� �

ℎ

��

�

�⎦⎥⎥⎥⎤

���

40

Similar to previously studied analytic solutions that consider in-plane stiffness, the

new solution has two parameters, h/t and f. The plot of the new solution shows

greater dependence on f by ignoring in-plane stiffness from the system.

Considering only bending stiffness enables more proper explanation of data in the

high h/t region. From these points of view, we can indirectly confirm that in-plane

contraction/extension of nanopatterns should be ignored in nanostructured top-film

buckling. Figure 2.6. shows effect of aspect ratio of nanopatterns on the buckling

wavelength ratio of vertical and parallel samples. Figure 2.7. shows effect of

spacing ratio of nanopatterns on the buckling wavelength ratio.

41

Figure 2.4. (a) Schematic representation of in-plane stiffness and

bending stiffness in the beam theory. (b) Conventional modeling of

patterned film buckling consider both in-plane stiffness and bending

stiffness of top film. (c) When the patterns are significantly small

compared to the buckling patterns, we assume that the in-plane

deformation almost does not appear to take into.

42

Figure 2.5. Defining unit cell of line/space nanopatterns

43

Figure 2.6. Effect of aspect ratio (ℎ/�) of nanopatterns on the buckling

wavelength ratio of vertical and parallel samples (�� ��⁄ ). Considering

only bending stiffness, without in-plane stiffness, we can explain more

precisely when the pattern aspect ratio is high.

44

Figure 2.7. Effect of spacing ratio (�) of nanopatterns on the buckling

wavelength ratio (�� ��⁄ ). Small numbers beside each point represents

corresponding h/t values. Considering both in-plane stiffness and

bending stiffness overestimates in high h/t region.

45

2.4. Conclusions

A precise and detailed structural prediction and explanation of microscale

buckling of nanoscale line/space patterns with various geometrical parameters were

described in this work. We suggested a new analytic solution for the buckling of a

patterned top film, ignoring in-plane deformation of nanostructures, which is

appropriate when the characteristic size of the nanostructure is negligible compared

to that of microscale buckling structures. Comparing experimental data and

proposed theory confirms the assumption, especially for highly geometric

heterogeneity in the top patterns, i.e., high aspect ratio or thin residual layer region.

We expect this precise explanation to provide design rules for high-functioning

flexible electronic devices based on buckling structures.

46

2.5. References

(1) Bowden, N.; Brittain, S.; Evans, A. G.; Hutchinson, J. W.; Whitesides, G.

M., Nature 1998, 393, 146-149.

(2) Bowden, N.; Huck, W. T. S.; Paul, K. E.; Whitesides, G. M., Appl. Phys.

Lett. 1999, 75, 2557-2559.

(3) Groenewold, J., Physica A 2001, 298, 32-45.

(4) Chandra, D.; Crosby, A. J., Adv. Mater. 2011, 23, 3441-3445.

(5) Khang, D.-Y.; Rogers, J. A.; Lee, H. H., Adv. Funct. Mater. 2009, 19,

1526-1536.

(6) Guo, J.; Kuo, H.; Young, D.; Ko, W. Solid-State Sensor, Actuator and

Microsyst. Workshop 2004; pp 344-347.

(7) Stafford, C. M.; Harrison, C.; Beers, K. L.; Karim, A.; Amis, E. J.;

VanLandingham, M. R.; Kim, H.-C.; Volksen, W.; Miller, R. D.; Simonyi, E. E.,

Nat. Mater. 2004, 3, 545-550.

(8) Amjadi, M.; Kyung, K.-U.; Park, I.; Sitti, M., Adv. Funct. Mater. 2016, 26,

1678-1698.

(9) Khang, D.-Y.; Jiang, H.; Huang, Y.; Rogers, J. A., Science 2006, 311,

208-212.

(10) Niu, Z.; Dong, H.; Zhu, B.; Li, J.; Hng, H. H.; Zhou, W.; Chen, X.; Xie, S.,

Adv. Mater. 2013, 25, 1058-1064.

(11) Wang, C.; Zheng, W.; Yue, Z.; Too, C. O.; Wallace, G. G., Adv. Mater.

2011, 23, 3580-3584.

47

(12) Yu, C.; Masarapu, C.; Rong, J.; Wei, B.; Jiang, H., Adv. Mater. 2009, 21,

4793-4797.

(13) Hong, J.-Y.; Kim, W.; Choi, D.; Kong, J.; Park, H. S., ACS Nano 2016, 10,

9446-9455.

(14) Kim, H. S.; Crosby, A. J., Adv. Mater. 2011, 23, 4188-4192.

(15) Miquelard-Garnier, G.; Croll, A. B.; Davis, C. S.; Crosby, A. J., Soft

Matter 2010, 6, 5789-5794.

(16) Khare, K.; Zhou, J.; Yang, S., Langmuir 2009, 25, 12794-12799.

(17) Tavakol, B.; Bozlar, M.; Punckt, C.; Froehlicher, G.; Stone, H. A.; Aksay,

I. A.; Holmes, D. P., Soft Matter 2014, 10, 4789-4794.

(18) Harrison, C.; Stafford, C. M.; Zhang, W.; Karim, A., Appl. Phys. Lett.

2004, 85, 4016-4018.

(19) Lee, W. –K, Engel, C. J., Huntington, M. D., Hu, J. Odom, T. W., Nano

Lett. 2015, 15, 5624-5629.

(20) Yoo, P. J.; Suh, K. Y.; Park, S. Y.; Lee, H. H., Adv. Mater. 2002, 14,

1383-1387.

(21) Jeong, H. E.; Kwak, M. K.; Suh, K. Y., Langmuir 2010, 26, 2223-2226.

(22) Lee, E.; Zhang, M.; Cho, Y.; Cui, Y.; Van der Spiegel, J.; Engheta, N.;

Yang, S., Adv. Mater. 2014, 26, 4127-4133.

(23) Lee, J.-H.; Ro, H. W.; Huang, R.; Lemaillet, P.; Germer, T. A.; Soles, C.

L.; Stafford, C. M., Nano Lett. 2012, 12, 5995-5999.

(24) Lee, J.-K.; Char, K.; Rhee, H.-W.; Ro, H. W.; Yoo, D. Y.; Yoon, D. Y.,

Polymer 2001, 42, 9085-9089.

(25) Suh, H. S.; Kang, H.; Liu, C.-C.; Nealey, P. F.; Char, K., Macromolecules

2010, 43, 461-466.

48

(26) Suh, H. S.; Kang, H.; Nealey, P. F.; Char, K., Macromolecules 2010, 43,

4744-4751.

(27) Rui, H.; Christopher, M. S.; Bryan, D. V., J. Aerospace Eng. 2007, 20,

38-44.

(28) Breid, D.; Crosby, A. J., Soft Matter 2011, 7, 4490-4496.

(29) Niu, K.; Talreja, R., J. Eng. Mech. 1999, 125, 875-883.

(30) Timoshenko, S., Theory of elasticity. McGraw-Hill: 1951.

(31) Meitl, M. A.; Zhu, Z.-T.; Kumar, V.; Lee, K. J.; Feng, X.; Huang, Y. Y.;

Adesida, I.; Nuzzo, R. G.; Rogers, J. A., Nat. Mater. 2006, 5, 33-38.

(32) Carlson, A.; Bowen, A. M.; Huang, Y.; Nuzzo, R. G.; Rogers, J. A., Adv.

Mater. 2012, 24, 5284-5318.

(33) Feng, X.; Meitl, M. A.; Bowen, A. M.; Huang, Y.; Nuzzo, R. G.; Rogers,

J. A., Langmuir 2007, 23, 12555-12560.

(34) Kroner, E.; Maboudian, R.; Arzt, E., Adv. Eng. Mater. 2010, 12, 398-404.

(35) Kim, T.; Yoon, H.; Song, H.-J.; Haberkorn, N.; Cho, Y.; Sung, S. H.; Lee,

C. H.; Char, K.; Theato, P., Macromol. Rapid Commun. 2012, 33, 2035-2040.

(36) Ko, J.; Song, J.; Yoon, H.; Kim, T.; Lee, C.; Berger, R.; Char, K., Adv.

Mater. Interfaces 2016, 3, 1600264

49

Chapter 3. Anisotropic Wrinkling of Cylindrical

Nanopatterned Films

3.1. Introduction

The hierarchical structure has traditionally attracted great interests in the field

of biomimetics. In nature, it is often seen that every little thing has remarkable

functionalities. Typically, the soles of the gecko lizard have the adhesion properties

to support weight without sticky adhesive,1-3 the lotus leaf has superhydrophobicity

far beyond the chemically possible hydrophobicity,4-8 and the butterfly or moth

wing can exhibit a smooth color without any chemical dye.9,10 These examples

have common features that is the hierarchical structures, and also have in common

that their characteristic properties are represented by structures rather than by

distinguished chemicals. Therefore, researches for creating various hierarchical

structures by combining patterns of various shapes have been made actively.

We expect that the wrinkle mechanics of the anisotropic line/space

nanopatterns introduced in Chapter 2 can be referred as a design rule when creating

wrinkle based hierarchical structures for various applications. However, when

actually creating a hierarchical structure and manifesting various functionalities, a

wider variety of patterns other than the line/space patterns should be used.

Especially, as shown in the hierarchical structure for enhanced adhesion,11-13 the

hierarchical structure for superhydrophobic structure,14-16 and the hierarchical

structure for optical gratings or antireflective properties,17-21 the hierarchical

50

structure using the cylinder patterns is important because of simplicity of

fabricating process comparable to line/space patterns, and because of various

functionalities.

Several studies have been made to build a dual scale structure using wrinkle

and cylinder patterns. In the work conducted by Shu et al.,22 they introduced a

bilayer platform to form a wrinkle with microscale square pillar arrays with of

which optical transparency can be controlled reversibly by applying external strain.

In addition, Cho et al.23 introduced a random cylinder array using an AAO

membrane as master pattern onto wrinkling system, with which also can adjust

optical properties according to the strain through the bilayer system. Although

these studies succeeded in expressing mechanoresponsive properties using cylinder

patterns and wrinkles, they were one step aside from systematic studies of wrinkle

structures with top surfaces embedding nano scale cylinder array, rather they used

microscale structures or random cylinder arrays. To improve this, we made a

wrinkle of a square cylinder array and a hexagonal cylinder array, followed by a

systematic study on the wrinkle mechanics according to the relationship between

the primitive direction vector of cylinder arrays and strain for each, and the wrinkle

mechanics according to the residual thickness of the patterned top surfaces.

51

3.2. Experimental Section

Materials

Organosilicate (OS), used as bottom substrate for polymer films, was

synthesized by the sol-gel reaction of methyltrimethoxysilane (MTMS, Aldrich)

and 1,2-bis(trimethoxysilyl)ethane (BTMSE, Aldrich). In more detail, refer to

Chapter 1. The feed ratio of MTMS to BTMSE was 7/2 by weight %. The 20-nm

thick OS films were prepared by spin coating with 1 wt% OS solution dissolved in

methylisobutyl ketone (MIBK) onto piranha-treated Si wafers. The OS substrates

were cured @ 360°C for 6 h under vacuum conditions to ensure their robustness.

The 75 kg/mol polystyrene (PS) with polydispersity index (PDI) of 1.05 was

purchased from Polymer Source Inc. and used without further purification. PDMS

(Sylgard 184, Dow Corning) sheets were prepared by mixing the base and curing

agent in a ratio of 15:1 or 20:1 by weight and pouring onto a flat petri dish,

followed by degassing and curing at 60°C for 6 h. The 15:1 PDMS sheets were cut

into 1.5 cm × 2.5 cm pieces and used for film transfer stamping, whereas 20:1

PDMS sheets were into 1.5 cm × 4.5 cm pieces and used as substrates for buckling.

Patterning of Polystyrene Thin Film

PS thin films were prepared by spin coating PS solutions dissolved in toluene

(Aldrich) onto organosilicate substrate, prepared as presented above. Film

thickness was controlled by changing the solution concentration and the spin speed

(2000-4000 rpm). Silicon master patterns with either hexagonal cylinder arrays or

square cylinder arrays were used as a basic mold to prepare a polyfluoropolyether

52

(PFPE) pattern. The PFPE mold was prepared with a mixture of PFPE prepolymers

(5101X, Fluorolink) and initiator onto the master pattern. After a short UV

exposure (~40 s) through a backplane poly(ethylene terephthalate) (PET) film, the

PFPE replica was carefully detached from the master. Further UV exposure was

applied for 2-3 h to fully cure the PFPE mold, and the patterned PFPE mold was

applied to heated PS thin films to make conformal contact. The temperature was

maintained at 150°C, above the Tg of PS thin film. The nanoimprint was performed

for 15 min with a weight to apply constant force. The film was cooled below the

glass transition temperature, with the patterned PFPE mold on top to lock in the

structure formed by the nanoimprint. The PFPE mold was carefully removed to

obtain the patterned PS thin film.

Film Transfer and Wrinkle Formation

The patterned PS thin film was fixed onto a flat surface, and a 15:1 stamp

PDMS was applied to the film. The PDMS stamp was quickly peeled off to transfer

the film onto the PDMS. Target 20:1 PDMS was placed on a custom-made PDMS

pull/press machine, with which applied strain could be controlled. The patterned

film on the stamp was conformally contacted onto a 1-D prestrained target PDMS,

followed by slow lifting of the PDMS stamp to leave the patterned film on the

target PDMS. The strain was slowly relieved, and the 0°, 45°, 90° buckled samples

were obtained as the direction between the micropattern of wrinkle and the

nanopattern of the PS thin film varied. The buckling structure was analyzed by

observing the height profile obtained from AC-mode AFM images (Nanowizard 3,

JPK Instruments).

53

3.3. Results and Discussion

3.3.1. Formation of Anisotropic Wrinkles with Cylindrical Top Patterns

As shown in the Experimental Section in 3.2., this work was basically

performed in a manner similar to the transfer and wrinkle formation of the

line/space patterns conducted in Chapter 2. The detailed schematic representation

of this work is shown in Figure 3.1. Si masters with square array cylinders and

hexagonal array cylinders with the same diameter and center to distance were

prepared. The imprint molds were made using UV-curable PFPE which can

replicate the nanostructures with superb precision. Later, the nanoimprint method

was used to successfully transfer the patterns onto the PS thin films coated on the

OS substrate.

In the case of the line/space pattern, there are two primitive direction vectors

along the line direction and cross the line direction. In this case, the primitive

direction vector is a translational vector that is defined by the pattern. We assume

that the wavelength difference between the vertical direction and the parallel

direction in Chapter 2 occurs as a difference between the primitive direction vector

and the external strain, and we apply this concept to the cylinder array similarly.

Figure 3.2. (a) briefly explained this concept. The direction vector in the square

cylinder array is set as vector a and vector b which is inclined by 45° to the vector a.

In the hexagonal cylinder array, the vector a and the vector b which is inclined by

90° to the vector a are set. The SEM images and the geometrical parameters of the

master PFPE mold used for this work are shown in Figure 3.2. (b).

In addition, as described in Chapter 2, the wrinkle wavelength is defined by

54

properly averaging bending stiffness of the top film, and the bending stiffness

increases with increasing film thickness. Also, if the residual thickness of the

pattern is reduced, the difference in bending stiffness between the patterned and

non-patterned areas is reduced, reducing the difference in the wrinkle wavelength.

In this study, we studied the formation of wrinkles by varying residual thickness in

square array cylinder patterns and hexagonal array cylinder patterns.

55

Figure 3.1. Schematic representation on the formation of wrinkled

structures with square/hexagonal cylinder array top surfaces. Transfer of

nanoimprinted PS patterns were conducted by utilizing offset polymer

transfer printing technique. According to the relationship between the

cylindrical array direction vectors and the external strain, two different

systems can be obtained for each square and hexagonal array pattern.

56

Figure 3.2. (a) Schematic representation on the cylindrical array

direction vectors defined in this work. External compressive strain was

applied along the direction vectors defined above. (b) Representative

SEM top view image for square and hexagonal array each.

57

3.3.2. Effect of Strain Direction to Primitive Direction Vectors of Cylindrical

Arrays on Wrinkled Structures

The AFM images on the wrinkles of the square array cylinder patterns can be

seen in Figure 3.3., and the AFM images on the wrinkles of the hexagonal array

cylinder patterns can be found in Figure 3.4.

For a square cylinder array, Strain can be given in 0° and 45°directions

according to the primitive direction vectors shown in Figure 3.2. (a). Here, the

angle of the wrinkle is changed depending on the correlation between the primitive

direction vector and the strain direction. The original wrinkle pattern should be

formed perpendicular to the external strain. However, especially when the residual

layer is thinned at 45° sample, wrinkle occurs at 45° angle to the strain direction.

For a hexagonal cylinder array, Strain can be given in 0° and 90° directions

according to the primitive direction vector shown in Figure 3.2. (a). Likewise, the

wrinkle pattern varies depending on the correlation between the primitive direction

vector and the strain direction. Especially, the hexagonal cylinder array has more

various wrinkles of which direction differs from the direction perpendicular to the

external strain than the square cylinder array case.

As described above, the wrinkles can be classified according to the angle

between the strain direction and the wrinkle patterns and represented in Figure 3.5.

In Figure 3.5., the cylinder patterns are indicated by the orange dots, and the

position of the furthest residual film to the centers of cylinders are represented by

red dots. As described in Chapter 2, if the film thickness varies with position, the

formation of the wrinkle is determined by the bending stiffness. In this case, the

bending stiffness at each position can be quantified as the area moment of inertia at

each position, and the area moment of inertia at each position � can be simplified

58

as follows;

�� =ℎ(�)�

12

In this case, ℎ(�) denotes the film thickness at each position �. Bending

stiffness represents the degree to which the material resists bending deformation.

Therefore, if the film thickness at each position is large, the position is more

resistant to the bending. As such, we assume that the formation of wrinkle through

bending appears preferentially in the residual film, which have small bending

stiffness and also have no patterned feature on it.

For all cases, Mode I refers to the wrinkle perpendicular to the strain direction.

Mode I is a basic wrinkle structure in all cases. In the square cylinder array with 0°

inclination sample, only the Mode I wrinkle appears, because there are no other

modes which cross fewer cylinder patterns where bending stiffness is relatively

large. In the square cylinder array with 45° inclination sample, Mode II, which

forms an angle of 45° to the strain direction, appears in addition to Mode I. This

can be explained by the fact that Mode II passes through a fewer cylinder patterns

than Mode I.

In a hexagonal cylinder array with 0° inclination sample, Mode II and Mode

III exist in addition to Mode I. In the case of Mode III, the minimum cylinder

pattern is passed, and Mode II also passes through a fewer cylinder patterns than

Mode I. Table 3.1. summarizes the above explanation. With same geometrical

parameters, the angle to the strain and the distance between adjacent identical

modes are shown. The spacing between identical modes is consequently associated

with the wavelength of the mode in the film having same geometrical parameters.

This phenomenon occurs because the spacing between identical modes means the

59

spacing between positions with smaller bending stiffness, which are shown in the

red dots in Figure 3.5.

60

Figure 3.3. Wrinkled Structures of square cylinder arrays. As the

residual thickness of the pattern increases, wrinkles become

perpendicular to the strain. When the strain and the primitive direction

vector lies parallel, wrinkles with direction other than perpendicular to

the strain exist. When the strain and the primitive direction vector form

45° angle, wrinkles are formed perpendicular to the strain.

61

Figure 3.3. Wrinkled Structures of hexagonal cylinder arrays. As the

residual thickness of the pattern increases, wrinkles become

perpendicular to the strain. When the strain and the primitive direction

vector lies parallel, wrinkles with three different direction to the strain

exist. When the strain and the primitive direction vector form 90° angle,

wrinkles are formed of which direction shows two different modes.

62

Figure 3.5. Schematic representations on the cylindrical arrays both

square and hexagonal. Orange dots represent cylinder patterns and red

dots represent the sites with longest distance between cylinder patterns.

Wrinkled directions when external strain is applied are marked as modes.

In all cases, mode I shows the direction perpendicular to the external

strain. In each case, mode number are defined with increasing number

when the mode across more red dots in same distance.

63

Table 3.1. List of modes in wrinkles with cylindrical top surfaces

according to the relationship between direction vector and external strain.

64

3.3.3. Effect of Residual Layer Thickness of Cylindrically Patterned Films on

Wrinkled Structures

The AFM images on the wrinkles of the square array cylinder patterns can be

seen in Figure 3.3., and the AFM images on the wrinkles of the hexagonal array

cylinder pattern can be seen in Figure 3.4. In both the square array cylinder pattern

and the hexagonal array cylinder pattern, the wrinkle wavelength increases as the

residual thickness increases.

λ = 2πℎ �������������

���������� �

���

In wrinkle mechanics, it is well known that the wrinkle wavelength λ follows

the above equation irrespective of the strain. This equation is derived through

balancing the deformation energy of the bottom substrate, and the strain energy

applied externally, and the bending energy of the top film. Here, h is the thickness

of the top film, and each Young's modulus with bar is a modulus that reflects the

material's Poisson's ratio. If there is a pattern, the film thickness changes depending

on the position as it can be regarded as a composite structure with different height

segments. However, in Chapter 2, we have introduced the effective thickness

concept of the composite structure when the wrinkle wavelength is very large

compared to the pattern size. In this regard, it can be assumed that as the residual

thickness of the top surface pattern increases for each wrinkle with cylinder

patterned top surfaces, the effective height increases, and thus the wavelength of

the wrinkle increases.

Also, with increasing residual thickness, it can be seen that the wrinkle modes

gradually change to perpendicular direction to the external strain. This is because

the ratio between the height of the cylinder pattern and the residual thickness gets

65

relatively low, thus the cylinder pattern cannot effectively function as a bending

resistant part. With the same logic, as the residual thickness increases, the

preference for the low inclination angle mode decreases and thus converges to

Mode I.

66

3.4. Conclusions

The wrinkle behavior with nanoscale cylindrical top patterns was investigated

according to the array of the cylindrical patterns and the residual thickness of the

patterned film. We investigated that the nanoscale cylindrical patterns with each

square and hexagonal array have different wrinkle behavior to the microscale

cylindrical patterns, also the wrinkle patterns align with different angles according

to the strain direction although the geometrical parameters are fixed. We suggested

that the wrinkle behavior, which is essentially a bending, occurs along the positions

with minimum area moment of inertia per unit length which is directly related to

the bending stiffness. Also in this regard, wrinkle behavior with varying residual

thickness of the patterns could be explained with varying influence of cylinder

patterns on the bending stiffness. We expect this work can provide a proper guide

for designing hierarchical structures with wrinkles and cylinder patterns.

67

3.5. References

(1) Autumn, K.; Sitti, M.; Liang, Y. A.; Peattie, A. M.; Hansen, W. R.; Sponberg, S.;

Kenny, T. W.; Fearing, R.; Israelachvili, J. N.; Full, R. J. Evidence for van der

Waals adhesion in gecko setae. Proceedings of the National Academy of Sciences

2002, 99 (19), 12252-12256

(2) Geim, A. K.; Dubonos, S. V.; Grigorieva, I. V.; Novoselov, K. S.; Zhukov, A. A.;

Shapoval, S. Y. Microfabricated adhesive mimicking gecko foot-hair. Nature

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Chapter 4. Mechanoresponsive Anisotropic

Wetting on Hierarchical Patterns Based on Wrinkles

and Cracks

4.1. Introduction

Wetting on structured surfaces have gained intense interest due to the potential

applications such as water repelling,1-6 self-cleaning surfaces7-10 or harvesting

water.11-14 Various reports have been inspired from plants, insects and even spider

webs and have the concept in common that the structure itself is the key in

manipulating wetting behavior with changing apparent interfacial correlations.

Among these wetting characteristics, anisotropic wetting found on rice leaves has

been widely investigated for water guiding in the surface structures.15-19 Rice leaves

have surfaces of hierarchical structures with microscale lines and nanoscale

roughness. When water is placed on the surface, the water flows along the line

patterns because there is an energy barrier to overcome in the perpendicular

direction. This unique wetting property makes anisotropic surface patterns more

interesting which can be extended to many other fields. For the application of

printing technology, strong anisotropic wetting on patterned surfaces was reported

and highlighted because the confinement of the liquid in the desired area is critical.

Moreover, the anisotropic studies have been extended to be tunable wetting by

mechanical20-25 or electrical signals.26 Chung et al.20 used the wrinkling by releasing

mechanical forces on the ultraviolet-ozone (UVO) treated surface of pre-strained

71

poly(dimethylsiloxane) (PDMS) to give a direction to flow along the one-

dimensional pattern. When the UVO treated PDMS stretched again, the anisotropy

was disappeared as the wrinkled pattern disappeared. Other tunable anisotropic

wetting studies have been reported after preparing hierarchical structures or using

dielectric elastomers for electrically responsive behaviors.26 Most recently there

was a few works to switch the axis of anisotropic wetting by mechanical stimuli.

Rhee et al.27 demonstrated the change of the wetting by switching the orientation of

line patterns formed by soft skins with mechanical stretching. Also, Cha et al.28

reported fluidic networks by switching the direction of capillary-driven water

movement. Nevertheless, previous studies could show only either control the

degree of anisotropy or switch the direction of anisotropy in one system. Here, we

propose a method to use hierarchical structures to manipulate the anisotropy itself

as well as the orientation of the anisotropic wetting. We prepared a line array with

PDMS and realized microscale wrinkles or cracks by applying compressive or

tensile stresses in the perpendicular direction to the line patterns. By controlling the

competition of the energy barriers in the two directions, we could change the shape

of anisotropy during water movement. When we applied compressive strain to

form wrinkles, we could control the anisotropy by balancing the barrier in two axes.

Because cracks had sharp edges compared to line pattern, the direction of the

smaller energy barrier was switched when the tensile strain was applied. We

explained the energy barrier by the critical contact angle concept29-30 and the

experimental results showed a reasonable agreement. Furthermore, we prepared a

prestrained and cracked hierarchical structures and demonstrated to control the

anisotropy by compressive strain and the orientation by tensile stress on one

structured surface.

72

73

4.2. Experimental Section

Fabrication of Patterned PDMS

Silicon master pattern with line/space patterns with 2400 nm line patterns and

spacing ratio of 0.33 was used as a basic mold to prepare a polyfluoropolyehter

(PFPE) pattern. The PFPE mold was prepared with a mixture of PFPE prepolymers

(5101X, Fluorolink) and initiator onto the silicon master. After a short UV

exposure (~55 s) through a transparent poly(ethylene terephtalate) (PET) films

which was applied on top of the silicon master. Crosslinked PFPE replica was

carefully detached from the silicon master to make the line/space patterns with 800

nm line patterns and inverted spacing ratio of 3. Further UV treatment was applied

for 3 h to fully cure the PFPE mold to ensure mechanical durability. PDMS

(Sylgard 184, Dow Corning) prepolymer 15:1-mixture (base:curing agent) was

poured on the PFPE replica fixed on the petri dish with scotch tape. After

degassing and curing at 60 °C for 6 h, line/space patterned PDMS sheets were cut

into ~4 cm × 1.5 cm pieces.

Fabrication of Hierarchical Structures Based on Winkles

The patterned PDMS was placed on a custom-made PDMS pull/press machine,

with which applied strain can be controlled. After applying 1-D prestrain ranging

0-40 %, the patterned PDMS was UVO treated for 1 h. With releasing the prestrain,

hierarchical structure with controlled 1-D wrinkles and smaller scale-line/space

patterns was obtained.

74

Fabrication of Hierarchical Structures Based on Cracks

The patterned PDMS was placed on PDMS pull/press machine, without any

prestrain applied. After UVO treatment for 1 h, 1-D tensile strain of 70-90 % was

abruptly applied to form 1-D cracks. With releasing abrupt tensile strain, controlled

tensile strain of 0-40 % was then reapplied to control hierarchical structures based

on cracks.

Fabrication of Hierarchical Structures Based on Wrinkles and Cracks

The patterned PDMS was placed on PDMS pull/press machine, with 40 %

prestrain applied. After UVO treatment for 1 h, 1-D tensile strain of 70-90 % was

abruptly applied to form 1-D cracks. Controlling tensile strain of 0-40 % was

applied on the PDMS leads to combined hierarchical structures with both wrinkles

and cracks. More detailed schematics on fabrication of hierarchical structures are

shown in Figure 4.1.

Characterizations

Surface structures were analyzed by observing the height profile obtained

from AC-mode AFM images (Nanowizard 3, JPK Instruments). AC mode

cantilevers (Length = 125 μm, width = 30 μm) with aluminum back coating were

used. Top view photographs of anisotropic water droplets on hierarchical structures

were obtained with camera sets over the PDMS pull/press machine and syringe

pump (KDS 100, KD Scientific) for flow control. Images for measuring drop

anisotropy were taken with fixed drop volume of 30 μL. (Apparatus setup

described in Figure 4.2.) Critical contact angles from parallel and perpendicular

direction against the line patterns were obtained through time resolved contact

75

angle analysis during taking images of advancing contact angles with drop shape

analysis system (DSA 100, Krüss GmbH). Maximum droplet volume was fixed to

10 μL, infuse rate was maintained with 10 μL min−1 for all video measurements.

76

Figure 4.1. Schematic representation of fabricating hierarchical

structures based on wrinkles /cracks and hierarchical structures based on

wrinkles and cracks

77

Figure 4.2. A photograph on liquid flow experimental apparatus which

can apply tensile strain to the prestrained samples.

78

4.3. Results and Discussion

4.3.1. Flow Anisotropy Control on Hierarchical Patterns Based on Wrinkles

Figure 4.3. shows the schematic illustration on the concept of manipulating

asymmetry and the orientation by microscale wrinkles and cracks formed in the

perpendicular direction to the line patterns. Line patterns with 2400 nm width and

800 nm space and 500 nm in space height were prepared by conventional

photolithography and dry etching process. From the twice replica molding method,

we could obtain the PDMS block with feature of line patterns (2400 nm in width,

800 nm in space). To realize wrinkles in perpendicular direction to the line patterns,

we stretched to the parallel direction of the line patterns with strain ranging from 0 %

to 40 % then exposed UVO over the line patterns to make stiff SiO2 layer on top of

the PDMS pattern and then released the prestrain to apply compressive stress on

the film. We harness the formation of hierarchical structures, of which direction is

perpendicular to the line pattern, which is the essential difference compared to

other previous works. As shown in Figure 4.3. (a), the water droplet lies along the

line patterns asymmetrically when there are no mechanical forces. After applying

compressive stress to form wrinkles in the perpendicular direction, the shape of

water droplet can be changed to isotropic.

79

Figure 4.3. Conceptual illustrations of anisotropic wetting on the

hierarchical structures originated from wrinkles and cracks. (a)

Anisotropy of water flow can be controlled by wrinkling in perpendicular

direction of line patterns. (b) Cracks on the line patterns can change the

direction of anisotropic water flow.

80

Figure 4.4. (a) shows atomic force microscopy (AFM) images and the

corresponding height profiles of UVO treated PDMS line patterns used in this

study. When the compressive stress was applied to make the prestrain before UVO

treatment, microscale wrinkles were formed as shown in the AFM image in Figure

4.4. (b). The microscale wrinkles have ~30 mm in wavelength regardless of applied

prestrain and amplitude changes from 0 to 5.6 μm when applied prestrain change

from 0 to 40%. From the characteristic wavelength of wrinkles,32-36 we could

predict the thickness of SiO2 layer formed by UVO treatment by the relation.

Wavelength � = 2�ℎ��� 3��⁄ �� �⁄

where ℎ is the thickness of the stiff layer, �� is the modulus of top film, and

��is the modulus of bottom elastomeric substrate. We assume that the UVO treated

top surface of PDMS is nearly isotropically changed to silicate top surface and the

bottom layer remains 15:1 PDMS. Calculated silicate layer thickness remains ~0.3

mm, which well agrees to former studies on the UVO treatment over PDMS

surfaces.37-39

In most previous works reporting anisotropic wetting on various patterned

surfaces,15-18,23 they use the drop distortion (DD) parameter which is defined as the

ratio of length of major axis and minor axis. However, this parameter is only valid

for systems which the change of the major axis is inexistent, i.e. no change in

wetting orientation, and exclude information of wetting directions. In our system, it

is necessary to redefine the drop anisotropy as following normalized length ratio to

include the anisotropy itself and the information of wetting orientation.

Anisotropy=��(∥)��(�)

�(∥)��(�)�

81

When this parameter is positive, i.e. the droplet length along the nanoscale

line pattern direction is larger, water droplet lies along the line patterns, while it

shows negative sign when the water droplet lies along the microscale wrinkle or

crack direction. Without any mechanical distortions on the UVO treated patterned

PDMS in Figure 4.5. (a) the water droplet wets along the line patterns which

describes the anisotropic wetting induced by surface structures. As shown in Figure

4.5. (b)-(c) the shape of water droplet become isotropic with decreasing drop

anisotropy as the applied prestrain on the system increases and the amplitude of the

wrinkle structure become larger to affect the anisotropic wetting phenomenon.

Note that the sign of the drop anisotropy remains positive during the change of the

prestrain, which means the direction of the wetting remains parallel to the line

patterns.

82

Figure 4.4. (a) Atomic force microscopy (AFM) images and height profile of

line/space patterns (a) before and (b) after wrinkling.

83

Figure 4.5. Drop anisotropy can be controlled with varying prestrain on

wrinkled structures. The direction perpendicular to the line patterns is defined

as⊥, while the direction parallel to the line patterns is defined as∥. Drop

anisotropy was defined as [l(∥)-l(⊥)]∕[l(∥)+l(⊥)] , where l(∥), l(⊥) represent

droplet length along ∥, ⊥ direction each. Scale bars represent 2mm each.

84

4.3.2. Strain Dependent Critical Contact Angles of Hierarchical Patterns

Based on Wrinkles

To explain the anisotropic wetting phenomena on groove-like patterns, Oliver

et al. introduced the critical contact angle concept.29 The critical contact angle is

defined as the contact angle on the moment that the water flow goes over to the

next periodic pattern after pinning to former pattern, which is closely related to the

critical energy to overcome the pattern, and this could be measured by taking

snapshot during the dynamic contact angle measurement. (Figure 4.6.)

The anisotropic shape of water droplets can be quantified by comparing both

critical contact angles of parallel and perpendicular to the line pattern direction. As

shown in Figures 4.7. and 4.8. (a), the critical contact angles parallel to the line

patterns increases, while the critical contact angles perpendicular to the line

patterns show no significant change as the applied prestrain increase. This result

quantitatively agrees with previous works on anisotropic wetting studies based on

wrinkles without any nanoscale features on the surface.20,22,23 Figure 4.8. (b) shows

that the difference between critical contact angles of each direction displays similar

tendency to the droplet anisotropy measured from the top view optical images,

which enables us to conclude that the critical contact angle difference corresponds

to the anisotropy of the water droplet

85

Figure 4.6. Critical contact angle measurement in line patterns, wrinkle

patterns, crack patterns. Critical contact angles were taken as contact angles at

the moment just before the water droplet overcomes groove-like patterns.

86

Figure 4.7. Critical contact angle measurement in line patterns, wrinkle

patterns, crack patterns. Critical contact angles were taken as contact angles at

the moment just before the water droplet overcomes groove-like patterns.

87

Figure 4.8. (a) Effect of the prestrain on the critical contact angles of both

perpendicular and parallel directions to the line patterns. (b) The difference in

critical contact angles in each direction shows similar trends with the drop

88

4.3.3. Flow Direction Control on Hierarchical Patterns Based on Cracks

To obtain dual scale structures with line patterns and cracks, patterned PDMS

was initially treated with UVO without any prestrain applied. Then tensile strain of

70-90 % was abruptly applied to form cracks perpendicular to the direction of

applied tensile strain. It is well known that the cracks emerge when applied tensile

strain exceeds a critical value in the consequence of mechanical fracture and the

anisotropic cracks are formed vertical to the applied uniaxial tensile or bending

strain.31 When we release the strain to the original state, the cracks could be closed.

When we generate cracks as shown in Figure 4.3., interestingly, the anisotropic

water droplet lies along the cracks, which means the change in the orientation of

the asymmetric behavior.

Figure 4.9. (a)-(c) show the AFM images and corresponding height profiles of

hierarchical structures based on uniaxial cracks. As the applied tensile strain

parallel to the line patterns increases, the pitch and the depth of cracks increase as

well. The optical images of the anisotropic water droplets are shown in Figure 4.10.

(a)-(c) of which measurements are conducted as the same way in the previous

wrinkle studies. When the tensile strain is small, which means that the pitch

remains small and the cracks are almost closed, the drop anisotropy remains

positive to show the direction of wetting remains parallel to the line patterns.

However, as the cracks are opened to affect the wetting property as the tensile

strain increase, the droplet anisotropy become negative, which means the direction

of anisotropic wetting is changed to the direction along the cracks. (More detailed

drop anisotropy measurements with varying droplet volumes are shown in Figure

4.11. (b), and crack-to-crack distance distributions are shown in Figure 4.12.)

89

Figure 4.9. Atomic force microscopy (AFM) images and corresponding

height profiles of line/space patterns (a) before applying tensile strain, (b)

after applying 20% and (c) 40% tensile strains.

90

Figure 4.10. (a) Top view photographs on anisotropic water droplet

along the line patterns when the tensile strain is inexistent. (b), (c) Top

view photographs showing that the direction of water droplet has

changed from the original direction after applying 20% and 40% tensile

strains each. Scale bars represent 2mm each.

91

Figure 4.11. (a) Anisotropy of water droplets with varying drop volume

in wrinkled patterns with different compressive strain. (b) Anisotropy of

water droplets with varying drop volume in crack patterns with different

tensile strain. (Tensile strains are indicated with negative signs.)

92

Figure 4.12. Adjacent crack-to-crack distance distribution in hierarchical

patterns based on cracks with applied tensile strain of (a) 0% (b) 10% (c)

20% (d) 30% (e) 40%.

93

4.3.4. Strain Dependent Critical Contact Angles of Hierarchical Patterns

Based on Cracks

To explain the anisotropic wetting phenomena on groove-like patterns, Oliver

et al. introduced the critical contact angle concept.29 The critical contact angle is

defined as the contact angle on the moment that the water flow goes over to the

next periodic pattern after pinning to former pattern, which is closely related to the

critical energy to overcome the pattern, and this could be measured by taking

snapshot during the dynamic contact angle measurement. (Figure 4.6.)

In the case of hierarchical structure system based on cracks, the critical contact

angles parallel to the line patterns shows much more variation compared to the

wrinkle based system, while the critical contact angles originated from line patterns

keep constant. (Figure 4.13., 4.14. (a)) When we apply tensile strain, (above ~10 %)

the critical contact angles across the cracks are higher than the angles through lines,

which is well agreed with the orientation change of droplet anisotropy as shown in

Figure 4.14. (b).

94

Figure 4.13. Optical images on critical contact angles on the hierarchical

structures (line patterns with microscale cracks in the perpendicular

direction) with varying tensile strain. The critical contact angles of the

direction parallel to the line patterns increases as the tensile strain

increase, while the critical contact angles of the direction perpendicular

to the line patterns remains almost the same.

95

Figure 4.14. (a) Effect of the tensile strain on the critical contact angles

of both perpendicular and parallel directions to the line patterns. (b) The

difference in critical contact angles in each direction shows similar trends

with the drop anisotropy.

96

4.3.5. Simplified Model of Cracks and Wrinkles for Calculation of Critical

Contact Angles Based on Height Profiles

We obtained the critical contact angles from the surface height profiles of the

line patterns, (Figure 4.15. (a)) wrinkle patterns, (Figure 4.15. (b)) and crack

patterns. (Figure 4.15. (c)). The microscopic definition of critical contact angles by

Oliver et al. is,

Critical Contact Angle (CA) ��� = � + �

where � is defined as the intrinsic contact angle on the flat surface, and � is

defined as the inclination of the simplified pattern. (Figure 4.16.) For 1-hour UVO

treated PDMS, which is studied over this study, the intrinsic contact angle �=68°.

(Figure 4.17.) We defined the simplified pattern inclination � for each system as

following, (Figure 4.15. (a)-(c))

�line = tan�� (depth)

(pitch/2)

�wrinkle = tan�� (amplitude)

(wavelength/2)

�crack = tan�� (depth)

(pitch/2)

The calculated critical contact angle for line pattern is 119° and well meets the

experimental value of CA⊥, which confirms that the simplified modeling of pattern

height profile gives us proper insights to the anisotropic wetting phenomena. We

further confirm that the calculated critical contact angles of wrinkle patterns or

crack patterns show similar tendency to the experimental values of CAll for each

system. (Figure 4.18. (a), (b))

97

Figure 4.15. Characteristic height profiles from atomic force microscopy

for each (a) line patterns, (b) wrinkles, (c) cracks and corresponding

simplified groove angle (�) each.

98

Figure 4.16. Definition of critical angle (qcr ) on patterned surfaces. Critical

angle is defined as the sum of intrinsic contact angle of the flat surface (q) and

pattern inclination (a)

99

Figure 4.17. Definition of critical angle (qcr ) on patterned surfaces. Critical

angle is defined as the sum of intrinsic contact angle of the flat surface (q) and

pattern inclination (a)

100

Figure 4.18. Definition of critical angle (qcr ) on patterned surfaces. Critical

angle is defined as the sum of intrinsic contact angle of the flat surface (q) and

pattern inclination (a)

101

4.3.6. Mechanoresponsive Tuning of Orientation and Anisotropy of Water with

Hierarchical Patterns

From the concept of manipulating anisotropic behavior of liquid flow by

harnessing hierarchical structures, we demonstrate how to control both orientation

and anisotropy of a water droplet in one system. We prepared the patterned PDMS

which is UVO-treated after applying prestrain. (AFM images and representative

height profiles are shown in Figure 4.19.) Then, we generated cracks by applying

abrupt tensile stress much greater than the prestrain. After the procedure, we

examine the anisotropic behavior of the droplet with increasing water volume.

When the tensile strain is greater than the prestrain, water flows along the cracks as

shown in Figures 4.20. (a), (b). When the applied tensile strain and the prestrain are

similar, the flow direction of water becomes along the lines because there is no

significant wrinkles or cracks. (Figures 4.20. (a), (c)) While there is no tensile

strain applied, wrinkles become dominant and the shape of water droplet is

isotropic.

Figure 4.21. shows the critical contact angles of directions both perpendicular

and parallel to the line patterns for this system. As we discussed in former systems

with only wrinkles or cracks, the critical contact angles perpendicular to the line

patterns shows little variation. However, the critical contact angles parallel to the

line patterns vary with applied strain and can be classified into three regimes.

(Figure 4.22.) When the tensile strain is greater than prestrain, only cracks are

formed, critical contact angle across the cracks becomes higher than that of the line

patterns. It means the energy barrier across the line patterns is smaller than that of

the cracks. If the applied tensile strain become similar to the prestrain, critical

contact angle through the line patterns is the highest, which means the energy

102

barrier of line patterns is dominant. Furthermore, when the applied prestrain is

dominant, the wetting phenomena is governed by wrinkles as well as line patterns

and the shape of the water droplet became isotropic.

103

Figure 4.19. (a)-(c) AFM images on the hierarchical structures based on

wrinkles and cracks. As the strain increases, both closing of cracks and

emerging of wrinkles can be observed.

104

Figure 4.20. (a) A schematic illustration showing the mechanoresponsive

tuning of the direction of anisotropic water droplet with crack formation and the

anisotropy with wrinkle formation. (b) Top view photograph of anisotropic

water droplet when the tensile strain is larger than prestrain, which leads to

relatively large crack structures. (c) Top view photograph of water droplet when

the tensile strain is similar to the prestrain, where the crack structures become

negligible. (d) Top view photograph of anisotropic water droplet when the

prestrain is larger than the tensile strain, which is the condition of wrinkle

formation. Scale bars represent 2mm each.

105

Figure 4.21. Critical contact angles on the hierarchical structures based on

wrinkles and cracks with varying strain.

106

Figure 4.22. (a) Effect of the strain on the critical contact angles and the drop

anisotropy on hierarchical structures based on both wrinkles and cracks. When

applied strain is small, which leads to large crack features, critical contact

angles perpendicular to the strain are larger. With increasing strain, close of

cracks change the direction of wetting and the anisotropy of water droplet can

be controlled in the same way to the case where only wrinkles exist. (b) The

difference in critical contact angle in each direction and the flow anisotropy

shows similar trends with varying strain.

107

4.4. Conclusions

Mechanoresponsive anisotropic wetting was demonstrated in this work which

can control anisotropy as well as orientation with hierarchical structures based on

wrinkles and cracks. Nanoscale line patterns of PDMS were produced with replica

molding method. Compressive or tensile stress were applied to the UVO treated

PDMS with line patterns to generate wrinkles or cracks in the perpendicular

direction to the line patterns. We could manipulate the anisotropy of the water

droplets by using microscale wrinkles and the orientation by forming cracks. We

measured the critical contact angles and explained the anisotropy change with the

model. . Combining effects of wrinkles and cracks on the anisotropic wetting

enabled control of both anisotropy and orientation of water droplets in one platform.

The mechano-responsive tuning of anisotropic liquid behavior with hierarchical

structures presented here could be easily applicable to wetting based applications

such as microfluidics, water harvestings, etc.

108

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Chapter 5. Conclusions

Mechanical instability has long been an important area of engineering mainly

originated from the architectural engineering, of which focus had in large part in

inhibiting formation to prevent unwanted failures. However, recent trends rather

encourage the formation of controlled mechanical instability in order to make

unique nano or micropatterns which was difficult to obtain with conventional

lithography or other conventional patterning processes. These kinds of works

gained more interests as the ability to easily construct easily construct three

dimensional structures for the applications with structural functionalities or to

generate applications with mechanoresponsive features. To satisfy increasing needs

for these kinds of high functioning applications, efforts to understand the

mechanics of mechanical instabilities of top surfaces with various patterns have

been emphasized.

In this context above, this thesis described further efforts to control and

engineer mechanical instabilities with top patterned surfaces. Meantime, most of

the studies conducted in this area chiefly concentrated on the system of which size

of the boundary condition is comparable to the size of the patterns rising from

mechanical instabilities mainly due to the simplicity of manipulation. Also, the

mainstream of the study remained on the intuitive control of shape or directions of

mechanical instabilities with large external constraints in the system. However, for

provide more sophisticated, fine-tuned, useful functionalities to the structure,

detailed knowledge and insight should be provided on the mechanical instabilities

with nanostructured top surfaces other than microstructured top surfaces which are

114

well known. In this regard, this thesis argued the engineering and control of

hierarchical structures consisting of nanopatterns and anisotropic mechanical

instabilities for high functionalities of mechanoresponsive structures.

The first chapter describes the necessity for systematic study on mechanical

instabilities with structured surfaces. Especially, the nanopatterns for the top

surface are of great importance to gain various functions. For seamless study of

hierarchical structures based on anisotropic mechanical instabilities, our group

invented a facile nanopattern transfer technique. This technique resembles

conventional offset printing and enables various patterns scaling from nano to

micropatterns to form stable bilayer system with elastomeric PDMS. With this

offset polymer film printing technique, we could easily fabricate hierarchical

structure consisting of block copolymer film and wrinkle patterns.

In the second chapter, a precise and detailed structural prediction and

explanation of microscale buckling of nanoscale line/space patterns with various

geometrical parameters were described. We suggested a new analytic solution for

the buckling of a patterned top film, ignoring in-plane deformation of

nanostructures, which is appropriate when the characteristic size of the

nanostructure is negligible compared to that of microscale buckling structures.

Comparing experimental data and proposed theory confirms the assumption,

especially for highly geometric heterogeneity in the top patterns, i.e., high aspect

ratio or thin residual layer region. We expect this precise explanation to provide

design rules for high-functioning flexible electronic devices based on buckling

structures.

The third chapter expands the systematic study of wrinkles with nanopatterned

top surfaces to more various patterns which can provide other structural properties

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than line/space pattern which is described in the second chapter. Cylinder

nanopatterns with hexagonal and square arrays were fabricated with nanoimprint

lithography and successfully transferred onto PDMS substrates to elaborate bilayer

system. Nano cylinder patterns show totally different wrinkling behavior to the

micro cylinder patterns which means the natural difference of stiffness.

In the last chapter, mechanoresponsive anisotropic wetting was demonstrated

which can control anisotropy as well as orientation with hierarchical structures

based on wrinkles and cracks. Compressive or tensile stress were applied to the

UVO treated PDMS with line patterns to generate wrinkles or cracks in the

perpendicular direction to the line patterns. We could manipulate the anisotropy of

the water droplets by using microscale wrinkles and the orientation by forming

cracks. We measured the critical contact angles and explained the anisotropy

change with the model. Combining effects of wrinkles and cracks on the

anisotropic wetting enabled control of both anisotropy and orientation of water

droplets in one platform. The mechanoresponsive tuning of anisotropic liquid

behavior with hierarchical structures presented here could be easily applicable to

wetting based applications such as microfluidics, water harvestings, etc.

Although this thesis has focused on anisotropic mechanical instabilities with

nanopatterns, the underlying principles discussed here can be widely applied to

isotropic mechanical instabilities or structures with both nano and micropatterns.

Especially the systematic study on various nanopatterns with a series of parameters

can provide design rules for fabricating hierarchical structures on mechanical

instabilities. Further, we showed one possible mechanoresponsive application with

anisotropic wetting, which can give insights to further applications. It is believed

that ceaseless devotion to the hierarchical structures based on mechanical

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instabilities can provide more detailed and interesting applications such as flexible

or stretchable electronic devices, mechanoresponsive functionality driven

applications.

117

국문 초록

구조를 가진 계의 기계적 불안정성은 구조를 무너뜨릴 수 있는 다

양한 종류의 응력이 계에 가해질 때 그를 완화시키기 위해 나타난다. 공

학의 한 분야로서의 기계적 불안정성은 다양한 계에서 흔히 구조적 실패

혹은 파손으로 간주되어 왔으며, 이 분야의 대부분의 연구는 많은 대형

구조에서의 구조적 실패 방지에 집중되어 있었다. 그러나 마이크로 및

나노 공학에 있어서 기계적 불안정성을 극복하거나 적극적으로 활용하고

자 하는 많은 노력이 있어 왔다. 특히, 기계적 불안정성 중 상대적으로

간단한 주름, 접힘, 균열 등을 인위적으로 만드는 선구적인 연구들이 있

은 이후, 얇은 경질의 상부 박막과 연질 엘라스토머 하부 기저물질로 구

성된 단순한 이중층 시스템이 공학설계된 패턴을 생성하는 새로운 방법

으로 각광을 받았다. 이후에 기계적 불안정성에 관한 관점은 고분자 박

막, 금속 박막, 반도체 나노리본 등과 같이 다양한 상부 박막을 이용하여

패턴을 만드는 데 까지 넓혀진다. 초기의 연구들은 금속 박막에 주로 집

중되었는데, 주로 열증착되어 열팽창/열수축의 등방성 성질에 기인한 헤

링본 모양 혹은 지그재그 구조를 이루는 이차원 주름을 특징으로 하였다.

그러나 단순한 등방성 이차원 주름은 유용한 기능성을 제공하지는 못한

다. 이러한 점을 보완하기 위해 이방성의 일차원 기계적 불안정성에 대

한 연구가 관심을 끌게 되었다. 특히, 금속 나노리본 혹은 반도체 나노리

본의 주름 구조는 신축성 혹은 굽힘 가능한 전자장치의 제조에 새로운

가능성을 보여주었기 때문에 관심을 모아 왔다. 게다가, 광학 격자, 마이

118

크로 유체역학에의 응용, 이방성 습윤거동, 건식 접착거동 등에 이용하기

위해 이중층 시스템의 주름이나 좌굴 현상을 이용하는 다양한 응용 분야

가 널리 연구되었다. 더불어 매우 큰 응력을 받는 이중층 시스템에서 나

타나는 균열 구조는 마이크로패턴을 만드는 방법으로서 주목을 받았다.

이러한 이차원 혹은 일차원 기계적 불안정성을 새로운 마이크로패턴 제

조 기술로서 이용하고자 하는 시도들은 결과적으로 이중층 시스템의 단

순하고 해석적인 역학구조를 밝히기까지 이어져왔다.

패터닝에 기계적 불안정성을 이용하는 것 이외에, 상부 박막에 패터

닝을 하여 기계적 불안정성을 유도할 수 있고 이를 이용해 보다 주기적

인, 보다 제어된 구조들을 만들 수 있다. 특히 좌굴 역학의 에지 효과는

잘 알려진 현상이며, 다양한 미세 패턴에 대해 널리 연구되었다. 이 에지

효과는 크기가 에지와 비슷한 주름의 형성에 있어서 경계조건의 중요성

을 설명한다. 주름은 형성된 에지에 직각으로 형성되는 경향을 보여, 이

를 이용해 주름을 이용한 마이크로패터닝에 응용이 가능하다. 또한, 연구

자들은 다양한 시스템에서 균열 역시 제어가 가능함을 보였다. 예를 들

어 인장응력이 계에 가해질 때 사전 절단 혹은 제어 노치를 형성하면 균

열 구조 형성의 시드로서 작용하도록 만들 수 있다. 이외에 콜로이드 박

막 시스템과 같은 경우에 있어서도 균열을 가열 속도, 막 두께 등을 이

용하는 등의 방법으로 제어할 수 있다. 기계적 불안정성을 이용하여 패

턴을 형성하는 분야의 핵심은 가공된 나노 혹은 마이크로패턴과 기계적

불안정성에 의해 형성되는 패턴 간의 관계를 이해하는 데 있다.

기계적 불안정성을 이용한 패터닝의 중요성이 다양한 응용분야에서

119

각광받음에 따라, 상부 표면의 구조가 점점 중요해졌다. 보다 정교하고

복잡한 기능성을 갖도록 하기 위해서 일반적으로 계층적 구조를 도입하

는 것이 강력한 방법 중 하나로 잘 알려져 있다. 기계적 불안정성을 이

용한 계층 구조를 만들 경우에, 시스템을 제어하기 위한 가장 중요한 점

은, 나노구조와 기계적 불안정성 간의 관계를 완전히 이해하는 것이다.

그러나 다양한 나노패턴에 대한 체계적인 연구가 부족한 실정이다. 이는

주로 나노패턴-엘라스토머 하부 기저물질 이중층 시스템을 형성하는 과

정이 어렵기 때문이다. 본 연구단에서는 다양한 계층적 시스템과 그 응

용에 대한 연구에 집중해 왔기 때문에 나노패턴-PDMS 이중층 시스템을

구축하기 위한 몇 가지 방법을 개발하고 발전시킨 바 있다.

본 박사학위 논문은 나노패턴과 이방성 마이크로스케일의 기계적

불안정성을 갖는 계층구조의 형성과 제어에 관한 체계적인 연구를 제시

한다. 나노패턴과 주름 혹은 균열 사이의 관계를 조사하기 위해 라인/스

페이스 패턴, 실린더 패턴 등의 다양한 나노 패턴을 연구하였다. 또한 이

방성 기계적 불안정성에 기반한 계층적 구조의 한 가지 응용 사례로서

기계적 조절이 가능한 이방성 젖음특성을 제시한다. 보다 구체적으로, 1

장에서는 박막-PDMS 이중층 시스템의 기계적 불안정성에 대한 개념과

다양한 적용가능한 분야에 대해 소개한다. 또한 나노 혹은 마이크로 패

턴을 갖는 고분자 박막을 PDMS 위에 전사하여 이중층 시스템을 구축하

는 새로운 전사 기술을 소개한다. 2장에서는 나노임프린트 리쏘그래피로

형성된 이방성 나노패턴 표면의 주름현상에 관한 연구를 수행하였다. 다

양한 너비, 높이 및 간격 비율을 갖는 나노라인의 주름 현상에 대해 깊

120

이 조사하였고, 패턴된 박막의 굽힘 강성만을 고려하여 주름 형성을 예

측하는 새로운 모델을 제시하였다. 3장에서는 육각 실린더 구조, 사각 실

린더 구조와 같은 다양한 나노패턴의 주름 구조에 대해 연구하였다. 나

노패턴된 상부 표면을 갖는 시스템의 경우, 마이크로패턴된 상부 표면을

갖는 시스템과 완전히 다른 방식으로 주름이 형성되며, 이차원 강성 파

라미터를 통해 현상을 설명할 수 있었다. 마지막으로 4장에서는 UVO처

리된 PDMS 시스템의 기계적 불안정성을 조절하여 방향성을 갖는 젖음

현상의 이방성과 방향성을 조절하는 방법을 제시하였다. 압축 응력으로

형성되는 주름과 인장 응력으로 형성되는 균열 구조를 이용하여 이방성

젖음 현상을 보이는 계층적 구조를 형성하였다. 이를 이용하여 기계적

자극에 반응하는 이방성 젖음 현상을 보일 수 있었으며, 이러한 현상을

능선 모양을 극복하기 위한 임계 접촉각 개념을 도입하여 설명할 수 있

었다.

이상의 성과는 기계적 불안정성 기반의 계층적 구조에 대한 체계적

인 연구를 제시하였으며, 이를 통해 기계적 변형을 통해 제어 가능한 패

턴의 형성과 기계적 불안정성 기반 기능성을 이용한 응용분야로의 영역

을 넓혀 줄 것을 기대한다.

주요어: 나노패턴, 기계적 불안정성, PDMS, 주름, 균열, 계층적 구조

학번: 2011-22913