dynamic adhesion and self-cleaning mechanisms of gecko
TRANSCRIPT
APPROVED: Zhenhai Xia, Major Professor Richard F. Reidy, Committee Member Thomas Scharf, Committee Member Peter Collins, Committee Member Jincheng Du, Committee Member Narendra Dahotre, Chair of the Department of
Materials Science and Engineering Costas Tsatsoulis, Dean of the College of
Engineering Mark Wardell, Dean of the Toulouse Graduate
School
DYNAMIC ADHESION AND SELF-CLEANING MECHANISMS OF
GECKO SETAE AND SPATULAE
Quan Xu
Dissertation Prepared for the Degree of
DOCTOR OF PHILOSOPHY
UNIVERSITY OF NORTH TEXAS
December 2013
Xu, Quan. Dynamic adhesion and self-cleaning mechanisms of gecko setae and spatulae.
Doctor of Philosophy (Materials Science and Engineering), December 2013, 130 pp., 5 tables, 65
illustrations, 165 numbered references.
Geckos can freely climb on walls and ceilings against their body weight at speed of over
1ms-1. Switching between attachment and detachment seem simple and easy for geckos, without
considering the surface to be dry or wet, smooth or rough, dirty or clean. In addition, gecko can
shed dirt particles during use, keeping the adhesive pads clean. Mimicking this biological system
can lead to a new class of dry adhesives for various applications. However, gecko’s unique dry
self-cleaning mechanism remains unknown, which impedes the development of self-cleaning dry
adhesives.
In this dissertation we provide new evidence and self-cleaning mechanism to explain how
gecko shed particles and keep its sticky feet clean. First we studied the dynamic enhancement
observed between micro-sized particles and substrate under dry and wet conditions. The
adhesion force of soft (polystyrene) and hard (SiO2 and Al2O3) micro-particles on soft
(polystyrene) and hard (fused silica and sapphire) substrates was measured using an atomic force
microscope (AFM) with retraction (z-piezo) speed ranging over 4 orders of magnitude. The
adhesion is strongly enhanced by the dynamic effect. When the retraction speeds varies from
0.02 µm/s to 156 µm/s, the adhesion force increases by 10% ~ 50% in dry nitrogen while it
increases by 15%~70% in humid air. A dynamic model was developed to explain this dynamic
effect, which agrees well with the experimental results. Similar dynamic enhancement was also
observed in aqueous solution. The influence of dynamic factors related to the adhesion
enhancement, such as particle inertia, viscoelastic deformations and crack propagation, was
discussed to understand the dynamic enhancement mechanisms.
Although particles show dynamic enhancement, Gecko fabrillar hair shows a totally
different trend. The pull off forces of a single gecko seta and spatula was tested by AFM under
different pull-off velocities. The result shows that both the spatula and the seta have a rate
independent adhesion response in normal retraction, which is quite different from micro-
particles. Further research indicated the shape of the contact area was a key factor to the dynamic
effect. In order to verify this hypothesis, artificial gecko spatula made of glass fibers was
nanofabricated by a focus ion beam (FIB) and tested by AFM. These manmade spatulae also
show a rate independent adhesion response. The dynamic adhesion of a single gecko seta and
spatula were simulated with finite element analysis and the results also confirm the rate
independent phenomena.. In conclusion, self-cleaning is induced by dynamic effect during gecko
locomotion. The relative dynamic adhesion change between particles and seta makes it possible
for gecko to shed the dirt particles while walking.
Finally, the fatigue property of gecko seta was examined with the atomic force
microscope under cyclic attachment/detachment process, mimicking gecko running. The
adhesion force versus cycles has been tested and evaluated. Fatigue mechanism of gecko seta
was also analyzed based on the experimental findings.
Copyright 2013
by
Quan Xu
ii
ACKNOWLEDGEMENTS
First I express my sincere gratitude to my advisor Professor Zhenhai Xia, for his constant
guidance, continuous advice and encouragement that lead me throughout this research. His
perceptiveness and sharp intuition in academic make me feel the research is interesting,
important and accessible. His tolerance and understanding, and continuous support during this
five research years help me and my family overcome many difficulties smoothly. He challenges
me with interesting research projects and I really appreciate those opportunities.
I am very grateful to Professor Richard Reidy. He gives me valuable suggestions on both
experiment design and dissertation writing. I should also thanks Professor Thomas Scharf, we do
the measurement with his sample with AFM and also learn many experiment skills in his lab.
And I should also thanks Professor Jincheng Du, he helps me broaden my view in modeling and
gives me many suggestion on career choosing. Finally I should thanks Professor Peter Collins,
most of my SEM, TEM and FIB skills are from him and his student. I do appreciate it.
Our collaborator Professor Narendra Dahotre, Professor Jun Lou and Professor Jianyu
Liang and Professor Peter Niewiarowski, Professor Sundeep Mukherjee, Professor Sheldon Shi,
give me a lot of inspiration and help during my research work. We have a wonderful cooperation.
I am very grateful to them. Thanks to my group members Mingtao Li, Shihao Hu, Lipeng Zhang,
Zhijun Ma, Jianbing Niu, Thanyawalai Sujidkul, Jie Wen, and Lili Li and my friend Wei Sun, Ye
Xiang, Hui Che, Han Wu, Wenshan Yu, Yee-Hsien Ho, Chuangwei Liu, Harpreet Singh Arora.
They give me many touching moments in my life.
Finally I want to thank my family, especially my wife Jie Li, for her continuous support
during these years, and my son Jaydon Xu, he gives me so much joy since his born, and my
parents and my parents in law, they always stand behind me. They are the love of my life.
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ........................................................................................................... iii
LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ....................................................................................................................... ix
CHAPTER 1 INTRODUCTION .................................................................................................... 1
Background ............................................................................................................. 1 1.1
Objective and Significance ..................................................................................... 2 1.2
Dissertation Outline ................................................................................................ 3 1.3
CHAPTER 2 LITERATURE REVIEW ......................................................................................... 6
Hierarchical Fibrillar Structure of Gecko Feet ....................................................... 6 2.1
Gecko Friction-Adhesion System ........................................................................... 9 2.2
Classic Contact Models......................................................................................... 10 2.3
2.3.1 Johnson-Kendall-Roberts (JKR) Model ................................................... 11
2.3.2 Derjaguin-Muller-Toporov (DMT) Model ............................................... 12
2.3.3 Maugis-Pollock (MP) Model .................................................................... 13
2.3.4 Comparison between JKR, DMT and MP Models ................................... 13
Self-Cleaning Mechanism ..................................................................................... 15 2.4
2.4.1 Wet Self-Cleaning Theory ........................................................................ 16
2.4.2 Super-Hydrophilic Self-Cleaning (TiO2) .................................................. 17
2.4.3 Super-Hydrophobic Surfaces (Lotus Effect) ............................................ 18
2.4.4 Gecko Dry Self-cleaning Mechanism ....................................................... 22
Gecko Mimic Materials ........................................................................................ 30 2.5
2.5.1 Cast-Molding Method ............................................................................... 30
iv
2.5.2 Soft and Rigiflex Lithography .................................................................. 32
2.5.3 Carbon Nanotubes ..................................................................................... 32
CHAPTER 3 DYNAMIC ENHANCEMENT IN ADHESION FORCES OF
MICROPARTICLES ON SUBSTRATES IN AIR AND NITROGEN ENVIRONMENT ......... 35
Introduction ........................................................................................................... 35 3.1
Experimental Setup ............................................................................................... 36 3.2
Results ................................................................................................................... 41 3.3
3.3.1 Dynamics Process during the Retraction of Microspheres ....................... 41
3.3.2 Effect of Retraction (Z-Piezo) Velocity on Adhesion Forces in Air ........ 44
3.3.3 Adhesion Forces vs. Preload and Loading Time ...................................... 47
3.3.4 Adhesion Forces vs. Particle Diameter ..................................................... 49
Discussion ............................................................................................................. 49 3.4
Modeling of the Dynamic Enhancement .............................................................. 51 3.5
Conclusions ........................................................................................................... 55 3.6
CHAPTER 4 DYNAMIC ENHANCEMENT IN ADHESION FORCES OF
MICROPARTICLES ON SUBSTRATES IN AQUEOUS SOLUTIONS ................................... 57
Introduction ........................................................................................................... 58 4.1
Experimental Setup ............................................................................................... 59 4.2
4.2.1 Surface Preparation ................................................................................... 59
4.2.2 Force Measurement ................................................................................... 59
Results ................................................................................................................... 61 4.3
4.3.1 Hydrodynamic Effect ................................................................................ 61
4.3.2 Adhesion Force Curve under Dynamic Loading in Aqueous Solution .... 63
4.3.3 Adhesion Forces vs. Loading/unloading Velocity .................................... 65
v
Discussion ............................................................................................................. 68 4.4
Conclusions ........................................................................................................... 72 4.5
CHAPTER 5 SHAPE-INDUCED DYNAMIC ADHESION AND SELF-CLEANING EFFECT
OF GECKO FOOT-HAIR AND ITS BIO-MIMICS.................................................................... 74
Introduction ........................................................................................................... 74 5.1
Experimental Methods .......................................................................................... 74 5.2
Results ................................................................................................................... 78 5.3
5.3.1 Direct Observation of Self-Cleaning Phenomena in an Individual Seta... 78
5.3.2 Adhesion of Single Seta and Spatula to Various Substrates in Air and
Under Water .............................................................................................. 79
5.3.3 Adhesion of Spatula in Air and Liquid ..................................................... 83
5.3.4 Adhesion of the Artificial Spatula and the Nanoparticles on the Artificial
Spatula in Air and Under Water ................................................................ 84
Discussion ............................................................................................................. 89 5.4
Conclusions ........................................................................................................... 95 5.5
CHAPTER 6 FINITE ELEMENT ANALYSIS OF SINGLE GECKO SETA AND SPATULA 97
Introduction ........................................................................................................... 97 6.1
Gecko Spatula Simulation..................................................................................... 97 6.2
6.2.1 Spatula Model ........................................................................................... 97
6.2.2 Results and Discussion ........................................................................... 100
Gecko Seta Simulation ........................................................................................ 102 6.3
6.3.1 Gecko Seta Model ................................................................................... 102
6.3.2 Results and Discussion ........................................................................... 105
Conclusions ......................................................................................................... 107 6.4
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CHAPTER 7 CYCLIC ADHESION BEHAVIORS AND FATIGUE FAILURE OF GECKO
SETA UNDER REPEATED ATTACHMENT AND DETACHMENT.................................... 108
Introduction ......................................................................................................... 108 7.1
Experimental Setup ............................................................................................. 108 7.2
Results ................................................................................................................. 111 7.3
Discussion ........................................................................................................... 112 7.4
Conclusions ......................................................................................................... 115 7.5
CHAPTER 8 CONCLUSIONS AND FUTURE WORK ........................................................... 116
Conclusions ......................................................................................................... 116 8.1
Recommended Future Works ............................................................................. 117 8.2
REFERENCES ........................................................................................................................... 119
vii
LIST OF TABLES
Page
Table 2.1. Typical materials and corresponding techniques to produce micro/nanoroughness ... 22
Table 4.1 Parameters of materials ................................................................................................. 60
Table 4.2 Parameters of materials for different surfaces obtained using atomic force microscope....................................................................................................................................................... 68
Table 6.1 Parameters used for gecko spatula adhesion model ...................................................... 98
Table 6.2 Parameters used for gecko seta adhesion model ......................................................... 103
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LIST OF FIGURES
Page
Figure 2.1. (a) A tokay Gecko climbing on vertical glass walls; (b) Gecko foot pad; (c)
microstructure of a single lamella with individual setae arrays on the top; (d) and (e)
nanostructure of a single seta array with branches at the end of the up-right terminating with
hundreds of spatulae tips [11]. ........................................................................................................ 7
Figure 2.2 (a) Terminal elements (circles) in animals with hairy design of attachment pads. Note
that heavier animals exhibit finer adhesion structures; (b) dependence of the terminal element
density (NA) of the attachment pads on the body mass (m) in hairy-pad systems of diverse
animal groups [21]. ......................................................................................................................... 8
Figure 2.3 Scanning electron microscopy of the spatulae terminal elements of Gekko gecko setae.
Detached seta are imaged to show (a) an array of spatulae at the tip of a seta; and (b,c) details of
individual spatula [23]. ................................................................................................................... 9
Figure 2.4 (a) F║ (lateral Force) and F┴ (normal force) versus time plot; (b) schematic of the
sliding motion of the gecko seta as modeling [25]. ...................................................................... 10
Figure 2.5. Illustration of a particle contact with a flat substrate, here P is the external force
exerted on the particle, the radius of the particle is d, and a is the contact radius between the
particle and substrate..................................................................................................................... 11
Figure 2.6 Predictions of JKR type contact mechanics models for the adhesion strength of an
elastic cylinder with a hemispherical tip on a rigid substrate: (a) geometry of a hemispherical tip
and its parabolic approximation; (b) classical models of contact mechanics (JKR, MD, DMT)
have adopted the parabolic approximation of the tip geometry and make incorrect predictions at
very small sizes. The exact solutions for a hemispherical tip are labeled as “hemispherical
ix
undeformable” if elastic deformation of the tip is neglected and as “hemispherical deformable” if
elastic deformation is taken into account. Unlike the JKR type models, the exact solutions show
saturation at the theoretical strength of Van der Waals interaction at very small sizes [27]. ....... 15
Figure 2.7 A typical equation represents contact angle ................................................................ 16
Figure 2.8. (a) A figure shows a water drop on the hydrophobic surface; (b) a drop of water on
the hydrophilic surface. ................................................................................................................. 17
Figure 2.9. Upon irradiation of TiO2 by ultra-band gap light, the semiconductor undergoes photo
excitation. The electron and the hole that result can follow one of several pathways: step 1.
electron-hole recombination on the surface; step 2. electron-hole recombination in the bulk
reaction of the semiconductor; step 3. electron acceptor A reduction by photo-generated
electrons; or step 4. electron donor D oxidization by photo-generated holes [43]. ..................... 18
Figure 2.10. (a) An almost ball-shaped water droplet on a non-wettable plant leaf [50]; (b) facade
paint, self-cleaning with rainfall thanks to the Lotus-effect; (c) SEM image of Lotus surface [53];
(d) enlarged picture of the lotus surface pattern [53]. ................................................................... 20
Figure 2.11. Schematic and wetting of the four different surfaces. The largest contact area
between the droplet and the surface is given in flat and microstructure surfaces, but is reduced in
nanostructured surfaces and is minimized in hierarchical structured surfaces [46]. .................... 21
Figure 2.12. . Typical methods to fabricate micro/nanoroughened surfaces[46]. ................. 21
Figure 2.13. Model of interactions between 𝑁 gecko spatula of radius 𝑅𝑠, a spherical dirt particle
of radius 𝑅𝑝, and a pnanar wall. Van der Waals, interaction energies for the particle-spatula
(𝑊𝑝𝑠), and particle-wall (𝑊𝑝𝑤) systems are shown. When 𝑁 ∗𝑊𝑝𝑠 = 𝑊𝑝𝑤, equal energy is
required to detach the particle from wall or 𝑁 spatulae. Our results suggest that 𝑁 is sufficiently
x
great so that self-cleaning results from energetic disequilibrium between the wall and the
relatively few spatulae that can attach to a single particle [11]. ................................................... 24
Figure 2.14. One cycle of simulated steps, with contact with an initially clean glass slide (A)
Applying normal compressive force; (B) Shear load added to the compressive load by a hanging
weight; (C) Removing the compressive load (pure shear loading); (D). Detaching the sample [71].
....................................................................................................................................................... 24
Figure 2.15. Scanning electron micrography images of the polypropylene fibrillar adhesive and
conventional pressure-sensitive adhesives (PSA), (A) Fibrillar adhesive contaminated by gold
microspheres, (B) Fibrillar adhesive after 30 contacts (simulated steps) on clean glass substrate,
(C) Conventional PSA contaminated by microspheres, (D) Conventional PSA after contact on a
clean glass substrate. All scale bars correspond to 10 um. Microspheres on fibrillar adhesive are
removed by simulated steps, but microspheres on PSA cover more area after the steps [71]. ..... 25
Figure 2.16 (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 shoes on the dorsal surface of a gecko foot. A gecko foot showing toes in (c) flat, and
(d) hyperextended position without the ‘shoe’ [12]. ..................................................................... 28
Figure 2.17 Schematics of gecko toe peeling induced by (a) digital hyperextension (DH) from
distal to proximal direction without gecko shoe and by (b) limb motion from proximal to distal
direction with gecko shoe; (c)A 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; (d) recovery
indices for trials with (black bars) and without digital hyperextension by steps (striped bars).
Numbers above bars are sample sizes. Error bars represent ±2.s.e [12]. ...................................... 29
xi
Figure 2.18 (a) SEM image of the isometric view of a polyurethane elastomer microfiber array
with 4.5 μm fiber diameter, 9 μm tip diameter, 20 μm length, and 44% fiber density scale bar: 50
μm using cast-model [91]; (b)PMMA pillars with high aspect radio here the diameter of fibers
can be as few as only 50nm using AAO template [94]; (c) mushroom shaped hairs with PDMS
with AAO template [96]; (d) template assistant polypropylene shows self-cleaning properties
[71]. ............................................................................................................................................... 31
Figure 2.19 (a) A book of 1480 g in weight suspended from a glass surface with use of VA-
MWNTs supported on a silicon wafer. The top right squared area shows the VA-MWNT array
film, 4 mm by 4 mm. (b and c) SEM images of the VA-MWNT film under different
magnifications. (d) Nanotube length– dependent adhesion force of VA-MWNT films attached
onto the substrate with a preloading of 2 kg. (e) Adhesion strength of VA- MWNTs with length
100 T 10 mm at different pull-away directions. The nanotubes and substrates shown in (e) are
not to scale [10]. ............................................................................................................................ 34
Figure 3.1 (a) SEM image of a 10.7 µm diameter SiO2 microsphere glued on a tipless AFM
cantilever. (b) SEM image of a 10.4 µm diameter Al2O3 microsphere glued on a tipless AFM
cantilever (c) SEM image of a 9.8 µm diameter polystyrene microsphere glued on a tipless AFM
cantilever (d) Schematic of AFM measuring system in air. ......................................................... 39
Figure 3.2 A typical ramping process: (a) z-piezo movement vs. time, and (b) force vs. time (here
the movement distance and the force were recalculated from input voltage and output detective
voltage, respectively). The cot(θ) is linearly related to retraction speed and can be adjusted from
0.02µm/s to156µm/s. .................................................................................................................... 40
Figure 3.3 Indentation curves of (a) PS-PS (soft-soft), (b) Al2O3-Sapphire (hard-hard), and (c)
PS-Sapphire (soft-hard) particle-substrate systems at low and high loading speeds. ................... 43
xii
Figure 3.4 (a) Displacement of Al2O3 microparticles on a sapphire substrate when the tip
snapped off at a velocity equal to 156 µm/s, measured by a HSDC technique, and (b) Particle
pull-off velocity vs. z-piezo velocity derived from HSDC technology for a loading time of 10s
and a pre-loading force of 1 µN. ................................................................................................... 44
Figure 3.5 The relationship between retraction speed and adhesion forces of (a) 10.7-µm-
diameter SiO2 microsphere, (b) 9.8-µm-diameter PS microsphere, and (c) 10.4-µm-diameter
Al2O3 particles on sapphire, polystyrene and fused silica substrates for a loading time of 10s and
a pre-loading force of 1µN. ........................................................................................................... 47
Figure 3.6 The adhesion forces between Al2O3 particle and sapphire substrate under different
loading time for a preload of 1µN and here the retraction velocity of 1 µm/s. ............................ 48
Figure 3.7 The adhesion force between Al2O3 particle and sapphire substrate under different
preloads for a loading time of 10s and here the retraction velocity is 1 µm/s. ............................. 48
Figure 3.8 The adhesion force between Al2O3 particle and sapphire substrate in dry nitrogen as a
function of particle diameter for a loading force of 1 µN and a loading time of 10 s. ................. 49
Figure 3.9 Normalized adhesion forces (ΔF/F0) versus velocity, measured and fitted for a
preloading of 1 µN and a contact time of 10 seconds. Al2O3-sapphire, SiO2-fused silica and PS-
PS refer to Al2O3 particle, on sapphire substrate, SiO2 particle, on fused silica substrate and PS
particle on PS substrate, respectively............................................................................................ 54
Figure 3.10 Dynamic scaling parameter n and coefficient C as a function of microsphere
diameters for adhesion force of Al2O3 particles on sapphire substrate in dry nitrogen. ............... 54
Figure 4.1 Schematic of AFM measuring system in liquid .......................................................... 61
Figure 4.2 DLVO theory curve of hydrodynamic force in water ................................................. 62
xiii
Figure 4.3 Experimental hydrodynamic force vs. retraction velocity ranging from 0.02µm/s to
156 µm/s. Here the solid line is the trend for this particular probe. ............................................. 63
Figure 4.4 Indentation curves of (a) SiO2 particle on silicon wafer (hard-hard), (b) PS particle on
PS (soft-soft), and (c) PS particle on silicon wafer (soft-hard) particle-substrate systems at low
and high loading speeds. Here the pre-loading is 1µN for all the experiments. ........................... 65
Figure 4.5 The relationship between retreating speed and adhesion forces (Fp-w) of (a) 10.7-µm-
diameter SiO2 microsphere, (b) 10.4-µm-diameter PS microsphere, and (c) 9.8 Al2O3
microsphere. Here the loading is 1µN and contact time is 10s. The hydrodynamic effect has been
removed from the measurement.................................................................................................... 67
Figure 4.6 Adhesion force between a SiO2 particle and fused silica substrate in a drop of water
under different times. Here the loading is 1µN and contact time is 10s. ...................................... 67
Figure 5.1 SEM picture of a gecko seta pre-glued at the end of AFM probe ............................... 76
Figure 5.2 Schematics of experimental setup for measuring the adhesive forces (A) between seta
and microsphere (Fs-p) with different diameter, and (B) between sphere and substrate (Fw-p) at a
given pull-off velocity................................................................................................................... 77
Figure 5.3 Procedure and observed results of a seta approaching, contacting and retracting from
a particles: (A) one gecko seta pre-glued at the end of AFM probe approaching sphere slowly, (B)
maintain contact (full relaxation) , (C) slow retraction; sphere was caught by the gecko seta, (D)
Fast approaching, (E) short relaxation time , and (F) Fast retraction (V=142µm/s), particles stays
on substrate. .................................................................................................................................. 79
Figure 5.4 Schematic of adhesion measurement setup in water ................................................... 80
Figure 5.5 Adhesion force of single gecko seta vs. pull-off velocity at different substrates (a) in
air and (b) in water. ...................................................................................................................... 82
xiv
Figure 5.6 Adhesion forces between a single gecko seta and SiO2 particles with different
diameter pre-fixed on substrate ..................................................................................................... 82
Figure 5.7 SEM picture of single gecko spatula. Other spatulas were carefully cut out by Focus
ion beam. ....................................................................................................................................... 83
Figure 5.8 Adhesion force of single gecko seta vs. pull-off velocity at different substrates in air
and in water ................................................................................................................................... 84
Figure 5.9 SEM images of (a) glass microfibers glued on AFM cantilever, (b) spatula-like flat
microstructure, (c) microsphere (d = 0.95 μm) welded on spatula-like glass nanofibers at the end
of AFM cantilever, ........................................................................................................................ 86
Figure 5.10 Adhesion force of artificial gecko spatula (A) in air and (B) in water as a function of
pull-off velocity. ........................................................................................................................... 87
Figure 5.11 Adhesion force of a 950 nm welded at the end of artificial gecko seta (a) in air and (b)
in water as a function of pull-off velocity. .................................................................................... 87
Figure 5.12 The dynamic factors (F/F0-1, where F0 is the force at a velocity of 0.02 µm/s)) versus
pull-off velocity. ........................................................................................................................... 88
Figure 5.13 Adhesive forces between 20 µm SiO2 sphere and substrate (𝐹𝑤 − 𝑝) at a given pull-
off velocity of AFM cantilever. Here the loading force is 1µN, 2µN and 5µN respectively. The
solid line is in air and dash line is in nitrogen environment ......................................................... 88
Figure 5.14 Schematics of crack propagation of spatula and sphere in contact with a flat substrate;
(a) Crack propagation during pulling off spatula [158] (b) crack propagation direction along the
spatula/substrate interface, where crack front length increases during pulling off; (c) Crack
propagation during pulling of a sphere; and (d) crack propagation direction along the
sphere/substrate interface, where crack front length reduces during pulling off. ......................... 90
xv
Figure 5.15 (a) and (b) dynamic parameters (n and c) obtained using Equation(5.1) by fitting the
experimental data for microspheres in contact with various substrates in humid air, and dry
nitrogen, and c) Trend of forces on seta-particle complex (Fs − p) and particles and walls
(Fw − p) with sphere diameter of 20µm under different velocities. m is the number of spatulae
attached to a microsphere; Points A and B are intersections that define the critical pull-off
velocity. ......................................................................................................................................... 92
Figure 6.1 (a) SEM pictures of single spatula, (b) A detail gecko spatula model top view (c) side
view. Here the cohesive element thickness is 0.01nm. ................................................................. 98
Figure 6.2 Typical traction-separation responses used in FEA simulations ................................. 99
Figure 6.3 Snapshot of spatula peeling from the substrate. (a-d) Front view of crack initiation and
propagation, (e-j) top view of crack initiation and propagation and Mises table. ...................... 101
Figure 6.4 Adhesion forces vs. times under different velocities ................................................. 102
Figure 6.5 Force-displacement curve of a single gecko spatula when pulled off from the substrate.
..................................................................................................................................................... 104
Figure 6.6 (a) Front view, (b) Bottom view, and (c) Side view of gecko seta generated by
computer simulation. (d) A single gecko seta ............................................................................. 104
Figure 6.7 (a) Initial Separation of gecko spatula from the substrate (b) Crack propagation from
one side to the other. (c) Complete separation of seta from the substrate. (d) force vs time at point
A, B and C................................................................................................................................... 107
Figure 6.8 (a) The maximum adhesion forces when velocity various from 0.1-50μm/s, and (b)
The maximum adhesion force versus the pull-off velocity. ....................................................... 107
xvi
Figure 7.1 (a) A typical gecko seta before fatigue test; (b) Spatulae are toward the same direction
before the fatigue test; (c) After the fatigue test, there is no crack or fracture damage of spatulas
on a single seta after the fatigue test. .......................................................................................... 111
Figure 7.2 Adhesion forces vs. cycles during the fatigue test for a typical seta pre-glued at the
end of AFM probe. Here the ramping velocity is 10HZ and approaching and retraction forces are
20um/s during the test. The substrate is a clean silicon wafer with a roughness of only 0.418nm.
Here in Stage I we see a fast damping at the beginning of the test. ............................................ 112
Figure 7.3 (a) a typical force distance curve at stage 1(b) a typical force distance curve at stage
2(c) a typical force distance curve at stage 3. ............................................................................. 114
Figure 7.4 Schematic diagram: (a) before the fatigue test, (b) after the fatigue test. ................. 115
xvii
CHAPTER 1
INTRODUCTION
“Nature does nothing in vain. - Aristotle
Background 1.1
Humans would have never invented fabrillar nanostructures if geckos had not evolved.
Geckos can freely climb on walls and ceilings against their body weight at speed of over 1ms-1.
Without considering the surface to be dry or wet, smooth or rough, dirty or clean, switching
between attachment and detachment is simple and easy for geckos. The secret of a gecko’s
strong adhesion and contradictory easy detachment was discovered with the help of the scan
electron microscope (SEM) [1]. Gecko hierarchical toe pad structure consists of millions of
micro-fibrils, called setae. Each seta has an average length of 110 μm and diameter of 5 μm and
further branches into hundreds of nano-sized branches, called spatulae. It has been shown [2] that
the adhesion forces of a single seta can be up to 10 N/cm2 and its adhesion force is oriented to let
the gecko easily lift its foot while running but adhere strongly on the shear directions when it
stops. This dry adhesion mechanism is quite different from that of conventional pressure
sensitive adhesives (PSAs), for which adhesion forces are linearly related to the pressure forces.
It fails after repeated usage because of contamination or self-adhesion to unwanted areas while in
use [3]. PSAs can easily lose their adhesion propensity because it can be contaminated by dust
and particles after 2-3 times of repeated use. In addition, these tapes cannot work in a liquid
environment such as in water, or in a chemical environment because surface wetting changes
their adhesion properties. However the gecko is different; Van der Waals [4] forces between the
β-keratin [5] lamellae structure and surfaces are considered the primary forces between gecko toe
1
pads and substrates. Capillary adhesion also contributes to the adhesion forces in certain
conditions [6].
Over the past decade, scientific interest in the gecko has rapidly grown and researchers
have mainly focused on the mechanisms of adhesion forces like their unique structure, and the
mechanical property of gecko adhesion systems [7]. Researchers attempt to mimic gecko-
structure materials with polymer arrays [8] or carbon nanotubes (CNTs) [9]. Reported on 2008
[10], scientists created CNTs that measured adhesive forces of ~100 newtons per square
centimeter. This is almost 10 times that of a gecko foot and is a much stronger shear adhesion
force than the normal adhesion force in order to ensure strong binding along the shear direction
and easy lifting in the normal direction [10]. Despite its strong adhesive qualities, CNTs begin to
lose its adhesion after hundreds to thousands times of use. However, geckos retain their strong
adhesion over millions of repeated adhesion/detachment within a molt cycle because they
manage to keep their feet clean while walking [11]. The mechanism for why the sticky toes clean
themselves remains a puzzle and awaits to be fully revealed [11,12].
Objective and Significance 1.2
Currently, there is no self-cleaning mechanism that can explain the gecko’s dry adhesion
system thoroughly, thus resulting in the slow development of artificial self-cleaning materials
based on gecko fabrilliar system. The object of this dissertation is to give a new self-cleaning
mechanism theory. Experimental evidence and modeling simulations are followed to support this
new dynamic self-cleaning mechanism.
The significance of this work will guide scientists to develop gecko mimicking structures
which show both strong adhesion and self-cleaning mechanisms. Our ultimate goal is to create a
2
smart tape that can be used thousands of times without losing its strong adhesive property while
cleaning itself during the peeling and adhesion process. These kinds of tapes have a widely
potential usage in commercial and also scientific research in some extreme environments
including high-pressure underwater practice and outer-space experiments in extreme dry and
cold conditions.
Dissertation Outline 1.3
This dissertation is divided into six chapters.
Chapter 2 provides a comprehensive literature review regarding the strong adhesion and
unique self-cleaning properties of gecko systems. The gecko adhesive system is discussed from
its structure-shape to its unique properties. Both theory and engineering products showcase the
progresses of making a gecko inspired adhesives system, followed by a summary of nature bio-
self-cleaning mechanism which highlights the unique properties of the gecko self-cleaning
system. In the conclusion, current challenges and future directions are discussed.
Chapter 3 introduces the dynamic effect of micro size particles in air and nitrogen
environments on different substrates. The adhesion force of soft (polystyrene) and hard (SiO2
and Al2O3) micro-particles on soft (polystyrene) and hard (fused silica and sapphire) substrates
was measured using an atomic force microscope (AFM) with retraction (z-piezo) speed ranging
over 4 orders of magnitude. The adhesion is strongly enhanced by the dynamic effect. It reveals
that micro particles ranging from micro toward nano show adhesion force that is strongly
enhanced by the dynamic effect. When the retraction speeds varies from 0.02 µm/s to 156 µm/s,
the adhesion force increases by 10% ~ 50% in dry nitrogen while it increases by 15%~70% in
3
humid air. A dynamic model was developed to explain this dynamic effect, which agrees well
with the experimental results.
Chapter 4 introduces the dynamic effect of micro size particles in an aqueous solution,
which further reveals that dynamic effect is a universal rule for micro particles in an aqueous
solution. The presence of a dynamic effect becomes clear upon observation of 20-100% increase
in adhesion force resulting from an increase in retraction velocity from 0.02 to 156 μm/s during
particle and substrate interactions.
Chapter 5 presents a new self-cleaning tool of the gecko seta named the dynamic self-
cleaning mechanism. Although particles show dynamic enhancement, the gecko fabrillar hair
shows a totally different trend. The pull off forces of a single gecko seta and spatula was tested
by the AFM under different pull-off velocities. The result shows that both the spatula and the
seta have a rate independent of adhesion response in normal retraction, which is quite different
from micro-particles. Further research indicated that the shape of the contact area was a key
factor to the dynamic effect. In order to verify this hypothesis, artificial gecko spatula made of
glass fibers was nanofabricated by a focus ion beam (FIB) and tested by AFM. These manmade
spatulae also show a rate independent adhesion response. In conclusion, self-cleaning is induced
by dynamic effect during gecko locomotion. The relative dynamic adhesion change between
particles and seta makes it possible for gecko to shed dirt particles while walking.
Chapter 6 discusses the finite element analysis (FEA) model of gecko seta and spatula. A
three-dimensional FEA model is presented which describes the adhesion and deformation of a
gecko seta and a spatula under different velocities. The relationship between pull-out forces vs.
velocities is evaluated in the model and the peeling process is discussed. The dynamic adhesion
4
of a single gecko seta and spatula were simulated with finite element analysis and the results also
confirm the rate independent phenomena.
Chapter 7 explores the fatigue properties of gecko seta the fatigue property of gecko seta
with the AFM under cyclic attachment/detachment process, mimicking gecko running. The
relationship of gecko fatigue properties and their molt cycle was discussed. Further, SEM
pictures display the reason that affects this adhesion decrease as time goes by. By looking at the
structure of the gecko spatulae, we can come to a conclusion it is extremely durable. The shape
and directions of the spatulas are considered key factors which affect the adhesion properties of
the gecko.
Chapter 8 summarizes the findings in this present dissertation and a new trend in gecko
research for which the future research directions are recommended.
5
CHAPTER 2
LITERATURE REVIEW
Hierarchical Fibrillar Structure of Gecko Feet 2.1
Geckos are the world’s most supreme climber; they can climb on walls and ceilings
quickly, even while upside-down. The hierarchical fibrillar structure of gecko toe pads have been
thoroughly revolved via scanning electron microscope (SEM) [2]. One toe pad of Tokay gecko
contains millions of high-aspect-ratio micro-sized fabrillar structure named setae. A single seta is
approximately 110 μm in length and 4.2 μm in diameter as shown in Figure 2.1 (d) [3]. At the
end of the seta, it branches into 100-1000 even smaller structure called spatulae. The two front
feet of a gecko can withstand 20.1 N for a force parallel to the surface with 227 mm2 of pad area;
as there are approximately 3600 setae in that area, a single seta can hand an average of 6.2 µN.
When properly oriented, preloaded, and dragged, a single seta can generate 200 µN in shear and
40 µN in adhesion force [2]. If all setae are engaged at the same time, (roughly half a million on
a foot), about 100 N of adhesive force can be generated. This is 10 times their averaged body
weight.
Although their toe pads are rather sticky, the gecko can detach within milliseconds when
in motion [7]. Experiments have proven that Van der Waals force is the main contribution to
gecko adhesion systems [4]. Few exceptions reveal that the surface wettability [13] and humidity
[6,14] also play a significant role in gecko adhesion systems. It remains that the secret of a
gecko’s adhesion system is still waiting to be discovered [15].
6
(a) (b)
(c) (d) (e)
Figure 2.1. (a) A tokay Gecko climbing on vertical glass walls; (b) Gecko foot pad; (c)
microstructure of a single lamella with individual setae arrays on the top; (d) and (e)
nanostructure of a single seta array with branches at the end of the up-right terminating with
hundreds of spatulae tips [11].
Hierarchical fibrillar structure have evolved in nature, such as lotus leaves [16], spider
silks [17], sharkskin [18], butterfly scales [19] and fish-hair flow sensor [20–22]. Comparative
7
structure data clearly show the areal density of these terminal elements strongly increase with
increasing body mass [21] (Figure 2.2). The gecko nanostructure provides a model for a wide
array of insects that display similar characteristics. It is also discovered that the pull-out force is
sensitive to small variations of the tip shape. Recent pictures show that a single gecko spatula is
smoothly translated from round to flat at the end of the spatula (Figure 2.3 [23]).
(a) (b)
Figure 2.2 (a) Terminal elements (circles) in animals with hairy design of attachment pads. Note
that heavier animals exhibit finer adhesion structures; (b) dependence of the terminal element
density (NA) of the attachment pads on the body mass (m) in hairy-pad systems of diverse
animal groups [21].
8
(a) (b)
Figure 2.3 Scanning electron microscopy of the spatulae terminal elements of Gekko gecko setae.
Detached seta are imaged to show (a) an array of spatulae at the tip of a seta; and (b,c) details of
individual spatula [23].
Gecko Friction-Adhesion System 2.2
Amonton’s first law tells us the ratio of shear force (F║) and normal force (F┴)is a
constant value, µ (the coefficient of friction) which is usually between 0-1. However, a gecko’s
setae can be adhesive under Van der Waals forces alone. In this case, a tangential force is
measured with a zero normal force or with a negative normal force. Adhesion depends directly
on shear force and is independent of detachment angle, which is quite different from the regular
Scotch tape. This concept of friction coefficient not reliable and a different description must be
used (as seen in Figure 2.4) [24].
9
(a) (b)
Figure 2.4 (a) F║ (lateral Force) and F┴ (normal force) versus time plot; (b) schematic of the
sliding motion of the gecko seta as modeling [25].
Classic Contact Models 2.3
Various mechanical models [10,11] have been developed to model specific surface-
contact interaction, so tracking them can help us develop a fabrilliar structure like adhesion
system. Among them the most popular ones are the Hertz model, JKR model followed by
Johnson, Kendall and Roberts [28], DMT model proposed by Derjaguin, Muller and Toporov
[29], and MP model proposed by Maguis and Pollock [30].
10
Figure 2.5. Illustration of a particle contact with a flat substrate, here P is the external force
exerted on the particle, the radius of the particle is d, and a is the contact radius between the
particle and substrate.
2.3.1 Johnson-Kendall-Roberts (JKR) Model
Based on Hertz model and considering the tension at the edge of the contact area and
compressive in the center, Johnson, Kendall and Roberts introduced JKR model (Figure 2.5),
where
a3 = d2K�P + 3
2WAπd + �3πWAdP + �3πWAd
2�2� (2.1)
where 𝑊𝐴 is the thermodynamic work of adhesion, and K is the composite Young’s
modulus.
K = 43�1−υ1
2
E1+ 1−υ22
E1�−1
(2.2)
where E is the elastic modulus and υ is the Poisson radio and subscript 2.1 and 2.2 refer
to the materials of the sphere and substrate.
If there is no surface force, WA =0 in equation (2-1) it is reduced to Hertz model which is
11
a3 = d2K
(2.3)
The JKR model predicts that the force needed to remove the particle, (the pull-off force),
is given as
𝐹𝑝𝑜𝐽𝐾𝑅 =
34𝜋𝑊𝐴𝑑 (2.4)
The contact radius at zero external force may be obtained by setting 𝑃 = 0 in equation
(2-1) that is
𝑎0 = �3𝜋𝑊𝐴𝑑2
2𝐾�
13
(2.5)
The contact radius at the separation is obtained by setting 𝑃 = −𝐹𝑝𝑜𝐽𝐾𝑅 in equation (2-1)
and the contact radius is
𝑎 = �3𝜋𝑊𝐴𝑑2
8𝐾�
13
=𝑎0
41/3 (2.6)
2.3.2 Derjaguin-Muller-Toporov (DMT) Model
DMT model assumes that adhesion force plays an important role. So the pull out force is
given as
FpoDMT = πWAd (2.7)
Contact radius at zero force is given at
𝑎0 = �𝜋𝑊𝐴𝑑2
2𝐾�
13
(2.8)
Contact radius at separation is consider as zero
𝑎 = 0 (2.9)
12
2.3.3 Maugis-Pollock (MP) Model
JKR and DMT models assume only elastic deformation occurs in the contact area.
However, experimental data suggests that in many cases the plastic deformation also affects the
adhesion force. Maugis-Pollock developed a model that takes plastic deformation into
consideration. The relationship between the contact radius and external force is given as
P + πWAd = πa2H (2.10)
where H is the hardness and
H = 3Y (2.11)
with Y being the yield strength
Note that the variations of contact radius with particle diameter at equilibrium are in the
absence of external force for which elastic and plastic deformation is different. That is
a0~d23 (elastic) (2.12)
a0~d12 (plastic ) (2.13)
The surface energy per unit are is given (also known as thermodynamic work)
WA = A12πz02
(2.14)
where A is the Hamaker constant and 𝑧0 is the minimum separation distance.
2.3.4 Comparison between JKR, DMT and MP Models
JKR model has been used to show that splitting of a single contact into multiple smaller
contacts always results in enhanced adhesion strength, thus providing a theoretical basis for
understanding the hairy attachment system. One of the puzzling predictions of the JKR type
model is that the spatula structure of geckos can be split infinitely to support arbitrarily large
body weight which is clearly impossible as the adhesion strength cannot exceed the theoretical
13
strength of Van Der Waals interactions (Figure 2.6). Recent clear SEM pictures of gecko spatula
[23] reveal (Figure 2-3) gecko spatula to be peeling from the substrate instead of direct contact-
detachment leading to new models focusing on the peeling process of gecko seta or spatula
[31,32]. Two pertinent concepts, namely “contact splitting” [21,33,34] and “shape insensitivity”
[35], have been theoretically derived accounting for the increased adhesion from a divided no-
continuum surface and its relatively weak intermolecular origin. However, other traits, such as
angled seta stalks, fiber aspect ratio, 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.
Recent experiment reveals gecko seta detachment from substrate is a dynamic effect. The
trigger velocity of gecko toe pad detach from the substrate can be up to 1000μm/s [12].
Traditional models are based on a balance between potential energy, surface energy, and
elastic/plastic deformation within the solid bodies and ignore kinetic effects during detachment.
Since a gecko detaches its toe in a millisecond, the detaching forces could be strongly influenced
by a dynamic effect. Work has been done on the dynamic effect of these microparticles [36,37].
It was shown in these studies that the adhesion force is dependent on contact frequency or pull-
off speed, applied force, and the loading duration [38,39]. Chapter 3-5 discusses a dynamic effect
of micro particles, a single gecko seta, and a single spatula. Dynamic modeling based on the
result is explained in details.
14
(a) (b)
Figure 2.6 Predictions of JKR type contact mechanics models for the adhesion strength of an
elastic cylinder with a hemispherical tip on a rigid substrate: (a) geometry of a hemispherical tip
and its parabolic approximation; (b) classical models of contact mechanics (JKR, MD, DMT)
have adopted the parabolic approximation of the tip geometry and make incorrect predictions at
very small sizes. The exact solutions for a hemispherical tip are labeled as “hemispherical
undeformable” if elastic deformation of the tip is neglected and as “hemispherical deformable”
if elastic deformation is taken into account. Unlike the JKR type models, the exact solutions
show saturation at the theoretical strength of Van der Waals interaction at very small sizes [27].
Self-Cleaning Mechanism 2.4
Self-cleaning is a desired property that makes the dream of a contamination-free surface
come true. Inspired by nature, bio-self-cleaning has been classified into three conceptual
approaches: (a) super hydrophilic self-cleaning (e.g TiO2-based), (b) lotus effect self-cleaning
(Figure 2.8), (c) the gecko dry self-cleaning mechanism [40].
15
2.4.1 Wet Self-Cleaning Theory
When liquid drops on various substrates, the shape of the liquid will be different. The
relationship of the shape with the contact surface energy was found by Young in 1805 [41] and is
Young’s equation (Figure 2.7).
𝛾𝑆𝐺 = 𝛾𝑆𝐿 + 𝛾𝐿𝐺𝑐𝑜𝑠𝜃𝐶 (2.15)
where 𝜃𝐶 is the contact angle which represents the angle where a liquid/vapor interface
meets a solid surface and 𝛾𝑆𝐺 , 𝛾𝑆𝐿 , and 𝛾𝐿𝐺 refer to the interfacial surface enations of solid,
liquid, and air, respectively.
If the contact angle is 𝜃𝐶 > 90° it is known as hydrophobic and if the contact angle is
𝜃𝐶 < 90° it is known as hydrophilic. The contact measurement is easily established, measured,
and repeated. These observations are considered an important parameter to explain the surface
energy of wet properties.
Figure 2.7 A typical equation represents contact angle
16
(a) (b)
Figure 2.8. (a) A figure shows a water drop on the hydrophobic surface; (b) a drop of water on
the hydrophilic surface.
2.4.2 Super-Hydrophilic Self-Cleaning (TiO2)
A super-hydrophilic surface possesses a self-cleaning property by its materials. When a
liquid drops on the surface, the liquid can spread into the space between substrate and dust, thus
washing the dust away. One example is TiO2, since its discovery in 1997 [42]. TiO2 shows a
unique self-cleaning property and the exact theory is still unknown. A basic model is as follows:
the band gap of bulk anatase TiO2 is 3.2 eV, corresponding to the light of a wavelength of 390
nm, which is near-UV light. When a TiO2 film is irradiated under UV light, excited charge
carriers (i.e., electrons and holes) are generated on the surface of the film. Photo-generated holes
decompose adsorbed organic dust molecules whereas electrons combine with atmospheric
oxygen to produce the superoxide radical, which quickly attacks nearby organic molecules.
During the photo-catalytic reaction, the TiO2 photo-catalyst decomposes organic contamination
17
through absorbing light with energy equal to or greater than its band gap energy and the TiO2
keeps the surface clean [40] (Figure 2.9).
Figure 2.9. Upon irradiation of TiO2 by ultra-band gap light, the semiconductor undergoes photo
excitation. The electron and the hole that result can follow one of several pathways: step 1.
electron-hole recombination on the surface; step 2. electron-hole recombination in the bulk
reaction of the semiconductor; step 3. electron acceptor A reduction by photo-generated
electrons; or step 4. electron donor D oxidization by photo-generated holes [43].
2.4.3 Super-Hydrophobic Surfaces (Lotus Effect)
The lotus effect refers to the super-hydrophobicity exhibited by the leaves of the lotus
flower. In Asia, the lotus has a symbol of purity in several religions. Even though it may become
dirty in dry conditions with many dusts and insects, its leaves will become super clean with the
18
help of a rain. In effect, water droplets falling onto the leaves bead up and roll off and bring all
the dust away.
The secret of the unique self-cleaning property of the lotus was first studied by Dettre and
Johnson in 1964 using rough hydrophobic surfaces [44]. Their work developed a theoretical
model based on experiments with glass beads coated with paraffin/PTFE telomer. With the help
of SEM, a great number of studies have been conducted to unravel the self-cleaning property of
the lotus effect [45–47]. Figure 2.10 is one example of such an effect. Lotus leaf surfaces have
randomly distributed micro papillae so that the contact angle will be large, thus water can roll
freely on the surfaces and transport the dust away. The contact angle is 160° and slide angle is
only 2°, which makes water roll on the surfaces much easier. An illustration is shown in Figure
2.11. Similar phenomena can also be found in other leaves such as taro, cicada, mantle, etc. [48–
50]. Superhydrophobic surfaces are widely used in energy conservation and conversion [51,52].
A summary of artificial materials can be found in Figure 2.12 and Table 2.1. Lotus effect
protects plants against pathogens like fungi or algae growth, and also help butterfiles, coccinella,
dragonflies clean their body. Another positive effect of self-cleaning is the prevention of
contamination of the area of a plant surface exposed to light resulting in a reduced
photosynthesis.
19
(a) (b)
(c) (d)
Figure 2.10. (a) An almost ball-shaped water droplet on a non-wettable plant leaf [50]; (b) facade
paint, self-cleaning with rainfall thanks to the Lotus-effect; (c) SEM image of Lotus surface [53];
(d) enlarged picture of the lotus surface pattern [53].
20µm 5µm
20
Figure 2.11. Schematic and wetting of the four different surfaces. The largest contact area
between the droplet and the surface is given in flat and microstructure surfaces, but is reduced in
nanostructured surfaces and is minimized in hierarchical structured surfaces [46].
Figure 2.12. . Typical methods to fabricate micro/nanoroughened surfaces[46].
21
Table 2.1. Typical materials and corresponding techniques to produce micro/nanoroughness
Materials Technique Contact Angle
References
Teflon Plasma 168 Zhang et al. [54], Shui et al. [55]
PFOS Electro-and chemical 152 Xu et al.[56] PDMS Laser treatment 166 Khorasani et al. [57]
PS,PC.PMMA Evaporation >150 Bormashenko et al. [58]
PS-PDMS block copolymer Electrospining >150 Ma et al. [59]
Silica Layer-by-Layer assembly[60] E-beam lithography[61] X-ray lithography[62] Casting[63]
>150 Zhao et al[60] Martines et al[61] Furstner et al. [62] Sun et al. [63]
Carbon nanotubes Chemical vapor deposition
>165 Lau et al. [64] Jung et al. [65] Huang et al. [66]
ZnO, TiO2 nanorods Sol-gel >150 Feng et al. [67] Ni based Nanorods Nanoimprint 110 Harpreet et al. [68] Copper Electrodeposition 160 Shirtcliffe et al. [61]
Nano-silica spheres Dig coating 105 Klein et al. [69] Au clusters Electrochemical
deposition >150 Zhang et al. [69]
PET Oxygen plasma etching >150 Teshima et al. [70]
2.4.4 Gecko Dry Self-cleaning Mechanism
Although the lotus leaf and TiO2 give two unique self-cleaning properties, the gecko [11]
shows a completely different self-cleaning mechanism. Due to the main forces between a gecko
hair and it’s substrate being the Van der Waals force [4], the gecko should shed the dust during
its locomotion’s, which is a paradoxical property because gecko setae can be both strongly
adhesive and easily detached. If comparing a gecko’s stickiness with conventional pressure-
sensitive adhesives such as Scotch tape, the tape will usually lose its strength to adhere after 2 or
22
3 times usage because dust is self-adhesive upon the surfaces of Scotch tape; whereas the
gecko’s feet, although it holds its strong adhesiveness, stay clean [11]. Contact mechanical
models hypothesize that self-cleaning occurs as the surface force between the gecko setae and
the particles is a force smaller than the particles-surfaces force. This alone cannot explain why
the dust that accompanies the setae are removed by itself ?
Only recently have there been several models that discuss the gecko’s self-cleaning
mechanism. Autumn et al. [11] believes that the different surface energy between particle-seta
and particle-substrates is the key factor that determines self-cleaning as shown in Figure 2.14 (a).
Fearing et al. [71] assumes the shearing process will decrease the actual spatulas contact with the
particles so that the attach/detach process of the particles will be shed away. Inspired by this idea,
they fabricated a high-aspect-ratio fibrillar adhesive from a stiff polymer and demonstrated self-
cleaning of the adhesive during contact with a surface as shown in Figure 2.14. Xia et al. [12]
believes dynamic effect is the key factor that needs to be considered. Since gecko detaches from
substrace surfaces under a unique dynamic hyperextension way, high retracting speed may help
gecko dislodge dirt particles thus keeps gecko toe pads clean. The details of this model is
explained below.
23
Figure 2.13. Model of interactions between 𝑁 gecko spatula of radius 𝑅𝑠, a spherical dirt particle
of radius 𝑅𝑝 , and a pnanar wall. Van der Waals, interaction energies for the particle-spatula
(𝑊𝑝𝑠 ), and particle-wall (𝑊𝑝𝑤 ) systems are shown. When 𝑁 ∗𝑊𝑝𝑠 = 𝑊𝑝𝑤 , equal energy is
required to detach the particle from wall or 𝑁 spatulae. Our results suggest that 𝑁 is sufficiently
great so that self-cleaning results from energetic disequilibrium between the wall and the
relatively few spatulae that can attach to a single particle [11].
(a) (b) (c) (d)
Figure 2.14. One cycle of simulated steps, with contact with an initially clean glass slide (A)
Applying normal compressive force; (B) Shear load added to the compressive load by a hanging
weight; (C) Removing the compressive load (pure shear loading); (D). Detaching the sample [71].
24
(a) (b)
(c) (d)
Figure 2.15. Scanning electron micrography images of the polypropylene fibrillar adhesive and
conventional pressure-sensitive adhesives (PSA), (A) Fibrillar adhesive contaminated by gold
microspheres, (B) Fibrillar adhesive after 30 contacts (simulated steps) on clean glass substrate,
(C) Conventional PSA contaminated by microspheres, (D) Conventional PSA after contact on a
clean glass substrate. All scale bars correspond to 10 µm. Microspheres on fibrillar adhesive are
removed by simulated steps, but microspheres on PSA cover more area after the steps [71].
10µm 10µm
10µm 10µm
25
A recent model believes geckos shed the dust particles with a unique dynamic self-
cleaning mechanism called digital hyperextension (DH) [12]. 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 per cent of their original stickiness in only four
steps (Figure 2.16 and Figure 2.17). The dynamic model predicts that when seta suddenly release
from the attached substrate, they generate enough inertial force to dislodge dirt particles from the
attached spatula. The predicted cleaning force on dirt particles significantly increases when the
dynamic effect is included. The extraordinary design of gecko toe pads perfectly combines
dynamic self-cleaning with repeated attachment/detachment, making gecko feet sticky yet clean
[12]. Experiment and model has been shown that the trigger velocity can be up to 1000 µm/s
when gecko toe pad peeling out from the substrate [12].
Custom-designed fitted “gecko shoes” were prepared (Figure 2.16 (a) and (b)). This
prevented DH but allowed the animal to walk, adhere to the surface, and release. The gecko toe
pads were dirtied and allowed to walk on a clean glass substrate with or without shoes, and
counted the steps it needed to recover its original adhesion force. When walking naturally with
hyperextension, geckos shed dirt from their toes twice as fast as they would if walking without
DH (Figure 2.17(d)).
As can be seen in Figure 2.16(d), the gecko toe pad detaches the feet by peeling from the
end towards the center which is different from previous understanding of adhesion-drag-
detachment. Here It is defined as a peeling zone (Figure 2.17(a) possessing a constant length, L,
in the x- direction (Figure 2.17 (c)), which is determined by the maximum displacement of the
seta before jump-off and the scrolling radius r.
𝐿 = 𝑟 ∗ 𝜃∗ (2.1)
26
The adhesion force on individual seta in the peeling zone (𝐹𝑤−𝑠) can be related to the
displacement of each seta in the y-direction (𝛥𝑦) by the beam theory.
𝛥𝑦 =𝐹𝑤−𝑠𝑙3
3𝐸𝐼 (2.2)
Where subscripts ‘w’ and ‘s’ represent wall and seta, respectively, while l, E and I are the
seta length, Young’s modulus and the second moment of area, respectively. At the point of seta
jump-off, assuming𝐹𝑤−𝑠 = 10 µ𝑁 , the maximum displacement of individual seta in the y-
direction is calculated as 𝛥𝑦 = 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 at
approximately 3mm in the animal trials. If we take 𝑟 = 3 𝑚𝑚 and 𝛥𝑦 = 18.6 µ𝑚 we get
𝛥𝑥𝑚𝑎𝑥 = 0.68 µ𝑚 , and a critical rotation angle 𝜃∗ = 0.11 for the peeling zone. Thus, the
peeling motion is lifting the seta root up instead of dragging it parallel with respect to the
substrate before jump-off. This indicates that the experimentally measured vertical pull-off force
(e.g. a 908 pulling in Autumn et al. [4]) could be adopted for our approximation. On this basis of
calculation, the length of the peeling zone and the force distribution in the peeling zone can be
determined by equation (2.2) and the scrolling geometry (i.e. r in Figure 2.17 (c)). Taking the
values of setae density, 14400 mm-2, and assuming that setae distribute in a square lattice
configuration, we get a setal spacing of approximately 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 three orders
of magnitude lower than the shearing force of a single toe at lower angles when clean [72]. Thus,
geckos can easily detach their toes through the sequential seta jump-off activated by DH.
27
(a) (b)
(c) (d)
Figure 2.16 (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 shoes on the dorsal surface of a gecko foot. A gecko foot showing toes in (c) flat, and
(d) hyperextended position without the ‘shoe’ [12].
28
(a) (b)
(c) (d)
Figure 2.17 Schematics of gecko toe peeling induced by (a) digital hyperextension (DH) from
distal to proximal direction without gecko shoe; and by (b) limb motion from proximal to distal
direction with gecko shoe; (c)A 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; (d) recovery
indices for trials with (black bars) and without digital hyperextension by steps (striped bars).
Numbers above bars are sample sizes. Error bars represent ±2.s.e [12].
29
Gecko Mimic Materials 2.5
Autumn et al. has summarized the gecko unique structure into the following properties.
(1)Anisotropic attachment, (2) a high adhesion coefficient, (3) a low detachment force, (4)
material-independent adhesion, (5) self-cleaning, (6) anti-self-adhesion, and (7) a nonstick
default state. Since the reveal of gecko structures, many attempts have tried to mimic gecko-like
materials [73–89].
Early attempts mimic the geometric features of gecko toe pad structures. Pioneer work
can be summarized in Figure 2.18. The method to mimic gecko strong adhesion systems can be
classified into the cast-molding, electron-beam lithography, soft and rigiflex lithography, and
chemical vapor deposition (CVD) method.
2.5.1 Cast-Molding Method
The pioneer attempt of making gecko fibrillar structure has been made as early as 2003
by Siddi et al. [90]. They use a stiff AFM probe indented into a soft flat wax surface to make a
master template. Then, liquid hydrophobic polymers (e.g silicone rubbers, polyester resin) are
obtained by consecutive peeling of the cured polymers off the template. They then develop this
method to fabricate polyurethane microfibers with wider fiber bases and a flat cap on top to
mimic gecko-like structure [91] (See Figure 2.18 (a)). This template assistant method was
further developed by Cho et al. [92] with PDMS micro-pillars , Chen et al. [93], and Kunstandi
et al. [94] (Figure 2.18 (b)) with PMMA pillars with AAA templates. Another template that is
widely used is photolithography defined silicon templates [95] and is based on the
microelectronics fabrication and affects the development of the entire information technology
and this method is led by Sargent et al. [96].
30
(a) (b)
(c) (d)
Figure 2.18 (a) SEM image of the isometric view of a polyurethane elastomer microfiber array
with 4.5 μm fiber diameter, 9 μm tip diameter, 20 μm length, and 44% fiber density scale bar: 50
μm using cast-model [91]; (b)PMMA pillars with high aspect radio here the diameter of fibers
can be as few as only 50nm using AAO template [94]; (c) mushroom shaped hairs with PDMS
with AAO template [96]; (d) template assistant polypropylene shows self-cleaning properties
[71].
20µm 2µm
30µm 100nm
31
2.5.2 Soft and Rigiflex Lithography
Soft-lithography [97,98] has a benefit of reducing cost which makes mass productions
possible. The mold can be directly created from the photoresist itself by photolithography. One
common choice for the mold is photoresist SU-8 which can massively duplicate negative PDMS
fibril arrays [99]. One significant drawback is its reduced resolution limitation due to the loss of
mechanical integrity when the pattern decreases to submicron range [100]. In order to overcome
the resolution limit, a modified soft lithography (known as capillarity-directed rigiflex
lithography) was proposed by Jeong et al. [101]. This technology can fabricate patterns with
resolution up to 100nm and high aspect ratios. Figure 2.18 demonstrates examples of soft
lithography.
Most of the methods described above are using polymers (e.g., poly(methyl methacrylate),
PMMA, polyurethane acrylate, and PUA. The advantages of using polymers are their similar
mechanical properties to gecko setae. They are easy to fabricate into fibrillar structures because
they are deformable. At the end it can easily transform into different shapes like mushrooms [102]
or branches, which show self-cleaning properties (not as good as gecko), yet are still very
impressive. Siddi et al. [102] and Gao et al. [35] discussed that the shape of the tip end plays a
key role in the gecko self-cleaning mechanism. This inspires us to discover the actual self-
cleaning mechanism and will be provided in detail in the following chapter.
2.5.3 Carbon Nanotubes
CNTs show outstanding mechanical properties [103], have a length-to-diameter ratio of
up to 132,000,000:1, and is considered as a good candidate to mimic gecko setae [88,104–118].
The Young’s modulus of CNTs is up to 1Tpa which makes it strong during the tension. Qu et al.
32
[10] have demonstrated that vertically aligned carbon nanotube (VA-CNT) arrays (Figure 2.19)
can generate an adhesive force 10 times than a gecko’s foot, which shows similar strong shearing
forces and easier detachment properties. Compared with polymers or gecko toe pads, CNTs are
smaller, harder and stiffer. It can dramatically increase the adhesion forces in a certain area.
Now scientists can adjust the radius, tube diameters, and packing density by changing the CVD
condition[119].
We now consider [120] the self-cleaning property of CNTs. Ali et al. [120] has
performed research on the self-cleaning property of CNTs and results show the CNTs regained
60% to 90% frictional strength when rinsed with water or under vibration. It is the surface
wettability difference that makes the self-cleaning properties change. This wetting variance has
also been reported elsewhere [121]. Since the gecko is actually a contact self-cleaning
mechanism demonstrated by Autumn et al. [11]. Until this point, there has been no report
demonstrating the dry self-cleaning property of CNTs. Future research directions to make self-
cleaning smart CNTs need to coat the CNTs with shape-memory materials or some smart
polymers.
33
Figure 2.19 (a) A book of 1480 g in weight suspended from a glass surface with use of VA-
MWNTs supported on a silicon wafer. The top right squared area shows the VA-MWNT array
film, 4 mm by 4 mm. (b and c) SEM images of the VA-MWNT film under different
magnifications. (d) Nanotube length– dependent adhesion force of VA-MWNT films attached
onto the substrate with a preloading of 2 kg. (e) Adhesion strength of VA- MWNTs with length
100 T 10 mm at different pull-away directions. The nanotubes and substrates shown in (e) are
not to scale [10].
34
CHAPTER 3
DYNAMIC ENHANCEMENT IN ADHESION FORCES OF MICROPARTICLES ON
SUBSTRATES IN AIR AND NITROGEN ENVIRONMENT
Introduction 3.1
The attachment/detachment of a micron-sized particle to and from a substrate is a
fundamental problem relevant to numerous natural phenomena and industrial processes. In-depth
understanding of the interfacial interactions between the particle and substrate may advance a
wide range of technologies including surface cleaning and self-cleaning, paper making [122],
printing [123], and coating [124]. The adhesiveness of a particle to a particular surface is
determined by complex interaction of forces. Although this adhesion force is only governed by
the deformation of the two bodies in contact, a full understanding of the properties of this contact
zone requires thorough analysis of elastic, plastic, and viscoelastic deformations of the particles
and surfaces [125]. Under high-speed contact, the dynamic effect must also be considered in the
analysis of particle-substrate interactions, which may alter the adhesive behavior of particles.
The first popular model to describe the interactions between micro-particles and substrates was
the Hertz model, followed by the JKR model derived by Johnson, Kendall and Roberts, and the
DMT model proposed by Derjaguin, Muller and Toporov [29]. Although the JKR and DMT
models include attractive inter-particle forces, the adhesion forces are only related the initial
surface energies and elastic deformation of particle and substrate in these models. Maugis and
Pollock (MP) further developed a model based on JKR model to discuss the plastic deformation
between particles and substrates [30].
The above models are based on a balance between potential energy, surface energy, and
elastic/plastic deformation within the solid bodies and ignore kinetic effects during detachment.
35
However, in most cases such as particles in turbulent air flow [126], centrifuge technology [38],
industrial powders for pharmaceuticals [127], and food applications [128], detachment is within
microseconds or even shorter periods of time, and the detaching forces could be strongly
influenced by a dynamic effect. Recently, some work has been done on the dynamic effect of
micro-particles [6,36,129]. It was shown in these studies that the adhesion force is dependent on
contact frequency or pull-off speed, as well as applied force [38] and the loading duration
[39,130]. Modified JKR models were developed to describe the dynamic phenomena by
introducing a damping coefficient [131]. However, the experiments were limited in small range
of pull-off velocity; and their results contradict to each other’s. Although the modified JKR
models were developed to describe the dynamic process, the dynamic mechanism is still unclear
in particle-substrate interaction systems.
In the present work, we report a dynamic adhesion effect for polystyrene (PS), SiO2 and
Al2O3 micro-particles on fused silica, polystyrene, and sapphire substrates. The adhesion (pull-
off) force was measured under different retraction (via z-piezo) velocities varying over four
orders of magnitude. It was found that the adhesion was drastically enhanced by the velocity. A
model was developed to explain the dynamic effect observed in the experiment. The effects of
pre-loading forces, loading duration, particle size and humidity on the adhesion forces were
measured and discussed.
Experimental Setup 3.2
PS, SiO2 and Al2O3 microspheres (Microsphere-Nanosphere.com) ranging from 5-50 µm
in diameter were carefully dispersed onto a fresh glass slide. Both the microspheres and the glass
slide were cleaned in DI water by an ultrasonic cleaner (Branson Inc.) for 15 minutes, then dried
36
in air under a lamp before being dispersed. Operated by an atomic force microscope (AFM)
micromanipulator system (Scan-Icon AFM, Bruker Co., Inc), a tipless cantilever (ACTA-TL-50,
AppNano) attached to the AFM first captured a tiny glue droplet (diameter: ~5 µm) dispersed on
a glass slide, then moved towards a target particle and glued it at the end of the tipless cantilever
by pressing the glue droplet on the particle. A 30 minute slow cure epoxy (30min Slow-Cure
Epoxy, Kite Studio Co., Inc.) was used as the glue so that there was sufficient time for the
operation. Before testing, the glued microsphere (Figure 3.1) was cured and dried in air for 24
hours at room temperature. Furthermore, the particles were examined under a scanning electron
microscope (SEM, FEI Quanta ESEM) to ensure that the particles surfaces were not
contaminated with excess glue. The approach and retraction of the microspheres on substrates
were made with a closed-loop AFM system at different retraction (z-piezo) velocities. Forces
between particles and substrates versus time were measured and recorded for different retraction
velocities during the test. Three kinds of substrates were used in the test, including sapphire,
fused silica and polystyrene, all of which were sample kits from Bruker, CA, USA. All the
samples were cleaned with the same procedure used to clean the glass slides described above.
Tests were carried out in a sealed electrochemical cell (Bruker ECAFM) filled with nitrogen
(99.99% dry nitrogen) at room temperature. The dry nitrogenous environment (humidity<1%)
was established by pumping the dry nitrogen into the sealed system for 1 hour. The same
experiment was also conducted in air with a humidity of 56% at room temperature. The spring
constant of the probe was measured with thermal tune methods in the AFM system. The spring
constants of the cantilevers with SiO2, PS and Al2O3 particles were 4.916, 5.353 and 4.130 N/m,
respectively. The spring constant was measured before and after the adhesion tests and a small
variation of ±2% was observed, which is negligible. Force-time curves were collected with an
37
approaching/retracting cycle of the tip by modulating the cantilever at a frequency well below its
resonance frequency, as shown in Figure 3.2. The approaching and retracting curves kept an
exact linear relationship even at a velocity of 156 µm/s. Thus, the effect of nonlinearity of the
system on the dynamic effect can be ruled out. In addition to the approaching and retraction
velocities, several factors such as preload and surface delay time (loading time), could affect the
final pull-out force. Here we controlled the preload and the surface delay time to eliminate the
effect of approaching velocity on the pull-out force. During the adhesion measurements, the tip
was pushed to the substrate until the desired normal preload value was reached. The load was
then kept constant until the withdrawal of the tip. All adhesion forces were measured 3 times to
ensure accuracy and consistency.
38
(a) (b)
(c) (d)
Figure 3.1 (a) SEM image of a 10.7 µm diameter SiO2 microsphere glued on a tipless AFM
cantilever; (b) SEM image of a 10.4 µm diameter Al2O3 microsphere glued on a tipless AFM
cantilever; (c) SEM image of a 9.8 µm diameter polystyrene microsphere glued on a tipless AFM
cantilever; (d) Schematic of AFM measuring system in air.
39
Figure 3.2 A typical ramping process: (a) z-piezo movement vs. time, and (b) force vs. time (here
the movement distance and the force were recalculated from input voltage and output detective
voltage, respectively). The cot(θ) is linearly related to retraction speed and can be adjusted from
0.02 µm/s to156 µm/s.
40
Results 3.3
3.3.1 Dynamics Process during the Retraction of Microspheres
The adhesion forces between the particles and substrates were measured at different
approach/retraction velocities. Here in Figure 3.3 are three typical pull-off forces for three
different substrates, which reveals that the adhesion forces are different under low and high
velocities on these three particles. Since the displacement and force at the particle-substrate
separation point is critical to the understanding of the dynamic loading effect, the displacement
and force of the microspheres were examined and recorded versus time during the indentation
loading by using a high speed data capture (HSDC) technique (Bruker) with a time resolution of
0.2 µs. Figure 3.4(a) shows the displacement of the cantilever tip versus time for Al2O3-sapphire
system. After snapping off from the substrate, the tip quickly returns to its original shape. For the
z-piezo in our system, the transition time from a standstill to target speed is about 1 µs and then
the speed reached a static state. The velocity of the particles before snapping-off was extracted
from the measurement and plotted against z-piezo velocity in Figure 3.3(b). The tip (pull-off)
velocity is slightly larger than and increases nonlinearly with increasing the piezo velocity. We
also measured the particle velocity against piezo velocity when the particle was not in contact
with the substrate. In this case, these two velocities are almost the same in the measuring range.
Therefore, the sphere-substrate interaction may be attributed to the difference between the pull-
off velocity and piezo velocity.
41
(a)
(b)
42
(c)
Figure 3.3 Indentation curves of (a) PS-PS (soft-soft); (b) Al2O3-Sapphire (hard-hard); and (c)
PS-Sapphire (soft-hard) particle-substrate systems at low and high loading speeds.
(a)
43
(b)
Figure 3.4 (a) Displacement of Al2O3 microparticles on a sapphire substrate when the tip
snapped off at a velocity equal to 156 µm/s, measured by a HSDC technique, and (b) Particle
pull-off velocity vs. z-piezo velocity derived from HSDC technology for a loading time of 10s
and a pre-loading force of 1 µN.
3.3.2 Effect of Retraction (Z-Piezo) Velocity on Adhesion Forces in Air
The effect of retraction (i.e., z-piezo) velocity on the adhesion force of SiO2 microspheres on
different substrates was tested. Here, the loading time was kept to 10s to eliminate the effect of
approaching velocity on the results. Figure 3.5 (a) shows the adhesion forces as a function of the
retreating velocity of the AFM piezo for SiO2 microspheres (diameter 𝑑 = 10.7 µ𝑚) in contact
with three substrates —sapphire, fused silica and polystyrene in dry nitrogen and in humid air.
The adhesion force increases by 30%~50% with increasing velocity for all three substrates in
both dry and wet environments. Humidity further increases the magnitude of this trend (Figure
3.5 (a)). Take the fused silica substrate as an example, the absolute adhesion force in air
44
(humidity=56%) is 25% greater than that in nitrogen when the retraction velocity is 0.02 µm/s
and 34% greater than the dry environment when retraction velocity is 156 µm/s. This can be
explained as a contribution of capillary forces [132] and the formation of water bridges, where
water has a contact angle of 40° on the hydrophilic SiO2 particles and the fused silica.
Similar dynamic effects were also observed for PS and Al2O3 micro-particles, as shown in
Figure 3.5 (b) and (c), respectively. For all these microspheres, the adhesion force significantly
increases when the retreating velocity exceeded approximately 1 µm/s. While hard SiO2
microspheres on soft PS substrate generate the highest adhesion force (Figure 3.5a), the adhesion
forces of hard Al2O3 microspheres on hard sapphire substrate increases the most rapidly (almost
67%) with increasing the retraction speed, as show in Figure 3.5(c). Overall, there is a 15%-70%
increase in adhesion force for these particle-substrate systems in response to the velocity increase
from 0.02 to 156 µm/s.
We also observed that the absolute adhesion forces in these three substrates are different
even when the tests are conducted with the same particle and the same parameters such as
retraction velocity and humidity. Here the differences cannot be solely explained by surface
energy. For example, PS has the lowest surface energy; however, the adhesion force between PS
and different substrates is not the weakest adhesion forces. This can be explained by the principle
of soft contact, which states that there are viscoelastic or plastic deformations found locally on
either particles or substrates which increase the contact area thus increasing the force of
adhesion. This incongruence between surface energy and adhesion forces has been established
and reported in other studies [133].
45
(a)
(b)
46
(c)
Figure 3.5 The relationship between retraction speed and adhesion forces of (a) 10.7-µm-
diameter SiO2 microsphere; (b) 9.8-µm-diameter PS microsphere; and (c) 10.4-µm-diameter
Al2O3 particles on sapphire, polystyrene and fused silica substrates for a loading time of 10 s and
a pre-loading force of 1 µN.
3.3.3 Adhesion Forces vs. Preload and Loading Time
Preload and loading time also affect the adhesion forces. Figure 3.6 shows the adhesion
force of Al2O3 microspheres (diameter d=10.4 µm) on sapphire as a function of loading time
under the same preload in dry nitrogen and air with a humidity of 56%. With increasing loading
time, the adhesion force stays nearly constant in the nitrogenous environment but it increases
rapidly in the air at the beginning and then reaches a plateau after 10 seconds. This phenomenon
can be explained by the capillary attraction of water between particles and substrates. Figure 3.7
shows the adhesion forces as a function of preload, measured in dry nitrogen and humid air. The
adhesion force keeps nearly the same until the preload reaches 10 µN. When measured in humid
47
air, the adhesion forces shift to a higher level but the trend is similar to those measured in dry
nitrogen—force increase after the preload exceeds the critical value.
Figure 3.6 The adhesion forces between Al2O3 particle and sapphire substrate under different
loading time for a preload of 1µN and here the retraction velocity of 1 µm/s.
Figure 3.7 The adhesion force between Al2O3 particle and sapphire substrate under different
preloads for a loading time of 10s and here the retraction velocity is 1 µm/s.
48
3.3.4 Adhesion Forces vs. Particle Diameter
In order to further understand the effect of the size of particles on dynamic adhesion, we
glued Al2O3 particles of varying sizes on tipless cantilevers and measured the adhesion force on
sapphire substrate in dry nitrogen. The results are plotted against particle diameter in Figure 3.8.
For a very low retraction velocity (0.02 µm/s), the adhesion force linearly increases as the
diameter of the particle increases, which is consistent with the reports in the literature [134]. In
the case of high retraction velocity (156 µm/s), the force-diameter curve becomes nonlinear. The
dynamic enhancement of the adhesion force was clearly shown for these microspheres with
different sizes.
Figure 3.8 The adhesion force between Al2O3 particle and sapphire substrate in dry nitrogen as a
function of particle diameter for a loading force of 1 µN and a loading time of 10 s.
Discussion 3.4
Our experiments show that the retraction velocity has a significant effect on the adhesion
forces between particles and substrates. Dynamic factors such as particle inertia and viscoelastic
49
deformation could be responsible for the increase in adhesion force. First, we consider the
inertial effect. In our experiment, shown in HSDC data, a velocity increase from 0 to 156 µm/s
was achieved in about 1µs. This velocity change can generate an inertial force 𝐹𝑖 = 1 𝑛𝑁 on a
10-µm-diameter SiO2 microsphere (𝑚𝑝 = 1 ∗ 10−11 𝑘𝑔). The AFM cantilever can also generate
an inertia which increases the force. The sudden release of the cantilever along with the attached
particle will generate inertial force Fi on both the AFM tip and the particle. According to the
beam theory, maximum force acceleration of the tip can be determined as
𝐹𝑖 = �𝑚𝑝 + 𝑚𝑒�𝑎𝑚𝑎𝑥 (3.1)
Where e s33 /140m m= is the effective mass of AFM cantilever [135]. The maximum
inertial force acting on the particle is estimated to be 𝐹 = 9 𝑛𝑁 for an AFM cantilever of 120 x
30 x 4.5 µm (𝑚𝑠 = 4 ∗ 10−11 𝑘𝑔), used in the experiment, which is negligible compared to the
measured adhesion force. In fact, the inertia estimated above was generated at the beginning of
the loading or after particle-substrate separation could not affect the final adhesion. Using the
HSDC technique, we have measured the displacement vs. time just before particle separation
from the surface, and further calculated the acceleration of the microsphere. The acceleration
increases with increasing loading velocity. The maximum acceleration of the particle is ~ 5 m/s2,
yielding an inertia of ~ 1 nN, which is also negligible. Thus, the inertia of the particle and
cantilever is not the major factor for the significant increase in adhesion force.
Second, we examined the effect of viscoelastic and plastic deformation in the contact
interactions between particles and substrate. As shown in Figure 3.7, when the preload exceeds
10 µN, there is a significant increase in adhesion force. This indicates that plastic deformation
may occur during the loading/unloading cycle if the preload exceed 10 µN. It is estimated from
Maugis Pollock theory [136] that plastic deformation may occur when the preload exceeds 1 µN
50
in PS-PS system. Thus, the material and testing conditions in this experiment are not in the range
of plastic deformation; all the substrates and particles elastically deform in the tests. On the other
hand, it is well known that polymer materials (PS) usually show larger viscoelastic deformation
than ceramics do. The adhesion forces due to the dynamic effect should be larger in PS-PS
contact systems than those in the ceramic-ceramic contact systems because of viscoelastic
deformation. However, our experiment results clearly show that the force gain with increasing
the velocity in PS-PS system is the smallest one among the contact systems in dry nitrogen.
Thus, the viscoelastic deformation plays a minor role in determining the dynamic effect of the
particles in the current system. The third reason is the local surface charge effect. We glued gold
particle at the end of AFM probe and tested the dynamic effect under different retraction
velocities on silicon wafer substrate. Since a dynamic enhancement was also observed in this
system, we believe the surface charge does not change the trend of dynamic enhancement of the
systems.
Modeling of the Dynamic Enhancement 3.5
The separation of a microsphere from substrate during the unloading process can be
considered as a crack propagation process along the sphere-substrate interface. In the general
context of fracture mechanics, several regimes of behavior are often reported. According to the
Griffith energy balance concept, in a quasistatic regime the energy release rate G is roughly
constant and equal to a material dependent critical energy release rate, G ∼ Gc [137]. In unstable
configurations or during fast loading the kinetic energy becomes important, leading to a dynamic
regime [37,138]. In the slow unstable regime, i.e. at rupture velocity lower than the Rayleigh
wave speed, the crack propagation speed is roughly proportional to the difference between G and
51
Gc (e.g. [139]). However, in these brittle regimes, the propagation is strongly controlled by the
loading type (imposed stress or imposed displacement), the loading rate and the material
rheology. In our case, as shown in Figure 3.3b, the retraction speed determines the pull-off speed
of the particles, consequently affecting the crack propagation rate and the energy release rate, as
well as the adhesion forces. Using basic models of adhesion and a power law relation for the
dependence of surface energy on crack propagation speed, we present a simple model for the
adhesion dependence on crack propagation speed for a single spherical indenter. Maugis [57]
showed that for displacement-control system (such as the AFM used in this experiment) and a
spherical indenter, the pull-off (adhesion) force is related to the critical energy release rate G by
the equation
𝐹 =56
𝜋𝑅𝐺 (3.2)
where R is the radius of the spherical indenter. The dependence of G on crack
propagation speed u can be represented by [140]
𝐺 = 𝐺0 �1 + � 𝑢𝑢0�𝑚� (3.3)
where G0 is the critical energy release rate as u is approaching zero, m is a scaling
parameter that is empirically fitted to the experimental data, and u0 is the crack propagation
speed at which G doubles to G0. Such a power law has been shown to hold for polymer materials
at low crack propagation speeds. It was shown that the speed of particles is proportional to AFM
piezo speed V (Figure 3.3b) while crack propagation rate u increases with increasing the speed of
the particle. So, it is reasonable to assume that the crack speed u is also a power law relation for
the retraction speed V, 𝑢 = 𝑏𝑉𝑘, where b and k are the parameters. Combing the relationship
with Equations (3.2) and (3.3) yields
52
𝐹 = 𝐹0 �1 + 𝐶 �𝑉𝑉0�𝑛� (3.4)
Where 𝐹0 = 5𝜋𝑅𝐺0/6 is the adhesion force as V is approaching zero, V0 is the reference
velocity when 𝐹 = (1 + 𝐶)𝐹0 , and n and C are the dynamic parameters depending on the
systems.
The above model was compared with the experimental results. For small retraction
velocity, it is predicted that adhesion force is proportional to particle diameter, which is
consistent with the experiments (Figure 3.8). We have used Equation 3.4 to fit the experiments,
and the results of the least square estimate are shown in Fig.8. Basically, the theoretical relation
agrees well with experimental data. Among the tested systems, soft-soft (PS particle on PS
substrate) system exhibits the weakest dynamic effect while hard-hard systems show the largest
dynamic enhancement. The dynamic enhancement may be attributed to the “bridging” due to
mechanical interlocks at rough contact interface in the case of ceramic-ceramic contact systems
or the formation of polymer chains bridges [140] between the particles and substrates. Humidity
strongly enhances the dynamic effect of the soft-soft and soft-hard systems. As mentioned
before, this may be attributed to the capillary forces. In humid air, extra water ‘bridging’ may be
formed at the interface between the particles and substrates, further enhancing the dynamic effect
at the interface.
53
Figure 3.9 Normalized adhesion forces (ΔF/F0) versus velocity, measured and fitted for a
preloading of 1 µN and a contact time of 10 seconds. Al2O3-sapphire, SiO2-fused silica and PS-
PS refer to Al2O3 particle, on sapphire substrate, SiO2 particle, on fused silica substrate and PS
particle on PS substrate, respectively.
Figure 3.10 Dynamic scaling parameter n and coefficient C as a function of microsphere
diameters for adhesion force of Al2O3 particles on sapphire substrate in dry nitrogen.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.01 0.1 1 10 100
Nor
mal
ized
adh
esio
n fo
rce
Retraction Velocity (µm/s)
PS-PS in nitrogenSiO2-Fused silica in nitrogenAl2O3-Sapphire in nitrogenSiO2-Fused silica in air (50%)Al2O3-Sapphire in air ( 50%)PS-PS in air (50%)fitting lines
0
0.05
0.1
0.15
0.2
0.25
0.3
0
0.1
0.2
0.3
0.4
0.5
0 20 40 60
Cn
Diameter of particle (µm)
n
C
54
Dynamic scaling parameter n and coefficient C were extracted by fitting the experimental
results with Equation 3.4 and the best least square methods, and plotted against particle diameter
(Figure 3.9) for the adhesion forces between Al2O3 particles on sapphire substrate. The scaling
parameter n is nearly constant (n~ 0.45) while the coefficient C is dependent on the particle
diameter for particle diameter ranging from 5 to 50 µm. This suggests that the scaling parameter
n is not closely related to these material properties but determined by the contact geometry.
Interestingly, the measured parameter (n) is in the range of the measurements for other crack
propagation systems.
Conclusions 3.6
In this chapter, the dynamic loading of PS, SiO2 and Al2O3 micro-particles on PS, fused
silica and sapphire substrates have been tested using AFM. Increasing the retraction velocity
from 0.02µm/s to 156 µm/s leads to an increase in the adhesion forces by 15% ~ 70%. Hard-hard
(Al2O3 particle on sapphire) material contact interaction shows the highest increase in adhesion
force while soft-soft (e.g., PS particle on PS) contact couples give the lowest values of adhesion
increase. Humidity enhances both static and dynamic adhesion.
A dynamic model based on crack propagation was developed to predict the adhesion
forces of the dynamic interactions, which matched well to experiments. The dynamic
enhancement is induced by fast crack propagation along the particle-substrate interface which is
bridged by mechanical interlocks, polymer chain entanglement or water.
Further research is to test the dynamic enhancement in different environment and
particles in different scale. The dynamic effect need to be verified under nanoscale particles and
55
also particles in aqueous solution. Will the dynamic enhancement increase or decrease in liquid
solutions and what is the reason behind this? This will be discussed in the next chapter.
56
CHAPTER 4
DYNAMIC ENHANCEMENT IN ADHESION FORCES OF MICROPARTICLES
ON SUBSTRATES IN AQUEOUS SOLUTIONS
The mechanisms of attachment and detachment of a micron-sized particle to and from a
substrate in an aqueous environment is a fundamental concept relevant to numerous natural
phenomena and industrial processes. Here we report a dynamic-induced enhancement in
adhesion interactions between colloidal particles and substrates in an aqueous solution. This
effect was identified by studying the trends of various particles (SiO2, Al2O3, and Polystyrene)
on various substrates (silicon wafer, polystyrene, fused silica). Multiple tests were conducted to
determine the impact of several factors including loading speed, loading force, and Young’s
modulus. We were able to isolate the change in retraction velocity over four orders of magnitude
as the cause of the dynamic effect using the colloid probe technique on an atomic force
microscope (AFM). The presence of a dynamic effect became clear upon observation of 20-100%
increase in adhesion force resulting from an increase in retraction velocity from 0.02 to 156 μm/s
during particle and substrate interactions. A dynamic model was developed to predict the
adhesion forces resulting from this dynamic effect, and these predictions correlate well with the
experimental results. The influence of dynamic factors related to adhesion enhancement, such as
hydrodynamic effect, particle inertia, surface charging, viscoelastic deformation, and crack
propagation were discussed to understand the mechanisms of dynamic enhancement.
57
Introduction 4.1
Among material scientists there is an interest in understanding the nature of dispersion or
agglomeration phenomenon in liquids. This effect, which is the key factor in a number of
industrial processes such as paper coating [122,141], drug delivery [142], pharmacology and
chemical development [127], is currently known to be governed by four forces: Van der Waals,
electrostatic, intermolecular, and surface forces. Although theoretically all four of these forces
affect the dispersion phenomenon, many experimental studies [143–145], concerning adhesion
have revealed that only the Van der Waals and electrical double layer (electrostatic) forces play
significant roles in the dispersion phenomenon. Van der Waals forces are the long-range
attraction forces that attract particles. The Electrical double layer force is the stronger medium-
range repulsion force that prevents particles from self-assembling. In order to describe the
interaction between particles in liquid due to these forces, scientists have created well developed
theories and mathematical models. One popular model that discusses such particle interactions is
the DLVO theory [146], which is built on the assumption that the Van der Waals and electrical
double layer forces are the key factors that affect the adhesion force between particles in liquid.
The limit of DLVO theory is that the particle must be static or quasi-static while detaching.
However, in industries such as food [128], pharmaceutical [127] and centrifuge technology [38],
the detachment process occurs within a microsecond. Thus the detachment forces in these
situations are strongly influenced by the dynamic effect. Until now, there has not been any
integrate study concerning the effect in aqueous solutions.
The study of the adhesion force required to separate two surfaces plays a critical part in
understanding the dispersion affect, and has been greatly furthered by the development of the
Atomic Force Microscope (AFM) and more specifically the Colloidal probe technique. This
58
innovative technique involves gluing a micro-size particle at the end of a tipless AFM probe
allowing researchers to test the interaction force between colloidal particles and a substrate in a
liquid environment, with accuracy up to a nano-newton [125,147]. The adhesion forces in liquid
were previously analyzed by Vakarelski et.al. [148] and show the existence of electrostatic
repulsive force and the Van der Waals attraction forces as predicted by DLVO theory. Other
factors such as pH [148], hydrodynamic forces, applied load [149], contact time, scan speed,
stiffness, the effects of the previously stated parameters in water, surface polymerization, and
solution ion concentration will affect the adhesion forces [149]. No group before this had ever
investigated the dynamic effect of micro-particles on adhesion forces in aqueous solutions.
Experimental Setup 4.2
4.2.1 Surface Preparation
For the experiment three difference surfaces were prepared: a clean hydrophilic PS
sample, a clean hydrophilic silicon wafer, and a fused silica sample. The summary of materials
properties can be found in Table 2. All substrate samples were cleaned in acetone and then in DI
water in an ultrasonic cleaner for 15 minutes and dried in compressed air before testing.
4.2.2 Force Measurement
Microspheres (Microsphere-Nanosphere.com) with diameter of 10µm made of PS, SiO2
and Al2O3 were carefully dispersed onto a piece of fresh glass slide. The particles were picked up
from the glass and glued at the end of a tipless probe with spring constants of 6N/m (AppNano
Co., Inc) by a 30 minute slow cure epoxy (30min Slow-Cure Epoxy, Kite Studio Co., Inc.) using
an atomic force microscope (AFM) initial manipulator system (Scan-Icon AFM, Bruker Co., Inc).
59
The glued microsphere was cured and dried for 24 hours before testing. Particles diameters and
composite were measured under SEM and EDAX system inside SEM (FEI Quanta ESEM) to
ensure that no glue ran on to the upper surface of the cantilever so as to obscure the laser beam
reflection of the AFM or covered the particle to contaminate the contact surface. The spring
constants were determined by thermal tune method in Bruker system before and after the
experiment and showed variation within 1%. The glued particle was then cleaned with DI water
carefully before each test.
In the test a drop of approximately 200µL of DI water was applied onto the surface of the
substrate, and the cantilever was then completely immersed into the drop so that a meniscus
formed around the edge of the scanner, well away from the cantilever. The laser was then
recalibrated to adjust for the bending of light caused by Snell’s law. After waiting thirty minutes
to minimize the mechanical noise of the system, the experiment was conducted in an enclosed
room where the temperature was controlled at 22°C.
The attachment and detachment of the attached microspheres from clean substrates were
carried out at speeds ranging from 0.02 µm/s to 156 µm/s by the AFM(Scan-Icon AFM, Bruker
Co., Inc). The force between particle and substrates (Fw-p) versus retreating speed were
measured and recorded during the test.
Table 5.1 Parameters of materials
Substrates Particles Material Fused Silica Silicon Wafer PS PS SiO2 Al2O3
Young’s Modulus (E, GPa)
73±5
130-188
2.7
2.7
70
70
Surface Energy (Δγ, N/m)
4.3
2.04
0.0406
0.0406
2.672
2.672
Contact Angle (pure water)
40±1
43
86±2
86±2
40
40
60
Figure 5.1 Schematic of AFM measuring system in liquid
Results 4.3
4.3.1 Hydrodynamic Effect
During colloidal probe ramping in liquid, there is a hydrodynamic effect that the AFM
probe must overcome, especially at high velocities. The effect of velocity on the hydrodynamic
forces was previously discussed by Zhu et. al. [150] and Horn et.al. [151].
Fh = −6πηR2h
h (h ≪ R) (4.1)
where η is the viscosity of the liquid, R is the radius of the microsphere ℎ is the
61
velocity of the microsphere relative and perpendicular to the substrate and ℎ is the separation,
which is the distance of closest approach of the sphere surface to the substrate surface.
In theory, hydrodynamic forces increase linearly with respect to velocity and also depend
on the distance between the particle and the substrate: the smaller the distance is, the more
difficult it is for the liquid to move out of the remaining gap. An approaching colloid probe
produces a repulsive force and a retracting probe produces an attractive force. In classical
theories one can assume that when the probe is immersed in water, the probe and the piezo can
be considered to move jointly. In practice, the local hydrodynamic force is affected by surface
properties and local charges and roughness. Both simulation and experimentation show that
liquids can undergo a liquid-to-solid transition when confined between solid walls separated by
only a few molecular diameters [125]. In Figure 4.2 is the theory hydrodynamic force curve
between particle and substrate in aqueous solution.
Figure 5.2 DLVO theory curve of hydrodynamic force in water
In the AFM test, the detachment system contains both the particle and cantilever. Thus,
the cantilever’s resistant force during the rapid retraction in water should also take into
62
consideration, especially at high retracting speed. In the test, the probe was immerging into the
water (in Figure 4.1). The resistant force was measured by ramp the particle in the water under
different velocities. In the test, the distance between the particle and substrate is long enough to
eliminated surface charge and potential influences from the substrate. The deflection of the
cantilever under different velocities was measure and is considered as the hydrodynamic forces
of the cantilever-particle system (in Figure 4.3).
Figure 5.3 Experimental hydrodynamic force vs. retraction velocity ranging from 0.02 µm/s to
156 µm/s. Here the solid line is the trend for this particular probe.
4.3.2 Adhesion Force Curve under Dynamic Loading in Aqueous Solution
After the forces resulting from the hydrodynamic effect were determined, the interaction
forces between the particles and substrate were be measured via dynamic indentation loading at
different approach/retraction velocities. Figure 4.3 shows a typical force-displacement curve of a
SiO2 particle on fused silicon substrate, PS particle on PS substrate and SiO2 particle on PS
substrate in liquid with ramping velocity of 0.02 µm/s and 156 µm/s respectively. During the
63
approach process, there is a long range repulsive force which is explained as the electrostatic
double layer force in DLVO theory. Therefore there is no jump in contact force coming from the
Van der Waals forces during the approaching process as seen in indention in air. During the
retraction process we are interested in the adhesion forces and from the curve in Figure 4.3(a) we
can see that for hard-hard couple systems, the interaction force reduces to zero quickly when the
displacement reaches the critical point during the retreat of the AFM cantilever. When the
particle or substrate is soft (PS materials), the force gradually reduces to zero after the
displacement reaches the breaking point instead of jumping. If both the substrate and particles
are soft (PS-PS), the force reduces to zero even more slowly. It can be clearly seen from these
figures that the loading speeds strongly affect the jumping points or adhesion forces. The
temperature was 22°C for all the experiments.
(a) (b)
64
(c)
Figure 5.4 Indentation curves of (a) SiO2 particle on silicon wafer (hard-hard), (b) PS particle on
PS (soft-soft), and (c) PS particle on silicon wafer (soft-hard) particle-substrate systems at low
and high loading speeds. Here the pre-loading is 1 µN for all the experiments.
4.3.3 Adhesion Forces vs. Loading/unloading Velocity
The adhesion force was calculated by substrate the hydrodynamic force from the
measured pull our forces. It is noticed that each probe has different hydrodynamic forces. The
final adhesion forces in Figure 4.5 were calculated by measurement forces substrate the
hydrodynamic forces for each particular probe at particular speed. This eliminated them from
consideration when analyzing the dynamic effect.
From Figure 4.5 we noticed that the adhesion forces increase as the velocity increases for
SiO2-fused silica and PS-silicon wafer systems but the percent of increasing is much smaller in
the PS-PS system. Furthermore, we tested the effect of loading speed on the adhesion force of
SiO2 microspheres on different substrates at different velocities and kept the preload at 1 µN for
the entire experiment. Figure 4.5(a) shows the adhesion force as a function of the retreating
65
velocity of the AFM tip for SiO2 microspheres (diameter d= 10.7 µm) in contact with three
substrates —fused silica, polystyrene, and silicon wafer. The adhesion force increases with an
increase of the velocity for all four substrates. When the velocity changes from 0.02 µm/s to 156
µm/s, the adhesion force doubles. Another interesting result in Figure 4.6 shows that when the
particle enters the water from the air, the adhesion force decreases with respect to time before a
stable level is reached. The final adhesion force is only around 25% of the initial adhesion force
and can be explained by the air bubble surrounding the particle when it crosses the threshold
from water into air. It has been reported that roughness [132] is an important factor which
affects the adhesion forces. Here, the three substrates have a roughness less than 1nm so the
roughness effect can be ignored.
(a) (b)
66
(c)
Figure 5.5 The relationship between retreating speed and adhesion forces (Fp-w) of (a) 10.7 µm
diameter SiO2 microsphere, (b) 10.4-µm-diameter PS microsphere, and (c) 9.8 µm Al2O3
microsphere. Here the loading is 1 µN and contact time is 10s. The hydrodynamic effect has
been removed from the measurement.
Figure 5.6 Adhesion force between a SiO2 particle and fused silica substrate in a drop of water
under different times. Here the loading is 1 µN and contact time is 10 s.
67
Table 5.2 Parameters of materials for different surfaces obtained using atomic force microscope
Sample Fused silica PS Silicon wafer
Average roughness 𝑅𝑎(nm) 0.793±0.041 0.587±0.031 0.404±0.038
Correlation length, ξ (nm) 12.12±1.1 13.92±1.6 9.03±0.3
Discussion 4.4
Despite the prevalent use of DLVO theory, there is a general consensus that it is not a
complete theory. This inconsistency is due to the presence of well documented forces and
environments that affect adhesion but are not included in the DLVO theory. Although many of
such forces have already been studied, the concept of understanding the adhesion force in water
with respect to changes in velocity is a new direction. The results of the current study, however,
do indicate that velocity significantly influences the adhesion force.
In order to verify the presence of the dynamic effect we must first understand the
complicated system in which the experiment is taking place, taking into account the effects of
every parameter from the simplest to the most obscure and make certain that they are not the
cause of the variation we find. The first forces that must be discussed are the DLVO forces. This
model takes into consideration the Van der Waals force and the electrical double layer forces.
When considering these forces we found that the Van der Waals interaction forces are the
primary adhesion force. However, Van der Waals forces are very thoroughly understood and are
neither the cause nor the result of the dynamic effect trend. The influence of electrical double
layer forces can similarly be eliminated because all tests were conducted in water at all times to
keep the double layer force constant. In a previous study, Vakarelski et. al [148] analyzed the
68
adhesion force between a silica particle and a mica surface in water and electrolyte solutions and
showed that the adhesion force is sensitive to contamination and roughness of the surfaces, and
that adhesion force increases as the surface contact time increases. The effects of these
parameters can be ignored as the roughness of fused silica, PS, and silicon wafer that is 0.793 nm,
0.587 nm and 0.404 nm respectively (as shown in Figure 4.8) Given these small values, the
distortion due to roughness has a negligible impact on the adhesion forces.
Our result showed that the retreating velocity has a significant effect on the adhesion
force between SiO2 and Al2O3 particles and substrates. Dynamic factors such as particle inertia,
hydrodynamic forces under high velocity, and material damping could be responsible for the
positive difference between forces recorded at high-speeds and those recorded at low speeds.
Probes with various particle tips were also tested. Thus, hydrodynamic forces were accounted for
by determining the adhesion force caused by the hydrodynamic effect before measuring adhesion
forces. This eliminates them from consideration when analyzing the dynamic effect.
Apart from the conspicuous effects of the dynamic adhesion forces there are other trends
that must be addressed. First and foremost is the effect of the Young’s Modulus of the particles.
Figure 4.4 shows that for hard-hard and soft-hard particle-substrate interactions, the dynamic
effect is demonstrated; as there are noticeable differences in the two different curves. The
dynamic effect is present more for SiO2 and Al2O3 particles, but less in PS particles. Figures
4.4(a) and 4.4(c) demonstrate a significant change in hard-soft particle-substrate adhesion as well.
This phenomenon can be attributed to the fact that SiO2 and Al2O3 are materials with high
Young’s Moduli, while PS has a low Young’s Modulus. Table 4.1 shows the material properties
of particles and substrates. With 1 µN of pre-loading force soft particles exhibit the tendency to
swiftly conform to the surface via elastic deformation, while hard particles do not conform. This
69
shows that the dynamic effect is not only dependent upon velocity but also upon the elastic
deformation determined by the Young’s Modulus of the materials. This phenomenon was
originally described by Xu et al [152]. Visualizing the separation of the particle as a crack
forming between the particle-substrate interfaces, we must recognize that the force caused by the
dynamic effect is roughly proportional to the crack propagation speed. The propagation speed of
a crack depends upon the shape of interface being cracked. Thus, the value of Young’s Modulus
determines how much the particle will deform in order to conform to the substrates’ surfaces.
This is due to the Young’s modulus being a measure of stiffness, therefore a particle with a
larger Young’s Modulus will be stiffer and less compliant to deforming into another shape. The
conformation of the particle determines the shape of the interface which in turn affects the
propagation of the crack. The crack propagation determines the strength of the adhesion force.
This is clearly shown in our results: the hard particles do not conform to the surface of the
substrate so much of the contact are is limited to asperities, and the adhesion force exhibits
evidence of the dynamic effect. Crack propagation in such an interaction would differ from the
crack propagation of a soft particle, which would readily deform across a substrate and its
surface asperities, resulting in a lower adhesion force that does not show evidence of the
dynamic effect.
There is additional force, capillary force, which must be accounted for in this study. The
interaction between a particle and a substrate in a liquid environment can be represented as either
a solid-solid contact interaction between a solid particle and the substrate or as a solid-liquid-
solid contact between the particle and substrate with a thin layer of water between them. The
second model design of solid-liquid-solid contact interactions have been shown to be more
accurate than a simple solid-solid contact interaction. The solid-liquid-solid interaction
70
encompasses the full scope of the interactions occurring within an aqueous environment. The
interactions between these the two solid surfaces and their liquid interface are heavily influenced
by capillary forces. Previous studies [149] demonstrated how the resulting capillary force created
by several molecular layers of water between two layers of glass greatly increased the adhesion
force required to pull apart the glass layers. Previous Chapter showed that an increase in
humidity resulted in an increase in adhesion forces for dynamic and quasi-static contact in an air
environment. At high humidity levels, a layer of water will form between the particle and
substrate, which would create capillary forces that would augment the strength of the adhesion
force. This theory brings up an interesting point concerning our results in this study: the aqueous
environment that we tested in would undoubtedly result in the creation of capillary forces. Based
on previous studies, the presence of capillary forces should result in adhesion forces in water
greater than the forces measured in air. This, however, is not the case. We found that the
adhesion forces in aqueous solutions were significantly lower than the adhesion forces measured
in air. This situation can be explained by the presence of long range repulsion forces in water:
since the adhesion forces in water is several orders of magnitude smaller than the adhesion forces
in air, it can be assumed that the repulsion forces in water are several orders of magnitude
stronger than standard adhesion forces such as the Van der Waals interaction forces and capillary
forces.
Another interesting phenomenon is the disappearance of a “jump” in the force curves in a
liquid medium. This peculiarity found in aqueous solutions was first discussed in a paper by
Thormann et al.[153] , which discussed how long ranged repulsive forces found in water prevent
adhesive forces from pulling the particle and the substrate together, causing the “jump” in the
graph. Thormann et. al analyzed interactions between a polystyrene particle and hydrophilic and
71
hydrophobic surfaces in aqueous solutions. He found that the DLVO theory can explain
hydrophilic surface contact, but cannot explain contact on hydrophobic surfaces. Hydrophobic
surfaces with high contact angles (shown in Table 4.1) repulse water, in effect creating an air
bubble that allows for direct contact between the particle and the substrate. Direct evidence of a
bubble on the particle have also been reported by several groups [149,154]. The mechanism and
stability of the gas bubble is still under discussion. The data presented in Figure 4.6 shows that as
time in water increases, the adhesion force decreases, suggesting that this theory is possible
because it does explain exactly what is happening in the data. According to the theory, a
significant amount of the adhesion force comes from the hydrophobic interaction taking place in
the air bubbles. As time passes however, these air bubbles begin to diminish, eventually
completely disappearing and releasing the hydrophobic interaction with it thus lowering the
adhesion force.
Conclusions 4.5
The mechanisms of attachment and detachment of a micron-sized particle to and from a
substrate in an aqueous environment is a fundamental concept relevant to numerous natural
phenomena and industrial processes. Here we report a dynamic-induced enhancement in
adhesion interactions between colloidal particles and substrates in an aqueous solution. This
effect was identified by studying the trends of various particles (SiO2, Al2O3, and Polystyrene)
on various substrates (silicon wafer, polystyrene, fused silica). Multiple tests were conducted to
determine the impact of several factors including loading speed, loading force, and Young’s
modulus. We were able to isolate the change in retraction velocity over four orders of magnitude
as the cause of the dynamic effect using the colloid probe technique on AFM. The presence of a
72
dynamic effect became clear upon observation of 20-100% increase in adhesion force resulting
from an increase in retraction velocity from 0.02 to 156 μm/s during particle and substrate
interactions. A discussion section was followed The influence of dynamic factors related to
adhesion enhancement, such as hydrodynamic effect, particle inertia, surface charging,
viscoelastic deformation were discussed to understand the mechanisms of dynamic enhancement.
73
CHAPTER 5
SHAPE-INDUCED DYNAMIC ADHESION AND SELF-CLEANING EFFECT OF GECKO
FOOT-HAIR AND ITS BIO-MIMICS
Introduction 5.1
In this chapter we report an unprecedented dynamic adhesive phenomenon induced by
the nanoscale spatula-shaped fibrils (i.e., spatula and seta) in both dry and wet conditions.
Unlike most symmetrical contact geometries (e.g., spherical or flat punch) that exhibit a
significant increase in adhesion force on substrates with increasing pull-off velocity, individual
gecko spatula as well as seta shows a rate independent adhesion response in normal retraction.
This finding underpins the origin of the ‘easy-foot-removal’ and ‘contact-self-cleaning’
phenomena. Copying the design seen in geckos, inspired by this designing principle, we have
fabricated artificial micro-/nano- fibrils featuring spatula tips and geometry that show similar
dynamic effects, allowing us to manipulate and transfer micro-/nano- particles and matters by
actuating the pull-off rate. Such shape-induced dynamic effects have profound implications in
smart biomimetic design, micro-nano- manipulation, bio-nano- device fabrication and etc.
Experimental Methods 5.2
Tokay Gecko setae arrays have been collected from live adult animals and immediately
stored in a sealed container to prevent it from contacting dust. A single seta was carefully
separated from the setae arrays under microscope by micromanipulator (Micromanipulator Mode
2525) and then dispersed onto a fresh glass slice. The glass slide was cleaned in DI water by a
ultrasonic cleaner (Ultrasonic cleaner 1510, Branson Co., Inc.) for 15min, then dried in air under
a lamp before being dispersed. Operated by an atomic force microscope (AFM)
74
micromanipulator system (Scan-Icon AFM, Bruker Co., Inc.), a tipless cantilever with average
spring constant (40 N/m) (ACTA-TL-50 AppNano) attached to the AFM first captured a tiny
glue droplet (diameter is around 10 µm) and was dispersed on a glass slide. It was then moved
toward a target gecko seta and glued at the end of the tipless cantilever by pressing the glue
droplet on one seta end. In the preparation, care must be taken to choose only those setae facing
down such that the seta can properly come into contact surface with their tip. A 30 minute slow
cure epoxy (30min slow cure epoxy, Kite studio Co., Inc.) was used as the glue so that there was
sufficient time for the operation. Before testing, the glued seta was cured and dried in air for 24
hours at room temperature. The glued gecko seta (Figure 5.2) was examined under an optical
microscope to validate the correct direction of the gecko seta.
To examine the interaction between the seta and microparticles, glass microspheres
ranging from 5 to 50 µm in diameter were selected and cleaned by ethanol using ultrasonic
cleaner. These microspheres were then dispersed onto a piece of clean glass slide. The particles
were also distributed onto a piece of glass freshly coated with a thin epoxy film by a spin coater
at 1000 rpm (Spin coater KW-4A, Chemat Technology Co., Inc, ), and cured and dried for 24
hours, such that the microspheres were tightly bonded to the glass surface.
The attachment and detachment of gecko seta from substrate and dirt particles were
operated by the closed-loop AFM system. The interaction force between gecko seta and
microspheres 𝐹𝑠−𝑝 was measured, as schematically shown in Figure 5.1A. In the test, the AFM
tip movement was controlled with the resolution up to 1 nm, allowing the seta tip to approach a
microsphere, make contact with it under a given pressure for a certain period of time (1 s), and
then retreat at a given speed in the range of 0.02~156 µm/s. The interaction force versus
displacement of the AFM tip was recorded during the test. For comparison, a microsphere was
75
adhered firmly to the gecko seta tip to form microsphere-seta complex probe (Figure 5.1B). This
microsphere-seta complex was then brought to contact with clean substrates by the AFM system
with the same procedure as described above. The force between particle and wall (Fw-p) versus
pull-off speed was measured and recorded during the test. Several kinds of substrates were used
in the test including glasses, mica, sapphire, fused silica, and polystyrene (PS), (all of which
were sample kits from Bruker, CA, USA). All the samples were cleaned by DI water then dried
in compression air before testing. Tests were carried out at room temperature under a humidity of
40±5%. The spring constant of the probe was measured before testing with thermal tune method.
After all the tests, the seta glued on the AFM probes were observed by a scanning electronic
microscope (FEI Quanta ESEM) to measure the length, diameter and the curve angle of the seta.
We collected 10 datas for each velocity and the variety was shown as the error bar in the
adhesion force-velocity curves.
Figure 6.1 SEM picture of a gecko seta pre-glued at the end of AFM probe
76
(a)
(b)
Figure 6.2 Schematics of experimental setup for measuring the adhesive forces (A) between seta
and microsphere (Fs-p) with different diameters, and (B) between sphere and substrate (Fw-p) at
a given pull-off velocity.
77
Results 5.3
5.3.1 Direct Observation of Self-Cleaning Phenomena in an Individual Seta
Micro particles made of PS, SiO2 and Al2O3 with an average diameter of 10µm
(Microsphere-Nanosphere Inc.) were cleaned in DI water under ultrasonic for 15mins and
dispersed randomly in a fresh glass slide and dried at room temperature for 24hrs before testing.
The particles can stay on the glass slides because of the weak Van der Waal or capillary forces
between particles and substrates. The single gecko seta was pre-glued at the end of AFM probe
and the details of the procedure have been discussed in the above section. The spring constant of
this cantilever is 45.2N/m, much larger than that of the gecko seta, such that the effect of the
cantilever is negligible.
The test on the single seta, mimicking a gecko’s walk, was run in a lab control
environment with room temperature at 22°C and a humidity of 40%. Figure 5.3 schematically
illustrates the experimental procedure and observed results. In the first step of the experiment
(Figure 5.3A-C), the seta slowly approached (v = 0.1 µm/s) and contacted a PS micro particle
(diameter d = 10 µm) on a glass substrate, and then pulled off from the substrate at a velocity of
v = 0.1 µm/s. We notice that the particle was successfully caught by the single seta, which
represents the condition of gecko foot containment: Fs-p > Fp-w during the slow approach.
Immediately after the particle was caught, we did a fast ramp with a velocity of 142µm/s. The
same seta-particle complex approached, contacted, and retracted at the same position (Figure 5.3
D-F). This time the particle was dislodged from the seta. As Fp-w is velocity sensitive and Fs-
p<Fp-w at high pull off velocity, the particle was unable to adhere to the seta at the high speed and
thus self-cleaning occurred. Similar phenomena have been observed for Al2O3 and SiO2 particles
as well. Since the same particle and the same seta were used at the same location under the same
78
environment, other factors like surface roughness, humidity, temperature, particle surface
conditions can be ruled out.
(a) (b) (c)
(d) (e) (f)
Figure 6.3 Procedure and observed results of a seta approaching, contacting and retracting from
a particles: (A) one gecko seta pre-glued at the end of AFM probe approaching sphere slowly, (B)
maintain contact (full relaxation) , (C) slow retraction; sphere was caught by the gecko seta, (D)
Fast approaching, (E) short relaxation time , and (F) Fast retraction (V=142µm/s), particles stays
on substrate.
5.3.2 Adhesion of Single Seta and Spatula to Various Substrates in Air and Under Water
The adhesion tests in air followed the same procedure described in the above section. In
liquid test a drop of approximately 200 µL of DI water was applied onto the surface of the
substrate, and the cantilever was then completely immersed into the drop so that a meniscus
79
formed around the edge of the scanner, well away from the cantilever (Figure 5.4). The laser was
then recalibrated to adjust for the bending of light caused by Snell’s law. The attachment and
detachment of microspheres from clean substrates were carried out at retracting speeds ranging
from 0.02 to 156 µm/s by the AFM. A contact time of 10 seconds was set to eliminate the effect
of approaching velocity. In the pull-off test in water, in addition to the particle, AFM cantilever
itself also generates dynamic effect (drag force). The dynamic effect of the cantilever has been
removed during the data acquisition. Therefore, the adhesion force originates only from the
particle-substrate interaction. The pull off force between seta/particles and substrates (Fw-p)
versus retreating velocity is discussed in the following sections.
Figure 6.4 Schematic of adhesion measurement setup in water
80
We have measured the adhesion of single seta on various substrates. Figure 5.5 shows the
adhesion forces of a single seta on fused silica, PS, Teflon, and mica substrates in air or liquid
water. The values of adhesion forces vary significantly for different substrates. It is also
interesting to note that for fused silica, mica and PS, the adhesion forces in liquid is much
smaller than that in the air, but Teflon shows a reverse result—the adhesion in liquid is much
larger than that in the air. In all cases, the adhesion force of gecko seta is insensitive to pull-off
velocity. Nevertheless, the adhesion forces for all the substrates keep unchanged when the pull-
off velocity increases, which clearly shows that the gecko foot adhesion is not influenced by the
dynamic effect at a magnetic range from 0.02 to156 µm/s.
Figure 5.6 shows the adhesion forces between a single seta and SiO2 particles with
different diameter pre-fixed at the substrate. It is noticed that the adhesion varies on different
substrates because the actual spatula that come in contact with the substrates are different.
However, the adhesion force is independent with the retraction velocities which are similar to the
seta-substrate forces in Figure 5.5.
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(a) (b)
Figure 6.5 Adhesion force of single gecko seta vs. pull-off velocity at different substrates (a) in
air and (b) in water.
Figure 6.6 Adhesion forces between a single gecko seta and SiO2 particles with different
diameter pre-fixed on substrate
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5.3.3 Adhesion of Spatula in Air and Liquid
Here we examine the adhesion forces between single spatula and different substrate in
both air and aqueous solutions. FIB with Ga ion was used at a current of 30 KeV to achieve a
clean cut on a fresh gecko seta. After carefully cutting the result spatulas, only one gecko spatula
was left, displayed in Figure 5.7.
The results in Figure 5.5 and 5.6 and 5.8 show a similar rate independency for a
different set of the materials and chamber conditions. Interestingly, while the adhesion force on
Teflon in air is nearly zero, the adhesion force of the spatula stays unusually high under water,
with a wide range of pull-off rate. This may explain why geckos living in rain forests can
generate strong adhesion on wet leaves [13] [e.g. consistent with Alyssa’s PNAS paper for
animal scale measurements]. Since both spatula and seta show an invariant adhesion in normal
direction with increasing pull-off rate, whether on hydrophilic or hydrophobic surfaces, dry or
wet, we speculate that the tip shape of spatula plays a key role in stabilizing the dynamic
responses in general.
Figure 6.7 SEM picture of single gecko spatula. Other spatulas were carefully cut out by Focus
ion beam.
83
Figure 6.8 Adhesion force of single gecko seta vs. pull-off velocity at different substrates in air
and in water
5.3.4 Adhesion of the Artificial Spatula and the Nanoparticles on the Artificial Spatula in
Air and Under Water
In order to verify this hypothesis, we have fabricated two distinctive tip shapes at the end
of glass microfibers (10 μm in diameter), via FIB (Figure 5.9A). One is a submicron platelet at
the tip end (~ 500 nm in size; Figure 5.9B) mimicking gecko spatula (i.e., triangular thin film),
and the other is a submicron sphere (~490 nm in radius; Figure 5.9C) welded onto the
submicron-platelet by platinum.
A glass fiber with length of 140 µm and diameter of 10 µm was pre-glued at the end of
tipless AFM probe with the method described before. FIB with Ga ion was used at a current of
30KeV to achieve a clean cut, which provided the artificial tip shape. In the first step of the
cutting, we tilted the stage to make cuts on the sides of the fiber such that the cutting made a
smaller slope at the bottom and larger one on the top. This cut maximized the contact area
between the tip and surface. In the second step, we tilted the stage 90 degree with respect to
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former position which allowed us to shape the fiber from the top to ensure a reasonable contact
area. Current of 7nA was used for the area larger than 5 µm and 0.1 nA was used for the size
below 5µm during the cut process. The final result is shown in Figure 5.9 (A) and (B), and the
spring constant of the artificial-seta probe is 21.436 N/m. An artificial spatula with a
microparticle was also fabricated using the FIB system. A SiO2 particle with average diameter of
0.98 µm was picked up by micromanipulator inside the SEM, and then welded at the end of the
artificial seta by platinum (Pt) (Figure 5.9 C). The spring constant of artificial-spatula probe with
microsphere is 2.78N/m.
These nano-crafted microfibers were then tested on AFM in the same setup as for the
spatula pull-off experiments to measure the maximum adhesion forces at different pull-off
velocities. Similar to gecko spatula, the micro-platelet terminated artificial fibril exhibits almost
invariant adhesion strengths with increasing pull-off velocity (Figure 5.10); in comparison
sphere-tipped samples indicate a strong rate dependent behavior under both dry and wet
conditions (Figure 5.10). This evidence strongly suggests the influence of the contacting shape
on the dynamic adhesion responses.
85
(a)
(a) (c)
Figure 6.9 SEM images of (a) glass microfibers glued on AFM cantilever, (b) spatula-like flat
microstructure, (c) microsphere (d = 0.95 μm) welded on spatula-like glass nanofibers at the end
of AFM cantilever,
1µm
86
(a) (b)
Figure 6.10 Adhesion force of artificial gecko spatula (A) in air and (B) in water as a function of
pull-off velocity.
(a) (b)
Figure 6.11 Adhesion force of a 950 nm welded at the end of artificial gecko seta (a) in air and (b)
in water as a function of pull-off velocity.
87
Figure 6.12 The dynamic factors (F/F0-1, where F0 is the force at a velocity of 0.02 µm/s)) versus
pull-off velocity.
Figure 6.13 Adhesive forces between 20 µm SiO2 sphere and substrate (𝐹𝑤−𝑝) at a given pull-off
velocity of AFM cantilever. Here the loading force is 1 µN, 2 µN and 5 µN respectively. The
solid line is in air and dash line is in nitrogen environment
A clearly dynamic effect was observed for the artificial spatula with a submicron-particle
in both liquid and air. The particle on PS substrate shows the largest dynamic effect in air and it
88
increases 33% from 0.02 µm/s to 156 µm/s, while on Teflon the adhesion force increases 7.8%,
which is the weakest one. The dynamic value was dramatically enhanced in liquid. For example,
the adhesion force on fused silica in liquid reveals up to 123% increase, several times higher than
that force in air.
From the above experiments, it is noted that the similar shape patterns without the
particle do not illustrate any dynamic effect while artificial seta-particle complex proves to have
a dynamic effect. This behavior is similar to gecko seta and spatula although the materials used
in the artificial gecko spatula are quite different from that for gecko spatula. Since the types of
materials is not important in determining the adhesion behavior, the shape of the contact zone is
considered a key factor in triggering the dynamic effect.
Discussion 5.4
In fact, the distinctive dynamic responses are attributable to the manners of how a crack
propagates within the spatula-substrate interfaces as opposed to the sphere-substrate interfaces.
As simulated, (will be discussed in detail in the next chapter), with finite element analysis(FEA)
after a spatula is properly applied onto a substrate, a triangular shaped contact area forms in such
a way that the possible crack propagation will be constrained in the direction from the vertex to
the edge, as spatula retract (refer to Figure 5.14A and B). The crack propagates in a rather
stabilized manner since the crack front line will have to increase in length while it advances; and
this in turn greatly enhances the insensitivity of the adhesion force to the large increase in
loading rate (i.e., pull-off velocity) for both spatula/seta and its artificial mimics. On the other
hand, in the case of a sphere contacting a flat substrate, the crack growth is considerably unstable
because the crack front length (i.e., a closed circular or loop, Figure 5.14C and D) rapidly
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decreases during separation due to the contacting geometry (Figure 5.14D). This unstable
configuration results in rate-dependent behaviors at larger loading rates (Figure 5.14D).
(a) (b)
(c) (d)
Figure 6.14 Schematics of crack propagation of spatula and sphere in contact with a flat substrate;
(a) Crack propagation during pulling off spatula [158] (b) crack propagation direction along the
spatula/substrate interface, where crack front length increases during pulling off; (c) Crack
propagation during pulling of a sphere; and (d) crack propagation direction along the
sphere/substrate interface, where crack front length reduces during pulling off.
90
At a quasi-static state, in general, fracture mechanics the energy release rate G is roughly
constant and equal to a material-dependent critical-energy-release rate, G ∼ Gc [137], while
under a fast loading condition or unstable configuration, kinetic energy becomes dominant,
leading to a transformation to the dynamic regime [37,138] . The adhesion force for a
microsphere is related to the pull-off velocity v by the following equation:
𝐹 = 𝐹0 �1 + 𝐶 �𝑣𝑣0�𝑛� (5.1)
Where 𝐹0 = 5𝜋𝑅𝐺0/6 is the adhesion force as v is approaching zero, v0 is the reference
velocity when 𝐹 = (1 + 𝐶)𝐹0 , and n and C are the dynamic parameters depending on the
systems. Obviously, when either n or C is zero (or close to zero), dynamic effect ceases. The
dynamic parameters were evaluated against contact size and shape by fitting the experimental
data using Eq. 5.1 and are shown in Figure 5A and B. Values of n ~ 0.45 and C ~ 0.1 were
obtained for the spherical shape while the values for the spatula pads and seta are several times
smaller.
The observation that spatula (nanoscale) adhesion forces are independent of the pull-off
velocity in dry and humid air or under water has a profound implication for not only the ‘easy
foot removal’ but also ‘self-cleaning’ properties for the gecko’s dry adhesive system and its
duplicates. To investigate the adhesion and self-cleaning performance of gecko seta during the
animal’s locomotion, we measured the forces between the particle and the seta or spatula (Fs-p)
and those between wall (substrate) and the particle (Fw-p) at different pull-off velocities using an
atomic force microscope (AFM) attached with single seta (Figure 5.2). Figure 5.13 expresses
Fw-p as a function of the pull-off velocity for a 20 µm glass microsphere adhered to a seta
retreating at different velocities from different substrates. For this microsphere-seta complex, the
adhesion force (Fw-p) increased with increasing pull-off velocity for all the substrates. When the
91
velocity varied from 0.02 to 156 µm/s, the adhesion force almost doubled. Similar phenomenon
was also observed for microspheres directly glued on AFM cantilevers has been discussed in
Chapter 3.
(a) (b)
\
(c)
Figure 6.15 (a) and (b) dynamic parameters (n and c) obtained using Equation(5.1) by fitting the
experimental data for microspheres in contact with various substrates in humid air, and dry
nitrogen, and c) Trend of forces on seta-particle complex (Fs−p) and particles and walls (Fw−p)
with sphere diameter of 20µm under different velocities. m is the number of spatulae attached to
a microsphere; Points A and B are intersections that define the critical pull-off velocity.
2
4
6
8
10
12
14
0.01 0.1 1 10 100 1000 10000
Adh
esio
n fo
rce
(µN
)
Pull-off velocity (µm/s)
Experiment (Seta-particle)Experimental (Particle-substrate)Predicted (seta-particle)
m =1000
m =600 A
B
Vc Gec
ko s
peed
zon
e
Self-cleaning zone
92
The adhesion force between the single seta and glass microspheres was also measured
using the same method and the results are plotted in Figure 5.6. Unlike particle-substrate
interactions, the seta-particle adhesion force (𝐹𝑠−𝑝) keeps almost constant in a large range of
pull-off velocities. The variation of the force is within 5% for the velocity change across four
orders of magnitude. It is worth noting that the same seta was used in the above measurements
for the single seta and sphere-seta complex, under identical testing conditions. The uncertainties
such as seta variation, temperature, and humidity can be ruled out. It should also be noted from
Figure 5.15 (A) and (B) that the dynamic effect is also strong at the nano-scale level, thus
allowing nanoparticles to be cleaned in the same mechanism.
It is expected from the above observations that self-cleaning could occur if 𝐹𝑤−𝑝 > 𝐹𝑠−𝑝
when the pull-off speed exceeded a critical value. Indeed, this self-cleaning mechanism exists in
gecko seta and was directly observed at the micro-scale level (Figure 5.3). In the first step of the
experiment, a single gecko seta pre-glued to the end of an AFM probe slowly approached and
contacted a micro-particle (diameter d = 10 µm) on a glass substrate, and then pulled off from
the substrate at a velocity of 𝑣 = 0.1 µ𝑚/𝑠. The seta was able to pick up the micro-particle
under the single ramping process. In the second step, the same seta holding the particle
approached, contacted, and retracted from the substrate at the same position but at a relatively
high retreating velocity (𝑣 = 142 µ𝑚/𝑠). This time the particle was dislodged from the seta
because of the increased force 𝐹𝑤−𝑝 caused by the dynamic effect. The seta was also put in
contact with the particle and then retracted from it in a single ramp at a pull-off velocity of
𝑣 = 142 µ𝑚/𝑠. The particle was unable to adhere to the seta at the high speed, and thus self-
cleaning occurred. This is the first evidence of the self-cleaning mechanism ever observed at the
micro-scale. Since the experiment was carried out using the same particle and the same seta in
93
the same place, other factors, such as surface conditions that affect the adhesion forces, can be
ruled out. Thus, the insensitivity of seta adhesion to velocity is critical for gecko seta to achieve
self-cleaning.
The critical velocity 𝑉𝑐 for a seta to exhibit self-cleaning characteristics can be predicted
based on the seta-particle and particle-substrate interactions. For seta-particle interaction, the
adhesion force simply depends on the number of spatulae that attaches on the particles but is
independent of pull-off speed. The seta of Tokay geckos each contain ~1000 spatulae and each
spatula generates about 10 nN adhesion force on glass [6]. The particle-substrate interactions
prove to be more complex and the force generated during the contact is related to the dynamic
effect and can be described by Equation (5.1). For seta-particle complex systems, the dynamic
parameter C was measured by fitting the experimental results (Figure 5.15(c)), yielding n = 0.2
and C =0.6. Using those data, one can calculate the critical velocity of many material systems
and predict the self-cleaning zone (shaded area in Figure 5.15(c)). On the other hand, if the
number of spatulae attachments is known (e.g., m =1000), the adhesion force, 𝐹𝑠−𝑝 can also be
determined. The intersection of these two curves or the critical velocity for self-cleaning can
then be determined (Point B in Figure 5.15). For this extreme case, the critical velocity is
calculated to be ~1000 µm/s.
We have estimated the pull-off velocity of seta due to hyperextension during gecko
locomotion. Before taking each step, geckos (i.e., many species) DH their toes to disengage the
feet in a progressive-peeling manner. In this particular process, individual seta is sequentially
pulled off from the substrates at a relatively high speed and at large angles [12] in Figure 5.15. If
toe pad scrolling is modeled as a rolling motion of a circle, with setae arrays along a horizontal
plane, where each seta is lifted sequentially, then the toe pad’s trajectory follows the
94
corresponding cycloid (Figure 5.16). Specifically, the pad motion will sequentially exert on the
seta roots a vertical displacement of 𝛥𝑦 = 𝑟(1 − cos(2𝜋𝜔𝑡)) and a lateral displacement of
= 𝑟(2𝜋𝜔𝑡 − cos(2𝜋𝜔𝑡)) , 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), t is time, and ω is the rotation
speed of a seta root. From above model, one can calculate the vertical retreating speed of the seta
by 𝑉𝑦 = 2𝜋𝑟𝜔sin (2𝜋𝑟𝜔). Taking 𝑟 = 3 𝑚𝑚, 𝜔 = 20 round per second and 𝛥𝑦𝑚𝑎𝑥 = 18.6 µ𝑚
(the maximum distance the setae root can travel before the setae snaps off from the substrate)
[12] , we estimate Vy > 2000 µm/s. Thus, setae and spatulae stays in a strong self-cleaning zone
during setae array peeling. Based on the analysis above, it is concluded that a live gecko cleans
its feet at each step during movement. The unique shape of the nano-scale spatulae plays a
critical role in generating macro-scale robust adhesion and efficient self-cleaning. This work
thus points out a new direction for biomimetic design of highly efficient self-cleaning adhesive
materials and micro/nano-manipulation devices.
Conclusions 5.5
Here we report a dynamic adhesive phenomenon induced by the nanoscale spatula-
shaped fibrils (i.e., spatula and seta) in both dry and wet conditions. Unlike most symmetrical
contact geometries (e.g., spherical or flat punch) that exhibit a significant increase in adhesion
force on substrates with increasing pull-off velocity, individual gecko spatulae as well as setae
show a rate-independent adhesion response in normal retraction. This finding underpins the
origin of the ‘easy-foot-removal’ and ‘contact-self-cleaning’ phenomena. Most importantly,
inspired by this designing principle, we have fabricated artificial micro-/nano- fibrils featuring
spatula tips and geometry that show similar dynamic effects. This allows us to manipulate and
95
transfer micro-/nano- particles and matters by actuating the pull-off rate. Such shape-induced
dynamic effects have profound implications in smart biomimetic design, micro-/nano-
manipulation, bio-nano- device fabrication and so on.
96
CHAPTER 6
FINITE ELEMENT ANALYSIS OF SINGLE GECKO SETA AND SPATULA
Introduction 6.1
FEA has been proved as a valid tool to exam the adhesion forces between the interface of
different materials [117,118,155]. Pioneer adhesion modeling has been reviewed in Chapter 2.
Modeling of gecko fabrillar system has been pioneered by Gao et al.[27,35,156] who focuses on
the contact area shape between bio-fibers and the substrate, Autumn et al. [25,157] derived the
gecko adhesion model from classical theory, and Xia et al. [32,107] using multi-scale modeling
to mimic gecko seta/artificial CNTs arrays on the substrate. Recently Sauer [158,159] et al.
followed the experiment SEM images of gecko seta and spatula shape and mimicked the peeling
process under FEA. Up until now, there is no group discussion on the dynamic effect of gecko
fabrile structure and the adhesion forces vs. velocities. Here, based on Sauer’s geometry model
and creative insert in the cohesive element for the model under Abaqus Explicit, we can analyze
the adhesion forces vs. velocities for both seta and spatula.
Gecko Spatula Simulation 6.2
6.2.1 Spatula Model
A three-dimensional FEA model of gecko spatula was developed and shown in Figure 6.1.
The model consists of a gecko spatula, and a contact area with a cohesive element. Because of
the symmetry, only half of the model was used here as shown in Figure 6.1(b) and (c).
97
Figure 7.1 (a) SEM pictures of single spatula, (b) A detail gecko spatula model top view (c) side
view. Here the cohesive element thickness is 0.01nm.
Table 7.1 Parameters used for gecko spatula adhesion model
Contact area
size(nm2)
Spatula Young’s
modulus(Gpa)
Cohesive strength Tn0(Gpa)
Damage Displacement
δn0(nm)
Cohesive energy(J/m2)
Separation Displacement
δnf (nm) 26250 1.8 0.04 0.1 0.01 0.5
98
Figure 7.2 Typical traction-separation responses used in FEA simulations
Appropriate boundary conditions were used along the symmetry plane and displacements
were prescribed at the edge of the spatula to simulate the load applied during testing (Figure
6.1(c)). The spatula interface was modeled using cohesive elements. Traction-separation law was
used in the cohesive element to simulate the crack propagation. The bilinear traction-separation
laws, as shown in in Figure 6.2 were used to describe the normal traction-separation law of each
cohesive element. The traction-separation response in shearing direction takes the same form as
Equation 6.1 and 6.2,
𝑇𝑛 =𝑇𝑛0
𝛿𝑛0𝛿𝑛 𝑤ℎ𝑒𝑛 0 ≦ 𝛿𝑛 ≦ 𝛿𝑛0 (6.1)
𝑇𝑛 =𝑇𝑛0
𝛿𝑛𝑓 − 𝛿𝑛0
(𝛿𝑛𝑓 − 𝛿𝑛) 𝑤ℎ𝑒𝑛 𝛿𝑛0 ≦ 𝛿𝑛 ≦ 𝛿𝑛
𝑓 (6.2)
Where Tn0 is the normal cohesive strength, δn0 is the normal displacement jump between
two cohesive surfaces when damage initiates, and δnf is the normal displacement jump when
separation completes.
99
For fracture problems, where one is concerned with the propagation of a steady-state
crack front, only the critical strain energy is required and hence the maximum separation stress
𝜎𝑚𝑎𝑥 and cohesive zone length 𝛿𝑐 can be adjusted. Given the work of fracture 𝐺𝐼𝐶 , and
maximum separation stress 𝜎𝑚𝑎𝑥, the cohesive zone length is defined as
𝛿𝑐 =𝐸𝐺𝐼𝐶𝜎𝑚𝑎𝑥2 (6.1)
To properly model crack growth in a finite-element/cohesive-zone model, the numerical
mesh must be several times smaller than the characteristic cohesive zone length. In our
calculations, the mesh size is six times smaller than the cohesive zone length. The calculations
were performed using the commercial finite element package ABAQUS 6.10 version. The
parameter and material properties used in the calculation are listed in Table 4.
The discretized FE model contains about 18039 nodes and 17916 elements with very fine
meshes in the contact region between spatula and cohesive elements. The final mesh density was
determined through a series of convergence studies. Appropriate boundary conditions were used
along the symmetry plane and displacements were prescribed at the edge of the specimen to
simulate the load applied during testing. The substrate/spatula interface was modeled using
cohesive elements. Traction-separation law was used in the cohesive element to simulate the
crack propagation. The bilinear traction-separation laws, as shown in Figure 6.3, were used to
describe the normal traction-separation law of each cohesive element (Equation 6.1).
6.2.2 Results and Discussion
The peeling of spatula stripe from the substrate was simulated using the FEA model, as
shown in Figure 6.3. For a given interfacial fracture energy, 𝐺𝐼𝐶, the crack initiated at the contact
edge as shown in Figure 6.3(a) and then propagated to the end of the spatula. The maximum
100
separation force was occurred at almost the end of the spatula (Figure 6.3(e) and Figure 6.3). So
that the spatula’s shape is the key factor affect the adhesion forces.
The peeling of spatula from the composite substrate was simulated using the finite
element model, as shown in 6.3. For a given interfacial fracture energy, GIC , the crack initiates at
the tip of chevron contact area (Figure 6.3 (a)). The crack then gradually propagates along the
surface (Figure 6.3(b)-(d)). The crack grows unstably after Figure (e) and the spatula was peeled
off from the substrate. In Figure 6.4 are three typical pull-off curves vs. times curves.
From the previous chapter we know that the gecko detach from the substrate with a
minimum peeling velocities of 1000 µm/s. In Figure 6.3, the maximum adhesion force is nearly
independent of the pull-off velocity, which is consistent with the experiment.
Figure 7.3 Snapshot of spatula peeling from the substrate. (a-d) Front view of crack initiation and
propagation, (e-j) top view of crack initiation and propagation and Mises table.
101
.
Figure 7.4 Adhesion forces vs. times under different velocities
Gecko Seta Simulation 6.3
6.3.1 Gecko Seta Model
Finite element model for a single gecko seta have been created to simulate the adhesion
force during seta retraction from substrates at different pull-off velocities. The seta shaft and
brunches are modeled by beam elements. Following the report [160], the basic parameters for the
seta is given by the seta height H0 and setae base width D0 and the seta inclination angle αse.
The two hyperbolas shown in Figure 6.5 are described by the equation:
𝑋2
𝐶12−𝑍2
𝐶22= 1,𝑋,𝑍 > 0 (6.2)
𝑍𝐶4
=𝐶3|𝑌| − 1, 𝑍 > 0 (6.3)
Where C1=0.5D0, C2=C1tanαse and C3=0.5D0 and C4=0.4D0. Each level branches and
further splits into four new branches. Five levels were generated in this study (i=0 to 5); the first
102
level (Level 0) is composed of only one seta shaft while the final level (Level 4) contains 256
branches (Figure 6.5).
2D cohesive elements (truss elements) were used to model the interaction between the
seta brunches and the substrate. At the final branch level, each branch (spatula) is connected by a
cohesive element at its end; the other end of the element is fixed. The typical force-displacement
curve of the cohesive elements is shown in Figure 6.6, and it represents the Van der Waal
interactions between the spatula and the substrate. The force-displacement curve was obtained
according to the Lennard-Jones potential. The maximum separation force was set to be 5 nN, and
the cutoff distance is 1.2nm. The parameters used in the simulations are listed in Table 6.2. The
dynamic simulations were carried out with the explicit of Abaqus (6.10). Mimicking the seta
pulling off, we pulled the end of the seta shaft up at different velocities, calculated the adhesion
force versus time, and observed the failure modes at the setae-substrate interface.
Table 7.2 Parameters used for gecko seta adhesion model
Height H0(µm)
Width D0(µm)
Seta Angle
αse
Young’s modulus
E (Gpa)
Poisson Ratio
υ
Damage Displace
ment δ(nm)
Cohesive energy (J/m2)
Cutoff distanc
e δnf (nm)
49.14 13.5 30° 2 0.2 0.1 0.01 2
103
Figure 7.5 Force-displacement curve of a single gecko spatula when pulled off from the substrate.
Figure 7.6 (a) Front view, (b) Bottom view, and (c) Side view of gecko seta generated by
computer simulation. (d) A single gecko seta
10µm
104
6.3.2 Results and Discussion
The snapshots of the seta under loading are shown in Figure 6.7(a)-(c). At certain pull-off
displacement, cohesive elements start to fail mostly at the back edge of the contact interface of
the final level (Figure 6.7(a)) due to stress concentration at the edge. Further pulling leads to the
failure of more cohesive elements near the failed cohesive element. Eventually, crack-like
propagation takes place from back edge to front edge along the spatula-substrate interface
(Figure 6.7(b)). Finally, complete separation between spatula and the substrate occurs (Figure
6.7(c)). Therefore, the pull-off process is the process of crack propagation along the interface.
Figure 6.8 shows the pull-off force during loading at different pull-off velocities. Several
peaks were observed during loading, indicating that the adhesion failure of the spatula occurs
during the entire process before pull-off force reaches its maximum value. The highest peaks
represent the final separation events and the maximum adhesion force of the seta. As shown in
Figure 6.7(b), the maximum adhesion force is nearly independent of the pull-off velocity, which
is consistent with the experiment.
(a)
105
(b)
(c)
(d)
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Figure 7.7 (a) Initial Separation of gecko spatula from the substrate (b) Crack propagation from
one side to the other. (c) Complete separation of seta from the substrate. (d) force vs time at point
A, B and C.
(a) (b)
Figure 7.8 (a) The maximum adhesion forces when velocity various from 0.1-50μm/s, and (b)
The maximum adhesion force versus the pull-off velocity.
Conclusions 6.4
Three-dimensional FEA model is presented which describes the adhesion and
deformation of a gecko seta and a spatula under different velocities. The adhesion forces vs.
different velocities between seta-substrate and spatula-substrate with a cohesive element was
shown in the result. As can been seen in the gecko seta model, the adhesion forces are insensitive
to the final pull-off forces and the spatula model of the adhesion forces are sensitive to the final
pull-off forces.
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CHAPTER 7
CYCLIC ADHESION BEHAVIORS AND FATIGUE FAILURE OF GECKO SETA UNDER
REPEATED ATTACHMENT AND DETACHMENT
Introduction 7.1
The mechanical properties of gecko seta and spatula have been successfully evaluated by
AFM [6,26,161] and review papers of gecko evolutionary adhesion and gecko inspired fibrillar
systems can be found [3,8]. Further research of gecko setae derives the questions: How long can
the gecko keep its strong adhesion during movement? When does the gecko start losing its
adhesion during repeated attach/detachment and what is the reason for this? Is there any
relationship between gecko molt cycle and its adhesion property? The successful explanation of
gecko molt cycle could be from the gecko setae fatigue property. A fundamental understanding
of fatigue mechanisms can guide scientist into making gecko-inspired bio-mimic materials. Until
now, there has been no discussion of the fatigue properties of gecko setae and hair like structures.
In this chapter the fatigue mechanisms of gecko seta will be discussed. In the experiment, one
single gecko seta has been pre-glued at the end of a tipless AFM probe and it’s
attachment/detachment has been tested under continuous ramping process to evaluate the
adhesion force changes vs. cycles in AFM system. The fatigue mechanism of the gecko seta is
discussed.
Experimental Setup 7.2
The method how to glue gecko seta on AFM tips has been described in detail in Chapter
5. Briefly, Tokay gecko setae arrays were peeled from live adult animals and immediately stored
in the sealed container to remove it from contacting the air and dust. Then, a single seta was
carefully separated from the seta arrays under microscope by micromanipulator
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(Micromanipulator Mode 2525) and then dispersed onto a fresh glass slice. The glass slide were
cleaned in DI water by a ultrasonic cleaner (Branson Inc.) for 15min, then dried in air under a
lamp before being dispersed. Operated by an AFM micromanipulator system (Scan-Icon AFM,
Bruker Co., Inc.), a tipless cantilever (ACTA-TL-50 AppNano) with average spring constant of
40N/m was used. The cantilever that attached to the AFM first captured a tiny glue droplet
(diameter is around 10µm) dispersed on a glass slide, then moved toward a target gecko seta and
glued it at the end of the tipless cantilever by pressing the glue droplet on one seta end. Here we
needed to be very careful because only those setae facing down were chose as target. So during
the fatigue test it was spatula contact the surface first and not the seta body. A 30 minute slow
cure epoxy (30min slow0cureepoxy, Kite studio Co., inc. ) was used as the glue so that there was
sufficient time for the operation. Before testing, the glued seta (Figure 5.1) was cured and dried
in air for 24 hours at room temperature. The directions of gecko seta was quickly examined
under optical microscope ensure no further contaminated with excess glue and the gecko spatulas
were facing to substrates. Silicon wafer with roughness of 0.418 nm was used as substrate here.
Substrate was cleaned in DI water under ultrasonic for 15minutes and dry in air before using. It
is noticed that the fatigue test was in a sealed large box to eliminate air dust. 24 hours passed
before the test to eliminate the potential dust in the air deposited on the substrate. The approach
and retracting of gecko seta on silicon wafer (Bruker, PFQNM Sample kit) were made with a
closed-loop AFM system at continuous ramping approaching with frequency of 10 Hz and all the
forces between seta and substrate versus time were measured and recorded during the test. Since
AFM can load/unload in a high frequency simulating a gecko’s run, it is a perfect tool to mimic
gecko seta adhesion forces changes during the high frequency long time fatigue test. The
temperature was 22±1°C and humidity was 56±2° during the fatigue test and the spring constant
109
of the cantilever was 37.5N/m and a variation of 2% was observed after the test by thermal tune
method comes with AFM system. Notice that the system has a 15 minute rest every hour and the
laser was re-centered to eliminate the laser drift errors. Each single ramp we see clearly pull-out
forces as shown in Figure 7.3, suggesting that the gecko seta has been successfully detached
from the substrate for every single ramping process and reattach for the next ramp. Three
adhesion force curves were selected from the force curves every 36000 cycles and a curve of
adhesion force vs. cycles was drew as shown in Figure 7.2. Here the ramping size was 1µm and
ramping frequency was 10Hz with approaching and retraction velocity 20um/s for all the tests.
The directions of gecko seta were then examined under SEM (FEI Quanta ESEM) to check the
surface of gecko seta (Figure 7.1(c)). In comparison, a fresh gecko seta was examined under the
SEM (Figure 7.1(b)).
(a)
50µm
110
(b) (c)
Figure 8.1 (a) A typical gecko seta before fatigue test; (b) Spatulae are toward the same direction
before the fatigue test; (c) After the fatigue test, there is no crack or fracture damage of spatulas
on a single seta after the fatigue test.
Results 7.3
Figure 7.2 is the adhesion forces vs. cycles of a seta ramping on the substrate during the
fatigue test. It can be clearly seen that the adhesion force decreases as time increases. This seta
with adhesion forces start at 3900 nN and after 4*106 cycles the adhesion forces decrease to
359nN which is 8% of its original adhesion forces. It is interesting that there is a long-time
platform in Stage 2 where the adhesion forces only vary 5%. Every time the adhesion force
decreases, the force curve changes its shape. Three typical forces vs. cycles were captured in
Figure 7.3. In Stage 1 (Figure 7.3(a)), a clear viscoelastic property was observed in the force-
displacement curve. In Stage 2 (Figure 7.3(b)), the force was changed and no viscoelastic
property was observed. In Stage 3 the force curved was changed again, it revealed two small
pull-off curves shown in in Figure 7.3(c). From SEM pictures, we noticed that the spatulas
3µm
3µm
111
changed its directions to two bundles. This means toward the end of the experiment, spatulas
were bundles together and no longer distributed uniformly (Figure 7.1(c)).
Figure 8.2 Adhesion forces vs. cycles during the fatigue test for a typical seta pre-glued at the
end of AFM probe. Here the ramping velocity is 10HZ and approaching and retraction forces are
20um/s during the test. The substrate is a clean silicon wafer with a roughness of only 0.418nm.
Here in Stage I we see a fast damping at the beginning of the test.
Discussion 7.4
Why does the gecko lose its adhesion force during the fatigue test? Generally, fatigue
failure in metal is a process of crack initiation, propagation, and failure which is cumulative and
cycle dependent [162]. The fatigue behavior of the polymer is influenced by viscoelastic effects
and is frequency dependent [163]. However, the gecko fatigue test is different from metals or
polymers. A gecko walks on different natural surfaces meaning most of the time it is
attached/detached on substrates. Thus the fatigue mechanism is related to adhesion and pressure.
If the gecko follows the metals fatigue mechanism, broken spatulas should be seen on the
112
surfaces after the test. If the gecko follows the polymer viscoelastic properties fatigue
mechanism, hysteresis loop different should be observed in the force curve during the test. In
Figure 7.3 we see some loop changes between Figure 7.3(a) (b) and (c) which indicate the
viscoelastic property of the gecko seta varies. It is worth mentioning that the loading rate and
loading force is constant during the test. However, this change itself is not strong enough to
explain why the gecko loses up to 90% of adhesion forces.
The secret of why a gecko loses its adhesion property is displayed in the SEM pictures
(Figure 7.1). Before the test, the gecko spatulas were uniformly distributed in one direction
(Figure 7.1(b). All the spatulas were easily in contact with the substrate during gecko contact-
drag-remove movement. However, after the fatigue test, the directions of spatulas changed. More
spatulas changed their directions towards the inside and lost their ability to contact the surfaces.
The interesting part is that no spatulae were damaged in the test. The spatula’s directions
changed which made the effective overall contact area decrease. It represents that the spatula’s
material is very unique to resist up to 4*107 cycles of usage. Because of this, both the effective
contact area and contact shape reduce. This is why a gecko decreases their adhesion forces
during the fatigue test. In result, the effective numbers of spatulas which can come into contact
with the substrate are much smaller than fresh seta (Figure 7.4).
The relationship between the gecko molt cycle and its adhesion change time in the fatigue
test is interesting. Recorded data [164] shows the gecko runs with a velocity of 77cm/s. We can
assume the gecko runs 10 steps a second and that the gecko can move for at least 1 hour every
day. A regular gecko molt cycle is 3 months. A total of 1*106 cycles are made before a gecko
molts its skin. Here for these two fatigue tests we notice that the gecko keeps an adhesion of
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almost 10 times its own weight; 10% of the adhesion force is strong enough to maintain the
gecko’s weight and let the gecko move freely on different substrates.
(a) (b)
(c)
Figure 8.3 (a) a typical force distance curve at stage 1(b) a typical force distance curve at stage
2(c) a typical force distance curve at stage 3.
Stage 1 Stage 2
Stage 3
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Figure 8.4 Schematic diagram: (a) before the fatigue test, (b) after the fatigue test.
Conclusions 7.5
In this chapter, the fatigue mechanism of the gecko seta was discussed. A single gecko
seta was glued at the end of a tipless probe and the fatigue property of gecko seta was examined
with the AFM under cyclic attachment/detachment process which mimicked a gecko running.
Results shows that a seta lost 90% of its adhesion force when the cycles reach 4*107 times. The
SEM pictures reveal that the spatula changed its directions and that the effective contact area
decreased which results as the main cause for gecko setal fatigue. The fatigue mechanism of a
gecko is not like metal which is dominated by local crack propagation, but similar to polymer, in
which failure is caused by local plastic deformation. For setal fatigue, it is the direction changes
of spatulas at the end of the seta (due to plastic deformation) that causes the decrease in adhesion
forces during cyclic loading.
115
CHAPTER 8
CONCLUSIONS AND FUTURE WORK
Conclusions 8.1
In this dissertation we reported a dynamically-induced enhancement in interfacial
adhesion between micro-sized particles and substrates in nitrogen, air and water. The adhesion
force of soft (polystyrene) and hard (SiO2 and Al2O3) micro-particles on soft (polystyrene) and
hard (fused silica and sapphire) substrates is measured using an AFM with retraction (z-piezo)
speed ranging over 4 orders of magnitude. The adhesion is strongly enhanced by the dynamic
effect. When the retraction speed varies from 0.02 µm/s to 156 µm/s, the adhesion force
increases by 10% ~ 50% in dry nitrogen while it increases by 15%~70% in humid air and 20-
100% in water. Among the materials systems tested, the soft-soft contact systems exhibit the
smallest dynamic effect while the hard-hard contacts show the largest enhancement. A dynamic
model was developed to predict this dynamic effect, which agrees well with the experimental
results.
Although micro-particles exhibit strong dynamic effect in air, nitrogen, and an aqueous
environment, the gecko fibrillar hair shows a completely different trend. The fibrillar structure is
considered as a key factor which affects the dynamic effect. We report an unprecedented
dynamic adhesive phenomenon induced by the nano-scale spatula-shaped fibrils (i.e., spatula and
setae) in both dry and wet conditions. Unlike most symmetrical contact geometries (e.g.,
spherical or flat punch) that exhibit a significant increase in adhesion force on substrates with
increasing pull-off velocity, individual gecko spatula as well as seta shows a rate of independent
adhesion response in normal retraction. This finding underpins the origin of the ‘easy-foot-
removal’ and ‘contact-self-cleaning’ phenomena. Most importantly, inspired by this designing
116
principle, we have fabricated artificial micro-/nano- fibrils featuring spatula tips and geometry
that show similar dynamic effects. This allows us to manipulate and transfer micro-/nano-
particles and matters by actuating the pull-off rate. Such shape-induced dynamic effects have
profound implications in smart biomimetic design, micro-/nano- manipulation, bio-nano- device
fabrication and etc. A 3D finite element models for the gecko seta and spatula peeling from the
substrate were developed. A cohesive zone model was used to predict the peeling process.
Maximum pull off forces at the end under different velocities were examined using dynamic
explicit FEA software. Both seta and spatula show a rate independent adhesion response to
normal retraction with velocities ranging from 1 µm/s -10000 µm/s
Finally a single gecko seta was pre-glued at the end of a tipless AFM probe. The fatigue
properties of gecko seta were examined with AFM under cyclic attachment/detachment process.
The initial adhesion force of the seta starts at 3900 N and after 4*106 cycles the adhesion force
decreases to 359 nN, which is 8% of its initial adhesion force. The adhesion force-displacement
curve changed in shape at different stages. SEM pictures revealed that the adhesion force
decreased because the spatulae at the end of the seta changed their directions, reducing the
effective contact area.
Recommended Future Works 8.2
Future work includes:
Self-cleaning mechanism: Dynamic self-cleaning mechanism was a novel explanation to
solve the long puzzle question, “How can a gecko keep its feet sticky yet clean.” The next step is
to synthesize the artificial self-cleaning materials by controlling the shape and contact area at the
117
end of fabrillar structure. The mass productions and manufacturing process also need to be
developed.
The second path is to utilize dynamic self-cleaning theory to find out the optimal contact
shape that generates the strongest dynamic effect and the contact shape which gives the weakest
dynamic effect. What is the different from the microscale contact area to nanoscale contact area?
For the research on gecko setal fatigue, it is revealed that gecko spatula and seta are
durable for up to 107 cycles. There may be unique setal structure or surface chemistry that makes
gecko feet so durable. Further analysis of the composite structure of gecko seta may provide
clues for the development of durable, self-cleaning materials.
A recent discovery was made that beetles have a gradient property along their hairs [165] .
Research has yet to be done on whether a gecko seta or spatula has the same gradient property.
Does this mean the mechanical properties of bio-mimic materials should also have gradient
properties and what is the reason for that? The answer to this question can bring a new era for
artificial bio-mimic material design.
118
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