GECKO AND BIO-INSPIRED HIERARCHICAL FIBRILLAR ADHESIVE
STRUCTURES EXPLORED BY MULTISCALE MODELING AND SIMULATION
A Dissertation
Presented to
The Graduate Faculty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Shihao Hu
August, 2012
GECKO AND BIO-INSPIRED HIERARCHICAL FIBRILLAR ADHESIVE
STRUCTURES EXPLORED BY MULTISCALE MODELING AND SIMULATION
Shihao Hu
Dissertation
Approved Accepted
Advisor Department Chair Dr. Zhenhai Xia Dr. Celal Batur
Co-advisor Dean of the College Dr. Xiaosheng Gao George K. Haritos
Committee Member Dean of the Graduate School Dr. Gregory Morscher George R. Newkome
Committee Member Date Dr. Juay Seng Tan
Committee Member Dr. Hendrik Heinz
ii ABSTRACT
Gecko feet integrate many intriguing functions such as strong adhesion, easy detachment and self-cleaning. Mimicking this biological system leads to the development of a new class of advanced fibrillar adhesives useful in various applications.
In spite of many significant progresses that have been achieved in demonstrating the enhanced adhesion strength from divided non-continuous surfaces at micro- and nano- scales, directional dependent adhesion from anisotropic structures, and some tolerance of third body interferences at the contact interfaces, the self-cleaning capability and durability of the artificial fibrillar adhesives are still substantially lagging behind the natural version. These insufficiencies impede the final commercialization of any gecko inspired products. Hence here, we have focused our attentions on these critical issues in both (i) the gecko adhesive systems and (ii) the synthetic counterparts.
(i) We tested the self-cleaning of geckos during locomotion and provided the first evidence that geckos clean their feet through a unique dynamic self-cleaning mechanism via digital hyperextension. When walking naturally with hyperextension, geckos shed dirt from their toes twice as fast as they would if walking without hyperextension, returning their feet to nearly 80% of their original stickiness in only 4 steps. Our dynamic model predicts that when setae suddenly release from the attached substrate, they generate enough inertial force to dislodge dirt particles from the attached spatulae.
The predicted cleaning force on dirt particles significantly increases when the dynamic
iii effect is included. The extraordinary design of gecko toe pads perfectly combines dynamic self-cleaning with repeated attachment and detachment, making gecko feet sticky yet clean. This work thus provides a new mechanism to be considered for biomimetic design of highly reusable and reliable dry adhesives and devices.
(ii) A multiscale modeling approach has been developed to study the force anisotropy, structural deformation and failure mechanisms of a two-level hierarchical
CNT structures mimicking the gecko foot hairs. At the nanoscale, fully atomistic molecular dynamics simulation was performed to explore the origin of adhesion enhancement considering the existence of laterally distributed CNT segments. Tube-tube interactions and the collective effect of interfacial adhesion and friction forces were investigated at an upper level. A fraction of the vertically aligned CNT arrays with laterally distributed segments on top was simulated by coarse grained molecular dynamics. The characteristic interfacial adhesive behaviors obtained were further adopted as the cohesive laws incorporated in the finite element models at the device level and fitted with experimental results. The multiscale modeling approach provides a bridge to connect the atomic/molecular configurations and the micro-/nano- structures of the
CNT array with its macro-level adhesive behaviors, and the predictions from the modeling and simulation help to understand the interfacial behaviors, processes and mechanics of the gecko inspired fibrillar structures for dry adhesive applications.
iv ACKNOWLEDGEMENTS
I would like to thank all those who helped me through my PhD program. Without them, I could not have completed this multidisciplinary project.
First of all, having Dr. Zhenhai Xia as my advisor is a blessing. In this four years span, he nurtures me not only a unique way of approaching intriguing scientific problems and demanding technical challenges, but also gives me many great opportunities to expose myself into the real scientific and engineering communities through a variety of conferences and symposium, presenting my research, talking with my peers and learning from the authorities. Luckily as his first PhD student here in Akron U, I have got the chance to experience the growth of our group from the very beginning. Those early days that he and I build up our lab pieces by pieces are still vividly pictured in my mind. Now, four years later he is supervising a group of highly motivated students in the area of advanced composite materials, biomimicry, energy related projects and biomedical devices. Here, I wish to express my truthful gratitude and appreciation to him for his support, patience and understanding at this critical stage of my life, and am also looking forward to continuing our strong connections in the future.
Life is full of surprises. At the third year of my PhD program I met Dr. Peter H.
Niewiarowski, from a Tropical Vertebrate Biology Class (Outfield in Florida), who later on helped make the third capture possible. He is a very knowledgeable and experienced experimental biologist, who has a special sense of humor and super fun to be around. We
v recognized the same interest in gecko self-cleaning and initiated collaboration right away.
This unexpected experience broadens my horizon and fosters me to think more critically across disciplines under different and often contrasting contexts. I would like to thank him for giving me a chance to work in his lab and using his resources especially for the geckos. I really appreciate the time and efforts he had put in our joint project. Besides, I believe that some of the interesting American conventions as well as his perspectives in life science will have a much longer impact of my career and life.
I am very grateful to my co-advisor Dr. Xiaosheng Gao, for his supervision, countless intellectually stimulating conversations, kindness, always ready to help. I am also deeply thankful to Dr. Gregory Morscher, Dr. Juay Seng Tan and Dr. Hendrik Heinz for serving as my committee members. It is not an easy job to thoroughly and carefully read a PhD thesis and give constant feedbacks for improvement. From my proposal to the final defense, they offered me great encouragement and many positive suggestions.
I would want to thank all our group members and fellow students in Dr. Xia’s group, Thanyawalai Sujidkul, Lipeng Zhang, Craig Smith, Lili Li, Jianbing Niu, Quan Xu and Jie Wen, for being so supportive and friendly. Those are the experiences that I will never forget.
Finally, I wish to give my parents the full credit. Their endless love, care, support and understanding, from the very start of my life, are what make me to become me today.
I am very thankful to them for giving me the strength to grown as a person and offering me the opportunities to stretch my potentials.
vi TABLE OF CONTENTS Page
LIST OF TABLES ...... x
LIST OF FIGURES ...... xi
CHAPTER
I. INTRODUCTION ...... 1
1.1 Background ...... 1
1.2 Problem Statement ...... 2
1.3 Objectives ...... 2
1.4 Hypothesis ...... 3
1.5 Dissertation Outline ...... 4
II. LITERATURE REVIEW ...... 6
2.1 Hierarchical Fibrillar Structure of Gecko Toe Pads ...... 6
2.2 Polymer Based Fibrillar Dry Adhesives ...... 9
2.2.1 Cast-molding ...... 10
2.2.2 Electron-beam lithography ...... 12
2.2.3 Soft and rigiflex lithography ...... 13
2.2.4 Tip shape variations ...... 15
2.2.5 Anisotropic fibrillar structures ...... 17
2.2.6 Hierarchical fibrillar structures ...... 20
vii 2.3 Carbon Nanotube Based Fibrillar Dry Adhesives ...... 23
2.3.1 Single-level CNT arrays/forests ...... 23
2.3.2 Multi-level patterned CNT arrays/forests ...... 24
2.4 Rational Design Based on Geometric Replications of Gecko Adhesive System .... 26
2.5 Rational Design beyond Geometric Replications of Gecko Adhesive System ...... 33
2.6 Self-Cleaning in Artificial Fibrillar Adhesives...... 38
2.7 Summery and Outlook ...... 39
III. DYNAMIC SELF-CLEANING IN GECKO SETAE ...... 41
3.1 Introduction ...... 41
3.2 Materials and Methods ...... 43
3.3 Results ...... 46
3.3.1 Self-cleaning of toe pads in unrestrained geckos ...... 47
3.3.2 Observations of dirt particles on live gecko toe pads ...... 49
3.4 Discussion ...... 51
3.4.1 Gecko detachment mechanisms with and without digital hyperextension ...... 51
3.4.2 Dynamic self-cleaning mechanism ...... 56
3.4.3 Effect of DH on dynamic self-cleaning ...... 64
3.4.4 Revisiting the easy detachment mechanism of gecko feet...... 67
3.5 Conclusions ...... 71
IV. MECHANICAL ANALYSES OF THE HIERARCHICALLY STRUCTURED CARBON NANOTUBE ARRAYS FOR DRY ADHESIVE APPLICATIONS ...... 72
4.1 Introduction ...... 72
viii 4.2 Outline of the Multiscale Modeling and Simulation Approaches ...... 74
4.3 Fully Atomistic Molecular Dynamics ...... 76
4.3.1 Introduction ...... 76
4.3.2 Methodology ...... 78
4.3.3 Results ...... 80
4.3.4 Discussion ...... 89
4.3.5 Conclusions ...... 103
4.4 Coarse Grained Molecular Dynamics ...... 103
4.4.1 Model description ...... 103
4.4.2 Results and discussion ...... 109
4.4.3 Conclusions ...... 116
4.5 Finite Element Analysis...... 117
4.5.1 Model description ...... 118
4.5.2 Results and discussion ...... 122
4.5.3 Conclusions ...... 138
V. CONCLUSIONS AND FUTURE WORK ...... 139
5.1 Conclusions ...... 139
5.2 Recommended Future Works ...... 141
REFERENCES ...... 143
ix LIST OF TABLES Table Page
4-1 Parameters calculated for the adhesion enhancement of various materials………...102
x LIST OF FIGURES Figure Page
2-1 Structural hierarchy of Tokay gecko adhesive system from naked-eye pictures (A, B) to SEM micrographs (C, D, E). (A) Gecko hanging upside down; (B) underside of a gecko foot, where the toe pads are striped into ridges, laminae; (C) side and (D) top views of setal array at different magnifications; (E) the finest terminal branches of seta, spatulae. ST: seta; SP: spatula; BR: branch. [3, 4] ...... 7
2-2 Connections between the structures, characteristic features/parameters, functions and performances identified in the gecko dry adhesive systems...... 9
2-3 SEM micrographs of (A) nano-cast-molded PMMA nanotube arrays, (B) UV nano- embossed nanopillar arrays and (C) hierarchical PMMA fibrillar structure featuring ~10 μm wide and ~70 μm long microfibrils, each of which branches in to ~60 nm wide and ~0.5 μm long nanofibrils utilizing AAO templates; (D) electron beam lithography defined polyimide nanohairs; (E) PDMS micropillar arrays, with a radius of ~2.5 μm, a height of ~20 μm and the minimum inter-pillar distance of ~5 μm, by softlithography; (F) PMMA nanohairs fabricated by adding a sequential drawing in rigiflexlithography, resulting a fiber necking effect down to ~80 nm in diameter. [34-36, 41, 43, 48] ...... 14
2-4 SEM micrographs of PDMS fibrillar structures with (A) flat, (B) spherical, (C) symmetric spatula, (D) asymmetric spatula, (E) tube and (F) concave tips; (G) mushroom-shaped PVS and (H) polyurethane fibrillar microstructures; (I) an array of PDMS micro-pillars with a continuous film on top. [49, 51, 57, 58] ...... 17
2-5 SEM micrographs of (A) directional polyurethane microstalks, 1 mm long, 380µm in diameter, with 20° tilted stalks and 45° angled wedge endings; (B, C) arrays of 35-µm diameter tilted polyurethane microfibers with 23° angled mushroom tips; (D, E) 27° tilted PDMS micro pillars having 9.3 µm diameter, 30 µm length and 10 µm spacing. [61, 63, 67] ...... 19
2-6 SEM micrographs of (A, B and C) multilevel integrated compliant structures of photoresist nanorods on top of one pillar supported compliant MEMs platform; (D, E and F) hierarchical PUA polymeric hairs with well-defined high aspect ratio and angled nanofibers with bulged flat tips formed on 5-µm-diameter, 25-µm-height and 5-µm- spacing straight micropillars; (G, H, I and J) three-level hierarchical polyurethane fibers: (G) 400-μm-diameter curved base fibers, (H) base fiber tip with midlevel 50-μm- diameter fibers, (I) midlevel fibers in detail, (J) third level fibers at the tip of the midlevel fibers, 3 μm in diameter and 20 μm in height and having 5-μm-diameter flat mushroom tips. [70, 73, 75] ...... 22
xi 2-7 SEM images of (A) natural gecko setae terminating into thousands of smaller spatulae, (B) side view and (D) close up of the 100 µm wide square patterned VA-CNT arrays. SEM micrographs of the structure similarity between the cross section views of (D) gecko’s aligned elastic hairs and (E) hierarchically structured vertically aligned MWCNTs with (C) entangled top layer resembling spatulae. (D) TEM image of a single MWCNT at the top layer. [83, 84] ...... 26
2-8 Comparison of (A) gecko hierarchical fibrillar adhesive system and (B-G) various biomimetic fibrillar dry adhesives. Lower right picture in (A) shows the setal array with spatular braches. (B) Vertically aligned PMMA nanotube arrays. (C) Free-standing vertical polyimide nanohairs. (D) Mushroom-shaped PVS microfibrillar structure. (E) Tilted polyurethane microfiber arrays with slanted mushroom tips. (F) Hierarchical PUA hairs with angled bulge-tip nanofibers formed on straight micropillars. (G) Hierarchically structured vertically aligned MWCNTs with entangled top layer resembling spatulae. [34, 41, 51, 63, 73, 84] ...... 28
2-9 Characteristic fiber/tube sizes in diameter obtained for various fabrication and synthesization methods. Cast molding and lithography belong to the top-down approaches while stochastic growth is classified into the bottom-up approaches. CVD: chemical vapor deposition; AAO: anodic aluminum oxide...... 30
2-10 Maximum adhesion strength vs. fiber/tube size in diameter for various material candidates, along with live gecko toe pad shear adhesion [14]. SWCNT: single-walled carbon nanotube; MWCNT: multi-walled carbon nanotube; E-MWCNT: entangled multi- walled carbon nanotube; PUA: polyurethane acrylate; PVS: polyvinyl siloxane; PDMS: polydimethylsiloxane; PMMA: poly (methyl methacrylate) PS: polystyrene...... 32
2-11 Extension from gecko geometric features in designing hybrid and stimuli-responsive smart adhesive systems. (A) Gecko-mussel inspired hybrid fibrillar adhesive for both dry and wet applications. (B) Stretchable wrinkled adhesive patch with caped micropillars. (C) Mushroom-shaped micropillar array with embedded phase-change backing substrate. (D) Nickel paddles and polymeric nanorods integrated hierarchical adhesive system, showing the “ON” and “OFF” states regulated by applying magnetic field. (E) Microfibrillar structure fabricated from shape memory thermoplastic elastomer, deformed by heating of the original vertical pillars, followed by pulling of a glass slide over the top of the surface. Cooling the system in the deformed position stabilizes the non-adhesive, tilted pattern. Recovery occurs by heating the pattern above its transition temperature. (F) Double-faced fibrillar structure obtained by obliquely depositing a thin platinum layer on one side of free-standing PUA nanopillars, where the nanopillars could be bended against the metal side by annealing or the polymer side by E-beam treatment. [87-89, 91-93] ... 37
3-1 (A) Tokay gecko with fitted “braces” (i.e., “gecko shoes”) that prevented digital hyperextension but allowed the animal to walk, adhere to the surface, and release. (B) Close up of the “gecko shoe” on the dorsal surface of gecko foot. A gecko foot showing toes in (C) flat and (D) hyperextended positions without the “shoe”...... 46
xii 3-2 Recovery indices for trials with and without DH by steps. Numbers above bars are sample sizes. Error bars represent ± 2SE...... 49
3-3 Optical micrographs of live gecko toe pads adhering to glass surface when (A) it is clean (never dirtied), (B) right after dirtied, (C) self-cleaned by 8 steps of free walking with DH on clean glass substrate, and (D) the footprint after one step. Arrows in (C) point to some of the remaining dirt particles that can be easily identified after 8 steps of self-cleaning...... 50
3-4 Schematic of the toe pad scrolling motion under DH, which is modeled as a rolling motion of a circle, with a radius r, along a horizontal plane. The trajectory (e.g., from point A to A’) follows the corresponding cycloid curve (e.g., blue dashed line) depending on the specific location of each seta. Point B’ is the critical separation point of setae with respect to the substrate/wall, which determines the length of a peeling zone, L. θ* is the critical rotation angle that generates the cycloid curve from point B to B’...... 52
3-5 Schematics of gecko toe peeling induced by (A) DH from distal to proximal direction without gecko shoe and by (B) LM from proximal to distal direction with gecko shoe. . 55
3-6 Single seta detachment during setal rolling: (A) a particle adhering to both the spatular braches of a single seta and substrate/wall, totally blocking the seta from reaching the substrate/wall (nw-sp = 0), and (B) a particle adhering to some of the spatular branches of a single seta and the substrate/wall, while partially/not blocking the seta from the substrate/wall (0 < nw-sp ≤ total number of spatulae within a seta). Note: for both configurations, the particles are in contact with the substrate/wall. nsp-p × Fsp-p = Fs-p; nw- sp × Fw-sp = Fw-s, where the subscript “sp”, “p”, “s” and “w” refer to spatula, particle, seta and wall, respectively...... 56
3-7 The ratio Fi/Fw-p as a function of particle radius Rp for a number of spatular branches within a single seta adhering to the wall (nw-sp = 0, 100 and 200). Each spatula is assumed to generate an adhesion force Fw-sp = 10 nN if contacting the wall...... 60
3-8 Inertial force, Fi, on particle adhering only to seta, versus (A) the adhering force between the wall and seta, Fw-s, and (B) radius of particle, Rp. Note: Fw-s = nw-sp × Fw-sp = nw-sp × 10 nN...... 64
4-1 SEM micrographs of (E) hierarchically structured vertically aligned MWCNTs with (C) entangled top layer resembling spatulae. (D) TEM image of a single MWCNT at the top layer. [84] ...... 73
4-2 Modeling and simulation scheme across multiple time and length scales, from fully atomistic to coarse grained molecular dynamics (MD) and to finite element analysis (FEA)...... 74
4-3 A, Close view of B, fixed peeling of 30 nm long SWCNT, armchair T (6, 6), from an a-C substrate with nanoroughness. Purple tube represents SWCNT, red beads represent
xiii saturating hydrogen atoms, pink beads represent a-C substrate, and white beads represent fixed carbon atoms at bottom...... 79
4-4 Friction and adhesion forces of 30 nm SWCNT during (A) fixed peeling and (B) free peeling. Insets in (A) are snapshots of the nanotube configurations at the points of (a), initial peeling, (b), peak force, and (c), pulling off. Inset in (B) is a snapshot of CNT free peeling, maintaining negligible frictional force...... 83
4-5 Maximum adhesion and friction forces as a function of SWCNT length under the fixed and free peeling conditions. Since there is no distinctive peaks and coupling effect during the free peeling (e.g., Figure 4-4B), average forces are taken instead of maximum values, which are roughly at the level of 0.2~0.5 nN in terms of adhesion forces...... 85
4-6 Adhesion force as a function of friction force for 30 nm long SWCNT under fixed peeling. Ѳcri is the averaged critical angle. Ѳapp in the inset is the instantaneous angle of the reaction force, F, from the horizontal plane under displacement controlled peeling. 88
4-7 (A) Close view and (B) fair view of 30 nm long SWCNT, armchair T (6, 6), fixed peeling from an atomically smooth diamond substrate. Purple beads represent carbon atoms, red beads represent saturating hydrogen atoms. (C) Friction and adhesion forces of 30 nm SWCNT under fixed peeling from an atomically smooth diamond substrate. .. 89
4-8 (A) Snapshot of nanotube peeling from a-C substrate with nanoscale roughness and asperities, showing different interfacial regions of tube-substrate interaction and local tube deformation. (B) CNT axial strain, height profiles of CNT and substrate near peeling region when the coupled adhesion and friction forces reach a peak for 30 nm SWNCT...... 92
4-9 Molecular mechanism of friction-enhanced adhesion. (A) Schematic of single asperity as mechanical interlock to generate extra normal (adhesion) force. (B) Snapshot of nanotube peeling from an a-C substrate with nanolevel roughness/asperities, showing different interfacial regions of tube-substrate interaction...... 94
4-10 The center-line deflections of SWCNT in the region predicted by MD simulation and Timoshenko beam theory...... 99
4-11 Initial configuration of 100 hexagonally-distributed vertically aligned CNTs with 600 nm laterally distributed segments represented by beads...... 105
4-12. Beads and small segments of a fully atomistic nanotube. Each bead represent a small segment of the nanotube...... 107
4-13 Snapshots of the CNT array with 360 nm laterally distributed segments under normal loading, (A) to (D), and shear loading, (E) to (H)...... 110
xiv 4-14 (A) normal and (B) shear stresses of CNT array with different length of laterally distributed segments. The numbers in the legends represent the lengths of the laterally distributed segments...... 112
4-15. Effective stress and displacement curves under shear and normal loading, derived by combination of MD simulation results and normal distribution of the laterally distributed length, where m = 135.38 nm and SD = 240.11 nm...... 116
4-16 Schematic of the CNT based dry adhesive pad contacting a target surface...... 119
4-17 Typical traction-separation responses used in FEA simulations...... 120
4-18 Friction and adhesion strength as a function of the height of vertically aligned CNTs i i f f h, where TN = 0.2 MPa, TL = 0.8 MPa, E = 0.5 MPa/µm, G = 2 MPa/µm, and N = L = 3.0 µm...... 123
4-19 Snapshots of FEA-predicted deformation of vertically aligned CNT array with h = 150 μm, (A) under shear loading, (B) under normal loading and (C) at initial state...... 125
4-20 Effect of cohesive law parameters, (A) for = 0.2 MPa, and (B) for = 0.8 MPa, on the friction and adhesion strengths for E = 0.5 MPa/µm, G = 2 MPa/µm, = = 3 µm and, h = 100 µm...... 127
4-21 Predicted and measured friction and adhesion of CNT dry adhesives with different height of vertically aligned segments. Dashed lines represent the friction strength under shear loading, predicted by FEA using obtained from the fitting under normal loading. By increasing the values of displacement jump defining the complete separation, f f f NL , from 3 μm to 10 μm, the fracture energy of the cohesive zone increases and predicted adhesion strength increases slightly...... 131
4-22 (A) Normal cohesive strength as a function of vertically aligned CNT height, required for fitting the experimental data under normal and shear loading respectively. Inset (a) shows deformed VA-CNT array under shear/lateral loading, inset (b) is the VA- i i CNT array under normal loading. (b) Adhesion enhancement factor (TsN ()/TnN ()) against the height of VA-CNTs body, predicted by fitting FEA results to experimental data...... 135
4-23 Failure angles of the hierarchical VA-CNT arrays with different heights of VA- CNTs body under shear loadings in FEA simulation. A critical peeling angle of Ѳcri* = 22.2° is extracted from the experimental data through FEA. The inset illustrates a corresponding deformation of the VA-CNT array at interfacial failure...... 136
xv CHAPTER I
INTRODUCTION
1.1 Background
The adhesion strategies found in nature are sometimes quite different from our daily experiences. Unlike chemical glues and conventional pressure sensitive tapes, gecko toe pad structure offers strong yet reversible adhesion, with great durability and self-cleanness. In fact geckos can climb and maneuver on almost any surfaces at any angle, regardless of unpredictable surface conditions, whether smooth or rough, wet or dry, with or without contaminants. The extraordinary climbing ability stems from the hierarchical toe pad structure consisting of millions of microfibrils, called setae, with billions of nano-sized branches, called spatulae. Mimicking this hierarchical fibrillar structure could lead to the development of a new class of advanced adhesives useful in various applications, including but not limited to climbing robots, reusable tapes, biomedical bandages, super-grip tires, high efficiency breaks and rapid patch repairs on military vehicles.
Over the past decades, extensive efforts have been made to create artificial gecko foot hairs via micro-/nano- fabrication and chemical synthesization methods. The materials adopted span a wide range, from soft to hard polymers, to carbon nanotubes and in certain case hybrid materials. In spite of great improvement on adhesion strength, the reversibility and durability of artificial fibrillar adhesives still substantially lag behind the
1 natural version, even on smoother and cleaner surfaces. These insufficiencies impede final commercialization of gecko inspired products.
1.2 Problem Statement
Gecko feet at least possess the following two unique functions/properties that current manmade adhesives cannot compete yet:
. Easy detachment - gecko can fast attach and detach their feet on smooth and
rough surfaces, enabling them walk and even run on vertical walls or ceilings.
. Highly re-useable and reliable adhesion - geckos use their toe pads over thousands
of cycles on natural substrates between molting periods, and still able to keep
them clean around everyday contaminants.
Although a large number of design parameters have been identified in many gecko biomimetic researches both experimentally and theoretically (e.g., fiber radius, aspect ratio, spacing, Young’s modulus, setal angles and etc.), some of the key factors that prevent the success of artificial fibrillar adhesives are still not so clear at the present stage.
1.3 Objectives
Currently, the durability or robustness issues are the main obstacles encountered in the gecko inspired biomimetic designs. The problems are directly related to the self- cleaning properties and reversible adhesive capacities of a particular artificial micro/nano
2 structures. With these regards, two aspects of the concurrent issues both in gecko adhesive structures and artificial fibrillar adhesives will be assayed in this dissertation:
. Investigate the dynamic self-cleaning mechanisms in gecko toe pad structures.
. Carry out detailed mechanical analyses of hierarchically structured carbon
nanotube arrays for dry adhesive applications.
1.4 Hypothesis
. Self-cleaning extents/rates in geckos are much higher/faster at the whole animal
scales when animal triggered toe-peeling motions of digital hyperextension are
included, compared to isolated elements from the toe pad hierarchy and
manipulated intact gecko toes.
. Very high accelerations of rotational setae are generated as they ‘snap’ away from
the substrate during digital hyperextension, such that dirt particles are effectively
dislodged from the setae by each step taken.
. Carbon nanotube side/line contacts are responsible for the significant force
anisotropy between normal and lateral directions.
. Nanoscale surface roughness plays a key role in generating the strong force
coupling of adhesion and friction at the interface.
. When large adhesive forces are achieved at the nanoscale contact interface,
significant local deformations ought to occur, leading to structural failures of
individual nano- fibrils/tubes.
3 1.5 Dissertation Outline
This dissertation is divided into 5 chapters. Chapter II provides a comprehensive literature review regarding the practice of gecko inspired biomimetic designs for achieving various manmade smart adhesives. The natural gecko adhesive structures are briefly discussed at first. Then, the story line moves on to the engineering part, from simple to complex, showcasing the historical progresses in making the gecko inspired adhesives over the past decade. The relations from structures to properties are scrutinized in a material scientist’s perspective. In the end highlights current challenges and future directions.
Chapter III elaborates a novel finding of the dynamic self-cleaning mechanism in gecko toe pad structures. Live animal trials were carefully designed to minimize the human interferences, in order to study the effect of physiological behaviors of the geckos on the much quicker adhesive force recovery commonly observed in free ranging animals.
Mathematical derivations and theoretical models were then developed to elucidate the underlying physics/mechanics of this intriguing anisotropic and hierarchical fibrillar structures, considering the dynamics when the setae are snapped off surfaces in the phase of foot detachment via digital hyperextension.
Chapter IV presents a systematic study of the hierarchically structured CNT based dry adhesives mimicking gecko toe pad structure. Multiscale modeling approaches were employed to tackle: (i) reversibility issues – adhesion, friction, adhesive force anisotropy and coupling; (ii) durability issues - local deformation and possible structural failure.
Fully atomistic molecular dynamics simulations were implemented to trace the molecular origin of the adhesive forces. Peeling tests of individual CNTs on nano-roughness
4 amorphous carbon substrates were simulated under both constrained and unconstrained loading conditions. Coarse grained molecular dynamics simulations were employed to study the vertically aligned CNT deformations as well as the tube-tube interactions between the vertical and lateral segments. Collective interfacial adhesive behaviors were simulated for a fraction of the two-level CNT arrays under pure normal and shear loadings against an imaginable flat surface. Finite element models featured with a cohesive zone were developed at the device level. Parameter study was carried out and then compared with the results from the coarse-grained simulations. Potential determinant parameters of the cohesive laws were indentified and extracted via a data fitting process with the results obtained in the experimental force measurements.
Chapter V summarizes the major findings in the present dissertation and the possible impacts in the gecko inspired biomimetic field. Limitations are pointed out, upon which continuations of the current work are envisioned.
5 CHAPTER II
LITERATURE REVIEW
2.1 Hierarchical Fibrillar Structure of Gecko Toe Pads
The intricate structures underneath gecko toes have been thoroughly resolved via scanning electron microscopy (SEM) [1, 2]. As illustrated in Figure 2-1, gecko toe pad is hierarchically structured from macro- down to nano- levels [3, 4]. The tiny hair seta is usually considered as the basic adhesive unit (Figure 2-1C, D). It is proximally curved, averagely ~100 µm in length and ~5 µm in diameter for Tokays (Figure 2-1A). Each single seta further branches out at the tip and splits into hundreds of spatulae (Figure 2-
1E), which function as the ultimate contacting elements. These terminals are tapered spatular pads, ~200 nm wide and 5~10 nm thick [5]. Setal arrays distribute on the outer portion of the overlapping stripes known as lamellae that are distally narrowed, 0.3~0.6 mm across at the mesoscale (Figure 2-1B). Usually 15~20 lamellae occupy the entire area of a single toe and can be easily spotted by our naked eyes.
6
Figure 2-1 Structural hierarchy of Tokay gecko adhesive system from naked-eye pictures
(A, B) to SEM micrographs (C, D, E). (A) Gecko hanging upside down; (B) underside of a gecko foot, where the toe pads are striped into ridges, laminae; (C) side and (D) top views of setal array at different magnifications; (E) the finest terminal branches of seta, spatulae. ST: seta; SP: spatula; BR: branch. [3, 4]
When being properly applied, a single seta renders maximum adhesive forces of
~200 µN in shear and ~20 µN in normal directions against a smooth clean glass substrate
[6]. Normal pull-off force was also obtained for individual spatulae as ~10 nN by utilizing atomic force microscopy (AFM) [7]. If all the setae were to engage at a time, roughly half million on one foot, a single foot of geckos could generate ~100 N of adhesive force, which could support ~10 times of their averaged body weight. However,
7 caution should be taken, since the seemly huge “overbuilt” were extracted from rather idealistic substratum (e.g. glass or silicon wafers) and static measurements, which could be drastically decreased when the geckos are set free in their natural environments and in motion [8-13]. Van der Waals interaction has been proven to be the primary molecular origin for this surface phenomenon [14], while humidity does have a strong effect of altering the measured forces [15-18]. More recently, based on experimental evidences and theoretical analyses, the strong correlation between relative humidity and measured adhesive forces has been attributed to the change of material property (Young’s modulus) as an alternative explanation for the possible capillary effect [19-21].
Tokay gecko is by far the most scrutinized species for exploring fibrillar dry adhesives mainly because of their fairly large sizes and more sophisticated hierarchical system. Fibrillar structures have evolved in the leg attachment pads of many insects as well, including beetles, flies and spiders [22]. Even though the adhesion mechanism involved are not necessarily the same, some are dry, some involve secretions, a general trend is as the body size increases the radius of the terminals decreases among different wall climbing species [23]. This morphological change, from large to small (micro- to nano- level), simple to complex (single level to hierarchy), has been theoretically explained by applying contact mechanics principles.
Two pertinent concepts, namely “contact splitting” [23-25] and “shape insensitivity” [26], have been theoretically derived accounting for the increased adhesion from a divided no-continuum surface and its relatively weak intermolecular origin.
However, the size and weight challenges overcome by geckos utilizing highly branched tiny hairs is merely one facet. Other traits, such as angled setal stalks, fiber aspect ratio,
8 tip shapes, patterns, hierarchy, the materials as well as the attaching and releasing motions that the animal triggers, are equally crucial for the systems to be functional in their ecological settings. Analytical and numerical analyses are theoretically implemented by many groups for conceptualizing the gecko adhesive features. Figure 2-
2 summarizes the relevant parameters in a material scientist perspective. Detailed information can be easily found elsewhere from many review articles [27-31] in the open literatures and will not be repeated here.
Figure 2-2 Connections between the structures, characteristic features/parameters, functions and performances identified in the gecko dry adhesive systems.
2.2 Polymer Based Fibrillar Dry Adhesives
For the polymeric materials, cast-molding into micro-/nano- porous featured master templates and the direct lithographic methods are the two widely used techniques for obtaining negative fibrillar structures at smaller scales: micro or down to nanoscale.
Nano-fiber arrays were firstly demonstrated and then followed by micro-sized pillars.
Later on, integrations of micro- and nano- sized fibrils/structures were carried out to achieve hierarchy. In the latest versions, anisotropic geometries of the fiber stems along with different tip shapes and tip angles were incorporated, aiming to achieve not only
9 greater conformity to the opposing surfaces but also directional dependent responses for achieving switchability. Following discussion will firstly base on the different master templates that have been utilized in the cast-molding processes, then focus on some of the prominent examples in direct lithography, and finally shift gear to categorize the additional gecko features that have been introduced to the polymeric fibrillar systems by implementing other decorating methods.
2.2.1 Cast-molding
(i) AFM indented wax
The first attempt to make gecko inspired fibrillar dry adhesives was demonstrated via an AFM aided nano-molding [32]. AFM probe was adopted as a nano indenter to make patterned dimples on a flat wax surface. The indented surface was then used as a master template to mold liquid hydrophobic polymers such as silicone rubbers (soft;
Young’s modulus is ~0.57 MPa) and polyester resin (hard; Young’s modulus is ~0.85
GPa). Arrays of polymer based nano-hairs were obtained by consecutive peeling of the cured polymers off the template. AFM pull-off forces of ~181 nN and ~294 nN were obtained for silicon rubber with tip radius ranging from 230~440 nm and polyester resin with tip radius of ~350 nm, respectively, which are roughly 10 times higher than individual gecko spatulae.
(ii) AAO templates
AAO templates prepared by the well-known two-step anodization process possess hexagonally distributed straight nano-pores. The special structural features and the
10 thermal and chemical stability make it suitable to produce nanofibrillar materials mimicking gecko’s foot hair. The diameter and depth of the highly ordered holes could be adjusted by changing the anodization parameters for designing purposes. Cho et al.
[33] utilized the AAO templates to mold PDMS. Carefully peeled off, the fibrillar structures exhibit not only superhydrophobicity but also high adhesion to water droplet and large contact angle hysteresis. Chen et al. [34] created free standing high aspect ratio
PMMA nanopillars via capillary driven AAO template filling, as well as PMMA nanotubes (Figure 2-3A) via pressure driven AAO template wetting. Kim et al. [35] invented a UV nano embossing machine that can massively print high aspect ratio nanopillar arrays of UV curable polymer resin from AAO template. The time efficiency had been greatly improved, even though clumping issue still existed (Figure 2-3B).
Kunstandi et al. [36] fabricated high aspect ratio free standing PMMA fibrils as a two-level hierarchy (Figure 2-3C). An AAO template was selectively etched out by conventional lithography to define micro-channels and another thin AAO membrane with nanopores was placed against it forming a hierarchical porous template. The parameters of micro- and nano- pores could be adjusted separately before the integration. Clumping issue is significantly alleviated by introducing two-level hierarchy, such that stability is greatly improved without sacrificing too much compliancy for initiating conformal contacts.
(iii) Photolithography defined silicon templates
Photolithography is a well-developed technique for creating extremely small patterns, from micro down to nano levels, which is the base of microelectronics
11 fabrication and affects the development of the entire information technology. Sometimes it serves as a prerequisite step in other micro-/nano- fabrication processes, for instance softlithography and rigiflexlithography. Standard procedures include: surface preparation of silicon wafer, spin coating of photoresist, pre-backing, alignment and exposure, development, post-backing, stripping, and processing.
It has been demonstrated as a feasible way of making wafer based templates for cast-molding polymeric micro-/nano- fibrils in dry adhesive fabrication. Highly ordered straight micro-/nano- rods and pillars were obtained by different groups with various diameters but mostly low aspect ratios [37-40]. Kim et al. [39] modified the etching process and fabricated polyurethane microfibers with wider fiber bases and flat cap on each fiber tip. Davies et al. [40] prepared mushroom shaped PDMS micropillars.
Anisotropic plasma etching was adopted as usual, but the etching areas were defined with the aid of CAD on both sides of the wafer: smaller discs and bigger discs are lined up in the center, each of which corresponds to the specific stalks and heads. Enhanced adhesion was reported for both of the decorated structures.
2.2.2 Electron-beam lithography
Election beam lithography was implemented by Geim et al. [41] as a patterning method to create sub-micrometer hairs that mimicking gecko spatulae (Figure 2-3D).
Polyimide film was prepared on silicon wafer. Electron beam was use to pattern aluminum films into disk arrays. Then the two films were brought together, followed by oxygen plasma etching. The fibrillar structure was copied onto the polymer film, because of a much slower etching rate of the metal. Biased D.C. voltage was also applied to
12 increase the aspect ratios of the finishing fibrils. Transferring a 1 cm2 fibrillar patch on to a soft bonding substrate results a 1,000 times adhesion improvement, 3 N in normal pull- off. Durability was one of the main issues. After couple times of repeated preloading and pulling the polyimide fiber arrays were found to be bunching to the neighbors leading to quick adhesion degradation.
2.2.3 Soft and rigiflex lithography
Softlithography came out as an alternative technique to replace photolithography in order to significantly reduce cost. Yet it usually depends on photolithography to create a so called master at the very beginning [42]. The replicas of the photolithography defined rigid silicon masters are relatively soft and flexible polymeric materials, typically
PDMS, that could be used either as the stamps for replica stamping or as the molds for the consecutive replica molding. In fibrillar dry adhesives fabrication, instead of being replicated from a rigid silicon master, the soft mold can be directive created from the photoresist itself by photolithography. One common choice is the photoresist SU-8 soft mold to massively duplicate negative PDMS fibril arrays [43-45] (Figure 2-3E). Even though the cost-effectiveness is extremely attractive for massive productions, one significant drawback of soft lithography is the reduced resolution because of the loss of mechanical integrity when the size going down to the submicron range [46, 47].
A modified softlithography, known as capillarity-directed rigiflexlithography, was proposed by Jeong et al. [48] managing to refine the patterning resolution (< 100 nm) and fiber geometry (e.g., aspect ratios). PUA was chosen as the replica mold over SU-8 or
PDMS, since it offers not only better mechanical strength, flexibility and stability, but
13 also small shrinkage and UV light transmittance [46]. PMMA and PS were used as the targeting polymers. They were firstly spin coated on silicon wafers. Then the as prepared PUA replica mold was placed on top of the polymeric layer to form a sandwich structure, and after elevated temperature and vacuum condition were held for > 1 hour, the PUA mold was removed by retracting in a certain direction at a constant speed. Due to capillary action and adhesion force, the molded fibers were further stretched, resulting in an aspect ratio of > 20 and bulged tips. Under a non-normal retraction the fibrils curved to one side, resembling the angled setal stalks of geckos. Except the smaller sizes and un-branched tips, this structure looks very close to the geometric appearance of gecko setae (Figure 2-3F).
Figure 2-3 SEM micrographs of (A) nano-cast-molded PMMA nanotube arrays, (B) UV nano-embossed nanopillar arrays and (C) hierarchical PMMA fibrillar structure featuring
~10 μm wide and ~70 μm long microfibrils, each of which branches in to ~60 nm wide and ~0.5 μm long nanofibrils utilizing AAO templates; (D) electron beam lithography
14 defined polyimide nanohairs; (E) PDMS micropillar arrays, with a radius of ~2.5 μm, a height of ~20 μm and the minimum inter-pillar distance of ~5 μm, by softlithography; (F)
PMMA nanohairs fabricated by adding a sequential drawing in rigiflexlithography, resulting a fiber necking effect down to ~80 nm in diameter. [34-36, 41, 43, 48]
2.2.4 Tip shape variations
The moderate increase of adhesion strength in the early versions of polymeric fibrillar adhesives has been claimed to be the cause of tip shape oversimplification.
Theoretical analysis also points out the importance of resembling the tip geometries in the animal system. Campo et al. [49] added post-processing, such as inking, printing and partial hardening followed by retarded molding after softlithography. PDMS micropillar arrays with various tip shapes were formed, including a control sample with flat punch tips (Figure 2-4A-F). Mesoscale pull-off tests show that pillar array with spatular tips have the highest adhesion than all other geometries. Follow up work [50] takes into account the effect of pillar radius, aspect ratio, Young’s modulus and etc.. Results show a superior adhesion performance with mushroom shaped tips. Moreover finer pillars render higher pull-off forces for all tip geometries indicating possibly the contact splitting efficiency.
The mushroom shaped fibrillar geometry was proven to have a better performance by other groups as well, among which Gorb’s group [51-54] implemented many measuring techniques to characterize adhesion, friction and peeling behaviors of this kind.
Their samples were made of PVS (E = ~3 MPa) and micrometer in size, named as beetle inspired fibrillar adhesive (Figure 2-4G). These capped micropillars show high adhesion
15 strength, good contamination tolerance and easy-to-clean property for repeatable use.
However, the frictional behavior found in mushroom like fibrillar structures with symmetric caps exhibits opposite response comparing to gecko setal arrays with asymmetric setal stalks and spatular pads [52]. Shearing displacement reduces normal pull-off resistance and makes it vanish beyond a critical point as opposed to gecko frictional adhesion, where high adhesion strength is shear induced and even keeps increasing after lateral slippage [55, 56]. Additionally, underwater pull-off tests were performed suggesting a superposition of van der Waals dispersion force and suction effect [53]. Cheung et al. [57] fabricated polyurethane microfibers with mushroom tips
(Figure 2-4H) through a dip-transfer process. Significant adhesion enhancement was captured for the structured surface over flat control on both hemispherical and flat F-15 polyurethane soft substrates.
Glassmaker et al. [58] built a continuous terminal film on top of fibrillar arrays
(Figure 2-4I). Instead of dipping, PDMS fiber array obtained by photolithography aided molding was brought in contact with a liquid PDMS thin film and cured together. This seemingly “odd” structure however offers not only a good structural stability but also a halting effect to impede interfacial crack propagation. Their results show a 2~9 folds increase of interfacial energy during de-bonding processes but at the same time a significant increase of compliance over a flat control. Cyclic indentation and pull-off experiments were also performed and a distinctive adhesion hysteresis was captured [59].
Besides, static friction of the film terminated structure depends on the fiber spacing which could be adjusted without altering its sliding frictional resistance [60].
16
Figure 2-4 SEM micrographs of PDMS fibrillar structures with (A) flat, (B) spherical, (C) symmetric spatula, (D) asymmetric spatula, (E) tube and (F) concave tips; (G) mushroom-shaped PVS and (H) polyurethane fibrillar microstructures; (I) an array of
PDMS micro-pillars with a continuous film on top. [49, 51, 57, 58]
2.2.5 Anisotropic fibrillar structures
Although adhesion enhancement was achieved by dividing bulk contacting surfaces into micro-/nano- fibrils, in certain cases with characteristic tip shapes, the reversibility and durability of gecko’s attaching system stimulates researchers and engineers by all means to include anisotropic geometry in the artificial system, which
17 could possibly render directional dependency and additional conformability for obtaining switchable adhesion.
Santos et al. [61] fabricated angled fibrillar adhesives with 20° tilted stalks and 45° angled wedge endings (Figure 2-5A). The geometric merits yield significant improvement over an isotropic control when applied in wall climbing robots. Aksak et al.
[62] applied two layers of SU-8 on a glass wafer, which were cured at separate stages.
One was to form the backing layer aiming to alleviate the delamination at the fiber base, and the other was to form the polymeric angled fibrils. Simply by tilting the coated wafer during exposure, angled fibrils were obtained with flat tips that are parallel to the substrate. Murphy et al. [63] fabricated polyurethane microfibrillar arrays with both angled stalks and mushroom like tip endings with various orientations (0~90°) by dipping angled fibril arrays into liquid polymer. The geometries are very similar to gecko setae if we over look the size difference and some of the details (i.e., setal branches) (Figure 2-5B,
C).
Lee et al. [64] made angled microfibers by roller pressing a vertically aligned polypropylene fibrillar patch against a clean glass at elevated temperature. Shearing along and against the fiber orientation with a glass slide produced pure frictions of 4.5
N/cm2 and 0.1 N/cm2, respectively. Kim et al. [65, 66] invented softlithography aided
“post e-beam exposed” replica molding, to create angled PUA and Teflon nanohairs with distinct stiffness. Frictional strengths were reported as 11 N/cm2 and 2.2 N/cm2 in opposing directions, and maintained over 100 times of cyclic loading before significant degradation. Moon et al. [67] fabricated angled PDMS micropillars by integrating softlithography with ion beam irradiation (Figure 2-5D, E). Rather than post treatment of
18 the coated fibers by electron beams, Ar+ ion beam irradiation could directly induce the pillars bend towards the laser direction and form anisotropic geometries. Ion beam irradiation caused a modification of the stiffness of the pillars to increase by a factor of
70~100 and wrinkled the surface on the exposure side. Three times of force difference was obtained in directional shearing. Parness et al. [68] fabricated wedge shaped PDMS microfibrillar arrays by softlithography along with an angled exposure technique. Force anisotropy between normal and shear directions was reported as 2.1 N and 13 N, respectively, for an 8.2 cm2 patch. 67% of initial adhesion and 76% of initial friction forces were retained after 30,000 cycles of attachment and detachment.
Figure 2-5 SEM micrographs of (A) directional polyurethane microstalks, 1 mm long,
380µm in diameter, with 20° tilted stalks and 45° angled wedge endings; (B, C) arrays of
35-µm diameter tilted polyurethane microfibers with 23° angled mushroom tips; (D, E)
27° tilted PDMS micro pillars having 9.3 µm diameter, 30 µm length and 10 µm spacing.
[61, 63, 67]
19 2.2.6 Hierarchical fibrillar structures
According to gecko toe pad structure, two or more levels of hierarchy is necessary to prevent self-matting while maintaining maximal contact fraction by decreasing the terminal size. A possible solution for building hierarchy was demonstrated by utilizing photolithography modified AAO templates for polymeric cast molding as mentioned above [36]. Whereas the first batch fabricated multilevel conformal system mimicking gecko adhesive was proposed by Northen et al. [69, 70]. Their idea is to synthesize (i.e., stochastic growth method) dielectric polymer nanorods on top of micro-sized platforms which are supported by single high aspect ratio pillars (Figure 2-6A, B and C).
Significant increase of adhesion was evidenced in this hierarchical design. Other examples of incorporating hierarchy involve UV aided soft molding, featured with multiple transferring steps and procedures [71, 72].
Latest versions of hierarchical fibrillar dry adhesives are the combinations of different fiber diameters, characteristic tip shapes along with fiber and tip orientations.
Jeong et al. [73] implemented angled etching to make slanted nano-holes out of poly Si substrate with a SiO2 stopping layer. PUA nanorods with different angles have been made along with asymmetric tip shapes. These slanted nanorods were further transferred onto straight micro-sized pillars (Figure 2-6D, E and F). It offers not only better performance on rough surfaces, but also great force anisotropy between a strong shear attachment along fiber curvature (~26 N/cm2) and an easy detachment against fiber curvature (~2.2 N/cm2). Hierarchical structures with angled stalks but symmetric disc like tips were fabricated by Sameoto et al. [74]. Murphy et al. [75]created 2- and 3- level structures with inclined or vertical polyurethane (E = ~3 MPa) pillars at macro- and
20 meso- scales, and vertical pillars at the micro scale with self-similar mushroom caps at each level (Figure 2-6G, H, I and J). The ultimate tip structure was created by a dip- transfer process. Increased adhesion was obtained by structuring the surfaces into multiple levels: two levels > single level > unstructured, especially in situations of high preloading. Lee et al. [76] fabricated laminar structures with high aspect ratio nanofiber arrays on top . High density polyethylene (E = 0.9 GPa) was chosen as the patterning material. Laser patterning, heated rolling, laminating and selective etching processes were implemented to create the two level integration. This hierarchical design exhibits easy detachment when shear loading is removed, returning the structure to a non- adhesive default state just like that of gecko toe pad.
21
Figure 2-6 SEM micrographs of (A, B and C) multilevel integrated compliant structures of photoresist nanorods on top of one pillar supported compliant MEMs platform; (D, E and F) hierarchical PUA polymeric hairs with well-defined high aspect ratio and angled nanofibers with bulged flat tips formed on 5-µm-diameter, 25-µm-height and 5-µm- spacing straight micropillars; (G, H, I and J) three-level hierarchical polyurethane fibers:
(G) 400-μm-diameter curved base fibers, (H) base fiber tip with midlevel 50-μm- diameter fibers, (I) midlevel fibers in detail, (J) third level fibers at the tip of the midlevel fibers, 3 μm in diameter and 20 μm in height and having 5-μm-diameter flat mushroom tips. [70, 73, 75]
22 2.3 Carbon Nanotube Based Fibrillar Dry Adhesives
Carbon nanotube arrays/forests are proposed as an opposing candidate for mimicking gecko toe pad structures to achieve high adhesion, mainly because of the fine hairy resemblance and superior mechanical properties which enables even higher fiber/tubular aspect ratio and larger packing density. Synthesization of carbon nanotube arrays was relatively unitary and this bottom up approach currently does not allow much geometrical controls than that of the polymeric counterpart. Vertically aligned carbon nanotubes (VA-CNTs) arrays are usually grown on quartz or silicon substrates through chemical vapor deposition (CVD) process under controlled environmental conditions allowing different aspect ratio, numbers of CNT layers as well as packing density.
2.3.1 Single-level CNT arrays/forests
Yurdumakan et al. [77] created high aspect ratio MWCNT arrays, and transferred onto PMMA substrates. Adhesion forces that are ~200 times higher than that of gecko hairs were calculated based on their scanning probe microscopy (SPM) pull-off tests.
However caution has to be made since the seemingly huge adhesion force may just come from the side contact of nanotubes with the cantilever and probe tip. Zhao et al. [78] performed normal pressing and sequent pulling in normal or shear to characterize the macroscopic adhesive properties of vertically aligned MWCNTs. 5~10 µm thick CNT arrays offer normal adhesion strength of 11.7 N/cm2 for a 4 mm2 patch and frictional strength of 7.8 N/cm2 for a 8 mm2 patch under ~2 kg weight of preloading.
Maeno et al. [79] transferred CNT forests on to polypropylene substrates forming
CNT based dry adhesive tapes. The effect of nanotube layer distribution on frictional
23 strength was studied by applying different preloading via a cylindrical roller. CNT forest with narrow distribution of triple-walled carbon nanotubes (i.e., TWCNTs) has higher macroscopic frictional response than that of double- and quadruple- walled nanotubes
(i.e., DWCNTs and QWCNTs), while CNT forest with a broad layer distribution offers the highest shearing strength, 44.5 N/cm2, under the medium preloading, 47 N/cm2. Qu et al. [80] synthesized high quality vertically aligned SWCNTs via plasma enhanced
CVD along with a fast heating process. The results show a macroscopic normal adhesion strength of 29 N/cm2 and shearing strength of 16 N/cm2 for a 4 × 4 mm2 patch under ~2 kg weight of preloading. The substantial increase of the as-grown adhesive strength is attributed to the finer contacting element of the SWCNT, higher packing density and the presence of π-π conjugated carbon structure over the more commonly obtained MWCNT arrays [77, 78, 81, 82].
2.3.2 Multi-level patterned CNT arrays/forests
Ge et al. [83] created vertically aligned MWCNT patterns on flexible polymer tapes achieving 36 N of shearing force for a 1 cm2 patch under a preloading of 25~50
N/cm2. Photolithography was implemented to define different square patterns, 50~500
µm in width, of the catalyst layers on silicon substrate, and then ~8 nm diameter vertically aligned MWCNTs was grown to 200~500 µm long under CVD. Finally the
MWCNT patterns were transferred onto scotch tapes (Figure 2-7A, B and C). Unlike conventional viscoelastic adhesive tapes, the “gecko tape” offers good time independency such that strong and stable shear force could be maintained for 8~12 hours.
24 Later on hierarchically structured vertically aligned MWCNT arrays were synthesized by Qu et al. [84] through a low-pressure CVD process. Analogous to gecko setal arrays, this two-level MWCNT array features a straight aligning body mimicking setal stalks and a curly entangled end segment at the top mimicking spatulae (Figure 2-
7D, E, F and G). Under shear loading, the entangled segment enables readily sidewall contact formation with the target surface rendering high macroscopic force, ~100 N/cm2.
Whereas normal pulling imposes peeling of each entangled tip at the interface leading to a drastic reduction of adhesion force down to ~10 N/cm2. Time dependent adhesion measurements demonstrate 24 hours durability under a shear loading of 40 N/cm2 and a normal pull away force of 12 N/cm2. This system offers strong shear bonding on and easy normal lifting off capabilities that are promising for mimicking live gecko walking.
The friction force was determined to be entangled length dependent, while the longer vertically aligned segment might also make contributions by inducing more CNT sidewall contacts to the substrates when dragged laterally [85, 86].
25
Figure 2-7 SEM images of (A) natural gecko setae terminating into thousands of smaller spatulae, (B) side view and (D) close up of the 100 µm wide square patterned VA-CNT arrays. SEM micrographs of the structure similarity between the cross section views of
(D) gecko’s aligned elastic hairs and (E) hierarchically structured vertically aligned
MWCNTs with (C) entangled top layer resembling spatulae. (D) TEM image of a single
MWCNT at the top layer. [83, 84]
2.4 Rational Design Based on Geometric Replications of Gecko Adhesive System
The biomimetic design of fibrillar dry adhesives is basically driven by the understanding of the corresponding biological system. Early attempts show a convergent designing trend in mimicking the geometric features of gecko toe pad structure (Figure 2-
8A). Basically, there are four distinctive stages that can be identified: i) making free
26 standing vertically aligned micro-/nano- fibrillar arrays (Figure 2-8B, C); ii) creating various tip shapes (Figure 2-8D); iii) including anisotropic geometry: angled fibril stalks, slanted tips or both (Figure 2-8E); and iv) building hierarchy (Figure 2-8F, G). Two main types of materials, polymers and carbon nanotubes (CNTs), have been adopted as competing candidates for creating superior mimics [34, 41, 51, 63, 73, 84]. Fabrication and synthesization techniques can be classified into, i) top-down approaches: template assisted micro-/nano- cast molding and different lithographic methods for defining polymeric fibrils [34, 41, 51, 63, 73]; and ii) bottom-up approaches: stochastic growth for both CNTs [84] and polymers [69, 70, 87].
27
Figure 2-8 Comparison of (A) gecko hierarchical fibrillar adhesive system and (B-G) various biomimetic fibrillar dry adhesives. Lower right picture in (A) shows the setal array with spatular braches. (B) Vertically aligned PMMA nanotube arrays. (C) Free- standing vertical polyimide nanohairs. (D) Mushroom-shaped PVS microfibrillar structure. (E) Tilted polyurethane microfiber arrays with slanted mushroom tips. (F)
Hierarchical PUA hairs with angled bulge-tip nanofibers formed on straight micropillars.
(G) Hierarchically structured vertically aligned MWCNTs with entangled top layer resembling spatulae. [34, 41, 51, 63, 73, 84]
28 Figure 2-9 summarizes the methodologies for creating fibrillar adhesive structures with respect to their characteristic terminal sizes. In cast molding, the smallest features are pre-determined by the specific molding templates chosen. Photolithography patterned silicon wafers are most commonly used, where the negative porous of the templates could be either fairly large (microscale) or relatively small (nanoscale) [39, 88].
AAO templates and polycarbonate filters are used to mold nanofibrils, usually hundreds of nanometers in diameter comparable to gecko spatulae [34-36]. Other nano-featured templates include atomic force microscopy (AFM) dimpled wax and electron beam defined PMMA [32, 89]. On the other hand, for direct lithographic method, soft lithography is frequently adopted. It offers great cost-effectiveness over conventional photolithography, which is crucial for massive production [42]. The lithographic resolution, however, are sacrificed because of the loss of mechanical integrities of the polymeric masters (e.g., SU-8 or PDMS) when getting down to the nano regime [47].
Finer fibrils could be obtained by either resorting more expensive and time consuming lithographic methods such as photolithography and electron beam lithography [41], or improving the performance of imprinting masters. Rigiflex lithography is a modified version of soft lithography, where a stronger yet flexible polymer, PUA, is adopted as the master for consecutive processing [48]. An additional drawling process at elevated temperatures could further reduce the fibril diameter down to ~80 nm. In contrast, stochastic growth method intrinsically generates nano-sized fibril structures even ~100 times smaller than that of gecko spatulae. Single-wall and multi-wall CNT arrays/forests have been synthesized through conventional, plasma enhanced and low pressure CVD processes [80, 83, 84]. The ultimate contacting elements possess a characteristic size of
29 2~30 nm in diameter. Meanwhile, dielectric polymers have been plasma-induced grown on single pillar supported silicon dioxide platforms and nickel based micro-cantilevers
[69, 70, 87]. The active polymeric fibrils have diameters ranging from 50 to 250 nm.
Figure 2-9 Characteristic fiber/tube sizes in diameter obtained for various fabrication and synthesization methods. Cast molding and lithography belong to the top-down approaches while stochastic growth is classified into the bottom-up approaches. CVD: chemical vapor deposition; AAO: anodic aluminum oxide.
Figure 2-10 shows the maximum adhesion strength vs. fiber/tube diameter evaluated at the nano- and macro- scales for both polymer and CNT based adhesives.
30 AFM pull-off tests indicate the adhesion of individual fibrils/tubes while macroscale normal pulling and shearing measurements show the adhesive performance of an entire patch. In general the smaller the fiber size, the higher the adhesion strength, especially for AFM tests where individual fibrils is in contact. For macroscopic measurements the collective effect of fibrillar arrays allows other factors such as packing density, fiber compliancy, backing materials and preloading come into play. Consequently, a relatively scattered force distribution is observed, whereas the general trend is still consistent with the nanoscale measurements. In order to minimize the effect of preloading on adhesive performances at large scales, we use the highest achievable strengths for evaluation.
Apparently, CNTs render the highest adhesion within both nano- and macro-scale measurements.
31
Figure 2-10 Maximum adhesion strength vs. fiber/tube size in diameter for various material candidates, along with live gecko toe pad shear adhesion [14]. SWCNT: single- walled carbon nanotube; MWCNT: multi-walled carbon nanotube; E-MWCNT: entangled multi-walled carbon nanotube; PUA: polyurethane acrylate; PVS: polyvinyl siloxane; PDMS: polydimethylsiloxane; PMMA: poly (methyl methacrylate) PS: polystyrene.
In general, the top-down approaches for defining polymeric mimics are relatively easy, flexible and cost effective. Whereas surface phenomena become dominant when size shrinks down to the nanolevel, clumping of neighboring fibers and weak fiber strength are some of the inherent issues. Accommodations have been made by switching
32 materials from soft to hard polymers and resorting hierarchical design. Vertically aligned
CNT arrays/forests are created in the bottom-up manner offering extraordinary structural and mechanical properties. The ultimate features are typically ~10 times smaller than gecko spatulae. With extremely high aspect ratio and great packing density, CNT based adhesive patches outperform the polymer counterpart as well as natural gecko hairs in terms of adhesion strength. However, buckling and breakage at the base, limited geometric control and scalability are some of the drawbacks that prevent CNT based dry adhesives from more stabilized reversible adhesion. Therefore, for both polymer and
CNT based adhesives one of the big challenges is to significantly increase the durability of the samples under repeated attach and detach cycles.
2.5 Rational Design beyond Geometric Replications of Gecko Adhesive System
The essence of learning design strategies from nature (i.e., biomimicry) is mostly enlightened in the way of how certain simple but intriguing structure generates functionality in a compatible and sustainable manner to cope with the constraining resources and environment. However, it is also intuitive to combine those strategies with other physical, chemical and biological principles to tailor the functions for various ends.
As more and more gecko features are successfully included in the artificial fibrillar dry adhesives, this fast growing field also undergoes a branch-out process due to the multidisciplinary nature of the subject. This has been witnessed in the rational designs for more application oriented purposes, as shown in Figure 2-11.
An outstanding example is the rationale of integrating gecko setal structures with adhesive proteins found in mussels (Figure 2-11A) [89]. After a thin layer of mussel
33 mimicking adhesive coating, p (DMA-co-MEA), was applied onto PDMS nanofiber arrays, AFM pull-off forces were increased by ~3 folds in air and ~15 folds underwater.
Similar idea was demonstrated in polyurethane microfiber arrays, where a continuous p
(DMA-co-MEA) terminal film was jointed on top [90]. When fully submerged in water, the film terminated microfiber arrays showed superior adhesive ability that is ~23 folds greater at best than the mushroom shaped controls. Another progress made in this hybridization approach is a biodegradable adhesive for wet-tissue-like environments commonly encountered in many biomedical procedures [38]. A tunable biodegradable elastomer, known as poly (glycerol sebacate acrylate), was chosen as the structural material for creating nanofibrillar features, while the ingredient of functional coatings was switched to oxidized dextran. Notably, the performance of this hybrid adhesive was characterized not only in vitro but also in vivo with supreme adhesion strength.
In addition, multi-physical stimuli-regulated smart adhesives came into the picture for achieving reversible/responsive adhesion in a strictly controlled manner (e.g., mechanical, magnetic, thermal and electrical; Figure 2-11B-F). Several examples are discussed as follows.
Firstly, a stretchable wrinkled adhesive patch with PDMS micropillars was fabricated, which shows great adhesion tunability under different straining conditions
(Figure 2-11B) [91]. 100 cycles of attachment and detachment were reported without detectable degradation. The mechanical properties of the backing substrate could also be actively controlled by inserting phase change materials (Figure 2-11C) [92]. To maximize adhesion, a soft backing was used to increase the conformability to irregular surfaces by initiating large real contact area. The following phase transformation to a
34 rigid state locked in the deformed backing profile for equal load sharing. Upon release, the elastic properties (e.g. stiffness) could be switched backwards. One of the advantages of this actively switching mechanism is free from building fibrillar hierarchy because even unstructured PDMS surfaces with phase change backings were shown to have enhanced adhesion. Along this line, we speculate that integrating CNT arrays with stimuli-regulated backings may improve the durability by eliminating the buckling issues due to large preloading.
Secondly, a field-controlled mechanism is demonstrated in a nickel-polymer integrated system [87]. This hierarchical structure consists of vertically aligned photoresist nanorods, analogous to spatulae, coated on top of micro-sized nickel cantilever paddles, analogous to setae. The key structure, nickel paddles, offers not only additional conformability to the polymeric nanorods but also a magnetically controlled switching mechanism. Specifically, this adhesive system could be actuated through externally applied magnetic field. The rotational motions of the cantilever paddles under magnetic signals could either expose or conceal the active polymeric nanorods coated surfaces (Figure 2-11D). This resulted in a 40-times drop of normal pull-off force from
“ON” to “OFF” states.
Last but not least, thermally stimuli-responsive adhesive has been made by taking advantage of shape memory polymers. Patterned vertical micropillar arrays, based on shape memory thermoplastic elastomer, are able to bend into temporary angles (i.e., non- adhesive state) by hot pressing at the temperature above transition but below permanent deformation (Figure 2-11E) [93]. Reheating to the same temperature range could reverse the temporary angled pillars to their original and permanent vertical position (i.e.,
35 adhesive state). More recently a double-faced fibrillar structure has been fabricated by obliquely depositing a thin layer of platinum on one side of free-standing polymeric nanopillars (Figure 2-11F) [88]. This unique structure renders directional dependent frictional responses even when vertical. Besides, the distinctive physical properties of metal and polymer make it possible to bend the pillars towards the metal side upon thermal annealing. The thermally bended structure could also be switched back to its original upright position upon electron beam irradiation and even bend toward the polymer side within just a few seconds. Hence, for multiple and quick reactions, this type of controlling mechanism is more desirable than that in the pure shape memory thermoplastic fibrils.
36
Figure 2-11 Extension from gecko geometric features in designing hybrid and stimuli- responsive smart adhesive systems. (A) Gecko-mussel inspired hybrid fibrillar adhesive for both dry and wet applications. (B) Stretchable wrinkled adhesive patch with caped micropillars. (C) Mushroom-shaped micropillar array with embedded phase-change backing substrate. (D) Nickel paddles and polymeric nanorods integrated hierarchical adhesive system, showing the “ON” and “OFF” states regulated by applying magnetic field. (E) Microfibrillar structure fabricated from shape memory thermoplastic elastomer, deformed by heating of the original vertical pillars, followed by pulling of a glass slide over the top of the surface. Cooling the system in the deformed position stabilizes the non-adhesive, tilted pattern. Recovery occurs by heating the pattern above its transition temperature. (F) Double-faced fibrillar structure obtained by obliquely depositing a thin
37 platinum layer on one side of free-standing PUA nanopillars, where the nanopillars could be bended against the metal side by annealing or the polymer side by E-beam treatment.
[87-89, 91-93]
2.6 Self-Cleaning in Artificial Fibrillar Adhesives.
Self-cleaning property is fundamental to the success of not only gecko’s everyday life but also the artificial alternatives over traditional pressure sensitive adhesives. It was suggested that, having stronger affinity to the walking substrate than the attaching spatulae, dirt particles could be deposited onto the surface gecko walks about and gradually removed from the toe pads by each step taken (i.e., energetic disequilibrium governed contact self-cleaning mechanism) [94]. However, studies in this area are still in a very preliminary stage. An inconsistency still exists between the empirical observation that gecko toes remain remarkably clean and functional for long periods of time in non- dust free environments and the lab measurements that only 40-50% adhesive force is recovered for dirtied “isolated setal arrays” or “manipulated intact gecko toes”. Other mechanisms, for instance gecko foot print or animal triggered peeling motion (i.e., digital hyperextension), might be overlooked, which may be crucial to fully understand the self- cleaning in gecko toe pads. A recent published paper demonstrates that geckos actually leave residuals (or footprints) as they walk [95]. This evidence has important implications for explaining self-healing, wear prevention and self-cleaning phenomena in gecko toe pads, which will potentially revolutionize the whole design concepts in this area.
38 There are a few reports on the self-cleaning properties in artificial adhesive systems. The first one pertains to the patterned multi-wall CNT arrays, which are superhydrophobic and resistant to multiple water exposures [96]. The soiled samples regained 60% or 90% frictional strength when rinsed with water or subjected to mechanical vibration, respectively. Likewise, the wet easy-to-clean property was demonstrated on superhydrophobic parylene nanofibrillar surfaces as well [97]. Strictly speaking, however, these wet cleaning abilities are not the same as the self-cleanness found in geckos but rather a lotus effect. Moreover, a contradictory result was reported that wetting behaviors of CNT forests were characterized being very unstable by static contact angle measurements. A change from Cassie to Wenzel state took place during water exposure and the tube alignment matted and collapsed [98]. More recently, stiff polypropylene fibrillar arrays were claimed to have dry contact self-cleaning abilities similar to gecko setal arrays [99]. 25-33% of original shear adhesion was recovered after
30 simulated steps for particle radius < 2.5 µm, whereas larger particles were not self- cleaned at all. The relatively poor performance of this polymer mimic may be attributed to their single-level structure and the static contact and release. Further improvement of self-cleaning in artificial dry adhesives could be achieved by introducing gecko-like structural hierarchy and dynamic motions.
2.7 Summery and Outlook
Significant advancement has been achieved in the realm of gecko inspired biomimetic fibrillar adhesives over the past decade. Two main types of materials, polymers and CNTs, have been adopted for creating micro-/nano- fibrillar structures that
39 exhibit not only enhanced but also reversible adhesion. Various fabrication and synthesization methods have been utilized to make such tiny structures, including template-assisted cast molding, lithography, and oxygen plasma growth for polymers as well as chemical vapor deposition for CNTs. However, for both polymer and CNT based adhesives one of the big challenges is to prevent premature structural failure and significantly increase the durability of the samples under repeated attach and detach cycles.
“Nature Does Nothing in Vain”, so it is believed that all structural features in gecko toe pads are useful to generate functions. A convergent designing trend has been identified in the progress of making vertical micro-/nano- fibrils, to characteristic tip shapes, to angled stalks/tips and to hierarchy. On the other hand, divergent rational design approaches are evolved for obtaining smart and responsive adhesives by combining other physical, chemical and biological principles with what nature already has. The gecko and mussel inspired hybrid adhesives demonstrate drastic adhesion improvement under both dry and wet conditions, showcasing potential applications in biomedical related fields. Smart adhesives controlled by external stimuli, such as mechanical, thermal, electrical, and magnetic fields, have also been shown to be not only practical but also promising. Finally, self-cleaning similar to gecko toe pads were reported in some of the artificial systems; however, a more fundamental understanding of the underlying mechanism in the biological system is still needed in order to create highly durable and reusable artificial fibrillar adhesives.
40 CHAPTER III
DYNAMIC SELF-CLEANING IN GECKO SETAE
3.1 Introduction
Gecko feet are sticky on almost any surface, but in order to be functional through thousands of cycles of stick and release in natural environments, they must remain relatively free of dust and other debris. The extraordinary ability of gecko feet to be both sticky and clean presumably stems from their hierarchical fibrillar adhesive system, which consists of millions of micro-fibrils, called setae, with billions of nano-sized branches, terminating in small plates called spatulae [1, 2, 6, 28, 100]. Efforts to mimic gecko toe pad structure and function seek to develop a new class of advanced adhesives that are not only sticky, but also non-fouling. An impressive variety of synthetic mimics which capture the adhesive qualities of the gecko system has already been developed [41,
49, 63, 69, 73, 77, 78, 83, 84, 87]. Some prominent examples include designs based on photoresist nanorods on solid micropillar supported platforms and micropaddles [69, 87], polyurethane microfibers with angled mushroom tips [63], micro- and nano- integrated hierarchical polymeric hairs [73], and CNT brushes/forests [83, 84]. Notably, the adhesion of some synthetics has even reached up to 1000 KPa [84, 86], about 10 times higher than what a gecko can achieve. Given this success, it is striking that the non- fouling performance of both the gecko and synthetic adhesive systems has received comparatively little attention. However, this non-fouling property is fundamental to the
41 desire to produce innovative adhesives that work under circumstances where traditional pressure sensitive adhesives fail. It is therefore crucial to explore how geckos combine high adhesion and self-cleaning together within their toe pads.
A few possible self-cleaning mechanisms have been proposed, including: i) an ultra-hydrophobic surface that resists unwanted adhesion [101-104], and ii) the lotus effect [105, 106]. These mechanisms, however, which arise from hydrophobic surfaces with micro- and nano- roughness combined topology, do not explain self-cleaning in gecko toe pads. More recently, it was suggested that setal self-cleaning occurs due to an energetic disequilibrium between the adhesive force attracting a dirt particle to the substrate and those attracting the same particle to one or more spatulae [94, 107]. In other words, small solid particles may bind more strongly to the substrate surface (e.g., a stone wall or glass) than to the constituents of toe pad (i.e., setae or spatulae), such that after pressing and dragging a contaminated setal array or toe pad against a clean surface, the particles are removed and deposited onto the opposing surface. However this mechanism was proposed based on the empirical measurements of self-cleaning in isolated setal arrays and intact gecko toes by simulated “steps”. The natural pealing motion, digital hyperextension (DH), which many geckos use, was not included in their experiments because the rate at which toes move during DH was concluded to be too slow to measurably affect the rate of self-cleaning [94].
Here we demonstrate that when walking naturally across a surface and scrolling their toe pads using DH, geckos clean their feet more rapidly than previously suggested.
The rate and extent of the self-cleaning in unrestrained geckos are two times higher than those without DH or previously reported for arrays of setae isolated from geckos and
42 extrinsically manipulated gecko toes [94]. We propose an intrinsic dynamic self-cleaning mechanism that is associated with both the gecko toe pad structure and animal induced motion. A mathematical model accounting for dynamics under the influence of DH explains the self-cleaning phenomena observed at the whole animal scale, and the general observation that gecko toes remain highly functional in free-ranging animals even when they move on dirty surfaces.
3.2 Materials and Methods
We obtained 10 Gekko gecko (Tokay Gecko) from California Zoological Supply.
Gekko gecko is a nocturnal gecko found in Southeast Asia. Geckos weighed between 56-
100 g, with snout-vent lengths (SVLs) ranging between 12.9-15.2 cm. All geckos were housed in individual 10 gallon glass tanks with paper towel substrate, maintained within a dedicated animal research facility at the University of Akron. Each tank was misted with water as well as provided with a fresh bowl of water daily. These geckos were fed vitamin dusted crickets 5 times a week and the other 2 days they received a fruit supplement. The room was maintained at 25±1°C and set to a12 hour photoperiod with
UVA/UVB full spectrum lights. Heating tape along the underside of each tank allowed geckos to thermo regulate within the range of body temperature typical for free-ranging geckos (~25-35°C) [17].
All experimental trials were conducted in a walk-in environmental chamber maintained at 25 ± 1ºC and 55 ± 2% relative humidity (RH). We used a custom designed apparatus with glass as a substrate to estimate maximum clinging force of individual geckos [17]. It contains a motor driven force gauge (Shimpo FGV-10X) which moved
43 relative to the substrate. Digital output from the force gauge was collected by a
LabVIEW program allowing us to save traces of each adhesion trial. For all trials, the apparatus was held in a horizontal position and shear forces were tested by pulling on the gecko in a direction parallel to the surface. Each gecko was fitted with specially designed harness positioned around the pelvis and allowing unimpeded movement of legs and minimizing abrasion to the gecko’s skin. At the start of each test, the harness was attached to the force gauge which was subsequently driven horizontally by the motor.
Silica particles, ranging from 5 µm to 50 µm in diameter, were used as a fouling agent for the gecko’s feet. Clinging force was recorded as the maximum force immediately prior to all four feet of the gecko slipping. A trial consisted of placing a gecko on the clean glass of our force apparatus and measuring its clinging capacity under different conditions through multiple “pulls” in quick succession. The first pull was with clean feet. Subsequent to the initial “clean” pull, the gecko was slowly lowered onto a glass tray filled with silica dust until it supported its own body weight and all four feet were in contact with the dust. A second “dirty” pull was then immediately conducted identically to the “clean” pull. To collect data for self-cleaning, trials were conducted as described above, except that following the fouling induced by exposure to silica dust, the gecko was lowered onto the clean glass substrate and induced to walk. Once at rest, the number of steps taken was recorded and clinging force measured as above. After each and every trial, the glass was cleaned with ethanol and allowed to dry. This sequence in protocols allowed us to estimate self-cleaning rate as in Ref. [94], where clinging ability when fouled is compared directly with the clinging ability when clean. Finally,
44 subsequent to any trial in which we applied silica dust to the feet of geckos, we thoroughly washed them with water to remove any remaining particles.
Trials with animals unable to use DH were conducted exactly as above but prior to the start of a trial, each gecko was fitted with custom designed “gecko shoes” (Figure
3-1A, B). “Gecko shoes” were constructed to restrict the extent of DH possible (Figure
3-1C, D) without blocking access of toe pads to the substrate. Geckos fitted with “shoes” could still walk, but only with minimal to zero capacity for DH. “Shoes” were made from adhesive ends of BAND-AID® Tough-Strips (each BAND-AID® made 2 “gecko shoes”). Strips were applied to the dorsal surface of the foot and then a very thin, flexible, adhesive, aluminum strip was laid over the top of the BAND-AID®. These “shoes” were easily removed by peeling with no discernible effect on the underlying skin. The “shoes” were also extremely lightweight.
Statistical analyses were conducted to account for the experimental design in which every gecko was exposed to all possible treatment combinations, a repeated measures analysis of variance. Dependent variables were transformed when necessary to satisfy assumptions of parametric analysis.
45
Figure 3-1 (A) Tokay gecko with fitted “braces” (i.e., “gecko shoes”) that prevented digital hyperextension but allowed the animal to walk, adhere to the surface, and release.
(B) Close up of the “gecko shoe” on the dorsal surface of gecko foot. A gecko foot showing toes in (C) flat and (D) hyperextended positions without the “shoe”.
3.3 Results
We assayed the self-cleaning ability of live geckos walking naturally across a horizontal, clean glass surface under two different conditions. After dusting gecko feet with silica particles, we allowed geckos to freely walk across a clean glass surface, with or without custom-fitted toe braces that prohibited toe scrolling (DH). In both cases,
46 geckos were able to adhere to the glass such that we could measure the shear forces they generated as a function of the number of steps taken before they voluntarily stopped.
Data collected over a large number of trials allowed us to compare shear forces generated by geckos with dirtied feet after taking from one to up to eight steps.
3.3.1 Self-cleaning of toe pads in unrestrained geckos
We used a recovery index (RI), the proportion of adhesion strength when feet are dirty relative to that when feet are clean, to estimate rate and extent of self-cleaning [94].
All geckos showed improved adhesion (self-cleaning) with each step taken (RI; F3,10 =
12.7, P < 0.001; Figure 3-2), but geckos that were able to use DH when they took steps experienced a self-cleaning rate that was approximately twice as fast as geckos that could walk but not use DH (Steps * DH; F4,7 = 5.26, P < 0.002; Figure 3-2). Moreover, geckos using DH ended up with a greater degree of self-cleaning that approached 80% of clean forces after just 4 steps. Note that after 5 steps, the 95% confidence interval (CI) of the average recovery rate is very close to 100% recovery, suggesting that after just 5 or 6 steps with DH enabled, adhesion of self-cleaned toes would be statistically indistinguishable from toes that were never exposed to dust. On the other hand, the extent of self-cleaning leveled off for geckos not able to use DH, stalling at approximately 40-50% even after taking 8 steps. In general, self-cleaning in geckos without DH began to level off after approximately 4 steps (Figure 3-2). Rates and extent of self-cleaning for geckos without DH in our study are very comparable to previously reported self-cleaning rates in isolated setal arrays and intact gecko toes manipulated through simulated stick and release cycles [94].
47 Geckos with clean feet and the ability to hyperextend their toes were able to adhere to a glass substrate with an average force (15.7 ± 3.6 N; Mean ± 2SE) roughly equal to 20 times that required to support their body weight; however, the force decreased by nearly a factor of 6 with dirtied toes (2.59 ± 2.63 N). Geckos unable to perform DH generated force (5.8 ± 2.14 N) about 1/3 as great when clean without shoes, but still substantially higher than that required to support their body weight. When dirtied, adhesive force fell close to that required to support average body weights of the largest animals in our sample (0.85 ± 1.50 N). The absolute clinging force generated by geckos with clean feet and the ability to use hyperextension were greater than that generated by geckos with clean feet and lacking the ability to hyperextend. However, the rate at which self-cleaning occurred was not related to the magnitude of the clean clinging force recorded for an individual, only to whether toes could hyperextend or not (Covariate =
Maximum Clean Adhesion in ANCOVA; F1,10 = 1.6, P > 0.23; Not significant). Thus,
DH plays a major role in self-cleaning of gecko feet.
48
Figure 3-2 Recovery indices for trials with and without DH by steps. Numbers above bars are sample sizes. Error bars represent ± 2SE.
3.3.2 Observations of dirt particles on live gecko toe pads
We examined the toe pad structure of a live gecko using optical microscopy
(Mitutoyo America Corporation, FS-70 Series 378-Microscope Unit). A gecko was coaxed to adhere to a glass plate allowing us to capture images when the foot was clean
(never dirtied), right after it had been dirtied, and after it walked freely with DH through
8 steps; we were also able to capture an image of the footprint after the first step was taken (Figure 3-3). Although the effect of DH on self-cleaning could not be quantitatively evaluated by counting the particles removed for each step, significant removal of dirt particles was clearly evident (Figure 3-3A, B, C). After 8 steps of free walking the toe pad returned nearly to its original state (Figure 3-3A, C). Larger particles
49 are more likely to be deposited onto the glass surface compared to smaller particles especially for those stuck in between lamellae: the footprint after one step contained many of the larger particles within the gap between setal arrays (Figure 3-3D), while the remaining particles after self-cleaning appear substantially smaller (Figure 3-3C).
Figure 3-3 Optical micrographs of live gecko toe pads adhering to glass surface when (A) it is clean (never dirtied), (B) right after dirtied, (C) self-cleaned by 8 steps of free walking with DH on clean glass substrate, and (D) the footprint after one step. Arrows in
50 (C) point to some of the remaining dirt particles that can be easily identified after 8 steps of self-cleaning.
3.4 Discussion
Our experimental results demonstrate that DH has a significant effect on the self- cleaning experienced by geckos walking on a smooth and clean substrate. In this section we will discussion the underlying mechanisms that are responsible for this strong empirical correlation. A mathematic model was developed by including both the animal induced motion during foot release and the special geometrical feathers of gecko setae.
3.4.1 Gecko detachment mechanisms with and without digital hyperextension
When walking naturally, before taking each step, geckos peel their toe pads from the substrate by scrolling their toes from distal to proximal direction under the action of
DH (Figure 3-1C, D). If we model toe pad scrolling as a rolling motion of a circle with setal arrays along a horizontal plane, where each seta is lifted sequentially, then its trajectory follows the corresponding cycloid (Figure 3-4; e.g., from point A to A’).
Specifically, the pad motion will sequentially exert on the setal roots a vertical displacement of yr (1 cos ) and a lateral displacement of xr ( sin ) , depending on the specific location of each seta, where r is the scrolling radius of the toe pad (i.e., the radius of rolling circle) and θ is the rotation angle of a seta in radians.
51
Figure 3-4 Schematic of the toe pad scrolling motion under DH, which is modeled as a rolling motion of a circle, with a radius r, along a horizontal plane. The trajectory (e.g., from point A to A’) follows the corresponding cycloid curve (e.g., blue dashed line) depending on the specific location of each seta. Point B’ is the critical separation point of setae with respect to the substrate/wall, which determines the length of a peeling zone, L.
θ* is the critical rotation angle that generates the cycloid curve from point B to B’.
It has been measured that a single seta could sustain pull-off forces of ~40 µN in the normal direction (90°) and ~200 µN in shear (<30°), whether the substrate is hydrophobic or hydrophilic [6, 14]. For an isolated setal array, detaching strength maintains relatively constant, when the detaching angle is varied from 30° to 90° under a load-drag preloading condition [108]. Such a high adhesion force at the microscale will lead to setal jumping off during toe pad scrolling. This jump-off event is a common phenomenon that has been observed in many other systems such as atomic force
52 microscope (AFM) pull-off tests for measuring micro-/nano- adhesion [14, 89, 109-112] and single CNT peeling tests [113, 114].
Even though individual setae experience a relatively large adhesion force during its jump-off in the detachment, the total peeling force on the whole toe pad is comparatively small relative to that generated in attachment. Using the scrolling model above, at any instance of toe pad scrolling only a fraction of the setae generate adhesion forces that are contributing to the overall peeling force experienced by gecko. This region is defined as a peeling zone possessing a constant length, L, in the x-direction
(Figure 3-4), which is determined by the maximum displacement of the setae before jump-off and the scrolling radius r (i.e., L = r × θ*). The adhesion force on individual setae in the peeling zone, Fw-s, can be related to the displacement of each seta in the y- direction, ∆y, by the beam theory:
3 y Fw-s l/3 EI (3-1)
where the subscript “w” and “s” represent wall and seta, respectively, while l, E and I are the setal length, Young’s modulus and the second moment of area, respectively. At the point of setal jump-off, assuming Fw-s = 10 µN, the maximum displacement of individual setae in the y-direction is calculated as ymax = 18.6 µm by taking l = 120 µm, E = 2 GPa and diameter of seta ds = 4.2 µm for calculating I. The averaged toe pad area for a single toe is measured as 24.2 mm2 with length of 9.42 mm and width of 2.57 mm, and the scrolling radius is captured as ~3 mm in the animal trials. According to the cycloid, taking r = 3 mm and ymax = 18.6 µm, we get xmax = 0.68 µm (i.e., displacement from
53 point B to B’ in the x-direction; Figure 3-4), and a critical rotation angle θ* = 0.11 for the peeling zone. Therefore, the peeling motion is mostly lifting the setal root up rather than dragging it parallel with respect to the substrate before jump-off, indicating that the experimentally measured vertical pull-off force (e.g., a 90° pulling in Ref. [14]) could be adopted for our approximation. Based on this calculation, the length of the peeling zone and the force distribution in the peeling zone can be determined by Equation (3-1) and the scrolling geometry (i.e., r in Figure 3-4). Taking the values of setal density, 14400 setae/mm2 [14], and assuming that setae distribute in a square lattice configuration, we get a setal spacing of ~8.3 µm. Integrating the reaction forces on the setae over the peeling zone, we obtain a total peeling force of 4.2 mN, which is 3 orders of magnitude lower than the shearing force of a single toe at lower angles when clean [115]. Thus, geckos can easily detach their toes through the sequential setal jump-off activated by DH.
Since the sequential setal jump-off can generate high inertial forces, we hypothesize that it contributes to the higher cleaning rate. During the hyperextended peeling, setal arrays on each toe roll up and spread out progressively from the substrate, as schematically shown in Figure 3-5A. The pad scrolling lifts the setal root, while the spatulae at the setal tip are adhering to a substrate/wall or dirt particles or both. This scrolling motion builds up elastic energy in each contacting seta within the peeling zone and eventually causes it to dynamically jump-off at a critical separation point (i.e., B’ in
Figure 3-4; separation front in Figure 3-5A), generating inertial force high enough to dislodge dirt particles. As will be discussed in the following sections, this dynamic self- cleaning mechanism is unique to gecko toe structures.
54 In contrast, when geckos wear the “shoes”, DH is disabled during animal walking.
Without the help of DH, geckos must lift their limbs to detach toes from the substrate.
We observed that this limb motion (LM) results in a proximal-to-distal peeling of the toe pads in a crack growth manner, as schematically shown in Figure 3-5B, which is in the opposite direction to that with DH enabled. The change in peeling mechanism leads to a crowding of the restricted setal arrays ahead of the possible jump-off direction at the separation front (Figure 3-5B). Consequently, the setal jump-off is substantially inhibited and the static and passive self-cleaning takes over.
Figure 3-5 Schematics of gecko toe peeling induced by (A) DH from distal to proximal direction without gecko shoe and by (B) LM from proximal to distal direction with gecko shoe.
It should be clarified that limb motion or the toe pad scrolling alone can also generate inertial force at the setal tip, but its magnitude is on the order of 100 times lower
55 than that required to remove the particles from setae [94], which is not the dynamic effect proposed and discussed below.
3.4.2 Dynamic self-cleaning mechanism
To demonstrate the dynamic self-cleaning mechanism due to setal jump-off activated by DH, we calculate the inertial force that could separate dirt particles from setae during setal rolling. We first consider two possible configurations when a seta contacts the interface: i) a seta contacting particles on a substrate/wall while being totally blocked from reaching the substrate/wall (the number of spatulae attaching on the substrate/wall nw-sp = 0; Figure 3-6A), and ii) a seta contacting particles on a substrate/wall while being partially or entirely exposed to the substrate/wall (0< nw-sp ≤ total number of spatulae within a single seta; Figure 3-6B).
Figure 3-6 Single seta detachment during setal rolling: (A) a particle adhering to both the spatular braches of a single seta and substrate/wall, totally blocking the seta from reaching the substrate/wall (nw-sp = 0), and (B) a particle adhering to some of the spatular branches of a single seta and the substrate/wall, while partially/not blocking the seta from
56 the substrate/wall (0 < nw-sp ≤ total number of spatulae within a seta). Note: for both configurations, the particles are in contact with the substrate/wall. nsp-p × Fsp-p = Fs-p; nw- sp × Fw-sp = Fw-s, where the subscript “sp”, “p”, “s” and “w” refer to spatula, particle, seta and wall, respectively.
A single seta is modeled as a cantilever beam with length l, diameter ds, and mass ms. For the first configuration (Figure 3-6A), when the adhesion force between the seta and particle, Fs-p, is smaller than that between the wall and particle, Fw-p, (Fs-p < Fw-p), the particle will stay on the wall while being separated from the seta upon setal retraction.
This self-cleaning mechanism is static and passive, based on an energetic disequilibrium, and has been proposed as the primary basis for gecko self-cleaning [94]. In the case of
Fs-p > Fw-p, the particle will separate from the wall but still adhere to the seta at a critical point. The sudden release of the seta along with the attached particle will generate inertial force Fi on both the setal tip and the particle. According to the beam theory, maximum acceleration of the setal tip can be determined as
22 amax 4 y max f (3-2)
where ymax is the bending displacement at the setal tip and f is the natural frequency.
3 3 With ymax F w-p l/3 EI , and f3 EI / ( mpe m ) l / 2 , where EI is the bending
stiffness of seta and mmes 33 /140 is the effective mass of seta [116], we have amax F w-p/ ( m p 33 m s /140) . The maximum inertial force acting on the particle is then described as 57
Fi m p F w-p/ ( m p 33 m s /140) (3-3)
From Equation (3-3) we have Fi < Fw-p < Fs-p, which implies that as long as the seta is being pulled off the wall, the particle will stay on the setal tip and self-cleaning will never happen. Therefore, self-cleaning is governed by the static and passive mechanism when setae are being totally blocked by dirt particles from target surfaces.
The setae of Tokay geckos each contain ~1000 spatulae and each spatula generates about 10 nN adhesion force on glass [6, 7]. The inertial force that a particle experiences at setal retraction (i.e., setal jump-off event) will be significantly greater if a fraction of spatulae adhere to the glass wall (nw-sp > 0), as in the case of second configuration (Figure 3-6B). Here we designate the attractive force between the wall and seta as Fw-s, and the inertial force becomes
Fi m p( F w-p F w-s ) / ( m p 33 m s /140) (3-4)
Hence, the inertial force, Fi, increases with increasing Fw-s for a given particle.
To quantitatively determine the inertial force as a function of particle size, we first derive the interaction force between the wall and particle, Fw-p, by taking the derivative of the interaction energy [117], as
RHp w-p Fw-p (3-5) 6D2
58 where D denotes the distance between the wall and particle, Hw-p is the Hamaker constant for wall-particle interactions and Rp is the radius of the particle. There is a cut-off gap distance, D = Dw-p, representing the effective separation between the wall and particle, at which maximum attractive force is estimated [117]. Secondly, Fw-s is determined by assuming that a number of spatular branches within a single seta adhere to the glass wall
(i.e., Fw-s = nw-sp × Fw-sp), each of which generates 10 nN adhesion force [7]. Combining
Equation (3-4) and (3-5), we plot the force ratio Fi/Fw-p as a function of particle radius,
Rp, in Figure 3-7, with different numbers of exposed spatulae to the wall (nw-sp = 0, 100 and 200).
3 In the calculation, a density of ρp = 2.65 g/cm is used for spherical silica particles
3 to calculate mp, and ds = 4.2 µm, l = 120 µm and density of seta ρs = 1.36 g/cm to
-20 calculate ms in Equation (3-4). Hw-p = 6 × 10 J and Dw-p = 0.3 nm are taken as the wall- particle interaction parameters in Equation (3-5) [117]. Our results show that even when only 10% of spatula attaches on the wall (i.e., nw-sp = 100), the ratio of Fi/Fw-p is in the range of 1.5-2.5 for particle size Rp ranging from 2.5 µm to 25 µm (Figure 3-7), which is the size distribution of silica particles used in the animal trials. This suggests that the dynamic effect can overcome substantially higher adhesion force between the seta and particle, Fs-p, than that in the static self-cleaning mechanism. As more dirt particles are removed by each step, the fraction of spatulae exposed to the wall becomes larger (i.e., nw-sp increases with step), and consequently the dynamic effect is more effective.
59
Figure 3-7 The ratio Fi/Fw-p as a function of particle radius Rp for a number of spatular branches within a single seta adhering to the wall (nw-sp = 0, 100 and 200). Each spatula is assumed to generate an adhesion force Fw-sp = 10 nN if contacting the wall.
As seen in Figure 3-7, the inertial force is quite low for small particles (e.g., Rp <
1.5 µm). However, for such small particles, it is likely that each particle adheres only to a few or a single spatula [14]. We have estimated interaction force between a single spatula and a small particle, Fsp-p, assuming that the spatula tip is round with radius Rsp, and taking the derivative of the interaction energy [117], as
RRH p sp sp-p Fsp-p 2 (3-6) RRp sp 6D
60 where D is the distance between the spatula and particle, Dsp-p is the cut off gap distance at which the attractive force, Fsp-p, reaches a maximum value, and Hsp-p is the Hamaker constant for spatula-particle interaction. We assume that Hsp-p ≈ Hw-p, and Dsp-p ≈ Dw-p, which are reasonable for most materials systems [117]. Dividing Equation (3-6) by
Equation (3-5) yields force ratio as
FR sp-p sp (3-7) FRRw-p p sp
According to Equation (3-7), in the case of single spatula attaching to a small particle, the force between the wall and particle is always larger than that between the spatula and particle, Fw-p > Fsp-p, which suggests that a small particle adhering to a single spatula could always be removed through the static self-cleaning mechanism if the particle contacts the wall.
It is possible that the particles adhering to a seta do not contact the wall at all. In this situation, Fw-p = 0 in Figure 3-6, indicating that the static self-cleaning mechanism becomes ineffective. However, the particles are not blocking the seta to reach the target surface. The spatulae on the same seta are more likely adhering to the wall (i.e., nw-sp > 0 or Fw-s > 0) comparing to the configurations shown in Figure 3-6. With more exposed spatular branches to the wall, the particles ought to experience a larger inertia to separate itself from the seta during setal retraction. Using the same formula as Equation (3-4), we calculated the inertial force on a particle that only adheres to a seta being pulled away from a wall (Figure 3-8). The inertial force, Fi, generated at the setal jump-off event increases linearly with the wall-seta interaction force, Fw-s, for different particle sizes
61 (Figure 3-8A). The higher the adhesion force, Fw-s, the larger the dynamic effect becomes. Figure 3-8B shows the inertial force, Fi, as a function of particle radius, Rp, for given numbers of spatulae within the seta adhering to the wall. As the particle size enlarges, the inertial force, Fi, rapidly increases at first but levels off beyond Rp = 5 µm.
However, as the particle radius increases to the size comparable to setal spacing (~8 µm), it is more likely that the particle contacts the substrate. Therefore, the self-cleaning mechanism may change to the static or the dynamic one mentioned above in Figure 3-6.
For substantially larger particles, gravitational force overrides the surface phenomena, and geckos are not able to pick them up. In our experiment, we have observed that larger particles are more likely to be deposited onto the glass surface compared to smaller particles after one step (Figure 3-3D). In general, if the inertial force defeats the adhesion force between the seta and particle (Fi > Fs-p), the particle will be dislodged at the jump- off event. For example, if Fw-s = 400 nN (assuming nw-sp = 40), a 2.5-µm-radius silica
-13 microsphere (mp = 1.7 × 10 kg) adhering only to the seta is acted on by an inertial force
Fi = 100 nN, one order of magnitude higher than the force of a single spatula (~10 nN)
[7]. This suggests that a particle can be efficiently removed by inertia even if it adheres to multiple spatulae, in this case up to 10.
62
(A)
(B)
63 Figure 3-8 Inertial force, Fi, on particle adhering only to seta, versus (A) the adhering force between the wall and seta, Fw-s, and (B) radius of particle, Rp. Note: Fw-s = nw-sp ×
Fw-sp = nw-sp × 10 nN.
3.4.3 Effect of DH on dynamic self-cleaning
The above analysis suggests the dynamic self-cleaning mechanism is effective only when setae experience jump-off. The combination of the hierarchical fibrillar structure of gecko toe pads and the distal-to-proximal peeling motion induced by DH at detachment are crucial for achieving this dynamic effect at the micro-/nano- interface.
Strong frictional adhesion is generated when geckos place their foot and drag proximally, maintaining the angle lower than a critical value: ~25.5°, ~24.6° and ~30.0° for a single toe, isolated setal array and single seta, respectively [55]. A crowding model was proposed to calculate the minimum angle prior to tetrads/setae coming into contact with one another under significant loading [118]. In fact, the smaller the angle is the more crowded the setal arrays become. A minimum angle of ~12.6° was proposed at the point of maximum crowding. Thus, setal arrays in an attachment state are highly crowded.
In our animal trials, geckos were allowed to walk either freely (with DH) or their toes were inhibited from scrolling (without DH), as schematically shown in Figure 3-5.
With restricted toes, the geckos are still able to take steps and walk but cannot scroll their toes. In this case, gecko toes peel in the direction from proximal to distal, solely influenced by limb motion in each step (Figure 3-5B). During this proximal-to-distal peeling, the displacement of setal roots at the separation front is in a direction between
64 vertical and distal (i.e., an angle larger than 90°). Based on the detachment measurements of isolated setal arrays in various linear directions [108], the setal jump-off will be significantly damped or prohibited. Therefore the proximal-to-distal peeling would only lead to a minimum to zero dynamic effect, and a maximal static self-cleaning.
More importantly, because of the asymmetric geometry of angled setal arrays, the crowed region (i.e., densely packed setae in an attachment state) is located ahead of the possible jump-off direction (Figure 3-5B). With limited space in the jump-off direction, the possibility of setal jump-off is further eliminated. Such confined setal arrays are very similar to those used by Hansen and Autumn [14]. In their experiment no peeling in either direction was performed. After pressed engaging, the setal arrays were simply sheared off their glass wall in each force measurement. As a result, the important phenomenon of dynamic self-cleaning was not observed. The restricted setal arrays and manipulated toes correspond to the static and passive self-cleaning, which accounts for
40-50% of the total recovery (Figure 3-2).
The scenario is profoundly changed when DH is enabled (Figure 3-5A). The distal-to-proximal peeling of flexible toes under DH promotes setal jump-off in three ways. First, displacement of the setal roots at the separation front is in a direction between vertical and proximal (i.e., an angle smaller than 90°). Thus, the elastic energy pre-stored in the setal shafts could not return to the interface but is instead frictionally dissipated [108] or contributes to the jump-off through higher seta adhesion force.
Second, the crowed region is located behind the jump-off direction. Setae can easily separate from one another during toe scrolling and retreat independently from the substrate/wall (Figure 3-5A). Finally, with DH, gecko toes could be substantially curved
65 into a hyperextended position. The setal angles, originally ~45°, are significantly increased beyond the separation front (i.e., peeled-off region; Figure 3-5A). Peeled-off setae are progressively spread out after sequential jump-off event, leaving larger spaces for the consecutive dynamic retraction at the propagating separation front. All these aspects work together activating the dynamic self-cleaning that can overcome much higher adhering force on the particles compared to the static mechanism. As a result, the rate and extent of self-cleaning can be significantly increased, which is supported by our experimental observations (Figure 3-2).
Our analysis and model suggest that DH significantly enhances the self-cleaning performance of the gecko adhesive system, which raises at least two questions worthy of further study. First, what role did self-cleaning effectiveness play in the evolution of the best characterized components of the adhesive system such as setal morphology (e.g., setal size, curvature, density, etc.)? In general, studies have largely focused on interpreting design and function by analyzing static attachment and release of individual or isolated patches of setae, even though setae operate as part of an integrated locomotor system. More studies which incorporate whole organism performance trials should help us identify and test specific hypotheses about the origins and significance of features such as DH not just to self-cleaning, but to adhesive locomotion in general. Second, how effective is active self-cleaning due to DH in other fibrillar adhesive systems like those that were independently evolved in lizards belonging to the genus Anolis in the
Polychrotidae? Anolis lizards use DH, but the direction of “roll-off” is opposite to that seen in geckos, and the process of “roll-off” is driven by changes in the angle of the limb as it moves through a step cycle rather than by hypertrophied muscles in the toes.
66 There are some synthetic dry adhesives with self-cleaning capability. Stiff polymer fibrillar adhesives, for example, show self-cleaning properties with gold microspheres (radius ≤ 2.5 μm), as samples recovered 25-33% of the original shear adhesion force after 30 simulated steps [99]. Synthetic micro-patterned CNT-based gecko tapes regained 60% of the shear stress when the tape was dusted and cleaned by water [96]. These synthetic dry adhesives show either lotus effect or similar contact self- cleaning rate as gecko toe pads without DH. The relatively low recovery rate in both isolated natural and synthetic adhesives is attributed to the static and passive self-cleaning.
As demonstrated in the present work, a superior self-cleaning rate can be achieved by introducing dynamic self-cleaning mechanism in biomimetic structures, which provides a new route for the design of highly re-useable and reliable dry adhesives.
3.4.4 Revisiting the easy detachment mechanism of gecko feet.
The jump-off event at the setal level raises the necessity of rethinking the easy detachment mechanisms of gecko feet at all length scales. Because the new dynamic model we developed here for explaining the rate and extent of gecko self-cleaning has not only agreements but also divergences of other mathematical models that concerning the easy detachment of the same system [4, 119, 120].
In our analysis, the adhesion/peeling forces between individual spatular pads and the opposing surfaces contribute to the setal jump-off force all at once during setal rolling.
In other words, it is assumed that spatular pads are not coming off in sequence within a single seta as the setae do at the upper level, especially when each seta is being pulled off in an angle ≤ 90°. This is opposed to the seta detachment model proposed by Tian et al.
67 [119], where a propagation separation process is introduced at the spatula level when seta is released from a angle of ~30° to ~90°, which results a drastically decrease of the detachment force to 32 nN, a force level that will virtually eliminate setal jump-off.
However, first supporting evidence of setal jump-off is the empirical measurements of single isolated seta being detached perpendicularly and paralleling from microelectromechanical systems [6, 14]. Whether the substrate is hydrophobic or hydrophilic, the pull-off forces are documented as ~40 µN in normal (~90°) and ~200 µN in shear (<30°). Second is that, for isolated setal arrays, detaching strength maintains a relatively constant value with the detaching angles raging from 30° to 90°: ~35 KPa under average load-drag preloading condition [108]. If one assumes all setae are in contact, each of them contributes a fraction of force: ~2.43 µN. Notably, a couple µN force makes a huge different between the static and dynamic mechanism as shown in
Figure 3-6 (nw-sp = 200, Fw-s = 2 µN), which results in a much faster recovering rate of contaminated gecko toes. Finally when considering the different morphologies between setae and spatulae, one can easily spot that the setae/tetrads are distributed evenly on
“large areas”, toe pads, whereas spatulae are flushing out from the top point of setal stalk as out-grown braches with substantially wider spacing at the tip comparing to the base.
Toe pad scrolling have much significant effect in the peeling process of the individual setae, whereas when each seta is rolling out the spatulae within this seta are not undergoing the same scrolling mechanism (DH) as setae do. At the ultimate contacting level, propagation separation process (sequential detachment of spatulae) is not likely to occur.
68 To push it further, using the propagation models and assumptions from Tian et al.
[119], if single seta is being pulled in a direction of 10° (the phase of engagement; toe rolling in), each single spatular pad could sustain 70 nN of peeling force. Due to the moment exerted on the pulling point at the far end of setal root, the attached spatulae will be opened up at a critical point, starting from the distal end and the separation of spatular pads will happen in sequence and propagate to the proximal end upon loading. The total force of detaching a single seta in 10° is calculated as 140 nN, which is 3 orders smaller than the empirical measurements of single seta detaches at lower angles (~200 µN).
Moreover, a single seta could also sustain a ~40 µN of pulling force in the normal direction as mentioned above. Obviously, in their argument, this catastrophic failure is avoided by stating that in lower angles (<30°) the peeling force of individual spatular pads adds up leading to 35 µN of adhesion. However the transition of sequential separation to detachment all at once by changing the pulling direction of single seta within an angle ≤ 90° is neither physiologically plausible nor strictly proven. A “halting effect” or “propagation saturation” at the nanoscale (i.e., spatular level) is favored based on the analysis of empirical data, such that the pull-off forces are not very much
“sensitive” with respect to the loading directions, especially lower than 90°, in the sense that the detaching force decrease smoothly when the loading angle increase without a distinct transition into the crack propagating manner of detachment.
The mechanism, “jump-off,” that leads to an almost two-fold faster rate of self- cleaning of gecko toe pads when digital hyperextension is permitted vs. when it is not
(shoes in our experiment, and isolated setal arrays in previous experiments), arises from the morphology and function of the hierarchical toe pad system as it is currently
69 understood. When toe pads are brought into contact with the substrate with the normal and shear preloads characteristic of a gecko walking [55], contact forces on the setae can be decomposed into two components, a shear force (parallel to the substrate) and an adhesive force (normal to the substrate). As long as the setae are experiencing a non-zero shear force, they also will be subject to a non-zero normal force. During hyperextension, the peeling of the toe pad from its distal to proximal end, the point at which each seta detaches is accompanied by a spontaneous jump-off due to the non-zero normal force
(adhesion) acting on the seta. Our model (described below) is consistent with the assumptions and parameters used in a previous force analytic model of gecko toe attachment/detachment mechanics [119]. Our model differs in two prominent ways.
First, we incorporate ‘dirt’ into the adhesive system to analyze self-cleaning, and second, our detachment mechanics are consistent with the kinematics of hyperextension during active toe-detachment from the substrate. We postulate that peeling of the toes, setae and spatula proceed from the distal end of the toe to the proximal. In the model of Tian et al.
[119], peeling during hyperextension proceeds from the distal to proximal margins of the toe, detaching of the spatulae within each and every seta, however, propagates in an opposite direction. Although there is currently no direct evidence of the direction in which peeling occurs, it is difficult to imagine how spatula peeling could proceed in a direction opposite to toe peeling induced by hyperextension. This latter difference leads to the phenomenon of ‘jump-off’ in our model. Future works will be making efforts of implementing setal pull-off tests with dirt particles in between the interface, so that the dynamic self-cleaning mechanisms proposed above could be experimentally verified.
70 As demonstrated in section 3.4.1, the cycloid model explains both the setal jump- off event and the easy detachment of toe pad at the whole animal scale, whereas previously models could only predict the latter but being contradictory to the almost doubled self-cleaning rate, when geckos actively peel their feet for surface while third body interferences at the interfaces.
3.5 Conclusions
We have demonstrated that geckos walking naturally and using DH exhibit a self- cleaning rate that is considerably higher than previously observed rates based on passive mechanisms with isolated elements of the toe pad hierarchy. When DH was disabled, the extent of self-cleaning leveled off at 40-50% even after taking 8 steps. Whereas, a two- fold increase in self-cleaning rate was observed with DH enabled, returning the feet nearly to their original state in only 4 steps. More rapid self-cleaning and the observation that gecko toes remain clean and functional for long periods of time in non-dust free environments suggest a dynamic self-cleaning mechanism that efficiently removes dirt particles during animal locomotion. Because of the nature of the adhesion force, asymmetric geometry and animal triggered distal-to-proximal peeling via DH, the rotating setae suddenly release from the attached substrate, generating acceleration high enough to dislodge dirt particles from the toe pads. While some dirt can be removed statically, the dynamic self-cleaning adds another dimension to remove the particles that more strongly adhere to the setae. The fine design of gecko toe pad structures by nature perfectly combines dynamic self-cleaning with attachment/detachment, making gecko feet sticky yet clean.
71 CHAPTER IV
MECHANICAL ANALYSES OF THE HIERARCHICALLY STRUCTURED
CARBON NANOTUBE ARRAYS FOR DRY ADHESIVE APPLICATIONS
4.1 Introduction
Vertically aligned carbon nanotube (VA-CNT) arrays have been demonstrated as a promising candidate for creating fibrillar dry adhesives by virtue of their superior structural and mechanical properties [77, 78, 80-83, 96, 98, 121]. Comparing with their counterpart (i.e., polymeric patterns of micro/nano fibers [35, 37, 39, 41, 43, 49, 63, 73,
75, 122]), VA-CNT arrays comprise densely packed high aspect ratio (~10000:1) CNTs with nano-sized ultimate contacting elements (1~2 orders smaller than the size of gecko spatulae), which is crucial in achieving high interfacial adhesive strength based on the
“contact splitting principle” [23, 24, 26].
Of particular interests are the hierarchical fibrillar nanostructures that can be regulated on and off between strong attachment and easy detachment, mimicking gecko walking. A recent breakthrough was led by the synthesization of hierarchically structured VA-CNT arrays (Figure 4-1) [84]. Curly entangled segments (mimicking spatulae) laterally distributed on top of a straightly aligned body (similar to setae) enables a readily formalization of CNT side/line contacts when applied to a target surface [85,
86]. Macroscopically, this two-level gecko-foot-mimetic CNT patch renders a frictional force of ~100 N/cm2, about 10 times that a gecko can achieve in shear, and a low
72 adhesion force of ~10 N/cm2 in normal direction. This adhesive force anisotropy ensures a strong binding on along the shear direction while an easy lifting off in the normal direction.
Figure 4-1 SEM micrographs of (E) hierarchically structured vertically aligned
MWCNTs with (C) entangled top layer resembling spatulae. (D) TEM image of a single
MWCNT at the top layer. [84]
We have assayed this particular CNT based fibrillar adhesive system by implementing a series of mechanical analyses at multiple time and length scales via molecular dynamics simulations, finite element methods, along with analytical derivations. Critical issues that are being elucidated include: i) effect of the entangled/lateral CNTs on adhesion and friction behaviors at the nano- contact interface; ii) mechanics of local deformation in the lateral CNT peeling; iii) the force anisotropy transition from nano- to micro- and to macro- levels; iv) adhesion and friction force coupling that ensures enhanced adhesion at attachment, while the relatively easy to disengage in detaching.
73 4.2 Outline of the Multiscale Modeling and Simulation Approaches
Multiscale modeling and simulation approaches were developed for studying the mechanical characteristics and processes of the CNT hierarchical fibrillar structures.
Systematic relations between the structures and adhesive properties were established by linking the molecular configurations to the meso-/macro- scale functions and performances. As illustrated in Figure 4-2, this multiscale computational framework spans three levels of structural hierarchy from fully atomistic molecular dynamics to coarse grained molecular dynamics and finally to finite element analysis.
Figure 4-2 Modeling and simulation scheme across multiple time and length scales, from fully atomistic to coarse grained molecular dynamics (MD) and to finite element analysis
(FEA).
74 In principle, all properties of all materials and phenomena are describable by quantum mechanics. However directly use this exquisite theory is sometimes impractical, especially for the systems with large numbers of atoms and/or molecules. Hence, simplifications are often made according to the specific problems that are under focus. In our nanoscale simulations, atomistic degrees of resolution are retained where the equations of motions between discreet atoms are based on non-reactive force fields.
Eliminating the electronic degrees of resolution enables us to study the effect of van der
Waals interactions on the adhesive behaviors between the CNTs and substrate at an appropriate fundamental scale with less computational expenses. Classical approximations are further carried out in the coarse-grained models to include complex tube-tube interactions as the systems are up-scaled into a higher level. At the ultimate functional level, phenomenological-based continuum methods are implemented, which offers a feasible a way of directly comparing and validating the simulation results with that of the experimental measurements. Transitions and propagations between the models at different levels were also emphasized and addressed in detail to give an insight into the justifications as well as limitations. As illustrated in Figure 4-2, the present multiscale modeling and simulation strategies form a closed loop via the up-scaling and down-scaling pathways. With the combinations of numerical simulations, analytical derivations and experiments, this work sheds lights on the underlying mechanisms of fibrillar interfacial phenomena by bridging the theoretical principles to the critical engineering issues.
75 4.3 Fully Atomistic Molecular Dynamics
At the nanoscale, fully atomistic molecular dynamics simulations were performed to explore the origin of the adhesion enhancement by studying different peeling behaviors of the laterally distributed CNT segments.
4.3.1 Introduction
Friction and adhesion are combined phenomena at the micro-/nano- scale interfaces. As the dimensions of current manmade devices shrink down, these forces become more significant and are considered as the key design factors in many applications [123-125], such as data storage computer chips and micro-/nano- electromechanical systems (MEMS/NEMS). On the other hand, many species in nature, geckos for example, sophisticatedly make use of these interfacial forces in their daily lives [6, 23, 126]. Mimicking nature, tunable dry adhesives have been obtained in synthetic materials with structures similar to gecko’s feet [30, 127], as in the case of hierarchically structured VA-CNT arrays. In general, a fundamental understanding of the friction and adhesion mechanisms are of great importance for designing miniaturized devices, making synthetic biomimetic materials, and controlling the interfacial properties
[84, 128-130].
It is well-known that in the presence of adhesion, friction occurs even without normal compressive loading applied on the touching objects. The mechanism of the adhesion-assistant friction is well described by a molecular friction law [131]:
FFFLONμ , with the friction force FL, normal force FN, frictional coefficient µ, and adhesive friction FO. Adhesion effects were analyzed by a number of models, including
76 Johnson-Kendall-Roberts (JKR) model for soft materials [132], Derjaguin-Muller-
Toporov (DMT) model for hard materials [133] and Maugis-Dugdale theory [134]. The origin of the friction force because of adhesion at the molecular level has also been discussed intensively in literatures [123, 124, 135, 136].
Conversely, a fundamental question is whether friction generates or enhances adhesion force. There are some evidences that a friction force can generate adhesion force at the nanoscale. Autumn and his collaborators [55] first observed in gecko toe pad structure that dragging along the natural curvature of the setae is necessary to generate sufficient adhesion for attachment. Further analyses on this phenomenon were made by
Tian et al. [119] and Chen et al. [137], in order to describe the underlying mechanism of frictionally enhanced adhesion. However, molecular mechanism remains unclear, mainly because of the breakdown of the continuum level principles and/or energy based nature of their theoretical derivations.
In our studies for the CNT based dry adhesive system, we hypothesized that the curly entangled segments on top play a crucial role in regulating the adhesion and friction at the nanoscale contact interface. Moreover, investigating the interfacial adhesion and friction forces and their effects on CNT peeling is essential for understanding the local contact deformation and premature failure of the fibrillar-like materials, which determine the durability of artificial dry adhesives. Hence, at the nanoscale, fully atomistic molecular dynamics (MD) simulation was performed to study the peeling behaviors of a single laterally distributed CNT from an amorphous carbon (a-C) substrate.
77 4.3.2 Methodology
The systems simulated are composed of a single-walled carbon nanotube
(SWCNT) adhering to an a-C substrate (Figure 4-3). SWCNTs in armchair configurations (T (6, 6)) were generated with the graphitic C-C bond length of 0.142 nm.
The nanotubes with a diameter of d = 0.81 nm and lengths of L = 15 ~ 60 nm were used in calculations. The length of the a-C substrate is larger than the SWCNT such that the entire contact interface undergoes peeling and sliding within the substrate. Specifically, a diamond substrate of ~ 2.4 nm in width and ~ 1.2 nm in thickness was created first with
[100] direction parallel to the SWCNT axis. The amorphous substrate was then generated by melting of the diamond atoms at 7000 K and subsequent quenching into 0.5
K, while keeping the SWCNT frozen in their ideal positions. During the heating and cooling processes, the substrate was allowed to expand and homogenize in a certain space to control the final density of the a-C substrate to be in the range of ρ = 2.2 ~ 2.4 g/cm3.
After that, the a-C surface was saturated by hydrogen atoms so as the left end of
SWCNTs and further relaxed, in order to produce truly non-polar dispersive surfaces.
The ideal SWCNT structures were also relaxed separately at 0.5 K and then moved to gradually approach the substrate to initiate a contact. Finally, the entire system was fully relaxed to equilibrium at 0.5 K.
78
Figure 4-3 A, Close view of B, fixed peeling of 30 nm long SWCNT, armchair T (6, 6), from an a-C substrate with nanoroughness. Purple tube represents SWCNT, red beads represent saturating hydrogen atoms, pink beads represent a-C substrate, and white beads represent fixed carbon atoms at bottom.
Classical molecular dynamics method was employed via LAMMPS simulator.
With a Langevin thermostat to control temperature, the equations of motion were integrated with a time step of 0.1 fs. Simulation was performed by holding the two carbon rings of the SWCNT right-end as a rigid body, moving upward with/without lateral constrains, at a constant speed of ~5 m/s, achieving near equilibrium. To
79 eliminate the possible effect of the thermostat on measured friction, the thermostat coupling in the SWCNT and saturating hydrogen portion of the substrate was eliminated while the rest was still under the control of Langevin thermostat. Periodical boundary conditions were applied to the substrate in length (x-) and width (y-) directions.
The interactions between atoms were calculated using an AIREBO potential [138], with a modified cutoff scheme [139]. This many-body potential has been used to study the mechanical properties of CNTs and friction of diamond and amorphous carbon films
[124, 125, 140-142]. The Lennard-Jones (L-J) terms in AIREBO was turned off, instead, a general L-J potential with a cutoff distance of 10 Å was introduced between the
SWCNT and a-C substrate such that chemical bonding between them was avoided. The
SWCNT/a-C interfacial interaction is then described only by the L-J potentials:
12 6 U( r ) 4 r / r r / r 00 where the length r0 and energy ε are 0.3465 nm and 2.86 meV for carbon, and 0.281 nm and 0.741 meV for hydrogen, respectively, and the parameters for hydrogen-carbon interactions are obtained from the Lorentz-Berelot rules.
As an explicit method, energy dissipation mechanisms such as viscoelasticity and buckling of CNTs were naturally included in the model.
4.3.3 Results
Individual SWCNT was peeled off from an a-C substrate by pulling one end of the CNT upwards in the direction normal to the substrate. For comparison, we studied two cases of displacement controlled loading conditions: the lateral displacement of the
CNT pulling end is (i) fixed (namely fixed peeling) or (ii) unfixed (i.e., free peeling) while it is pulled upwards. In the fixed peeling, the end of the CNT is fixed in lateral (x-)
80 direction, similar to that in CNT peeling experiment done by Ishikawa et al. [113]. For the free peeling, the end is not fixed and can freely move in the x-direction.
Under the fixed peeling condition, after an initial peeling stage at the pulling end
(inset (a) of Figure 4-4A), both friction force (FL) and adhesion force (FN) gradually build up with a strong coupling effect. At this stage, the peeling occurs in a stick-slip manner and multiple peaks can be seen on the force-pulling distance curves. These peaks occur randomly due to the rough nature of the substrate; their magnitude depends on local
CNT-asperity interactions. Maximum friction and adhesion forces are achieved simultaneously at a point (inset (b) of Figure 4- 4A). After a significant separation, the
CNT configuration suddenly transforms from s- to arc-shape (inset (c) of Figure 4-4A), resulting in a rapid drop of the coupled forces. After this critical point, the edge of the other CNT end slides on the substrate, the coupling effect could also be observed but its value becomes much lower. Eventually, the SWCNT is pulled off from the substrate.
These results well agree the experimental results on single CNT peeling [113]. However, the frictional force was not measured simultaneously in these experiments.
Consequently, the important feature of peeling, frictional-adhesion coupling, was not observed. Nonetheless the normal force – distance curve obtained in our MD simulation is consistent with the experimental data available in the open literature. The friction- adhesion coupling captured by the MD simulation is similar to that observed in gecko footpads [55].
The boundary conditions have a significant effect on the friction and adhesion peaks. For the 30 nm long SWCNT, maximum adhesion force synchronically achieves
5.67 nN when frictional force reaches its peak value of 9.54 nN (Figure 4-4A). In
81 contrast, when the constraint of CNT pulling point in the lateral direction is set free, i.e., under free peeling boundary condition (inset of Figure 4- 4B) where no force is applied in shear direction during peeling, the adhesion force drops to much lower values (< 2 nN).
There is neither distinguishable peak nor significant force coupling effect during free peeling, as shown in Figure 4-4B. Obviously, a substantially high adhesion force FN is generated when high levels of friction force FL exist, whereas it becomes significantly low in the case of low friction.
(A)
82 (B)
Figure 4-4 Friction and adhesion forces of 30 nm SWCNT during (A) fixed peeling and
(B) free peeling. Insets in (A) are snapshots of the nanotube configurations at the points of (a), initial peeling, (b), peak force, and (c), pulling off. Inset in (B) is a snapshot of
CNT free peeling, maintaining negligible frictional force.
The effect of the lateral CNT length on the friction and adhesion forces (FL and
FN) was also analyzed and plotted in Figure 4-5. As the tube length increases, both of the maximum forces increase and eventually reach a plateau under the fixed peeling condition. However, for the free peeling with negligible frictions, the maximum normal peeling force is independent of the tube length and its value is much lower (FN = ~0.5 nN). This clearly demonstrates that frictional force can significantly enhance normal peeling force. There is a critical tube length beyond which the enhancement will level off. It is attributed to an additional bending moment imposed by the “fixed end”
83 boundary condition, which tends to open the crack tip at peeling front. For a CNT shorter than the critical length (e.g., tube length = 15 nm), this additional bending moment strongly affects the CNT contact region, preventing the peeling forces to build up.
However, this additional bending moment has a limited working distance (longitudinally
~20 nm). For a longer CNT (tube length ≥ 30 nm), the peeling front quickly moves out of the working distance upon loading. High friction and adhesion can then develop.
Since the achievable local friction force largely depends on the surface condition, rather than CNT length, increasing the tube length over the critical value cannot further increase the coupled reaction forces.
To quantitatively show the adhesion enhancement at this isolated “ideal case”, we define the ratio of the maximum adhesion force with friction over that without (or with negligible) friction as the nanoscale adhesion enhancement factor (analogous to in
FEA). The maximum value of reaches ~10, as extracted from Figure 4-5.
84
Figure 4-5 Maximum adhesion and friction forces as a function of SWCNT length under the fixed and free peeling conditions. Since there is no distinctive peaks and coupling effect during the free peeling (e.g., Figure 4- 4B), average forces are taken instead of maximum values, which are roughly at the level of 0.2~0.5 nN in terms of adhesion forces.
To further explore the enhancement mechanism, adhesion force is plotted against friction force in Figure 4-6 when the 30 nm tube undergoes fixed peeling. At zero friction there is an initial adhesion force of ~0.28 nN. There is a large scattering of the data mainly due to the thermal fluctuation, but a roughly linear relationship between the adhesion and friction forces can be extracted with a slope of 0.5057. The angle associated with the forces applied in normal and shear directions is determined to be
26.8°. Since it was measured throughout the peeling process, the adhesion force corresponds to the critical peeling force that the CNT can sustain at a given frictional
85 force. Hence, the angle extracted here represents a critical angle Ѳcri under which the adhesion enhancement is maximized. If the angle imposed by external loadings (Ѳapp in the inset of Figure 4-6) exceeds this critical value the nanotube will be peeled off spontaneously.
It is noteworthy that the peeling angle Ѳ defined here indicates the instantaneous relationships between the normal and shear reaction forces (FN/FL; adhesion force/friction force), when certain displacement controlled peeling is applied on one end of the tube. It is conceptually different from the peeling angle designated in the well- known Kendall model and the ones based on it [5, 137, 143], where the peeling angle is defined as the angle between the peeling film and substrate. We have calculated the angles between the CNT and substrate for a long CNT (tube length > 30 nm), and compared it with that defined by the forces applied in normal and shear direction. We found that the peeling angle associated with the force is very close to that between CNT and substrate except for those at the initial peeling stage. The difference in peeling angles at the initial peeling stage is caused by the effect of the “fixed end” boundary conditions which alters the configuration of the CNT near the peeling end. As the peeling front moves out of the effective distance of the “fixed end”, the two angles merge.
As will be discussed in Section 4.3.4, the critical angle Ѳcri used here is intrinsically determined by the conditions of surface roughness at a corresponding scale. In contrast,
Kendall elastic tape peeling model does not deal with the surface conditions of the contacting substrates because of its energy based nature.
We have calculated Ѳcri for different nanotube lengths (15~60 nm) and found that it is nearly constant (Ѳcri = 25.2 ± 1.3°) on the substrates with the same levels of
86 roughness. Interestingly, the critical angle calculated in MD simulation is very close to the value (24~30°) found in gecko setal release [55]. Presumably, the orientations of angled setal stalks are evolved in such a geometrical setting that gages the adhesion by controlling friction under the influence of surface conditions (i.e., roughness) at micro/nanoscale. From the above analysis, we can establish an empirical relationship between the adhesion FN and friction FL forces as:
FFFNOL (4-1)
where FO is the initial adhesion force, and η is the adhesive coefficient, which is the slope of the adhesion-friction curve or the tangent of critical peeling angle (η = tan Ѳcri).
87
Figure 4-6 Adhesion force as a function of friction force for 30 nm long SWCNT under fixed peeling. Ѳcri is the averaged critical angle. Ѳapp in the inset is the instantaneous angle of the reaction force, F, from the horizontal plane under displacement controlled peeling.
For comparison, an atomically smooth diamond substrate was generated to replace the a-C substrate used in the MD simulations, as shown in Figure 4-7A, B.
Figure 4-7C shows the friction and adhesion forces of the nanotube being peeled from an atomically smooth diamond substrate under the fixed peeling condition. With negligible frictional force, the adhesion force keeps lower than 2 nN, excluding the initial crack opening stage from the displacement of 0 to ~0.3 nm, and there is no distinguishable coupling effect between the two forces. These results suggest that surface condition (i.e., roughness) is of great importance in adhesion enhancement.
88
Figure 4-7 (A) Close view and (B) fair view of 30 nm long SWCNT, armchair T (6, 6), fixed peeling from an atomically smooth diamond substrate. Purple beads represent carbon atoms, red beads represent saturating hydrogen atoms. (C) Friction and adhesion forces of 30 nm SWCNT under fixed peeling from an atomically smooth diamond substrate.
4.3.4 Discussion
Obviously, there is a great advantage of utilizing atomistic molecular dynamics simulations to build the nanoscale pealing systems atoms by atoms, and explicitly calculate the interaction force distributions at the interface along with the reaction forces at the pulling end for different boundary conditions. In this way the missing picture between the discrete and continuum scales may be completed, whenever an emphasis on the nanoscale phenomena is highly important.
The adhesion enhancement revealed here is the result of molecular interactions between CNT and a-C substrate. Usually for a fiber/elastic-tape being peeled from a
89 substrate, three regions are classified as contact region (Region I), peeling zone (Region
II) and peeled region (Region III), as shown in Figure 4-8A. The friction force (lateral force; FL) is generated due to the frictional contact in the contact region (Region I) while the adhesion force (normal force; FN) is attributed to van der Waals interaction between the fiber and substrate in the peeling zone (Region II) [119]. The net normal force on the
CNT is assumed to be zero in Region I and III. However, to achieve enhanced adhesion force, there must be a region in which extra normal force is generated by friction to balance the total applied load. We found that this particular region is located right in front of the peeling zone, namely adhesion-enhancing zone (Region IV as shown in
Figure 4-8B). This region has a unique geometric feature, where the nanotube curves up, forming an upward slope due to a pre-existing asperity. This configuration could also be reinforced by sink-in of the nanotube into the substrate and pile-up of the substrate superficial atoms under the local adhesion and friction forces, given a relatively soft substrate. It has been indentified that both of the aforementioned effects exist in our MD simulations with the former being more dominant. In either case, the slope will cause a resultant of local friction force in the normal direction (z-direction) due to the hindering effect of the asperity. Such friction resultant directly contributes to the resistance to the normal peeling force, FN.
Figure 4-8B shows the tube axial strain, along with the height profiles of the CNT and that of the substrate contacting surface underneath the CNT, when adhesion and friction forces (FN, and FL) reach a peak. At this point, the axial strain in the contact region (Regions I) is low but it jumps up to a higher level in the Region IV and become nearly constant in Regions II and III. The rapid change in strain reveals the existence of a
90 large static frictional force on the nanotube in Region IV. Such a high frictional force is attributed to the mechanical interlock of the nanotube on a single asperity, which results in a severe local CNT deformation, as shown in Figure 4-8A. In fact, at the left side of the asperity (adhesion enhancing zone, Region IV), large lateral compressive force between the tube and sloping surface of the substrate are generated under fixed peeling conditions, because of the drastically increased Pauli repulsion of the particles having overlapping orbitals at short ranges. Such compressive force (or resisting force) is different from the van der Waals attractive force (dispersion force), which is generated due to correlations in the fluctuating polarizations of nearby particles and relatively weak.
As previously described, we have performed nanotube peeling from an atomically smooth diamond surface with hydrogen saturation under the same fixed peeling conditions (Figure 4-7). No such enhancing phenomenon is observed mainly because there is a lack of asperity on the flat diamond surface, which is also very dense and hard.
Apparently proper asperities are necessary to generate large friction force and in turn large adhesion force. For the SWCNT/a-C systems in our MD simulations, the height of the single asperity is measured as 2.0 nm, and the length of the adhesion-enhancing zone is l 2 nm.
91
Figure 4-8 (A) Snapshot of nanotube peeling from a-C substrate with nanoscale roughness and asperities, showing different interfacial regions of tube-substrate interaction and local tube deformation. (B) CNT axial strain, height profiles of CNT and substrate near peeling region when the coupled adhesion and friction forces reach a peak for 30 nm SWNCT.
92 We consider the peeling of a fiber from a substrate, as shown in Figure 4-9. Four regions are classified as Region I: contact zone, Region II: peeling zone, Region III: peeled zone and Region IV (located in contact zone to the right, bordering with peeling zone): adhesion-enhancing zone. As seen in Region IV there is a unique geometric feature, in which both the nanotube and substrate surfaces curve up forming a positive slope because of the pre-existed single asperity on the substrate (the effect of “sink-in” of the tube and “pile-up” of the substrate might also make significant contribution). In
either case, the slope will cause a resultant of local friction ( FF ) in the normal direction
(z-direction) ( FF,z ). Since the normal force on the fiber is zero in Regions I (excluding
Region IV) and III, the total normal force (adhesion) FN is the sum of the normal force in
Region II and IV, as follow:
FN fz () x dx (4-2) Regions II, IV
93
Figure 4-9 Molecular mechanism of friction-enhanced adhesion. (A) Schematic of single asperity as mechanical interlock to generate extra normal (adhesion) force. (B) Snapshot of nanotube peeling from an a-C substrate with nanolevel roughness/asperities, showing different interfacial regions of tube-substrate interaction.
For a fiber attached on a substrate, the attractive force arises from the van der
Waals interaction per unit length on the fiber is described as:
Hd f (4-3) vdW 16D2.5
94 with the Hamaker constant H, the nanotube diameter d and the gap distance D between the nanotube outer layer and the substrate [84]. There is a cut-off gap distance D = DO, representing the effective separation between the nanotube and substrate, at which
max maximum attractive force FvdW is estimated. The contribution of the van der Waals forces to the normal force is described as:
x x 2 H d3 H d F dx dx (4-4) vdW,z 16DD2.5 16 2.5 xx12IV II
where x1 to x2 represents Region IV having a horizontal length of l and x2 to x3 represents
Region II. At the critical peeling condition, fvwd at the asperity point of x = x2 will be reaching a maximum value, beyond where the contacting surfaces detach spontaneously.
Assuming that DIV = DO in Region IV, and the bending angle Ѳ of the fiber as well as the curvature of corresponding substrate keeps the same across, so that the curved slop is simplified as a straight line making a constant angle of Ѳ with the imaginary horizontal plane. Moreover if the slope on the other side of asperity is shallow, DII in the second term (Region II) becomes DO + x tanѲ and Equation (4-4) can be simplified as:
Hl d D 0 FvdW,z 2.5 (1 ) (4-5) 16Dl0 1.5 tan
Similarly, we can get the van der Waals interaction induced forces in the lateral direction (x-direction) located in Region IV as:
95
Hl d FvdW,x 2.5 tan (4-6) 16D0
The local friction force FF in Region IV can also contribute to the normal force
by generating a resultant force FF,z as:
x2 FF,z f F () x dx (4-7) x1
where fF(x) is the friction force on the nanotube. If there is a single asperity, the friction force generated by mechanical locking should act on the asperity point of x = x2. Since the friction force is relatively small in the contact region, as predicted by molecular dynamics simulation, the total frictional force can be approximated as the force on the asperity point in Region IV. Then we will have the following relationships:
FFF,zx F, tan (4-8)
FFFF,xx vdW, L (4-9)
Adding together the normal contributions from the van der Waals interaction and that of local friction at Region IV, i.e. combining Equation (4-5), (4-6), (4-8) and (4-9) yields:
96
Hl d D 2 0 FFFN vdW,zz F, 2.5 (1 tan ) FL tan (4-10) 16Dl0 1.5 tan
Obviously there is a linear relationship between FN and FL and if we designate the constant tanѲ as the adhesive coefficient η, Equation (4-10) could be rewritten concisely as:
FFFNOL (4-11)
Hl d D 2 0 where tan and FO 2.5 (1 tan ) are both constants for a 16Dl0 1.5 tan specific peeling system.
We assume the deformation of the fiber in Region IV can be described by the
Timoshenko beam theory with a constant angle Ѳ. From the theory, the adhesive coefficient can be written as
F F l 2 NN (4-12) k2 GA2 EI
where EI and GA are bending and shear stiffness respectively, and k is the Timoshenko correction factor (k = ~ 0.638 for circular cross section). At the asperity point, the normal displacement should be equal to the height of the asperity δ:
97 F l F l3 NN (4-13) k2 GA3 EI
Combining Equation (4-12) and (4-13) we have:
1/ 2 (4-14) l 1/ 3
EI (4-15) k22 l GA
where is a dimensionless parameter related to bending stiffness EI and shear stiffness
E GA. For isotropic materials, G , where ν is the Poisson ratio. Taking do and di 2(1 ) as the outer and inner diameters of SWCNT, respectively, we have:
(1 )(dd22 ) oi (4-16) 8kl22
Interestingly Equation (4-14) and (4-16) suggest that the adhesive coefficient η depends mostly on the geometry of fiber and substrate asperity, since the only material parameter involved is the Poisson ratio which usually varies from 0.2 to 0.5 for most materials.
The deformation of the CNT in Region IV of Figure 4-9 (l = 2 nm), predicted by the Timoshenko beam theory, is compared to the molecular dynamics (MD) simulation.
98 When the normal applied force on the asperity is FN = 5 nN, which is the case in MD simulation, the deflection of the CNT in Region IV is:
FF w() xNN x [ l2 3 l 2 x ( l x )3 ] (4-17) k2 GA6 EI
Figure 4-10 shows that the center-line deflections of SWCNT in Region IV predicted by the MD simulation and the Timoshenko beam theory well match each other, which confirms the assumption made above.
Figure 4-10 The center-line deflections of SWCNT in the region predicted by MD simulation and Timoshenko beam theory.
99 Taking the value of do= 0.97 nm, di = 0.63 nm, v = 0.19, δ = 0.2 nm and l = 2 nm, we have η = 0.159 or Ѳ = 9.0°. The value is relatively low compared to the MD simulations, mainly due to the neglect of local CNT deformation at the asperity (Figure
4-8A). Accounting for the local deformation yields η = 0.368 and Ѳ = 20.5°, much closer
-20 to the MD results. Using the values of H = 6×10 J, D0 = 0.34 nm, [84] we estimate FO
= 0.26 nN, which also agrees with the MD simulations. From these analyses, it is clear that the adhesion enhancement depends largely on the nanotube geometry, surface roughness and local deformation.
As shown in Equation (4-10), the adhesive coefficient η or the critical angle Ѳcri is an important factor in determining the adhesion enhancement. The adhesion enhancement factor for CNT systems is ~10, calculated the fully atomistic MD simulations at the nanoscale. This enhancement factor could also be estimated by other types of analytical models such as energy-based Kendall’s model [143]. Although the geometrical conditions in Kendal’s peeling model are not the same as those in our multiscale simulations, it is justifiable to see if the predictions from the energy-based approach are consistent with the detailed force analysis, at the continuum/macroscopic level for similar peeling processes. According to the definition, the adhesion enhancement factork is the ratio of the normal peeling force with friction to that without friction. From Kendall’s model, the resultant peeling force in shear direction is zero for a peeling angle of Ѳ = 90°. It is reasonable to assume that frictional force is zero at Ѳ =
90°. Thus, the enhancement factor can be determined from Kendall’s model as
100 2 sin 1 sin EA k . (4-18) 2 2 1 cos 1 cos EA
where is the van der Waals interaction energy, and E and A are the Young’s modulus and tape thickness, respectively. A simple analysis on Equation (4-18) shows that there is a critical angle, at which k reaches a maximum value. Taking the value of A = do =
0.97 nm, E = 500 GPa, and= 0.3~0.4 J/m2, [78] we estimate the maximum enhancement factor k= 6.1~6.6, very close to our results from FEA and MD simulation.
Analysis via Equation (4-18) also shows that the enhancement factor is a weak function of Young’s modulus, which is consistent with our analysis. However, the critical angle
(~12°) predicted from Kendall model is quite lower than those obtained from FEA and
MD simulation. More recently, a modified Kendal’s peeling model has been proposed by introducing a pre-tension term [137]. Critical angles derived in their models are much more consistent with our results. They show a ~26° force-independent critical angle for gecko fibrillar structures when pretension makes the pull-off force plunges to zero.
Table 4-1 lists the critical angles and adhesion enhancement factors for various fibrillar materials, calculated from the experiments [55, 84, 144] and simulations. The critical angles are in a narrow range between 20~30° for the materials with completely different properties. This suggests that the critical peeling angle is relatively insensitive to materials types, which agrees with the predictions of the analytic models described above.
101 Table 4-1. Parameters calculated for the adhesion enhancement of various materials
Critical angle Adhesion Enhancement Materials (°) coefficient factor
Gecko setal array 24.6~30 0.430~0.597 20~29
Polypropylene fiber array 15~24 0.268~0.445 9~11
MWCNT array 21~24 0.383~0.445 2~5
Individual SWCNT 25.2 0.468 ~10
As shown in Table 4-1, among these fibrillar nanostructures, gecko setal arrays exhibit the highest adhesion enhancement ( = 20~29) while most synthetic materials have relatively low enhancement factors (< 10). According to our analytical derivations, to achieve a large enhancement factor or force anisotropy in synthetic dry adhesives, it is important to reduce the initial adhesion force FO, or increase the interfacial friction force
FL. This could be done by modifying the geometry and surface chemistry of the contacting layer (i.e., the laterally distributed segments in VA-CNT arrays). For example, mimicking gecko seta-spatula structure, one could make all the second-level
CNT segments oriented in one direction instead of randomly distributed. When the hierarchal CNT arrays are peeled freely in the normal direction, the initial adhesion force
FO would be significantly reduced. As a result, the force anisotropy between the normal and shear directions could be further promoted.
102 4.3.5 Conclusions
A molecular mechanism of interfacial adhesion enhancement due to the lateral
CNTs was revealed, in which the adhesion force is strongly enhanced by interfacial friction because of pre-existing asperities on substrate. A linear adhesion-friction relationship was established based on MD simulations and theoretical analysis. The critical angles of the CNT segment peeling from a-C substrate were calculated and the values are comparable to those for gecko and other synthetic adhesives. The analytic model predicts that the critical angle is mostly dependent on the fiber geometry and surface roughness but relatively insensitive to the material types and mechanical properties, which is consistent with experimental data published in open literature. Most importantly, a significant buckling of the lateral CNT at peeling front is captured on the molecular level, which provides a basis for the fundamental understanding of local deformation, and failure mechanisms of nanofibrillar structures, and gives an insight of the durability issues that preventing the success of artificial dry adhesives.
4.4 Coarse Grained Molecular Dynamics
At the intermediate level, a fraction of the vertically aligned CNT arrays with laterally distributed segments on top were simulated by coarse grained molecular dynamics.
4.4.1 Model description
Coarse grained molecular dynamics models were developed to simulate the deformation, friction and adhesion of CNT arrays, by including the fiber-to-fiber and
103 fibers-to-substrate interactions at the micro-/meso- scale. The present models consist of
100 hexagonally-distributed vertically aligned CNTs with a diameter of d = 30 nm and a spacing of b = 68 nm, each of which attaches a segment of randomly oriented laterally distributed CNT of certain length at its top. To create the laterally distributed segments, we first generated an entire vertically aligned CNT array of certain height, in which each
CNT was divided into two portions. The beads in the upper portion were fixed in all degrees of freedom, while those in the lower portion were free in deformation. The nanotube array was then pressed onto a rigid surface. Under the pressing, the laterally distributed CNT segments were curved and completely contact the target surface on their sides. Finally, the bond length and bending angles of the beads in the deformed configuration were used as initial parameters to form the aligned CNT array with lateral segments. The deformed configuration was fully relaxed and then taken as the initial state of the hierarchical CNT structures. Figure 4-11 shows the initial state of a CNT array with 600 nm lateral segments on a target surface, modeled as chains of beads. Each bead represents a CNT segment with an aspect ratio L/d= 1. The target surface was modeled as an analytical plan and is not shown in Figure 4-11. Note that the initial state of the CNT array shown in Figure 4-11 is in a free state without applying any external load or boundary conditions.
104
Figure 4-11 Initial configuration of 100 hexagonally-distributed vertically aligned CNTs with 600 nm laterally distributed segments represented by beads.
The general expression of total steric potential energy, in coarse grained molecular dynamics, is the sum of energies due to valence or bonded interactions and non-bonded interactions between the beads, which is given in Equation (4-19)
1 2 1 2 1 2 U ks ()()() l L kb kt UV (4-19) 2 2 2
105 where the first three terms on the right-hand side of Equation (4-19) represent the potential energies for the stretching with bond length l and original bond length L, bending with bending angle θ and original angle Θ, and torsion with torsional angle φ and original angle Ф between bonded beads, respectively, as schematically shown in Figure
4-12. ks , kb and kt in Equation (4-19) are the corresponding constants of stretching, bending, and torsion, respectively. Based on structural mechanics, only three stiffness parameters need to be determined for deformation analysis of CNTs, due to their rounded cross-sections. These parameters are tensile stiffness (EA), bending stiffness (EI), and torsional rigidity (GJ). The energy principle leads to a direct relationship between the parameters within structural mechanics and the force field constants of molecular
mechanics [145]. It can be established as ks EA/ l , kb EI/ l and kt GJ/ l , where l is the distance between the centers of each bead the same as the bond length in Equation
(4-19). In this study is set to be zero. The potential in Equation (4-19) leads to a linear model which is accurate in describing relatively small CNT deformations. For large deformations, more accurate models exist [146, 147].
The parameters used in Equation (4-19) were derived from a fully atomistic simulation [86, 148-150]. Briefly, an ideal multi-walled carbon nanotube of the desired length and diameter was generated. Molecular dynamics was used to simulate the stretching, bending and buckling behaviors using Brenner potential [151]. Young’s modulus, bending stiffness of the nanotube were then abstracted from the simulations.
106
Figure 4-12. Beads and small segments of a fully atomistic nanotube. Each bead represent a small segment of the nanotube.
The last term in Equation (4-19) represents the potential energy of interactions between non-bonded beads (fiber-fiber interaction), and those between beads and target surface (fiber-target surface interaction). These interactions are realized by introducing van der Waals forces between the beads and the “imaginary” target surface. The fiber- target surface interaction potential is determined by integrating the Lennard-Jones potential and can be approximated as:
AB U() r2 R (4-20) ct 1260rr7 6
107 12 6 where A and B are Lennard-Jones parameters ( A 4er0 , B 4er0 , where e = 2.286 meV, and r0 = 3.468 Å for carbon materials [150]), R is the nanotube radius, r is the distance between the bead and target surface, and ρc and ρt are the density of CNT and the
3 target surface (ρc = ρt = 2.0 g/cm ), respectively. The fiber-fiber interaction potential takes the same form as Equation (4-20), with ρt and r replaced by the density of CNT and fiber-fiber distance, respectively.
Since the target surface is simplified as an analytical surface, the frictional force
Ff between the CNT beads and the surface is introduced by the friction law:
2 A FF R (4-21) f tc 180r 8
where F┴ is the normal force on the target surface and µ is the friction coefficient (µ =
0.2 is assumed in this study) between the beads and the target surface. The direction of the frictional force on a bead is always in opposite direction of the total force (excluding the frictional force) on the bead. During the simulations, if the frictional force calculated based on Equation (4-21) is larger than the total force on a bead, the frictional force is set equal to the force but in the opposite direction, such that the bead is kept in the same position due to static friction.
During MD simulation, the upper two layers of the beads of the vertically aligned
CNTs were dragged laterally or normally with respect to the target surface at a constant speed of 3.64 m/s, which is generally sufficient to reach a near-equilibrium structure at a temperature of 300 K. The overall loading displacement was set up to 0.3 µm in each dragging direction. Periodical boundary conditions were applied on the CNT array.
108 4.4.2 Results and discussion
The snapshots of the CNT array with 360 nm laterally distributed segments under normal and shear loadings are shown in Figure 4-13. When the array is subject to normal loading, the whole CNT patch is lifted all at once, causing an immediate peeling of the laterally distributed segments from the target surface, i.e. a series of beads that contact the surface are successively separated from the surface. After peeling, as shown in
Figure 4-13B, C, the beads at the far ends still contact the target surface but each segment has only one bead at the tip contacting the surface. While the laterally distributed segments are gradually pulled straight, the tip beads slide along the target surface and are eventually pulled off simultaneously. As the CNT array being loaded in shear direction, the randomly-oriented CNT segments are dragged almost straight along the lateral direction (Figure 4-13E-H) mainly because of their frictional interactions with the target surface. The vertically aligned CNT “trunks” are also tilted toward the shear loading direction to an extent, which is determined by the values of friction coefficient. These phenomena are consistent with the experimental observations in Ref. [84].
109
Figure 4-13 Snapshots of the CNT array with 360 nm laterally distributed segments under normal loading, (A) to (D), and shear loading, (E) to (H).
Normal and shear stresses between the laterally distributed CNTs and target surface were calculated for various lengths of the lateral segments, and the stresses versus displacement curves were plotted in Figure 4-14.
110
(A)
(B)
111 Figure 4-14 (A) normal and (B) shear stresses of CNT array with different length of laterally distributed segments. The numbers in the legends represent the lengths of the laterally distributed segments.
Figure 4-14A shows the normal adhesive behaviors. For a given laterally distributed length, there is a peak stress at the displacement of approximately 2~5 nm, followed by a secondary peak at a larger displacement. The displacement at which the secondary peak occurs also becomes larger as the laterally distributed length increases.
In all cases, the first peak stresses are relatively lower than the secondary ones. As the length of laterally distributed segments increases, the altitudes of the first peaks vary while the heights of the secondary peaks keep nearly constant. The presence of duel peaks and the historical adhesive behaviors captured above are attributed to the unique deformation mechanisms of the two-level CNT structures under normal pulling.
As mentioned earlier, when a normal displacement is applied to the CNT array, the laterally distributed segments will be peeled off in a first stage. But at the very beginning of this stage, since the initial geometry of each CNT side/line contact is generated randomly and “locked-in” before loading, within a very short displacement range, there is a crack opening process for each lateral CNT and the collective effect results in a suddenly increase of the reaction stress (i.e., first peaks). Because of the random orientations of the lateral CNTs, this peak values varies among different arrays.
At this very stage the curves are very sharp, so that the corresponding separation energy becomes trivial. Beyond this peak the peeling undergoes a crack propagation process from the stems towards the tips. Depending on the frictional input (i.e., frictional
112 coefficient), the curves drop to a lower level, in our case virtually zero comparing to the peaks. Then, after a pinning or transition point, the interfacial stress builds up again, by gradually involving the pulling of the tip end of each CNT all at once. After consecutive pulling-off of the lateral beads, the tip beads, which are still in contact with the target surface, undergo a sliding along the target surface. Ultimately, the separation between the last beads and the target surface generates the second peak in the traction- displacement curves. CNT array with longer lateral segment would need larger applied displacement to be pulled off. Thus, for longer laterally distributed CNTs, the secondary peak appears at larger displacements. However the intervals of the pinning/transition points becomes smaller and smaller upon increasing the lateral lengths of CNTs, and almost merges at the displacement about 2 µm. In turn, fracture energy (or separation energy), corresponding to the secondary peak, becomes larger as the length of laterally distributed segments increases. However, the height of the secondary peak almost remains constant because the same separation mechanism occurs at the final pull-off event. From the above analysis, it is clear that the first peak is due to the crack initiation while the secondary peak is caused by the peeling and separation of the tip beads from the target surface. The effect of secondary peak overrides the first peak regarding the contribution to separation energy.
Figure 4-14B demonstrates the fictional adhesive behaviors. For the length of the laterally distributed segments longer than a certain value (e.g. 360 nm), the frictional force increases almost linearly to a maximum value (failure initiation point) and then decreases slowly (failure evolution process). Further simulation processes are cut-off for the sake of reasonable computational expenses. But comparing the different reaction
113 stresses/forces among the samples, we could expect a level-off of the corresponding curves after the random-oriented segments are dragged into laterally aligning side/line contact CNTs. Once the laterally distributes segment are deformed into a more stable configurations, a constant frictional behaviors will be established. The tube-tube interactions tend to prolong such lining-up processes. Our observations on the deformation of CNT array, during shear loading, show that the frictional peaks are caused by the adjustment of the orientations of the laterally distributed segments before the onset of significant sliding of the whole patch. Longer laterally distributed segment results in higher peaks and also higher fracture energy (area under each curve). For the case of the laterally distributed segments less than 360 nm, the frictional stress increases slowly, and there is no obvious peak generated. This suggests that for short laterally distributed
CNTs, the interfacial tube-tube crowding is much lower and the interference between tubes are minimal, so that the friction reactions due to the orientation adjustment is not large enough to generate a peak before a relatively stable frictional behavior is achieved.
It should be noted that friction and adhesion behaviors shown in Figure 4-14 are the collective effects of 100 nanotubes with the same length of laterally distributed segments. In reality, the length of the laterally distributed segments may vary within the same array. To account for the effect of the length variations, one can simply use the same procedure described above to compute the shear and normal stresses by varying the length of the laterally distributed segments within the array. This, however, requires developing large collection of models to possibly capture the effect of the length distribution and the work is nontrivial. Instead of performing such a large amount of
114 simulations, here, we assume that the probability p(x) of certain length of the laterally distributed segments in a CNT array can be described by a Gauss distribution
1 (xm )2 px() exp( ) (4-22) (SD ) 2 2(SD )2
where x, m and SD are certain length of the laterally distributed segments, mean and standard deviation, respectively. The effective stress or traction in normal or shear
direction (Tns, ) can be calculated by integrating Equation (4-22) with respect to laterally distributed length:
Tn,, s p()(,) xn s x dx (4-23) 0
where ns, (,)x represents the normal or shear stress calculated using CGMD simulation for certain laterally distributed length (x) at certain displacement (δ) under normal or shear loading. can be obtained by interpolating the data from Figure 4-14.
The results derived are the effective stress-displacement curves in shear or normal direction with respect to certain normal distribution parameters, mean (m) and standard deviation (SD). Figure 4-15 shows an example of the effective stress as a function of displacement under shear and normal loading, where m = 135.38 nm and SD = 240.11 nm. The first peak effect was neglected in the calculation of the normal stress due to the domination of the secondary peak for breaking the fiber-target surface interactions. The
115 effective stress-displacement curves can be used as an appropriate input for the traction- separation law in FEA. As shown in Figure 4-15, the separation behaviors in both normal and shear directions could be described by bilinear curves with one peak values that represent the onset of the specific interfacial failure initiation points.
50 Shear
40 Normal
) 2 30
20 Stress (N/cmStress
10
0 0 0.2 0.4 0.6 0.8 Displacement (µm)
Figure 4-15. Effective stress and displacement curves under shear and normal loading, derived by combination of MD simulation results and normal distribution of the laterally distributed length, where m = 135.38 nm and SD = 240.11 nm.
4.4.3 Conclusions
Coarse grained molecular dynamics simulations enable us to study the normal and lateral interfacial adhesive behaviors of a small fraction within an entire hierarchical CNT patch. This intermediate model serves as a bridge to connect the atomistic simulations to
116 the device-level continuum FEA models. On this microscopic level, tube-tube and tubes- substrate interactions were explicitly calculated under pure normal and shear loadings. In normal pulling tests, duel peaks were generated on the displacement vs. stress curves, with the secondary one being more dominant in terms of separation energies. For shear loadings, single peak stresses were obtained especially for those having longer laterally distributed CNT segments. The randomly oriented lateral CNTs are proven to be crucial in regulating the adhesion and friction behaviors through different detaching mechanisms, for instance, consecutive peelings, pull-off, parallel dragging, as well as interactions among them when the interfacial CNT crowding builds up. Gaussian distributions of the lateral CNT lengths were incorporated with the simulation results with identical ones, to account for the real length variations in the experimental samples. Bilinear relations between loading displacement and interfacial stresses were extracted, which could be further utilized as the interfacial input at a height length and time scale. Even though the substrates were setup as imaginable idealized flat surfaces with van der Waals interactions and macroscopic concept of frictional coefficient, the adhesive behaviors capture are setting up the base line for studying the adhesion and friction, where the atomistic force coupling and the enhanced adhesion forces when interfacial friction exits meet.
4.5 Finite Element Analysis
At the device level, a cohesive zone featured finite element model was established for simulating the entire CNT arrays, where the key interfacial cohesive parameters were
117 not only indentified but also quantified via a data fitting process with the results from the experimental force measurements.
4.5.1 Model description
Two dimensional finite element models were created to simulate the macro-level deformation, failure, and friction and adhesion behaviors of the hierarchical CNT array with the same dimension (4×4 mm2) as the experimental samples reported in Ref. [84].
Software package Abaqus 6.8-2, was employed to perform the finite element analysis
(FEA). The finite element models consist of four parts: a cohesive zone, a number of vertical beams, a horizontal beam, and an analytical plane, representing laterally distributed CNTs, vertically aligned CNTs, substrate and target surface, respectively, as schematically shown in Figure 4-16.
118
Figure 4-16 Schematic of the CNT based dry adhesive pad contacting a target surface.
Specifically, friction and adhesion behaviors of CNT array at the device-level were treated as the fracture resistance of a cohesive layer. Thus, a cohesive zone model was adopted to simulate the interactions between the laterally distributed CNTs and the target surface. This cohesive zone features distinct traction-separation relations in pure shear and pure normal directions, and a layer of cohesive elements serve as an interface or path for crack initiation and propagation. The bilinear traction-separation laws, as shown in Figure 4-17, were derived from the coarse grained MD simulations discussed earlier. Equation (4-23) describes the normal traction-separation law of each cohesive element.
119 T i T N when 0 i NN i NN N (4-24) T i N f i f TN fi(NN ) when NNN NN
where the subscript “N” refers to “normal direction”, the superscripts “i” and “f” refer to
i “damage initiation point” and “damage finishing point”, such that TN designates the
i normal cohesive strength, N designates the normal displacement jump between two
f cohesive surfaces when damage initiates, and N designates the normal displacement jump when separation completes. Likewise the traction-separation law in lateral direction takes the same form as the pair wise Equation (4-24) with the subscript “N” being substituted by “L”. So, there are totally six coefficients for this uncoupled cohesive law.
Figure 4-17 Typical traction-separation responses used in FEA simulations.
120 i i ii ii In our simulation, the N and L was controlled by ET NN/ and GT LL/ ,
ff respectively. NL = 3 µm, E = 0.5 MPa/µm and G = 2.0 MPa/µm were taken in the
i i simulation. TN and TL were obtained by matching the experimental results. In doing so, two provisional values for and , together with other four fixed coefficients, were loaded into an initial FE input file, run in Abaqus, and normal and shear force data from the analysis were extracted from the FE output files. Adjustments to the coefficients were then made to reduce the error between experimental and FEA values.
Using this approach, the empirical dependency between interfacial adhesion and friction forces, which are represented by the normal and shear cohesive strengths respectively, could be easily deduced by fitting with the experiment data since adjusting the cohesive law parameters in one direction would not disturb the other. In this phenomenological model, possible energy dissipation mechanisms in the VA-CNTs body, such as the slightly unbuckling process and/or viscoelastic properties, will be implicitly reflected in the cohesive parameters that are calibrated with experimental data.
Thus, the vertical CNT segments are modeled as an ideal elastic system.
The vertical aligned CNTs were modeled by 101 vertical beams with a spacing of
40 µm. Each beam represents a number of vertically aligned CNTs. The effective mechanical properties of the beam were calculated from an array of 5~6 layer multi-wall
CNTs with an outer diameter of d = 15 nm, density of ρ = 5×1010 tube/cm2, and Young’s modulus of 1040 GPa. The effective cross section (radius) of the beams was calculated as S = ~362 nm for a straight CNT array with no interaction between CNTs. However, the CNTs in the synthetic adhesives are not perfectly straight and contact with each other, which could significantly increase the bending stiffness of the CNT array. To include the
121 effect of fiber-fiber contact, we obtained the effective radius of the beams by fitting the height of deformed samples under shear loading. The effective radius of the beams could be described as: S = -2.8×10-5h2+0.021h+0.25, (h = 5~150 µm), where h is the height of the vertical beams. Each vertical beam was meshed into a number of three-node beam elements and the element at its bottom shares a node with the cohesive elements.
The substrate was modeled by one horizontal beam with a length of 4000 µm, and a rectangular cross section with an out-of-plane thickness of 4000 µm and a height of 380
µm. The horizontal beam was meshed into 100 two-node beam elements, and the nodes were sheared by the top nodes of the vertical beams. The bottom surface of the cohesive zone represents the target surface, the nodes of which were constrained in all translational degrees of freedom.
4.5.2 Results and discussion
The CNT adhesive structures simulated in FEA have two-level hierarchy: the vertically aligned CNT segments and laterally distributed CNT segments. The lengths of the vertical segments contribute to the sample thickness predominantly, when the experimental samples are gown thicker, yet the lateral segment may also vary especially then the sample thickness is extremely small. Both could be potentially affect the over performance of the CNT adhesive patches.
We first investigated the effect of the vertically aligned CNTs on the friction and adhesion strengths. Figure 4-18 shows the results of the CNT adhesive patches with a fixed set of cohesive zone parameters (i.e., an averagely fixed length of laterally distributed CNT segments x, or fixed degree of lateral CNT crowding), but different
122 height of the vertically aligned CNT array h. The adhesion is almost independent of h, while the friction slightly changes with an increase of h.
35 Adhesion Strength Friction Strength
30
) 2
25 Stress(N/cm
20
15 0 25 50 75 100 125 150 175 Height of Vertically Aligned CNTs (μm)
Figure 4-18 Friction and adhesion strength as a function of the height of vertically
i i aligned CNTs h, where TN = 0.2 MPa, TL = 0.8 MPa, E = 0.5 MPa/µm, G = 2 MPa/µm,
f f and N = L = 3.0 µm.
These effects are attributed to the distinct deformation mechanisms of the entangled CNT adhesive structures under normal and shear loadings. The CNT array is highly anisotropic materials, which is stiff in the axial direction but much compliant in the transverse direction. The vertically aligned CNT array is highly curved under shear loading, as shown in Figure 4-19A. The shear loading also induces a bending moment on the CNT array, which depends on the height of the vertical CNTs. As a result, the
123 cohesive elements are subjected to both normal and shear forces under pure lateral pulling, and the adhesives may fail in normal direction since the normal force may
i exceed the normal cohesive strength TN . With an increase of the height of vertically aligned CNTs, the normal force acting on the cohesive zone increases, leading to the reduction of the friction strength because of the normal failure of the cohesive elements occurs before reaching the highest obtainable shear strengths. However, increasing shear loading also reduces the effective height of the CNT array due to a curving-down deformation, which alleviates the bending moment or normal force on the cohesive elements. These two factors are almost cancelled out during shear loading in our case, making the friction less sensitive to the height of the vertically aligned CNTs. On the other hand, during normal loading, the whole adhesive pad is stretched uniformly (Figure
4-19B) and the change in the height of vertically aligned CNTs does not affect the deformation of the cohesive elements, such that a relatively constant normal strength is observed. Hence the vertical CNT heights are ruled out for significantly influence the microscopic adhesive behaviors.
124
Figure 4-19 Snapshots of FEA-predicted deformation of vertically aligned CNT array with h = 150 μm, (A) under shear loading, (B) under normal loading and (C) at initial state.
The effect of the laterally distributed CNTs (described by the traction-separation laws) on friction and adhesion behaviors were studied by adjusting the cohesive parameters for a given height of vertically aligned CNT array (h = 100 µm). There are
i i f i i f totally 6 parameters ( TN , N and N in normal direction, and TL , L and L in shear direction) in the bilinear cohesive laws, describing the damage initiation and evolution of the cohesive elements in normal and shear directions. We have studied the influence of
and on friction and adhesion, and found that the effects of these parameters are trivial. Similar results are obtained for the parameters, and .
125 Figure 4-20 shows the friction and adhesion of the adhesive pads as a function of
i i shear and normal cohesive strengths, TL and TN , respectively. For a given , the friction linearly increases and then reaches a plateau with an increase of , while the adhesion keeps constant (Figure 4-20A). The turning point of the friction suggests that there is a mode-transition from shear failure to normal failure of the cohesive elements.
As increases to the critical point, the adhesive patch will fail in normal direction due to the increase of bending moment induced by the shear loading. In comparison, if is fixed, the adhesion is a linear function of , but the friction increases gradually at first and then becomes independent of when exceeds a critical value, as shown in
Figure 4-20B. In this case, there exists an opposite mode-transition shifting from normal dominant to shear dominant failures after a critical value.
50 Adhesion Strength
40 Friction Strength
) 2 30
20 Stress (N/cmStress
10
0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Shear Cohesive Strength, TL (MPa)
(A)
126 100 Adhesion Strength 90 80 Friction Strength 70
) 2 60 50 40 Stress (N/cmStress 30 20 10 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Normal Cohesive Strength, TN (MPa)
(B)
i i Figure 4-20 Effect of cohesive law parameters, (A) TL for TN = 0.2 MPa, and (B) for
= 0.8 MPa, on the friction and adhesion strengths for E = 0.5 MPa/µm, G = 2
f f MPa/µm, N = L = 3 µm and, h = 100 µm.
From the above parametric studies, it is obvious that among all the parameters in the cohesive laws, the cohesive strengths and are the critical ones in determining the macroscale friction and adhesion of the nanotube array. Because and are directly related to the laterally distributed segments of the CNT array, the combination of fully atomistic MD, coarse grained MD and FEA enables us to link the nanoscale structures of the dry adhesives to their macroscale friction and adhesion performance systematically. However, before any meaningful conclusion could be drawn upon any combinations of these three models, limitations and assumptions have to be justified
127 firstly, and then the connections, relations and interfaces between these three level simulations should be clearly indentified.
In principle, when the numerical models moving up into a higher length and time scale, some of the detailed information are giving up for the sake of including more structural complexities. From the fully atomistic MD to coarse grained MD, nanoscale surface roughness is simplified and described by macroscopic concept of friction coefficients, so that tube-tube interaction could be effectively studied. Likewise, when
FE models are built at the device level, the interfacial adhesion and friction interactions are decoupled from one another and described by distinctive traction-separation laws in normal and shear directions. These unavoidable treatments are aiming to facilitate the implementation of these models at a corresponding level, instead of scientifically proven.
Following analyses layout the basic logics of this multiscale modeling scheme and the underlining mechanisms will be revealed along with them. Generally speaking, the atomistic simulations and experimental measurements are deterministic, while the coarse grained MD and FEA models are the tools to bridge the two by correlating the interfacial micro- / nano- structure with the macroscale performances.
We first consider how the nanoscale structure and properties are related to
i macroscale adhesion of the adhesives. The normal cohesive strength TN for the dry adhesives can be determined from the FEA models by fitting the experimental data. On
the other hand, maximum adhesion force per unit area Pmax , generated by the interaction between CNTs and target surface, can be calculated using microscale interfacial interaction models. Since the same interfacial force is calculated from different approaches, the normal cohesive strength should be equal to the maximum adhesion force
128 i per unit area TN = Pmax . According to the CGMD simulation, the maximum adhesion force is the result of the nanotubes contacting with the target surface at their top ends.
Thus, the maximum adhesion force per unit area can be calculated by Equation (4-20)
2 which is simplified as Pmax Ad /12r , with the Hamaker constant A, the nanotube diameter d, and the gap distance between the nanotube surface and the target surface r.
There is a gap distance r = r0, representing the effective separation between the nanotube and the target surface, at which maximum attractive force is achieved. Using the
10 11 2 -20 values of d = 15 nm, ρ = 10 ~10 tubes/cm , r0 = 0.34 nm and A = 6.5×10 J, for glass surface [15, 117], the maximum adhesion force is estimated to be = 0.007~0.07
MPa, which is very close to the normal cohesive strength ( = 0.07~0.22 MPa) calculated from FEA by data fitting.
We further analyze the effect of interfacial nanostructures on the macroscale friction forces. It has been shown in CGMD simulations that friction force could be generated by the van der Waals interactions between the laterally distributed CNT segments and idealized flat target surfaces with a characteristic fictional coefficient. The
max maximum friction force per unit area of the nanotubes, Pf , should be equal to the shear
i cohesive strength, TL , which can be calculated with the FEA model by adjusting the shear cohesive strength to fit the experimental friction (Figure 4-21). Noticeably, in
max CGMD, is directivity related to Pn through an assumed fictional coefficient, 0.2, which is actually an undetermined parameter due to the simplifications of the surface roughness of the target surface. In fully atomist simulations, however, the relations between interfacial adhesion and friction are highly correlated and even a nano-scale
129 roughness will drastically increase the both adhesion and friction to a much higher level.
Most importantly, except for short CNT array, it is impossible to match the experimental
i results when previously-fitted TN for normal loading is used. As shown in Figure 4-21, for CNT height larger than 25 µm, the predicted macroscale friction strength starts to divert from the experimental curve, and the difference between them becomes large with the increase of the height of vertically aligned CNTs. We also tried to change other parameters of the traction-separation laws, e. g. changing f , from 3 µm to 10 µm, which is considered to be the upper limit since the actual laterally distributed length of the samples are just a couple of microns. But still the predicted friction strength could not match the experimental data. This clearly demonstrates that interfacial adhesion and friction are highly coupled phenomena, which is a special feature of the CNT fibrillar adhesive.
130 120 Adhesion Strength (Experimental Data)
Friction Strength (Experimental Data) 100 Friction Strength (Predicted from FEA, δf=3 μm)
Friction Strength (Predicted from FEA, δf=10 μm)
80 ) 2
60
Stress (N/cmStress 40
20
0 0 25 50 75 100 125 150 175 Height of Vertically Aligned CNTs (μm)
Figure 4-21 Predicted and measured friction and adhesion of CNT dry adhesives with different height of vertically aligned segments. Dashed lines represent the friction
i strength under shear loading, predicted by FEA using TN obtained from the fitting under normal loading. By increasing the values of displacement jump defining the complete
f f f separation, NL , from 3 μm to 10 μm, the fracture energy of the cohesive zone increases and predicted adhesion strength increases slightly.
Under shear loading, the cohesive zone elements (or laterally distributed CNT segments) are subject to not only shear stresses but also normal stresses due to the bending moment induced by the shear loading. When the normal stress on the cohesive elements exceeds their normal cohesive strength , failure will occur in the normal failure mode. In other words, high normal cohesive strength is required under shear loading conditions because the applied FL* can introduce a large moment (M=hFL*,
131 where h is the height of the adhesive pad, as shown in Figure 4-22, inset (a)) on the
i device, which could cause premature normal failure through the interface if TsN () were too small.
The simulation results show that the normal failure does occur for the CNT adhesives with a height larger than 25 µm. To match the experimental results (friction),
i the normal cohesive strength TN must be increased. Thus, there must be an enhanced adhesion in the biomimetic CNT based adhesives under shear loading conditions. Such an enhanced adhesion increases with an increase of frictional force. We have calculated the normal cohesive strength (denoted as ) of the interface under shear loadings by
i adjusting the cohesive parameters of and TL simultaneously to match the experimental results of FL* (inset (a) of Figure 4-22A) [84]. Likewise, the normal
i cohesive strength (refers to TnN ()) of the interface under normal loadings (inset (b) of
Figure 4-22A) was also calculated and both were plotted in Figure 4-22A. Compared to
, the normal cohesive strengths at shear loadings, , are much higher, especially for thicker samples.
The ratio of the normal cohesive strength under shear loading over that under normal loading ( / ) is defined as the adhesion enhancement factor , and shown in Figure 4-22B for samples with different VA-CNT heights. With increasing the height of the vertically aligned CNTs body, the enhancement factor increases and becomes constant (~ 5) after the height exceeds 100 µm. We have also fitted FEA with the experimental results for VA-CNT arrays without the laterally-distributed CNT segments [84]. No such enhancement is found. Apparently, the enhancement of the
132 adhesion forces under shear loadings is due to the existence of the laterally distributed segments.
Both FEA and fully atomistic MD simulations demonstrate that there is a strong enhancement of adhesion force due to the presence of friction force on the laterally distributed CNT segments. The FEA with experimental fitting suggests that the adhesion force could be increased by a factor of ~5, while the MD calculation indicates that the maximum enhancement value reaches ~10 for the SWCNT/a-C systems. Note that the interfacial behaviors predicted in FEA represent the collective effect of single laterally distributed CNT segments. Since the lateral segments on VA-CNT arrays distribute randomly in all directions, free peeling of those lateral segments within an array is prevented even under pure normal pulling (inset (b) of Figure 4-22A). Consequently, nontrivial amount of friction forces are generated, which in turn increases the adhesion forces under normal loadings. Thus, the enhancement factor that we derived at the device level is relatively low. However, the enhancement factor can be further optimized by making unidirectionally oriented lateral CNTs similar to that of gecko spatulae, so that upon normal pulling (in the releasing direction) most of the ultimate contacting elements could be peeled freely.
133
(A)
(B)
134 i Figure 4-22 (A) Normal cohesive strength TN as a function of vertically aligned CNT height, required for fitting the experimental data under normal and shear loading respectively. Inset (a) shows deformed VA-CNT array under shear/lateral loading, inset
(b) is the VA-CNT array under normal loading. (b) Adhesion enhancement factor (
i i TsN ()/TnN ()) against the height of VA-CNTs body, predicted by fitting FEA results to experimental data.
It should be clarified that, due to the pre-existing entangled top layer, the CNT side/line contacts readily forms once the adhesive patch is brought together with the target surfaces, without the need of inducing significant buckling of the vertical CNTs.
Theoretically, the CNT side/line contacts will spontaneously occur when the two surfaces are close enough in the working range of intermolecular forces, especially on smooth surfaces like glass and silicon wafer. Besides, the density of CNT side/line contacts could not be significantly modified by increasing the preloading because of the crowding of the contacting elements at the interface and the parallel tube-tube interference between neighbors. During the experimental force measurements the compressive preloading was a fixed value for each and every trial (i.e., a preload of about 2 kg) and was withdrawn before consecutive pulling tests were performed in either normal or shear directions.
Hence, the initial contact fractions (i.e., CNT side/line contacts) before shear or normal loadings should be comparable, and does not contribute to the adhesion enhancement factors.
In the fitting process above, in addition to the pulling force (FN* and FL*), the deformation of VA-CNT arrays was also matched up with the experimental results by
135 adjusting the shear modulus of the vertical beams in FEA (modeling vertically aligned
CNT stalks). The shear modulus is directly related to the fiber-fiber contact within VA-
CNT arrays, which has been observed in the experiment [84]. Under shear loadings, the moment induced angles between the bended “CNT stalks” and target surface at the failure point of cohesive interface were measured and plotted in Figure 4-23. This angle is almost constant with a value of 22.2 ± 0.6° (average value ± standard deviation) for different VA-CNT heights, indicating that it is independent of the geometry of CNT stalks. Since it was at the failure initiating point, the angle is defined as the critical peeling angle for interfacial failure, Ѳcri*.
Figure 4-23 Failure angles of the hierarchical VA-CNT arrays with different heights of
VA-CNTs body under shear loadings in FEA simulation. A critical peeling angle of Ѳcri*
= 22.2° is extracted from the experimental data through FEA. The inset illustrates a corresponding deformation of the VA-CNT array at interfacial failure.
136 The phenomena of the enhanced adhesion during shear loading have been observed in gecko adhesives and other frictional systems. Autumn et al. [6] observed that dragging along the natural curvature of setae is necessary to generate sufficient adhesion.
They also found that the ratio of the shear reaction force to the normal force remains almost constant, although the magnitude of the force varies. To explain their experimental findings, Autumn et al. [55] proposed a phenomenological frictional adhesion model, which was also adopted by Tian et al. [119] in modeling the adhesion of a spatula pad. Using a generalized Kendall model incorporating the effect of pre-tension,
Chen et al. [137] also show that peel-off force of a thin film from a substrate depends on the magnitude of pre-tension on the film. The pre-tension can significantly increase the peel-off force. These observations and analyses suggest that pre-tension/friction- enhanced adhesion may be a general phenomenon and may also exist in the CNT array although the underlying mechanism has not been look at in the discrete atomistic or molecular scales. However, our fully atomistic simulations explicitly capture the friction and adhesion coupling and give the friction enhanced adhesion a real physical explanation.
Since the strong friction force is mainly generated by the laterally distributed
CNT segments at the top of vertically aligned CNT array, the laterally distributed CNT segments must play an important role in regulating the adhesion. Controlling the morphology of the laterally distributed CNT segments could lead to dry adhesives with improved adhesion and friction. Thus, the multi-level hierarchical structures are critical to achieve high adhesive anisotropy and friction-enhanced adhesion. Our multiscale models link these unique phenomena to the microstructures of synthetic adhesives,
137 providing an insight into the friction and adhesion mechanisms in the bio-mimicking dry adhesives.
4.5.3 Conclusions
A phenomenological FEA model has been built to study the adhesive behaviors of the hierarchically structured CNT arrays at the device level. This numerical approach enables us to directly break down the structural and interfacial mechanics that lead to the anisotropic adhesive performances characterized in the experimental force measurements.
A cohesive layer featuring distinct cohesive laws in normal and lateral directions was incorporated to model the interfacial phenomena. Normal and lateral cohesive strengths have been proven as the curtail factors in determining the overall reaction forces on the loading ends. It has been shown during the data fitting processes that the adhesion and friction cohesive strengths are highly correlated, and a friction enhanced adhesion was revealed. A critical failure angle was extracted from the simulations with different vertical CNT heights under shear loadings, an intrinsic phenomenon captured in many other fibrillar adhesive systems.
138 CHAPTER V
CONCLUSIONS AND FUTURE WORK
5.1 Conclusions
(i) Dynamic self-cleaning in gecko setae
Geckos walking naturally and using DH exhibit a self-cleaning rate that is two-
fold higher than that measured without activating the animal triggered peeling
motions under DH. The extent of self-cleaning also ended up with much higher
values with DH enabled. 80% of clean forces were recovered after just 4 steps.
When DH was disabled, the extent of self-cleaning leveled off at 40-50% even
after taking 8 steps.
A cycloid model has been adopted for explaining the dynamic self-cleaning
mechanisms in gecko adhesive systems for the free ranging animals during
locomotion. Because of the nature of the adhesion force, asymmetric geometry
and animal triggered distal-to-proximal peeling, the rotating setae suddenly
release from the attached substrate, generating acceleration high enough to
dislodge dirt particles from the toe pads.
The peeling monition induced by gecko DH from distal to proximal ends plays a
crucial role in activating the dynamic setal jump-off event. This effect may be
introduced into the artificial fibrillar adhesives through external stimuli
responsive controls for achieving a higher self-cleaning capability.
139 (ii) Multiscale modeling and simulation of the hierarchically structured carbon nanotube arrays
A molecular mechanism of interfacial adhesion enhancement was elucidated for
individual carbon nanotubes peeling in fully atomistic MD. The adhesion force is
strongly enhanced by interfacial friction because of pre-existing asperities on
substrate, even with very tiny surface irregularities at the molecular or nano- scale.
A linear adhesion-friction relationship was established based on the large-scale
simulations with realistic force fields and theoretical analyses.
Significant local deformations and bucking of the carbon nanotube tube were
evidenced under the constrained peeling conditions manly results from a
mechanical interlock at the surface asperity. This effect is responsible drastically
increased adhesive forces, but at the same time, will cause structural ruptures
under cyclic loading and limit the serving life of CNT based adhesives.
The coarse grained MD simulation results show that increasing the length of the
laterally distributed CNT segments can largely promote the shearing force, while
keeping normal adhesion force almost constant. Bilinear cohesive laws have been
proven to be a good approximation for the consecutive computations at the
continuum level.
The adhesion and friction behaviors, as well as the structural deformations were
analyzed at multiple time and length scales using molecular dynamics simulations
and finite element methods, so that atomic configurations and microscopic
structures are linked to the macroscale adhesive performances.
140 The critical peeling angle derived at the nano- and macro- scale simulations has
been demonstrated to be intrinsically related to the adhesion enchainment factor,
which is mostly dependent on the fiber/tube geometry and surface roughness
while relatively insensitive to the material types and mechanical properties.
With a second-level hierarchy, laterally distributed CNT segments on top of
vertically aligned CNT arrays, the adhesion force could be enhanced by a factor
of 5 and 10 under macro-level pulling and nanoscale peeling, respectively. Thus,
further improvement on force anisotropy could be achieved by controlling the
morphology of the randomly oriented lateral segments to make them more
informally distributed as that of gecko setae.
5.2 Recommended Future Works
(i) Gecko self-cleaning mechanisms
Experimentally implement the AFM pull-off tests of individual setae on smooth
and flat surfaces to directly prove the jump-off event in highly branched
microfibrils.
Substitute the idealized substrates with others that have different attributes of
hydrophobicity or hydrophobicity and roughness, and then put dirt particles in
between the interface or attached freely on the functional fibrillar structures.
(ii) Carbon nanotube based synthetic dry adhesives
Integrate the hierarchically structured CNT arrays on stimuli-responsive
substrates or devices.
141 Utilize the prominent thermal and electrical properties of CNT based adhesives
for multi-functional controls and multi-physical applications.
Study the mechanisms of interfacial friction in micro-/ nano- fibrillar structures
and their transitions from nano- to micro- and to macro- levels.
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