論文 / 著書情報
Article / Book Information
題目(和文)

ブロックコポリマー系熱可塑性エラストマーのモルフォロジーおよび
ナノメカニカル特性評価

Title(English)

Morphological and Nanomechanical Characterization of Block
Copolymer-Based Thermoplastic Elastomers

著者(和文)

劉浩男

Author(English)

Haonan Liu

出典(和文)

学位:博士（工学）,学位授与機関:東京工業大学,
報告番号:甲第11801号,
授与年月日:2022年3月26日,
学位の種別:課程博士,
審査員:中嶋 健,福島 孝典,原 正彦,古屋 秀峰,澤田 敏樹

Citation(English)

Degree:Doctor (Engineering),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第11801号,
Conferred date:2022/3/26,
Degree Type:Course doctor,
Examiner:,,,,

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)

Tokyo Institute of Technology
School of Materials and Chemical Technology
Department of Chemical Science and Engineering

Morphological and Nanomechanical
Characterization of Block Copolymer-Based
Thermoplastic Elastomers
byHaonan LIU
M.E., Tokyo Institute of Technology (2019)

Submitted in part fulfillment of the requirements forthe degree ofDoctor of Engineering
at theTokyo Institute of Technology, March 2022

Morphological and Nanomechanical Characterization of Block
Copolymer-Based Thermoplastic Elastomers
byHaonan LIU
Submitted to the School of Materials and Chemical Technology
in partial fulfillment of the requirements for the degree ofDoctor of Engineering

Abstract
Thermoplastic elastomers (TPEs) retain permanent deformation after elongation, preventing
them from replacing rubber as an environmentally friendly material. To address TPE’s vulnerability, in this thesis, an in situ atomic force microscopy (AFM) is used to characterize theevolution of TPEs’ microstructure and micromechanical properties before, during, and after
stretching. A finite element analysis (FEA) is then developed and implemented to visualize thelocal behavior of TPE at the nanoscale. Experiments and data analysis show that solving thehard-domain splitting problem in TPE’s microphase separated structure is crucial to increasing
its strength.
Chapter 1, ”Introduction A: Thermoplastic Elastomers”, gives an overview of the TPEs’
microphase-separated structure of the hard domain and soft matrix, as well as their mechanicalproperties, which combine flexibility and toughness like crosslinked rubber. In TPE materials, however, because the hard domain acts as a physical crosslinking point, the crosslinking
point’s binding force is weaker than that of chemically crosslinked rubber, and stress relaxation
and residual strain are considered inferior. The importance of elucidating the macroscopic andmicroscopic structure-property relationships for TPE materials under deformation is discussed
to provide design guidelines for TPE materials that can replace cross-linked rubbers. It isalso discussed that, while molecular dynamics (MD) simulations predict hard domain behavior
during deformation, experimental techniques to validate the predictions are lacking.
Chapter 2, ”Introduction B: Atomic Force Microscopy for Polymer Science”, discusses theprinciple of simultaneous measurement of structure and properties of polymeric materials by anano-palpation technique based on AFM, as well as the effect of deformation of the AFM tip
on the sample. It also presents a typical Johnson-Kendall-Robert (JKR) contact theoreticalimodel for analyzing the load-deformation curve produced when an AFM probe is deformed
into a sample. The in-situ nano-palpation AFM is also developed and described, which allows
in-situ observation of nanostructure and physical properties of specimens under deformation,
as well as investigation of stress relaxation and residual strain in TPE materials.
Chapter 3, ”Dynamic Stress Network in the TPE”, investigates the macroscopic stress relaxation phenomenon of TPE materials under constant strain using a block copolymer TPE,
styrene-ethylene-butylene-styrene (SEBS). At 50% elongation, in situ AFM is used to investigate the microstructure and properties of SEBS. It has been confirmed that when the soft
matrix is elongated, stress chains connecting the hard domains form in the soft matrix, andthat the soft matrix modulus decreases while the number of hard domains increases in the earlystages of the relaxation process, before stabilizing in the later stages. Furthermore, by focusing
on a specific local region, the formation of hard domains, the emergence of new stress chains,
and the splitting of hard domains, i.e., the existence of a dynamic stress network, have beenclarified. The topology of the polymer is permanently changed by the dynamic stress network,
implying that it is caused by stress relaxation phenomena.
Chapter 4, ”Nanoscale Strain-Stress Mapping for the TPE”, develops an FEA program for
AFM images to better understand the relationship between the ”dynamic stress network” andthe property changes of TPE materials. In this program, the hard domain distributed in the
AFM deformation image is extracted as a set of discrete points and divided into each image byDelaunay triangulation. The strain in each triangle region is calculated during the relaxation
process and combined with the AFM modulus image, the local strain and local stress canbe discussed. In the early stage of the relaxation process, severe contraction occurs inside
the material along the tensile direction and stress concentration is observed. In the later stage,
unlike the early stage, the average strain in the tensile direction becomes close to zero, the regionof stress concentration disappears, and the stress is uniformly distributed over a small area,
describing the visualization of the stress relaxation behavior of TPE materials at a microscopic
level.
Chapter 5, ”Heterogeneously Formation of the Stress Network in the TPE”, observes the microstructure and physical properties of the initial elongation process of the TPE material from
unelongated to about 45% elongation by in situ nano-palpation AFM. The micro-elastic modulus and macro-stress were measured. Since both micro-elastic modulus and macro-stress showii

a non-linear correlation with strain, the FEA method will be used to study them in detail.
Initially, almost all regions deformed regularly, but at the cost of stress concentration in someregions. As the strain increases, non-uniform deformation due to accumulated stresses begins. Finally, all the domains are simultaneously undergoing negative deformation with stressrelaxation. The number of domains decreases and then increases during this process, which
establishes consistency with the MD simulation prediction.
Chapter 6, ”AFM Characterization of Triptycene-Appended Polymers”, investigated triptyceneappended polymers by AFM. The triptycene units in the side chains of the block copolymer andboth terminals of the polymer are described as a special aggregation structure that improves
the mechanical properties of the original polymer.
Chapter 7, ”Summary and Open Questions”, summarizes the contents of this thesis and describes the prospects.

iii

iv

Acknowledgements

The content presented in this thesis represents over three years of research and experimentation that would not have been possible without the outpouring support from family, faculty,
colleagues, and friends.
First and foremost I would like to express my sincere gratitude to my research supervisor
Ken Nakajima-sensei for the academic guidance and financial support, for encouraging me tochallenge unprecedented research topics, and for allowing me the freedom to pursue my own
ideas.
I am also deeply thankful to the members of my dissertation committee: Takanori Fukushimasensei, Masahiko Hara-sensei, Hidemine Furuya-sensei, Toshiki Sawada-sensei for generously
offering their time throughout the review of this thesis.
I wish to thank various people for their contribution to this thesis, Tomoya Fukui-sensei, Yugen
Chen-san and Ayami Itagaki-san of Laboratory for Chemistry and Life Science, for providing
samples and valuable discussion; Tadahiko Shinshi-sensei and Rina Nishida-san of Departmentof Mechanical Engineering for their help in designing the in-situ stretcher.
My deep appreciation goes out to Xiaobin Liang-san, for his patient guidance, enthusiastic
encouragement and useful critiques of this research work. I also deeply thank to Makiko Itosan for her invaluable advice, guidance and taking some time to discuss and enrich my work.
Many thanks also to researchers: Ling Gao-san, Kim Hung Nguyen-san and clerical assistant:
Hiromi Araki-san for lab facilities and kind help during the research and lab life.
I do extend my profound regards to PhD colleagues: Koji Okamoto-san, Ryohei Hosoya-san,Akihiro Naruke-san, Hiroyuki Watabe-san, Ayumi Ando-san for their kind help, encouragement
and suggestions, which helped me in successful completion of this thesis.
With great appreciation I shall acknowledge all my labmates: Mishael Eleosca Gunawan, Xu
Li, Yuki Okinaga, Ryusei Nomura, Koki Hara, Hayate Haruno, Qingyan Shen, Takashi Kikuchi,
Hiroki Sagawa, Kohei Shiomi, Kei Sekine, Dingrui Wang, Toru Kobayashi, Ren Tajiri, Yuto
Miyata, Ryo Miyata, Kaede Mogi, Pijak Thidaychanun, Mingjun Tang, Kotaro Osako, Yasuharu Kashimori, Airi Sato, Masato Mori, Shun-ichi Nomura, Mari Hanai, Kazuhiko Fujimoriv

for the stimulating discussions, for the sleepless nights we were working together before deadlines, and for all the fun we have had in the last years.
I would like to thank my family for the continuous support they have given me throughout mytime in graduate school. My special thanks goes to my beloved girlfriend Xinqi Cong for her
understanding and encouragement not only during my thesis studies but also my life.
The research work in this thesis is mainly supported by JST “Core Research for Evolutionary
Science and Technology (CREST)” JPMJCR17J4 and partially supported by JST “Support
for Pioneering Research Initiated by the Next Generation (SPRING)” JPMJSP2106. Chapter
6 was performed under the Cooperative Research Program of “Network Joint Research Center
for Materials and Devices”.
Main Building, Ookayama Campus
Haonan Liu
March 2022vi

Contents

Abstracti

Acknowledgementsv

1 Introduction A: Thermoplastic Elastomers

1

1.1

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Structure of BCP-Based TPE . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.3

Methods to Improve the Mechanical Strength of TPE . . . . . . . . . . . . . . .

5

1.4

Analytical Techniques for TPE . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1.5

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72 Introduction B: Atomic Force Microscopy for Polymer Science

11

2.1

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2

The Working Principle of AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3

2.2.1

Basic Operation Modes of AFM . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2

AFM Nanomechanical Mode . . . . . . . . . . . . . . . . . . . . . . . . . 16

In-Situ AFM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
vii

viii

CONTENTS
2.3.1

In-Situ AFM Nanomechanics . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4

The Objective of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Dynamic Stress Network in the TPE

23

3.1

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1

Tensile Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2

AFM Nanomechanical Mapping . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.3

Dynamic Stress Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Nanoscale Strain-Stress Mapping for the TPE

37

4.1

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.1

Micro Behavior of the Stress-Relaxing Process . . . . . . . . . . . . . . . 40

4.2.2

Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Heterogeneously Formation of the Stress Network in the TPE
5.1

51

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

CONTENTS
5.2

ix

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2.1

In-Situ AFM Nanomechanical Mapping . . . . . . . . . . . . . . . . . . . 52

5.2.2

Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.3

The Origin of Permanent Deformation . . . . . . . . . . . . . . . . . . . 56

5.3

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 AFM Characterization of Triptycene-Appended Polymers

61

6.1

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.1

Polymer with Appended Triptycene in the Side Chain . . . . . . . . . . . 62

6.2.2

Polymer with Appended Triptycene in Two Terminals . . . . . . . . . . . 65

6.3

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

7 Summary and Open Questions

69

7.1

Summary of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

7.2

Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

7.3

List of Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Appendix A Materials and Methods

75

A.1 Materials and Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A.1.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.1.2 AFM Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A.1.3 Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.2.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.2.2 Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
A.2.3 Sample’s Pre-Polishing for AFM . . . . . . . . . . . . . . . . . . . . . . . 78
A.2.4 AFM Nanomechanical Mapping . . . . . . . . . . . . . . . . . . . . . . . 78

Appendix B Description for SSMapping

79

B.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.2 Step-by-Step Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xList of Tables
A.1 AFM probe information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.2 Instrument information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

xi

xii

List of Figures
1.1

The molecular structures of SEBS, SBS, and SIS triblock copolymer. . . . . . .

3

1.2

Schematic of BCP-type TPE’s microphase-separated structure. . . . . . . . . . .

5

1.3

Schematic of the elastic deformation of BCP-type TPE. . . . . . . . . . . . . . .

6

1.4

Schematic diagram of the dynamic behavior of the TPE during the stretchingprocess. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.1Inter-atomic interaction potential U vs. distance z. . . . . . . . . . . . . . . . . 13

2.2

Schematic diagram of the principle of AFM. . . . . . . . . . . . . . . . . . . . . 14

2.3

Schematic diagram of the deformation of the sample surface by the probe tip.

2.4

The working principle of in-situ AFM nanomechanics. . . . . . . . . . . . . . . . 19

2.5

Common macroscopic stress-strain characteristics of TPE and the in situ AFM
nanomechanics corresponding to them. . . . . . . . . . . . . . . . . . . . . . . . 20

3.1

Two typical tensile curves for TPE. . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2

(Left) Typical force-deformation curves on hard domain and soft matrix with superimposed elastic theoretical curves. (Right) Deformation and elastic modulus
maps of TPE. Scale bar, 100 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3

The elastic modulus map and its value distribution of (left) unstretched sampleand (right) strecthced sample which is kept 0.5 strain for 262 min. Scale bar,
100 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4

Binarized modulus maps and statistics on the number of hard domains. . . . . . 28

3.5

The elastic modulus map and its value distribution of strecthced sample whichis kept 0.5 strain for (left) 262 min and (right) 597 min. Scale bar, 100 nm. . . . 29

3.6(Top) 2D FFT images extracted from obtained modulus maps. Scale bar, 0.1
nm-1 . (Bottom) Schematic diagram of the spacing between hard domains whenthe material is stretched and relaxed. . . . . . . . . . . . . . . . . . . . . . . . . 30

3.7

Dynamic stress network observed in stretching TPE. Image size, 100 nm. . . . . 32
xiii

. 17

xiv

LIST OF FIGURES
3.8

Dynamic stress network observed in another region. Image size, 100 nm. . . . . 33

4.1

AFM deformation maps captured from different relaxing time (Image size: 500nm), where the observed regions are approximately the same. . . . . . . . . . . . 38

4.2

Basic FEA principle for AFM images. . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3

(Left) A typical AFM deformation map of BCP-type TPE in the tensile state.
The arrow indicates the stretching direction. (Right) Schematic diagram of theDelaunay triangulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.4

Notations for the three-node triangle and the schematic diagram of its deformation. 40

4.5

Correlation between the average AFM modulus, the number of hard domains,
and the relaxing time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6

DSC profile of SEBS-15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.7

Relaxing time versus soft matrix modulus in another set of data. . . . . . . . . . 43

4.8(Top) AFM deformation and modulus map of TPE after keeping elongation for
262 and 326 min. (Bottom) Linear-strain maps in the x and y coordinate derived
from deformation maps with the stress map derived from modulus maps. . . . . 44

4.9(Top) Value distribution of local strain and local stress. (Bottom) Schematic
diagram of domain splitting during elongation and its effect on the strain. . . . . 45

4.10 Linear-strain maps in the x and y coordinates derived from deformation maps
with the stress map derived from modulus maps in (top) early and (bottom) latestages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.11 (Top) The distribution of εx , εy , and ∆E at the early and late stages. (Bottom)
Schematic diagram of the dynamic fluctuations of the stress network in the laterelaxation period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.1

AFM modulus maps of BCP-type TPE under different strains. All the images
are in the similar observing area. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.2

Microscopic strain of each stretched state calculated from jig and camera, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3

(Left) Distributions of elastic modulus in each image of Fig. 5.1. (Right) A
macroscopic reproduction for in-situ AFM procedure. . . . . . . . . . . . . . . . 54

5.4

An example of selecting vertices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.5

FEM analysis result on each stage of elongation. . . . . . . . . . . . . . . . . . . 56

5.6

Elastic modulus maps of the sample after releasing the load and relaxing 182
and 393 min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.7

The analysis of the hard domain motion during the relaxing process and its
schematic diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.1

Schematic of triptycenes and their ‘2D + 1D’ structure. . . . . . . . . . . . . . . 62

6.2

Chemical structures of triptycene-appended polymers. . . . . . . . . . . . . . . . 63

6.3

Height and phase images of Trip-Block obtained in AFM tapping mode. . . . . . 64

6.4

Height and phase images of Trip-Random obtained in AFM tapping mode. . . . 64

6.5

Nanomechanical mappings with the distribution of modulus of Trip-Block andTrip-Random. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.6

A first attempt at trip-PDMS in a small scan size. (phase images in tapping
mode, 500 nm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.7

Phase and height images of Trip-PDMS with its layer spacing from the crosssection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.1 Notations for the three-node triangle and the schematic diagram of its deformation. 80
B.2 Flow chart of the program SSMapping. . . . . . . . . . . . . . . . . . . . . . . . 81
B.3 The binarized deformation map and the numbered domains. . . . . . . . . . . . 83
B.4 The renumbered domains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
B.5 The Delaunay meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.6 The modified meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
B.7 Strain maps in x and y coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . 87
B.8 The stress map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B.9 The method of determining the mapping between two triangles. . . . . . . . . . 94

xv

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Chapter 1
Introduction A: Thermoplastic
Elastomers

1.1

GeneralThermoplastic elastomer (TPE) is a thermoplastic high molecular-weight material that behaves like a rubbery elastic material at room temperature and undergoes plastic deformation
at high temperatures 1;2 . Therefore, it is easy to obtain TPE products with rubber elasticity
by using a molding machine for thermoplastics. Usually, rubber products are manufactured
by kneading reinforcing fillers, vulcanizing agents, and other auxiliary agents to chain polymers with low glass transition temperature and capable of micro-Brownian motion at room
temperature, then heating them at high temperature after preforming to cause intermolecularcrosslinking (vulcanization) reactions. The rubber industry has long been energy-intensive andhuman resource-intensive. On the other hand, the thermoplastic products that make up mostplastics can be obtained by simply shearing the raw plastic at a high temperature above thesoftening point to make it flow, then injecting it into a cold mold and manufacturing it using
various molding machines. Unlike the case of vulcanized rubber, material recovery is also easy.
Therefore, it was thought that there should be a rubber that could be molded and processed
like plastic.
1

2

Chapter 1. Introduction A: Thermoplastic Elastomers

By combining the processing advantages of thermoplastics with the performance properties
of elastomers, TPEs can be processed relatively easily using thermoplastic methods such as
extrusion and injection molding, eliminating time-consuming and environmentally unfriendly
methods of rubber processing, especially vulcanization. Industrial production of TPE products
began in the 1960s. In 1965, Shell developed and industrialized a linear styrene-butadienestyrene triblock copolymer (SBS, Fig. 1.1) copolymer by a three-step sequential dosing method
using anionic polymerization technology, under the trade name Kraton D. At high temperatures,the polystyrene (PS) and polybutadiene (PB) blocks in SBS are compatible and mobile. Still,
at low temperatures, they spin off and form a microphase-separated structure in which the PS
domain is finely dispersed as a spherical/cylinder phase in the PB domain on a scale of morethan 10 nm. Since the PS domain plays the role of both crosslinking point and reinforcing
material in vulcanized rubber, elastic properties can be achieved without adding vulcanizing
agents or reinforcing fillers. SBS is considered a pioneer in polymer nanotechnology due to thecharacteristic length of the microphase-separated structure.
At present, there are many types of TPE that have been industrially produced 3;4;5 , mainly
divided into the following types: styrenics, olefins, dienes, vinyl chloride, ammonia esters,
esters, amides, organofluorine, silicone, and vinyl, etc. Below is a brief introduction.
1. Styrene-based thermoplastic elastomers (TPS, TPE-s). The type of products such as
SBS, SEBS, SIS, SEPS, SIBS, etc. The characteristic molecular structure is a three-block
polymer, the hard segment is polystyrene, the rest are soft segments (rubber phase).
2. Polyolefin thermoplastic elastomer (TPO, POE), composed of rubber and polyolefin, usually rubber components for EPDM, NBR and butyl rubber; polyolefin components aremainly polypropylene (PP) and polyethylene (PE), TPO products in the largest amountof EPDM/PP. TPO prepared by dynamic vulcanization process is referred to as TPV.
Such as PP/EPDM (Santoprene), PP/NBR (Geolast), thermoplastics/silicone rubber
(TPSiV), etc.
3. Polyurethane thermoplastic elastomer (TPU), from the reaction with isocyanate ammonia
ester hard chain segment and polyester or polyether soft chain segment of the mutual block1.1. General

3

CH2

CH

CH2

CH2

CH2

CH2

l

m

CH2

CH
n
CH2

CH2

CH
o

p

CH3

Styrene-ethylene-butylene-styrene triblock copolymer (SEBS)

CH2

CH

CH2

CH

CH

CH2

l

m

CH2

CH
n
CH

CH2

CH
o

p

CH2

Styrene-butadiene-styrene triblock copolymer (SBS)
CH3
CH2

CH

CH2
l

CH

C

CH2

m

CH2

CH
n
C

CH2

CH

p

o

CH3

CH2

Styrene-isoprene-styrene triblock copolymer (SIS)
Figure 1.1: The molecular structures of SEBS, SBS, and SIS triblock copolymer.
combination of thermoplastic polyurethane rubber, referred to as TPU.
4. Polyester ether thermoplastic elastomer (TPEE), polybutylene terephthalate (PBT) as a
hard segment, polyether or polyester as a soft segment of the block copolymer.
5. Polyamide thermoplastic elastomer (TPAE), such as polyester amide, polyether ester
amide, polycarbonate-ester amide, polyether-amide and other hard segments for polyamide,
soft segments for polyether and/or polyester segmented block copolymers.
6. Diene thermoplastic elastomers, mainly natural rubber isomers, is called trans-natural
rubber (T-NR). The main varieties are T-NR-trans polyisoprene rubber (TPI) and be-4Chapter 1. Introduction A: Thermoplastic Elastomers
tween the same 1,2-polybutadiene (TPB).
7. Organofluorine thermoplastic elastomer (TPF)
8. Polyvinyl chloride thermoplastic elastomer, mainly divided into thermoplastic PVC (TPVC)
and thermoplastic chlorinated polyethylene (TCPE) two categories.
9. Acrylate thermoplastic elastomer
10. Silicone rubber thermoplastic elastomer

All TPE terms used in this thesis default to the most widely used styrene-based TPE.

1.2

Structure of BCP-Based TPE

The nature of the molecular structure gives TPEs a higher degree of elasticity. All TPEs
are composed of crystalline (glassy) and non-crystalline (amorphous) domains. They can bephysical blends or alloys of crystalline and non-crystalline polymers or block copolymers, which
are chemical mixtures of crystalline and non-crystalline structural blocks in the polymer chain.
In the case of TPEs and blends, the hard chain segments are responsible for the plastic properties of the final product, including ease of processing and high-temperature resistance, as wellas material properties such as tensile strength or chemical resistance. Adhesion is also determined by these properties. Soft chain segments are responsible for elastic or resilient properties.
They determine material properties such as hardness, elasticity, and the degree of permanent
deformation (Fig. 1.2).
From the SBS example, there must be a soft segment domain that shows the elasticity of therubber and a hard segment domain that prevents plastic deformation and provides reinforcement in the material to show properties as a TPE. Since SBS development, a wide variety of
TPEs has been developed and marketed. In addition to those TPEs based on polymer synthesis, such as block copolymers and graft polymers, the types of TPEs are further increased
when rubber/resin blends are included. In particular, Toyota super olefin polymer (TSOP),

CH2

CH

CH2
l

CH

C

CH2

m

CH2

CH
n

C
1.3. Methods to Improve the Mechanical Strength of TPE

CH2

CH
o

p

5

CH3

CH2

which was developed by reversing the concept of impact-resistant plastics, was introduced by

Styrene-isoprene-styrene
triblockToyota in 1991 and has
become the global standard
forcopolymer
automotive(SIS)
bumper materials. This
technology, in which the elastomer is a continuous phase, and the polypropylene (PP) microcrystals are finely dispersed, can be regarded as a model for TPE materials. However, there arestill many issues to be solved in terms of materials, such as heat resistance, creep resistance,
and fatigue resistance. In addition, TPEs have difficulties in long-term durability and stressretention under large deformations like crosslinked rubber.

Soft matrix
BridgeHard domain

Loop
BCP-type TPE

Figure 1.2: Schematic of BCP-type TPE’s microphase-separated structure.

1.3

Methods to Improve the Mechanical Strength of TPE

In an ideal TPE material, where complete elastic deformation can occur after stretching without
damage to the internal structure, it is necessary that the phase separation structure remains
extremely stable. The material deformation pattern in this case is shown in Fig 1.3, thebridge chain formed between the hard domains can maintain the stretch and avoid further
collapse. However, this ideal elasticity variation is very difficult for the currently marketed
TPE materials. The reason is that in a discontinuous phase separation structure like TPE,
the percentage of hard phase has to be controlled in a low range (usually less than 30%),
which results in insufficient strength of the hard phase. In this regard, there are two generalsolutions, one is to improve the strength of the hard phase by molecular design 6;7;8;9 or polymer
blending 10 , and the other is to construct new topological networks 11 so that the individual hard
phases are subjected to smaller forces during the stretching process. However, either method
requires the most profound characterization of the formation mechanism of TPE deformation,

ylindrical (Cscc spherical (SChapter 1. Introduction A: Thermoplastic Elastomers
ocp spherical6
s cp
STyroid (Gdamage, deterioration,etc., which
the cooperation of the state-of-the-art analyticalVolume fractionof A,requires
fA
oddd (O70)
O70
G
L
l
Macromolecules
Macromolecules 2018, 51, 1529-1538.
Figuretechniques.
2. Phase diagram
analogous to2012,
that45,of2161-2165.
Figure 1, but forssymmetric ABA triblock copolymers. Here N is the degree ofnpolymerization of the diblocks formed by snippingdeformation
the triblocks indirection
half.
y
e
limit,47 previously investigated by Matsen and Schick.34 Figurel3 extends that calculation bydeformplotting the complex phase
recover
l

n

l
y
t
,
e
e
e
o
s

(no loop chain)
The present commercial
TPEs havelowelastic
limiting
value (fPS of< 0.3)
for recoverable
elasticity.
Figure 1.3: Schematicof athedeformation
BCP-type
TPE.
)

)

1.4

Analytical Techniques for TPE

To date, in addition to traditional testing techniques such as tensile test, rheomter, dynamic
analysis,
etc.,tocharacterization
Figuremechanical
3. Phase diagram
analogousthat of Figure 1, buttechniques
for infinite at the nano level are becoming more
linear ABAB... multiblock copolymers. Here N is the degree of
12;13;14;15;16;17
and moreof dominant.
smallinangle,
polymerization
the diblocks Many
formedresearchers
by cutting allused
the blocks
the X-ray scattering (SAXS)
middle.
Fourier transform infrared spectroscopy (FT-IR) 18;19;20;21 , and transmission electron microscopy

x
e
t
s
l
s
e
t
,
e

channelto far16;22;23;24;25;15;7
higher segregationand testing
the O70, Sofcp,BCP-based TPEs. More recently, in-situ(TEM)
to investigate
the fordeformationand SA15 phases. As expected, the topology of the phase
SAXS
has beenused totoobserveof TPE during macroscopic elongation 26 . So
diagramremains
equivalentthat ofthe
themicrostructure
diblock copolymer
melt, since the multiblock architecture is justa string offar, as shown in Fig. 1.4, by experiment 17;26 and simulation 27;28 , it is found that hard domain
diblocks joined together. In the limit of an infinite number ofblocks,the phase
diagram fused,again becomes
symmetricabout
f = of strain. Although the simulations
could
be deformed,
and divided
with theincrease
0.5. Continuing the trend from the diblock to the triblock, thegive many
predictions
the dynamicof theanddomain, however, the existence of factors
multiblockarchitecture
has ofslightly
larger behavior
O70 regions
narrower
suchScp
as regions.
different stretching speeds in the simulations than in the real experiments and theAnother way of joining diblocks together is by connecting,inabilitytheof theset parameters
to fully restore
for example,
B-endsto form a diblock-arm
star. theThisreal
is situation make it urgent to repeat the
18−20
observed
evidently the first system for which experiments
results of the simulations using experimental techniques. Alternatively, AFM has the functiona gyroid morphology, although it was mistakenly identified as a
double-diamondmorphology. Thismisassignment
wasbycorto get the force-distancecurvesof the surface
deforming the material with a probe andrected48 shortly after SCFT calculations34 predicted gyroid to
employingcontactmechanics to The
obtainthe elastic
modulus, adhesion energy, and other physicalbe morestable thandouble-diamond.
SCFT
calculations,however,
only exploredthemakescomplexphase
channelat weak available that can simultaneously derivecharacteristics,
which
AFM
the onlytechnology
70
segregations and furthermore did not test for the O , Scp, and29;30;31
the target
microscopic
region’s astructure
and mechanical.
Figure4 now provides
more complete
phase properties
SA15 phases.
diagram for 9-arm stars. Although the topology of the diagram
remains equivalent to that of the diblock, there are particularly
large shifts in the phase boundaries. Equally significant is thefact that the O70 regions are far bigger than those of the

A
r
s
s
r
e
e
s
.
d
e
s
e

y
e
c
2162

dx.doi.org/10.1021/ma202782s | Macromolecules 2012, 45, 2161−2165

1.5. References

7

Hard segment pulling out

Domain deformation
strainstrain

Domain fusion

Domain divisionstrainstrainbridge → loop

loop → bridge

Figure 1.4: Schematic diagram of the dynamic behavior of the TPE during the stretchingprocess.

1.5

References[1] Akiba, M. a. & Hashim, A. Vulcanization and crosslinking in elastomers. Progress inpolymer science 22, 475–521 (1997).
[2] Spontak, R. J. & Patel, N. P. Thermoplastic elastomers: fundamentals and applications.
Current opinion in colloid & interface science 5, 333–340 (2000).
[3] Bhowmick, A. K. & Stephens, H. Handbook of elastomers (CRC Press, 2000).
[4] Shanks, R. A. & Kong, I. General purpose elastomers: structure, chemistry, physics andperformance. Advances in Elastomers I 11–45 (2013).
[5] Drobny, J. G. Handbook of thermoplastic elastomers (Elsevier, 2014).
[6] Shi, W. et al. Toward strong thermoplastic elastomers with asymmetric miktoarm block
copolymer architectures. Macromolecules 47, 2037–2043 (2014).
[7] Shi, W. et al. Mechanics of an asymmetric hard–soft lamellar nanomaterial. ACS nano10, 2054–2062 (2016).

8

Chapter 1. Introduction A: Thermoplastic Elastomers[8] Rosenbloom, S. I. & Fors, B. P. Shifting boundaries: controlling molecular weight distribution shape for mechanically enhanced thermoplastic elastomers. Macromolecules 53,
7479–7486 (2020).
[9] Weidisch, R. et al. Tetrafunctional multigraft copolymers as novel thermoplastic elastomers. Macromolecules 34, 6333–6337 (2001).
[10] Puskas, J. E., Kwon, Y., Altstädt, V. & Kontopoulou, M. Blends of poly (2, 6-dimethyl1, 4-phenylene oxide)(ppo) with polystyrene-based thermoplastic rubbers: A comparative
study. Polymer 48, 590–597 (2007).
[11] Hayashida, K., Dotera, T., Takano, A. & Matsushita, Y. Polymeric quasicrystal: Mesoscopic quasicrystalline tiling in a b c star polymers. Physical Review Letters 98, 195502(2007).
[12] Inoue, T., Moritani, M., Hashimoto, T. & Kawai, H. Deformation mechanism of elastomeric block copolymers having spherical domains of hard segments under uniaxial tensilestress. Macromolecules 4, 500–507 (1971).
[13] Séguéla, R. & Prud’Homme, J. Affinity of grain deformation in mesomorphic block polymers submitted to simple elongation. Macromolecules 21, 635–643 (1988).
[14] Prasman, E. & Thomas, E. L. High-strain tensile deformation of a sphere-forming triblock
copolymer/mineral oil blend. Journal of Polymer Science Part B: Polymer Physics 36,
1625–1636 (1998).
[15] Honeker, C. C. et al. Perpendicular deformation of a near-single-crystal triblock copolymer
with a cylindrical morphology. 1. synchrotron saxs. Macromolecules 33, 9395–9406 (2000).
[16] Cohen, Y., Albalak, R. J., Dair, B. J., Capel, M. S. & Thomas, E. L. Deformation oforiented lamellar block copolymer films. Macromolecules 33, 6502–6516 (2000).
[17] Tomita, S. et al. Strain-induced deformation of glassy spherical microdomains in elastomeric triblock copolymer films: simultaneous measurements of a stress–strain curve with
2d-saxs patterns. Macromolecules 50, 677–686 (2017).
[18] Zhao, Y. Structural changes upon annealing in a deformed styrene-butadiene-styrene
triblock copolymer as revealed by infrared dichroism. Macromolecules 25, 4705–4711(1992).
[19] Sakurai, S., Sakamoto, J., Shibayama, M. & Nomura, S. Effects of microdomain structures on the molecular orientation of poly (styrene-block-butadiene-block-styrene) triblock
copolymer. Macromolecules 26, 3351–3356 (1993).
[20] Kraus, G. & Rollmann, K. Effects of domain and molecular orientations on the mechanicalproperties of a styrene-butadiene block polymer. Journal of Macromolecular Science, Part
B: Physics 17, 407–425 (1980).
[21] Duan, Y. et al. Deformation behavior of sphere-forming trifunctional multigraft copolymer.
Macromolecules 41, 4565–4568 (2008).
[22] Odell, J. & Keller, A. Deformation behavior of an s-b-s copolymer. Polymer Engineering& Science 17, 544–559 (1977).

9[23] Yamaoka, I. & Kimura, M. Effects of morphology on mechanical properties of a sbs triblock
copolymer. Polymer 34, 4399–4409 (1993).
[24] Yamaoka, I. Effects of morphology on mechanical properties of styrene-butadiene-styrene
triblock copolymer/methyl methacrylate styrene copolymer blends. Polymer 37, 5343–
5356 (1996).
[25] Yamaoka, I.
Anisotropic behaviour of styrene-butadiene-styrene triblock copolymer/methyl methacrylate-styrene copolymer blends. Polymer 39, 1081–1093 (1998).
[26] Dechnarong, N. et al. In situ synchrotron radiation x-ray scattering investigation of a
microphase-separated structure of thermoplastic elastomers under uniaxial and equi-biaxial
deformation modes. Macromolecules 53, 8901–8909 (2020).
[27] Morita, H., Miyamoto, A. & Kotani, M. Recoverably and destructively deformed domain
structures in elongation process of thermoplastic elastomer analyzed by graph theory.
Polymer 188, 122098 (2020).
[28] Aoyagi, T., Honda, T. & Doi, M. Microstructural study of mechanical properties of theaba triblock copolymer using self-consistent field and molecular dynamics. The Journal ofChemical Physics 117, 8153–8161 (2002).
[29] Nakajima, K. et al. Nano-palpation afm and its quantitative mechanical property mapping.
Microscopy 63, 193–208 (2014).
[30] Wang, D. & Russell, T. P. Advances in atomic force microscopy for probing polymer
structure and properties. Macromolecules 51, 3–24 (2018).
[31] Garcia, R. Nanomechanical mapping of soft materials with the atomic force microscope:methods, theory and applications. Chemical Society Reviews 49, 5850–5884 (2020).

10

Chapter 1. Introduction A: Thermoplastic Elastomers

Chapter 2
Introduction B: Atomic ForceMicroscopy for Polymer Science

2.1

GeneralIn the recent history of instrumentation development, microscopy has been developing rapidly
along with the progress of human science and technology. Scientific research and materials
development have been pushed to an unprecedented level of miniaturization with the inventionof new microscopy techniques. Since the invention of the scanning tunneling microscope (STM)
by Binning et al. in 1982 1 , humankind’s desire to explore the atomic scale has taken a giant
leap forward, and the study of material surface phenomena has become more profoundly understood. Before that, the only instruments that could directly see the size of atoms were field
ion microscopy (FIM) and electron microscope (EM). The invention of STM overcame these
problems, as the study of atomic dimensions was extremely limited due to the conditions ofpreparation and operating environment. The principle of STM is to use the electron tunneling
effect to obtain atomic images. Still, the sample for STM is basically a conductor, and the surface must be very flat, limiting the use of STM. In 1986, Binning et al. developed the atomic
force microscope (AFM) 2 , which not only has the ability to resolve atomic dimensions, but also
solves the limitations of STM on conductors, making it more convenient for application.
11

12

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer Science

Since the introduction of STM, dozens of types of probe microscopes have been continuously
developed. Scanning probe microscope (SPM) is a large family of probe-based microscopes,
among which the more familiar techniques are: STM, AFM, near field optical microscope(NSOM), magnetic force microscope (MFM), chemical force microscope (CFM), scanning thermoprobe microscope (SThM), phase probe microscope (PDM), electrostatic force microscope(EFM), lateral frictional force microscope (LFM), etc. Among the various SPM techniques,
AFM is the most widely used and can be applied to a variety of items, such as metallic materials, polymers, biological cells, etc. It can be operated in atmospheric, vacuum, electricaland liquid phase environments for different physical properties analysis. Therefore, AFM has
a wide range of applications in the study of biological materials, crystal growth, and action
forces.
Depending on the tip-sample material and the tip-sample distance, the forces between the tip
and the sample can be interatomic repulsion, van der Waals attraction, elastic force, adhesion,
magnetic and electrostatic forces, and the frictional forces generated by the tip during scanning.
Fig. 2.1 shows the typical inter-atomic interaction in imaging. The black curve is a combinationof long-range attractive and short-range repulsive interaction forces called the Lennard-Jones
Potential. At larger distances, the force is attractive, which switches to a repulsive force when
two atoms are brought closer together. The orchid curve represents a repulsive interaction,
while the teal curve represents an attractive interaction. By controlling and detecting theseforces between the tip and the sample, not only the surface morphology of the sample can becharacterized at high resolution, but also the surface properties corresponding to the forces canbe analyzed: LFM can analyze the friction coefficient of the studied material; MFM can study
the magnetic domain distribution on the sample surface; EFM can analyze the sample surface
potential, the dielectric constant of the film, and the deposited charge. In addition, AFM canmanipulate, modify and process atoms and molecules, and design and create new structuresand substances 3

2.2. The Working Principle of AFM

13

Potential, U
Contact
Repulsive
Distance, zNon-contact
Attraction
Total interaction
Figure 2.1: Inter-atomic interaction potential U vs. distance z.

2.2

The Working Principle of AFM

The principle of operation is that a micro-cantilever, which is sensitive to very weak forces,
is fixed at one end and has a tiny tip at the other end, which is in gentle contact with thesample surface. Due to the extremely weak repulsive force between the atoms at the tipof the tip and the sample surface, the cantilever with the tip will move in an undulating
direction perpendicular to the sample surface by controlling this force to be constant during
the scan, corresponding to the isotope of the force between the atoms. Using optical detection
or tunneling current detection, the change in position corresponding to each point of the scanis measured, and the signal is amplified and converted to obtain a three-dimensional image ofthe sample surface at the atomic level.
The AFM consists of a piezoelectric scanner that performs raster scanning and z-positioning,
feedback electronics, an optical reflection system, a probe, an anti-vibration system, and acomputer control system (Fig. 2.2). The piezoelectric ceramic tube controls the movement of
the sample in the x, y, and z directions. When the sample is scanned along the x/y direction
relative to the probe tip, the distance between the probe tip and the sample surface is changed
due to the high and low undulations of the surface. When the laser beam is irradiated to theback of the cantilever and then reflected to the position-sensitive photo-detector, the difference14

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer Science

Feedback
Laser+
Detector

z
x

Probe

SamplePiezoelectricscanneryFigure 2.2: Schematic diagram of the principle of AFM.
in laser intensity received by the detector in different quadrants forms a certain proportional
relationship with the deformation of the cantilever. Feedback loop according to the detector
signal and the difference between the preset value, and constantly adjust the distance between
the tip and the surface. Keeping the force between the tip and surface unchanged can get themorphology image. This measurement mode is called constant force mode. When the surfaceof the sample is known to be very smooth, the scanning can be performed in constant height
mode, i.e., the distance between the tip and the sample is kept constant. At this point themagnitude of the force directly reflects the surface morphology image.

2.2.1

Basic Operation Modes of AFM

At present, there are three basic modes of AFM operation, which can be distinguished as contact, non-contact, and tapping modes. Contact and non-contact are susceptible to other external
factors, such as the attraction of water molecules, which can cause scratches on the surface ofthe material and image distortion by poor resolution; thus, there are limitations on their use,
especially in biological and polymer soft materials. The following is a brief introduction to thebasic principles of the three basic forms.

2.2. The Working Principle of AFM

15

Contact Mode

The tip is used to interact with the atomic force on the surface (must be in contact), so thatthe very soft probe arm is deflected. The back of the probe arm is irradiated with a special
tiny laser light, and the laser light reflected by the probe arm is used as a two-phase photo
diode (laser light phase detector) to record the change of laser light deflection by the probearm. The interatomic repulsive force between the probe and the sample is about 10−6 to 10−9
N. However, since the tip is in contact with the surface, excessive forces can still damage thesample, especially on soft materials such as polymers and cellular organisms. However, better
resolution is usually obtained on harder materials.

Non-Contact ModeIn order to solve the shortcomings of contact AFM that may damage the sample, non-contact
AFM was developed, which operates by using the long distance attraction - van der Waals
force. The distance between the probe and the sample and the amplitude of the probe muststrictly follow the van der Waals force principle, so the distance between the probe and thesample must not be too far, the amplitude of the probe must not be too large (about 2 to 5nm), and the scanning speed must not be too fast. When the sample is placed in atmosphericenvironment and the humidity exceeds 30%, a 5 to 10 nm thick film of water molecules will
cover the surface of the sample, which makes it difficult or wrong to feedback.

Tapping Mode

Tapping mode is improved by bringing the tip closer to the sample and increasing the amplitudeof the probe (10-300 kHz) with force of about 10−12 N. The probe has resonant vibration andthe amplitude can be adjusted to have intermittent slight beating contact with the material
surface. The amplitude in the tapping mode AFM can be adjusted to be small enough not
to interfere with the water molecule film, and large enough not to damage the probe by hard
knocking on the sample surface, with an ultimate resolution of 2 nm in the XY plane. It does

16

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer Sciencenot cause permanent damage in the z-direction. In the x-y direction, because the probe isintermittently bouncing in contact, it will not cause permanent damage as in contact mode,
where the probe is dragged in the x-y direction. However, due to the high frequency of probe
strikes, the tip of the probe can be damaged for very hard samples.

2.2.2

AFM Nanomechanical Mode

From the beginning of the development of AFM, there were signs that it would be applied tonanomechanics not only in polymers but also in various other materials fields. Nowadays, there
are various modes for imaging mechanical property information 4;5;6 . In these modes, the AFM
tip is not scanned along the surface of the sample, but is repeatedly brought into contact withthe sample perpendicular to the surface, and then pulled away. The relationship between thesample deformation and the interaction force is then combined with contact mechanics such as
Hertz theory, Derjaguin-Muller-Toporov (DMT) 7 theory and JohnsonKendall-Roberts (JKR) 8
theory. The DMT and JKR theories provide information on the condensation energy as well as
the elastic modulus. The DMT and JKR theories provide information on the cohesive energy
as well as the elastic modulus. The elastic modulus of an unstretched sample often correlates
well with the tensile modulus (Young’s modulus). On the other hand, when the AFM probe ispressed against a macroscopically elongated sample, the obtained modulus is generally larger
than that of the unelongated sample. This is natural because stress is applied at various
locations corresponding to the macroscopic strain, but the resulting stress distribution is very
non-uniform, reflecting the local nature of the sample.
For the static AFM force mapping mode, two different measurement modes are commonly used.
Force-volume (FV) AFM is the mode in which a series of force-distance curve are recorded ateach point of the specimen surface. The rate of force-distance curve acquisition is about 1–10
Hz. The PeakForce quantitative nanomechanical mapping (QNM) mode was also utilized. The
method can also generate force-distance curves and has a much higher acquisition rate (0.5–2
kHz). In the case of iroprene rubber (IR) specimens, both FV and QNM provide an accurate estimate of rubbery modulus 4 , whereas QNM provides an incredibly higher modulus for2.2. The Working Principle of AFM

17

z

R
x
a
δ
r
Figure 2.3: Schematic diagram of the deformation of the sample surface by the probe tip.
styrene-butadiene rubber (SBR) due to the faster acquisition rate, where the time-temperature
superposition (TTS) principle is important.
In analyzing force-distance curves on rubbery materials with significant adhesive interaction, acontact mechanics model, first developed by Johnson et al. and thus known as the JKR model 8 ,can be used to relate the applied force F to the contact radius a for an indenting probe of theradius R (Fig. 2.3) as follows;


a=

R
K

1/3 p
2/3
p
F − Fc + −Fc
,

(2.1)

where K, Fc are the reduced modulus and the maximum adhesive force, respectively. The
contact radius directly correlates with the sample deformation δ by the following equation,

a2 4
δ=
−
R
3

r

a (−Fc )
.
KR

(2.2)

To obtain a direct relationship between F and δ, it is difficult to perform implicit-function curve
fitting by eliminating a. To overcome this difficulty, instead of fitting the F −δ curve completely,
two special points on the curve can be chosen to directly calculate the sample modulus, which is
known as the JKR two-point method 9 . The balance point (delta0 , 0), where the apparent force
F exerted on the cantilever becomes zero, and the maximum adhesion point (delta1 , Fc ), where18

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer Science

the adhesive force reaches the maximum negative value on the unloading curve, are the twopoints. Combining the above equations yields an algebraic formula for calculating the reduced
modulus.

K=

1 + 161/3
3

3/2(−Fc )q.
(δ0 − δ1 )3 R

(2.3)

This JKR two-point method has been shown to accurately determine the elastic modulus of avariety of rubbers and glassy polymers.

2.3

In-Situ AFM

As the research in materials science is gradually moving to depth, there is an urgent need forresearchers to conduct more in-depth studies on the mechanism of action, structural changes,
and factors affecting the properties of materials. Then, the traditional ex-situ research methods
can no longer meet the current needs. In-situ characterization techniques, which have beendeveloped in the last three decades, allow ‘on-line’ analysis of specific reaction processes using
different instrumentation. This technique is often used to elucidate the changes in a material
process by means of a specific device that performs continuous and simultaneous analysis of thesubstance and traces a series of structures parameterized by time or other relevant conditions.

Because AFM testing causes little damage to the sample, in situ AFM techniques are widelyused to measure the mechanical and electromechanical properties of nanomaterials 10 . So far,in situ AFM has been used to study batteries 11;12 , crystallization 13;14 , phase transition 15;16 ,biomolecules 17;18 etc. Since AFM can combine various external stimuli such as light, electricity,heat, and chemical reactions to observe the structure and physical properties of the sample, it
makes in situ AFM a very promising application.

2.4. The Objective of This Thesis

2.3.1

19

In-Situ AFM Nanomechanics

In-Situ AFM Nanomechanics is based on the In-Situ AFM technique, which combines the analysis of force curves obtained from tests to grasp changes in the properties of substances in
response to external stimuli (Fig. 2.4). Since obtaining force curves requires applying deformation to the material surface, the test objects are usually soft materials, especially polymers.
The external stimuli that can be applied include tensile, compressive, etc. However, polymers,
especially block copolymers, often have a structural scale of just a few tens of nanometers, andin order to maintain a high resolution, the scan size is usually only a few hundred nanometers or micrometers. It becomes very difficult to continuously track the same region after theapplication of external stimuli, and this challenge is the main research object of this thesis.

Under deformation
Force, F / nN

1probe tip

Force curve

0
-1
-2
-60

surface-40-20
0Deformation, δ / nm

20

In-Situ AFM Nanomechanics
Figure 2.4: The working principle of in-situ AFM nanomechanics.

2.4

The Objective of This Thesis

In this thesis, in order to solve the common macroscopic stress-strain characteristics of TPE(Fig. 2.5), including stress relaxation, permanent deformation, etc., I developed and used in situz
AFM nanomechanics to make real-time structuraland nanomechanical property observationsof TPE materials under deformation. Since AFM can simultaneously obtain the structuraland physical properties of an observed region, there is no suitable analysis method to analyze aRseries of in situ images in depth; therefore, a corresponding program is planned to be developed.

x
a
δ
r

20

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer Science

Finally, in order to develop new high-strength TPEs, in addition to the marketed TPE samples,
unmarketed polymer materials with potential were also characterized using AFM.

0.45 0.45“stress“stressrelaxation”
relaxation”

0.40 0.40*keeping*keeping
50% strain
50% strain
0.35 0.35
00200 200 400 400 600 600
Relaxing
Relaxing
Time /Timemin / minStress / MPa

Stress / MPa

Stress / MPa

0.50 0.50

1.5

Stress / MPa

1.50.55 0.55

1.0

1.0

0.5

0.5

“residual“residual
strain”strain”
0.0

0.0
0

050

50
100 100
150 150200 200
Strain Strain
/% /%
0.5

e.g., keeping 0.5 strain
0.3
e.g., 0.1

Fixed strain &di erent relaxing time

Increasing strain &similar relaxing time

Chapter 3 & 4

Chapter 5time

ff

strainFigure 2.5: Common macroscopic stress-strain characteristics of TPE and the in situ AFM
nanomechanics corresponding to them.

2.5

References[1] Binnig, G., Rohrer, H., Gerber, C. & Weibel, E. Surface studies by scanning tunnelingmicroscopy. Physical review letters 49, 57 (1982).
[2] Binnig, G., Quate, C. F. & Gerber, C. Atomic force microscope. Physical review letters56, 930 (1986).
[3] Custance, O., Perez, R. & Morita, S. Atomic force microscopy as a tool for atom manipulation. Nature nanotechnology 4, 803–810 (2009).
[4] Nakajima, K. et al. Nano-palpation afm and its quantitative mechanical property mapping.
Microscopy 63, 193–208 (2014).

21[5] Wang, D. & Russell, T. P. Advances in atomic force microscopy for probing polymer
structure and properties. Macromolecules 51, 3–24 (2018).
[6] Garcia, R. Nanomechanical mapping of soft materials with the atomic force microscope:methods, theory and applications. Chemical Society Reviews 49, 5850–5884 (2020).
[7] Derjaguin, B. V., Muller, V. M. & Toporov, Y. P. Effect of contact deformations on theadhesion of particles. Journal of Colloid and interface science 53, 314–326 (1975).
[8] Johnson, K. L., Kendall, K. & Roberts, a. Surface energy and the contact of elastic solids.
Proceedings of the royal society of London. A. mathematical and physical sciences 324,
301–313 (1971).
[9] Sun, Y., Akhremitchev, B. & Walker, G. C. Using the adhesive interaction between atomic
force microscopy tips and polymer surfaces to measure the elastic modulus of compliant
samples. Langmuir 20, 5837–5845 (2004).
[10] Li, X., Sun, M., Shan, C., Chen, Q. & Wei, X. Mechanical properties of 2d materials studied
by in situ microscopy techniques. Advanced Materials Interfaces 5, 1701246 (2018).
[11] Beaulieu, L., Beattie, S., Hatchard, T. & Dahn, J. The electrochemical reaction of lithiumwith tin studied by in situ afm. Journal of the Electrochemical Society 150, A419 (2003).
[12] Beaulieu, L., Hatchard, T., Bonakdarpour, A., Fleischauer, M. & Dahn, J. Reaction of li
with alloy thin films studied by in situ afm. Journal of the Electrochemical Society 150,
A1457 (2003).
[13] Malkin, A., Kuznetsov, Y. G. & McPherson, A. An in situ afm investigation of catalase
crystallization. Surface science 393, 95–107 (1997).
[14] Land, T., De Yoreo, J. & Lee, J. An in-situ afm investigation of canavalin crystallization
kinetics. Surface Science 384, 136–155 (1997).
[15] Seantier, B., Breffa, C., Felix, O. & Decher, G. In situ investigations of the formation of
mixed supported lipid bilayers close to the phase transition temperature. Nano Letters 4,
5–10 (2004).
[16] Wiedemair, J. et al. In-situ afm studies of the phase-transition behavior of single thermoresponsive hydrogel particles. Langmuir 23, 130–137 (2007).
[17] Ando, T. et al. A high-speed atomic force microscope for studying biological macromolecules. Proceedings of the National Academy of Sciences 98, 12468–12472 (2001).
[18] Ando, T., Uchihashi, T. & Fukuma, T. High-speed atomic force microscopy for nanovisualization of dynamic biomolecular processes. Progress in Surface Science 83, 337–437(2008).

22

Chapter 2. Introduction B: Atomic Force Microscopy for Polymer ScienceChapter 3
Dynamic Stress Network in the TPE

3.1

GeneralElastomers’ numerous benefits make them useful in a wide range of applications 1;2 . Traditional thermoset elastomers, like filler-reinforced vulcanized rubber, have outstanding mechanical qualities because of their chemical-crosslink network. They can recover almost completelyfrom strain-induced distortion. The irreversibility of the permanent chemical cross-linking,on the other hand, make the material difficult to reprocess or reuse 3 . Because of their highelasticity and processing benefits 4;5 , thermoplastic elastomers (TPEs) are currently a preferred
substitute to thermoset materials. Noncovalent interactions, including as hydrogen bonding 6 ,ionic bonding 7;8 , and metal-ligand coordination 9 , have been used to increase the performanceof TPEs. However, the permanent set after deformation remains a key challenge to solve inorder to achieve tough TPEs with the same property as thermoset materials.
TPEs are structurally divided into two groups: block copolymers and their blends, both ofwhich contain hard and soft phases in their microstructure. Hard and soft segments along the
backbone chain of the polymers develop by microphase separation in block copolymer (BCP)based TPEs, resulting in hard segmental domains and soft segmental domains, respectively.
Soft-segmental rubbery domains (soft matrix) extend in response to strain-induced deformation, whereas hard-segmental glassy domains (hard domains) produce the physical cross-links
23

24

Chapter 3. Dynamic Stress Network in the TPE

required for elastic recovery. To make a robust TPE with little residual strain, the TPE’s polymer network must recover almost completely after deformation; consequently, it is worthwhile
to investigate the nanoscale structural changes in TPEs during deformation.

Many studies used small angle X-ray scattering (SAXS) 10;11;12;13;14;15 , Fourier transform infrared spectroscopy (FT-IR) 16;17;18;19 , and transmission electron microscopy to investigate thedeformation of BCP-based TPEs (TEM) 14;20;21;22;23;13;24 . They revealed that when BCP-based
TPEs were stretched, spherical hard domains were deformed and orientated from an isotropic
structure, which exhibited a meaningful association to stress relaxation and fracture of thestretched TPE. SAXS 15 and TEM 14 also revealed that affine deformation occurs in a fully
deformed lattice constituted of hard domains when the plane spacing grows proportionately.
However, the distribution and evolution of stress, which is a major issue in deformed BCPbased TPEs, have yet to be identified by test procedures and must be explained by direct andreal-time viewing methods. AFM-based nanomechanics have been developed in recent years
to obtain nanomechanical mapping of soft materials, particularly BCPs 25 . This method allows
the mechanical properties of the material surface, including the elastic modulus, adhesion, dissipation, and stiffness, to be simultaneously probed with nanometer resolution. We anticipate
that this measuring approach will disclose basic difficulties regarding the deformation processof BCP-based TPEs.

The strain-induced change of microdomains in a TPE specimen composed of a SEBS triblock
copolymer was the focus of this chapter. The morphological and mechanical development
was seen in-situ using AFM nanomechanics. An inhomogeneous distribution of internal stress
was found during stretching using elastic modulus mapping, resulting in deformation, relative
displacement, and partial separation of the phase-separated structure.

3.2. Results

25

3.2

Results

3.2.1

Tensile Behavior

The left part of Fig. 3.1 depicts a typical strain-stress curve of TPE obtained from a strain-rate
controlled tensile test. Unsurprisingly, when the specimen recovered to zero stress after being
stretched to a strain of 200%, a residual strain (∼10%) was formed. The specimen’s elastic
modulus was determined to be ∼3.2 MPa based on the average slope of the elastic section of
the stress-strain curves, which corresponded to strains ranging from 2% to 4%.
In a macroscopic view, the right part of Fig. 3.1 depicts the stress-time curve of the TPE
extended to 50%. During a 12-hour period with a fixed 50% strain, tension reduced fast at
the start of relaxation (≤1 hour) and then gradually declined with subsequent relaxation. This
stress-relaxation process, as described above, implies that some significant structural evolution
happened as the stretching period increased, and this structural evolution is thought to beconnected to the material’s failure to fully elastically recover.

0.45 0.45“stress“stressrelaxation”
relaxation”

0.40 0.40*keeping*keeping
50% strain
50% strain
0.35 0.35
00Stress / MPa

Stress / MPa

Stress / MPa

0.50 0.50

1.5

Stress / MPa

1.50.55 0.55

1.0

1.0

0.5

0.5

0.0

0.0

“residual“residual
strain”strain”

200 200 400 400 600 600
Relaxing
Relaxing
Time /Timemin / min

0

050

50
100 100
150 150200 200
Strain Strain/% /%Figure 3.1: Two typical tensile curves for TPE.

3.2.2

AFM Nanomechanical Mapping

SEBS, a triblock copolymer made up of rigid poly(styrene)(PS) segments and poly(ethylene-cobutylene) (PEB) segments, has a phase-separated morphology and has had its nanomechanical26

Chapter 3. Dynamic Stress Network in the TPE

characteristics extensively researched 26;27;28;29;30;31 . Sphere-like PS domains with a high modulus, namely hard-segmental amorphous domains (hard domain), and PEB domains aroundthe hard domains with a low modulus, namely soft-segmental rubbery matrix (soft matrix),
were identified in the microstructure of a SEBS sample with a low PS component of 15%, asshown in elastic modulus map in Fig. 3.2. The color bar in the right can be used to estimate
the associated elastic modulus values. Similarly, the deformation map depicts the indentation
depth for AFM probe tip pushing the specimen surface.The hard domain and soft matrix inthe deformation map correspond to low and high deformation regions, respectively, with their
typical force-deformation curves (FCs) depicted in the left. Because of the softness of the SEBS
with a low PS content, the overlaid elastic theoretical curves accurately duplicate each FC in theretraction section. With values of 4.6 nm, 290 pN, and 8.5 MPa, the FC from the hard domainsuggests a low deformation, low adhesive force, and high elastic modulus during the tip-surface
interaction. In contrast, with values of 9.4 nm, 435 pN, and 4.3 MPa, respectively, the FC
from the soft matrix suggests a high deformation, high adhesive force, and low elastic modulus.
Because the influence of the soft matrix beneath the surface could not be avoided, the measured
elastic modulus from the hard domain did not reflect its actual value. The neighboring soft
matrix buffered the hard domain’s deformation, resulting in a lower value.

We firstly have a comparison of elastic modulus maps before and after elongation, as shownin Fig. 3.3. The left part is the modulus map of unstretched TPE as described before. The
right part is the stretched TPE with keeping 0.5 strain for 262 minutes. The bottom partare the value distribution of two elastic modulus maps. Although they are in different areasof the same sample, from the value distribution of modulus, we could clearly see a right shiftof the modulus after stretching, which means the elastic modulus of the sample has increased
after stretching. Furthermore, the peak of the left histogram in appears at ∼3.50 MPa, which
agrees with the elastic modulus calculated from the strain-stress curve (∼3.2 MPa). However,consistency, which is affected by the tip radius and pushing force and has a strong relationshipwith the amount of sample deformation 32 , could only be achieved through a very delicate
operation. The elastic modulus obtained from tensile testing reflected the soft matrix’s initialelastic deformation. The elastic modulus obtained from AFM increased in value as the sample

3.2. Results

27

500

SEBS (Mw: 133 kDa, PS%:
15 wt%)
400
nm

-2.0

on soft matrix (PEB)
100

66

100

44

0

22

20

0

100
500
400

nm

300

300

200
on hard domain (PS)

nm

-2.0

8

200

-100 -80 -60 -40 100
-20 0

20

200
100

100

200 300
300 nm
400

400

500

200
Elastic modulus 500
map
nm

20

Elastic
Modulus// MPa
MPa
Elastic
ModulusForce / nN-100 -80 -60 -40 -20 0
5000
Deformation / nm
0
1.0
400

8 10

nm

Force / nN

200

-1.0

1012

300

-1.0

0.0

1214

400

300

0.0

14
Deformation/ /nm
nm
Deformation

1.0

Deformation map

500

1620
16

12

12

88

44
Deformation / nm
000100 200 300 400 500
Figure 3.2: (Left) Typical force-deformation
curvesonand soft matrix withnm
0100 200 hard
300 domain
400 500
superimposed elastic theoretical curves. (Right) Deformation and elastic modulus maps ofnm
TPE. Scale bar, 100 nm.

underwent additional deformation because the surrounding hard domains were involved when
the soft matrix deformed.
Then, if we binarize these two maps to pick up 15% high modulus area, which is the ratio of
hard domain, we could obtain the domain numbers in each map, as shown in Fig. 3.4 Afterelongation, the domain number decrease compared with the unstretched sample. This result
could be explained by this illustration that some hard domains get closer in x direction andfused after elongation, as described in Chapter 1.
The nanostructural change depicted in Fig. 3.1 was revealed using AFM nanomechanics. Although the stress decreased rapidly during the initial stage of stretching, which is consideredappropriate for study, imaging during this stage was extremely difficult because the sample
drifted significantly at the nanoscale. This situation improved approximately 3 hours after webegan stretching, and we obtained clear images between 4 and 10 hours. The elastic modulus
maps of the TPE stretched 50% that was probed at nearly the same region after 262 and 597

28

Chapter 3. Dynamic Stress Network in the TPE

500
500

400

nm

nm

16
stretch

200

200

12

100 8
0

0
05000100

4000
3000
2000
1000
0

200 300
nm

400

500

4

0
Frequency

100

16

Elastic Modulus / MPa

300 20300

Frequency

20

12
8
4
5000200 300
100
4000 nm
3000
2000
1000
0

0
5
10
15
20
Histogram of Modulus Map / MPa

400

Elastic Modulus / MPa

400

500

0
5
10
15
20
Histogram of Modulus Map / MPa

Figure 3.3: The elastic modulus map and its value distribution of (left) unstretched sample and(right) strecthced sample which is kept 0.5 strain for 262 min. Scale bar, 100 nm.

minutes are shown in Fig. 3.5. The stretching direction is represented by the double-headed arrows. Hard domains deformed and oriented parallel to the stretching direction per a comparison
with Fig. 3.2, which is a similar result to those reported by SAXS 15 and TEM analyses 13 . Utilizing a two-dimensional (2D) fast Fourier transform (FFT) algorithm implemented in ImageJ,
the average separation distance between the hard domains was extracted from each obtained
modulus map, as shown in Fig. 3.6. The distance between the hard domains in the unstretched
TPE was approximately 23 nm regardless of direction. Interestingly, in the stretched TPE,
500
400

Elastic Modulus / MPa

20

16
stretch

200

12

nm

300

8

100

100 nm280 domains

0

4

217 domains

0 3.4:
100Binarized
200 300
400 maps
500 and statistics on the number of hard domains.
Figuremodulusnm3.2. Results

29

the average distance of the hard domains in the stretching direction increased from ∼41 nm to∼38 nm after 262 minutes and decreased from ∼41 nm to ∼38 nm after 597 minutes. At thesame time, there was almost no change in the average distance perpendicular to the stretching500

direction.

300

nm

L2
D1

16

relax12

200

L1

8

D2

100
L4

4

D3

L3’
L2’

D1’
L1’

16
16

12
12

D2’
L4’

20
20

Young's modulus / MPa
Elastic Modulus / MPa

20

Young's modulus / MPa

400

L3

D3’

8
8
4
4

5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
00

0
Frequency

Frequency

0

00
55
10
10
15
15
20
20
Histogram
Histogram ofof Modulus
Modulus Map
Map // MPa
MPa

5000200 300
100
4000 nm
3000
2000
1000
0

400

500

0
5
10
15
20
Histogram of Modulus Map / MPa

Figure 3.5: The elastic modulus map and its value distribution of strecthced sample which is
kept 0.5 strain for (left) 262 min and (right) 597 min. Scale bar, 100 nm.
It is also worthwhile to discuss the modulus distribution of the sample during deformation.
The histograms in Fig. 3.3 represent the modulus distribution before and after stretching,respectively, and show peak values of ∼3.50 MPa and ∼4.84 MPa, indicating that the elastic
modulus increased after stretching to a strain of 0.5. Furthermore, when compared to theunstretched sample, an increased proportion of the elastic modulus distribution occurred in thehigh modulus area in the stretched TPE, which was attributed to the formation of a stress chain.
In general, a stress chain in BCP-based TPEs is made up of soft matrices within a deformed
portion of the material that are held together to form a stress network with hard domains asjunction points. As a result of the stress network’s contribution, the elastic modulus of some
soft matrices increased, resulting in a nonuniform distribution.
With increasing stretching time, the peaks shifted to the left (from ∼5.7 MPa to ∼4.8 MPa),
indicating a decrease in the elastic modulus in TPE, as indicated by the color change from left

30

Chapter 3. Dynamic Stress Network in the TPE

unstretched

262 minstretch597 minrelax

Figure 3.6: (Top) 2D FFT images extracted from obtained modulus maps. Scale bar, 0.1
nm-1 . (Bottom) Schematic diagram of the spacing between hard domains when the material isstretched and relaxed.

to right. A modulus decrease is consistent with the tensile test results, as shown in Fig. 3.1.
However, the stress decrease in the TPE stretched 50% obtained in the macroscopic stress-time
curve, as shown in Fig. 3.1, is ∼0.03 MPa from 4 hours to 10 hours, which is much less than
the result obtained from AFM (decrease of ∼0.9 MPa). A future study will be carried out toestimate the macroscopic stress value from the microscopic change in the elastic modulus in
the tensile state.

It was further found that a relative displacement of the hard domains occurs in the stretching direction. We measured the distance between the hard domains distributed parallel andperpendicular to the stretching direction at different relaxation times. In the direction parallelto the stretching direction, as shown in Fig. 3.5, L1 (∼398 nm) and L2 (∼250 nm) in theleft were significantly shortened to L1’ (∼299 nm) and L2’ (∼211 nm) in the right; however,L3 (∼340 nm) and L4 (∼377 nm) in the direction perpendicular to the stretching direction
maintained almost the same value as L3’ (∼339 nm) and L4’ (∼374 nm). Shrinkage in such a
local area along the stretching direction, which should not have happened during a fixed strain
relaxation, indicates a nonuniform change in the polymer network within the material. Thisconclusion could also be drawn from the previous discussion of the hard domain morphology.
The average separation distance between the hard domains after 262 minutes of stretching (∼41nm) indicated a 78% elongation compared to the unstretched hard domains (∼23 nm) at 50%

3.2. Results

31of the macroscopic deformation, indicating that other areas were stretched less than 50%.
Despite the fact that the majority of the material retained its morphology, some hard domains
separated significantly during the relaxation process, as shown by the marked dotted circles in
Figs. 3.5; these areas represent the same hard domains in the microstructure with a different
stretching time. A polymer network, also known as a bridge chain, was formed structurally
by amorphous hard domains acting as junction points and rubbery soft matrixs bridging thesejunction points 33 . When a macroscopic strain was applied, the bridge chains stretched first
because the hard domains were relatively hard, resulting in an increase in local stress. A
local stress in a polymer can be transferred along a stress network. As a result, in order torelieve the local stress, the stretched bridge chains exerted a strong force on the hard domains,causing them to deform and separate at the weak junctions. The split hard domains formed
new stress networks, which meant that bridge chains that were previously assigned to one
junction point were now assigned to two junction points. Furthermore, if the subordinatedhard domain was split into two new domains, the chains that originally belonged to only
one hard domain, known as a loop chain, could evolve into a bridge chain. The deformation,
separation, and reorganization of microdomains, as well as the stress network, partially reformed
the polymer’s microstructure. The domain deformation was relatively easy to recover; however,
the topological change caused by separation had a long-term impact on the material, andresidual strain was present. In a future work that incorporates data assimilation and simulation,a dynamic stress network will be visualized and explored 34 .

3.2.3

Dynamic Stress Network

Using continuous AFM observations over a short time period, we investigated the details of theseparation behavior. As shown in Fig. 3.7, we chose one hard domain, D1 in 289 min, whose
separation was observed as described above, and studied the structural evolution surrounding
it before and after the separation. A small hard domain, denoted as D2, grew from 289 to
298 minutes, which could be explained by the aggregation of hard PS segments, and continued
to grow at the times shown in 307 and 317 minutes. The elastic modulus of domain D2

289 min400400D1400400298 min

307 min

500
400

D2
D3

300300300300400400200

21820 18

1

16

16 16
12

1

148

1
20

1
18

1
16

8
14

6
12

nm

nm

100

4
10

MPa

MPa

nm

nm

14
D1.2
400
4
400
D1.1
201220012
0100 200 300 400 500
D2’200181018
200
D3’
nm
200
200
10
30030016345 min 300
326 min
317 min
8 16
300
8Figure 3.7: Dynamic stress network observed in stretching TPE. Image 14
size, 100 nm.
6 14
100
100
6 as aand its surroundings,100
which included the area between domains D2 and D1,
124increased
100
200
12
200 The newly formed bridge chains between D1 and D2 gradually
200result of this growth behavior.
4
10200
separated the soft matrix in the interval of domains D2 and D1. This strain-induced
10structural

nm
nm

nm

300

20 20

MPa

nm

Chapter 3. Dynamic Stress Network in the TPE

Elastic Modulus / MPa MPa

nm

32

8

0
0 resulted in the formation
8 and D1 within
evolutionof a new connection between domains D2

6
80 3000 chain.
100 chain
200 domains
0 soft matrix,
0 200
200The400
300 between
400 D1300
100
theknown100
as a stressstressand D3 also 400
100
100
nm 6
nm
100had an effect. The arrow
nmin 289-326
min indicatesof the stress chain
generated
0
100 the direction200
300
4004

400 6
200 100 300 200 400 300
nm4 hard domains,by domains D2 and D3.
nm to split into two smaller
nmFinally, domain D1 began4
domain D1.1 and D1.2, that moved away from each other after 345 min of continuous
stress0100

0from two directions. For the 0
first time, the aggregation and separation of the hard domains, as

0

0

100
200
300
400
nm
100
200
300
400
0
100
200
300 described above
400is not accidental;
nm
were observed. Thenm
dynamic evolution of the stress network
0
100
200
300

well as the subsequent generationand dynamic 200changes in the stress0
0of stress chains
100
300 network, 400

nm
100 besides this200
300
400
region, this phenomenon was also found in other regions innm
the same time frame,nm
as shown in Fig. 3.8. This overall behavior eventually also leads to a permanent change in

the network topology, which in turn causes the annihilation of the stresses in this process,eventually manifesting itself in a macroscopic stress-relaxing behavior.

400

3.3. Summary

400

33

289 min

298 min

307 min

317 minnm

300

Figure 3.8: Dynamic stress network observed in another region. Image size, 100 nm.

3.3

Summary
200

This study visualized the strain-induced evolution of the structure and mechanical propertiesof a SEBS-based TPE material using AFM nanomechanics. Microdomains in the stretched

100

SEBS exhibited deformation, separation, and reorganization during the stress relaxation process, according to the nanoscale elastic modulus maps. The stress network underwent dynamic
evolution, which permanently altered the polymer’s topological structure. An atomic force
microscope was used to take continuous images of the polymer microstructure during deformation, which could be a powerful approach for understanding the continuous morphological0changes of various materials under the action of external forces. Furthermore, the deterioration

0

100

200

300

mechanism of polymer materials can be studied further using a combination of mathematical

nm

modeling, molecular dynamics simulation, and experimentation. These basic microscopic studies provide the theoretical foundation for the development of high-strength polymer materials.
Based on this new technique, more research on polymer morphology will be conducted in the
future. The content of this chapter is based on the authors’ published paper 35 with additional
explanations.

3.4

References[1] Bhowmick, A. K. & Stephens, H. Handbook of elastomers (CRC Press, 2000).

40

34

Chapter 3. Dynamic Stress Network in the TPE[2] Shanks, R. A. & Kong, I. General purpose elastomers: structure, chemistry, physics andperformance. Advances in Elastomers I 11–45 (2013).
[3] Akiba, M. a. & Hashim, A. Vulcanization and crosslinking in elastomers. Progress inpolymer science 22, 475–521 (1997).
[4] Spontak, R. J. & Patel, N. P. Thermoplastic elastomers: fundamentals and applications.
Current opinion in colloid & interface science 5, 333–340 (2000).
[5] Drobny, J. G. Handbook of thermoplastic elastomers (Elsevier, 2014).
[6] Kautz, H., Van Beek, D., Sijbesma, R. P. & Meijer, E. Cooperative end-to-end and lateralhydrogen-bonding motifs in supramolecular thermoplastic elastomers. Macromolecules 39,4265–4267 (2006).
[7] Datta, S., Bhattacharya, A., De, S., Kontos, E. & Wefer, J. Reinforcement of epdm-basedionic thermoplastic elastomer by precipitated silica filler. Polymer 37, 2581–2585 (1996).
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36

Chapter 3. Dynamic Stress Network in the TPE[33] Matsumiya, Y., Watanabe, H., Takano, A. & Takahashi, Y. Uniaxial extensional behavior of (sis) p-type multiblock copolymer systems: Structural origin of high extensibility.
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Chapter 4
Nanoscale Strain-Stress Mapping for
the TPE

4.1

General

We previously reported on the development of in situ atomic force microscopy to explore themicrophase splitting structure and elastic modulus of BCP-type TPEs in the continuously
stretched state 1 . It demonstrated a correlation between the hard domain splitting observed
under the microscope and the residual strain observed at the macroscopic level. Furthermore,
we argue that the microscopic motion of the hard domains is driven by the visible stressnetwork formed under strain. To understand the dynamic behavior of this network, in thiswork we employ image segmentation based on the Delaunay triangulation method for finite
element analysis (FEA) of a series of in situ AFM images (Fig. 4.2). Microscopic strain-stress
distribution maps are used to explain the reasons behind the dynamic evolution of the network
structure in BCP-type TPEs.
We were inspired by the work of Jinnai et al. 2 , who performed in situ TEM experiments on filledrubber and evaluated the local strain of the material by Delaunay triangulation of the filler
particles. In this work, all image processing methods were based on a self-developed Matlab
program. The TPE used in this experiment contains a 15 wt% proportion of hard segments;
37

400

38

280 min

289 min

298 min

307 min

20
10

400
200

0
335 min

345 min

356 min

365 min

20
10

400
200
0
0
393 min

405 min

300
nm

0

400

417 min

435 min

20
10

400
200
0
0
462 minnm

300
480 min

0400
489 min

20
10

400
200
0
0
516 minnm

300
533 min

0400
543 min

20
10

400
200
0
0
570 minnm

300
588 min

0400
597 min

20
10

200
0
0

100

200

300

400

0

Deformation / nm

561 min 300
100

200
579 minnm

552 min100

Deformation / nm

507 min 300
100

200
525 minnm

498 min100

Deformation / nm

453 min 300
100

200
471 minnm

444 min100

Deformation / nm

384 min 300
100

200

nm

374 min100

Deformation / nm

326 min 300
100
nm

317 minDeformation / nm

271 min 300
nm

262 min

Chapter
4. Nanoscale
Strain-Stress Mapping for the TPE
FigureS1

nm

Figure 4.1: AFM deformation100
maps captured from different relaxing time (Image size: 500nm), where the observed regions are approximately the same.
0
0

100

200

300

400

nm
therefore, in the AFM deformation map, the small 15%
deformation region is considered asa hard phase, which naturally yields a discontinuous set of domains. The geometric centerof each domain is chosen as a representative point. the Delaunay triangulation algorithm ismodified by Matlab syntax for AFM image processing (Fig. 4.3). Since the Delaunay meshuses the nearest neighbor rule, the automatically generated mesh is reconstructed accordingly,
so that triangles from different images can correspond exactly. The calculation of the individual
triangle deformations is shown in Fig. 4.4, which is often used during FEA. linear strains in
the x (εx ) and y (εy ) coordinates can be derived separately using the strains of the respective

4.1. General39

triangles. Note that in all figures, the macroscopic stretching direction is parallel to the ycoordinate. To further explore the variation of the nanomechanical properties in the observed
regions, the Delaunay mesh obtained from the deformation maps was used to delineate theregions on the corresponding modulus maps so that the modulus variation in each triangle

Finite Element Analysis of AFM Maps

could be evaluated. The median value of the soft matrix modulus in each triangle is taken as
the representative modulus. The stress transfer in the network brings about a change in themodulus in the local region; therefore, we treat this change as the nano stress (∆E) in eachtriangle.
289 min

345 minSoft matrix

400

Hard domain~ 20 nm

20

18

18

16

16

14

14

12

12

Loop chain Bridge chain

300

MPa

nm

Figure 4.2: Basic FEA principle for AFM images.

As mentioned earlier, potential BCPs for TPE applications must feature a discontinuous

200microphase-separated structure in the form of spheres or cylinders, which10
makes the hard 10
phases therein very suitable for abstraction into two-dimensional point sets to provide trian-88

gulation treatment. The microstructure of BCP-type TPE is shown schematically in Fig. 4.2.

6
6100Hard segments of BCP are aggregated into the domain, while soft segments form the bridge
chain and loop chain during the packing of the hard domain, which together
4 form the soft
matrix. Although how the loop chain affects material’s mechanical properties has not been0

completely solved 3;4 , most researchers believe the network formed by bridge chains bears andtransmits the stress generated during the material deformation 5;6;7 , namely stress network. Fig.

0
400
100
2001003002004003004.3 is a typical AFM deformation map of a TPE captured after holding 50% elongation for 570
nm
nm
min. The details of the experiments have been described in the previous report 1 . We built
the Delaunay mesh using the geometric center of each small-deformed hard domain, as shownin Fig. 4.3. Since all captured maps are in similar regions, a series of comparable Delaunaymeshes can be generated by this method.

4

MPa

20

500

400

300

200

Triangulation mesh
100

Deformation map

0
0

10

Delaunay
triangulation

300

15

200

5
400

Deformation / nm

20

100

0

100 nm
500

0 300
nm

Chapter 4. Nanoscale
Strain-Stress
A self-developed
analysis program
based Mapping for the TPEon the concept of nite element method.

40

400

500

Changesin the structuraland mechanicalFigure 4.3: (Left) A typical
AFM deformation
map of BCP-type
TPE in the tensile state.
localized(Right)
regions
could bederived.
The arrow indicates properties
the stretchingofdirection.
Schematic
diagramof the Delaunay
triangulation.

Finite Element Analysis of AFM Mapsv3fiY(x3, y3)u3

deformv2
v1(x1, y1)

E2

E1
u1

(x2, y2)u2
The soft matrix exerts the stress.

X

Changesfor
in thelocal
AFM elastic
modulus→schematicthe localdiagram
AFM stress:
Figure 4.4: Notations
three-nodetriangle
and theof its deformation.
ΔE = MedianE2 − MedianE1

4.2

Results

4.2.1

Micro Behavior of the Stress-Relaxing Process

The stress map could also be obtained.

Let’s first look at the whole stress relaxation process. It is well known that the stress in a TPE
decreases when a fixed elongation is maintained 8 , and this phenomenon can be observed at the
microscopic level. As shown in Fig. 4.5, we plot the average modulus of the soft matrix foreach capture during stress relaxation. The modulus undergoes an approximately exponential
decay until 400 min, after which it slows down and gradually stabilizes after 500 min.
Things get interesting when we analyze the relationship between the soft matrix modulus andthe number of hard domains. Note that the hard domains are the small deformation regions

Finite Element Analysis of AFM Maps

4.2. Results

early stage
heavily domain-splitting& decreasing modulus

late stage
stable domain number& stable modulus

7.5

300
280

7.0

260
6.5
240
6.0

220

5.5

Number of domains

Average modulus / MPa

41

200
300

400
500
Relaxing time / min

600

Figure 4.5: Correlation between the average AFM modulus, the number of hard domains, andthe relaxing time.

in the AFM deformation map, where we remove the incomplete domains at the edges of theimage. During the early relaxation, the number of hard domains increases rapidly as the soft
basis modulus decreases. Then, after 500 min, the number of domains and the soft matrix
modulus stabilize simultaneously. Although the data at some time points are biased due tosome misalignment of the observation area, we can establish a sufficient correlation between
the decrease in modulus and the increase in the number of lattices. The increase in the numberof domains, i.e., the splitting of some domains, is a finding that is well documented in bothexperiments 1 and simulations 6;9 . On the other hand, the decrease in modulus of soft substrates
is usually considered to be due to the loss of stress tolerance of the bridge chains, accompaniedby splitting from the hard phase to form ring chains or pulling out to form dangling chains 10;11 .
Also, the higher domain density and closer spacing due to splitting may contribute to the stressrelaxation in the bridge chains. The above statement is very reasonable; however, studying therelationship between the kinetic and physical properties of such polymer networks is almost only
possible through simulations, which makes us eager to observe these phenomena experimentally.

Chapter 4. Nanoscale Strain-Stress Mapping for the TPE
Exothermic >42

Scan Rate 10 °C/min
CoolingHeating-100 -80 -60 -40 -20 0 20 40 60
Temperature (°C)

80 100 120

Figure 4.6: DSC profile of SEBS-15.

In fact, the decreasing trend of the modulus under the microscope does not correspond to themacroscopic stress-relaxation curve in the same time period, but is closer to the beginning of themacroscopic relaxation, as shown in Fig. 3.1. Therefore, another concern here is whether theinconsistency in macroscopic and microscopic behavior is due to the difference in temperature.
In the AFM experiment, the temperature inside the cavity increased slightly compared to room
temperature due to the fact that the sample was in a closed, soundproof container during thescan. The temperature was 27.3 ℃ at the beginning of the scan, i.e. after 262 min of relaxation,
while it increased to 28.7 ℃ after 597 min. Compared to the standard room temperature atwhich the tensile test was performed (25 ℃), we were not able to determine whether thistemperature difference could bring about an appreciable change in the sample properties. In
addition, as shown in the Fig. 4.6, in the differential scanning calorimetry (DSC) measurementof this sample, we did not succeed in observing the glass transition process due to the hard
PS phase, as the PS content was only 15%. In future experiments, we will further develop thein situ AFM test at variable temperature to demonstrate the effect of temperature on AFM
measurement of TPE.

It is also worth mentioning that in another set of experiments, at a similar relaxing time, we
also observed slightly different results than in Fig. 4.5. As shown in Fig. 4.7, there is arecovery of the modulus rising after the initial decrease, which indicates that the observationof the tiny region of 500 nm produces different results depending on the observation area, and43

Average modulus / MPa

4.2. Results

8.5
8.0
7.5
7.0
6.5
340 360 380 400 420
Relaxing time / minFigure 4.7: Relaxing time versus soft matrix modulus in another set of data.
we believe that this is one of the possible reasons for the inconsistency between macroscopic
and microscopic phenomena.

4.2.2

Finite Element Analysis

We chose two time points of early (262 to 326 min) and late (507 to 570 min) captures as
the subjects of our study, respectively. As shown in Fig. 4.5, from 262 to 326 min, the soft
matrix modulus decreases rapidly and the hard domain splits severely, while from 507 to 570
min, the modulus and the number of domains remain relatively stable. Fig. 4.8 shows thechanges of deformation and modulus in the same region in the early stage. Although there isa high degree of similarity between the images before and after the one-hour relaxation, themotion of each particular hard domain can be amplified by triangulation. Negative strain,i.e., shrinkage, occurs in most of the grid region along the stretch direction, with an averagevalue of -6.4% for all varepsilony . As an experiment with fixed elongation throughout, suchnegative strain values require splitting the hard phase to compensate for the new area causedby shrinkage. Admittedly, there are still regions where positive strain occurs and appear toshow a hierarchical structure along the x-direction, as indicated by the purple band in the
figure. A similar heterogeneous behavior of the block copolymer has been demonstrated in
the case of high elongation, 12;7 , and we found that long-term maintenance of this behavior
also occurs at low elongation rates of 50%. Moreover, during deformation, the TPE network

44

Chapter 4. Nanoscale Strain-Stress Mapping for the TPEtransfers externally applied stresses to each other through physical bridging points, i.e., using
the hard domain as a medium, and also overcomes topological constraints that cause the mesh
to develop mutually perpendicular strain trends in the x and y directions 13;14 . Such a trend

Strain-Stress Mapping of the Early Stage

can also be observed during the later relaxation process and we will discuss it later.

AFM deformation maps
262 min

326 min

AFM elastic modulus maps
262 min

326 minrelax forrelax for64 min64 minstrain mapping

stress mapping

100 nmThe strain map in X

The strain map in Y

0.20

The stress map

0.20

0

1
-1

-0.10

-0.10

-3

-0.20

-0.20

-5

ΔE / MPa

0

3
εy

0.10
εx

0.10

5

Figure 4.8: (Top) AFM deformation and modulus map of TPE after keeping elongation for 262
and 326 min. (Bottom) Linear-strain maps in the x and y coordinate derived from deformation
maps with the stress map derived from modulus maps.
As shown in Fig. 4.9, we use a simple schematic diagram to explain the relationship between
hard-domain splitting and local strain, although the realistic situation would be more complex.
The external stretching deforms the hard domain and imposes stress on the bridge chain, while
stretching the network in the y-direction and compressing it in the x-direction. After reaching
the stress limit, the hard domain splits, and the bridge chain is then relaxed, causing a network
recovery in the y-direction. Finally, the network in x-direction is also recovered due to thepacking requirement. The above behavior makes the splitting of the hard domain does nothave a large impact on the x-direction, and its average εx is only -0.2%. This result can also
be related to the FFT analysis in Chapter 3. Comparing with Fig. 3.6, it can be found thatthe strain is mostly negative in the Y-direction parallel to the stretch, and the ellipse in the4.2. Results

45

FFT image has some recovery after relaxing, indicating that the domains’ distances are also
approaching each other. In contrast, in the X direction perpendicular to the tensile direction,

Strain-Stress Mapping of the Early Stage

there is no significant change in either the strain map or the FFT image.

The strain map in Y

0.20

0

εx = − 0.2 %-0.2 0.0
εx

-1

-0.10

-0.20
DensityDensity

0.4
0.3
0.2
0.1
0.0

1

0.2

0.4
0.3
0.2
0.1
0.0

εy = − 6.4 %-0.2 0.0
εy

split

-3

-0.20

0.2

ΔE / MPa

0

5
3

εy

0.10
εx

0.10

-0.10

The stress map

0.20

Density

The strain map in X

0.4
0.3
0.2
0.1
0.0

-5
ΔE = − 0.78 MPa

-10

0
10
ΔE (MPa)

springback

concentrated
stressStretched sample

Figure 4.9: (Top) Value distribution of local strain and local stress. (Bottom) Schematic
diagram of domain splitting during elongation and its effect on the strain.
The stress distribution shown in Fig. 4.8 is obtained by combining two modulus maps with the
Delaunay mesh. Although 0.7 MPa reduces the average stress in the grid, we observe a stressconcentration zone in the purple circle, which corresponds to the strain interface region. Such a
stress concentration zone is detrimental to the stability of the network, and it seems reasonable
to establish its correlation with the local strain. However, not all strain interfaces produce
considerable stress concentrations, so we do not have enough evidence to prove whether thepresence of strain interfaces is a sufficient condition for stress concentrations to occur. Then, we
studied the strain and stress distributions in the late stage and compared them with the earlystage. Numerically, εy and ∆E derived from Fig. 4.10 are -0.3% and -0.2 MPa, respectively,
which are moderated compared to the early stage. The εx yields a value of -0.5%, which issimilar to the results obtained from Fig. 4.5. We also observe a similar hierarchy in the strain

46

Chapter 4. Nanoscale Strain-Stress Mapping for the TPE

distribution in Fig. 4.10 as in the early stages. Such a before-and-after variation originatesfrom the stress relaxation obtained through the early domain splitting, which is also evidenced
by the stress diagram: no stress concentration similar to that in Fig. 4.10 is observed in theStrain-Stress Mapping of the Late Stagesame region of Fig. 4.5.

The strain map in X

The strain map in Y

0.20

The stress map

0.20

0

1
-1

-0.10

-0.10

-3

-0.20

-0.20

-5

0.20

0.20

5

0.10

0.10

3

0

0

ΔE / MPa

0

3
εy

0.10
εx

0.10

5

after relaxation

-1

-0.10

-0.10

-3

-0.20

-0.20

-5

ΔE / MPa

εy

εx

1

Figure 4.10: Linear-strain maps in the x and y coordinates derived from deformation maps
with the stress map derived from modulus maps in (top) early and (bottom) late stages.

We further analyzed the numerical distribution of stresses and strains for all triangles in theearly and late meshes. These values were normalized due to the large increase in the number oftriangles through domain splitting in the early stages. Fig. 4.11 shows the strain distribution in
the x-direction. In the later stages, the presence of large strains is reduced and the distribution
becomes more concentrated at zero. For the y-direction shown in Fig. 4.5, although theconcentration of values is not as pronounced as in the x-direction, the distribution is clearlyshifted to the right and the center approaches zero, indicating that the strain behavior in they-direction gradually approaches that of the x-direction. Considering that the y-direction is theelongation direction, this similarity between the strains in the x and y directions indicates thatthe network has been sufficiently moderated and converged to a stable state under prolonged
elongation. However, such a steady state is not static, and the uniform distribution of strains

4.2. Results

47in the late x and y directions on either side of the zero point means that the entire network
is still in a state of elastic fluctuation, as shown schematically in Fig. 4.11. As mentioned
before, the stress concentration may be related to the interface of strains. At a later stage, thereduction of large local strains makes the stress concentration disappear, as shown in Fig. 4.5.
By comparing the stresses, it is found that their distribution undergoes a clear convergence toStrain-Stress Mapping of the Late Stagezero at a later stage.

The strain map in Y

0.20

0

DensityDensity-0.2 0.0
εx

0.2

1
-1

-0.10

-0.20
late

0.4
0.3
0.2
0.1
0.0

3

-3

-0.20

0.4
0.3
0.2
0.1
0.0

late

-0.2 0.0εy

0.2

ΔE / MPa

0

5

εy

0.10
εx

0.10

-0.10

The stress map

0.20

Density

The strain map in X

0.4
0.3
0.2
0.1
0.0

late

-10

-5

0
10
ΔE (MPa)

elastic uctuation(slightly)
flFigure 4.11: (Top) The distribution of εx , εy , and ∆E at the early and late stages. (Bottom)
Schematic diagram of the dynamic fluctuations of the stress network in the late relaxation
period.

The above discussion shows that the TPE network has dynamic and stable elasticity in the laterstages after the early hard domain splitting. Although strain still occurs in each local region,
the effective stress transfer of the bridge chain avoids stress concentration and thus prevents
further domain splitting in the later stages. When designing high strength TPE materials withsmall residual strains, the topic often discussed is how to increase the strength of the harddomains to reduce the likelihood of hard domain splitting, and this is certainly true. However,assuming that the concentrated stress can be efficiently transferred through bridge chains in the

48

Chapter 4. Nanoscale Strain-Stress Mapping for the TPE

network, possible solutions in this case, such as increasing the elasticity of the soft segments inthe block copolymer, i.e. bridge chains, or reducing the formation of ring chains by molecular
design, may also be able to protect the hard domains themselves. To verify the correctness of
the above deduction, the relevant molecular design is already in progress.

4.3

Summary

We developed a tool that combines in situ AFM nanomechanics and Delaunay triangulation to
analyze topological changes in materials. When applied to the mechanical analysis of TPEs,
we discovered the microscopic causes of macroscopic stress relaxation in TPEs during holding
stretching. The internal stress network was sufficiently moderated to achieve stress and strain
homogenization and dynamic elasticity after the dramatic evolution of the early phases. The
hard phase in the microphase-separated structure relieves the local stress concentration by
splitting, but at the same time, this irreversible change induces a permanent deformation of
the material. This technique is also being applied to study other polymeric materials, such as
filled rubber. Related work will be reported in the near future.

4.4

References[1] Liu, H., Liang, X. & Nakajima, K. Direct visualization of a strain-induced dynamic stressnetwork in a sebs thermoplastic elastomer with in situ afm nanomechanics. Japanese
Journal of Applied Physics 59, SN1013 (2020).
[2] Miyata, T. et al. Nanoscale stress distribution in silica-nanoparticle-filled rubber as observed by transmission electron microscopy: Implications for tire application. ACS Applied
Nano Materials 4, 4452–4461 (2021).
[3] Watanabe, H., Sato, T., Osaki, K., Yao, M.-L. & Yamagishi, A. Rheological and dielectric behavior of a styrene- isoprene- styrene triblock copolymer in selective solvents. 2.
contribution of loop-type middle blocks to elasticity and plasticity. Macromolecules 30,
5877–5892 (1997).

49[4] Watanabe, H., Matsumiya, Y., Sawada, T. & Iwamoto, T. Rheological and dielectric
behavior of dipole-inverted (sis) p-type multiblock copolymers: estimates of bridge/loop
fractions for respective i blocks and effect of loops on high extensibility of bridges. Macromolecules 40, 6885–6897 (2007).
[5] Parker, A. J. & Rottler, J. Molecular mechanisms of plastic deformation in sphere-forming
thermoplastic elastomers. Macromolecules 48, 8253–8261 (2015).
[6] Morita, H., Miyamoto, A. & Kotani, M. Recoverably and destructively deformed domain
structures in elongation process of thermoplastic elastomer analyzed by graph theory.
Polymer 188, 122098 (2020).
[7] Dechnarong, N. et al. In situ synchrotron radiation x-ray scattering investigation of a
microphase-separated structure of thermoplastic elastomers under uniaxial and equi-biaxial
deformation modes. Macromolecules 53, 8901–8909 (2020).
[8] Hsiue, G.-H., Chen, D.-J. & Liew, Y.-K. Stress relaxation and the domain structure ofthermoplastic elastomer. Journal of applied polymer science 35, 995–1002 (1988).
[9] Aoyagi, T., Honda, T. & Doi, M. Microstructural study of mechanical properties of theaba triblock copolymer using self-consistent field and molecular dynamics. The Journal ofChemical Physics 117, 8153–8161 (2002).
[10] Shen, J., Liu, J., Gao, Y., Li, X. & Zhang, L. Elucidating and tuning the strain-induced
non-linear behavior of polymer nanocomposites: a detailed molecular dynamics simulation
study. Soft Matter 10, 5099–5113 (2014).
[11] Ozmusul, M. S., Picu, C. R., Sternstein, S. & Kumar, S. K. Lattice monte carlo simulationsof chain conformations in polymer nanocomposites. Macromolecules 38, 4495–4500 (2005).
[12] Inoue, T., Moritani, M., Hashimoto, T. & Kawai, H. Deformation mechanism of elastomeric block copolymers having spherical domains of hard segments under uniaxial tensilestress. Macromolecules 4, 500–507 (1971).
[13] Di Lorenzo, F. & Seiffert, S. Nanostructural heterogeneity in polymer networks and gels.
Polymer Chemistry 6, 5515–5528 (2015).
[14] Ronca, G. & Allegra, G. An approach to rubber elasticity with internal constraints. The
Journal of Chemical Physics 63, 4990–4997 (1975).

50

Chapter 4. Nanoscale Strain-Stress Mapping for the TPE

Chapter 5

Heterogeneously Formation of theStress Network in the TPE

5.1

GeneralMaterials science has been pursuing intuitive, efficient, and high-resolution characterization
techniques to visualize the structure and properties of target samples. Among them, in situ
microscopy is a particularly popular approach because of its ability to witness the dynamic
behavior under externally stimulating conditions, such as strain, temperature, and the introduction of other substances 1 . However, in situ measurement means that the window displacement induced by the external stimuli need to be overcomed. Very noteworthy in this field isthe high-speed AFM, which, although often not titled with ‘in-situ’, explains many dynamic
processes of biomolecules 2;3 . As for the block copolymer with nanoscale microphase-separated
structure, when stemming the macroscopic strain, such window displacment could make thein-situ observation much more difficult. In this chapter, I will use a newly-developed in-situ
jig combined with AFM nanomechanics to investigate the initial elongation of the BCP-type
TPE.
51

52

Chapter 5. Heterogeneously Formation of the Stress Network in the TPE

5.2

Results

5.2.1

In-Situ AFM Nanomechanical Mapping

Fig. 5.1 shows modulus maps of BCP-type TPE using in-situ AFM nanomechanics. Somefeature hard domains are helpful to distinguish the similar observing area. With the increasingof macroscopic strain, yellow/brown hard domains are gradually connected by formed stresschain from the soft matrix. In the initial stage of elongation, easily-deformed soft segments ofthe block copolymer bear the imposed strain, and thus increases their stress. The dynamic behavior of stress network has already been well-discussed in Chapter 3 and Chapter 4. However,the formation of stress network, which was predicted 4;5;6 and simulated 7;8 for a long time, wasfirst observed by in-situ AFM nanomechanics.
0

9%

18%

5005001h

1h15.015.0

nm

nm

45%

20.020.030030036%2002001h10010001h

0010.010.026%

5.0 5.0

Elastic modulus / MPa

100 nmElastic modulus / MPa

4004001h0100100
200200300300400400500500nm nm

Figure 5.1: AFM modulus maps of BCP-type TPE under different strains. All the images arein the similar
Localobserving
Strain in X area.
In Y (tensile direction)
Local Stress
εx = − 2.8 %εy = − 4.4 %

0.20

0.20

0.10

0.10

0

0

ΔE = − 0.3 MPa

1

εy

εx

0

ΔE / MPa

The calculated microscopic strain shown in Fig. 5.1 is obtained from in-situ jig itself. However,the strain was also calculated by the camera window, the value comes to be a bit different.
-0.10

0 → 9%

-0.20

-0.10

0 → 9%-0.20

0 → 9%

Fig. 5.2 shows the photos of each stretched state. The difference of these two-1calculated valves
1
0.20
0.20
increase with theincreasethat ΔE
due= totheMPapositioning
and AFMεy = +be
2.1mentioned%
εx =− 5.1 % of strain. It should
+ 0.8
0.10

0.10

0

0

ε = − 3.3 %

-0.20
0.20

εy

εx

-0.10

-0.10
18% → 26%

018% → 26%εy = − 7.3 %

-0.20
0.20

18 → 26%

ΔE = − 0.8 MPa-1
1

ΔE / MPa

capturing time, each photo was taken about an hour apart. Combining the above phenomena,5.2. Results

53

it can be learned that the polished surface in the figure undergoes a relative shrinkage withincreasing strain, accompanied, of course, by an elongation of the area beyond the polishedarea. Such anTPE初期伸⻑過程に対するininhomogeneous variation will be
fully
discussed in the subsequent analysis.
situ
AFM観察
Unstretched

94 pt

L

Jig value：45.0%
Camera value：36.5%

Jig value：8.8%
Camera value：7.4%

101 pt~7.4%

Jig value：36.0%
Camera value：28.7%

7

Jig value：17.7%
Camera value：16.0%

109 pt~16.0%

Jig value：25.6%
Camera value：20.2%

算値 = 2L
128 pt~36.2%

121 pt~28.7%

113 pt~20.2%

Figure 5.2: Microscopic strain of each stretched state calculated from jig and camera, respectively.
The distribution of elastic modulus of above AFM modulus images are then produced in Fig.
5.3. The maximum value of the modulus shows an overall nonlinear variation. From 0 to 9% ,the overall modulus distribution remains basically the same, even the maximum value has someleft shift with stretching. This indicates that at the earliest elongation, the bridge chain formedby soft segment was not fully stretched. From 9% to 26%, the maximum value continues tomove to the right, indicating that the bridge chain has carried the stress adequately. Then,
unexpectedly, after 26%, the maximum value of the modulus decreases again. This phenomenon
is interesting so I tried to reproduce the experimental flow of the AFM on a macroscopic level.
As shown in Fig. 5.3, macroscopic staged tensile test was performed and each stage is held
for one hour after stretching to approximate the AFM experimental procedure. The starting
stress of each segment is summed with the slope of the curve of that stage as the representative

54

Chapter 5. Heterogeneously Formation of the Stress Network in the TPE

modulus. Interestingly, although the absolute values of the macroscopic and microscopic moduli
are not comparable with each other, both of them show similar nonlinear variations, whichsuggests that the AFM results are reasonable and warrant further analysis.
3000
3500
2500
3000
2000
3500
2500
1500
3000
2000
3500
3500
1000
2500
1500
3000
500
2000
3500
3000
1000
2500
0
1500
3000
500
2000
3500
2500
1000
2500
0
1500
3000
500
2000
2000
1000
2500
0
1500
1500
500
2000
1000
0
1500
1000
500
1000
0
500
500

0.5

6

8

10
12
14
16
Histogram of jkrSphereModuliMap / MPa

6

8

10
12
14
16
Histogram of jkrSphereModuliMap / MPa

6

8

10
12
14
16
Histogram of jkrSphereModuliMap / MPa

6

8

10
12
14
16
Histogram of jkrSphereModuliMap / MPa

6

8

10
12
14
16
Histogram of jkrSphereModuliMap / MPa

6

8

6

8

6

8

10

10

12

12

14

14

16

16

10 of jkrSphereModuliMap
12
14
16
Histogram/ MPa
Histogram of jkrSphereModuliMap / MPa

0
9%20
18
18%20
18
26%20
18
36%20
18
45%20
18

18

18
18

Stress / MPa

0.4

0
0

1.18 MPa
1.26 MPa

0.3

1.49 MPa0.2

1.54 MPa

0.1

1.46 MPa

0.0

20

20
20

0

20
40
True Strain / %Histogram of Elastic Modulus

60

Figure 5.3: (Left) Distributions of elastic modulus in each image of Fig. 5.1. (Right) A
macroscopic reproduction for in-situ AFM procedure.

5.2.2

Finite Element Analysis

1.5 In the previous chapters, the sample
FEA analysis gives a detailed explanation of AFM results.
0.55

Stress / MPa

were sufficiently relaxed to become very stable for AFM capture; thus, most of the domains

Stress / MPa

Frequency
Frequency
Frequency
Frequency
Frequency
Frequency
Frequency

3500

0.50

1.0

could be used for the vertices of the triangulation. However, in this test, if every image is
0.45

capture after enough relaxation(which usually takes0.5more than three hours), not only the“stress relaxation”
0.40

image positioning will become extremely difficult, but also the ultrathinsamples“residual
strain”used in the*keeping 50% strain

0.35

0.0time, only domains that are sufficiently
experiment are at great risk of breaking. Therefore, this
0

200

400

600

0

50

100

150

200

distinct are used as vertices
for triangular segmentation to the extent that
relatively few regions
Relaxing Time / min
Strain / %are segmented. As shown in Fig. 5.4, in this chapter, The points were selected in such a waythat all resolvable areas were taken into account as much as possible, and all points withsignificant splitting or fusion were excluded. For example, we exclude the region in the redbox where fusion occurs after stretching, even though it is very easy to identify in the modulusmap.
As shown in Fig. 5.5, I divided the six diagrams into three groups for image resolution, and5.2. Results

55

Figure 5.4: An example of selecting vertices.
calculated the strain and stress changes for each group separately. In the first stage, i.e., from0 to 9%, almost all triangular meshes undergo regular triangular deformation. The Y-directionof the stretching is positive strain and the corresponding X-direction is negative strain. Suchdeformation indicates that the entire stress network is still in the elastic range. If the load isreleased at this point, then the material will fully recover its original length without permanent
deformation. At the same time, the deformation of the network does not completely offset
the external macroscopic deformation in stress, causing the creation of a stress concentration
region.
The second stage i.e., from 18% to 26% shows a different change from the first stage. While thex-direction still presents negative strain throughout, which seems to be inevitable in a uniaxial
stretching. In the y-direction, on the other hand, positive and negative strains alternate in the
direction perpendicular to the stretching. The generation of inhomogeneous strain indicatesthe loss of the previous stability of the polymer network and the onset of hard phase splitting.
However, the hard-domain splitting does not fully compensate for the external macroscopicstrain, which causes an increase in stress in all regions at this stage.
The last stage, i.e. the leftward shift of the maximum value of the modulus distribution, is also
reflected in the stress map where all regions are negative. The y-direction strain also shows all
negative values at this point, indicating that the hard domain has produced a large number of56

Chapter 5. Heterogeneously Formation of the Stress Network in the TPE
Local Strain in X

εx = − 2.8 %In Y (tensile direction)

εy = − 4.4 %0.20

0 → 9%

1

0

-0.20
0.20

-1
1

0

-0.10
36 → 45%-0.20

36 → 45%

ΔE / MPa0

ΔE = − 0.8 MPa
εy

0

εx

0.10

18 → 26%

ΔE / MPa

18% → 26%

0.10

-0.20

ΔE = + 0.8 MPa

-1

-0.10

εy = − 7.3 %0.20

0 → 9%

εy

0

εx

0

-0.10
36 → 45%

0.20
0.10

-0.20

εx = − 3.3 %

-0.20

0.10

-0.10
18% → 26%

0

-0.10

εy = + 2.1 %0.20

1ΔE / MPa0

ΔE = − 0.3 MPa
εy

0

εx

0.10

-0.20

εx = − 5.1 %

0.20

0.10

-0.10
0 → 9%

Local Stress-1

Figure 5.5: FEM analysis result on each stage of elongation.
splits and caused permanent and irreversible topological changes to the polymer network. At
the macroscopic level, a permanent deformation of the material has been created.

5.2.3

The Origin of Permanent Deformation

In the previous section, we argued through FEM analysis that stress concentration occurs in the
TPE during the stretching process, accumulating and eventually leading to massive splittingof the hard-domain. Another experiment was conducted to verify the full correlation between
the domain splitting and the permanent deformation of the TPE during cyclic stretching. A
TPE specimen was released after being held in 50% tension for two hours, and in situ AFM
nanomechanics was used to test the structural and physical properties of the sample afterwards.

5.2. Results

57
500

182 min

393 min

400

nm

300

1540

40
300

nm

relax
200

200

30

30

MPa

nm

300

10

200

100
100

20

20

5

100
10

10

MPa
Elastic modulus
/ MPa

2050

50
400

400

0
0
0

100

200

300

0

0

400

0

nm

100 100200 200300 300400 400500
nm nm

Figure 5.6: Elastic modulus maps of the sample after releasing the load and relaxing 182 and393 min.
Fig. 5.6 shows elastic modulus maps of the sample after releasing the load and relaxing 182
and 393 min. The modulus of the soft matrix undergoes a significant decrease in the relaxing
process. In addition, as shown in the circled position, the hard domain inevitably splits even at
0 load. We used a central hard domain as a reference and analyzed the relative movement of the
182 min

393 min

40
300

40

300

relax
30

30

nm

reference
domain

200

100

0
0

100

200
300
393
min
nm

nm

50

200
20

20

100
10

10

MPa

50
400

MPa

400

0
400

0

100

200

300

400

nm

50

400

40

30
200

MPa

nm

300

×

relax

20
100

10

0
0

100

200

300

400

nm

Figure 5.7: The analysis of the hard domain motion during the relaxing process and its
schematic diagram.
domain during the relaxing process, and the results are shown in Fig. 5.7. Surprisingly, unlike
the expected behavior of network recovery, the hard domains did not approach each other58

Chapter 5. Heterogeneously Formation of the Stress Network in the TPE

along the stretching direction due to stress relaxing, but instead underwent relative motion
perpendicular to the stretching direction. Such a phenomenon indicates that the topology ofthe material has been irreversibly changed during the stretching process, which has also been
derived in the mathematical model 9 . During the stretching process, the bridge chain becomesloop chain due to domain fusion, or breaks away from the hard domain to form a free hard
segment. During the relaxing, along with the splitting of the domain again, the bridge bondundergoes a recombination for the belonging relationship of the hard domain, i.e., a permanent
topological change. Graph theory can also give a parsimonious explanation of this process 7 .

5.3

Summary

We use a novel in-situ AFM nanomechanics combined finite element analysis to investigate
the initial elongation of a BCP-type TPE. It has been proven that the nonlinear curves in theinitial stage of tensile test as well as AFM modulus images are driven by internal hard-domain
splitting. In addition, such a splitting brings permanent topological changes to the material,
which affects the macroscopic mechanical properties.

5.4

References[1] Li, X., Sun, M., Shan, C., Chen, Q. & Wei, X. Mechanical properties of 2d materials studied
by in situ microscopy techniques. Advanced Materials Interfaces 5, 1701246 (2018).
[2] Ando, T. et al. A high-speed atomic force microscope for studying biological macromolecules. Proceedings of the National Academy of Sciences 98, 12468–12472 (2001).
[3] Ando, T., Uchihashi, T. & Fukuma, T. High-speed atomic force microscopy for nanovisualization of dynamic biomolecular processes. Progress in Surface Science 83, 337–437(2008).
[4] Rubinstein, M. & Panyukov, S. Elasticity of polymer networks. Macromolecules 35, 6670–
6686 (2002).
[5] Meng, F., Pritchard, R. H. & Terentjev, E. M. Stress relaxation, dynamics, and plasticityof transient polymer networks. Macromolecules 49, 2843–2852 (2016).

59[6] Hölzl, T., Trautenberg, H. L. & Göritz, D. Monte carlo simulations on polymer network
deformation. Physical review letters 79, 2293 (1997).
[7] Morita, H., Miyamoto, A. & Kotani, M. Recoverably and destructively deformed domain
structures in elongation process of thermoplastic elastomer analyzed by graph theory. Polymer 188, 122098 (2020).
[8] Aoyagi, T., Honda, T. & Doi, M. Microstructural study of mechanical properties of theaba triblock copolymer using self-consistent field and molecular dynamics. The Journal ofChemical Physics 117, 8153–8161 (2002).
[9] Kodama, H. & Yoshida, K. A mathematical model of network elastoplasticity. arXiv
preprint arXiv:2107.04310 (2021).

60

Chapter 5. Heterogeneously Formation of the Stress Network in the TPE

Chapter 6
AFM Characterization of
Triptycene-Appended Polymers

6.1

GeneralThis chapter uses AFM to measure triptycene-appended polymers for phase structure andnanomechanical properties. As shown in Fig. 6.1, tripodal triptycenes, a member of tripthcenefamily, could have a 2D nested hexagonal packing with a 1D stacking layers 1 . This so-called‘2D + 1D’ structure has also been found in polymers where tripodal triptycene is appended inmain chain 2 , side chain 3 , and two terminals 4 . However, this structural feature has not beenvisualized in AFM measurement. Therfore, the purpose of this chapter is to analyze the local
characteristics of ‘2D + 1D’ structure at the nanoscale and the effects on the structure andphysical properties of the polymer.

61

62

Chapter 6. AFM Characterization of Triptycene-Appended Polymers

1,8(,13)-Substituted Triptycenes (Tripodal Triptycenes) -2“2D” Nested Hexagonal
Packing of Triptycenes

(13)

1

8
Tripodal Triptycenes

Self-Assemblye.g.)“1D” Stacking of
Triptycene-Layers

OO

Trip-C12O

O

Trip-C12’Highly Ordered “2D + 1D” Structurewith a Large Domain Size

Figure 6.1: Schematic of triptycenes and their ‘2D + 1D’ structure.

6.2

Results

Fig. 6.2 shows the chemical structures of triptycene-appended polymers used for AFM characterization. Among them, the control polymer using the same backbone without appending
triptycene is liquid in 25 ℃, making it impossible to be measured. I will talk about the detailsof other three functional polymers.

6.2.1

Polymer with Appended Triptycene in the Side Chain

Trip-Block and Trip-Random are two polymers with appended triptycene in their side chains.
The order of the monomers results in two polymers with very different phase structures. Fig.
6.3 shows the height and phase images of Trip-Block capturing in AFM tapping mode. Unlike
the conventional spherical, cylinder or lamellar microphase-separation structures 5 , the phaseseparation structure induced by triptycene seems to be slightly more complex. However, localized lamellar structures can be observed and the interlamellar distances are consistent with
the SAXS results (not shown in this thesis). Note that this film has not been annealed overits melting point. Although we believed that the observed ‘1D’ structure would be clearer6.2. Results

トリプチセン含有ポリブチルアクリレート
トリプチセン含有ポリブチルアクリレート

2
2

63

ABAトリブロック共重合体
ABAトリブロック共重合体
M = 24Trip-BlockkDa, M /M = 1.09nwn

Mn = M
24 nkDa,
Mw/M
三脚型トリプチセンの重量比
n = 1.0937%= 24
kDa
三脚型トリプチセンの重量比 37%（トリプチセンのモル比：11.3%）
11 mol% triptycene（トリプチセンのモル比：11.3%）

ランダム共重合体

Trip-Random

Mn =ランダム共重合体
23 kDa, Mw/Mn = 1.09
= 23
Mn = M
23 nkDa,
Mw/MkDa
三脚型トリプチセンの重量比
n = 1.0937%
11 mol% triptycene
三脚型トリプチセンの重量比
37%（トリプチセンのモル比：11.3%）（トリプチセンのモル比：11.3%）

O (CH2)11

Me
Si O
Me

n

Me
Si (CH2)11 O
Me

1 cm

ホモポリマー

MeO
OMe
ホモポリマー
Mn = 25 kDa, Mw/Mn = 1.09
OC11H23
C11H23O
Mn = 25 kDa, Mw/Mn = 1.09

Trip-PDMS
Mn = 20 kDa

Figure 6.2: Chemical structures of triptycene-appended polymers.
and more orderly after annealing, the main chains of the polymer tend to float to the surface,causing the triptycene induced phase structure to be difficult to observe 6 .
Trip-Random shows totally different behavior compared with Trip-Block. As shown in Fig. 6.4,
previously unseen sheet-like microphase-separated structures were observed. There is no doubtthat phase separation are more difficult to form in random copolymers that possess lower ordercompared to block copolymers. Another speculation here is that the melting point of TripRandom is lower than 25℃, so the film is annealed for a long time after it is made. Because of
the higher degree of freedom of the main chain in the random copolymer, the triptycene has ahigher probability of forming microcrystals. In order to verify this speculation, there is a plan
to make a higher resolution observation of the sheet portion in the figure.
AFM nanomechanics was then performed in Trip-Block and Trip-Random. As shown in Fig.
6.5, similar layer structure is also observed in the modulus map of Trip-Block. As for TripRandom, part of the high modulus region can also be observed, which also illustrates the64

Chapter 6. AFM Characterization of Triptycene-Appended Polymers
Phase, 3 µm
Phase, 2 µm

Phase, 1 µm

20 nm 24 nm

34

30 26 (nm)Figure 6.3: Height and phase images of Trip-Block obtained in AFM tapping mode.

possibility of microcrystalline formation as described above. The modulus distributions of thetwo polymers can give a visual comparison of the nanomechanical properties. Both have thesame interval in the low modulus region, while Trip-Block has more components in the highmodulus region compared to Trip-Random, which suggests that the formation of self-assembled
structures with more triptycene in Trip-Block contributes to the mechanical strength of thematerial. We still want to emphasize that the unannealed samples have a high probability of
being in a non-equilibrium state,so additional experiments
will be performed in the future.
AFM観察：Tapping
Mode
Height, 3 µm

Phase, 3 µm

Height, 1 µm

Phase, 1 µm

Figure 6.4: Height and phase images of Trip-Random obtained in AFM tapping mode.

6.2. Results

65
Trip-Block, 3 µm

2.52.52.0

2.02.0

100
100

80

8080

1.51.5 60

6060

1.01.0 40

4040

0.5

0.50.5 20

2020

MPa

1.0

0.00.0

0.0
3000

0.0

0.5

1.0

1.5
µm

2.0

2.5

3.0

3000 0.0
0.0

2500

2500

2000

2000

Frequency

Frequency

100

Elastic Modulus
/ MPa
MPa

µm
µm

2.5

1.5

Trip-Random, 3 µm

3.03.0

MPa

µm

3.0

1500
1000

0.50.51.01.01.51.5µmµm

2.02.02.52.53.03.0

1500
1000

500

500

0

0
20

40
60
80
Histogram of jkrSphereModuliMap / MPa

100

20

40
60
80
Histogram of jkrSphereModuliMap / MPa

100

Figure 6.5: Nanomechanical mappings with the distribution of modulus of Trip-Block and TripRandom.

6.2.2

Polymer with Appended Triptycene in Two Terminals

Another polymer in a more extreme form, namely Trip-PDMS with just one triptycene unit
added to each end of Polydimethylsiloxane (PDMS), will also be discussed. It has been shownthat PDMS with bipodal triptycene at both ends can form long-range ordered structures andsubstantially increase the viscosity and modulus of PDMS 4 . Tripodal triptycene has a stronger
tendency to self-assemble compared with the former, so it is expected to further enhance themechanical properties of PDMS.
We first characterized Trip-PDMS using a small scan size. As shown in Fig. 6.6, some strip-likestructure was observed and it was traced by window displacement. Interestingly, we found thatthese strips are kept connected all the time, which prompted us to scan a larger size to grasp
the overall morphology of this phase structure. Therefore, we replaced an AFM with a larger
scan size to re-characterize it. The result is shown in Fig. 6.7.
We observed a large area of continuous mesh structure at a scan size of 20 µm, as shown in Fig.
6.7. This result is undoubtedly surprising because the change in this polymer compared to theoriginal amorphous PDMS is only two small molecules at each end. The self-assembly of thissmall molecule, i.e., tripodal triptycene, drives the formation of a network-like phase separation

66

Chapter 6. AFM Characterization of Triptycene-Appended Polymers
AFM観察：Tapping Mode
1.0

0.8

0.6
µm

1.0

0.4
0.8
1.0
0.2
0.6
µm

0.8
0.0
0.4

1.0
0.0

0.2

0.4

0.6
0.6

0.8

µm

µm

1.0

0.8

0.2
0.4

0.6
0.0

0.2

0.4

0.6

0.2

µm

0.0
0.8

1.0

µm

1.0
0.4
0.0
0.0

0.2
0.2

0.4

0.6
µm

0.8

0.8

1.0
1.0

0.6

0.8

0.0

0.2

µm

0.0
0.4

0.6

0.8

1.0

µm
0.4
µm

0.6

0.4

0.2

0.2

0.0
0.0

0.2

0.4

0.6

0.8

1.0

µm

0.0

0.0

0.2

0.4

0.6

0.8

1.0

µm

Figure 6.6: A first attempt at trip-PDMS in a small scan size. (phase images in tapping mode,
500 nm)structure inside the polymer and greatly increases the mechanical properties of PDMS. The
macroscopic manifestation of this enhancement is the transformation of PDMS, which was aliquid at room temperature, into a stretchable solid (Fig. 6.2). The cross-section drawn in its
height image shows a layer spacing of ∼25 nm, which is consistent with previous reports and
SAXS data (not shown in this thesis).

6.3. Summary

67

AFM観察：Tapping Mode

Phase, 20 µm

Phase, 10 µm

20Phase, 2 µm

2.0

10

8

15

1.5

µm

µm

1.0 2

4

0

2

0

-2

-2

5

0.5
2

0

-4

0.0

0

0

5

10
µm

15

20

-4

0

2

4

6

8

10

0.0

0.5

µm

1.0
µm

1.5

2.0

Hight, 2 µm
2.0

1.0
1.5
2

0.0
µm

1

-0.5

1.0
0

-1.0

-1

Height Sensor / nm

Height / nm

0.5

0.5

-1.5

-2

0

100

200

300

400 500
X / nm

600

700

800
0.0
0.0

0.5

1.0
µm

1.5

2.0

Figure 6.7: Phase and height images of Trip-PDMS with its layer spacing from the cross-section.

6.3

Summary

Polymers with appended triptycene in side chain and two terminals were investigated by AFM.
The introduction of triptycene allows the polymer to form special phase separation structures.
Meanwhile, triptycene as a hard phase in the phase separation structure helps to improve themacroscopic mechanical strength of the material. As a future plan, higher resolution AFM
characterization is expected to be implemented, thus challenging the de-observation of thecomplete ‘2D + 1D’ structure.

6.4

References[1] Seiki, N. et al. Rational synthesis of organic thin films with exceptional long-range structural
integrity. Science 348, 1122–1126 (2015).

Phase / degµm

4Phase / deg

10

6
4

6

68

Chapter 6. AFM Characterization of Triptycene-Appended Polymers[2] Ishiwari, F., Okabe, G., Kajitani, T. & Fukushima, T. Introduction of triptycene with aparticular substitution pattern into polymer chains can dramatically improve the structuraland rheological properties. ACS Macro Letters 10, 1529–1534 (2021).
[3] Liu, H. Synthesis, structure, and physical properties of tripodal triptycene-appended vinylic
polymers and copolymers. Master Thesis of Tokyo Institue of Technology (2019).
[4] Ishiwari, F. et al. Terminal functionalization with a triptycene motif that dramaticallychanges the structural and physical properties of an amorphous polymer. Journal of theAmerican Chemical Society 140, 13497–13502 (2018).
[5] Matsen, M. W. Effect of architecture on the phase behavior of ab-type block copolymer
melts. Macromolecules 45, 2161–2165 (2012).
[6] Saito, M., Ito, K. & Yokoyama, H. Mechanical properties of ultrathin polystyrene-bpolybutadiene-b-polystyrene block copolymer films: Film thickness-dependent young’s
modulus. Macromolecules 54, 8538–8547 (2021).

Chapter 7
Summary and Open Questions

7.1

Summary of Thesis

In this PhD thesis, in-situ AFM nanomechanics was developed using TPE as the object ofstudy and the formation and dynamic evolution of the stress network inside the TPE wasobserved. Also, in the local stress-strain analysis of AFM maps using FEA, we found thatthe topology inside the TPE is permanently changed under the influence of the stress networkand directly affects the macroscopic physical properties of the TPE. As a tool for microscopic
characterization combined with image analysis, the method described in this thesis gives anano-scale mechanism for the macroscopic physical behavior of the material, which may be
widely used in the in situ analysis of other structural polymer materials.

7.2Open Questions

In addition to the study of methodology, the starting point of this thesis is how to guide thedevelopment of new TPE materials by solving the deformation mechanism of TPE. In fact,
in addition to the research documented in the thesis, research on TPE materials based on
novel polymers or polymer blends is already being implemented. It must be acknowledged that69

70

Chapter 7. Summary and Open Questions

the development of new materials is a complex process and that the molecular design fromthe principles or the polymer blending ratios from the simulations can be easily influenced
by the subsequent processes, impurities, processing temperatures, and testing methods. On
the other hand, there may be potential to improve traditional industrial practices, such asincreasing molecular weight, improving the purity of raw materials, etc. For this complex
object of research, I hope that one day experiments, simulations and mathematical models will
cooperate perfectly to truly understand the nature of the structure and properties of materials.

7.3

List of Achievements

Original Papers
Papers Related to This Thesis
1. Chapter 3: Direct Visualization of a Strain-Induced Dynamic Stress Network in a SEBS
Thermoplastic Elastomer with In Situ AFM Nanomechanics
Haonan Liu, Xiaobin Liang, and Ken Nakajima, Japanese Journal of Applied Physics
2020, 59, SN1013. DOI: 10.35848/1347-4065/ab948a.
2. Chapter 4: Nanoscale Strain-Stress Mapping for Thermoplastic Elastomer Revealed Usinga Combination of In-Situ AFM Nanomechanics and Delaunay Triangulation
Haonan Liu, Xiaobin Liang, and Ken Nakajima, submitted to Physical Review Letters.
3. Chapter 5: Heterogeneously Formation and Dynamic Evolution of a Stress Network during the Initial Elongation of a SEBS Thermoplastic Elastomer, in preparation.

Papers not Related to This Thesis
1. Direct visualization of interfacial regions between fillers and matrix in rubber composites
observed by atomic force microscopy-based nanomechanics assisted by electron tomography

7.3. List of Achievements

71

Makiko Ito, Haonan Liu, Akemi Kumagai, Xiaobin Liang, Ken Nakajima, and Hiroshi
Jinnai, Langmuir 2022, DOI: 10.1021/acs.langmuir.1c02788
2. Tracking the evolution of the morphology and stress distribution of SIS thermoplastic
elastomers under tension using atomic force microscopy
Ling Gao, Haonan Liu, Xiaobin Liang, Makiko Ito, and Ken Nakajima, submitted.
3. Programmable Reversible Shape Transformation of Hydrogels Based on Transient Structural Anisotropy
Kangkang Liu, Yue Zhang, Heqing Cao, Haonan Liu, Yuhui Geng, Wenhua Yuan, Jian
Zhou, Zi Liang Wu, Guorong Shan, Yongzhong Bao, Qian Zhao, Tao Xie, and Pengju
Pan, Advanced Materials 2020, 32, 2001693. DOI: 10.1002/adma.202001693.

Awards and Recognitions
1. Best Poster Award, 27th International Colloquium on Scanning Probe Microscopy, 2019
2. Tokyo-Tech Pioneering Doctoral Research Program, 2021-2022
3. Tokyo Tech Tsubame Scholarship, 2019-2021
4. Monbukagakusho Honors Scholarship, 2017-2018, 2021-2022

Conferences and Presentations
International Conferences in PhD Course
1. Local Strain-Stress Evolution of Polymeric Materials Revealed by In-Situ AFM Nanomechanical Mapping
Haonan Liu, Xiaobin Liang, and Ken Nakajima, 29th International Colloquium on Scanning Probe Microscopy, 9-10 December 2021, Online

72

Chapter 7. Summary and Open Questions
2. AFM Nanomechanical Studies on Dynamic Stress Networks of Stretched Thermoplastic
Elastomer (Best Poster Award )Haonan Liu, Xiaobin Liang, and Ken Nakajima, 27th International Colloquium on Scanning Probe Microscopy, 5-7 December 2019, Shizuoka, Japan
3. Direct Visualization of Dynamic Stress Networks of TPE Based on AFM Nanomechanics
Haonan Liu, Xiaobin Liang, and Ken Nakajima, 13th China-Japan Seminar on Advanced
Engineering Plastics, Polymer Alloys and Composites, Shandong, China, , 19-23 November 2019

Domestic Conferences in PhD Course
1. 熱可塑性エラストマーの初期伸長過程における応力ネットワークの形成とその動的挙動
劉 浩男・梁暁斌・中嶋健

第３２回エラストマー討論会

2021年11月24日〜25日 九州大学稲盛財団記念館
2. Self-assembling Behavior and Mechanical Properties of Triptycene-Appended Block Copolymers
Ayami Itagaki, Fumitaka Ishiwari, Tomoya Fukui, Takashi Kajitani, Haonan Liu, Xiaobin
Liang, Ken Nakajima, Takanori Fukushima

第７０回高分子討論会

2021年9月6日〜8日 オンライン
3. ドロネー三⾓形分割に基づく応⼒下の熱可塑性エラストマーにおける動的ネットワークの構造解析劉 浩男・ 梁暁斌・中嶋健

第７０回高分子学会年次大会

2021年5月26日〜28日 オンライン
4. In situナノ触診AFMによるブロックコポリマー型TPEの変形挙動解析
劉 浩男・梁〜22日 中止

暁斌・中嶋健

日本ゴム協会２０２０年年次大会

2020年5月21日

7.3. List of Achievements

73

5. ナノ触診原子間力顕微鏡によるブロックコポリマー型TPEの変形挙動解析
劉 浩男・梁暁斌・中嶋健

第２９回日本ＭＲＳ年次大会

2019年11月27日〜29日 横浜情報文化センター
6. ナノ触診原子間力顕微鏡による熱可塑性エラストマーの変形挙動解析
劉 浩男・梁暁斌・中嶋健

第６８回高分子討論会

2019年9月25日〜27日

福井大学文京キャンパス

Domestic Conferences in Master Course
7. 三脚型トリプチセン含有ビニルポリマーおよびコポリマーの合成と自己集合化挙動
劉 浩男・石割文崇・梶谷2018年5月23日〜25日

孝・福島

孝典

第６７回高分子学会年次大会

名古屋国際会議場

8. 三脚型トリプチセン含有ビニルポリマーおよびコポリマーの合成と自己集合高分子の自己集合挙動と物性に影響を与える三脚型トリプチセンユニットの特異な効果
石割

文崇・岡部

・福島

孝典

玄・劉 浩男・荻原

日本化学会第９８春季年会

響・山下

幸大・木村

2018年3月20日〜23日

忠弘・梶谷

孝

日本大学船橋キャンパスOther Presentations

1. (Invited, online) Study of Polymer Nanomechanics Based on Atomic Force Microscopy, 3June 2021, Invited Lecture for State Key Laboratory of Chemical Engineering of Zhejiang
University, online
2. (若 手 発 表) ド ロ ネ ー 三 角 形 分 割 に 基 づ く 応 力 下 の 熱 可 塑 性 エ ラ ス ト マ ー に お
ける動的ネットワークの構造解析
2020年11月14日

オンライン

JST CREST 革 新 材 料 開 発 第 ５ 回 領 域 会 議74

Chapter 7. Summary and Open Questions
3. AFM Nanomechanical Studies on Dynamic Stress Networks of Deformed Thermoplastic
Elastomer, 2020 Dalian University of Technology-Tokyo Institute of Technology Joint
Workshop on Advanced Materials, 21 November 2020, online
4. Direct Visualization of Dynamic Stress Networks of TPE Based on AFM Nanomechanics,
Tokyo Tech-Imperial College London 3rd Workshop on Plastic Electronics and Related
Science and Technology, 18 November 2019, Tokyo Tech FrontAppendix A
Materials and Methods

A.1

Materials and Instruments

A.1.1

Materials

Unless otherwise stated, all commercial reagents were used as received. The specimen usedin Chapter 3-5, i.e., SEBS triblock copolymer (JSR Dynaron 8600P, styrene content = 15wt%), namely, SEBS15, was purified by reprecipitation from a toluene solution into methanol.
The sample was dried under vacuum at 50 ℃ for three days to remove the residual solvent.
The triptycene-related block polymers were obtained from Fukushima group, Department ofChemical Science and Engineering, Tokyo Institute of Technology.

A.1.2

AFM Probe

This thesis used two probes, OMCL-AC160TS with high resonance frequency for observing thebasic material phase structure in tapping mode, and ScanAsyst-Air for observing the nanomechanical properties of materials with higher resolution and more accurate physical properties.
The basic information for them is shown in Table A.1. The radius R of the ScanAsyst-Air probe
was evaluated by scanning a Nioprobe TipCheck sample (Aurora NanoDevices Inc., Canada)75

76

Appendix A. Materials and Methods

in QNM mode with a scan rate, scan size, and image resolution of 0.5 Hz, 400 × 400 nm2 , and1024 × 1024 pixels, respectively, and the probe radius was determined to be 2∼5 nm from theobtained height maps following the method in the previous report 1 . The spring constant k ofthe cantilever was measured to be 0.4∼0.5 N/m using the thermal tuning method 2 .
ScanAsyst-Air

OMCL-AC160TS

Brand and origin
Bruker, USA
Geometry
Triangular
Normal tip radius (nm)2Normal frequency (KHz)70
Normal spring constant (N/m) 0.4

Olympus, Japan
Rectangular
7
300
26

Table A.1: AFM probe information

A.1.3

Instruments

The basic information of all scientific instruments used in this thesis is shown in Table A.2.
Instrument nameBrand and origin

Model

Atomic force microscope
Atomic force microscope
Ultramicrotome
Tensile tester
Thickness gauge
Vacuum drying oven
Spin Coater
Analytical balance
Mini test press

Bruker, USA
Bruker, USA
Leica Microsystems, Germany
Shimadzu, Japan
Asker, Japan
Yamato Scientific, Japan
Mikasa, Japan
Shimadzu, Japan
Toyoseiki, Japan

MultiMode 8
Dimension Icon
EM UC6EZ-S
SDA-25
ADP200MS-B100
AUX120
MP-2F

Table A.2: Instrument information

A.2

Methods

A.2.1

Sample Preparation

Three preparation methods were used to observe the surface and internal structure and physicalproperties of the samples. The surface structure was observed by spin coating into a film, andA.2. Methods

77

the internal structure was observed by hot pressing (for SEBS) or solvent casting (for others).

Spin Coating

The sample was configured as a 5 mg/ml solution of toluene. 0.5 ml of the solution was added
dropwise to a 10 mm diameter glass substrate and spin-coated at 2000 rpm for 30 seconds. The
prepared films were glued to a 15 mm diameter stainless steel base with carbon tape for thesubsequent annealing step. The annealing temperature varies depending on the sample andwill be described in each chapter.

Hot Press

The SEBS15 film was then prepared by a hot-press casting procedure. The sample is firstpreheated at 150 ℃ for 5 min and hot pressed at 10 MPa for 1 min. Then presure released andcold pressed again at 10 MPa for 2 min. The thickness of the sample was made to be 0.2 mm
or 1 mm depending on the application.

Solvent Casting

2 g of sample was dissolved in 10 ml of toluene solution and poured in a 75 mm round Teflon
Petri dish. The film was dried in a fume hood at 25 ℃ for one week and then vacuum dried at
80 ℃ for one week to obtain a final thickness of 0.3 mm to 0.6 mm.

A.2.2

Tensile Test

All tensile tests were carried out at a temperature of 25 ℃. The specimen was cut into a
dumbbell shape (20 mm gauge length and 2 mm width) and uniaxially stretched at 40 mm/min
crosshead speed. To obtain comparable results, the same experiment was repeated at least threetimes on different specimens.

78

A.2.3

Appendix A. Materials and Methods

Sample’s Pre-Polishing for AFM

To create a polished sample for AFM investigation, the bulk specimen was cut into an ultrathin
section with a thickness of 300 nm at -120 ℃.

A.2.4

AFM Nanomechanical Mapping

Elastic modulus maps were recorded at 25 ℃using the PeakForce quantitative nanomechanicalmapping (QNM) mode. A Nanoscope V controller and version 9.1 of the Nanoscope software
were used. Force-deformation curves (FCs), which were converted from the original deflectiondisplacement curves 3 , were obtained during a typical AFM nanomechanical mapping processby moving the AFM cantilever-probe tip assembly forward and backward along a randomly selected surface while measuring the relationship between the force and deformation. Meanwhile,an E-type Z-piezo scanner’s oscillated the sample at frequencies, peak forces, and peak force
amplitudes of 1 kHz, 0.5 nN, and 100 nm, respectively. The FCs were gathered at a digital resolution of 256 x 256 pixels. Each FC was subjected to topographical imaging and simultaneous
mapping of mechanical properties. Johnson-Kendall-Roberts (JKR) contact mechanics wereapplied to the retraction part of the FCs during data analysis to account for the corresponding
Young’s modulus E 4 . Chapter 2 contains specifics.

Appendix B

Description for SSMapping

B.1

GeneralA Matlab-based program SSMapping was developed and used to analyze in-situ AFM images.
I was inspired by the work of Jinnai et al 5 , who performed in-situ TEM experiments on filledrubber and evaluated the material’s local strain by Delaunay triangulation of the filler particles.
Fig. B.2 shows the flow chart of SSMapping. For example, if the TPE contains a 15 wt%
proportion of hard segments, in the AFM deformation map, the 15% small-deformed area
is regarded as the hard phase and the discontinuous set of domains is naturally obtained.
The geometric center of each domain was selected as the representative point. The Delaunay
triangulation algorithm was modified from Matlab syntax to apply to the processing of AFM
images. Since the Delaunay mesh adopts the nearest neighbor rule, the auto-generated meshis reconstructed accordingly so that the triangles from different images can correspond exactly.
The calculation of a single triangular deformation is shown in Fig. B.1, which is often used in
the FEA process. The strain in the x (εx ) coordinate, strain in y (εy ) coordinate, and shear
strain (γxy ) can be derived separately using the strains of the respective triangles:

εx =(y2 − y3 )u1 + (y3 − y1 )u2 + (y1 − y2 )u3,
x2 y3 + x1 y2 + x3 y1 − x2 y1 − x3 y2 − x1 y3
79

(B.1)

80

Appendix B. Description for SSMapping

εy =
γxy =

(x3 − x2 )v1 + (x1 − x3 )v2 + (x2 − x1 )v3,
x2 y3 + x1 y2 + x3 y1 − x2 y1 − x3 y2 − x1 y3(B.2)(y2 − y3 )v1 + (y3 − y1 )v2 + (y1 − y2 )v3 + (x3 − x2 )u1 + (x1 − x3 )u2 + (x2 − x1 )u3.
x2 y3 + x1 y2 + x3 y1 − x2 y1 − x3 y2 − x1 y3(B.3)

Note that the macroscopic stretching direction is parallel to the y coordinate in all figures. To
further explore the variation of nanomechanical properties in the observed regions, the DelaunaySImesh obtained from the deformation map was used to divide the areas on the corresponding
modulus map so that the modulus variation for each triangle could be evaluated. The medianvalue of the soft-matrix modulus in each triangle is treated as the representative modulus. The
stress transfer of the network brings about the modulus variation in a local area; thus, I treat

Figure S2

this variation as the nano stress (∆E) in each triangle.

v3
Y(x3, y3)

u3
v2

v1

T’

T
(x2, y2)u1(x1, y1)u2

X
Figure B.1: Notations for the three-node triangle and the schematic diagram of its deformation.

Figure S3Macroscopic stress / MPa

0.40
0.39
0.38
0.37
0.36
0.35
300

400
500
Relaxing time / min600

B.1. General81

raw deformation images

start

restore image size

binarizemodify domainsnonumberingdomain number

do domains
correspond?

yes
modify meshs

triangulation

no

mesh

do meshs
correspond?

yesstrain map

calculate strains

raw modulus images

calculate stresses

stress map
Figure B.2: Flow chart of the program SSMapping.

82

B.2

Appendix B. Description for SSMapping

Step-by-Step Explanation

Input

Two AFM deformation maps are imported into the program. If stresses will also be calculated,the corresponding modulus maps need to be imported at the same time (no necessary in thestrain mapping). Since only the resolution of the images (e.g., 256 × 256 pixels) is identified
during import, their true size (e.g., 500 × 500 nm2 ) needs to be artificially specified. In order toobtain the true modulus, the modulus range used in the original modulus diagram also needs
to be defined manually. The specific code for the above operation is as follows.
1

clc , clear , close a l l% image i n f o r m a t o n

3

5

7

9

ImageSizeInNm= 500;% S i z e o f AFM images (nm)ResolutionInPixel= 256;% R e s o l u t i o n o f AFM images (nm)% d e f o r m a t i o n maps ( o n l y ‘ gray c o l o r ’ can be used )OriginalROI1= imread ( ‘ 5 0 7 ’ ) ;OriginalROI2= imread ( ‘ 5 7 0 ’ ) ;ROIRatio1= 0.15;

ROIRatio2= 0.15;% Read d e f o r m a t i o n maps

% ROI r a t i o o f d e f o r m a t i o n maps

% modulus maps ( o n l y ‘ gray c o l o r ’ can be used )11

OriginalModulusMap1 = imread ( ‘ 5 0 7m’ ) ; % Read modulus maps
OriginalModulusMap2 = imread ( ‘ 5 7 0m’ ) ;1315% f o r moving out i n t e r f a c e moduli
ModuROIRatio1= 0.15;ModuROIRatio2= 0.15;% ROI r a t i o o f modulus maps

% s e t modulus s c a l e f o r c o n v e r t i n g c o l o r v a l u e s t o moduli v a l u e s
17

19

ModulusMin= 3000000;% d e f a u l t c o l o r s c a l e o f gray image :ModulusMax= 20000000;% [0 65535]% f o r domain renumbering ( w i l l be used l a t e r )TargetDN1 = { [ 5 ] ; [ 2 22123];[19];[48];...}

TargetDN2 = { [ 4 ] ; [ 2 3 ] ; [ 1 9 ] ; [ 4 6 ] ; [ 5 4 ] ; . . . }% f o r mesh m o d i f i c a t i o n ( w i l l be used l a t e r )23

PreModifiedTN1= [124;129;...];

B.2. Step-by-Step Explanation

83

VertexesOfPMTN1 = [ 3 9 48 4 9 ; 3 8 39 4 8 ; . . . ] ;25

PreModifiedTN2= [271;285;...];

VertexesOfPMTN2 = [ 1 5 5 156 1 8 5 ; 1 5 4 156 1 8 5 ; . . . ] ;Part 1: The input and definition of AFM images.

Binarization and Domain Numbering

The program will binarize the deformation images to obtain a set of discontinuous domains.
The center of each domain is calculated to obtain a set of discrete points. These points will benumbered for post-processing. The results are shown in the Fig. B.3.
[ ExpandROI1 , DomainCenter1 , CDSize1 ] = DomainNumbering ( ImageSizeInNm ,R e s o l u t i o n I n P i x e l , OriginalROI1 , ROIRatio1 , TargetDN1 ) ;2t i t l e ( ‘ ROI Image 1 ’ )[ ExpandROI2 , DomainCenter2 , CDSize2 ] = DomainNumbering ( ImageSizeInNm ,SI

R e s o l u t i o n I n P i x e l , OriginalROI2 , ROIRatio2 , TargetDN2 ) ;4t i t l e ( ‘ ROI Image 2 ’ )Part 2: Binarization and domain numbering.

Figure B.3: The binarized deformation map and the numbered domains.

84

Appendix B. Description for SSMapping

Modification of NumberingSI

For the subsequent triangulation operation, the domains of the area to be calculated mustcorrespond to each other; thus, the automatically generated numbering needs to be adjusted.
The adjustments include the deletion of domains that exist only in one map, and the countingof multiple centers when the same domain splits in another map. The results are shown in theFig. B.4.
ModifiedDC1 = DomainModification ( DomainCenter1 , TargetDN1 , ImageSizeInNm , CDSize1 ,ExpandROI1 ) ;2t i t l e ( ‘ M o d i f i e d ROI Image 1 ’ )ModifiedDC2 = DomainModification ( DomainCenter2 , TargetDN2 , ImageSizeInNm , CDSize2 ,ExpandROI2 ) ;4t i t l e ( ‘ M o d i f i e d ROI Image 2 ’ )Part 3: Domain renumbering.

Figure B.4: The renumbered domains.

Delaunay Triangulation
The two sets of points of the two obtained images will be subjected to the first Delaunay
triangulation using Matlab’s built-in syntax. The results are shown in the Fig. B.5.

B.2. Step-by-Step Explanation

85

D e l T r i 1 = D e l a u n a y T r i a n g u l a t i o n ( ExpandROI1 , ModifiedDC1 , ImageSizeInNm ) ;2t i t l e ( ‘ D e l a u n a y T r i a n g u l a t i o n f o r ROI Image 1 ’ )D e l T r i 2 = D e l a u n a y T r i a n g u l a t i o n ( ExpandROI2 , ModifiedDC2 , ImageSizeInNm ) ;4t i t l e ( ‘ D e l a u n a y T r i a n g u l a t i o n f o r ROI Image 2 ’ )Part 4: Delaunay triangulation.

Figure B.5: The Delaunay meshes.

Modification of Delaunay Mesh

The auto-generated Delaunay mesh needs to be fine-tuned so that each triangle corresponds tothe other, and the result is shown in the Fig. B.6..
[ ModifiedDT1 , ˜ , ˜ ] = DTModification ( ExpandROI1 , ModifiedDC1 , DelTri1 , PreModifiedTN1, VertexesOfPMTN1 , ImageSizeInNm ) ;2t i t l e ( ‘ M o d i f i e d D e l a u n a y T r i a n g u l a t i o n f o r ROI Image 1 ’ )[ ModifiedDT2 , ˜ , ˜ ] = DTModification ( ExpandROI2 , ModifiedDC2 , DelTri2 , PreModifiedTN2, VertexesOfPMTN2 , ImageSizeInNm ) ;4t i t l e ( ‘ M o d i f i e d D e l a u n a y T r i a n g u l a t i o n f o r ROI Image 2 ’ )Part 5: Modification of Delaunay mesh.

86

Appendix B. Description for SSMapping

Figure B.6: The modified meshes.

Strain Mapping
The local stress distribution map can finally be successfully generated. The Fig. B.7 shows two
examples in the x and y directions.
[ L1X1 , L1Y1 , L1X2 , L1Y2 , L1X3 , L1Y3 , AllDomainX1 , AllDomainY1 ] = S u p p l y D i s p l a y i n g (ExpandROI1 , ModifiedDT1 , ImageSizeInNm , LocalTN1 ) ;2[ L2X1 , L2Y1 , L2X2 , L2Y2 , L2X3 , L2Y3 , AllDomainX2 , AllDomainY2 ] = S u p p l y D i s p l a y i n g (ExpandROI2 , ModifiedDT2 , ImageSizeInNm , LocalTN2 ) ;[ ALStrain , AllX , AllY ]= StrainAnalyzation (ModifiedDT1 , ExpandROI1 , AllDomainX1 , AllDomainY1 , L1X1 , L1Y1 , L1X2 , L1Y2 , L1X3 , L1Y3 ,L2X1 , L2Y1 , L2X2 , L2Y2 , L2X3 , L2Y3 , ImageSizeInNm , LocalTN1 , LocalTN2 ) ;Part 6: Strain mapping.

Stress Mapping
The stress map can also be further derived in conjunction with the modulus maps. Fig. B.8
shows an example.
1[ Table , ResizedModulusMap1 , ResizedModulusMap2 , L o c a l S t r e s s ] = S S F i t t i n g ( ALXStrain ,OriginalROI1 , OriginalROI2 , OriginalModulusMap1 , OriginalModulusMap2 , LocalTN1 ,B.2. Step-by-Step Explanation

87

Figure B.7: Strain maps in x and y coordinates.

AllDomainX1 , AllDomainY1 , ModuROIRatio1 , LocalTN2 , AllDomainX2 , AllDomainY2 ,ModuROIRatio2 , ModulusMin , ModulusMax , ImageSizeInNm , R e s o l u t i o n I n P i x e l ) ;t i t l e ( ‘ S t r e s s Mapping on ROI Image 1 ’ )Part 7: Stress mapping.

Figure B.8: The stress map.

88

Appendix B. Description for SSMapping

Functions used in SSMapping
Binarization and Domain Numbering

In this function, the program first binarizes the deformation map. The domains located at
the edges are then discarded before numbering because the domains at the edges cannot becalculated with the correct geometric centers.
f u n c t i o n [ ExpandROI , DomainCenter , CDSize ] = DomainNumbering ( ImageSizeInNm ,R e s o l u t i o n I n P i x e l , OriginalROI , ROIRatio , CombinedDN )2% recover to o r i g i n a l s i z e
IRFactor

4= ImageSizeInNm / R e s o l u t i o n I n P i x e l ;ResizedROI = i m r e s i z e ( OriginalROI , IRFactor ) ;% b i n a r i z e image

6

ROI= imcomplement ( i m b i n a r i z e ( ResizedROI , ROIRatio ) ) ;h o l d on
8

% expand one a r r a y f o r 4 e d g e s t o remove edge p a r t i c l e s by 8−c o n n e c t e d ‘ bwlabel ’ExpandROI= z e r o s ( ImageSizeInNm +2,

ImageSizeInNm +2) ;
10

12

14

16

ExpandROI ( 2 : ImageSizeInNm +1 ,2: ImageSizeInNm +1) = ROI ;ExpandROI ( : , 1 )= 1;ExpandROI ( : , ImageSizeInNm +2)= 1;

ExpandROI ( 1 , : )= 1;

ExpandROI ( ImageSizeInNm + 2 , : )= 1;[ ROILabel , NumDomain ]= b w l a b e l ( ExpandROI ) ;DomainCenter= z e r o s (NumDomain , 2 ) ;% d e c i d e domain c e n t e r
18

f o r i = 1 : NumDomain[ DomainX , DomainY ] = f i n d ( ROILabel == i ) ;DomainCenter ( i , : )20= [ mean ( DomainX−1) , mean ( DomainY−1) ] ; % used f o r move t h ematrix t o t h e o r g i n a l c o o r d s a f t e r expandingend
22% d e l e t e ROILable= 1 ( edge p a r t i c l e s which have been 8−c o n n e c t e d )[ DomainX , DomainY ] = f i n d ( ROILabel == 1 ) ;24nfor i = 1:n= s i z e ( DomainX , 1 ) ;B.2. Step-by-Step Explanation

89

ExpandROI ( DomainX ( i ) , DomainY ( i ) ) = 2 ;

26

end
28

DomainCenter ( 1 , : ) = [ ] ;% o p e r a t i o n f o r combining domain

30n= s i z e ( CombinedDN , 1 ) ;CDSize = [ ] ;32

i f n ˜= 0
for i = 1:n
PreCombinedDN = c e l l 2 m a t ( CombinedDN ( i , : ) ) ;34

f o r j = 1 : s i z e ( PreCombinedDN , 2 )[ DomainX , ˜ ] = f i n d ( ROILabel == PreCombinedDN ( 1 , j ) +1) ;36

CDSize ( i , j ) = s i z e ( DomainX , 1 ) ;
end

38

end
40

end
ExpandROI ( : , [ 1 ImageSizeInNm +2]) = [ ] ;42ExpandROI ( [ 1 ImageSizeInNm + 2 ] , : ) = [ ] ;i m a g e s c ( ExpandROI , ‘ AlphaData ’ , . 2 )44

DomainCenter= r o t 9 0 ( DomainCenter ) ;% label points46= a r r a y f u n (@( x ) { s p r i n t f ( ‘P%d ’ , x ) } , ( 1 : NumDomain

DomainLabel−1) ’ ) ;t e x t ( DomainCenter ( 1 , : ) , DomainCenter ( 2 , : ) , DomainLabel , ‘ H o r i z o n t a l A l i g n m e n t ’ , ‘c e n t e r ’ , ‘ Color ’ , ’ b l a c k ’ )48

hold o f fendFunction 1: Binarization and domain numbering.

Domain Renumbering
1

f u n c t i o n ModifiedDC = DomainModification ( DomainCenter , CombinedDN , ImageSizeInNm ,CDSize , ExpandROI )% z e r o matrix

3n = s i z e ( CombinedDN , 1 ) ;90Appendix B. Description for SSMapping

ModifiedDC = [ ] ;5% make a new matrix
for i = 1:n
PreCombinedDN

7= c e l l 2 m a t ( CombinedDN ( i , : ) ) ;PreCombinedDCoord = DomainCenter ( : , PreCombinedDN ) ;9

CDCSumX= 0;

CDCSumY= 0;

f o r j = 1 : s i z e ( PreCombinedDN , 2 )11

CDCSumX = CDCSumX + CDSize ( i , j ) ∗ DomainCenter ( 1 , PreCombinedDN ( j ) ) ;CDCSumY = CDCSumY + CDSize ( i , j ) ∗ DomainCenter ( 2 , PreCombinedDN ( j ) ) ;13

end
CombinedDCoordX = CDCSumX / sum ( CDSize ( i , : ) ) ;15

CombinedDCoordY = CDCSumY / sum ( CDSize ( i , : ) ) ;17

19

CombinedDCoord= [ CombinedDCoordX ; CombinedDCoordY ] ;ModifiedDC= [ ModifiedDC , CombinedDCoord ] ;end% o r i g i n a l image

21

i m a g e s c ( ExpandROI , ‘ AlphaData ’ , . 2 )h o l d on

23

% label points
Domainlabel = a r r a y f u n (@( x ) { s p r i n t f ( ‘P%d ’ , x ) } , ( 1 : s i z e ( ModifiedDC , 2 ) ) ’ ) ;25t e x t ( ModifiedDC ( 1 , : ) , ModifiedDC ( 2 , : ) , Domainlabel , ‘ H o r i z o n t a l A l i g n m e n t ’ , ‘ c e n t e r’ , ‘ Color ’ , ‘ blac k ’ )hold o f f

27

end

Function 2: Domain renumbering.

Delaunay Triangulation1

f u n c t i o n D e l T r i = D e l a u n a y T r i a n g u l a t i o n ( ExpandROI , ModifiedDC , ImageSizeInNm )i m a g e s c ( ExpandROI , ‘ AlphaData ’ , . 2 )3h o l d on
D e l T r i = d e l a u n a y T r i a n g u l a t i o n ( ModifiedDC ’ ) ;5t r i p l o t ( DelTri , ‘ Color ’ , ‘ blue ’ , ‘ LineWidth ’ , 1 )B.2. Step-by-Step Explanationh o l d on
7

% label points
Domainlabel = a r r a y f u n (@( x ) { s p r i n t f ( ‘P%d ’ , x ) } , ( 1 : s i z e ( ModifiedDC , 2 ) ) ’ ) ;9t e x t ( ModifiedDC ( 1 , : ) , ModifiedDC ( 2 , : ) , Domainlabel , ‘ H o r i z o n t a l A l i g n m e n t ’ , ‘ c e n t e r’ , ‘ Color ’ , ‘ blac k ’ )h o l d on

11

% l a b e l domains ’ c e n t e r
TriCenter = i n c e n t e r ( DelTri ) ;13

TriLabel= a r r a y f u n (@( x ) { s p r i n t f ( ‘T%d ’ , x ) } , ( 1 : s i z e ( DelTri , 1 ) ) ’ ) ;text ( TriCenter ( : , 1 ) , TriCenter ( : , 2 ) , TriLabel , ‘ HorizontalAlignment ’ , ‘ center ’ , ‘Color ’ , ‘ blue ’ )15hold o f fendFunction 3: Delaunay triangulation.

Delaunay-Mesh Modificationf u n c t i o n [ ModifiedDT ,DTN, AllTC ] = DTModification (ROI , ModifiedDC , DelTri ,PreModifiedTN , VertexesOfPMTN , ImageSizeInNm )2

i m a g e s c (ROI , ‘ AlphaData ’ , . 2 )h o l d on4

% e x t r a c t delaunay mesh t o e d i t l a t e r
ModifiedDT = s t r u c t ( ‘ P o i n t s ’ , D e l T r i . P o i n t s , ‘ C o n n e c t i v i t y L i s t ’ , D e l T r i .
ConnectivityList ) ;6% e d i t meshn = s i z e ( PreModifiedTN , 1 ) ;8for i = 1:n
ModifiedDT . C o n n e c t i v i t y L i s t ( PreModifiedTN ( i ) , : ) = VertexesOfPMTN ( i , : ) ;10

end% new mesh12

t r i p l o t ( ModifiedDT . C o n n e c t i v i t y L i s t , ModifiedDT . P o i n t s ( : , 1 ) , ModifiedDT . P o i n t s(: ,2) )h o l d on

14

% label points

91

92

Appendix B. Description for SSMapping

Domainlabel = a r r a y f u n (@( x ) { s p r i n t f ( ‘P%d ’ , x ) } , ( 1 : s i z e ( ModifiedDC , 2 ) ) ’ ) ;16t e x t ( ModifiedDC ( 1 , : ) , ModifiedDC ( 2 , : ) , Domainlabel , ‘ H o r i z o n t a l A l i g n m e n t ’ , ‘ c e n t e r’ , ‘ Color ’ , ‘ blac k ’ )h o l d on

18

% new t r i a n g l a r c e n t e r
DTN20= s i z e ( ModifiedDT . C o n n e c t i v i t y L i s t , 1 ) ;AllTC = z e r o s (DTN: 2 ) ;f o r i = 1 :DTN
VertexNum

22= ModifiedDT . C o n n e c t i v i t y L i s t ( i , : ) ;VertexCoord = ModifiedDT . P o i n t s ( VertexNum ’ , : ) ;24

26

TriCenter= mean ( VertexCoord ) ;AllTC ( i , : )= TriCenter ;end% label centers

28

T r i L a b e l = a r r a y f u n (@( x ) { s p r i n t f ( ‘T%d ’ , x ) } , ( 1 :DTN) ’ ) ;t e x t ( AllTC ( : , 1 ) , AllTC ( : , 2 ) , T r i L a b e l , ‘ H o r i z o n t a l A l i g n m e n t ’ , ‘ c e n t e r ’ , ‘ Color ’ , ‘ blue’)

30

hold o f f

Function 4: Delaunay-mesh modification.

Vertices Extraction

This function is used to extract the vertices of the triangle in advance to facilitate the stresscalculation later.
f u n c t i o n [ X1 , Y1 , X2 , Y2 , X3 , Y3 , AllDomainX , AllDomainY ] = S u p p l y D i s p l a y i n g (ROI ,ModifiedDT , ImageSizeInNm , LocalTN )2% local analysisn4= s i z e ( LocalTN , 2 ) ;AllDomainX = z e r o s ( n , 3 ) ;AllDomainY = z e r o s ( n , 3 ) ;

6

8

X1

= zeros (n , 1 ) ;Y1= zeros (n , 1 ) ;X2= zeros (n , 1 ) ;B.2. Step-by-Step Explanation

10

12

Y2

= zeros (n , 1 ) ;X3= zeros (n , 1 ) ;Y3= zeros (n , 1 ) ;93

for i = 1:n

14

TriNum= LocalTN ( : , i ) ; % t r i a n g l e numbers

TriVertexes= ModifiedDT . C o n n e c t i v i t y L i s t ( TriNum , : ) ; % v e r t e x e s o ftriangles
DomainX= ModifiedDT . P o i n t s ( T r i V e r t e x e s , 1 ) ; % x c o o r d i n a t e s o fvertexes
DomainY

16= ModifiedDT . P o i n t s ( T r i V e r t e x e s , 2 ) ; % y c o o r d i n a t e s o fvertexes

18

20

22

X1( i )= DomainX ( 1 ) ;Y1( i )= DomainY ( 1 ) ;X2( i )= DomainX ( 2 ) ;Y2( i )= DomainY ( 2 ) ;X3( i )= DomainX ( 3 ) ;Y3( i )= DomainY ( 3 ) ;AllDomainX ( i , : ) = DomainX ;AllDomainY ( i , : ) = DomainY ;

24

end
26

end

Function 6: Vertices extraction

Strain Mapping

In this function, since the correspondence of each vertex in the two triangles needs to be
determined, the calculation of the vector relationship between the three vertices is used todetermine the deformation direction of the triangle, which makes the function complicated, as
shown in Fig. B.9. Optimization methods are being considered.
f u n c t i o n [ ALStrain , AllX , AllY ] = S t r a i n A n a l y z a t i o n ( ModifiedDT1 , ROI1 , AllDomainX1 ,AllDomainY1 , L1X1 , L1Y1 , L1X2 , L1Y2 , L1X3 , L1Y3 , L2X1 , L2Y1 , L2X2 , L2Y2 , L2X3 , L2Y3 ,ImageSizeInNm , LocalTN1 , LocalTN2 )2

AllXStrain = zeros (n , 1 ) ;94Appendix B. Description for SSMapping

C’

C

T’

T

B

A

The simplest case: sort the coordinates
B’

A’
C’

C

Sorting has changed: determine

T

B

A

T’
A’

the rotation of the triangle
B’

resortA’C

Worst case: manual con rmation (almost

T’

T

B

A

C’

impossible to occur with small deformations)

B’
Figure B.9: fiThe method of determining the mapping between two triangles.

4

AllX

= zeros (n , 1 ) ;AllY= zeros (n , 1 ) ;for i = 1:n
6

A = [ L1X1 ( i ) ; L1X2 ( i ) ; L1X3 ( i ) ] ;B = [ L2X1 ( i ) ; L2X2 ( i ) ; L2X3 ( i ) ] ;8% Decide X1 ( min )i f L1X1 ( i ) == min (A)10i f L2X1 ( i ) == min (B)

12

14

T1X1

= L1X1 ( i ) ;T1Y1= L1Y1 ( i ) ;T2X1= L2X1 ( i ) ;T2Y1= L2Y1 ( i ) ;Table1Para1 = 1 ;Table2Para1 = 1 ;

16

else
18

i f L2X2 ( i ) == min (B)B.2. Step-by-Step Explanation

20

22

95

T1X1

= L1X1 ( i ) ;T1Y1= L1Y1 ( i ) ;T2X1= L2X2 ( i ) ;T2Y1= L2Y2 ( i ) ;Table1Para1 = 1 ;Table2Para1 = 2 ;

24

else
i f L2X3 ( i ) == min (B)

26

28

30

T1X1

= L1X1 ( i ) ;T1Y1= L1Y1 ( i ) ;T2X1= L2X3 ( i ) ;T2Y1= L2Y3 ( i ) ;Table1Para1 = 1 ;Table2Para1 = 3 ;

32

end
end

34

end
36

end
i f L1X2 ( i ) == min (A)38

i f L2X1 ( i ) == min (B)

40

42

T1X1

= L1X2 ( i ) ;T1Y1= L1Y2 ( i ) ;T2X1= L2X1 ( i ) ;T2Y1= L2Y1 ( i ) ;Table1Para1 = 2 ;Table2Para1 = 1 ;

44

else
46

i f L2X2 ( i ) == min (B)

48

50

T1X1

= L1X2 ( i ) ;T1Y1= L1Y2 ( i ) ;T2X1= L2X2 ( i ) ;T2Y1= L2Y2 ( i ) ;Table1Para1 = 2 ;Table2Para1 = 2 ;

52

else

96

Appendix B. Description for SSMapping
i f L2X3 ( i ) == min (B)

54

56

58

T1X1

= L1X2 ( i ) ;T1Y1= L1Y2 ( i ) ;T2X1= L2X3 ( i ) ;T2Y1= L2Y3 ( i ) ;Table1Para1 = 2 ;Table2Para1 = 3 ;

60

end
end

62

end
64

end
i f L1X3 ( i ) == min (A)66

i f L2X1 ( i ) == min (B)

68

70

T1X1

= L1X3 ( i ) ;T1Y1= L1Y3 ( i ) ;T2X1= L2X1 ( i ) ;T2Y1= L2Y1 ( i ) ;Table1Para1 = 3 ;Table2Para1 = 1 ;

72

else
74

i f L2X2 ( i ) == min (B)

76

78

T1X1

= L1X3 ( i ) ;T1Y1= L1Y3 ( i ) ;T2X1= L2X2 ( i ) ;T2Y1= L2Y2 ( i ) ;Table1Para1 = 3 ;Table2Para1 = 2 ;

80

else
82

84

86

i f L2X3 ( i ) == min (B)T1X1= L1X3 ( i ) ;T1Y1= L1Y3 ( i ) ;T2X1= L2X3 ( i ) ;T2Y1= L2Y3 ( i ) ;Table1Para1 = 3 ;88

Table2Para1 = 3 ;B.2. Step-by-Step Explanation

97

end
end

90

end
92

end
% Decide X2 (max)94

i f L1X1 ( i ) == max(A)i f L2X1 ( i ) == max(B)

96

98

T1X2

= L1X1 ( i ) ;T1Y2= L1Y1 ( i ) ;T2X2= L2X1 ( i ) ;T2Y2= L2Y1 ( i ) ;Table1Para2 = 1 ;100

Table2Para2 = 1 ;
else

102

i f L2X2 ( i ) == max(B)
104

106

T1X2

= L1X1 ( i ) ;T1Y2= L1Y1 ( i ) ;T2X2= L2X2 ( i ) ;T2Y2= L2Y2 ( i ) ;Table1Para2 = 1 ;108

Table2Para2 = 2 ;
else

110

i f L2X3 ( i ) == max(B)
112

114

T1X2

= L1X1 ( i ) ;T1Y2= L1Y1 ( i ) ;T2X2= L2X3 ( i ) ;T2Y2= L2Y3 ( i ) ;Table1Para2 = 1 ;116

Table2Para2 = 3 ;
end

118

end
end

120

end
122

i f L1X2 ( i ) == max(A)i f L2X1 ( i ) == max(B)98Appendix B. Description for SSMapping

124

126

T1X2

= L1X2 ( i ) ;T1Y2= L1Y2 ( i ) ;T2X2= L2X1 ( i ) ;T2Y2= L2Y1 ( i ) ;Table1Para2 = 2 ;128

Table2Para2 = 1 ;
else

130

i f L2X2 ( i ) == max(B)
132

134

T1X2

= L1X2 ( i ) ;T1Y2= L1Y2 ( i ) ;T2X2= L2X2 ( i ) ;T2Y2= L2Y2 ( i ) ;Table1Para2 = 2 ;136

Table2Para2 = 2 ;
else

138

i f L2X3 ( i ) == max(B)
140

142

T1X2

= L1X2 ( i ) ;T1Y2= L1Y2 ( i ) ;T2X2= L2X3 ( i ) ;T2Y2= L2Y3 ( i ) ;Table1Para2 = 2 ;144

Table2Para2 = 3 ;
end

146

end
end

148

end
150

i f L1X3 ( i ) == max(A)i f L2X1 ( i ) == max(B)

152

154

T1X2

= L1X3 ( i ) ;T1Y2= L1Y3 ( i ) ;T2X2= L2X1 ( i ) ;T2Y2= L2Y1 ( i ) ;Table1Para2 = 3 ;156

Table2Para2 = 1 ;
158

else

B.2. Step-by-Step Explanation

99

i f L2X2 ( i ) == max(B)
160

162

T1X2

= L1X3 ( i ) ;T1Y2= L1Y3 ( i ) ;T2X2= L2X2 ( i ) ;T2Y2= L2Y2 ( i ) ;Table1Para2 = 3 ;164

Table2Para2 = 2 ;
else

166

i f L2X3 ( i ) == max(B)
168

170

T1X2

= L1X3 ( i ) ;T1Y2= L1Y3 ( i ) ;T2X2= L2X3 ( i ) ;T2Y2= L2Y3 ( i ) ;Table1Para2 = 3 ;172

Table2Para2 = 3 ;
end

174

end
end

176

end
178

% Decide X3 ( t h e o t h e r )Table1Para3 = 6 − Table1Para1 − Table1Para2 ;180

Table2Para3 = 6 − Table2Para1 − Table2Para2 ;i f Table1Para3 == 1

182

i f Table2Para3 == 1
T1X3 = L1X1 ( i ) ;T1Y3 = L1Y1 ( i ) ;184

T2X3 = L2X1 ( i ) ;T2Y3 = L2Y1 ( i ) ;

186

else
188

i f Table2Para3 == 2
T1X3 = L1X1 ( i ) ;T1Y3 = L1Y1 ( i ) ;190

T2X3 = L2X2 ( i ) ;T2Y3 = L2Y2 ( i ) ;

192

else

100

Appendix B. Description for SSMapping
i f Table2Para3 == 3

194

T1X3 = L1X1 ( i ) ;T1Y3 = L1Y1 ( i ) ;196

T2X3 = L2X3 ( i ) ;T2Y3 = L2Y3 ( i ) ;

198

end
end

200

end
202

end
i f Table1Para3 == 2
i f Table2Para3 == 1

204

T1X3 = L1X2 ( i ) ;T1Y3 = L1Y2 ( i ) ;206

T2X3 = L2X1 ( i ) ;T2Y3 = L2Y1 ( i ) ;

208

else
i f Table2Para3 == 2

210

T1X3 = L1X2 ( i ) ;T1Y3 = L1Y2 ( i ) ;212

T2X3 = L2X2 ( i ) ;T2Y3 = L2Y2 ( i ) ;

214

else
i f Table2Para3 == 3

216

T1X3 = L1X2 ( i ) ;T1Y3 = L1Y2 ( i ) ;218

T2X3 = L2X3 ( i ) ;T2Y3 = L2Y3 ( i ) ;

220

end
end

222

end
224

end
i f Table1Para3 == 3

226

i f Table2Para3 == 1
T1X3 = L1X3 ( i ) ;228

T1Y3 = L1Y3 ( i ) ;B.2. Step-by-Step Explanation

101

T2X3 = L2X1 ( i ) ;T2Y3 = L2Y1 ( i ) ;

230

else
i f Table2Para3 == 2

232

T1X3 = L1X3 ( i ) ;T1Y3 = L1Y3 ( i ) ;234

T2X3 = L2X2 ( i ) ;T2Y3 = L2Y2 ( i ) ;

236

else
i f Table2Para3 == 3

238

T1X3 = L1X3 ( i ) ;T1Y3 = L1Y3 ( i ) ;240

T2X3 = L2X3 ( i ) ;T2Y3 = L2Y3 ( i ) ;

242

end
end

244

end
246

end
% Check i f xmin o r xmax have changed t o o t h e r p o i n t s d u r i n g two f i g u r e ’ s
time

248

i f ( ( T1X2 − T1X1) ∗ (T1Y3 − T1Y2) − (T1Y2 − T1Y1) ∗ (T1X3 − T1X2) ) ∗ ( ( T2X2
− T2X1) ∗ (T2Y3 − T2Y2) − (T2Y2 − T2Y1) ∗ (T2X3 − T2X2) ) < 0
i f ( abs (T2X2 − T2X3) < abs (T2X1 − T2X3) ) && ( abs (T2X2 − T2X3) < abs (T2X1 − T2X2) )T 2 I n t e r = T2X3 ;

250

252

T2X3

= T2X2 ;T2X2= T2Inter ;T 2 I n t e r = T2Y3 ;
254

256

T2Y3

= T2Y2 ;T2Y2= T2Inter ;endi f ( abs (T2X1 − T2X3) < abs (T2X2 − T2X1) ) && ( abs (T2X1 − T2X3) < abs (T2X2 − T2X3) )258

T 2 I n t e r = T2X3 ;T2X3= T2X1 ;102

Appendix B. Description for SSMapping
T2X1

260

= T2Inter ;T 2 I n t e r = T2Y3 ;
262

T2Y3

= T2Y1 ;T2Y1= T2Inter ;

end

264

end
266

268

U1

= T2X1 − T1X1 ;U2= T2X2 − T1X2 ;U3= T2X3 − T1X3 ;XStrain= ( ( T1Y2 − T1Y3) ∗ U1 + (T1Y3 − T1Y1) ∗ U2 + (T1Y1 − T1Y2) ∗U3) / . . .
(T1X2 ∗ T1Y3 + T1X1 ∗ T1Y2 + T1X3 ∗ T1Y1 − T1X2 ∗ T1Y1 − T1X3 ∗ T1Y2 −270

T1X1 ∗ T1Y3) ;A l l X S t r a i n ( i ) = XStrain ;
272

274

AllX ( i )= (T1X1+T1X2+T1X3) / 3 ;AllY ( i )= (T1Y1+T1Y2+T1Y3) / 3 ;[ X, Y, Z ]= g r i d d a t a ( AllX , AllY , ALStrain , l i n s p a c e ( min ( AllX ) ,max( AllX ) ) ’ ,l i n s p a c e ( min ( AllY ) ,max( AllY ) ) , ‘ v4 ’ ) ;PColorMap= p c o l o r (X, Y, Z ) ;shading i n t e r p

276

colorbaru i s t a c k ( PColorMap , ‘ bottom ’ )278

h o l d on
280end
t r i p l o t ( ModifiedDT1 . C o n n e c t i v i t y L i s t , ModifiedDT1 . P o i n t s ( : , 1 ) , ModifiedDT1 . P o i n t s(: ,2) )282

h o l d on
TriangleNumber1 = LocalTN1 ’ ;

284

286

288

TriangleNumber2 = LocalTN2 ’ ;Table= t a b l e ( TriangleNumber1 , TriangleNumber2 , ALStrain ) ;Table ( n + 1 , : )= {NaN, NaN, mean ( ALStrain ) } ;BaseImage= i m a g e s c ( ROI1 , ‘ AlphaData ’ , . 2 ) ;u i s t a c k ( BaseImage , ‘ bottom ’ )h o l d on

290

end

B.2. Step-by-Step Explanation

103

Function 7: Strain mapping (x coordinate as an example).

Local Modulus

Exporting the stress mapping first requires extracting the modulus of each triangle, which isthe function below.
f u n c t i o n [ ALModulus , ResizedModulusMap ] = LocalModulus ( OriginalModulusMap ,ModulusMin , ModulusMax , LocalTN , AllDomainX , AllDomainY , OriginalROI , ModuROIRatio ,ImageSizeInNm , R e s o l u t i o n I n P i x e l )2% rescale
ModulusMap

46= r e s c a l e ( OriginalModulusMap , ModulusMin , ModulusMax ) ;% resize
IRFactor= ImageSizeInNm / R e s o l u t i o n I n P i x e l ;ResizedROI= i m r e s i z e ( OriginalROI , IRFactor ) ;ResizedModulusMap = i m r e s i z e ( ModulusMap , IRFactor ) ;8% r e c o r d non−ROI c o o r d s ( s t u p i d method )% crop f o r a c c e l e r a t i n g

10

12

14

16

18

i1

= f l o o r ( min ( min ( AllDomainX ) ) ) ;i2= c e i l (max(max( AllDomainX ) ) ) ;j1= f l o o r ( min ( min ( AllDomainY ) ) ) ;j2= c e i l (max(max( AllDomainY ) ) ) ;ModuROI= imcomplement ( i m b i n a r i z e ( ResizedROI , ModuROIRatio ) ) ;LROI= ModuROI ( ( j 1 : j 2 ) , ( i 1 : i 2 ) ) ;n= l e n g t h ( f i n d (LROI == 0 ) ) ;NROICoord= zeros (n , 2 ) ;k = 1;
for j = j1 : j2

20

for i = i1 : i2
i f ModuROI( j , i ) == 0
NDomainCoord = [ i , j ] ;22

NROICoord ( k , : ) = NDomainCoord ;k = k+1;

24

end

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Appendix B. Description for SSMapping
end

26

end
28

NROICoordX = NROICoord ( : , 1 ) ;NROICoordY = NROICoord ( : , 2 ) ;30

32% local analysisn= s i z e ( LocalTN , 2 ) ;ALModulus= zeros (n , 1 ) ;for i = 1:n
34

36

38

DomainX= AllDomainX ( i , : ) ;DomainY= AllDomainY ( i , : ) ;[ AreaIn , ˜ ]= i n p o l y g o n ( NROICoordX , NROICoordY , DomainX , DomainY ) ;AreaNROIX= NROICoordX ( AreaIn ) ;AreaNROIY= NROICoordY ( AreaIn ) ;FullSize= [ ImageSizeInNm ImageSizeInNm ] ;% change matrix t o l i n e

40

LineNumber= s u b 2 i n d ( F u l l S i z e , AreaNROIX , AreaNROIY ) ;M o d ul u s F o r Al l P o i nt s = ResizedModulusMap ( LineNumber ) ;42% median o f a l l modulus
44

46

AverageModulus= median ( M o d u lu s F o r A ll P o i n t s ) ;ALModulus ( i )= AverageModulus ;

end
end

Function 8: Extracting the representative modulus of each triangle.

Stress Mapping1

f u n c t i o n [ Table , ResizedModulusMap1 , ResizedModulusMap2 , L o c a l S t r e s s ] = S S F i t t i n g (ALStrain , OriginalROI1 , OriginalROI2 , OriginalModulusMap1 , OriginalModulusMap2 ,LocalTN1 , AllDomainX1 , AllDomainY1 , ModuROIRatio1 , LocalTN2 , AllDomainX2 ,AllDomainY2 , ModuROIRatio2 , ModulusMin , ModulusMax , ImageSizeInNm ,ResolutionInPixel )[ ALModulus1 , ResizedModulusMap1 ] = LocalModulus ( OriginalModulusMap1 , ModulusMin ,ModulusMax , LocalTN1 , AllDomainX1 , AllDomainY1 , OriginalROI1 , ModuROIRatio1 ,ImageSizeInNm , R e s o l u t i o n I n P i x e l ) ;B.3. References

3

105[ ALModulus2 , ResizedModulusMap2 ] = LocalModulus ( OriginalModulusMap2 , ModulusMin ,ModulusMax , LocalTN2 , AllDomainX2 , AllDomainY2 , OriginalROI2 , ModuROIRatio2 ,ImageSizeInNm , R e s o l u t i o n I n P i x e l ) ;5

7

ALStress= ALModulus2 − ALModulus1 ;LocalModulus1= ALModulus1 ;LocalModulus2= ALModulus2 ;TriangleNumber1 = LocalTN1 ’ ;TriangleNumber2 = LocalTN2 ’ ;

9

Table

= t a b l e ( TriangleNumber1 , TriangleNumber2 , LocalModulus1 ,LocalModulus2 , L o c a l S t r e s s , L o c a l S t r a i n ) ;[ X, Y, Z ]= g r i d d a t a ( XAllX , XAllY , L o c a l S t r e s s , l i n s p a c e ( min ( XAllX ) ,max( XAllX) ) ’ , l i n s p a c e ( min ( XAllY ) ,max( XAllY ) ) , ‘ v4 ’ ) ;11

PColorMap= p c o l o r (X, Y, Z ) ;shading i n t e r p
13colorbaru i s t a c k ( PColorMap , ‘ bottom ’ )15

h o l d ont r i p l o t ( ModifiedDT1 . C o n n e c t i v i t y L i s t , ModifiedDT1 . P o i n t s ( : , 1 ) , ModifiedDT1 . P o i n t s(: ,2) )17

h o l d on
BaseImage = i m a g e s c ( ExpandROI1 , ‘ AlphaData ’ , . 2 ) ;19

u i s t a c k ( BaseImage , ‘ bottom ’ )h o l d on

21

end

Function 9: Stress mapping.

B.3

References[1] Wang, D., Liang, X., Russell, T. P. & Nakajima, K. Visualization and quantification of thechemical and physical properties at a diffusion-induced interface using afm nanomechanicalmapping. Macromolecules 47, 3761–3765 (2014).

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Appendix B. Description for SSMapping[2] Hutter, J. L. & Bechhoefer, J. Calibration of atomic-force microscope tips. Review ofscientific instruments 64, 1868–1873 (1993).
[3] Nakajima, K. et al. Nano-palpation afm and its quantitative mechanical property mapping.
Microscopy 63, 193–208 (2014).
[4] Johnson, K. L., Kendall, K. & Roberts, a. Surface energy and the contact of elastic solids.
Proceedings of the royal society of London. A. mathematical and physical sciences 324,
301–313 (1971).
[5] Miyata, T. et al. Nanoscale stress distribution in silica-nanoparticle-filled rubber as observedby transmission electron microscopy: Implications for tire application. ACS Applied Nano
Materials 4, 4452–4461 (2021).