MOLECULAR ADHESION AND FRICTION AT ELASTOMER/POLYMER INTERFACES. A Dissertation. Presented to. The Graduate Faculty of The University of Akron

Transcription

1 MOLECULAR ADHESION AND FRICTION AT ELASTOMER/POLYMER INTERFACES A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Betul Buehler December, 2006

2 MOLECULAR ADHESION AND FRICTION AT ELASTOMER/POLYMER INTERFACES Betul Buehler Dissertation Approved: Accepted: Advisor Dr. Ali Dhinojwala Department Chair Dr. Mark D. Foster Committee Member Dr. Alexei P. Sokolov Dean of the College Dr. Frank N. Kelley Committee Member Dr. Gary R. Hamed Dean of the Graduate School Dr. George R. Newkome Committee Member Dr. Darrell H. Reneker Date Committee Member Dr. Arkadii I. Leonov ii

3 ABSTRACT We have studied the contact interface between elastomeric poly(dimethyl siloxane) (PDMS) lenses with various solid surfaces during adhesion and friction using IRvisible sum frequency generation spectroscopy (SFG). SFG in total internal reflection geometry can be used to determine molecular structure at the polymer/solid and polymer/polymer contact interfaces. It is a nonlinear optical technique, which detects the orientation and density of molecules at interfaces. In this study, we have designed a novel approach to couple SFG with adhesion and friction experiments. The solid surfaces were chosen to be octadecytrichlorosilane monolayer (OTS), poly(vinyl n- octadecyl carbamate-co-vinyl acetate) (PVNODC), polystyrene (PS), poly(n-butyl methacrylate) (PnBMA), and poly(n-propyl methacrylate) (PnPMA). In the first part of the research, we have concentrated on the importance of characterizing the static contact interface to understand adhesion. Our results for the contact between two macroscopic rough surfaces, OTS and oxygen plasma treated PDMS, show surprising surface restructuring, which results in adhesion hysteresis. The short PDMS chains generated during plasma treatment are locally confined between two flattened asperities and are as strongly ordered as OTS. SFG spectra from iii

4 other surfaces (sapphire substrates and fluorinated monolayers) indicate that short PDMS chains require not only confinement but also an ordered template provided by the methyl groups of OTS. In the second part, we have studied the sliding contact interfaces of various polymers with PDMS. The friction forces between PDMS lenses and glassy PS are a factor of four higher than PDMS sliding on crystalline well-packed PVNODC surfaces. This cannot be explained by the difference in adhesion energy or hysteresis. The in-situ SFG measurements indicate local interpenetration during contact, which is evident from the change in orientation of PS phenyl groups upon mechanical contact and during sliding compared to that at the PS surface. Such a local penetration is unexpected at room temperature (T R ) that is much below the T g of PS. For comparison, we have also studied PnBMA and PnPMA having T g below and above T R, respectively. Preliminary studies at the contact and sliding interfaces with PDMS exhibited similar interpenetration based on adhesion, friction and SFG results regardless of the bulk T g. Our results indicate that the adhesion energy and hysteresis of surfaces are not sufficient to predict their friction properties, which makes the characterization of the molecular structure at the static and dynamic contact essential. Finally, we have reported a fabrication process of constructing polymer surfaces with multiwalled carbon nanotube hairs. The force measurements with scanning force microscope indicated strong nanometer level adhesion forces, 200 times higher than those observed for Gecko foot-hairs. These forces are a combination of van der iv

5 Waals forces and energy dissipation during the elongation of the carbon nanotubes which comes from their material properties. v

6 ACKNOWLEDGEMENTS This work would not have been possible without my parents, Behra and Süer Yurdumakan, my brother, Süheyl Yurdumakan, as well as my husband, Erich Buehler, who have given me endless love, support, and guidance. They never stopped believing in me which kept me up on my feet even in the most difficult times. It was not easy to leave my loved ones behind and move to an unknown country by myself. But it is here in Akron, Ohio that I met the most wonderful person, my beloved husband, who always work hard to provide a beautiful life for us. I am also very grateful to the whole Buehler family who treated and loved me like one from the family and made me feel at home. Special thanks to my advisor Dr. Ali Dhinojwala for giving me the opportunity to fulfill my dream. He was brave enough to accept somebody across the globe without knowing what he was getting into. I always admired his dedication to his work and the excitement he gets out of it. Sickness, freezing cold, medical operation, sweating hot or electric shortage never stopped him. He has always been a door away for even the simplest discussion. I enjoyed working on my research subject and using the many equipments provided by The University of Akron. I also enjoyed being vi

7 a part of the scientific community even though there are some things about it that terribly disappointed me. I thank to the members of my dissertation committee: Drs. Alexei P. Sokolov, Gary. R. Hamed, Darrell H. Reneker, and Arkadii I. Leonov (Polymer Engineering) for their patience, time, effort and valuable input in this work. I especially owe many thanks to Dr. Ardadii I. Leonov, who read almost every page of this thick dissertation and spent hours with me to greatly improve my work. I thank Dr. Alexander D. Schwab for contributing a very useful fitting program for SFG data and his training on the SFG theory. He is an excellent teacher. I thank Dr. Gary P. Harp for building the JKR apparatus and getting us started with the adhesion measurements as well as for providing me always with the right literature on any subject. My first time in the student office was during lunch time in summer break. Gary was the only student in the office and he was reading some papers at his desk. This image of him did not change for another four years. He is probably still the most literate person that this group has ever seen. I thank Dr. Ali Dhinojwala, Kumar Nanjundiah, and Ed Laughlin for putting the friction equipment together. I am also thankful to Ed for many other things he machined with great craftsmanship. I thank Shishir Prasad for his kindness and help on various occasions. The rest of my groups members: Vikas Varshney and Liehui Ge also contributed in various ways, and I thank each of them. vii

8 Special thanks to Drs. Stephen Z. D. Cheng, Alaxei P. Sokolov, William J. Brittain, and Richard R. Thomas (OMNOVA Solutions, Inc., Akron, OH) for use, respectively, of their AFM instrument, Raman spectrometer, Rame-Hart goniometer, and Dynamic Contact Angle Analyzer. I am thankful to Rick especially for all the thinks he taught me during my internship at OMNOVA Solutions, Inc. and the nice chats we had, which still continues today. I appreciate the assistance of Drs. Alexander Kisliuk and Gökhan Çalişkan in the operation of the Raman spectrometer as well as Mr. Jon R. Page with the various instruments in his lab. I thank 3M Corp. for supplying the PVNODC. I also thank Peggy Richards (English Department) for proof-reading this dissertation. My deepest gratitude to Keshav S. Gautam, Hasnain Rangwalla and Veronique Lachat for all their contribution to my professional and personal life. Their friendship made a big difference in my Ph.D. experience. I am very grateful to Dr. Gökhan Çalişkan, Dr. Bariş Yalçin and David Valladares for their friendship, putting up with me during my first year, and helping me adjust to America, Akron and the Ph.D. life. Furthermore, I am indebted to my dearest friends Simin Atayman and Özlem Özgül (Korku) for their love, support, and trust all the way from Turkey. I am also very grateful to my friends Bülent Akgün, İbrahim Eryazici, Gökçe Uḡur, and Emilie D. Gautriaud whom I met here in Akron. I thank Dr. Ashwin Rao, Vicki England Patton, and Marsha Weidknect for their inspiring smile they always have on and their positive attitude. I will surely miss the viii

9 flower chats and seed exchanges I had with Vicki and Marsha. I also thank Marsha for her help in various scientific matters. My deepest thanks to Ryan Hartschuh because he stands as a great example for every science student with his hard and smart working habits, proper attitude, great social skills, and sincerity. Last, but not least, I owe many thanks to Robert Seiple and Critt Ohlemacher for giving me a research position at the Applied Polymer Research Center, The University of Akron. Not only did they helped me acquire industrial experience through their valuable knowledge but they also provided me an income during my graduation period and a very nice research environment to be in. I acknowledge the University of Akron and National Science Foundation for their financial support of this work and OMNOVA Solutions, Inc. for the industrial fellowship. ix

10 TABLE OF CONTENTS Page LIST OF TABLES LIST OF FIGURES xii xiii CHAPTER I. INTRODUCTION II. HISTORICAL PERSPECTIVE Polymer Adhesion Polymer Friction Nature s Way of Adhesion and Friction III. EXPERIMENTAL Sample Preparation IR-Visible Sum Frequency Generation (SFG) Apparatus and Measurements JKR Apparatus and Measurements Friction Apparatus and Measurements Scanning Probe Microscopy (SPM) Measurements Contact Angle Measurements x

11 3.7 Thickness Measurements IV. RESULTS AND DISCUSSION Template-Induced Enhanced Ordering of Methyl Groups of Short PDMS Chains under Confinement Molecular Origins of the Adhesion and Friction Behavior of Elastomers Sliding on Glassy Polymers Synthetic Gecko Foot-hairs from Multiwalled Carbon Nanotubes. 202 V. CONCLUSIONS BIBLIOGRAPHY xi

12 LIST OF TABLES Table Page 2.1 The value of (n-1) for various polymers Symbolic representation of all the vibrational modes observed in the spectra taken for this study. The given assignments to resonances were determined from the SFG fits The contact angle values of distilled water on the polymers used in this study xii

13 LIST OF FIGURES Figure Page 1.1 The contact between two elastic spheres of radii R 1 and R 2 under a normal load of P 0. When the surfaces forces are taken into consideration, the contact radius increases from the Hertzian value a 0 to the JKR value a 1 due to the intermolecular interactions across the interface. δ is the elastic displacement. (From ref [6], p.303.) Depiction of bulk and surface molecules. F is the net attraction on a surface molecule which is balanced in the case of a bulk molecule Critical surface tension of some commonly used polymer surfaces whose chemical structure is indicated. (from ref [28], p. 100.) Zisman s contact angle results of n-alkane liquids on various perfluorinated surfaces. (From ref [34], p.231.) The contact of a liquid with a solid surface at equilibrium The edge of a liquid drop on a polymer surface. (Adapted from ref [34], p.222.) Work of adhesion between liquids and a surface with γ c = 21.5ergs/cm 2. (From ref [37], p.49.) The contact of a deformable sphere on a rigid surface at equilibrium. The Hertzian contact excludes and the JKR contact includes adhesion forces at the interface. (Adapted from ref [39], p.327.) The main features of the Hertz and JKR theories. (Adapted from ref [40], p.481.) xiii

14 2.9 The cube of the contact radius, a 3, as a function of applied load, P, when two rubber hemispheres are brought into contact. The predictions of the Hertz and JKR theories are shown with lines. Data taken from Johnson et al. [6] A general depiction of adhesion hysteresis in JKR type experiments where the cube of contact radius, a 3, is plotted as a function of applied load, P. This is the adhesion behavior between a PDMS elastomeric lens that has filled with silica particles and a poly(styrene) flat surface Stresses around a crack tip for a tensile type loading. (From ref [51], p.23.) The three fracture modes. The displacements of atoms are indicated on the right for each mode. A) Cleavage mode : mode I, B) In-plane shear mode : mode II, C) antiplane shear mode : mode III Irwin model of the plastic zone at the crack tip. (From ref [46], p.280.) A crack at an interface of two dissimilar materials Contact between a PDMS lens and flat plate. The area of contact is exaggerated for clarity. (From ref [57], p.1015.) Adhesion measurements at the PDMS/PS and PDMS/PMMA interfaces. Both interfaces are free from adhesion hysteresis A)PDMS and PS with W a of 49±3mJ/m 2, B) PDMS and PMMA with W a of 57±1mJ/m 2. (From ref [60], p.431.) The depiction of the interdigitation of the dangling chains at the interface between two PDMS elastomer. (From ref [64], p.1401.) Analogy of the adhesion behavior between polyisoprene and glass with that of magnetic spaghetti and electromagnet. A) before contact while current is off, B) contact through attraction when current is switched on, C) separation where disentanglement and orientation take place while current is still on Amontons original sketches of his friction experiments. (From ref [67].) Euler s studies of friction. (From ref [70,71].) A) Surface roughness represented by triangular shapes inclined at angle α, B) Analysis of kinetic friction xiv

15 2.21 The roughness effect on friction The frictional force and coefficient of friction as a function of load for polytetrafluoroethylene. (From ref [49], p.105.) The coefficient of friction as a function of load for polymethyl methacrylate where the surfaces are (From ref [49], p.110), A) smooth, B) abraded, C) turned Coefficient of friction as a function of load. Full lines are the theoretical predictions. The dotted line is experimental points for hard rubber. (From ref [83].) Master curve for the friction data of acrylonitrile-butadiene rubber sliding over a hard surface. (From ref [91], p.25.) Master curves for the friction data of acrylonitrile-butadiene rubber on various surfaces; dash, wavy glass; dots, polished stainless steel; solid line, clean silicon carbide; dash dot, dusted silicon carbide. Find out how to make the symbols in latex. (From ref [91], p.29.) On the left, a representative plot of area density, Σ, of contact points and the force per adsorption point, f( f) as a function of velocity is shown. On the right, the product of these two quantities which is the shear stress is depicted. (From ref [14], p Real time images showing the propagation of Schallamach waves. (From ref [99], p.56.) Adhesion hysteresis between PDMS and self-assembled monolayers (SAM). The open and closed circles represent the data taken during approach and withdraw of the PDMS elastomeric lens, respectively. The solid lines are predictions of the JKR theory. The inset shows a schematic of the adhesion apparatus and the well-packed SAM monolayers. A) Fluoroalkylsiloxane monolayer with adhesion energies of 32.2 (±1.4) and 62.7 (±6.1) ergs/cm 2 from approach and withdraw, respectively and B) Alkylsiloxane monolayer with adhesion energies of 38.4 (±1.3) and 45.6 (±3.7) ergs/cm 2 from approach and withdraw, respectively. From ref [8], p xv

16 2.30 Schematic of the three phase states of the monolayer and their behavior at the interface during adhesion and friction. A) Crystalline monolayers exhibit little interpenetration across the interface and thus only little energy is dissipated. B) Amorphous monolayers penetrate significantly during adhesion and friction. Each energy dissipation occurs over a characteristic molecular length δ laterally and l normally with a relaxation time τ. C) Liquid-like monolayers also penetrate significantly but the entanglement and disentanglement times are fast and the system is always close to equilibrium. The energy dissipation is low. (From ref [61], p ) Sketch of the two different situations at the contact interface between PDMS network and PS surface covered with a very thin layer of endattached mobile PDMS chains. A) The layer thickness of the PDMS chains (shown by the bold lines) is relatively thick. The contact occurs between the PDMS network and PDMS chains with little interpenetration. B) The thickness of the PDMS layer is only 1.2nm and the chains penetrate deep into the network. (From ref [15], p.1412.) A) Schematic of the SFM probe and substrate used in the adhesion and friction measurements. Both surfaces were coated with an unsymmetrical dialkyl sulfide. B) Average adhesion forces for the given combinations. The lines are guide to eye. C) Friction forces of a 10/18-coated probe on given combinations. The lines are linear least-square fits. (From ref [112], p.3250, 3251, and 3253.) Schematics of some representative deformations at the molecularlevel during contact and friction. (From ref [122], p.70.) Shear stress of PDMS sliding on PS (black box) and SAM (gray box). The solid line is the prediction of the absolute reaction rates theory. (From ref [14], p.6786.) Photograph of the first laser built by Maiman in A ruby rod is surrounded by a helical flash lamp Schematic of the experimental setup used by Franken et. al. to observe the second harmonic generation from a quartz crystal The interface between two media that is probed by SFG. The subscripts i and r denotes incident and reflected directions. Here n 1 > n xvi

17 2.38 The relationship between the molecular coordinate system (a,b,c) and the laboratory coordinate system (x,y,z) through the Euler angles (ψ, θ, φ) SFG spectra of octadecanethiol monolayers from; A) Surface, B) Contact under 320 MPa pressure, C) Contact under pressure increased to 660MPa, D) Contact under pressure decreased back to 320 MPa, E) Surface after contact (From ref [140], p.5072.) SFG spectra (SSP polarization) of PnBMA as well as PnPMA surface ( ) and deformed PnBMA as well as PnPMA interface with sapphire (bigcircle). (From ref [141], p ) SFG spectra (SSP polarization) of PVNODC/PS interface before and during mechanical contact (top) as well as annealed PVN- ODC/PS bilayer film (bottom). (From ref [142], p.375.) Pictures and schematic of a lizard and its foot structure. A) A lizard attached to a nearly vertical surface. B) The schematic of the fibrillar structure on the foot of a lizard. The skin is covered by fibers called setae that are 100 µm in length. Each setae (st) is made up of 1000 thinner fibers that are 10µm in length. These fibers end with a plate called spatulae (sp). C) Scanning electron microscopy (SEM) micrograph of st. D) Enlarged SEM micrograph of the box in (C) showing sp and terminal branches (tb). E) Transmission electron microscopy (TEM) micrograph of two tb with sp. (From ref [147], p.1401.) The fibrillar structure of the attachment pads of various animals. The terminal element which is circled becomes finer as the body mass of the animal increases. (From ref [151], p.1401.) Unit structures and representation of the materials used in this study. OTS is chemically bonded to an oxidized surface from the top oxygen atom. The monolayers are crosllinked to each other through the side oxygen atoms. For PVNODC, x = 0.9 and y = Schematic diagram of the SFG setup. Components are named as appears in the text. Symbols represents: H, half-wave plate; C, IR chopper; DM, dichroic mirror; and P, polarizer xvii

18 3.3 Schematic diagram of the TIR geometry used in SFG measurements. Shown here for a polymer film coated on sapphire prism that is in contact with a PDMS lens. The incident visible and IR beams are represented with one arrow that strikes the prism at the entry face with φ i and refracted with φ r. A small region that includes both the sapphire/polymer and PDMS/polymer interfaces is magnified where φ 1 and φ 2 are the critical angles, respectively, for the total internal reflection to take place. The mediums of refractive indices n i are as indicated. The x, y, and z Cartesian axes are the lab frame-of-references; the y-axis is perpendicular to the plane of the paper A typical SFG spectrum where the SFG intensity (number of photon counts) is normalized with the average IR intensity and plotted as a function of the IR wavenumber. The solid lines are fits to the data. This SFG spectrum was taken from an OTS surface. The detected resonances represents the C H stretching vibrations of the CH 3 groups present at the OTS surface Schematic diagram of the JKR apparatus home-built by Harp A typical contact spot image of the PDMS/OTS interface at 0.1g using a PDMS lens with radii of curvature 1mm A typical side image of a PDMS lens. The height (h), diameter (2r), and radii of curvature (R) are shown A typical JKR plot with contact radius, a, plotted as a function of load, P. The measurement shown here was performed on a PS surface using an extracted PDMS hm (PDMS exhm ) lens The linear JKR plot of the data shown in Figure 3.8 measured from the PDMS exhm /PS interface Strain energy release rate, G, as a function of contact radius for the same measurement shown in Figure 3.8 between PDMS exhm and PS Schematic diagram of the friction apparatus home-built by Nanjundiah for in situ adhesion and friction measurements using SFG in TIR geometry A typical friction plot with shear stress, σ, plotted as a function of time, t. The measurements shown here was performed on a PVN- ODC surface using a PDMS exhm lens xviii

19 3.13 Cantilever deflection during the approach/retraction cycle and the corresponding deflection versus tip position as measured with SPM. 1) Tip approaches the surface (non-contact region). 2)Tip makes contact and bends up due to surface interactions (contact region). 3) Force is applied up to a desired amount. 4) The direction of the applied force is changed to retract the tip. 5) Cantilever bends down due to surface interactions. 6) Tip jumps out of contact once the applied force reaches the threshold depending on the strength of the interactions. (from the SPM manual.) SFG spectra of A) OTS, B) PDMS, C) PDMS ox /OTS, D) PDMS/OTS, E) PDMS liq /OTS, and F) PDMS ox /sapphire in SSP polarization. The solid lines are fits to the square of the sum of the Lorentzian functions (eq 4.1). B) and F) are taken with a broader wavenumber resolution (full width half maximum (fwhm) 20cm 1 ) to improve the signal-to-noise ratio. The SFG spectra were offset along y-axis by an arbitrary amount and A), B) and F) were scaled for clarity JKR plot of A) PDMS ox /OTS, B) PDMS/OTS, C) PDMS ox /sapphire, and D) PDMS/sapphire. The contact radius, a, cubed is plotted as a function of the applied load. The strain energy release rate on unloading for both PDMS ox /OTS and PDMS ox /sapphire depends neither on the contact time within each load increment nor the time at maximum load A) cos(θ), B) number of CH 3, C) and D) histograms of cos(θ) for the methyl groups next to α-quartz and air interfaces, respectively A) The PDMS ox lens deforms to make contact with OTS. The area of contact is larger than the SFG laser spot (radius 0.5mm). B) and C) The atomic force microscopy images of the OTS (2 2 µm) and PDMS ox (50 50 µm) surfaces and the section analysis of an arbitrary (white) line on the surface (height as a function of length). D) Depiction of the asperity contacts at the interface based on the section analysis of the OTS surface. E) Short PDMS chains confined between the oxidized PDMS surface (silica-like layer) and OTS in a local contact region. The number of layers may depend on the amount of short PDMS chains present at the interface Shear stresses of PDMS on PS (black box) and SAM (gray box). The trendline on the PS data is the prediction of a thermally activated rate theory using an Arrhenius shift factor xix

20 4.6 The shear stress values are shown for the different types of PDMS lenses sliding on PVNODC. The PDMS syl and PDMS exsyl lenses are prepared from a Sylgard-184 elastomeric kit (Dow Corning) and the PDMS hm and PDMS exhm lenses are homemade. The symbol ex is used for lenses whose sol fraction is extracted The elastic modulus (K) as well as work of adhesion (W a ) values are shown for PDMS syl (top) and PDMS hm (bottom). The filled and open symbols represent data taken during loading (approaching two surfaces) and unloading (separating two surfaces), respectively. In these JKR experiments the counter surface was PVNODC SFG spectra of the PDMS syl (top) and PDMS hm (bottom) surfaces in SSP polarization (S-polarized SFG beam, S-polarized visible beam, P-polarized IR beam) SFG spectra in SSP polarization of the PS surface before (î) and after ( ) it was held in contact with an unextracted PDMS syl sheet A) The shear stress as a function of time for PDMS exhm sliding on PVNODC (wine) and PS (navy) at a velocity of 3µm/s. B) The shear stress during sliding plotted as a function of velocity for PDMS exhm sliding on PVNODC ( ) and PS ( ) JKR plots of PDMS on PVNODC ( ) and PS ( ) during loading (open symbols) and unloading (filled symbols). A) and C) Contact radius cubed, a 3, as a function of applied load, B) and D) Strain energy release rate as a function of contact radius A) SFG spectra in SSP polarization for PVNODC ( ) before contact, during contact ( ), and after the PVNODC surface has experienced sliding, B) SFG spectra in SSP polarization for PS ( ) before contact, in contact ( ), and after the PS surface has experienced sliding. 176 xx

21 4.13 The sketch illustrates the experimental geometry used to probe the SFG spectra during contact and sliding. A) and C)The SFG spectra in the SSP polarization for PDMS exhm /PVNODC ( ) and PDMS exhm /PS ( ), respectively. The spectra were acquired when the laser beam is at the contact spot (bold symbols), is ahead of the contact spot ( ), and is superimposed once again with the contact spot after sliding (open symbols), B)SFG intensity as a function of time associated with the r + (black line) and r + Fr (gray line) of the methyl groups of the PVN- ODC side chains, D)SFG intensity as a function of time associated with the phenyl vibrations (ν 2, black line) of the PS side chains and symmetric vibration of the PDMS exhm methyl groups (r + PDMS, gray line) SFG spectra for the PDMS/PS interface in SSP ( ) and SPS ( ). The SSP spectrum is shifted vertically for improving the clarity. The solid lines are fit to a Lorentzian equation discussed in the text The prediction of A q,ν20b or 2 (SPS)/A q,ν20b or 2 (SSP) as a function of tilt angle of PS phenyl groups with respect to the surface normal. The experimental values determined from the fit in Figure 4.14 are shown in the figure as dotted lines A) The shear stress as a function of time for PDMS exhm sliding on PnBMA (dark gray) and PnPMA (dark yellow) at a velocity of 3µm/s. The PnPMA data is shifted on the time axis for clarity. B) The shear stress during sliding plotted as a function of velocity for PDMS exhm sliding on PnBMA ( ) and PnPMA ( ). The shear stress behaviors of the PDMS exhm /PS (navy, ) and PVN- ODC (wine, ) interfaces are shown for comparison JKR plots of PDMS exhm on PnBMA ( ) and PnPMA ( ) during loading (open symbols) and unloading (filled symbols). A) and C) The contact radius cubed, a 3, as a function of applied load, B) and D) The strain energy release rate as a function of contact radius A) SFG spectra in SSP polarization for PnBMA ( ) before contact, during contact ( ), and after the PVNODC surface has experienced sliding, B) SFG spectra in SSP polarization for PnPMA ( ) before contact, in contact ( ), and after the PS surface has experienced sliding. The solid and dashed lines are fits of the spectrum before and after sliding, respectively xxi

22 4.19 A) and C) show the SFG spectra in the SSP polarization for PDMS exhm /PnBMA ( ) and PDMS exhm /PnPMA ( ), respectively. The spectra were acquired during contact (bold symbols), when the laser beam is ahead of the contact spot ( ), and after sliding when the contact spot and the laser beam superimposed once again (open symbols). B) and D) are the plot of the SFG intensity as a function of time associated with the r + (black line) and r + Fr (gray line) of the methyl groups of the PnBMA (B) and PnPMA (D) ester side chains. The solid and dashed lines are fits of the spectrum before and after sliding, respectively Comparison of the SFG intensity of the r + vibrations at incident angle of 12 (open symbols) for A) PDMS exhm /PVNODC, B) PDMS exhm /PnPMA, and C) PDMS exhm /PnPMA interfaces with that at incident angle of 42 (filled symbols) Scanning electron microscope images of vertically aligned multiwalled carbon nanotube structures: (left) grown on silicon by chemical vapor deposition ( 65 ñm long), (right) transferred into PMMA matrix and then exposed on the surface ( 25 ñm) after solvent etching with a rate of 0.5 µm/min Topography and force measurement of multiwalled carbon nanotube brushes on PMMA with scanning force microscope (SPM). A) and B) show real SPM height images taken by tapping mode for vertically and horizontally aligned MWNT, respectively. The bars represents 5 ñm and 150 nm, respectively. C) shows a typical deflection-versus-displacement curve during a step loading/unloading cycle with high hysteresis loop. The silicon probe on approach sticks to the nanotubes (triangle) and requires a pulloff force to detach the probe from the surface (filled circles), D) The deflection-versus-displacement curve from Figure 2b with negligible adhesion, and E) with double pull-offs xxii

23 CHAPTER I INTRODUCTION Polymers are becoming the choice of material in many different applications due to their unique properties and light weight. Without the availability of these materials, the manufacturing and functioning of many mechanisms, both artificial and natural, would be difficult. All these mechanisms involve the interaction of polymers with the surrounding environment or with solid materials such as other polymers and metals, at the boundary of their common surfaces (interfaces) within length scales of a few angstroms. It was Langmuir who realized that the intermolecular interactions across surfaces are dictated from their outermost molecular layers [1 5]. By adsorbing organic films onto high-energy surfaces, he manage to change their surface energy, γ, to a lower value. The molecular origin of this observation, as proposed by Langmuir, is the fact that molecules can be highly oriented in a highly packed state and only expose a certain portion outward which determines the surface energy regardless of the portion that faces towards the inner layer. Langmuir also studied the effect of surface structure on their wetting behavior and observed that liquids with higher surface energy can bead up and roll off the surface of closed-packed molecules with lower surface energy. This finding is important considering the interaction of two surfaces such as 1

24 that between a polymer and a drop of water because the strength of the interfacial interactions depends on the ability of these surfaces to induce wetting of water which is determined by their relative surface energy. Therefore, it is possible to estimate the surface energy of this polymer from the angle, θ, that the water droplet makes with the polymer surface using some simplifications provided by Young s equation. These simplifications are practical only as a result of the Dupré equation which takes into account the conservation of total energy during the reversible process of adhesion (contact interfaces) of two phases. A combination of the Young and Dupré equation gives the work of adhesion, W a, at the solid/liquid interface, W a = γ lv (1+cosθ). This can be simplified further according to Good and Girifalco by expressing W a as a geometric mean of the surface energies of the two phases, W a = 2(γ sv +γ lv ) 0.5. However, this is an indirect way of determining the surface energy of solids because this method relies on inexact models of intermolecular interactions and does not take into account accurate mechanics of deformations near the interface. In addition, it requires the usage of a liquid whose surface energy should be known. Johnson, Kendall, and Roberts (JKR) [6] developed a direct method based on Hertzian contact mechanics [7] which measures the deformation of an elastic semisphere against a rigid surface under the influence of an external load. Figure 1.1, taken from the original work, depicts the contact between two elastic solids in the absence (Hertzian contact radius a 0 ) and presence (JKR contact radius a 1 ) of surface forces. Since, equilibrium is established between the applied load and the surface forces, the deformation can be directly used 2

25 to estimate the adhesion and surface energies. This method is also advantageous in eliminating the liquid phase and makes it possible to study the interactions between two condensed phases which is the case in many scientific and technological areas such as biomedical implants, adhesion, friction, wear, and nanotechnology. Figure 1.1: The contact between two elastic spheres of radii R 1 and R 2 under a normal load of P 0. When the surfaces forces are taken into consideration, the contact radius increases from the Hertzian value a 0 to the JKR value a 1 due to the intermolecular interactions across the interface. δ is the elastic displacement. (From ref [6], p.303.) Regardless of the nature or shape of materials, the formation of two new surfaces by the separation of a contact interface is controlled by the fracture mechanics. The contact mechanics approach which is a thermodynamic processes is only valid when the formation of surfaces is reversible. Then W a is the reversible work necessary to separate two surfaces in the absence of energy dissipation. In the fracture process, 3

26 the production of surfaces by rupture usually involves the irreversible dissipation of energy. Fracture occurs only if sufficient energy (the strain energy release rate, G) is larger than the critical energy necessary to extend a crack over a unit area. In the absence of dissipative processes, G = W a but for irreversible processes, G is higher than W a indicating that more energy is needed to separate the two surfaces than to form an interface by bringing them together. This phenomenon is known as adhesion hysteresis. This hysteresis indicates that nonequilibrium processes take places at the interface such as interdigitation, restructuring, disentanglement and inelastic deformations [8]. However, the values of W a, G, or adhesion hysteresis alone are not reliable to determine which one of these mechanisms is the origin because they do not provide the knowledge of the molecular structure. The intermolecular interactions mentioned so far for contact interfaces are also involved when one of the surfaces is in relative motion against the other which describes friction. The understanding of friction is important in areas such as energy conservation, controlling road traction of tires, nanotribology, and design of prosthetic devices. The frictional behavior is controlled by interfacial dynamics besides the surface forces. It is well accepted that higher adhesion leads to higher friction for smooth surfaces [1]. However, the exact relationship between adhesion and friction is still not understood [9 12]. The presence of dissipative processes or adhesion hysteresis can affect the friction in a complex way [8,13]. In the early friction studies, Briscoe and coworkers, Kendall, Roberts and Thomas as well as Briggs and Briscoe speculated a 4

27 direct relationship between adhesion hysteresis and friction. By using poly(dimethyl siloxane) (PDMS) elastomer as the counter surface, Chaudhury and Owens [8] also suggested that the cause of higher friction is related to adhesion hysteresis. This energy dissipation during adhesion was attributed to partial interdigitation of the chains across the interface which also increases the dissipation of energy during sliding. Even though there has been a vast number of observations that indicate a strong correlation between adhesion, adhesion hysteresis, and friction, there still are some striking anomalies. For example, Vorvolakos and Chaudhury reported higher friction for PDMS elastomer sliding on poly(styrene) (PS) surfaces in comparison to that on a well-packed hydrocarbon monolayer (SAM) [14] in the low velocity range where surface wear is minimal. This was unexpected because the adhesion energies of the PDMS/SAM and PDMS/PS interfaces are only slightly different. In addition, the adhesion behavior of both interfaces were found to be nonhysteretic. Vorvolakos and Chaudhury have pointed that the higher shear stress for PDMS/PS could be due to interdigitation of PS chains in the PDMS elastomer. A local penetration of 0.5nm (the size of a phenyl group) can stay unresolved by adhesion measurements but can lead to higher friction. However, it is not clear why we should expect interpenetration across the interface between a glassy polymer and a crosslinked rubber. Brown has also shown that the friction forces of PDMS sliding on a glassy PS surface are much higher than that on a PDMS surface [15]. Brown interpreted his finding as the rigid PS slowing down the molecular mobility of the PDMS segments at the interface 5

28 leading to higher energy dissipation during sliding. Both these arguments, mobility and interpenetration, involve the changes in the structure of the interfacial molecules upon contact or during sliding. Thus, the need for a technique that can probe the structure of the interfacial molecules is vital in the understanding of friction, adhesion and their relationship. Recently, it has been demonstrated that infrared-visible sum frequency generation (SFG) spectroscopy can be used to determine molecular structure at the polymer/solid and polymer/polymer contact interfaces [5, 6]. SFG is a nonlinear optical technique, which detects the orientation and density of molecules. According to the principles of non-linear optics, SFG can only be generated when the inversion symmetry is broken in a material such as most of the surfaces and interfaces within a few atomic layers. Therefore, SFG can selectively probe the surface and interfaces of many polymers without any contribution from the bulk. In this study, we designed a novel approach to couple SFG spectroscopy to study molecular structure (orientation and density of molecules) at the polymer/solid and polymer/polymer interfaces with adhesion and friction experiments. We have taken advantage of a model elastomeric network, PDMS, to generate large uniform contact areas with the solid surfaces. The deformable elastomer provides large uniform contact areas which is required to directly probe the interface. The size of the contact area can be controlled by the applied load and radius of curvature of the lens based on the JKR theory [6]. For solid surfaces, octadecyltrichlorosi- 6

29 lane monolayer (OTS), poly(vinyl n-octadecyl carbamate-co-vinyl acetate) (PVN- ODC), polystyrene (PS), poly(n-butyl methacrylate) (PnBMA), and poly(n-propyl methacrylate) (PnPMA) were chosen. We also designed synthetic adhesives using aligned multiwalled carbon nanotubes (MWNT) inspired from nature. These MWNT are embedded in polymer surfaces and can serve as dry adhesives similar to or stronger than Gecko foot-hairs. The historic perspective for adhesion, friction, and SFG is given in Chapter 2 following this introduction. This includes the historical development of important ideas for each subject as well as their experimental and theoretical investigations. Chapter 2 also mentions briefly the adhesion and friction phenomena seen in nature. Then, Chapter 3 gives details of the materials used, explains the experimental procedures and describes the experimental techniques. Chapter 4 covers the studies performed in quest of understanding the molecular origins of adhesion and friction. Each study is presented with a short introduction specific to the study and the relevant results and discussions. The first section of this Chapter investigates the structure at a contact interface and its macroscopic consequences on adhesion. The contact was between an oxidized poly(dimethyl siloxane) (PDMS ox ) elastomer and a methyl-terminated self-assembled monolayer (OTS) on a flat sapphire substrate. OTS is an ideal surface due to its well packed long alkyl chains that are known to resist high pressures. Since the oxidation process generates short PDMS chains, this system provides an opportunity to investigate the restructuring of 7

30 these short chains under contact and its affect on the adhesion properties. The second section observes the molecular changes that take place when a friction force is applied to the contact interface. The surface of the PDMS elastomer was not oxidized because the existence of short chains will cause lubrication while the purpose is to study dry friction. We have investigated the interface of PDMS/PS and PDMS/poly(vinyl n-octadecyl carbamate-co-vinyl acetate) (PVNODC). These systems are similar to that studied by Vorvolakos and Chaudhury [14] and exhibits a complex friction behavior that cannot be explained by its adhesion properties. We have used PVNODC instead of the SAM because it is easier to prepare smooth surfaces. The surface of PVNODC is similar to that of the SAM [16]. Besides PVNODC and PS, the frictional behavior of PDMS was also studied on poly(n-butyl methacrylate) (PnBMA) and poly(n-propyl methacrylate) (PnPMA) in order to understand the role of chain mobility in friction. PnBMA has a T g below T R at 17 and PnPMA has a T g above T R at 35. Although the focus of this dissertation is on elastomer/polymer interfaces, in the third section, we report a novel structure based on multiwalled carbon nanotubes embedded in polymer surfaces with strong nanometer level adhesion that can serve as dry adhesives similar to or stronger than Gecko foot-hairs. Finally, this dissertation is concluded in Chapter 5 with some important highlights obtained from the studies mentioned in Chapter 4. 8

31 CHAPTER II HISTORICAL PERSPECTIVE In this chapter, the historical perspective of polymer adhesion and friction is presented. Relevant surface and interfacial phenomena and their theories are briefly explained. In this work, the word surface is defined as the outer or topmost boundary of a bulk phase when the surrounding environment is vacuum or more realistically air. The word interface is used as the common boundary formed between two surfaces when they come into direct (mechanical) contact. I would like to emphasize that adhesion, friction, and the relationship between them are still not fully understood and requires a good understanding of the surface and interfacial structure in terms of chemical composition, spacial orientation, and molecular packing. Using the modern surface techniques with molecular level sensitivity is one way to achieve this goal and is the theme of this study. The technique I have used is called IR-visible sum frequency generation spectroscopy and is also presented in this chapter. Finally, adhesion and friction mechanisms provided by nature are discussed for the purpose of designing biomimetic surfaces with controlled adhesion and friction properties. 9

32 2.1 Polymer Adhesion Adhesion is the phenomenon of binding the surfaces of two condensed phases together with intermolecular interactions when brought into contact. In general, these two solids in contact are considered to be different in phase and/or chemistry. However, they can be identical, a case that is called autoadhesion or selfadhesion, as long as they form an interface through solid-state contact. This is different from cohesion which is related to the interactions between atoms or molecules within the bulk of a material. Cohesion is an important concept in adhesion and friction studies because it can dictate the adhesion and friction forces measured at the contact interface. For example, in some systems, the binding at the adhesive interface or joint is stronger than the cohesive interactions in either of the materials. When the two surfaces in this system are forced apart by a normal force, the breakage (fracture) will most probably occur within the material of weak cohesive interactions rather than the interface. In this study, systems with cohesive failures are avoided and thus the measured adhesion and friction forces are assumed to originate purely from the interface. Adhesion is among the oldest technologies in human history [17]. Its ancient traces can be found in the first human made tools of the Stone Age, in the asphalt of the Tower of Babel, or in the furniture veneers of ancient Egypt. Up to the 20 th century, the basic adhesive materials were originated from nature such as the collagen in bones and skin, casein in milk or starch in plants (corn, potato, rice or wheat). After the advancements in the science of chemistry, synthetic polymers 10

33 took over as the major raw materials for adhesives. Adhesion over the years became crucial for variety of applications; packaging, book binding, footwear, construction, printing, paints, automobiles, and railways are just a few of these. Eventually, it developed into a separate science perhaps only 5 decades ago as a response to the growing needs of the industry [17]. The science of adhesion took such a long time to come into existence because it requires the study of surfaces, physics, rheology, and mechanical engineering all at once [18]. With the progresses in research, the adhesive technology began to bloom finding various new applications in biological systems, marine environment and recently in nanotechnology. This, eventually, initiated more fundamental studies concerned with the molecular origins of adhesion Adhesion Theories There are various underlying mechanics of polymer adhesion all of which have developed into separate theories. However, the obvious prerequisite for any of these mechanics to be effective is to establish an intimate interfacial contact. It is often claimed that everything should adhere to everything else if contact is sufficient. From a macroscopic point of view, an intimate contact may be possible with smooth surfaces or highly compliant materials that can deform to take the shape of any surface topography under a normal load. On a much smaller scale, the factors that influences intermolecular contacts are molecular structure, surface chemistry relevant to wetting, and thermodynamic equilibrium [18]. The molecular structure involves the size and shape of the atoms and interatomic spacing within the structural units. If the 11

34 equilibrium configuration of the two materials at the surface does not match, the real contact area can be significantly smaller than the apparent contact area. This is more pronounced for long-chain polymer molecules but also valid for small molecules [19]. Once the structure allows, one material has to wet the other for a complete contact. Even tough this wetting condition corresponds to a thermodynamic equilibrium, it may never be achieved due to some kinetic factors that depend on the viscosity and surface topography. Once an intimate contact is achieved between two surfaces, intrinsic intermolecular forces start to act across the interface which are the bases of adhesion. These forces are the same type of forces that bind atoms together to form molecules and molecules together to form liquids and solids (cohesive forces) [20]. The most general one is the long-ranged London dispersion forces (a type of van der Waals forces). It can be exhibited by all materials, polar or non-polar. Another long-ranged force is the Coulomb force that gives rise to electrostatic interactions between charged surfaces. Ionic and hydrogen bonds are also classified as Coulombic forces. At smaller separations, chemical bonds such as covalent and donor-acceptor interactions may come into play. The type and magnitude of these intermolecular forces determine the strength of an adhesive bond. There are mainly six theories of polymer adhesion; chemical, mechanical, electrostatic, diffusion, adsorption, and rheological. 12

35 The chemical theory explains adhesion as the formation of bonds at the interface through chemical reactions [21]. This is true for certain systems where surfaces can react with each other. One example is the adhesive behind postage stamps that can hydrogen bond to envelops. However, adhesion is also observed between surfaces incapable of chemical reaction. The mechanical theory [17] was respected for many years due to the first adhesion studies on porous materials such as wood. It is based on mechanical interlocking of the microfeatures (irregularities) of the two surfaces. The strong adhesion observed between smooth surfaces reduced the wide applicability of this theory. For example, the adhesion study of Tabor et al. between two atomically smooth mica surfaces and of Johnson et al. between optically smooth rubber surfaces clearly challenged the idea that mechanical interlocking is the major source of intrinsic adhesion [6, 22, 23]. A closer examination of surfaces revealed that a surface has to be specifically pretreated to obtain the appropriate topography for interlocking to occur. The electrostatic theory of adhesion suggests the Coulomb attraction forces between the surfaces to be the main component of adhesion. These forces are generated from contact or junction potentials whose existence has been observed clearly [24, 25]. However, their contribution to adhesion forces have not yet been proven to be significant. The diffusion theory is applicable to the adhesion of polymers. It was initiated by Voyutskii s observations of time, temperature, pressure, rate and structure 13

36 effects on autoadhesion [21]. Since interdiffusion in the bulk phase has already been known, the idea of diffusion at the interface of two chemically similar polymers was widely accepted. This diffused interface is described by the disappearance of a sharp boundary and the development of a gradual transition from one phase to the other. The interdiffusion requires the polymers to be mutually soluble and the chain segments to have sufficient mobility. This concept is highly used in the construction area where polymer parts are adhered to one another with a glue containing the solvent and specific polymer to ensure the diffusion. However, the theory is limited to certain systems and not applicable to interfaces such as polymer/metal or polymer/glass. According to the adsorption theory, adhesion takes place when one material spreads over the other allowing the surfaces to come close to molecular intervals (wetting). Only then, van der Waals dispersion forces that are mainly responsible for adhesion can become active [26]. These forces are the weakest among the others, but if complete wetting is achieved, they can provide strong adhesive bonds. Adhesion is thus determined by the surface energy differences of the two materials in contact. Those with high (glass, metal) or medium (paper, wood) surface energy levels may be bonded well with lower surface energy polymers. On the other hand, polymers can be difficult to be bonded and may require surface treatments to increase their surface energy. The adsorption theory provides many insights to adhesion by focusing on wetting but it is also not free from contradictions. The theory by itself is not enough to explain every adhesive system. 14

37 The rheology aspect of adhesion is important in the wetting process by which an adhesive bond is established. The conformation at the interface should correspond to the surface topographies to obtain full contact and good bond strength. However, the primary rheological effects are observed mostly during bond breakage. Depending on the material, a major portion of the energy required to break an adhesive bond may be spent on deformation. Due to the rate and temperature dependence of the viscoelastic properties of polymers, the adhesive bond is affected from the measurement conditions. This theory was first proposed by Bikerman, Sharpe, and Schonhorn and later on observed experimentally by many scientists [26, 27]. Among these studies, the experiment by Bright represents the first evidence of time-temperature superposition in adhesive bond strength. This experiment has also showed the dependence of a failure mechanism on temperature. With decreasing temperature (increasing rate) the failure changes from cohesion to adhesion. This theory predicts profound effects of rheology on adhesion but by excluding all the other possible factors, it stays insufficient to explain all aspects of adhesion. The common feature to all these different theories is that, each one of them can quantitatively explain some adhesion phenomena while they fail to explain some others. They can even lead to conflicting results. Adhesion seems to be a complex combination of many factors which are difficult to be estimated and separated. Besides, there are secondary factors that influence the adhesion strength of a bond; 15

38 surface roughness, contamination layer, stress developed at the interface, shape of the joint, and aging are some that we are aware of Thermodynamics of Polymer Adhesion Some of the thermodynamic terms such as surface energy or factors such as wetting have already been mentioned in the previous sections of this chapter. The objective here is to define them in detail and explain their role in the science of adhesion Surface Tension and Surface Energy A molecule in the bulk of a material is surrounded by other bulk molecules and is attracted equally from all sides (Figure 2.1). On the contrary, a surface molecule is exposed to the outside environment from one side and is attracted unequally. Therefore, the net attraction on this molecule is towards the bulk. This tends to reduce the number of molecules in the surface region. As a result, the distance between the surface molecules increases which requires work to be done in order to return to a normal configuration. The excess force per unit length at the surface is termed the surface tension and symbolized as γ. It is this phenomenon that causes a small volume of water to take a spherical drop shape and makes it possible for small beetles to walk on the surface of a lake. The surface tension can be related to a surface energy when work is done to extend the surface per unit area against surface tension forces at constant temperature (T), pressure (P), and moles (n). The necessary force is γ per unit length and the 16

39 Surface F Figure 2.1: Depiction of bulk and surface molecules. F is the net attraction on a surface molecule which is balanced in the case of a bulk molecule. work done is γ δa where A is the area of surface. The work done must be equal to the increase in total surface energy. For unit increase of surface area, the surface tension is the change in free energy of the whole system while the surface energy is the change in free energy of only the surface. For liquids, the surface tension (γ l ) is equal to its surface energy because when the surface is extended, liquid molecules from the bulk flow into the surface and the surface composition does not change. For solids, however, the chemical potential changes when the surface area is increased. Therefore, the surface tension (γ s ) and the surface energy of solids are different terms. Langmuir discovered that the surface energy of a surface is determined by its chemical composition at the outermost layer as seen in Figure 2.2 [1 5]. Following Langmuir, Zisman and coworkers investigated the contact angle (see section ) of various liquids on smooth low-energy solid surfaces [29 33]. The cosine of the 17

40 Figure 2.2: Critical surface tension of some commonly used polymer surfaces whose chemical structure is indicated. (from ref [28], p.100.) contact angle was found to change linearly with the surface tension of a family of liquids (Figure 2.3). Zisman defined the point where this line meets the Cosθ = 1 axis as the critical surface tension γ c. γ c is a measure of the surface free energy of solids but not equal to it unless the correction factor, φ for intermolecular interactions (section ) is equal to unity. Still, it is a useful empirical parameter that characterizes surfaces and gives us an idea of how their free energy behaves. In Figure 2.2, the typical values of γ c for some plastics, rubber and composites are given Interfacial Tension and Work of Adhesion When dealing with surface tension, the interaction of surface molecules with the surrounding environment (gaseous phase) is neglected. On the contrary, at the interface 18

41 Figure 2.3: Zisman s contact angle results of n-alkane liquids on various perfluorinated surfaces. (From ref [34], p.231.) the intermolecular forces play a crucial role in determining the interfacial tension. These forces are directed towards the bulk of each phase. As a starting point, if a unit area of one surface is placed in contact with a unit area of a second surface with zero interaction, the interfacial tension would be the sum of the surface tensions which are scalar quantities, γ 12 = γ 1 + γ 2 (2.1) When intermolecular interactions come into play, the free energy of the whole systems decreases to, 19

42 W a = γ 1 + γ 2 γ 12 (2.2) which is known as the Dupré equation. This energy difference (W a ) is called the adhesion energy and comes from the conservation of total energy in a reversible process of adhesion and cohesion of two phases. It represents the work necessary to separate the two surfaces from their adhesive contact. If the two surfaces that are brought into contact are identical, they will coalesce to form a homogenous body. Then, the decrease in free energy is the work of cohesion (W c ) which is the reversible work necessary to create two new surfaces, (W c ) 1 = 2γ 1 or (W c ) 2 = 2γ 2 (2.3) Girifalco and Good [19] reexamined the work of adhesion and developed an interaction parameter, φ, which is the ratio of the work of adhesion of an interface to the geometric mean of the individual works of cohesion, tensions, φ = (W a ) 12 [(W c ) 1 (W c ) 2 ] 1/2 = γ 1 + γ 2 γ 12 2(γ 1 γ 2 ) 1/2 (2.4) If W a and W c are written in terms of the individual surface and interfacial φ = γ 1 + γ 2 γ 12 2(γ 1 γ 2 ) 1/2 (2.5) 20

43 or γ 12 = γ 1 + γ 2 2φ(γ 1 γ 2 ) 1/2 (2.6) which gives, W a = 2φ(γ 1 γ 2 ) 1/2 (2.7) According to Girifalco and Good s approach, φ has to be known a priori in order to obtain W a. This is difficult because it requires a detailed knowledge of the chemical composition of surfaces. Fowkes [35] had a different approach and suggested that the surface tension can be decomposed into components corresponding to each specific type of intermolecular interactions, γ 1 = γ1 d + γh 1 + γp 1 + γi 1 + γe (2.8) where contributions from dispersion forces (d), hydrogen bonds (h), dipoledipole interactions (p), dipole-induced dipole interactions (i), and electrostatic interactions (e) are shown. Then, W a = 2(γ d 1 γd 2 )1/2 + 2(γ h 1 γh 2 )1/2 + 2(γ p 1 γp 2 )1/ (2.9) Fowkes further argued that for systems in which dispersion forces predominate on both sides and across the interface, W a may be written as, 21

44 W a = 2(γ d 1 γd 2 )1/2 (2.10) Wetting and Contact Angle The surface energetics of solids are commonly characterized through the measurement of contact angles of drops of liquids which results from surface and interfacial forces in equilibrium (Figure 2.4). Vapour γ lv Liquid φ Solid γ γ sl sv Figure 2.4: The contact of a liquid with a solid surface at equilibrium. When a spherical drop of a liquid makes contact with a solid, the liquid either spreads out and forms a thin film or it beads up and forms a finite angle with the solid surface. This angle is called the contact angle. For systems at equilibrium, it is designated as θ. 22

45 The equilibrium system here involves three homogenous phases, the liquid (l), the solid (s) and the saturated vapor from the liquid (v), intersecting along one line. If G donates the free energy, in equilibrium, the change in the free energy of the whole system due to change in the liquid-vapor, solid-liquid, or solid-vapor interfacial area must be zero, δg = (δg) sv + (δg) sl + (δg) lv = 0 (2.11) If the edge of the liquid drop as illustrated in Figure 2.5 advances from point B to C, the change in free energy is, Vapour γ lv Liquid φ φ ds Solid γ A γ sl dr B sv Figure 2.5: The edge of a liquid drop on a polymer surface. (Adapted from ref [34], p.222.) 23

46 δg = 2πRdRγ sv + 2πRdRγ sl + 2πRdSγ lv (2.12) where R is the radius of the circle which is the base of the liquid drop. Since ds = drcos and at equilibrium δg = 0 as well as θ = θ, eq 2.12 becomes, γ sv = γ sl + γ lv cosθ (2.13) which is the famous Young equation describing the contact angle as the vectorial balance of three surface forces. The equation can represent either a force or an energy equilibrium. The surface tension which is a force per unit length requires an energy input when the surface is extended per unit area. Young s equation received many criticisms especially because it ignores the fact that the vapor of the liquid drop will be adsorbed on the solid surface reducing its surface energy and tension. Harkins and Livingston [36] defined the amount of reduction in terms of a spreading pressure, π s, π s = g s γ sv (2.14) where g s belongs to the solid which is in contact with vacuum. Therefore, the true equilibrium of the three phase system is, g s π = γ sl + γ lv cosθ (2.15) 24

47 When the liquid drop is separated from the solid (no adsorbed vapor) to expose a unit area of the surface without any viscous or elastic deformation, the work of adhesion is, W a = γ lv + γ sv γ sl (2.16) because it is the work necessary to obliterate the unit area of interface of surface energy γ sl while creating two surfaces of unit areas with energy γ sv and γ lv. This is the Dupré equation as in eq 2.2. Combining eq 2.15 and 2.16 yields, W a = γ lv (1 + cosθ) + π (2.17) When π is negligible, eq 2.17 reduces to, W a = γ lv (1 + cosθ) (2.18) which is the well known Young-Dupré equation that expresses the work of adhesion in easily measurable quantities. This way the two unknowns, γ sv and γ sl can be neglected. Wetting, which is a requisite for strong adhesion bonds, is usually accompanied with a zero contact angle. Even though that gives the highest contact area, liquid and solid molecules can still be in close contact at an angle greater than zero. 25

48 The work of adhesion can be at maximum at a relatively high contact angle as shown in Figure 2.6. Figure 2.6: Work of adhesion between liquids and a surface with γ c = 21.5ergs/cm 2. (From ref [37], p.49.) All the discussion about contact angle and wetting so far are concerned with ideal systems. The solid surfaces are flat, smooth, homogenous, and incompressible. There is no solubility at the interface between the solid and liquid and their surface tension and chemical potential changes are neglected. The practical systems can deviate from ideality and equilibrium wetting may not be possible due to the kinetic factors. Surface tension gradients, dynamic contact angles, surface roughness, chemical inhomogeneity, restructuring, and time-temperature effects should be examined. 26

49 The surfaces in this study are accepted to be close to ideality and therefore such details will not be covered in this chapter Contact Mechanics The reversible work of adhesion (W a ) which is the energy difference between the separated surfaces of two phases and their interface (introduced in Section ) is a key parameter in the study of adhesion science. It determines the nature of the interface. A positive W a means work is required to separate two surfaces. Therefore, a negative W a represents spontaneous separation with free energy reduction. Since W a is quantified by two important material properties, surface and interfacial tensions, their experimental determination is a fundamental issue. The former can be estimated to a good degree with the wetting method as explained in Section This method can also provide energy values for the solid/liquid interface. However, it cannot be applied to the contact of two solids. The direct route to measure the work of adhesion between two solids is contact mechanics. The study of contact mechanics is claimed to have started in 1882 with the publication of On the Contact of Elastic Solids [7] by Henrich Hertz [38]. He was a 24 years old German research assistant to Helmholtz in the University of Berlin. Contact mechanics is a method that analyzes the deformation and the stress distribution of the contact of two elastic hemispheres (isotropic and homogenous) under the influence of surface forces and external loads. The analysis is also applicable to the contact of an elastic hemisphere and a rigid plane. The elasticity of these materials is 27

50 balanced by the surface forces between them. The deformation as a function of load provides information about the work of adhesion and the surface energies. The interface in contact mechanics is assumed to be frictionless where shear stresses cannot be sustained. This is straight forward for very stiff materials because the effect of adhesive forces is negligible. For softer materials such as elastomers, adhesive forces are very important deforming the materials and giving rise to a finite contact area under zero external loads. In these systems, the equivalent of frictionless boundary condition is full-friction where shear stresses at the interface are not allowed to relax. The Hertzian contact between a hemisphere and a rigid plane is depicted in Figure 2.7. In the rest of this section only the hemisphere-plane geometry will be discussed. The hemisphere flattens to make a circular contact with a radius of a against the rigid surface under an external load, P. The deformation occurs only within the softer component (here hemisphere) when the elastic modulus of one is much larger than the modulus of the other. The thickness of both components is assumed to be much larger than the radius of contact. The fundamental relations of such a system can be summarized in the following contact radius (a), displacement (δ), and normal stress distribution (s(x)) equations, respectively, a 3 = PR K (2.19) 28

51 P P HERTZ R JKR R a ρ Solid δ ρ a Figure 2.7: The contact of a deformable sphere on a rigid surface at equilibrium. The Hertzian contact excludes and the JKR contact includes adhesion forces at the interface. (Adapted from ref [39], p.327.) δ = a2 R (2.20) s(x) = 3Ka 2πR (1 x2 ) 1/2 (2.21) where R is the radius of curvature of the hemisphere, x = ρ/a is the normalized radial distance, and K is the elastic modulus given by, 1 K = 3 4 [1 ν2 1 E ν2 2 E 2 ] (2.22) 29

52 where E is the Young s modulus and ν is the Poisson ratio of the hemisphere (1) and surface (2). In the Hertzian contact the interaction is of a hard wall where the attraction between surfaces as they come closer is neglected. There is an infinitely steep repulsion at contact. Such a contact has zero contact area at zero load and can be separated without extra work done. The stress produced at the interface is compressive over the entire contact area and is zero at the edges which is valid for the contact of noninteracting surfaces. However, the behavior of elastic materials with high compliance deviates from the predictions of the Hertz theory. A major improvement to this contact theory for elastic materials was achieved by Johnson, Kendall, and Roberts (JKR) in 1971 [6]. The basic differences between the two theories regarding the physical behaviors are shown in Figure 2.8. In the JKR theory, the attractive interactions between surfaces due to their finite surface tension are incorporated. This leads to a finite contact area at zero load as well as a greater contact area compared to the Hertzian prediction under a given load (Figure 2.7). Attractive interactions introduces a tensile stress near the edges while it is compressive at the center of the contact area. The fundamental relations of the JKR contact is given analogous to that of the Hertzian contact, a 3 = R K [P + 3πRW a + [6πRW a P + (3πRW a ) 2 ] 1/2 ] (2.23) 30

53 HERTZ JKR F F Forces between surfaces D D σ σ Stress under compressive load ρ ρ Shape under zero load Figure 2.8: The main features of the Hertz and JKR theories. (Adapted from ref [40], p.481.) 31

54 δ = a2 R [1 2 3 (a 0 a )3/2 ] (2.24) s(x) = 3Ka 2πR (1 x2 ) 1/2 ( 3KW a 2πa )1/2 (1 x 2 ) 1/2 (2.25) Consequently, it requires extra work to be done to separate the two surfaces, i.e. the surfaces will jump out of contact at a higher applied load than the load applied to bring them together. The load at which the separation occurs abruptly (pull-off load) depends on the radius of curvature as well as the surface energy and is independent of the elastic moduli of the two materials, P pull off = 3 2 πrw a (2.26) The JKR theory predicts an infinite tensile stress at the edge of the contact (x = 1). This is physically impossible but it is a natural outcome of its assumption of infinitesimally short range attractive forces. In reality, the attractive force between two surfaces has a finite range following a Lennard-Jones force law. Unfortunately, a modification to the JKR theory is very complex. However, the theory has been experimentally tested and in general found to be applicable to solids with low elastic modulus and high radius of curvature [41]. The reason is that in these systems, the zone where long range attractive forces act outside the contact is vanishingly small compared to the contact area. For solids with high elastic modulus, the JKR theory has been challenged by another theory of Derjaguin, Muller, and Toporov (DMT) who 32

55 argued that attractive forces between such solids must be effective in a region just outside the contact area [42]. Later on, a thorough analysis by Muller, Yushchenko, and Derjaguin suggested that these theories are actually two limit cases of a general deformation behavior [43]. The details of the cross over from one theory to the other is discussed by Maugis [41]. The DMT theory will not be considered here since the deformable polymer [poly(dimethyl siloxane)(pdms)] used in this study is expected to follow the JKR theory. The JKR theory assumes atomically smooth surfaces and linearly elastic materials. Practical surfaces always have some scale of roughness. The effect of roughness is towards lowering the adhesion due to a lower contact area if mechanical interlocking does not strengthen the adhesion. The consequences can be severe with very rough surfaces but may be ignored for optically smooth and homogenous surfaces. Johnson and coworkers used two rubber hemispheres to test the theory and confirmed that the data from these practical surfaces obeys the JKR relations from which the work of adhesion was determined [6]. Their findings are shown in Figure 2.9 together with predictions from the Hertz and JKR theories. On the other hand, the linear elasticity assumption limits the application of the JKR theory because most deformable materials are either viscoelastic or nonlinearly elastic (at large deformations). Only those whose glass transition temperature is well below the ambient temperature behave purely elastic such as PDMS. For non-crosslinked viscoelastic materials the size 33

56 of the contact zone depends on the loading history and thus, their contact problem needs to be analyzed separately. Figure 2.9: The cube of the contact radius, a 3, as a function of applied load, P, when two rubber hemispheres are brought into contact. The predictions of the Hertz and JKR theories are shown with lines. Data taken from Johnson et al. [6] One last remark about the JKR theory is that it is based on an equilibrium state where the elastic forces are balanced by the interfacial forces. In this case, the mechanically applied energy that is available to decrease the contact area by a unit amount is equal to the thermodynamic work of adhesion. This energy is often called the energy release rate or fracture energy, G. When G = W a, the separation of the two surfaces from an adhesive bond does not involve extra energy dissipation. The 34

57 work necessary for this process is a direct measure of W a as stated in the JKR theory. However, a considerable amount of energy may be dissipated irreversibly during the formation of two new surfaces. Therefore, G may be higher than W a indicating that more energy is needed to separate the two surfaces than to bring them together. This phenomenon is known as adhesion hysteresis and is depicted in Figure This hysteresis indicates that nonequilibrium processes take place at the interface such as interdigitation, restructuring, disentanglement and inelastic deformations [8]. a 3 (m 3 x ) G > W a G = W a Loading Unloading P (N x 10-3 ) Figure 2.10: A general depiction of adhesion hysteresis in JKR type experiments where the cube of contact radius, a 3, is plotted as a function of applied load, P. This is the adhesion behavior between a PDMS elastomeric lens that has filled with silica particles and a poly(styrene) flat surface. 35

58 It is important to understand the distinction between these two energy terms and necessary to determine them separately. For this purpose, the fracture mechanics of adhesive bonds will be considered in the following section Fracture Mechanics Fracture mechanics is concerned with the formation of new surfaces or the separation of an interface by the initiation and propagation of cracks (adhesive fracture). The processes involved in such a fracture are highly irreversible compared to the processes mentioned in previous sections which may be considered as thermodynamically reversible. There are two main conditions that have to be satisfied for a crack to propagate. The first one was suggested by Griffith in 1920 from an energy point of view [44]. Sufficient energy has to be available in order to meet the energy requirements of the new surfaces formed by fracture. In other words, fracture occurs only if this energy (the strain energy release rate, G) is larger than the critical energy necessary to extend a crack over a unit area. The second condition was found by Irwin in 1973 [45]. It states that the stress field around a sharp crack has to be large enough to overcome the intermolecular forces. For a linearly elastic material, this field can be expressed by a stress intensity factor, K. Fracture only takes place when K exceeds a critical value called the fracture toughness. Studies on these two conditions of crack propagation led to the emergence of two different approaches in the fracture mechanics field, energy balance and stress intensity factor. Under certain circumstances these 36

59 two approaches are equivalent and the critical parameters, G and K, may be related. Both of these parameters are independent of the property and geometry of the materials in the system and, ideally, independent of the test conditions. Thus, analysis of each provides a fundamental understanding of fracture. The rest of this section gives a brief discussion on the theoretical aspects of the two main fracture mechanics approaches using ideas of Kinloch [46], Raphaël and de Gennes [47], Liechti [48], Cherry [49], Williams [50], and Man [51] Energy Balance Approach A certain amount of energy is required to create a unit area of fracture surface, δa. Therefore, the crack can only propagate if this amount of energy, or more, is available. The source of this energy is the work (w) done on the system by external forces and the release of the elastic energy (U) in the system due to the relaxation of the stresses at the crack. The difference between the two sources is the potential energy (Π) available for the fracture. The rate of change of Π (w U) in a lamina of thickness b with respect to crack extension δa (δa = bδa) is the strain energy release rate, G = δ(w U) δa 37 (2.27)

60 If P is the load acting on the system at the onset of crack propagation and u is the displacement, δw = Pδu and for a linearly elastic material and small displacements, U = 1 Pu, then, 2 GδA = PδP 1 (Pδu + uδp) (2.28) 2 If the compliance of the system is given by C = u/p, G = P 2 2 δc δa (2.29) The crack will only propagate when G is equal to or exceeds a critical strain energy release rate, G c, sometimes called the fracture surface energy. Naturally, this condition is satisfied when P corresponds to the minimum amount of force that can propagate the crack, P c. Consequently, the criterion for fracture is represented as, G G c = P 2 c 2 δc δa (2.30) When the length of crack growth is much smaller than the size of the whole system, the fracture process can be considered to be under fixed-growth or constantload. Therefore, C can be measured or calculated as a function of A and P c can be measured at the onset of crack growth. Then, G c can be unambiguously obtained by using eq This equation is also valid for cracks at or near an interface as it is in adhesion processes. Most importantly, G c may be related to W a. Since 38

61 two new surfaces are formed during fracture, G c should be converted into surface free energy. However, the energy required for crack propagation was found to be far greater than W a. This is firstly because crack growth along interfaces (or in materials) often incorporates rupture of intrinsic bonds such as secondary (e.g. van der Waals forces) and primary bonds (e.g. chemical bonds). This energy is the intrinsic fracture energy, G o. Secondly, fracture often causes viscoelastic and/or plastic deformation due to high strains. Therefore, realistically, in the presence of energy dissipation, G c = G o + ψ (2.31) where ψ is the energy dissipated in viscoelastic and plastic deformations at the crack tip. Through this parameter, the fracture energy becomes rate and temperature dependent. Gent and Kinloch [52], Andrews and Kinloch [53,54], as well as Gent and Schultz [55] proposed that ψ depends on G o as, ψ = G o f(ȧ, T, ǫ) (2.32) where f is a function that depends on crack growth rate (ȧ), temperature (T), and strain level (ǫ). This relationship is a result of the fact that there can only be stress developed around the crack tip if the region ahead of the crack tip is intact with intermolecular forces. When viscoelastic and plastic energy losses are negligible, f(ȧ, T, ǫ) 0 and the measured fracture energy is a measure of G o. If only secondary 39

62 bonds are effective at the interface, the value of G o should be equal to the value of W a Stress Intensity Factor Approach An unperturbed system is held together by intermolecular forces. A crack in such a system can only propagate if the stresses at the crack tip are large enough to rupture these forces. The crack tip stresses shown in Figure 2.11 can be calculated as has been done by Irwin who used an elastic solution derived by Westergaard in 1939 [56]. In this approach, it is assumed that the crack is uniformly stressed in a homogenous system, the strain is infinitesimal (r is much smaller than the overall length of the crack) and the behavior of the material obeys Hooke s law (Linear Elastic Fracture Mechanics). K I σ yy = (2πr) 1/2cos(θ/2)[1 + sin(θ/2)sin(3θ/2)] (2.33) σ xx = K I (2πr) 1/2cos(θ/2)[1 + sin(θ/2)sin(3θ/2)] (2.34) σ xy = K I (2πr) 1/2sin(θ/2)cos(θ/2)cos(3θ/2)] (2.35) where σ ij are the stress tensor components at the vicinity of the crack at a point P described by the polar coordinates r and θ. The analysis here is for plane stress where the out of plane stress σ z = 0. K is the stress intensity factor which depends on the applied stress and the geometry of the crack and the system. The subscript I refers to a mode I crack propagation. Considering a crack embedded 40

63 Figure 2.11: Stresses around a crack tip for a tensile type loading. (From ref [51], p.23.) in a linear elastic material which extends in the negative x-direction with its tip at x = 0, the crack may be stressed in three different modes as shown in Figure 2.12: (a) the cleavage (tensile-opening) mode (mode I), (b) the in-plane shear mode (mode II), (c) the antiplane shear mode (mode III). The superposition of all the three modes describes the loading. The fracture mode I is the most relevant to adhesion studies that results in failure [46]. From eq 2.35 it is seen that the stresses are effective when P approaches to the crack tip. Eventually, σ and becomes singular as r 0. This means that ahead of the crack tip a zone exits where the stresses exceed the plastic yield stress level of the polymer. In general, this plastic zone is assumed to be small enough not 41

64 Figure 2.12: The three fracture modes. The displacements of atoms are indicated on the right for each mode. A) Cleavage mode : mode I, B) In-plane shear mode : mode II, C) antiplane shear mode : mode III. 42

65 to disturb the elastic stress field. Only then it may be defined by the elastic stresses. This is shown in Figure 2.13 for an imaginary crack in the bulk of a material. δ t is the crack opening displacement and r y is the radius of the circular plastic zone. The imaginary crack tip is at the center of the plastic zone with length a + r y. There is an elastic stress field ahead of this crack which is equivalent to the stress field of a crack with length a and a plastic zone 2r y. If r y a, eq 2.35 can be used to calculate the crack tip stresses. A small correction can be applied to improve the accuracy by using a + r y instead of a. Figure 2.13: Irwin model of the plastic zone at the crack tip. (From ref [46], p.280.) 43

66 An important characteristic of the singularity mentioned above is that the stress field local to the crack tip is similar for all loadings. The difference is only apparent in the magnitude of K which makes this parameter the main interest in the stress intensity factor approach. As a result, the level of K uniquely defines the stress field around the crack. Thus, fracture occurs when K exceeds a critical value. This leads to the criterion for crack propagation postulated by Irwin, K I K Ic (2.36) where K Ic is a material property called fracture toughness. It is a measure of the stress intensity ahead of a crack Cracks at or near interfaces The fracture of cracks at or near the interface is a special case that has to be considered separately. It has practical importance in adhesion regarding the separation of two surfaces. Figure 2.14 illustrates a crack located parallel to an interface of two dissimilar materials. When tensile loads are applied normal to the crack, both tensile and shear stresses arise around the crack tip. Theoretical studies for linear elastic materials suggested that local stresses for such a system is proportional to, f(k I, K II ) (2πr) 1/2 ( ) sin (ζinr) (2.37) cos 44

67 Figure 2.14: A crack at an interface of two dissimilar materials. where ζ is a bimaterial constant. It is a function of the shear moduli, G 1 and G 2 and Poisson s ratios, ν 1 and ν 2 of the two materials forming the interface, ζ = 1 2π In[( β 1 G G 2 )/( β 2 G G 1 )] (2.38) where β is a function of ν. For plane stress where σ zz = 0, β = (3 ν)/(1 + ν) (2.39) The analysis of eq 2.37 shows that the stresses are oscillatory in the vicinity of the crack tip. The problem is that they change signs with increasing frequency as r 0. In addition, the crack face displacements also oscillate interfering with the oscillating stresses near the crack tip which is unphysical. Various modifications have been proposed but each one of them either violates a boundary condition or is based on an unrealistic assumption. The interference between the oscillating displacements 45

68 and stresses is usually ignored since it happens very close to the crack tip. It is assumed that the field stresses near to and far from the crack can still be characterized with the given relationships. It is evident from the brief discussion of the stress intensity factor approach that there are many problems to be resolved especially for its application to adhesive bonds. Therefore, the energy balance approach has been favored by many researchers for adhesion studies. However, under certain circumstances the two approaches can be related trough the critical values of G and K Relationship between G and K In linear elastic fracture mechanics, values of G and K that are necessary to propagate a crack in a homogenous body can be related under plane strain conditions where σ zz = ν(σ xx + σ yy ), G c = (1 ν2 ) E for mode I in plane stress, KI 2 c + (1 ν2 ) K 2 (1 ν) II E c + E K2 III c (2.40) G Ic = K2 I c E (2.41) and for plane strain, G Ic = K2 I c E (1 ν2 ) (2.42) 46

69 This expression is not valid for a crack at the interface. Since an accurate relationship has not been found yet, the most appropriate modification is to replace the modulus with an effective one that is some weighted average of moduli of the materials on both sides of the interface, where α m = (ξ + 1)/(χ + 1) G c = Kc ( ( 2α m 1 ) (2.43) E 1 E 2 αm 2 ξ = E 2 /E 1 χ = 1 + E 2 2 (1 + ν 1 E ν 2 E 2 ) (2.44) This equation is useful as providing conversion between the two fracture criteria. Once the effective modulus is known for a particular geometry, it can be used to determine both G and K. It should be noted that for non-lefm the concept of G is still valid but the interpretation of stress intensity factor is not always clear and thus the above relations are not generally applicable Relevant Adhesion Studies Using Contact Mechanics Techniques at the Elastomer/Polymer Interfaces Since the experimental verification of JKR theory by Johnson et al. [6] using two rubber hemispheres, many researcher have used the same concept to study directly 47

70 the adhesion at the solid/solid interfaces. In these studies a variety of experimental tools have been employed including JKR apparatus, surface forces apparatus (SFA), scanning probe microscope (SPM), and nanoindenters. Each of these has its own advantages and limitations. We have chosen the JKR apparatus to conduct our adhesion measurements because it is simple yet accurate, and it can be incorporated into the nonlinear optical technique used in this study. This experimental technique, called sum frequency generation spectroscopy (SFG), is explained in Section Modern JKR measurements are mostly based on a simple method developed by Chaudhury and Whitesides [57] which uses small ( 2mm) hemispheres of poly(dimethyl siloxane) (PDMS) elastomer. Carefully prepared PDMS has the proper specifications for a JKR study; it is deformable and has elastic behavior within the load range used in typical JKR measurements; its surface is smooth and homogeneous; it can be easily cast into semispherical shapes; and, its surface can be modified without affecting other physical properties. As seen in Figure 2.15, Chaudhury and Whitesides brought a deformable semispherical PDMS with radius of curvature R (1-2mm) into contact with a deformable flat PDMS sheet. The deformation at the contact forms a circular region with radius a ( µm). JKR measurements of this system was observed to be in equilibrium (G W a ) with no hysteresis. The measured W a values of 42-44mJ/m 2 were found to be in close agreement with the values estimated from contact angle measurements. Chaudhury and Whitesides [58] also studied the adhesion behavior of monolayer coated PDMS surfaces having dif- 48

71 ferent end groups. This simple method provided direct estimation of the surface free energy and was proven to be sensitive to small variations in the chemical composition of the surface. Figure 2.15: Contact between a PDMS lens and flat plate. The area of contact is exaggerated for clarity. (From ref [57], p.1015.) The flat PDMS plates used in these experiments can be replaced with any other flat solid substrate and can be coated in order to study the adhesion of any kind of polymer surface. Mangipudi and coworkers [59] studied the interface of PDMS/PS and PDMS/PMMA whose adhesion data fit well to the JKR model. The a 3 versus P plots shown in Figure 2.16 exhibit no adhesion hysteresis for both interfaces. With the obtained W a values from these measurements interfacial energies at each interface can be directly calculated by using the Dubré equation (eq 2.2) and surface free energies of PS and PMMA. For interfaces that are in equilibrium with no adhesion hysteresis such as those mentioned above, G = W a which is the classical Griffith criterion in fracture 49

72 Figure 2.16: Adhesion measurements at the PDMS/PS and PDMS/PMMA interfaces. Both interfaces are free from adhesion hysteresis A)PDMS and PS with W a of 49±3mJ/m 2, B) PDMS and PMMA with W a of 57±1mJ/m 2. (From ref [60], p.431.) mechanics. However, in nonequilibrium interfaces G W a and G corresponds to a nonequilibrium value. When the interface changes with time but not the elastic properties of the bulk, the difference (G - W a ) is the crack extension force where the edge of the contact surface is treated as a propagating crack in mode I. This difference signifies the degree of the hysteresis and can be the measure of the metastable process at the interface such as rearrangements, interdigitation, entanglements and chemical reactions. The magnitude of the hysteresis relates directly to the dissipation of interfacial energy during contact. However, the relationship is not straightforward because the specific process that is responsible for the hysteresis has to be known. This cannot be achieved by JKR measurements which only measures the macroscopic 50

73 consequences of the molecular level events. The rest of this section provides some examples from previous adhesion measurements not limited to JKR apparatus with such complications. The purpose is to reveal the necessity of direct in-situ measurements of the interfacial structure. Chen and coworkers [61] studied the adhesion behavior of Langmuir-Blodgett (LB) monolayers adsorbed on mica surfaces using SFA in order to understand the molecular mechanism behind the adhesion hysteresis. The phase state of these monolayers were varied with surface pressure resulting in crystalline, amorphous and liquid-like monolayers. No adhesion hysteresis was observed at the contact of crystalline/crystalline and crystalline/amorphous monolayers. Significant hysteresis was observed at the amorphous/amorphous contact while the hysteresis is relatively smaller at the liquid/liquid contact. This behavior was attributed to the difference in interdigitation and relaxation of the monolayers. The chains in the crystalline state do not interdigitate, thus they are free from hysteresis. The liquid-like chains interdigitate rapidly and can exhibit hysteresis if the surfaces are separated quickly enough. When the chains interdigitate in the amorphous state due to lower packing density, their relaxation is very slow leading to large hysteresis. Some of these findings are in agreement with the JKR measurements of Chaudhury and Owen [58] who also found that adhesion hysteresis depends on the phase state of the monolayer films. Their monolayers were adsorbed onto oxidized PDMS where the phase state was controlled by the amount of adsorption and was characterized by infrared spectroscopy. Mono- 51

74 layers in the crystalline state exhibited significant hysteresis which became negligible in the liquid-like state and increased back as the surface coverage decreased further. The absence of hysteresis for the liquid-like state is consistent with the previous observations. The reason of the hysteresis at low coverage was suspected to be the contact of bare silica patches from the two opposing oxidized surfaces. It was proposed that the unexpected hysteresis at the crystalline interfaces is due to the structural defects such as the coexistence of crystalline and amorphous regions which can lead to contact line pinning. Chaudhury and Owen also discussed the possible existence of a glassy amorphous region at the end of the chains which can cause interdigitation during contact. The authors noted that it is not possible to distinguish between these two mechanisms. They have concluded that the hysteresis is very sensitive to the molecular processes occurring within the few-angstrom region of the surfaces. Similarly, Chaudhury [28] observed that the adhesion behavior of an ether functional monolayer has much higher hysteresis compared to that of a methyl functional monolayer both in the pseudo-crystalline state. Chaudhury and Whitesides [57] also found an adhesion hysteresis on the surface of fluoroalkyl siloxane monolayers contrary to the negligible hysteresis on the alkyl siloxane surfaces. Interdigitation was speculated to be the reason based on previous contact angle measurements. According to Timmons and Zisman [62], small liquid molecules can penetrate into the porous fluorocarbon films depending on their sizes and cause contact angle hysteresis. Chaudhury and 52

75 Whitesides observed that liquid PDMS (M.W. of 5000 g/mol) exhibits higher contact angle hysteresis on fluorocarbon monolayers than on hydrocarbon monolayers. In a more recent study, Maeda and coworkers [63] studied the selfadhesion of PS which exhibited hysteresis when the surfaces were exposed to a UV/ozone treatment. This procedure is claimed to create free chain ends that can interpenetrate across the interface at a local level. Amouroux and Léger [64] studied the same effect in a controlled way with PDMS whose surface is tailored with dangling chains of different amounts. Adhesion hysteresis was observed at all interfaces which increased with the amount of dangling chains. The bridging of the interface by these chains was believed to be the cause of the hysteresis as depicted in Figure Figure 2.17: The depiction of the interdigitation of the dangling chains at the interface between two PDMS elastomer. (From ref [64], p.1401.) 53

76 The adhesion behavior between hydrolyzed PDMS surfaces was investigated by Perutz and coworkers [65]. The PDMS surfaces were exposed to a HCl solution to create silanol groups. This treatment introduced significant hysteresis whose degree increased with increases in hydrolysis time. The JKR and contact angle measurements on these hydrolyzed PDMS surfaces indicated that in air, the surface reconstructs to expose the methyl groups of the PDMS chain and bury the silanol groups. The buried silanol groups diffuse to the interface during the contact with another PDMS surface. This surface restructuring was further confirmed by chemically masking the silanol groups through reaction with hexamethyldisilazane. The adhesion hysteresis was observed to decrease dramatically. Shanahan and Michel [64] studied the adhesion behavior between polyisoprene and glass surfaces at different crosslink density of the rubber. This interface exhibited adhesion hysteresis that depends strongly on the crosslink density. The authors proposed three possible explanations; 1. The higher crosslinked systems are more elastic and reach equilibrium much slower exhibiting larger hysteresis, 2. Based on reptation model by de Gennes, the rubber chains are extracted from the bulk during the separation of two surfaces causing energy dissipation which is proportional to the crosslink density, 3. Based on the theory of Lake and Thomas, the chains go trough internal movement, disentanglement, stretching and relaxation during separation as shown in Figure 2.18 leading to energy dissipation which is proportional to the molecular weight. Chaudhury [66] commented that the W a values obtained from 54

77 the JKR measurements indicates van der Waals interactions and hydrogen bonding between polyisoprene and glass. Since these are much weaker than the cohesive interactions within the rubber, interfacial failure is expected in this system [66]. The adhesion hysteresis was found to be independent of the separation rate and thus energy dissipation due to viscoelastic relaxation was precluded as a possible cause of adhesion hysteresis. Figure 2.18: Analogy of the adhesion behavior between polyisoprene and glass with that of magnetic spaghetti and electromagnet. A) before contact while current is off, B) contact through attraction when current is switched on, C) separation where disentanglement and orientation take place while current is still on. As can be seen from this short review, the contact mechanics techniques can be used effectively to study the adhesion process at the solid/solid contact quantitatively in a wide range of applications. However, the molecular-level understanding of this interfacial phenomena cannot be achieved with this approach. It requires the direct measurement of the interfacial structure during contact. 55

78 2.2 Polymer Friction In Section 2.1 for polymer adhesion, the focus has been on interacting interfaces formed by two surfaces in contact where lateral motions are forbidden. If a relative motion is involved at this interface, it becomes the subject of the science and technology of friction. Friction is the force that resists the relative motion of two objects in contact. This force is tangential to the interface between these two bodies in the opposite direction to the motion. Friction is actually a part of a multi-disciplinary science and technology called tribology which also includes the study of wear and lubrication. Even though the subjects covered by tribology have been of an interest and a challenge to mankind long ago, it was officially mentioned for the first time in a report by the Department of Education and Science in The basic reason behind this emergence is most probably the increasing concern for energy conservation, reliability and efficiency of machinery, and limited resources. In addition, science and technology have progressed considerably over the years making it possible to study complex processes. In return, the size of the machines decreased down to nanometer scale which created the need to understand tribology at the molecular-level History of Friction The first practical application of friction is believed to be the invention of fire by using frictional heating which dates back to prehistoric times. In the case of fire which is 56

79 still crucial in our modern life, the existence of friction is used as an advantage. However, friction is usually undesirable and many efforts were spent to eliminate it. Around 3500 BC, history records the use of wheels to minimize the work required to transport goods. During the Renaissance period, the study of friction progressed considerably due to the scientific works by Leonardo da Vinci. He introduced for the first time the concept of the coefficient of friction which is the ratio of the friction force to the normal force that presses two bodies together, µ = F/N. Since the time is 200 years before Isaac Newton explained force, Leonardo never referred to a friction force but his observations in his notes are in accord with the statements of the first laws of friction that are named after the French engineer Guillaume Amontons in the seventeenth-century. Amontons presented his findings to the French Academy in 1699 which became the two basic laws of friction [67], 1. The force of friction is directly proportional to the applied load. 2. The coefficient of friction is independent of the apparent area of contact. The test specimens in Amontons studies were copper, iron, lead, and wood in various combinations (Figure 2.19). All the surfaces were coated with pork fat because that is how machine parts were used at the time. This is called boundary lubrication in today s modern studies. Like Leonardo, Amontons concluded that the test materials exhibited a constant coefficient of friction of 1/3 which is slightly different from that of 1/4 in Leonardo s observations. Amontons believed that the frictional resistance was due to surface irregularities. He argued that a force is re- 57

80 quired to lift the asperities of one surface over the asperities of the other to initiate sliding. Amontons studies were quickly confirmed and introduced into mechanics by the end of the century. However, his 1/3 rule was known to deviate with variations in materials, surface quality, and the type of lubricant. It was John Theophilus Desaguliers who tried to explain the deviation by cohesive forces. He proposed that cohesion (adhesion) might contribute significantly to sliding friction [68,69]. Since the idea of interlocking asperities was so popular at the time, his idea went into silence for about 200 years. Figure 2.19: Amontons original sketches of his friction experiments. (From ref [67].) 58

81 Another remarkable study on friction was presented to the Academy of Science by Leonhard Euler in 1748 [70, 71]. He suggested that the surface asperities pointed by Amontons have a triangular shape with a slope of α as shown in Figure If friction is the force required to lift one surface over the asperities of the other, then µ = tanα where the symbol µ is introduced by Euler as the coefficient of friction. It is not necessary for all the slopes to be equal as long as none exceed α. Euler also made a clear distinction between static and kinetic friction by analyzing the sliding motion down an inclined plane (Figure 2.20). He stated that the gain in kinetic energy when a block of weight P reaches point M is equal to the loss in potential energy and the energy dissipated by the frictional resistance. Until a limiting slope of the plane, the block is stationary at a static equilibrium. If the angle is increased by the smallest amount to disturb the equilibrium, the block starts to move down quickly. Euler concluded that the kinetic friction must be smaller than the static friction. More than a century later, Charles Augustine Coulomb published a detailed memoir on friction [72]. Like Amontons, he considered mechanical interlocking as the cause of friction but also mentioned the role of adhesion. The idea of adhesive forces was first introduced by Desaguliers but he was the one who developed a general expression for friction that included adhesion, F = A + P µ (2.45) 59

82 Figure 2.20: Euler s studies of friction. (From ref [70,71].) A) Surface roughness represented by triangular shapes inclined at angle α, B) Analysis of kinetic friction. where the first term is the adhesive effects and the second term is the deformation action. He announced that the contribution from adhesive forces is very small and can be neglected because in his observations friction was independent of the size of the surfaces. Coulomb also discussed the relationship between kinetic and static friction. He only confirmed what was observed by Euler but he conducted more detailed experiments and tried to explain the difference between the two. Coulomb thought that a tangential force at an interface causes the asperities of both surfaces, which are penetrated into each others void, to fold over. Sliding takes place after a certain amount of deformation. Therefore, frictional force depends on the nature of these asperities and load but not the size of the contact area. Once sliding is started, asperities fold over even more which decreases the slope and causes the kinetic friction to be lower than the static friction. This view explained why the difference between the two frictions is large for wood whose surface is covered with elastic fibres but very 60

83 small for metals whose asperities cannot fold over. His explanations won him credits for a third law of friction, 3. Kinetic friction is independent of the sliding velocity. Around the same time with Coulomb, a professor at Cambridge, Samuel Vince, was independently working on friction. He reported in 1785 that kinetic friction is independent of the sliding speed but not entirely independent of the apparent contact area. Thus µ s = µ k + adhesion, where s and k stand for static and kinetic, respectively [73]. Vince emphasized that if the surfaces are prepared with similar roughness, the smallest surface gives the least friction for a given weight. He claimed that previous studies that determined friction from the force necessary to start the motion were totally false because of the contribution of adhesion. He most probably believed that motion destroys adhesion. A generation after Coulomb and Vince, John Leslie reported his doubts about the role of adhesion in friction [74]. Leslie accepted adhesion to be perpendicular to the surface and to not affect the friction force whose direction is parallel. Therefore, he rejected the idea of using inclined planes to measure friction Adhesion Theory of Friction Starting from Leonardo and Amontons many findings on friction have been reported, some contradictory and all incomplete. However, they have laid down the foundations of the modern scientific studies. More progress in the study of friction depends on detailed characterization and molecular level understanding of surfaces and interfaces. 61

84 Such a development in science started in the 1920 s with a better understanding of surface chemistry trough Langmuir s work [1 5]. This led to the resurrection of the adhesion aspect of friction that was first proposed by Desaguliers in Since the mechanical interlocking approach was never able to explain friction in total, the adhesion hypothesis was the best alternative. In 1929, Tomlinson elaborated on the molecular adhesion approach and suggested that the normal load and the friction force are linearly related to the number of interacting atoms [75] but his attempts did not produce any quantitative result. Bowden and Tabor took the credit for developing the adhesion theory of friction. They recognized that two surfaces make contact only at points of asperities [76]. Under very high stresses these points are subject to local plastic deformations. If the real area of contact is A, the hardness of the softer material is H, and the shear strength of the bond is S, then the average normal pressure, P, and friction force, F, can simply be expressed by, P = AH (2.46) F = AS (2.47) µ = F P = S H (2.48) These expressions were not able explain many experimental results because the theory was built on the adhesion element of friction neglecting details about the deformation and even interactions. However, it was an important progress to include the mechanical properties of the materials in the equations. Bowden and Tabor 62

85 showed that plastic flow occurs at the asperities even for small static loads. Strang and Lewis claimed that the energy spent on the asperity deformation is only 10 % of the total energy of sliding. Bowden and Hughes further strengthen the adhesion theory when they measured very high µ values under a vacuum on surfaces cleaned by an abrasive cloth and heat [77]. µ was observed to decrease considerably with the introduction of oxygen to the environment due to the formation of an oxide layer on the metal surface which behaves like a lubricant. All these new findings initiated the emergence of new models on the plastic deformation of asperities supporting the adhesion theory of friction [78,79]. However, even the most improved adhesion theory had significant oversimplifications. First of all a general adhesion theory uses the shear strength of the interface in the calculations but this term has not been possible to measure independently. It miscalculates the friction force in elastic materials by about a factor of 10. The theory completely ignores the contribution of surface roughness which actually affects friction over a wide range of surface roughness as shown in Figure At very smooth surfaces the friction is high due to a large real area of contact, whereas at very rough surfaces the friction is high due to interlocking. The friction is at its minimum and almost independent of roughness in the intermediate range. Besides, plowing and electrical interactions are two other factors that contribute to the friction force. The former takes place when a surface with sharp asperities of slope θ slides over a softer surface. These asperities dig into the soft material producing grooves. The plowing term has 63

86 been considered by the adhesion theory and added to the adhesion term as tanθ since it creates additional resistance to sliding. tanθ may be large for very rough surfaces such as sandpaper causing the plowing contribution to be large [80]. However, tanθ usually has a value around 0.05 and the plowing term is negligible. The electrical interactions are effective when an electrical double layer exists at the interface. Sliding requires the separation of opposite charges and thus causes an increase in the friction force [81]. There is no term in the adhesion theory to count for the electrical interactions but it is believed to have an extremely small contribution. Figure 2.21: The roughness effect on friction. There has been other criticism of the adhesion theory of which some have validity and some lost their point as a consequence of modern studies. Despite all 64

87 these objections, the theory has proved to be useful in practice. The science of friction is convinced that there is adhesion at every interface between any two surfaces. A complete theory cannot be developed unless the contribution of adhesion is resolved Friction of Polymers In the early studies of friction the emphasis has been on plastically deformed metals. Polymers differ greatly from metals and their deformation during sliding is elastic or viscoelastic rather than plastic. Therefore, it is not surprising that polymers do not generally obey Amontons laws beyond a crude approximation. This was discovered by Ariano in 1929 for the friction of rubber which was observed to increase with sliding speed and was then confirmed by Derieux in Roth and coworkers, in 1942, published the first systematic study of the friction of commercial rubber on steel presenting the same monotonic increase of friction force with velocity. They have also observed a stick-slip sliding behavior beyond a certain velocity. In the same study, Roth and coworkers observed the sliding coefficient of friction to decrease with load which was investigated systematically four years later by Thirion who proposed an empirical relationship. A typical variation of frictional force with applied load is shown in Figure 2.22 for polytetrafluoroethylene [82]. The relationship can be represented as, 65

88 Figure 2.22: The frictional force and coefficient of friction as a function of load for polytetrafluoroethylene. (From ref [49], p.105.) F = kp n (2.49) µ = F P = kp n 1 (2.50) where k is a constant and (n-1) is between -0.2 and -0.3 for many polymers at static friction [78]. The value of (n-1) is given in Table 2.1 for various polymers. µ in Figure 2.22 is decreasing with an increase in the normal load. Considering eq 2.48, µ = SA/P, one possibility for the unexpected decrease is that the real contact area is not proportional to the normal load. This is the case if the deformation is plastic. Another explanation for the decrease can be elastic deformation which was brought into attention by Schallamach in 1952 [83]. He explained the unique frictional 66

89 Table 2.1: The value of (n-1) for various polymers. Polymer (n-1) Polyvinylidene chloride Polytetrafluoroethylene Polymethyl methacrylate Nylon Polyethylene terephthalate Polyethylene (branched) behavior of polymers by assuming an elastic deformation of spherical surface asperities under pressure where the frictional force is proportional to the true area of contact. Bowden and Tabor have already shown in 1950 that due to the irregularities of the surfaces, the true area of contact is smaller than the apparent area [84]. As an example, the coefficient of friction for poly(methyl methacrylate) as a function of load is given in Figure 2.23 [85]. For the surfaces in (b) and (c), at low loads the true area of contact is proportional to the applied load and µ is independent of load as in Amontons laws. At higher loads, the asperities are flattened and the true area of contact is equal to the apparent area of contact i.e. single point contact. The consequence for elastic deformation is, 67

90 Figure 2.23: The coefficient of friction as a function of load for polymethyl methacrylate where the surfaces are (From ref [49], p.110), A) smooth, B) abraded, C) turned. 68

91 A P 2/3 (2.51) F P 2/3 (2.52) µ = kp 1/3 (2.53) These relationships were based on a Hertzian contact since the JKR theory which accounts for the surface forces was not developed yet. They are still valid except for low modulus materials. The exponent in eq 2.53 may be represented with 2/m for viscoelastic deformation as proposed by Pascoe and Tabor in 1956 where 2 < m < 3 because m = 2 at plastic contact and m = 3 at elastic contact. A viscoelastic behavior is more appropriate for polymers whose value of µ will then take the form, µ = kp (2 m)/m (2.54) Here the exponent is same as the exponent (n-1) of eq The transition for surfaces in (b) and (c) indicates the load where surface asperities are elastically flattened to give single point contact. The absence of a transition point in (a) of Figure 2.23 is due to the smoothness of the surface which provides single point contact even at low loads. Schallamach, in his study of the load dependency of the frictional force, has experimented with rubbers of different modulus; hard, medium, and soft [83]. As 69

92 seen in Figure 2.24, the frictional force increases with modulus for all systems but at low loads the behavior of hard rubber departs from the theoretical predictions. Schallamach avoided the modulus dependency but tried to explain the behavior of the hard rubber with the contact area dependency. Since contact is achieved by the asperities, at low loads only the tallest asperities are in touch and the true area of contact is smaller than the ideal case. The smaller asperities come gradually into contact as the load is increased and the true area of contact eventually reaches the ideal case. According to Schallamach, this should be most pronounced with the hard rubber. Figure 2.24: Coefficient of friction as a function of load. Full lines are the theoretical predictions. The dotted line is experimental points for hard rubber. (From ref [83].) 70

93 In the same year, Schallamach investigated the effects of velocity and temperature on rubber friction [86]. He observed that at a constant temperature frictional force increases with sliding velocity and at a constant velocity it decreases with an increase in temperature. Schallamach concluded that such a behavior follows Eyring s theory of reaction rates. Therefore sliding of an interface is solely an adhesion mechanism where formation and breakage of molecular bonds take place in separate, thermally activated events. This sliding process is governed by an activation energy that he found to have a value of 30kcal/mole. Greenwood and Tabor argued that some part of the energy must be dissipated for the deformation of the elastomeric material [87]. The idea of a hysteresis contribution besides the adhesion factor initiated other scientists such as Flom and Bueche, Norman, and Sabey to investigate the subject [87 90]. However, Grosh is known to perform the most systematic study among all [91]. He tested the friction of various rubbers with different viscoelastic properties for temperature, velocity and roughness effects. Friction increased nonlinearly with velocity and decreased with increasing temperature. This velocity and temperature dependence was transformed into a master curve shown in Figure 2.25 by using the superposition principle of Williams, Landel, and Ferry [92]. Grosch s results showed that both adhesion and deformation contributes to friction (Figure 2.26). The friction curves from smooth surfaces, wavy glass (dash) and polished stainless steel (dots), exhibit a symmetrical peak. When the smooth surface is dusted with magnesia powder to prevent contact, the friction remains almost 71

94 Figure 2.25: Master curve for the friction data of acrylonitrile-butadiene rubber sliding over a hard surface. (From ref [91], p.25.) constant (not shown) indicating that friction on smooth surfaces is due to interfacial adhesion. This adhesion component correlates well with the relaxation spectrum of the rubber and thus the relaxations at the interface during sliding are related to the segmental relaxation of the polymer chain. The ratio of the velocity at the maximum friction to the frequency at the maximum viscoelastic loss is 60 A. This length scale represents the distance of the molecular jumps during sliding. On the other hand, the friction curves from rough surfaces, silicon carbide (solid line), exhibit an asymmetric peak at higher velocities than the peak that is due to the adhesion component. When the rough surface is dusted with magnesia powder (dash dot), the adhesion peak disappears indicating that the high velocity peak is related to the deformation losses. This deformation component of friction due to surface roughness 72

95 correlates well with the loss factor. Here the length scale is the spacing between the surface asperities. Grosch mentioned the possibility of frictional heating at high velocity but Schallamach showed that a single master curve can still be obtained by taking the true surface temperature into account [93]. A very interesting finding in Grosch s study is the frictional behavior at low velocities. In this region, considering viscoelasticity, friction is expected to fall to very small values while it actually becomes almost independent of velocity and temperature. Figure 2.26: Master curves for the friction data of acrylonitrile-butadiene rubber on various surfaces; dash, wavy glass; dots, polished stainless steel; solid line, clean silicon carbide; dash dot, dusted silicon carbide. Find out how to make the symbols in latex. (From ref [91], p.29.) 73

96 Based on the new arguments by Grosch, Schallamach refined his theory to correct for the insufficient explanations regarding the monotonic dependence of dynamic friction on velocity [93]. However, he maintained his view that friction is caused purely by molecular adhesion on smooth surfaces and tried to prove it by reproducing the experimental results of Grosch with his own theory. He proposed a general equation for friction that involves the number and average life of bonds as well as the average time between the breakage and reformation of a bond, F(u) = N 0kT λ ατ kt ϕ u( ατ kt ) (2.55) for a given value of u = e W/kT. Here N 0 is the number of sites that are available for bonding, λ is the length of molecular dimension, α = λmv where M is the force constant, τ is the average time between the breaking of a bond at a given site on one of the sliding surfaces and the reformation of a bond at the same site, and the function ϕ u stands for ( t/τ) 2 /(I + t/τ) where t is the average life of the bonds. The shape of the theoretical curves obtained from eq 2.55 are in qualitative agreement with those of the experimental curves in Grosch s study. Schallamach explains the shape with the opposing effects of two terms; the mean force at a bond, f, and the number of bonds, Σ. Figure 2.27 depicts the behavior of these two terms [ f( f) and Σ] as a function of velocity (log V) on the left and the outcome of their contribution to shear stress on the right. f has the form f = MV t and increases with velocity because t decreases at a slower rate with increasing velocity compared to the rate 74

97 of increase of the product MV. f increases only up to a value controlled by the interactions between the polymer chain and the countersurface. On the other hand, Σ decreases continuously with increasing velocity. The product of these two terms defines the response of friction to the variation in velocity. This theoretical response fails to represent the real behavior at high and low velocity regimes by approaching zero instead of reaching a constant finite value. At high velocities, rubber may no longer be elastic but behave like an ordinary solid which cannot be represented by the theory. At low velocities, there may be a dynamic equilibrium between the formation and breakage of bonds at a given site. According to Schallamach, this steady adhesion is possible if the stress on the bond is below a certain value. Figure 2.27: On the left, a representative plot of area density, Σ, of contact points and the force per adsorption point, f( f) as a function of velocity is shown. On the right, the product of these two quantities which is the shear stress is depicted. (From ref [14], p

98 After Schallamach, some other models were developed to explain the experimentally observed friction behavior of elastomers on rigid smooth surfaces. The drastic discrepancy between the findings of these studies and the experimental results led Chernyak and Leonov [94] to propose a molecular mechanism for the adhesive friction process based on Schallamach s ideas. In their model, adhesive friction is due to the elongation of the polymer chains that are attached to the countersurface or wall. These chains detach from their contact points when a thermal excitation takes place or an external force is applied to the chain ends. Every detached chain first relaxes dissipating energy and then attaches back to the wall. In the case of externally applied force, the reattachment occurs after a certain distance is traveled by the chain. This overall interaction process is represented by a stationary stochastic model. The mean lifetime of the contact is given by, < t b >= τ 0 [1 exp( t b τ 0 )] (2.56) where τ 0 is the mean time for which a polymer chain stays in contact and t b is the time when the stretching on the chain becomes sufficiently enough to break the attachment. For very small velocities, < t > b t b where t b τ 0 and the bond breakage is governed by a thermal mechanism. This is identical to the condition where there is no external force applied to the attached polymer chains. These chains at some point in time detach from the wall due to thermal excitations. After the relaxation process is complete they reattach to the wall. As a result, the mean 76

99 number of bonded chains is constant throughout the process. This is perhaps in parallel with Schallamach s steady adhesion explanation for low velocities. Savkoor as well as Ludema and Tabor are among those who believes that friction can never be purely adhesive even on very smooth surfaces [95, 96]. Savkoor suggested that the surface is made up of molecular size asperities that are in adhesive contact at the interface. When a tangential force is applied, the contact patches store elastic energy. Once the applied force overcomes the energy barrier of the work of adhesion which is approximately equal to the van der Waals potential, the shear crack at the interface propagates. As a result, the contact is broken until a new contact is made by undeformed patches. Therefore, the reason behind friction is adhesion but it proceeds with the deformation of the surface patches that are in contact. Savkoor also emphasized how the constant friction observed at very low and high velocities has not yet been explained by the existing molecular models. These models are controversial about the existence of a static coefficient of friction for elastomers. It has been denied theoretically but has been observed experimentally. However, the experiments are complicated due to its velocity dependence. Savkoor claimed that the velocity independent friction at extremely low speeds, when extrapolated, is equal to the static friction that he predicted theoretically. Therefore, at low velocities the static coefficient and the dynamic coefficient of friction must be equal. Another interesting aspect regarding the friction of elastomers has been discovered by Schallamach in 1971 [97]. For excessively compliant materials, sliding 77

100 does not proceed smoothly. The surface in front of the contact buckles due to surface instabilities across the area of contact which induces detachment waves (Figure 2.28). These waves, often called Schallamach waves, propagate across the area of contact. During the propagation, the surface first peels and then sticks again. Maugis and Barquins explained this behavior by applying the fracture mechanics concept to the adhesion of elastomers [98]. Every wave has two crack tips, one at the front and one at the rear, propagating in the same direction with the same velocity. The front crack is in the peeling mode and the rear crack is in the re-adhering mode [99]. Most energy is spent for peeling where the junction is vertical as in the fracture mechanics geometry. Figure 2.28: Real time images showing the propagation of Schallamach waves. (From ref [99], p.56.) The application of the continuum fracture mechanics to the science of adhesion (Section 2.1.4) and the recent discovery of the detachments waves propagating with a peeling process initiated Johnson to combine adhesion and friction under con- 78

101 tinuum mechanics [100]. He considered an elastic sphere in adhesive contact with a flat surface under a constant normal load, P. When a monotonically increasing tangential force, T, is applied to this contact, the interfacial fracture is of mixed mode type where mode I, mode II, and mode III are all effective. This assumption is valid if the adhesion and the slip zones are small compared to the overall contact area as in linear elastic fracture mechanics. Then the strain energy release rate is given by, G = 1 2E [K2 I + K2 II v K2 III ] (2.57) where E is the combined elastic modulus. Eq 2.57 can be simplified to, G = 1 2E [K2 I + 2 v 2 2v K2 II] (2.58) where K I and K II are given by, K I = P 2a πa K II = T 2b cosϑ (2.59) πb where a and b are the contact radii given by the JKR and Hertz theories, respectively, and ϑ is the angle between the radius vector at the contact point and the direction of T. In Johnson s model, the interaction of adhesion with friction is governed by surface forces at the periphery of the contact where both normal and tangential displacements take place. Therefore, during sliding the separation between two surfaces 79

102 increases compared to a static contact. Then, adhesion is related to the surface forces while friction is the propagation of dislocations throughout the whole contact area. Its comparison with some studies such as those by Savkoor and Briggs [101] and Barquins et. al. [102] showed good agreement. However, the model is not consistent with some other studies of hysteretic systems. As stated by Johnson, much remains to be done to establish the underlying physical processes. For this purpose, the nature of the interface and its response to normal and tangential forces needs to be investigated directly Recent Studies on the relationship between Adhesion and Friction of Polymer/Polymer Interfaces It is known from centuries that friction is related to adhesion; however, the exact relationship between adhesion and friction is still not understood [9 12]. The understanding of friction is important in areas such as energy conservation, controlling road traction of tires, nanotribology, and design of prosthetic devices. It is intuitive that the higher the adhesion energy between two surfaces, the higher the frictional forces [103]. However, in some cases adhesion has a dissipative component (adhesion hysteresis) which has a significant influence on friction [8, 13]. Early experiments of Levin and Zisman using a stainless steel ball as well as Briscoe and Evans using surface forces apparatus (SFA) showed that the interfacial friction is higher for fluorocarbon surfaces than it is for hydrocarbon surfaces even though the fluorocarbon surfaces have lower adhesion energy [104,105]. This was confirmed by DePalma and Tillman 80

103 who suggested that hydrocarbon surfaces are better lubricants than fluorocarbon surfaces [106]. Later, Overney et al. imaged a mixed monolayer of fluorocarbon and hydrocarbon surface using a friction force microscope (FFM) and proposed that the reason behind the difference in the frictional properties is the difference in the rigidity of the two surfaces [107]. This is consistent with Brown s study where friction stress on a rigid polystyrene (PS) surface was higher than that of a surface covered with mobile poly(dimethyl siloxane) (PDMS) chains [15]. The friction behavior of self-assembled monolayers (SAM) of hydrocarbon and fluorocarbon was also studied by Chaudhury and Owen using a PDMS elastomer as the counter surface [8]. The fluorocarbon surfaces exhibited adhesion hysteresis as seen in Figure 2.29 proving evidence that a strong relationship exists between these two types of energy dissipative processes: adhesion hysteresis and friction. Chaudhury and Owens attributed the higher friction to partial interdigitation of the chains across the interface increasing the dissipation of energy during sliding. In a later review, Chaudhury mentioned that the reason behind the higher friction of fluorocarbon surfaces apart from the difference in adhesion hysteresis, may be the higher rigidity of the CF 3 groups compared to more mobile CH 3 groups [66]. The interdigitation of molecules at the interface has been suggested as a cause of higher adhesion hysteresis and higher friction for many different systems. Israelachvili et al. studied the friction behavior of various hydrocarbon Langmuir- Blodgett (LB) monolayers on mica using SFA [108]. The friction forces of these 81

104 Figure 2.29: Adhesion hysteresis between PDMS and self-assembled monolayers (SAM). The open and closed circles represent the data taken during approach and withdraw of the PDMS elastomeric lens, respectively. The solid lines are predictions of the JKR theory. The inset shows a schematic of the adhesion apparatus and the well-packed SAM monolayers. A) Fluoroalkylsiloxane monolayer with adhesion energies of 32.2 (±1.4) and 62.7 (±6.1) ergs/cm 2 from approach and withdraw, respectively and B) Alkylsiloxane monolayer with adhesion energies of 38.4 (±1.3) and 45.6 (±3.7) ergs/cm 2 from approach and withdraw, respectively. From ref [8], p

105 monolayers did not correlate well with the adhesion energies but had a good correlation with the adhesion hysteresis similar to the findings of Chaudhury and Owen. The friction was high for the monolayers in the glassy amorphous state while it was low for monolayers in the crystalline or liquid-like state. According to the authors, the amorphous monolayers interdigitate at the interface and dissipate energy during their relaxation exhibiting adhesion hysteresis (Figure 2.30 B). On the other hand, the crystalline monolayers penetrate only a little amount (Figure 2.30 A) whereas the liquid-like monolayers penetrate but relax easily without any energy dissipation (Figure 2.30 C). This correlation between adhesion hysteresis and friction is expressed as S = W/δ where S is the friction stress, W is the adhesion hysteresis and δ is the length of the interdigitation. Here sliding is pictured as the nucleation and propagation of Schallamach waves at the molecular scale. However, the same equation predicted unrealistic δ values when one of the surfaces is a rubber indicating that it requires a modification to account for the elasticity contribution [8]. Israelachvili et al, in a later study using SFA, showed a similar correlation between adhesion hysteresis and friction on polymer surfaces resulting again from interpenetration [63]. The penetration was controlled with chain scission of poly(styrene) (PS) surfaces by UV radiation. This process creates free chain ends with restricted subsurface chain motion due to the attachment of their ends at the crosslinking sites (Figure 2.30 A). After the UV treatment, adhesion hysteresis and friction increased significantly which was attributed to the penetration of these chain ends deep into the counter surface 83

106 (Figure 2.30 B, C, and D). The authors noted the possibility of introducing oxygencontaining groups on the surface during the UV radiation. These groups may cause a polarity contribution to adhesion and friction. However, they claimed this effect to be minor because their separate measurements on polar poly(vinylbenzyl chloride) (PVBC) surfaces showed only small differences in adhesion hysteresis and friction compared to that of nonpolar PS surfaces. Brown used crosslinked elastomers to obtain measurable true contact areas as an alternative to the mica contact in SFA because the presence of mica can impose adsorption and constraint effects on the mobility of the interface molecules [15]. He studied the shear stress of PDMS on PS surface that is covered with a very thin layer of end-attached chains of mobile PDMS. The shear stress values suggested two different situations depending on the thickness of the tethered PDMS layer as shown in Figure When the PDMS layer is thick (above 1.2nm), the PDMS chains do not penetrate deep into the PDMS network and PS surface remains covered with PDMS. Therefore, the sliding occurs between the PDMS network and the tethered PDMS chains (Figure 2.31 A). When the PDMS layer is only 1.2nm, the PDMS chains penetrate deep into the network and sliding occurs between the PDMS network and PS surface (Figure 2.31 B). Here, sliding requires pulling the chains out of the network which increases the friction over that on the bare PS surface. For the latter situation, the shear stress is observed to be higher due to the chain interdigitation. 84

107 Figure 2.30: Schematic of the three phase states of the monolayer and their behavior at the interface during adhesion and friction. A) Crystalline monolayers exhibit little interpenetration across the interface and thus only little energy is dissipated. B) Amorphous monolayers penetrate significantly during adhesion and friction. Each energy dissipation occurs over a characteristic molecular length δ laterally and l normally with a relaxation time τ. C) Liquid-like monolayers also penetrate significantly but the entanglement and disentanglement times are fast and the system is always close to equilibrium. The energy dissipation is low. (From ref [61], p ) 85

108 Figure 2.31: Sketch of the two different situations at the contact interface between PDMS network and PS surface covered with a very thin layer of end-attached mobile PDMS chains. A) The layer thickness of the PDMS chains (shown by the bold lines) is relatively thick. The contact occurs between the PDMS network and PDMS chains with little interpenetration. B) The thickness of the PDMS layer is only 1.2nm and the chains penetrate deep into the network. (From ref [15], p.1412.) 86

109 The effect of grafted chains on the PDMS friction was also studied by Bureau and Léger [109]. Different from Brown s study, they used bimodal brushes made up of densely packed PDMS grafted short chains and long connectors. The long connectors were introduced to invoke the penetration into the PDMS network at the interface. The shear stress on the bimodal brushes increased with the grafting density in parallel with the increase in adhesion energy with the density. These findings are in good agreement with a similar study by Casoli et al. [110,111]. However, they are different from that of Brown s study due to the difference in the systems. The two studies are still not in contradiction because both point to a friction enhancement by chain penetration/pullout. Van der Vegte et al. examined adhesion and friction properties of self-assembled monolayers using scanning force microscopy (SFM). Both the SFM tip and the substrate were covered with unsymmetrical monolayer films as depicted in Figure 2.32 A. The length of one alkyl chain was increased in steps from 10 to 18 while keeping the other alkyl chain constant at 10 carbon atoms. The adhesion and friction forces increased with the increasing chain length or increasing difference between the two chain lengths (Figure 2.32 B and C). This trend was attributed to chain interdigitation at the molecular level. Overney et al. observed that the kinetic coefficient of friction increases as the length of the alkyl chain decreases [107]. This was also demonstrated by a number of other groups using SFM [ ]. The molecular chain length determines the 87

110 Figure 2.32: A) Schematic of the SFM probe and substrate used in the adhesion and friction measurements. Both surfaces were coated with an unsymmetrical dialkyl sulfide. B) Average adhesion forces for the given combinations. The lines are guide to eye. C) Friction forces of a 10/18-coated probe on given combinations. The lines are linear least-square fits. (From ref [112], p.3250, 3251, and 3253.) 88

111 structural order within the monolayers as it was reported by Camillone et al. [118]. They observed that a decrease in chain length decreases the packing density and thereby increases disorder and chain tilt. Two main hypothesis were proclaimed to explain the correlation between friction and order. Salmeron et al. argued that the number and type of deformation modes such as kinks, bending, distortions and gauche defects increases in disordered monolayers which leads to increased energy dissipation and higher friction [ ]. Examples of such deformations are shown in Figure Perry et al. suggested that the enhanced friction is due to the higher number of atomic contacts per unit area between the disordered (liquid-like) monolayers and AFM probe as a result of enhanced penetration or orientation of the chains [116, 117]. This is based on the fact that the C-C bond length (1.54Å) is much shorter than the intermolecular distance between the terminal methyl groups (4.99 Å) of well-packed SAMs. Thus, the van der Waals interactions between a probe and hydrocarbon backbone of loosely packed SAMs were believed to be greater than those between a probe and terminal methyl groups of well-packed SAMs. However, Perry et al. mentioned the possibility of other contributions such as conformational defects and dislocation mechanisms. In order to clarify the correlation between order and friction, a molecular dynamics simulation was applied to the friction between a tip and self-assembled monolayers [123]. The behavior of a tightly packed pure monolayer composed of 14 carbon atom chains was compared to that of a mixed monolayer composed of 12 and 16 carbon atoms in equal amounts. Pure monolay- 89

112 ers exhibited lower friction than mixed monolayers. The study concluded that the mechanical energy is retained efficiently by the pure monolayers when the monolayer is resisting sliding while the increased mobility of the protruding chain ends at the mixed monolayer surfaces causes energy dissipation and thus is the reason of higher friction. Figure 2.33: Schematics of some representative deformations at the molecular-level during contact and friction. (From ref [122], p.70.) Although there is mounting evidence for a strong correlation between adhesion, adhesion hysteresis, and friction, there still are some striking anomalies. Vorvolakos and Chaudhury reported much higher shear stress for PDMS elastomer sliding on PS surfaces in comparison to a well-packed hydrocarbon monolayer (SAM) [14]. This was unexpected because the adhesion energies of the PDMS/SAM and PDMS/PS interfaces are only slightly different. In addition, the adhesion behavior of both interfaces were found to be nonhysteretic. This behavior contradicts with the observations of fluorocarbon surfaces where the higher friction was explained by 90

113 the increase in adhesion hysteresis [8]. Roughness was also ruled out since the two surfaces were smooth down to the nanometer level (0.2nm for the monolayer and 0.5nm for PS). Vorvolakos and Chaudhury have pointed that the higher shear stress for PDMS/PS could be due to interdigitation of PS chains in the PDMS elastomer. If we consider the fact that an adhesion hysteresis of 1mJ/m 2 cannot be resolved experimentally and assume a local penetration of 0.5nm (the size of a phenyl group), we obtain an upper limit of 2MPa variation in the friction force. This could explain the difference in the shear stress between PDMS/SAM and PDMS/PS interfaces. However, it is not clear why we should expect interpenetration across the interface between a glassy polymer and a crosslinked rubber. Brown has also shown that the friction forces of PDMS sliding on a glassy PS surface are much higher than that on a PDMS surface [15]. Brown interpreted his finding as the rigid PS slowing down the molecular mobility of the PDMS segments at the interface leading to higher energy dissipation during sliding. Both these arguments, mobility and interpenetration, involve the changes in the structure of the interfacial molecules upon contact or during sliding. It is promising to see the amount and quality of the modern adhesion and friction studies using tools such as surfaces forces apparatus and scanning probe microscopy that can probe small scales with high resolution as well as powerful and progressive computer simulations. However, it is clear from the studies mentioned above that friction, adhesion and their relationships is quite complex. The molecular 91

114 Figure 2.34: Shear stress of PDMS sliding on PS (black box) and SAM (gray box). The solid line is the prediction of the absolute reaction rates theory. (From ref [14], p.6786.) origin of adhesion and friction is yet to be understood. This requires the direct measurement of the interfacial structure of molecules at the static (adhesion/adhesion hysteresis) and dynamic (friction) contact. Such experiments will also be an accurate source to improve the already existing adhesion and friction theories such as that of Schallamach, Chernyak and Leonov, as well as Johnson Probing Surfaces and Interfaces with IR-Visible Sum Frequency Generation Spectroscopy Sum-frequency generation (SFG) is a second-order nonlinear optical phenomenon that is accessible with high intensity, monochromatic and coherent light sources called 92

115 lasers. When two laser beams of frequencies ω 1 and ω 2 are overlapped in a material, in space and time, a beam at the sum frequency of the two input beams, ω 3 = ω 1 +ω 2, is produced. According to the principles, SFG can only be generated when the inversion symmetry is broken in a material. This is the case for most of the surfaces and interfaces of polymers within a few atomic layers but not the bulk. The frequencies of the input laser beams are important because they define the frequency of the SFG beam which has to be detectable by an existing detector and the type of information obtained from this process. The common input beam choices are a visible light at a fixed wavelength and an infrared light which can be scanned over a certain wavelength region. When the infrared wavelength corresponds to a vibrational frequency of a molecule at the probed region, the SFG beam is enhanced. Therefore, by recording the SFG intensity over the scanned region, an SFG spectrum is obtained that contains peaks at the vibrational modes of the surface or interface molecules. This SFG spectrum indicates the presence of the chemical species at surfaces and interfaces. In addition, if the symmetry of the vibrational modes that appear in the spectrum is known, the spatial orientation of the chemical species can be determined. Besides, a spectrum can be taken without any material damage if the laser intensities are kept low enough. All these advantages led to the development of a new spectroscopic technique known as IR-visible sum frequency generation spectroscopy. SFG spectroscopy is a breakthrough for surface science because it makes it possible to study surfaces and interfaces in situ without the contribution of bulk 93

116 and obtain a molecular-level picture. This means there is a tool that we can use to understand the molecular origins of some important phenomena such as adhesion and friction which are the particular subjects of this work. Unfortunately, this is not going to be straight forward and we will have to develop a unique approach. But first, to better understand the process, relevant history and principals are presented in the remainder of this section History Einstein s idea in 1916 of spontaneous and stimulated emission led in 1955 to the invention of MASER (microwave amplification by stimulated emission of radiation). The maser design later on extended to the optical region with the idea of a LASER (light amplification by stimulated emission of radiation) in Soon this idea was used to invent the first optically pumped pulsed (ruby) laser seen in Figure 2.35 by Maiman which started the modern era of optical science and technology [124]. Lasers found important applications in almost all scientific disciplines due to their stunning characteristics. Laser beams compared to ordinary light sources are monochromatic, coherent, directional and have high intensity. Lasers also created many exciting new fields of which nonlinear optics is one of the first. The existence of nonlinearity had been known long before by Maxwell s electromagnetic wave studies in the second half of 19 th century, but in optics high intensity light sources were needed to observe the nonlinear optical effects. Using a pulsed ruby laser, Franken et. al. in 1961 demonstrated the second harmonic 94

117 Figure 2.35: Photograph of the first laser built by Maiman in A ruby rod is surrounded by a helical flash lamp. generation (SHG) for the first time (Figure 2.36) [125]. A quartz crystal placed in the path of a pulsed ruby laser beam with nm wavelength transmitted a beam at nm wavelength. The same group, a year later, also discovered the sum frequency generation (SFG) where a light at the sum of the two input beam frequencies is transmitted. Subsequently, the theoretical foundation of nonlinear optics was laid down for bulks by Armstrong et. al. and for surfaces by Bleombergen and Pershan in 1962 [126, 127]. These studies showed how light waves interact in a medium and explained some important criteria and properties. As an example, in SFG the two coherent laser beams that are overlapped in a medium, in time and space, induces oscillating dipoles on molecules of that medium at their sum frequency. These dipoles 95

118 Figure 2.36: Schematic of the experimental setup used by Franken et. al. to observe the second harmonic generation from a quartz crystal. are coherent as their sources are. Their radiation is directional because it is mostly efficient at the direction where the momentum is conserved. This is known as phasematching direction. By symmetry, SFG and all the other three-wave mixing (two input and one output) processes can not be generated where centro-symmetry exists. The bulk of many amorphous and crystalline materials has centro-symmetry and therefore no high order optical harmonic generation. However, at the surface of these materials the symmetry is broken in the first few atomic layers. Therefore, SFG from such materials is only generated at the surface without any bulk contribution. With all these characteristics, SHG and SFG phenomena initiated ideas of application in new surface-specific techniques. However, this required many improvements in the laser technology for 2-3 decades. One of them is the optical parametric 96

119 generation (OPA) which is the inverse process of SFG. Through OPA the laser sources became broadly tunable from THz to the deep uv region. In 1987, Zhu et. al. used this technology to obtain tunable infrared laser sources together with a fixed visible light source and pioneered a new spectroscopy technique called IR-visible sum frequency generation spectroscopy (SFG from this point onward) [128]. They had obtained the first SFG spectrum of coumarin 504 on a quartz substrate. The application of SHG as a spectroscopy technique took place before SFG in 1974 but SFG is preferred in probing surfaces and interfaces. The reason is the ability of SFG to provide vibrational spectrum of the surface and interface molecules by the tunable infrared light source. Since 1987, SFG found application in many areas related to surfaces and interfaces. Some important studies are liquid and polymer surfaces, chemical reactions at surfaces in various environments, surface microscopy and buried interfaces (e.g., solid solid, liquid liquid and solid liquid). Among these the study of buried interfaces gained great attention because of its importance in some practical areas such as biomedicine, polymer blends, adhesion, friction, and lubrication. The first polymer polymer interface study with SFG was published only recently in 2002 and there is yet much to be done [129]. 97

120 Fundamental Principles A simplified version of the SFG theory is presented here to understand the fundamental principles that are necessary to interpret the results of this work. The details have already been established in several publications [ ]. When an oscillating intense electric field is applied to a molecule, it induces a dipole whose strength is proportional to the applied electric field. Considering a condensed medium, the relation between the dipole per unit volume, known as polarization, and electric field is, P = χ (1) E + χ (2) : EE + χ (3).EEE +... (2.60) where E is the electric field vector and χ (1) χ (2) and χ (3) are the first-, second-, and third-order susceptibility tensors of the medium, respectively. The contribution from higher order susceptibilities are usually negligible. It is assumed that the medium has zero or negligible static polarizability and the intermolecular interactions have no effect on the induced dipole moment. Then the linear and second order nonlinear susceptibilities are expressed in terms of the number of molecules per unit volume, N, molecular polarizability, α, averaged over all orientations, and second order hyperpolarizability, β, χ (1) = N α χ (2) = N β (2.61) 98

121 The applied electric field is oscillating with time, t, at a certain frequency, ω and E can be replaced by Ecosωt. The corresponding polarization will also be oscillating and thus will emit light at an intensity, I, that is proportional to the square of the polarizability, I = [χ (1) Ecosωt + χ (2) : EEcos 2 ωt + χ (3).EEEcos 3 ωt + ] 2 (2.62) Concentrating only on the second term and using cos 2 ωt = 1 + cos2ωt, I = [χ (2) : EE(1 + cos2ωt)] 2 (2.63) The first term represents the static polarization while the second represents the oscillating polarization at a frequency of 2ω which emits light at 2ω. This process is known as SHG (Second Harmonic Generation). When the applied electric field consists of two separate electric fields, E 1 and E 2 with frequencies ω 1 and ω 2 the intensity in eq 2.63 becomes, I = (χ (2) : E 1 E 2 (cosω 1 tcosω 2 t)) 2 (2.64) In this case, the emitted light has components at the sum (ω 1 + ω 2 ) and difference (ω 1 ω 2 ) frequencies along with the fundamental frequencies, ω 1 and ω 2. The electromagnetic radiation at ω 1 +ω 2 is the SFG signal. χ (2) in the SFG expression is a third rank tensor and changes sign after an inversion symmetry operation, χ (2) = 99

122 χ (2). However, a media with inversion symmetry (centrosymmetry) is invariant under this operation which indicates that χ (2) must be zero and under the electricdipole approximation SFG signal is forbidden. This is a significant characteristic of SFG because the bulk of most polymers whether amorphous or semicrystalline is centrosymmetric. The centrosymmetry breaks down at the surface and interface and the SFG signal can be generated. As a result, SFG is surface/interface specific. In infrared-visible SFG, one of the two incident electric fields has a frequency, ω vis in the visible region and the other a frequency, ω IR in the infrared region. When these two light beams are incident from medium 1 into medium 2 and are overlapped in time at interface, an SFG signal of frequency ω vis +ω IR is generated in the reflected and transmitted directions (Figure 2.37). The angles of incidents for the visible and IR beams from the surface normal (z-axis) are θ i (ω vis ) and θ i (ω IR ) the angles of reflection are θ r (ω vis ) and θ r (ω IR ) and, the angles of transmission are θ t (ω vis ) and θ t (ω IR ) respectively. The reflected and transmitted SFG beams propagate with an angle φ r in medium 1 and φ t in medium 2, respectively. The refractive indices of the medias depend on the frequencies and are indicated in parenthesis. Some basic relationships are, θ i (ω vis ) = θ r (ω vis ), θ i (ω IR ) = θ i (ω IR ) (2.65) ω vis n 1 (ω vis )sinθ r (ω vis ) + ω IR n 1 (ω IR )sinθ r (ω IR ) = ω SFG n 1 (ω SFG )sinφ r (2.66) ω vis n 2 (ω vis )sinθ t (ω vis ) + ω IR n 2 (ω IR )sinθ t (ω IR ) = ω SFG n 2 (ω SFG )sinφ t (2.67) 100

123 The polarization of the beams in Figure 2.37 determines which components of χ (2) are active. A light beam is either S polarized, E s, if in the plane of the interface or P polarized,e p if in the plane of incidence. Then the overall polarization of SFG is a combination of the SFG beam, visible beam, and IR beam polarizations in this order. The expressions for SSP and PPP polarization combinations are given in eq 2.60 where χ (2) is replaced with an effective susceptibility, χ (2) eff. It can also be shown as χ (2) ijk because it is a sum of the nonvanishing χ(2) components. Here i, j, k = x, y, z and x, y, and z are the laboratory coordinates. For an azimuthal isotropy at the interface the seven nonvanishing components of χ (2) ijk and the relation among them are χ (2) xxz = χ (2) yyz, χ (2) xzx = χ (2) yzy, χ (2) zxx = χ (2) zyy, and χ (2) zzz. χ (2) eff,ssp = L yy(ω SFG )L yy (ω vis )L zz (ω IR )sinϕ ωir χ yyz (2.68) χ (2) eff,ppp = L xx(ω SFG )L xx (ω vis )L zz (ω IR )cosϕ ωsfg cosϕ ωvis sinϕ ωir χ xxy (2.69) L xx (ω SFG )L zz (ω vis )L xx (ω IR )cosϕ ωsfg sinϕ ωvis cosϕ ωir χ xzx (2.70) +L zz (ω SFG )L xx (ω vis )L xx (ω IR )sinϕ ωsfg cosϕ ωvis cosϕ ωir χ zxx (2.71) +L zz (ω SFG )L zz (ω vis )L zz (ω IR )sinϕ ωsfg sinϕ ωvis χ zzz (2.72) The L values are the optical Fresnel coefficients that relate the magnitudes of the electric fields at the interface to those of the input electric fields. They basically depend on the optical properties of the media that form the interface and therefore have a frequency dependence. 101

124 z 01 y E 01 p 00 11ω vis x E s ω SFG ω IR θ iωvis θ ωir 01 φ i 01 i n n ω 01 IR ω 01 ω SFG vis Figure 2.37: The interface between two media that is probed by SFG. The subscripts i and r denotes incident and reflected directions. Here n 1 > n 2. Finally, the total SFG intensity reflected from a surface is given by, I(ω SFG ) = 8π 3 ω 2 sec 2 θ SFG c 3 n 1 (ω SFG )n 1 (ω vis )n 1 (ω IR ) χ (2) eff As seen, the intensity of the SFG signal is proportional to is the sum of two terms, 2 I(ω vis )I(ω IR ) (2.73) χ (2) ijk 2 where χ (2) ijk χ (2) ijk = χnr ijke iφ + Q q=1 A ijk,q ω IR ω q + iγ q (2.74) The first term is the nonresonant component and is wavelength independent. It may be originated from the bulk of a material or from the substrate that the material is coated on [135]. The second term is the resonant component which is the 102

125 sum of Q resonances of each chemical species at the surface or interface. When the frequency of the incident IR beam, ω IR, matches the frequency of the q th molecular vibration of a specific chemical group, energy is absorbed from the IR beam. In eq 2.74, A ijk,q ω q, and Γ q are the amplitude, frequency, and width of this molecular vibration, respectively. Φ is the relative phase of the nonresonant term with respect to the resonant term. It takes into account the destructive or constructive interference of the SFG signals generated from the nonresonant and resonant components. The important result from eq 2.74 is that chemical information of the surface or interface can be deduced from an SFG signal. This is provided by the molecular hyperpolarizability, β which has characteristic resonance peaks corresponding to vibrational modes of the molecules. The component of β for a vibrational mode q is given by, β q,lmn = α q,lm µ q,n ω IR ω q + iγ q (2.75) where l, m, n = a, b, c and a, b, and c are axes of the molecule fixed coordinate system. α q,lm is the Raman tensor and µ q,n is the infrared transition dipole moment vector. As a consequence, only Raman- and IR- active vibrational modes contribute to β and are SFG-active. The β q,lmn can be projected on the lab axis (xyz) from the molecular axis (abc) by using Euler transformation coefficients which are functions of Euler angles, ψ, θ, and φ (Figure 2.38). This θ is different than the beam angles in Figure 2.37 and 103

126 χ in ref [131] is replaced here with ψ to avoid confusion with the susceptibility tensor. The coordinate transformation is performed by first rotating the z-axis by φ, second the x-axis by θ, and then rotating the z-axis once again by ψ. The transformation makes it possible to express β lmn in the molecular reference frame with the β ijk in the laboratory frame. Due to the symmetry of the molecule, many components of the molecular hyperpolarizability tensor vanish which simplifies the calculations. Finally, the summation of the β ijk s for each molecule at the surface or interface gives the resonant component of 2.74, Q q=1 A ijk,q ω IR ω q + iγ q = allmolecules β ijk = N β ijk f(ψ, θ, φ)dψdθdφ (2.76) where f(ψ, θ, φ) is the probability distribution function of the molecular orientation. The Euler angle ψ is in the plane of the surface and angle φ describes the rotational degree of freedom as seen in Figure Generally the orientations of the SFG-active groups at the surface or interface are isotropically distributed in these angles causing ψ and φ to be zero. Therefore, eq 2.76 depends only on the averages of the polar angle θ which is the angle that the molecule makes with the surface normal (z-axis). This result is very important because by analyzing θ from the total SFG intensity reflected from a surface given in eq 2.73 trough its contribution in eq 2.76 it is possible to tell the degree of orientational order of molecules at the surface or interface with respect to the surface normal. The SFG intensity also 104

127 c z θ φ b y ψ x a Figure 2.38: The relationship between the molecular coordinate system (a,b,c) and the laboratory coordinate system (x,y,z) through the Euler angles (ψ, θ, φ). indicates the number of molecules, N, that contribute to the SFG signal since the orientation factor is multiplied with N in eq In an infrared-visible SFG experiment, the SFG signal intensity (eq 2.73) is measured as an output when the visible and IR input beams are overlapped in space and time on a surface or interface. The frequency of the visible beam, ω vis is fixed while that of the IR beam, ω IR is scanned over a certain range. Depending on the relationships between the macroscopic and microscopic hyperpolarizabilities and the vibrational resonant frequencies of the chemical species an SFG spectrum is obtained. Since the SFG intensity is enhanced at an SFG-active vibrational mode, the spectra is composed of peaks unless one peak destructively interferes with another due to opposite phases. A vibration may also appear as a dip for the same reason. This 105

128 SFG spectrum is fit to a simplified version of eq 2.73 to determine the resonant and non-resonant components of χ eff, I(ω SFG ) [χ NR ijke iφ + Q q=1 A ijk,q ω IR ω q + iγ q ] 2 (2.77) Here ω q provides the chemical information directly. To obtain the orientational information, the fitted value of A q has to be related to the true macroscopic hyperpolarizability tensor elements by using priory known fresnel coefficients. The macroscopic hyperpolarizability tensor is calculated through the molecular hyperpolarizability tensor for various molecular orientations in order to find the one that matches the experimentally determined macroscopic hyperpolarizability tensor. While β can be estimated it is difficult to obtain an accurate value of N. The intensity of a spectrum may be effected from the experimental variables such as the alignment of incidence beams on the sample, the beam quality, the alignment of the SFG beam into the detector, or the detector quality. It is safer to compare relative peak intensities belonging to two different vibrational modes of the same molecule within one spectrum. This eliminates N, avoids the Fresnel coefficients and provides tilt information. If it is crucial to measure N in order to know the complete structure of the surface or interface especially when different molecules are involved, the ratio of the peaks in the same SFG spectrum can be used as a reference spectrum of a well characterized surface or interface. 106

129 SFG Studies of Adhesion and Friction Observable interfacial phenomena such as adhesion and friction are governed by the structure and dynamics of the interfacial molecules at the interface. As revealed from the representative studies in Sections and 2.1.5, adhesion, friction and their relationship are complex issues that require the analysis of the interface in-situ at the molecular level. Only recently it has been possible to directly probe the molecular orientation and composition of molecules in the contact region by SFG which is an ideal tool to study buried interfaces [136]. The SFG signal is forbidden in the bulk, which is centrosymmetric for most of the polymers, but allowed at interfaces where the symmetry breaks down [137]. SFG has also been used to study a variety of polymer interfaces including polymer/liquid and polymer/solid interfaces [138] and finally it has been extended to study polymer/polymer interfaces [129]. The initial studies of contact interfaces using SFG Spectroscopy were focused on understanding the structure of well-characterized Langmiur-Blodgett and Self-Assembled monolayers under pressure from 10 MPa to 660 MPa [136, 139, 140]. The pressure was applied with non-deformable solid (quartz or bronze) lenses onto monolayer coated sapphire prisms. Berg and Klenerman as well as Du and coworkers observed significant spectral changes. An example is shown in Figure 2.39 for octadecanethiol compressed between a bronze ball and a sapphire prism. The resonant signals were observed to weaken during contact with increasing pressure, shift to lower frequencies and broaden asymmetrically (Figure 2.39b, c, and d). According 107

130 to the authors, these spectral changes which recovered once the pressure was released (Figure 2.39e) indicated a loss of molecular order by increases in chain end gauche defects and tilt angle. On the contrary, Fraenkel and coworkers claimed no major structural changes for densely packed fatty acids at the modest pressures of 60 MPa. Their spectra before, during, and after contact appeared qualitatively similar. The SFG intensity of the spectrum after contact was lower which was suggested to be caused by material transfer from the prism to the lens but not gauche defects. Figure 2.39: SFG spectra of octadecanethiol monolayers from; A) Surface, B) Contact under 320 MPa pressure, C) Contact under pressure increased to 660MPa, D) Contact under pressure decreased back to 320MPa, E) Surface after contact (From ref [140], p.5072.) 108

131 In a more recent study, Kweskin and coworkers used SFG to determine molecular restructuring of poly(n-butyl methacrylate) (PnBMA) and poly(methyl methacrylate) (PMMA) surfaces in contact with a smooth sapphire surface (deformed) [141]. Based on the spectral changes seen in Figure 2.40 for PnBMA, the ester butyl side chains tilted away from the surface normal at this deformed interface compared to the conformation at the surface. The structure at the deformed interface was found to be identical to that at the annealed PnBMA/sapphire interface. This was attributed to the melt-like behavior of PnBMA since its glass transition temperature (T g ) is below room temperature. Unlike PnBMA, the PMMA surface did not show any restructuring upon compression with sapphire (Figure 2.40). In addition, the annealed PMMA/sapphire interface is different from the PMMA surface or compressed PMMA/sapphire interface. Based on these observations, it was claimed that compression freezes PMMA in a metastable state due to its high T g. These studies demonstrate that the mechanical contact between two solid surfaces (buried interfaces) can be detected in-situ by SFG. However, it is important to understand how the structure of a buried interface is related to the macroscopic adhesion and friction properties of this interface. Kim and coworkers, Miyamae and Nozoye, as well as Loch and coworkers took advantage of SFG results in order to understand the effect of molecular orientation at an interface on adhesion. However, the polymer surfaces studied were either in contact with a liquid or analyzed after contact ex-situ. A polymer/polymer contact interface was probed using SFG 109

132 Figure 2.40: SFG spectra (SSP polarization) of PnBMA as well as PnPMA surface ( ) and deformed PnBMA as well as PnPMA interface with sapphire (bigcircle). (From ref [141], p ) Figure 2.41: SFG spectra (SSP polarization) of PVNODC/PS interface before and during mechanical contact (top) as well as annealed PVNODC/PS bilayer film (bottom). (From ref [142], p.375.) 110

133 in-situ to examine the origins of adhesion hysteresis by Harp and Dhinojwala [142]. The PVNODC/PS contact interface was compared to the PVNODC/PS annealed interface which exhibits significant restructuring. The adhesion of the annealed interface exceeded that of the contact interface. Harp and coworkers observed negligible changes in the PVNODC interface during mechanical contact and thus connected the relatively strong adhesion to the structural differences in PVNODC at the annealed interface. Probing the structure independently during a mechanical contact has been possible by generating large uniform contact areas with a deformable elastomer [143]. This provides a unique opportunity for direct spectroscopic measurements that can be coupled with adhesion and friction experiments. 2.3 Nature s Way of Adhesion and Friction In nature, the survival of organisms ranging from single cells to insects relies on their interactions with their environments. Animals that can attach to vertical walls or even hang on a ceiling and then can easily detach are abundant in nature. Among them are insects such as flies, beetles and spiders [ ]. These organisms can effectively control their contact, adhesion and friction with any surface. The heaviest living creatures on earth that has the clinging ability are lizards such as the gecko. The skin of a lizard is made up of a relatively stiff material called keratin. It has an elastic modulus of 1GPa (1000 times higher than that of a commercial tire rubber) [147]. 111

134 However, strong adhesion is only possible through large contact areas and minimum energy dissipation which requires at least one of the solids to be elastically very soft (Section 2.1). It has been found that keratin is actually covered with an extremely soft elastic layer which provides the lizard the ability to strongly adhere to surfaces of various roughnesses. Besides, this layer is built in a hierarchical manner on different length scales and has a fibrillar structure as shown in Figure Similar to a lizard, the feet of all the other animals with clinging ability have variations of fibrillar surfaces (Figure 2.43) [ ]. In lizards, being the heaviest, these structures are thinner at every scale. Therefore, the elastic energy loss during the deformation of the fibers to increase the contact area is less and the adhesion is stronger. A comparison among animals shows that the fibrillar structure becomes finer and denser as the weight of the animal increases. The idea of mimicking the fibrillar structures using synthetic materials initiated extensive amount of studies. The interest is mainly towards designing surfaces with controlled adhesion mechanisms that can make contact with a variety of surfaces. It is also desirable to have systems that can be reused thousands of times, have self-cleaning ability, and do not require a counterpart with a specific structure. It has been shown that the fibrillar adhesion is enhanced by capillary forces in the presence of secretions [150] but for dry attachments systems such as those in spiders and geckos the adhesion relies on van der Waals interactions [148]. Based on the existent knowledge of such surface forces, some pioneering experiments have designed 112

135 Figure 2.42: Pictures and schematic of a lizard and its foot structure. A) A lizard attached to a nearly vertical surface. B) The schematic of the fibrillar structure on the foot of a lizard. The skin is covered by fibers called setae that are 100µm in length. Each setae (st) is made up of 1000 thinner fibers that are 10µm in length. These fibers end with a plate called spatulae (sp). C) Scanning electron microscopy (SEM) micrograph of st. D) Enlarged SEM micrograph of the box in (C) showing sp and terminal branches (tb). E) Transmission electron microscopy (TEM) micrograph of two tb with sp. (From ref [147], p.1401.) Figure 2.43: The fibrillar structure of the attachment pads of various animals. The terminal element which is circled becomes finer as the body mass of the animal increases. (From ref [151], p.1401.) 113

136 polymer surfaces with fiber array systems [ ]. The findings are towards enhancement of adhesion but no synthetic system has yet succeeded nature s precision. The gecko s foot-hairs have the proper aspect ratio, thickness, stiffness, and structure to adhere to any type and shape of surface with enough density to provide high adhesion forces. It was experienced that if the synthetic fibers are too long and thin, or the fiber material is too soft, the fibers collapse and form bundles or condense into layers due to the inter-fiber interactions. In addition, it has not possible to achieve the hierarchical structure found in nature by using the known techniques we have in this modern time. 114

137 CHAPTER III EXPERIMENTAL 3.1 Sample Preparation The glassware used in this study to prepare polymer or monolayer solutions as well as to contain the prepared samples is first cleaned from macroscopic residues with a soap-water solution or an appropriate solvent. After air dried on the rack or in the oven at 140 it was immersed in a base bath for 4-12h. The base bath is prepared by dissolving approximately g of solid KOH pellets in 4 L of isopropyl alcohol. After taken out of the base bath, the glassware was first rinsed with distilled water and then soaked in a distilled-water bath for at least 12h. Then it was rinsed with distilled water once more and blow-dried with flowing N 2 (Praxair grade 2). This is to prevent residues from water or dirt from air condensing on the glass surface. It was further dried in the oven at 140 for at least 10min. Just before being used, it was removed from the oven, cooled in a clean place and then plasma treated with air for 5min. The plasma treatment was done with a Harrick PDC-32G scientific plasma cleaner which has three intensity settings; low (40 W), medium (60 W), and high (100 W). Unless specified the plasma cleaner was operated at high. The vacuum 115

138 inside the plasma chamber was stabilized around 75 torr with a Varian 3201 direct drive rotary vane pump. For argon (Praxair grade 2) and oxygen (Praxair grade 2) plasma treatments, the chamber was purged with the gas and evacuated two times in succession. A slight flow of gas was provided with a needle valve during the operation. For air plasma, vacuum was applied to the chamber right away. At the end of the plasma treatment, the chamber was purged with the gas to disengage the vacuum and take the items out which were used within 10-15min. The substrates used in this study were sapphire prisms, sapphire plates and glass plates. The prisms were custom cut and 60 equilateral. The sapphire plates were circular with various diameters and thicknesses. The glass plates were cut from common glass slides with a diamond cutter. All the substrates were sonicated in an appropriate solvent for at least 1h with heat on. The solvent was a HPLC grade toluene in most of the cases while acetone or THF were also used in some instances. The sonicator was of a Branson model 610. If the substrates had a polymer coating from the previous experiments, they were gently wiped with Kim-Wipe after the sonication and sonicated one more time with a fresh solvent. If the sapphire substrates were previously modified with a monolayer, they were plasma treated with air for 5 min before sonication to sputter the monolayer out. The glass plates that were modified with a monolayer were discarded. After the sonication, all the substrates were taken out of the solvent with clean tweezers (1 min air-plasma) holding from 116

139 the edges and rinsed thoroughly with distilled-water. Then the rest of the glassware cleaning procedure was followed starting from N 2 blow drying. The monolayers were prepared from octadecyltrichlorosilane (OTS) and (tridecafluoro- 1,1,2,2-tetrahydrooctyl)trichlorosilane (FC) which were purchased from Gelest, Inc. They were kept in a fridge inside a sealed bottle to prevent moisture absorption and were equilibrated to room temperature before usage. The monolayers of OTS were prepared by immersing the cleaned substrates in a water saturated solution of hexadecane, carbon tetrachloride, chloroform, and OTS in individual glass beakers. These beakers were immediately sonicated for 20min at around 20. At the end, the substrates were taken out of the solution and immersed first in carbon tetrachloride and then in cyclohexane for at least 30s in order to stop the reaction and rinse out the unreacted OTS from the surface, respectfully. Once they were taken out of cyclohexane, they were blow-dried with N 2 and further dried in an oven at 130 for 4h under vacuum below 75torr. The monolayers of FC were prepared by immersing the cleaned substrates in a 2mM solution of FC and n-hexanes in individual glass beakers or in a big crystallization dish for at least 2h. At the end, the substrates were taken out of the solution and immersed in chloroform to rinse out the unreacted FC from the surface. Then, they were blow-dried with N 2 and further dried in an oven at 120 for 2-3h under vacuum below 75torr. The polymer films were prepared by spin coating a solution on the cleaned substrates with a Specialty Coating Systems model P6700 spin coater at specified 117

140 speeds. The spin coater was kept and operated inside a hood at all times. The substrates were held in place with a slight vacuum. The plates were placed on an appropriate size O-ring onto the stage while the prisms were placed in a screw tightened prism holder which was used in the place of the stage. The polymer solution was then dropped on the substrate with a pipette starting from the center of the surface and covering the whole area. The spin coater was immediately engaged and operated for 1min until it stopped automatically. Poly(vinyl n-octadecyl carbamate-co-vinyl acetate) (PVNODC) was a gift from 3M Corp. and was used as received. It has M w = 70kg/mol, PDI = 3.0, and the mole fraction of n-octadecyl carbamate units per chain 90 %. Thin films ( nm) were prepared by spin coating a warm 2wt% solution of PVNODC in toluene at 2000rpm. The solution was prepared one day ahead and kept sealed tightly until usage. After coating, the films were annealed at for 3-4h under vacuum. Poly(styrene) (PS) was purchased from Polymer Source, Inc., and was used as received. It has M w = 108kg/mol and PDI = Thin films ( nm) were prepared from a 5wt% solution of PS in toluene by spin coating at 2000rpm. The solution was prepared one day ahead and kept sealed tightly until usage. After coating, the films were annealed at for 3-4h under vacuum. Poly(n-butyl methacrylate) (PnBMA), poly(n-propyl methacrylate) (PnPMA), and poly(methyl methacrylate) (PMMA) were purchased from Scientific Polymer Products, Inc., and were used as received. PnBMA has M w = 319,200g/mol, M n = 118

141 123,900g/mol, PnPMA has M w 250,000g/mol, and PMMA has M w = 467,000kg/mol, M n = 440,500kg/mol. Thin films ( nm) were prepared by spin coating a warm 2 wt% solution of PnBMA, PnPMA, and PMMA in toluene at 2000 rpm. After coating, the films were annealed at 35, 45, and 110, respectfully, for 3-4h under vacuum. Poly(dimethyl siloxane) (PDMS) lenses were either prepared from an elastomeric kit (PDMS syl ) or were homemade using an addition cure reaction (PDMS hm ). The Sylgard 184 elastomeric kit was purchased from Dow Corning. It has two components, one is a vinyl-terminated silicone base polymer and the other is a methyl hydrosiloxane crosslinking agent and a platinum catalyst. The two were mixed according to the manufacturer s instructions in a 10 to 1 ratio. For PDMS hm, a desired amount of divinyl-terminated PDMS (6000 g/mol) was mixed with 10 % poly(methylhydrosiloxane-dimethylsiloxane) copolymer (1950 g/mol) which is a crosslinker. A platinum-cyclovinylmethyl complex (3-3.5% Pt) was added as a catalyst (10 µl for each gram of mixture). All materials were purchased from Gelest, Inc., and used as received. Both of the PDMS mixtures were stirred thoroughly for at least 1min. Any air bubbles introduced were removed by resting the mixture in air. PDMS sheets were prepared by pouring the mixture into a sterilized PS petri dish. Small hemispherical PDMS lenses were prepared by placing small drops of the mixture with a syringe needle on fluorosilane treated glass slides. The low-energy surface is necessary to form sufficiently hemispherical drops. The sheets and the small lenses 119

142 were then cured at 60 for 4h. The small lenses can also be cured at 100 for 1h. Big hemispherical PDMS lenses were prepared by placing drops of the mixture with a syringe needle on the surface of a sterilized PS petri dish filled with distilled-water. The combination of the surface energies of PDMS, PS, and H 2 O provides the proper conditions to form the drops which otherwise will flatten due to the gravity. The big lenses were first cured at room temperature overnight and then at 60 for 4h in the presence of water. After the curing was completed, the water was poured out, the lenses were gently dried under a slight flow of N 2, and then dried completely at 60 overnight under vacuum. Some of the sheets and lenses had the sol fraction (unreacted precursor) extracted with toluene. These were placed in a beaker lined with a filter paper and swelled in an excess amount of toluene for two days. Then the solvent was changed every day for 4-5 days. At the end, the solvent was removed and the sheets and lenses were first dried overnight in air at room temperature and then further dried overnight under vacuum at 60. The extracted PDMS sheets and lenses are represented as PDMS exsyl and PDMS exhm. The low molecular weight poly(dimethyl siloxane) (PDMS liq ) was purchased from Alfa Aesar in liquid form and was used as received. This PDMS liq is trimethylsiloxy terminated, it has a molecular weight of w = 1250 g/mol and viscosity of 10 centistokes. 120

143 ( OTS O O Si O ) PDMS CH 3 ( Si O ) CH 3 PVNODC ( CH 2 CH) CH X ( 2 CH ) Y O O C O C O NH CH 3 PnBMA CH 3 ( CH 2 CH) C O O PS ( CH CH ) 2 PnPMA ( ) CH 3 CH 2 CH C O O CH 3 CH 3 CH 3 CH 3 Figure 3.1: Unit structures and representation of the materials used in this study. OTS is chemically bonded to an oxidized surface from the top oxygen atom. The monolayers are crosllinked to each other through the side oxygen atoms. For PVN- ODC, x = 0.9 and y =

144 3.2 IR-Visible Sum Frequency Generation (SFG) Apparatus and Measurements The SFG apparatus is based on a laser system that uses a visible pulse at 800nm overlapped with a tunable infrared pulse at 3-10µm both having a 1ps width and 1kHz repetition rate. The laser setup is shown in Figure 3.2 with its basic components that were all manufactured by SpectraPhysics. The Millenia is a solid-state green laser with a continuous output at 532nm and power of 5W which is directed into the Tsunami. The Tsunami is a Ti:Sapphire laser cavity with regenerative mode locking whose output is used to drive the Spitfire. Tsunami Ti Sapphire Laser Merlin Solid Sate Laser Millenia Spitfire PMT Spectrometer OPA IR Detector Red IR H C Delay Stage DM Sample P SFG Photon Counter Lock in Amplifier Figure 3.2: Schematic diagram of the SFG setup. Components are named as appears in the text. Symbols represents: H, half-wave plate; C, IR chopper; DM, dichroic mirror; and P, polarizer. 122

145 The Spitfire stretches the input pulse and amplifies it to a 800nm laser pulse by using a 250ns pulse from the Merlin. The amplified pulse is compressed back and sent into the OPA-800 with 1ps width. The OPA (optical parametric amplifier) uses a part of the input pulse to generate a broadband white light (seed) by focusing into a transparent solid material. The rest of the 800 nm input pulse (pump) is directed to a separate path where it is again divided and directed to a second and third path. The seed beam is later combined with the pump beam from the second path and passed through a beta barium borate (BBO) non-linear crystal. Here, the pump is broken into two separate beams, signal and idler, through a process called optical parametric generation. The wavelengths of these beams are controlled by the tilt angle of the BBO crystal. The idler beam that comes out of the crystal is reflected back from a diffraction grating. Then it combines with the pump beam from the third path and passes through the BBO crystal one more time to further generate signal and idler beams. These beams are directed to an AgGaS 2 crystal where difference frequency mixing (DFM) takes place to generate an IR pulse of 1ps and 17.4cm 1. The crystal is rotated to the optimal phase matching condition between the signal and idler beams. While the IR beam is generated, the remainder of the pump intensity is taken to a separate path for the visible beam output. The IR wavelength output from the OPA can be tuned by the rotation of the BBO crystal which tunes the wavelengths of the signal and idler beams. This 123

146 is followed by the rotation of the diffraction grating and DFM crystal for maximum output intensity. This process is done by an ESP-6000 motor system manufactured by Newport. A computer program controls the operation of the motor system which also records the output SFG data during the experiments. The motor positions are periodically calibrated by optimizing the output power of the OPA while the IR wavelength is calibrated at the beginning of every experiment day based on an IR absorption spectrum from a standard poly(styrene). The IR and visible beams are then taken out of the OPA from separate exits to be overlapped on a sample in space and time. The visible beam is passed through a half-wave plate in order to control its polarization. Then it is reflected through a series of mirrors and a delay stage. Since it takes a shorter path inside the OPA, its path length outside the OPA has to be adjusted to ensure the time overlap with the IR beam. After the delay, the visible beam is sent to the dichroic mirror. The IR beam first passes through a filter to remove the remnants of the signal and idler wavelengths. Then it is taken to a CaF 2 beam splitter where a small part of it is sent to a pyroelectric photodetector through a chopper. The rest of the IR beam is transmitted and then focused on the dichroic mirror by a lens where the IR beam is transmitted and the visible beam is reflected. The two beams are kept separate on this mirror to avoid SFG generation from its optical coating. They are spatially overlapped on the sample surface by tilting the dichroic mirror. This overlap, in time and space, produces an SFG beam which is reflected by two mirrors into the path of 124

147 the photomultiplier tube (PMT). In this path, it is focused by a lens, passed through optical notch filters to reduce the noise and a polarizer to control its polarization. The SFG beam is taken through a 0.5 meter triple grating Acton Research Spectrapro 500i spectrometer to the PMT which is attached to the exit of the spectrometer. The spectrometer is controlled with the same SFG program that controls the wavelength of the IR beam because the 1200 groove/mm holographic visible grating inside the spectrometer has to be synchronously tuned to direct the expected SFG wavelength to the PMT. The entrance and exit slits of the spectrometer can be adjusted from 2mm down to 50µm in order to change the resolution of the SFG spectra from broad wavenumber (fwhm 20cm 1 ) to narrow wavenumber (fwhm<5cm 1 ). In order to take a narrow wavenumber spectrum, the exact wavelength of the visible input beam is measured with the spectrometer and then the grating is corrected prior to the experiment. The SFG signals from the PMT (Hammatsu 928P) are detected by a Stanford Research Systems SR400 gated photon counter. At the same time, the signals from the IR photodetector are detected by a Stanford Research Systems SR850 DSP lock-in amplifier that is triggered by the chopper. These two outputs are recorded simultaneously by the computer program as the number of photon counts and the average IR intensity. Then the SFG intensity (number of photon counts) is normalized with the average IR intensity and plotted as a function of the IR wavenumber which is the SFG spectrum (Figure 3.4). The background noise from the environ- 125

148 Visible and IR SFG entry face φ PDMS Lens i Sapphire Prism φ r exit face sapphire polymer PDMS φ1 φ 2 z y x n 1 n 2 n 3 Applied Load (P) Figure 3.3: Schematic diagram of the TIR geometry used in SFG measurements. Shown here for a polymer film coated on sapphire prism that is in contact with a PDMS lens. The incident visible and IR beams are represented with one arrow that strikes the prism at the entry face with φ i and refracted with φ r. A small region that includes both the sapphire/polymer and PDMS/polymer interfaces is magnified where φ 1 and φ 2 are the critical angles, respectively, for the total internal reflection to take place. The mediums of refractive indices n i are as indicated. The x, y, and z Cartesian axes are the lab frame-of-references; the y-axis is perpendicular to the plane of the paper. 126

149 ment if any is determined by blocking the IR input beam from the OPA and recording the photon counts. These counts are subtracted from the overall number of photon counts prior to the normalization. The SFG spectrum can be further analyzed later on by fitting the data with a program written by Schwab which is described in detail elsewhere [156]. 20 SFG data fit SFG Intensity (a. u.) IR Wavenumber (cm -1 ) Figure 3.4: A typical SFG spectrum where the SFG intensity (number of photon counts) is normalized with the average IR intensity and plotted as a function of the IR wavenumber. The solid lines are fits to the data. This SFG spectrum was taken from an OTS surface. The detected resonances represents the C H stretching vibrations of the CH 3 groups present at the OTS surface. 127

150 Table 3.1: Symbolic representation of all the vibrational modes observed in the spectra taken for this study. The given assignments to resonances were determined from the SFG fits. Symbol Vibrational Mode Resonance (cm 1 ) r + CH 3 symmetric stretch r + Fr Fermi resonance between the symmetric-stretch fundamental and an overtone of a bending mode of CH r CH 3 asymmetric stretch r + α α-ch 3 symmetric stretch 2930 r α α-ch 3 asymmetric stretch 2990 d + CH 2 symmetric stretch d + Fr Fermi resonance between the symmetric-stretch fundamental and an overtone of a bending mode of CH d CH 2 asymmetric stretch r + PDMS CH 3 symmetric stretch of Si (CH 3 ) r PDMS CH 3 asymmetric stretch of Si (CH 3 ) ν 20b phenyl stretch ν 2 phenyl symmetric stretch ν 7b phenyl asymmetric stretch

151 3.2.1 SFG in the Total Internal Reflection (TIR) Geometry SFG has been used in TIR geometry in all the experiments presented in this work. This geometry is depicted in 3.3 for a polymer film spin coated on a sapphire prism and in contact with a PDMS lens. In the case of OTS monolayer, the polymer film depicted in the TIR geometry is absent and the SFG signal is generated at the PDMS/sapphire interface. The PDMS lens is attached to a stainless-steel cell (not shown) with a double-stick tape. The cell design allows the lens to be moved up and down to control the contact area with the counter surface. The incident visible beam with frequency ω vis and IR beam with frequency ω IR are nearly collinear to the solid arrow. The beams strike the prism with an incidence angle,φ i, and refracted at the entry face of the prism with φ r. Then, they overlap at the sapphire/polymer interface with little or no attenuation by sapphire. An SFG beam with frequency ω SFG is generated at this interface and depending on φ i it is emitted in the reflection direction reaching the exit face of the prism where it is refracted out. Here, φ i is selected so that the incident angle at the sapphire/polymer interface, φ 1 is close to the critical angle for the total internal reflection to take place. In the same way, φ i can be selected to attain the critical angle, φ 2 at the PDMS/polymer interface. The polymer surface (air/polymer interface) can also be probed in the absence of the PDMS lens if the critical angle is achieved. Proper choice of φ i allows selective probing of the interface in question. φ i 42 was used for the polymer and monolayer surfaces, φ i 12 was used for PDMS/polymer interfaces, 129

152 and φ i 8 was used for the sapphire/ots or polymer interfaces. These angles were chosen by first modeling the SFG intensity enhancement from these various interfaces as a function of φ i and then experimentally optimizing the φ i that corresponds to the maximum intensity. 3.3 JKR Apparatus and Measurements The adhesion experiments are based on a protocol developed by Johnson, Kendall and Roberts (JKR) which is explained in section in detail. In JKR experiments, the contact area between a compliant PDMS lens and a flat substrate is measured as a function of force during loading (approaching two surfaces) and unloading (separating two surfaces). An apparatus home-built by Harp [157] that is similar to the one described by Mangipudi et. al. [59] was used. The apparatus is depicted schematically in Figure 3.5. A PDMS lens was attached to a microscope slide with a double-stick tape. The slide was secured to a translation stage through a post which was held in place by a heavy optical post. The optical post was attached to a Newport optical table supported on compressed air to minimize vibration. The stage was moved down using a Newport AD-100 micrometer operated with a piezoelectric drive until contact is made with the sample surface. Images of the contact area were taken in order to measure the contact area by a Marshall Electronics black and white CCD camera. The objective is a standard 5X, 0.12 numerical aperture Mitutoyo microscope objective and was attached to lens 130

153 CCD Camera Microscope Lens Sample Mirror Fiber Lite Balance Optical Table Figure 3.5: Schematic diagram of the JKR apparatus home-built by Harp. tubes of various length to control the magnification. The camera was mounted on a Newport AD-100 translation stage through a post. The stage was held in place by another heavy optical post attached to the optical table. The analog output from the CCD camera was captured with a parallel port Dazzle video capture device and recorded by a computer for later analysis. The Dazzle program was set for highest quality black and white images at a resolution of pixels. A typical image of the contact spot is shown in Figure 3.6. The scale for every magnification or tube length was calibrated prior to data analysis. All the images were analyzed with National Institutes of Health (NIH) Image Software Program. For the analysis, the contact radius, a, was calculated either by using the total area of the contact spot which was obtained from the images assuming a circular area or by using an average diameter which was measured from vertical and horizontal line 131

154 100 µ m Figure 3.6: A typical contact spot image of the PDMS/OTS interface at 0.1g using a PDMS lens with radii of curvature 1mm. fits to the contact area. The two calculations were compared for the same image to ensure an accurate value of the radius. This analysis was repeated for every image that corresponds to a specific force. The force, P, was measured by a Sartorius B120S analytical balance which has a g readout and a 120g capacity. The readout from the balance was hand-recorded to a lab notebook. The radii of curvature, R, of each lens was determined prior to contact from a side image of the lens mounted on a glass slide. A representative side image is shown in Figure 3.7. The height, h, and base, 2r, of this hemisphere was measured by line fits from which R is calculated, R = r2 + h 2 2h (3.1) 132

155 h R 2r Figure 3.7: A typical side image of a PDMS lens. The height (h), diameter (2r), and radii of curvature (R) are shown. R can also be calculated directly from the area of the circle fitted to the hemisphere. The calculations from these two methods were in good agreement with each other at all times. All the JKR experiments were performed in an uncontrolled lab environment where the temperature and humidity were and 35-45%, respectively. The apparatus was kept in a Plexiglass cage in order to avoid draft and to provide stable temperature and humidity throughout the measurements. Typical measurements were executed by increasing the load in steps of 200 µn (0.02g) at 5min intervals to a maximum load of mn ( g) and then decreasing the load in a similar fashion until pull off. The load was controlled by a Newport AD-100 micrometer with piezoelectric drive. An image and a load value were recorded at each step. After the images are analyzed as described above, the contact radius (a) was plotted as a 133

156 1.6 a 3 (m 3 *10-12 ) Loading Data Unloading Data P (N*10-3 ) Figure 3.8: A typical JKR plot with contact radius, a, plotted as a function of load, P. The measurement shown here was performed on a PS surface using an extracted PDMS hm (PDMS exhm ) lens. function of load (P) from which a strain energy release rate, G, value was extracted (Figure 3.8). The final unloading data points at the lowest load exhibited abnormal growth in area. This is due to instabilities caused by the stiff post and microscope slide [158]. Therefore, those final data points were avoided during the fits. In addition, the pull off forces obtained from these measurements were also ignored. Figure 3.8 can be re-plotted in a linear form as a 1.5 /R versus P/a 1.5 shown in Figure 3.9 and can easily fit to the modified JKR equation [66], a 1.5 R = ( 1 K )( P a 1.5) + (6πGK)0.5 (3.2) 134

157 a 1.5 /R (m 0.5 ) Loading Data Unloading Data P/a 1.5 (N/m 1.5 ) Figure 3.9: The linear JKR plot of the data shown in Figure 3.8 measured from the PDMS exhm /PS interface G (mj/m 2 ) Loading Data Unloading Data a (m -4 ) Figure 3.10: Strain energy release rate, G, as a function of contact radius for the same measurement shown in Figure 3.8 between PDMS exhm and PS. 135

158 The slope of this fit gives K from 1/K and the intercept gives G from 6πG/K 1/2 using the predetermined K. Then, G can be plotted as a function of contact radius as seen in Figure 3.10 based on the equation, G = P a3 K R (3.3) 6πKa Friction Apparatus and Measurements The friction measurements were conducted using an apparatus home-built by Nanjundiah based on the design described by Barquins [99]. It has been originally designed to be used within the SFG setup with TIR geometry for in situ adhesion and friction measurements (Figure 3.11). A PDMS lens attached to a thick Aluminum (Al) plate with a double stick tape was pressed against the sample that is held in place tightly with screws at the front panel. Then, an increasing tangential force was imposed on the Al plate. The area of contact before and during sliding was imaged in reflection with the same imaging system as in the JKR measurements (Section 3.3). Both the normal and tangential forces were applied with New Focus 8351 motors (picometer actuator) attached to the back and side panel, respectively, controlled by a New Focus 8758 picometer driver with 30nm steps. The normal load cannot be recorded in this design due to the thick Al plate which does not deflect in the low load range used here. A thick plate was used to keep the distance between the plate and sample surface constant which will prevent variations in normal load and contact area. Therefore, 136

159 the normal load was estimated by comparing the contact area during friction with the contact area during the JKR measurements using similar conditions. On the other hand, the friction force was measured using a strain gauge (sensitivity of 3960 µv/g 3%) attached to the flat springs holding the Al plate. The spring constant was determined by measuring displacement as a function of weight (k 300mN/m). The force was measured with a Keithley multimeter and recorded in voltage as a function of time using a program written by Nanjundiah. Figure 3.11: Schematic diagram of the friction apparatus home-built by Nanjundiah for in situ adhesion and friction measurements using SFG in TIR geometry. The flat springs were calibrated by hanging known amounts of weight on the Al plate and recording the response in terms of voltage. The slope of the fit to the voltage versus weight plot was used to convert the tangential force from volts to 137

160 0.06 (MPa) t (sec) Figure 3.12: A typical friction plot with shear stress, σ, plotted as a function of time, t. The measurements shown here was performed on a PVNODC surface using a PDMS exhm lens. Newton. A baseline was recorded at the beginning of each measurement after the lens has been put in contact with the sample and before the sliding has been started. This baseline was subtracted from the measured force data prior to analysis. The images of the contact area before and during sliding were analyzed as described in Section 3.3. For most of the measurements, a slight ( 1 %) reduction in contact area occurred during sliding. The tangential force was divided by the contact area to obtain the shear stress which was plotted as a function of time as seen in Figure The shear stress values at the dynamic friction region were averaged. When the interfaces exhibited stick-slip dynamics similar to that reported 138

161 by Grosch [91], the values at the highest point (stick) were averaged. The friction measurements were performed for each lens/surface pair at various normal loads and velocities. The shear stresses were independent of the normal load and contact area, which is consistent with previous findings of Homola and coworkers [159] as well as Chaudhury and coworkers [8, 160]. This indicated that the actual and apparent contact areas change with load in a similar manner. The velocity range was from 0.5 to 15µm. The values of shear stress were independent of velocity in this range. 3.5 Scanning Probe Microscopy (SPM) Measurements SPM measurements were performed with tapping mode at a 0.5Hz scan rate in order to prevent deformations or irreversible displacements. Standard rectangular silicon cantilevers (MikroMasch) with typical radius of curvature < 10 nm and spring constant of 3.5 N/m (accuracy of 10 % according to manufacturer specifications) were used. The apparatus is a Digital Instruments Nanoscope IIIa multimode AFM from Dr.Cheng s laboratory in the Department of Polymer Science, The University of Akron. All measurements were done under ambient conditions. The images were processed by the Nanoscope Control software (Digital Instruments) version 5.12r3. Adhesive interactions were characterized with SPM from force-versus-distance (f-d) curves between the cantilever and the surface. The f-d curves were obtained by recording the SPM cantilever deflection caused by the vertical movement of the SPM tip (Figure First, the tip approaches the sample surface without any deflec- 139

162 tion in the trace (Figure 3.131, non-contact region). Then, the tip makes contact with the surface where it is pushed against the surface and is bent up (Figure 3.132, contact region). Finally, the tip is retracted and withdrawn from the surface (Figure 3.134). Here, the cantilever is bent down due to the interactions with the surface (Figure 3.135). The deflection reverts back to the original condition in the non-contact region once the tip reaches a distance at which the tip-sample contact becomes broken and the tip jumps out (Figure 3.136). Depending on the strength of the interactions (adhesion), the retract trace may go off the approach trace exhibiting hysteresis. The jump height from the bottom of the retrace line corresponds to the total adhesive force strength. The absolute scale of the measured adhesion force was obtained by first converting the f-d curve to the deflection of the cantilever in nanometers. Then, the force applied to the cantilever was calculated in nanonewtons using Hook s law and the spring constant of the cantilever. The spring constant given by the probe manufacturer was used without further calibration. 3.6 Contact Angle Measurements The static and dynamic contact angle of various liquids on polymer and OTS surfaces were measured based on the sessile-drop method. The liquids used were distilled water, hexadecane, diiodomethane, and ethylene glycol. The apparatus is a Ramé- Hart goniometer (model , ramé-hart, Inc.) from Dr. Brittain s laboratory in the Department of Polymer Science, The University of Akron. All contact angles 140

163 Figure 3.13: Cantilever deflection during the approach/retraction cycle and the corresponding deflection versus tip position as measured with SPM. 1) Tip approaches the surface (non-contact region). 2)Tip makes contact and bends up due to surface interactions (contact region). 3) Force is applied up to a desired amount. 4) The direction of the applied force is changed to retract the tip. 5) Cantilever bends down due to surface interactions. 6) Tip jumps out of contact once the applied force reaches the threshold depending on the strength of the interactions. (from the SPM manual.) 141

164 were measured in an environmental chamber by equilibrating the atmosphere of the chamber with the liquid in use. A small drop of about 5 µl was formed on the surface using a micropipette. Then the static contact angle was measured within a few seconds. For the dynamic contact angle, the sample was tilted to 35 after the static angle measurement. The angle at both sides of the three-phase contact line was recorded each time and the measurement was repeated at least two times on each surface using at least three different samples prepared from the same solution under the same conditions. The final value reported is the arithmetic mean of all these contact angles. Table 3.2: The contact angle values of distilled water on the polymers used in this study. Polymer Contact Angle OTS 112 ± 2.6 PVNODC 109 ± 0.8 PS 93 ± 0.6 PnBMA 84 ± 1.4 PnPMA 84 ± 0.6 PDMS 111 ± 0.8 FC 116 ±

165 3.7 Thickness Measurements Thickness measurements were performed with a Gaertner model L116C ellipsometer from Dr. Brittain s laboratory in the Department of Polymer Science, The University of Akron. A He-Ne laser of 632.8nm wavelength was used at a 70 fixed angle of incidence. For the thickness calculations, refractive indices of n = 1.47 for PVNODC, n = for PS, n = for PnBMA, and n = for PnPMA were used [161]. All polymer films were coated on silicon wafers whose oxide layer thicknesses were measured prior to coating with the same technique. The laser was shined on each film within the center region and a thickness value was obtained from three different places of the same surface. The measurement was repeated on at least three different samples prepared from the same polymer solution under the same conditions. The final value reported is the arithmetic mean of all these thickness values. 143

166 CHAPTER IV RESULTS AND DISCUSSION The first part of this section investigates the molecular structure at a contact interface and its macroscopic consequences on adhesion. Then the changes in the molecular structure of various contact interfaces are analyzed during sliding in order to understand the origins of their frictional behavior. In the third part, we report a structure based on multiwalled carbon nanotubes constructed on polymer surfaces with strong nanometer level adhesion that can serve as dry adhesives similar to or stronger than gecko foot-hairs. 4.1 Template-Induced Enhanced Ordering of Methyl Groups of Short PDMS Chains under Confinement The first condition of an adhesion or friction process is to bring two solid surfaces into contact. The macroscopic consequences of this solid/solid contact such as adhesion and friction are very sensitive to the structure at the interface. According to Bowden and Tabor [84], a molecular intervening can affect the coefficient of friction by an order of magnitude. This interfacial structure may be different from the structures of the two surfaces before contact. The surface molecules can rearrange to minimize the 144

167 interfacial energy or reorient under confinement. Understanding the molecular chemical structure at the contact interface requires interface sensitive techniques that can probe the molecular conformation, orientation and composition in situ. It has been demonstrated that sum frequency generation spectroscopy (SFG), a nonlinear optical technique, can be used to study buried polymer interfaces including polymer/air, polymer/solid and polymer/liquid interfaces [138]. SFG has been recently extended to probe the mechanical contact between two hard solids and two polymers [129,136]. In this work [143], we have used SFG to demonstrate the first direct measurement of a confined structure at the contact interface between two surfaces. This is of fundamental importance not only in the areas of adhesion, adhesion hysteresis, and tribology, but also in rheology, grain boundary phases of composite materials, and colloidal particles. Liquids confined between smooth mica surfaces at separations comparable to their molecular dimensions show remarkable properties such as oscillatory force profiles, extreme enhancement in viscosity and relaxation time constants, and stick-slip behavior that is reminiscent of solid-to-liquid transition [13, 162, 163]. It has been suggested that upon confinement the symmetric molecules align in discrete layers [162, 164]. In the case of rough surfaces, the oscillatory force profiles vanish which has been explained by absence of layering [39, 165]. These results can also be interpreted as local layering which is not correlated over large areas. However, no direct measurement of the structure of confined molecules has been reported. Here, we have investigated the confinement of short PDMS chains between two rough 145

168 surfaces, oxidized poly(dimethyl siloxane) (PDMS ox ) elastomer and self-assembled alkylsiloxane monolayer (octadecyltrichlorosilane (OTS)) on sapphire surfaces, using surface-sensitive SFG. In order to understand the role of surface energy on the confined structure, similar measurements are performed with a high surface energy sapphire substrate and a disordered low surface energy fluoroalkylsiloxane monolayer (FC). PDMS is a silicone elastomer widely used in various diverse areas such as highvoltage outdoor insulation, biomedical applications, adhesives, microcontact printing of polymers or proteins, and anti-fouling coatings. Its low weight, hydrophobicity, high electrical resistance, easy processing and low toxicity are attractive to many applications. The chemical structure of PDMS is a Si (CH 3 ) 2 backbone with two methyl (CH 3 ) groups attached to every silicon atom (Section 3.1). These CH 3 groups are exposed to air minimizing the surface energy and providing an 110 water contact angle. As described in Chapter 3, PDMS is typically used in adhesion experiments as hemispherical lenses in contact with flat surfaces to generate uniform areas. The size of the contact area can be controlled by the applied load and radius of curvature of the lens as discussed in Section for JKR theory. We have taken advantage of this geometry to probe the structure of confined fluids since large uniform contact areas are required. The PDMS lens can deform to create a uniform contact with a rough sapphire substrate modified with low energy OTS. OTS is a self-assembled monolayer with 18-carbon-long alkyl chains and is chemically bonded 146

169 to a sapphire substrate (Section 3.1). The alkyl chains of a saturated and annealed OTS surface extend perpendicular to the surface where the C 3 symmetry axis of their end methyl groups are tilted at an angle of with respect to the surface normal [131,166]. The chains together form a crystalline well-packed structure in predominantly all-trans conformation. Well-packed OTS chains are known to resist high pressures up to 300MPa [140] and thus are expected to have a stable structure during the experiments performed in this study. Similar to PDMS, the end CH 3 groups are exposed to air and thus the water contact angle on OTS surface is also 110. OTS type self-assembled monolayers are attractive for the studies of adhesion and friction. They can dramatically alter the surface properties of the underlying substrate. While OTS is CH 3 terminated, the end groups can be functionalized with various chemical groups. The FC monolayer, also chemically attached to a sapphire substrate, is CF 3 terminated and thus is more hydrophobic than OTS. On the other hand, the chains are not as well packed as the alkyl chains of OTS [62]. We have exposed PDMS sheets to a short oxygen plasma before contact. The oxygen plasma contains high energy photons, electrons, ions, radicals, and excited species [167]. This is a common procedure to change the surface energy, improve the bondability of surfaces to dissimilar materials, and enable chemisorption of hydrolyzed alkyltrichlorosilanes to the surface [168]. Plasma treatment modifies only the surface region and produces no change in the bulk properties. The oxidized PDMS surface has been extensively analyzed using a sleuth of techniques such as XPS, SSIMS, ATR-IR, 147

170 Contact Angle, Wilhemly Plate, AFM, and SEM. During plasma exposure a brittle silica-like layer of 5nm thickness (depending on the time of exposure) is formed at the PDMS surface. In addition, low molecular weight (short) PDMS chains are produced due to chain scission and crosslinking [169]. On exposure to air, the short PDMS chains diffuse out over a period of hours to days through the cracks in the silica-like layer [ ]. These cracks are either caused by thermal and mechanical stress or are self-formed due to surface densification. The surface reconstruction is known as hydrophobic recovery. Here, the PDMS sheets were pressed against OTS surfaces immediately after plasma exposure. The migration of short PDMS chains is faster under finite pressure due to increased cracking of the silica-like layer. In this geometry, the short PDMS chains are locally confined between the silica-like layer and OTS. This is similar to a contact interface between macroscopic rough surfaces where a liquid is confined between flattened asperities. Interface sensitive SFG has been used in total internal reflection (TIR) geometry to probe the confined interface. As described in Section 3.2, SFG involves mixing a visible high intensity laser beam of frequency ω vis with a tunable infrared wavelength source of frequency ω IR. According to the dipole approximation, generation of SFG photons (at frequency ω vis + ω IR ) is forbidden in the centrosymmetric bulk but allowed at the interface where the inversion symmetry is broken. The SFG intensity is resonantly enhanced when ω IR overlaps with the resonant frequency of the vibration mode of the surface molecules. By the proper choice of incident angles in TIR, we 148

171 have selectively probed the hidden interface while reducing the contribution from the other interfaces. We have used 43 for the polymer (PDMS and PDMS ox ) and OTS surfaces while 8 for the polymer/solid (OTS, sapphire, FC) interfaces. The TIR geometry further enhances the SFG intensity by one to two orders of magnitude. The experimental geometry is shown in Figure The spectra taken with our SFG setup have either broad wavenumber (fwhm 20cm 1 ) or narrow wavenumber (fwhm<5cm 1 ) resolution. For the latter, a SpectraPro-500i monochromator is used in front of the detector. Figure 4.1 summarizes the SFG results and fits in the SSP polarization (Spolarized SFG beam, S-polarized visible beam, P-polarized IR beam). These spectra only cover the range of cm 1 which represents the C-H stretching vibrations of the CH 3 and CH 2 groups expected to be present at the interface. All the vibrational modes that appear in this study are listed in Table 3.1 together with their resonant assignments. In Figure 4.1C and D for OTS, the methyl Fermi band is slightly red-shifted and the ratio of the symmetric methyl and methyl Fermi intensity has changed upon contact. This effect is reversible as the spectra before and after contact are indistinguishable. The slight shifts are not related to changes in orientation, since well-packed SAM chains are known to resist high levels of pressures up to 300MPa [140]. Figure 4.1A and B are SFG spectra for OTS and PDMS, respectively before contact. The y-axis is the SFG intensity which is related to the number and ori- 149

172 A. OTS x B. PDMS x9 SFG Intensity (a. u.) C. PDMS ox /OTS D. PDMS/OTS x E. PDMS liq /OTS x F. PDMS ox /sapphire x IR Wavenumber (cm -1 ) Figure 4.1: SFG spectra of A) OTS, B) PDMS, C) PDMS ox /OTS, D) PDMS/OTS, E) PDMS liq /OTS, and F) PDMS ox /sapphire in SSP polarization. The solid lines are fits to the square of the sum of the Lorentzian functions (eq 4.1). B) and F) are taken with a broader wavenumber resolution (full width half maximum (fwhm) 20cm 1 ) to improve the signal-to-noise ratio. The SFG spectra were offset along y-axis by an arbitrary amount and A), B) and F) were scaled for clarity. 150

173 entation of the molecules at the interface. Figure 4.1A is a typical spectrum for a well-packed OTS monolayer with ordered methyl groups (symmetric vibration (r + ) at 2879cm 1 and Fermi resonance (r + Fr ) at 2938cm 1 ) [173, 174]. The methylene peaks (symmetric vibration (d + ) at 2850cm 1 and asymmetric vibration (d + Fr ) at 2920cm 1 ) [173] are absent for an all-trans conformation due to the inversion symmetry of the CH 2 groups that makes them SFG inactive [174]. In Figure 4.1B, the two main peaks, symmetric vibration (r + PDMS ) at 2906cm 1 and asymmetric vibration (r PDMS ) at 2962cm 1, are assigned to the methyl groups bonded to silicon [175]. The r PDMS is present as a dip in the spectrum because it has a negative phase. The r+ PDMS will be referred as the Si (CH 3 ) 2 peak, hereafter. In the case of PDMS ox, the oxygen plasma treatment destroys the surface methyl groups and the SFG spectrum from cm 1 does not have any resolvable features (not shown here). Figure 4.1C shows the spectrum for PDMS ox /OTS interface. The Si (CH 3 ) 2 peak is extremely strong at this interface. Since the PDMS ox surface before contact has no CH 3 peaks, this indicates a significant interfacial reconstruction. The presence of PDMS chains after interfacial reconstruction is also evident in the adhesion experiments (Figure 4.2A). For the PDMS ox /OTS contact, once the highest load is reached the reconstruction is completed and the unloading proceeds with an equilibrium interface. The strain energy release rate on unloading is equal to 43mJ/m 2. This value is similar to that expected for the thermodynamic work of adhesion of PDMS in contact with OTS (shown in Figure 4.2B). For example, the work of adhesion 151

174 between PDMS and OTS is 2 γ PDMS γ OTS = mj/m 2 (γ PDMS = 20 25mJ/m 2 and γ OTS = 20mJ/m 2 ) assuming only dispersion forces. These adhesion measurements of PDMS/OTS and PDMS ox /OTS are consistent with the SFG results. 0.8 A.PDMS ox / OTS 0.8 B.PDMS/OTS 0.6 unloading 0.6 unloading 0.4 loading 0.4 loading m 3 ) a 3-12 ( C.PDMS ox / sapphire unloading loading D.PDMS/sapphire unloading loading Load, P (10-4 N ) Figure 4.2: JKR plot of A) PDMS ox /OTS, B) PDMS/OTS, C) PDMS ox /sapphire, and D) PDMS/sapphire. The contact radius, a, cubed is plotted as a function of the applied load. The strain energy release rate on unloading for both PDMS ox /OTS and PDMS ox /sapphire depends neither on the contact time within each load increment nor the time at maximum load. Interestingly, the strong Si (CH 3 ) 2 peak observed at the PDMS ox /OTS interface is much weaker at the PDMS/OTS interface as shown in Figure 4.1D. The 152

175 spectrum is dominated by CH 3 peaks associated with the OTS layer. We can also quantitatively calculate the contribution from OTS and PDMS methyl groups by using the fit parameters obtained from eq 2.77, I(SFG) χ eff,nr + q A q ω IR ω q iγ q 2 (4.1) The ratio of A q,pdms /A q,ots 0.29 and 0.74 for PDMS/OTS and PDMS ox / OTS interfaces, respectively. This indicates that at the PDMS ox /OTS interface the CH 3 groups of PDMS have strong orientational order comparable to a well-ordered OTS, whereas the order is weaker at the PDMS/OTS interface. The only difference between the two interfaces is the presence of short chains as a result of oxygen plasma treatment and interfacial reconstruction. The important question is whether the presence of short PDMS chains next to OTS surface is sufficient to observe ordered Si (CH 3 ) 2 groups. For this purpose we have studied the SFG spectrum for low molecular weight PDMS (PDMS liq with M w = 1250 g/mol) in contact with OTS (Figure 4.1E). Here, the complete cell is filled with the PDMS liq without any confinement. The SFG spectrum shows CH 3 signals of the OTS layer with weak contribution from PDMS chains. This indicates that confinement is necessary to observe the enhanced ordering of Si (CH 3 ) 2 at the PDMS ox /OTS interface. The contact of PDMS ox with a high energy sapphire and a disordered low energy FC was also studied to understand the role of surface energy on the order 153

176 of PDMS chains at the interface. The spectrum of PDMS ox /sapphire interface is shown in Figure 4.1F. It is dominated by symmetric and asymmetric peaks associated with the CH 3 groups of PDMS signifying a reconstruction. However, the intensity of Si (CH 3 ) 2 peak is much weaker in comparison to PDMS ox /OTS interface. This can be attributed either to weak orientation or partial reconstruction. On the other hand, the adhesion measurements of the PDMS ox /sapphire contact (Figure 4.2C) give a clear indication of the presence of short PDMS chains at the interface. A strong adhesion and adhesion hysteresis is observed for PDMS/sapphire contact (Figure 4.2D) due to the formation of hydrogen bonds between the hydroxyl and silicon groups. The hysteresis decreases significantly at the PDMS ox /sapphire interface due to the enrichment of the interface in low molecular weight PDMS chains, thus forming a weak boundary layer (less energy dissipation due to reduced chain pull-out) [176]. Consequently, based on the adhesion results, the PDMS ox /sapphire interface has reconstructed with the diffusion of short PDMS chains. However, these short chains are poorly ordered next to the sapphire surface unlike the PDMS ox /OTS interface. For the PDMS ox /FC interface, we did not observe any detectable Si (CH 3 ) 2 signal between cm 1. Compared to OTS, FC does not pack into a condensed film and fluorocarbon groups are larger than the hydrocarbon groups [28]. This indicates that short PDMS chains require not only confinement but also an ordered template provided by the methyl groups of OTS. 154

177 We believe that the strong order of Si (CH 3 ) 2 groups at the PDMS ox /OTS interface is a signature of layering which was observed for molten PDMS confined between two mica surfaces with surface forces apparatus [164], PDMS thin films on silicon substrates with x-ray scattering [177], and PDMS oligomers next to hydroxylated α-quartz with molecular dynamics simulation (MD) [178]. The common ingredient in all these studies is the presence of smooth substrates. To confirm that the PDMS chains are layered next to OTS and develop a physical picture at the PDMS ox /OTS contact, we have compared the SFG experiments with the MD results. The PDMS/hydroxylated α-quartz system has been simulated by using the Compass Force Field (CFF) which is an explicit atom model [178]. The 001 surface of α-quartz with high OH concentrations has been chosen and generated from experimentally determined parameters. The potential in the explicit atom model cannot treat oxides but the necessary interactions are included. In order to avoid the contraction in the presence of a free surface due to CFF, the SiO 2 atoms on the surface have been frozen. The PDMS system has a molecular weight of g/mol which is high enough to account for a surface region and a bulk-like system in the middle of the film. The MD simulations were carried out in the canonical ensemble with the temperature controlled by the Nose-Hoover thermostat and were run using the LAMMPS code [179]. The van der Waals interaction was truncated and shifted at a cutoff distance of 1.2 nm. The PDMS melt was first equilibrated for at least 4 ns and then brought next to the α-quartz surface. Once the melt was completely adsorbed, 155

178 it was further equilibrated for approximately 2 ns. The atom positions were recorded every picosecond for the analysis. The ratio of the asymmetric to symmetric mode strengths is related to the tilt angle θ, the angle between the symmetry axis of the CH 3 molecule and the surface normal, and independent of the Fresnel coefficients, refractive index, and the incident angles of the input beams [166], A q,asym A q,sym = β caa (x x 3 ) β ccc ( (1 r) (x x 2 3 ) + r x) (4.2) where x = cos(θ), r = β aac /β ccc, β s are molecular hyperpolarizabilities, and a, b, and c are molecular axes where c coincides with the symmetry axis of the CH 3 group. For methyl vibrations, β aac β caa. We have used r 2.35 and βaac β caa 1 to determine the tilt angles [180]. Since the asymmetric peak assignment for the methyl groups of OTS and Si (CH 3 ) 2 overlap at 2960cm 1 and the line strength can take positive or negative values, we can only estimate the upper bounds on the orientation of Si (CH 3 ) 2. This comparison gives us a value of A q,asym /A q,sym 0.3 and x 0.85 for PDMS ox in contact with OTS monolayer (Figure 4.1C). The number of CH 3 groups and x as a function of film thickness from MD are shown in Figures 4.3A and B, respectively. The histograms of x for CH 3 groups next to α-quartz (from 0 to 35Å) and air interfaces (from 35-70Å) are shown in Figures 4.3C and D, respectively. The majority of the CH 3 molecules in Figure 4.3C are clustered on either side of x = 0 with the exception of the CH 3 groups within 156

179 Cos( ) Number of CH A Distance (A) 80 C D Cos( ) Number of CH 3100 B Figure 4.3: A) cos(θ), B) number of CH 3, C) and D) histograms of cos(θ) for the methyl groups next to α-quartz and air interfaces, respectively. 3 Å. x 0.7 for the methyl groups next to α-quartz substrate is in good agreement with the experimental results. The small difference in the orientation of the CH 3 groups (more vertical in contact with OTS) can be explained by the differences in the substrate and confinement. The average of x from the rest of the layers (3 to 35Å) is 0. In comparison, the histogram of x in the absence of layering at the air interface in Figure 4.3D is very different. The ratio Aq, asym/aq, sym is calculated using the simulation results in Figure 4.3 and eq 4.2 to be 1.2 for the PDMS/air interface. This is in good agreement with the experimental value of 1.4 (Figure 4.1B). 157

180 Oxidized PDMS Surface C A OTS Modified Sapphire Poly(dimethyl siloxane) (PDMS) D. Interface OTS Surface B nm nm E. SAPPHIRE CH 3 CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH Si Si Si Si Si Si O O O O O O CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH Si Si Si Si Si Si O O Si Si Si Si O O Si O O Si CH CH CH CH CH CH CH CH CH CH CH CH ox PDMS O O O O Si Si O O O O Si Si O O O O µ m 2.0 µ m Crosslinked PDMS bulk Silica like layer of oxidized PDMS Surface area filled with short PDMS chains Figure 4.4: A) The PDMS ox lens deforms to make contact with OTS. The area of contact is larger than the SFG laser spot (radius 0.5mm). B) and C) The atomic force microscopy images of the OTS (2 2 µm) and PDMS ox (50 50 µm) surfaces and the section analysis of an arbitrary (white) line on the surface (height as a function of length). D) Depiction of the asperity contacts at the interface based on the section analysis of the OTS surface. E) Short PDMS chains confined between the oxidized PDMS surface (silica-like layer) and OTS in a local contact region. The number of layers may depend on the amount of short PDMS chains present at the interface. 158

181 From MD, we have also calculated the density of CH 3 in the first 3Å region next to the α-quartz substrate to be 23.8Å 2 CH 3. Tidswell et. al. reported values of 22.3Å 2 CH 3 for a well-packed OTS layer with x-ray specular reflection [181] similar to the results of previous reflectivity studies of 22.5Å 2 [182]. This indicates that the densities of the methyl groups of the OTS and the PDMS chains are comparable. Therefore, the ratio of vibrational amplitudes A q,pdms /A q,ots 0.74 for PDMS ox /OTS interfaces from the SFG results is in good agreement with well-ordered Si (CH 3 ) 2 groups next to a smooth substrate. In summary, we propose that layering can exist between two macroscopic rough surfaces as depicted in Figure 4.4 at various scales. The PDMS ox lens deforms to make contact with OTS (Figure 4.4A). The area of contact is larger than the SFG laser spot (radius 0.5mm). The confinement is between the hard SiO 2 layers formed due to oxygen plasma treatment and the OTS coated on sapphire. The atomic force microscopy images of the rough OTS surface and the cracked silica-like layer at the PDMS ox surface is shown in Figure 4.4B and C. The short PDMS chains are ordered in layers with the Si (CH 3 ) 2 groups facing the terminal methyl groups of OTS (Figure 4.4E). The number of layers of PDMS chains may depend on the amount of short chains present at the interface. This layering only exists in a local contact region between two flattened asperities (Figure 4.4D). The deformability of PDMS is important in forming large enough uniform contact area to observe these effects. 159

182 4.2 Molecular Origins of the Adhesion and Friction Behavior of Elastomers Sliding on Glassy Polymers In the previous section, we have used the molecular information obtained from infraredvisible sum frequency generation (SFG) spectroscopy together with the adhesion results in order to understand the confined structure at the contact interface which also has practical applications. Here, we have coupled SFG with adhesion and friction measurements to determine the structure of the surface molecules at the static and sliding contact interfaces in order to understand the reason behind their adhesion and friction behaviors. It has been known for centuries that friction is related to adhesion; however, the exact relationship between adhesion and friction is still not understood [9 12]. The understanding of friction is important in areas such as energy conservation, controlling road traction of tires, nanotribology, and design of prosthetic devices. It is intuitive that the higher the adhesion energy between two surfaces, the higher the frictional forces [103]. However, in some cases adhesion has a dissipative component (adhesion hysteresis) which has a significant influence on friction [8, 108]. Early experiments by Levin and Zisman [104] as well as Briscoe and Evans [105] have shown that the friction for fluorocarbon surfaces was higher than that for hydrocarbon surfaces even though the fluorocarbon surfaces have lower adhesion energy. By using poly(dimethyl siloxane) (PDMS) elastomer as the counter surface, Chaudhury and Owens [8] suggested that the cause of higher friction on fluorocarbon surfaces is re- 160

183 lated to adhesion hysteresis. This energy dissipation during adhesion was attributed to partial interdigitation of the chains across the interface which also increases the dissipation of energy during sliding. The interdigitation of molecules at the interface has been suggested as a cause of higher adhesion hysteresis and higher friction for many other systems. Israelachvili and coworkers [108] have shown that the glassy amorphous state of the hydrocarbon Langmuir-Blodgett monolayers shows the highest friction in comparison to crystalline and liquid-like monolayers. According to the authors, the amorphous layers interdigitate across the interface which leads to higher energy dissipation during their relaxation and thus adhesion hysteresis in comparison to the crystalline monolayers. The liquid-like monolayers also interdigitate but have lower viscosity and this results in lower friction. To correlate friction and adhesion hysteresis, Israelachvili and coworkers proposed that the frictional stress is equal to W/δ where W is the adhesion hysteresis and δ is the length of the interdigitation. Both W and δ depend on the level of interdigitation [13]. Similar enhancement in friction due to interpenetration was also observed in polymer-polymer sliding [15,63]. Brown [15] showed that the higher friction of PDMS lenses sliding on surfaces with tethered (or grafted) polymer chains can be explained by the interpenetration of tethered chains into the crosslinked rubber. Israelachvili and coworkers [63] reported a factor of ten increase in friction for UV exposed polystyrene (PS) surfaces in comparison to that for crosslinked PS surfaces. The UV exposure results in chain scission and the cre- 161

184 ation of free chain ends which can penetrate and increase the friction similar to the case observed by Brown using tethered chains on surfaces. Figure 4.5: Shear stresses of PDMS on PS (black box) and SAM (gray box). The trendline on the PS data is the prediction of a thermally activated rate theory using an Arrhenius shift factor. Even though there is mounting evidence for a strong correlation between adhesion, adhesion hysteresis, and friction, there still are some striking anomalies. Vorvolakos and Chaudhury reported a much higher shear stress for PDMS elastomer sliding on a PS surface in comparison to that on a well-packed hydrocarbon monolayer (SAM) [14] in the low velocity range as seen in Figure 4.5. This was unexpected because the adhesion energies of the PDMS/SAM and PDMS/PS interfaces are only slightly different. In addition, the adhesion behavior of both interfaces were found 162

185 to be nonhysteretic. This behavior contradicts with the observations of fluorocarbon surfaces where the higher friction was explained by the increase in adhesion hysteresis [8]. Roughness was also ruled out since the two surfaces were smooth down to the nanometer level (0.2nm for the monolayer and 0.5nm for PS). Vorvolakos and Chaudhury have pointed that the higher shear stress for PDMS/PS could be due to interdigitation of PS chains in the PDMS elastomer. If we consider the fact that an adhesion hysteresis of 1mJ/m 2 cannot be resolved experimentally and assume a local penetration of 0.5nm (the size of a phenyl group), we obtain an upper limit of 2 MPa variation in the friction force. This could explain the difference in the shear stress between PDMS/SAM and PDMS/PS interfaces. However, it is not clear why we should expect interpenetration across the interface between a glassy polymer and a crosslinked rubber. Brown has also shown that the friction forces of PDMS sliding on a glassy PS surface are much higher than that on a PDMS surface [15]. Brown interpreted his finding as the rigid PS slowing down the molecular mobility of the PDMS segments at the interface leading to higher energy dissipation during sliding. Both these arguments, mobility and interpenetration, involve the changes in the structure of the interfacial molecules upon contact or during sliding. The studies mentioned above reveal the complexity of friction, adhesion and their relationship. Thus, the need for a technique that can probe the structure of the interfacial molecules is vital. For this purpose, we designed an approach to couple the infrared-visible sum frequency generation (SFG) spectroscopy to study 163

186 molecular structure (orientation and density of molecules) at the polymer/solid and polymer/polymer interfaces with adhesion and friction experiments. We have already demonstrated in Section 4.1 that SFG in total internal reflection (TIR) geometry can be used to directly probe the molecular structure at the elastomer/polymer contact interfaces [142, 143]. Similarly, we have taken advantage of the well-characterized model elastomeric network, PDMS, to generate large uniform contact areas with the polymer surfaces. As mentioned before, the size of the contact area can be controlled by the applied load and radius of curvature of the lens based on the JKR theory [6]. We have investigated the interface of PDMS/PS and PDMS/poly(vinyl n- octadecyl carbamate-co-vinyl acetate) (PVNODC). These systems are similar to that studied by Vorvolakos and Chaudhury [14]. We have used PVNODC instead of the SAM because it is easier to prepare smooth surfaces. We have shown before that the surface of PVNODC is similar to that of SAM [16]. The octadecyl side chains crystallize predominantly in all-trans conformation with the side chains aligned perpendicular to the surface. The surface energies of PVNODC and SAM as well as the adhesion energies of PDMS/PVNODC and PDMS/SAM interfaces are similar. Both of these interfaces do not show any energy dissipation (hysteresis) having only dispersion interactions. Besides PVNODC and PS, the frictional behavior of PDMS was also studied on poly(n-butyl methacrylate) (PnBMA) and poly(n-propyl methacrylate) (PnPMA) surfaces in order to understand the role of chain mobility in friction. PnBMA has a T g below T R at 17 and PnPMA has a T g above T R at 35. The 164

187 0.5 Shear Stress (MPa) PDMS exsyl PDMS syl PDMS exhm PDMS hm Velocity (microns/sec) Figure 4.6: The shear stress values are shown for the different types of PDMS lenses sliding on PVNODC. The PDMS syl and PDMS exsyl lenses are prepared from a Sylgard- 184 elastomeric kit (Dow Corning) and the PDMS hm and PDMS exhm lenses are homemade. The symbol ex is used for lenses whose sol fraction is extracted. 165

188 surfaces of all these polymer films are smooth based on our AFM results. Smoothness provides mainly adhesive sliding that is free of the ploughing term PDMS syl W UL = 46.0mJ/m 2 a 3 (m 3 x ) PDMS hm W L = 45.2mJ/m 2 K = 2.5 MPa W UL = 48.0mJ/m W L = 47.9mJ/m 2 K = 1.9 MPa P (N x 10-3 ) Figure 4.7: The elastic modulus (K) as well as work of adhesion (W a ) values are shown for PDMS syl (top) and PDMS hm (bottom). The filled and open symbols represent data taken during loading (approaching two surfaces) and unloading (separating two surfaces), respectively. In these JKR experiments the counter surface was PVNODC. Vorvolakos and Chaudhury have emphasized the importance of using model elastomeric networks due to the decoupling of the myriad factors contributing to interfacial friction. They have prepared PDMS lenses that are similar to our homemade 166

189 lenses (PDMS hm ) which are free of fillers. In addition their lenses were extracted from any resin that might have been left unreacted during the crosslinking process. We have first compared the friction behavior of the four different types of PDMS lenses we prepared as explained in Section 3.1; PDMS syl, PDMS exsyl, PDMS hm, and PDMS exhm. As a reminder, PDMS syl and PDMS exsyl lenses are prepared from the Sylgard-184 elastomeric kit while PDMS hm and PDMS exhm are homemade. The symbol ex represents lenses that have been extracted. Figure 4.6 shows the shear stress values of these PDMS lenses sliding on the PVNODC surface as a function of velocity. It is important to note that this velocity is the driving velocity but not the velocity resulting from the motion at the surfaces. In this low velocity range, friction is independent of velocity. First, the lenses fabricated from Sylgard-184 have higher shear stresses than the homemade lenses. The reason might be the presence of silica fillers that alter the mechanical properties of PDMS towards higher modulus. This is evident from the elastic modulus (K) values of these two type lenses measured in contact with PVNODC using JKR type adhesion experiments (Figure 4.7). In Figure 4.7, the work of adhesion (W a ) for PDMS syl and PDMS hm lenses, and in Figure 4.8, the SFG spectrum for PDMS syl and PDMS hm sheets are similar indicating that the surface properties are almost identical. The filler particles are hydrophilic and thus, are not expected to be exposed at the surface but they might be buried in the near-surface region. In conclusion, the presence of fillers in the PDMS matrix does not change the 167

190 chemical structure of the surface but increases the modulus which in return increases the friction. 300 PDMS syl SFG Intensity (a. u.) PDMS hm Wavenumber (cm -1 ) Figure 4.8: SFG spectra of the PDMS syl (top) and PDMS hm (bottom) surfaces in SSP polarization (S-polarized SFG beam, S-polarized visible beam, P-polarized IR beam). Second, the extracted lenses have higher shear stresses. This behavior can be explained by the presence of short PDMS chains (resins) at the surface of unextracted lenses. They are the chains that did not get incorporated into the crosslinking reaction. It is known that these reactions never go to 100 % completion. The unreacted 168

191 short chains are expected to bloom to the surface due to their higher mobility. Since they have the same chemical structure, the surfaces of the extracted and unextracted PDMS cannot be distinguished with SFG and are almost identical (Figure 4.8). However, the existence of the short chains becomes clear when the unextracted PDMS lens is put into contact with a surface and then removed. This is shown in Figure 4.9 for a PS surface that was held in contact with a PDMS syl sheet. The details of the spectral features are discussed later in this section but mainly the peaks above 3000cm 1 corresponds to the phenyl vibrations of PS while the ones below 3000cm 1 are assigned to the methyl groups of PDMS that are bonded to Si (Si (CH 3 ) 2 ). The PS surface before contact does not exhibit any Si (CH 3 ) 2 vibrations as expected but these vibrations appear in the SFG spectrum of the PS surface after being in contact with PDMS syl. In conclusion, the unextracted PDMS lenses contains short PDMS chains on the surface causing boundary lubrication and thus decreasing the friction. Based on our findings, we have chosen PDMS exhm to perform the experiments in this study. Figure 4.10 shows the friction data for PDMS exhm lenses sliding on PVNODC and PS surfaces. After the initial static force, a smooth and stable sliding is observed for PDMS/PVNODC while the sliding has an irregular sawtooth profile for PDMS/PS systems. This sawtooth modulation is characteristic of stick-slip sliding where the sliding surfaces alternately switch between sticking and slipping in a regular fashion. This type of motion leads to the common experience of squeaking doors and singing 169

192 SFG Intensity (a. u.) before contact after contact PS Wavenumber (cm -1 ) Figure 4.9: SFG spectra in SSP polarization of the PS surface before (î) and after ( ) it was held in contact with an unextracted PDMS syl sheet. 170

193 violins. It has been recently demonstrated that the stick-slip behavior is one-to-one related to energy loss during sliding [183]. It occurs below a critical velocity that is the transition point to smooth sliding. Due to the velocity limit of the friction apparatus used in this study, the critical velocity has never been achieved and we have observed stick-slip sliding for PDMS exhm on PS at all velocities. In the case of stick-slip sliding, the maximum force just before slip is recorded to determine the shear stress [91]. Shear stress as a function of velocity is plotted in Figure 4.10B. As expected for low velocity, the values of shear stress do not depend on the velocity and are load independent. The shear stress of PDMS exhm sliding on PS is about four times higher than that of PDMS exhm sliding on PVNODC. This ratio is consistent with that reported by Vorvolakos and Chaudhury [14]. The sheer stress values in Figure 4.10 are higher than the values reported by Vorvolakos and Chaudhury. The difference might be a result of the different experimental procedures of the two studies. Our PDMS exhm lenses were prepared from an oligomer with 6kg/mol molecular weight which is in the range of the molecular weights of the oligomers used by Vorvolakos and Chaudhury. Even though the crosslinking reaction systems are similar in the two studies, it is possible to obtain different PDMS networks depending on the mass ratio of oligomer/crosslinker/catalyst, the preparation method such as curing temperature and time, and the extraction conditions. As it is shown by Vorvolakos and Chaudhury, the friction is highly molecular weight dependent and thus different PDMS networks will have different sheer 171

194 0.4 B. A. Shear Stress (MPa) Time (s) Velocity (microns/s) Figure 4.10: A) The shear stress as a function of time for PDMS exhm sliding on PVNODC (wine) and PS (navy) at a velocity of 3µm/s. B) The shear stress during sliding plotted as a function of velocity for PDMS exhm sliding on PVNODC ( ) and PS ( ). 172

195 stresses. In addition the friction apparatus used in the two studies are different. For the low velocity range attained in our experiments, we have continuously slid a rigidly supported lens relative to the substrate with a velocity controlled motor and recorded the resistance (force) on a calibrated spring. In Vorvolakos and Chaudhury s apparatus the lens was placed on one end of a calibrated spring. Then the substrate was given a sudden displacement and the deflection of the spring was recorded while the lens first moved with the substrate and then relaxed back to its original position. The force acting on the lens was determined from this deflection. Considering all the experimental differences that might lead to differences in the absolute values of friction, we will only be concentrating on the relative values. To correlate the friction behavior with adhesion, JKR experiments were performed for the PDMS exhm /PVNODC (Figure 4.11A and B) and PDMS exhm /PS (Figure 4.11C and D) interfaces. Figure 4.11A and C show the contact radius cubed, a 3, as a function of the applied load and Figure 4.11B and D show strain energy release rate, G, as a function of a. The G values from the loading data are 40-45mJ/m 2 for PDMS exhm /PVNODC and 55-60mJ/m 2 for PDMS exhm /PS. In addition, both interfaces have negligible adhesion hysteresis and thus G = W a. As described in Section , a theoretical value of W a can be calculated assuming only dispersion forces (W a = 2(γ 1 γ 2 ) 0.5 ). The critical surface energies of PDMS exhm PVNODC, and PS are calculated from contact angles of various liquids by the geometric mean equation. The liquids used are distilled-water, di- 173

196 A. PVNODC unloading B a 3 (m 3 x ) C. PS unloading loading loading D G (mj/m 2 ) P (N x 10-3 ) a (m x 10-4 ) 20 Figure 4.11: JKR plots of PDMS on PVNODC ( ) and PS ( ) during loading (open symbols) and unloading (filled symbols). A) and C) Contact radius cubed, a 3, as a function of applied load, B) and D) Strain energy release rate as a function of contact radius. 174

197 iodomethane, and ethylene glycol. The average of the calculated values from each pair of liquid gives the surface energies of PDMS, PVNODC, and PS as 21.7, 23.1, and 41.4mJ/m 2 respectively. These values are consistent with those reported in the literature [184]. Assuming only dispersion forces, we predict W a 45mJ/m 2 for the PDMS exhm /PVNODC and W a 60mJ/m 2 for the PDMS exhm /PS interfaces. The experimental W a values are in good agreement with the theoretical predictions. The ratio of the adhesion energies measured for PDMS exhm /PS and PDMS exhm /PVNODC is 1.2, much smaller than the ratio of the shear stress if we assume that the shear stress is directly proportional to the adhesion energy. Since the adhesion hysteresis is negligible at both interfaces we can conclude that neither adhesion nor adhesion hysteresis provide an explanation for the large difference in shear stress. Figure 4.12 shows the SFG spectra for PVNODC and PS surfaces in the SSP polarization (S-polarized SFG beam, S-polarized visible beam, P-polarized IR beam) at an incident angle of 42. At this incident angle the SFG spectra correspond to the polymer/air surfaces with no contribution from the polymer/sapphire interface. The interfacial area during contact and sliding is kept larger than the laser spot (d 1mm) in these experiments to avoid any SFG signal contributions from outside the contact area. The bold symbols in Figure 4.12 correspond to the SFG spectra of the PVNODC (Figure 4.12A) and PS (Figure 4.12B) surfaces before bringing them in contact with the PDMS exhm lens. The SFG spectra shown in Figure 4.12 as black circles ( ) are measured during contact. Here, the SFG signals are weak because the incident angle 175

198 160 A. PVNODC SFG Intensity (a. u.) B. PS before contact after before contact after Wavenumber (cm -1 ) Figure 4.12: A) SFG spectra in SSP polarization for PVNODC ( ) before contact, during contact ( ), and after the PVNODC surface has experienced sliding, B) SFG spectra in SSP polarization for PS ( ) before contact, in contact ( ), and after the PS surface has experienced sliding. 176

199 of 42 is far from the critical angle for the PDMS exhm /polymer interface. The SFG spectra shown as open circles (PVNODC) and open squares (PS) in Figure 4.12 are acquired after the PDMS exhm lens has slid across the contact spot. The peaks in the PVNODC spectrum in Figure 4.12A are assigned to the methyl symmetric vibration (r + ) at 2875 cm 1 and Fermi resonance (r + Fr ) at 2935 cm 1. This spectrum is similar to the SSP spectrum of SAM reported previously [143] and indicates a surface structure expected for well-packed alkyl side-chains of PVNODC in predominantly alltrans conformation. The peaks in the PS spectrum in Figure 4.12B corresponds to the phenyl C-H stretching modes of PS. The dominant peak at 3065 cm 1 is assigned to the ν 2 symmetric vibration. There is a small contribution from the vibration of the methylene groups (2920cm 1 ). This spectrum is similar to that observed previously at the PS surface where the average orientation of the phenyl rings is parallel to the surface normal [137]. The most important outcome from Figure 4.12 is that the spectra after sliding, for both PVNODC and PS surfaces, are identical to those before contact. This indicates that either the surface molecules are not affected from sliding or the molecular changes that took place during sliding are reversible. The structure during contact is directly probed in situ using the incident angle of 8 for the PDMS exhm /PVNODC and 12 for the PDMS exhm /PS interfaces. Before discussing the SFG results, it will be helpful to understand the experimental procedure. The sketch of the experimental geometry is shown in Figure The symbol X corresponds to the spot that is probed by the SFG laser beams. The 177

200 bold symbols in Figures 4.13A and C correspond to the situation where the laser beam is superimposed with the contact spot (area) at the interface. The black circles ( ) correspond to the situation where the laser beam is positioned in front of the contact area. This is to ensure that there is no contribution from the polymer bulk or solid interface because in this condition, the incident angle is far away from the critical angle for the PDMS exhm /polymer interface. As seen, the SFG intensity is much weaker than that observed when the laser beam and the contact spot are superimposed. Any spectral features observed at this state are a combination of signals from the polymer/sapphire interface and polymer surface. The open circles (PDMS exhm /PVNODC) and open squares (PDMS exhm /PS) in Figures 4.13A and C correspond to the situation where the laser beam was first positioned in front of the contact spot and then the lens was moved in with the desired speed. The SFG spectra were acquired after the lens once again overlapped with the laser spot. In this condition, we are probing the contact interface that has experienced sliding. First, we will discuss the SFG spectra of the PDMS exhm /PVNODC (Figure 4.13A) and PDMS exhm /PS (Figure 4.13C) contact interfaces. The peak assignments of the PDMS exhm /PVNODC interface are similar to those of the PVNODC surface. The two main peaks correspond to the vibrations of the terminal CH 3 groups of the PVNODC side chains. The contributions from the Si (CH 3 ) 2 groups of the PDMS segments are expected at 2906 cm 1 (symmetric, r + PDMS ) and at 2962 cm 1 (asymmetric, r PDMS ). At this interface, the intensities of the PDMS exhm peaks are 178

201 (A) (B) SFG Intensity (a. u.) (C) (D) Wavenumber (cm -1 ) Time (sec) Figure 4.13: The sketch illustrates the experimental geometry used to probe the SFG spectra during contact and sliding. A) and C)The SFG spectra in the SSP polarization for PDMS exhm /PVNODC ( ) and PDMS exhm /PS ( ), respectively. The spectra were acquired when the laser beam is at the contact spot (bold symbols), is ahead of the contact spot ( ), and is superimposed once again with the contact spot after sliding (open symbols), B)SFG intensity as a function of time associated with the r + (black line) and r + Fr (gray line) of the methyl groups of the PVNODC side chains, D)SFG intensity as a function of time associated with the phenyl vibrations (ν 2, black line) of the PS side chains and symmetric vibration of the PDMS exhm methyl groups (r + PDMS, gray line). 179

202 negligible in comparison to the peak intensities of the well ordered PVNODC side chains. The structure of the contact interface is very similar to that of the PVNODC surface which is expected for a crystalline structure. In the case of PDMS exhm /PS interface, the two main peaks below 3000cm 1 correspond to the r + PDMS and r PDMS vibrations of the Si (CH 3 ) 2 groups of PDMS exhm. Above 3000cm 1, the dominant contribution is from the ν 2 symmetric vibration (3065 cm 1 ) with a shoulder at 3025cm 1 which is slightly higher than that observed at the PS surface. This additional contribution is probably not associated with the contact interface which is evident from the SFG spectrum of the area ahead of the contact (black circles ( ) in Figures 4.13A and C). Since there is no contact interface here, these spectral features are characteristics of both the PS/sapphire interface and PS surface generated at an off critical angle [137,180]. It was not possible to acquire a complete spectrum during sliding because the time to acquire a spectrum takes min. Instead, we have monitored the intensity of selected vibrations from the interface as a function of time (Figures 4.13B and D). We first position the laser spot ahead of the contact area and then begin sliding the lens towards the laser spot. Initially, the SFG intensity is weak since it is collected from the area ahead of the contact interface. Then the SFG intensity increases and reaches a plateau when the lens starts to overlap with the laser beam. After the lens slides past the laser spot, the SFG intensity drops back to its original low value. Figure 4.13B shows the SFG intensities of the r + (I PVNODC Symm ) and r + Fr (IPVNODC ) of the Fr 180

203 methyl groups of the PVNODC as a function of time. The ratio of the average intensities at the plateau, I PVNODC Fr /I PVNODC Symm, is 0.34 during sliding. The ratio is 0.33 and 0.32 for the PDMS exhm /PVNODC interface before and after sliding, respectively. The similarity between these three numbers indicates that there is very small difference, if any, in the spectral features of the PDMS exhm /PVNODC interface before, after, and during sliding. Consequently, we can argue that neither adhesion nor friction affects the molecular structure of PVNODC side chains as expected for a crystalline surface. In the case of PDMS exhm /PS interface (Figure 4.13C), we obtain the ratio of I PDMS exhm Symm /I PS ν 2 +ν 7b 0.38 and 0.43 before and after sliding, respectively. The analysis of contact interface during sliding from Figure 4.13D indicates that the peak ratio ( 0.36) is similar to the one at the contact before sliding. Thus the spectral features of the PDMS exhm /PS interface do not change during sliding. So far, neither adhesion behavior nor the spectral features in the SFG measurements during sliding explain the difference between the values of shear stress encountered in sliding PDMS exhm on PVNODC and PS. However, we believe that the structural changes have already taken place upon mechanical contact at the PDMS exhm /PS interface. To analyze the changes in the orientation of the phenyl groups at the PDMS/PS interface, we have compared the SFG spectra in SSP and SPS polarization in Figure The SPS spectrum shows three peaks associated with the asymmetric vibration of methyl group of PDMS (2965cm 1 ), asymmetric (ν 20b, 3025cm 1 ) and symmetric (ν 2, 3060cm 1 ) vibrations of the phenyl groups. The 181

204 ratio of the symmetric phenyl vibrations in the SPS and SSP polarization is related to the orientation of the phenyl groups at the interface. We can also calculate the relative contribution of the phenyl groups by fitting the spectra using the following Lorentzian equation [137] (shown as solid lines in Figure 4.14), I(SFG) χ eff,nr + q A q ω IR ω q iγ q 2 (4.3) where A q, Γ q, and ω q are the strength, damping constant, and angular frequency of a single resonant vibration, respectively. χ eff,nr is the nonresonant part of the signal. To quantify the changes in the tilt angles, we have plotted the prediction of A q,ν2 or 20b (SPS)/A q,ν2 or 20b (SSP) as a function of tilt angle in Figure The details of this SFG analysis are provided in previous publications [180]. There is a printing error in this publication and the right hand side of eq 11 and 12 should be interchanged. The ratio of the Fresnel factors for SSP/SPS polarizations at the incidence angle of 12 o is 1 and ratio of β aac /β ccc = Based on the experimentally determined ratios of A q, we estimate from Figure 4.15 that the phenyl groups are tilted with an angle o with respect to the surface normal. This tilt angle (30-40 o ) of the phenyl groups at PDMS/PS interface is larger than 20 o determined at the PS/air surface [137]. We interpret the changes in the orientation of the phenyl groups as the consequence of local interpenetration at the PDMS/PS interface. 182

205 SFG Intensity (a.u.) SSP SPS wavenumbers (cm -1 ) Figure 4.14: SFG spectra for the PDMS/PS interface in SSP ( ) and SPS ( ). The SSP spectrum is shifted vertically for improving the clarity. The solid lines are fit to a Lorentzian equation discussed in the text. 183

206 A 20b,SPS / A 20b,SSP A 2,SPS / A 2,SSP (degrees) Figure 4.15: The prediction of A q,ν20b or 2 (SPS)/A q,ν20b or 2 (SSP) as a function of tilt angle of PS phenyl groups with respect to the surface normal. The experimental values determined from the fit in Figure 4.14 are shown in the figure as dotted lines. 184

207 This interdigitation across the interface between a crosslinked elastomer and glassy polymer is unexpected. However, based on the arguments presented by Chaudhury, a penetration as small as nm can result in significant enhancement of friction [14]. Thus, the penetration does not need to be at the length scale of R g or even at a length scale associated with T g. An interpenetration of the phenyl groups at a local level is sufficient to explain the high friction forces at the PDMS/PS interface. Interestingly, an activation energy corresponding to sub-t g relaxation process was also observed for frictional forces measured using scanning force microscopy (SFM) [185]. This activation energy was attributed to the hindered rotation of the phenyl groups which are dissipating energy during sliding of the silicon tip on PS surface. Similarly, we propose that the energy dissipation during sliding occurs due to the phenyl groups that have intermingled at the PDMS/PS contact interface which results in higher friction. This local change in interfacial structure for PDMS in contact with PVNODC film is not possible since the surface of the PVNODC film is covered with crystalline alkyl side chains. However, a contact interface between PDMS/PVNODC would exhibit local interpenetration and higher friction if it was heated above the melting point of PVNODC. These experiments are in progress. In conclusion, we have showen direct evidence of change in orientation of PS phenyl groups which indicates interpenetration at the contact interface of PDMS with glassy PS. The changes in the orientation of the phenyl groups are reversible and the structure before contact is recovered once the PDMS lens is removed from 185

208 contact. The depth of the penetration is not clear. It is most probably not at the R g length scale but at a local level that involves only a few segments. This local interpenetration is absent for PDMS in contact with side chain crystalline PVNODC. This explains the higher friction forces for PDMS lenses sliding on PS surfaces in comparison to those sliding on PVNODC surfaces. In the past, interpenetration across an interface has been suspected to cause energy dissipation during friction but this was always accompanied with adhesion hysteresis. A local interpenetration can have a profound influence on the frictional forces and still remain unresolved by adhesion measurements. Several hypothesis may explain this interpenetration. First, from equilibrium thermodynamic arguments, a finite interfacial width is expected for the contact interface between the segments of the two polymer chains on each side of the interface even though they are immiscible. Second, the penetration is at such a small length scale that this effect is due to sub-t g relaxations and T g of the bulk polymer film is not the determining factor for this local rearrangements. Third, one could argue that the surface of the polymer film is more mobile than the bulk which has been observed with several experimental techniques [186]. Lastly, it is possible that the mobile polymer chains of one surface act as local plasticizer and increase the mobility of the counter surface groups. We postulate that the change in orientation of surface groups due to local interpenetration may be general for other glassy polymers. In order to test this hypothesis and gain more insight into the molecular mechanism of adhesion and friction, we 186

209 have also characterized the adhesion and frictional properties of PDMS exhm /poly(nalkyl methacrylates) (PnAMA) interfaces. The PnAMA were chosen because by increasing the length of the substituent chain, the mobility of the polymer backbone chain and thus the T g can be changed. The polymers studied were poly(n-butyl methacrylate) (PnBMA) and poly(n-propyl methacrylate) (PnPMA). PnBMA has a T g below T R at 17 and is liquid-like at our experimental conditions. On the other hand, PnPMA is glassy because it has a T g above T R at 35. Figure 3.1 in Chapter 3 shows the molecular structure of these PnAMAs. Figure 4.16 shows the friction data for PDMS exhm lenses sliding on PnBMA and PnPMA surfaces in comparison to PS and PVNODC surfaces. Similar to the PDMS exhm /PS interface, the shear stress as a function of time at these interfaces has a stick-slip characteristic indicating an energy loss during sliding (Figure 4.16A) [183]. Due to the velocity limit of our friction apparatus, we have observed stick-slip sliding for PDMS exhm on PnAMAs at all velocities and recorded the maximum force just before slip to determine the shear stress [91]. Shear stress as a function of velocity is plotted in Figure 4.16B. At this velocity range, the values of shear stress do not depend on the velocity and are load independent. Surprisingly, PnBMA, PnPMA, and PS exhibit similar shear stresses regardless of the differences in their chemical structure and chain mobility. Therefore, these shear stresses are much higher than that at the PDMS exhm /PVNODC interface. 187

210 0.4 A. B. Shear Stress (MPa) Time (s) Velocity (microns/s) Figure 4.16: A) The shear stress as a function of time for PDMS exhm sliding on PnBMA (dark gray) and PnPMA (dark yellow) at a velocity of 3µm/s. The PnPMA data is shifted on the time axis for clarity. B) The shear stress during sliding plotted as a function of velocity for PDMS exhm sliding on PnBMA ( ) and PnPMA ( ). The shear stress behaviors of the PDMS exhm /PS (navy, ) and PVNODC (wine, ) interfaces are shown for comparison. 188

211 To correlate the friction behavior with adhesion, JKR experiments were performed with PDMS exhm lenses on PnBMA (Figure 4.17A and B) and PnPMA (Figure 4.17C and D). Figure 4.17A and C show the contact radius cubed, a 3, as a function of the applied load while Figure 4.17B and D show strain energy release rate, G, as a function of a. The G values from the loading data are 52-55mJ/m 2 for PDMS exhm /PnBMA and 54-57mJ/m 2 for PDMS exhm /PnPMA. The PDMS exhm /PnPMA interface has negligible adhesion hysteresis and thus G = W a at all times. However, the PDMS exhm /PnBMA interface exhibits a small amount of hysteresis with a G value of 60-65mJ/m 2 during unloading and thus G load G unload. As described in Section , a theoretical value of W a can be calculated assuming only dispersion forces (W a = 2(γ 1 γ 2 ) 0.5 ) when there is no hysteresis. The critical surface energies of PnBMA and PnPMA are calculated from the contact angles of various liquids (distilled-water, diiodomethane, and ethylene glycol) by the geometric mean equation as explained above for PDMS exhm, PVNODC, and PS. The average surface energies of PnBMA and PnPMA were found to be 32.5mJ/m 2 and 33.6mJ/m 2 respectively. These values are consistent with those reported in the literature [184]. Assuming only dispersion forces and using 21.7mJ/m 2 for the PDMS exhm surface, we predict W a 53.1mJ/m 2 for the PDMS/PnBMA and W a 54.0mJ/m 2 for the PDMS/PnPMA interfaces. The experimental W a values from the loading data are in good agreement with the theoretical predictions. There is an extra energy loss of 13mJ/m 2 at the PDMS exhm /PnBMA interface during unloading. Since friction 189

212 A. PnBMA 2 W UL =62.6mJ/m 2 B a 3 (m 3 x ) W L =51.7mJ/m 2 C. PnPMA W UL =56.5mJ/m 2 W L =55.4mJ/m 2 P (N x 10-3 ) D a (m x 10-4 ) G (mj/m 2 ) Figure 4.17: JKR plots of PDMS exhm on PnBMA ( ) and PnPMA ( ) during loading (open symbols) and unloading (filled symbols). A) and C) The contact radius cubed, a 3, as a function of applied load, B) and D) The strain energy release rate as a function of contact radius. 190

213 involves the separation of two surfaces and it is an energy dissipation process, the adhesion hysteresis has to be considered while correlating friction behavior with adhesion. The ratio of the G value measured for PDMS exhm /PnBMA (from unloading data) and PDMS exhm /PnPMA (either loading or unloading data) to the value for PDMS exhm /PVNODC is 1.3 and 1.2, respectively. This ratio is similar to that between PDMS exhm /PS and PDMS exhm /PVNODC interfaces ( 1.2) which is again much smaller than the ratio of the shear stress between PDMS exhm /PnBMA and PDMS exhm /PVNODC as well as PDMS exhm /PnPMA and PDMS exhm /PVNODC. We can conclude that neither adhesion nor the small amount of adhesion hysteresis at the PDMS exhm /PnBMA interface provides an explanation for the large difference in the shear stresses. The origin of the hysteresis observed at the PDMS exhm /PnBMA is not clear from the friction or adhesion measurements. At T R PnBMA is above its T g and the chains are highly mobile. Israelachvili and coworkers [61, 108] as well as Chaudhury and Owen [58] have argued that liquid-like surfaces can exhibit a small amount of hysteresis. According to Israelachvili and coworkers, the mobile chains at these liquid-like surfaces interpenetrate across the interface but relax fast in the time scale of the JKR experiments due to their low viscosity. Therefore, the penetration may cause a small amount of energy dissipation but not a significant one. The interpenetration mentioned by Israelachvili and coworkers is not surprising between similar surfaces. Luengo and coworkers [187] have also shown molecular-level interdiffusion/entanglement 191

214 processes between two PnBMA surfaces at their liquid-like state. However, in our system, PnBMA and PDMS exhm are not miscible and the mobile PDMS chains are held in place by the crosslinks preventing any entanglements. Therefore, an interdiffusion is not expected but based on the information we obtained from the PDMS exhm /PS interface it may happen at a local level. In order to understand the molecular origins of the friction and adhesion results, SFG experiments were performed for PnBMA and PnPMA surfaces. Figure 4.18 shows the SFG spectra in the SSP polarization (S-polarized SFG beam, S-polarized visible beam, P-polarized IR beam) at an incident angle of 42. At this incident angle the SFG spectra correspond to the polymer/air surfaces with little if any contribution from the polymer/sapphire interface. The interfacial area during contact and sliding is kept larger than the laser spot (d 1mm) to avoid any SFG signal contribution from outside the contact area. The bold symbols in Figure 4.18 correspond to the SFG spectra of the PnBMA (Figure 4.18A) and PnPMA (Figure 4.18B) surfaces before bringing them in contact with the PDMS exhm lens. The SFG spectra shown in black circles ( ) are measured during contact where the SFG intensity is weak due to the off-critical angle. The SFG spectra shown as open symbols are acquired after the PDMS exhm lens has slid across the contact spot. In Figure 4.18A, the PnBMA surface shows strong features of the C-H symmetric and fermi stretches of the ester butyl chain. These assignments are based on the vibrational spectra of the PnBMA bulk [188]. The methyl symmetric (r + ) 192

215 and asymmetric (r ) vibrations and the fermi (r + Fr ) resonance of the ester butyl side chain appear at 2880, 2960, and 2940cm 1 respectively. The ester methylene, CH 2, vibrations at 2855cm 1 for symmetric and at 2915cm 1 for asymmetric as well as the α-methyl vibrations at 2930cm 1 for symmetric and at 2990cm 1 for asymmetric are not observed at the surface. Based on these, the SFG spectrum indicates that at the PnBMA surface, the ester side chains are oriented towards the air probably due to surface energy and steric effects in agreement with previous studies [189]. As seen in Figure 4.18B, the SFG spectrum of the PnPMA surface is almost identical to that of the PnBMA surface. This demonstrates that the PnPMA surface is also abundant in ester side chains whose end methyl groups are located at the outermost layer. The comparison of the SFG spectra of the PnBMA surface before contact and after sliding indicates that either the surface molecules are not affected from sliding or the molecular changes that took place during sliding are reversible. On the other hand, the PnPMA surface exhibited profound irreversible changes in the orientation of the ester propyl chains. The intensity of the r + and r + Fr vibrations decreased significantly and the CH 2 vibrations which were absent at the surface emerged after sliding. This may indicate that the ester side chains are tilted away from the surface normal or developed gauge defects exposing the CH 2 groups at the surface. Such molecular restructuring will also cause contribution from the r vibrations to the SFG spectrum in the SSP polarization. However, the r peak cannot be resolved due to the broadness of the r + Fr peak. Since the overall intensity of the PnPMA surface spectrum 193

216 SFG Intensity (a. u.) A. PnBMA B. PnPMA before contact after before contact after Wavenumber (cm -1 ) Figure 4.18: A) SFG spectra in SSP polarization for PnBMA ( ) before contact, during contact ( ), and after the PVNODC surface has experienced sliding, B) SFG spectra in SSP polarization for PnPMA ( ) before contact, in contact ( ), and after the PS surface has experienced sliding. The solid and dashed lines are fits of the spectrum before and after sliding, respectively. 194

217 is weak, we could not acquire a spectrum with narrower wavenumber resolution (see Section 3.2). The contact interface is directly probed in situ using the incident angle of 12 for the PDMS exhm /PnBMa and the PDMS exhm /PnPMA interfaces. The bold symbols in Figures 4.19A and C correspond to the situation where the laser beam is superimposed with the contact spot (area) at the interface. The black circles ( ) correspond to the situation where the laser beam is positioned in front of the contact area and where the incident angle is far away from the critical angle for the PDMS exhm /polymer interface. Any spectral features observed at this state are a combination of signals from the polymer/sapphire interface and polymer surface. The open triangles (PDMS exhm /PnBMA) and open lozenge (PDMS exhm PnPMA) in Figures 4.19A and C correspond to the situation where the laser beam was first positioned in front of the contact spot and then the lens was slid pass through it with the desired speed. The SFG spectra were acquired after the lens was stopped and the laser spot was overlapped with the contact area once again. In this condition, we are probing the contact interface that has experienced sliding. The SFG spectra of the PDMS exhm /PnBMA (Figure 4.19A) and PDMS exhm /- PnPMA (Figure 4.19C) contact interfaces before sliding have features similar to those of the PnBMA and PnPMA surfaces. The two main peaks correspond to the vibrations of the terminal CH 3 groups of the ester side chains whose assignments are given above. The contributions from the CH 2 group of the same side chain and from the 195

218 300 A. PnBMA before ahead after B SFG Intensity (a. u.) C. PnPMA before ahead after D Wavenumber (cm -1 ) Time (sec) Figure 4.19: A) and C) show the SFG spectra in the SSP polarization for PDMS exhm /PnBMA ( ) and PDMS exhm /PnPMA ( ), respectively. The spectra were acquired during contact (bold symbols), when the laser beam is ahead of the contact spot ( ), and after sliding when the contact spot and the laser beam superimposed once again (open symbols). B) and D) are the plot of the SFG intensity as a function of time associated with the r + (black line) and r + Fr (gray line) of the methyl groups of the PnBMA (B) and PnPMA (D) ester side chains. The solid and dashed lines are fits of the spectrum before and after sliding, respectively. 196

219 α-methyl group are negligible. However, the intensity of r + Fr vibration relative to r+ is stronger at these interfaces than it is at the surface. The changes in the Fermi resonance can be attributed to the changes in the surface chemical environment due to the contact with the PDMS exhm. The SFG spectrum of the area ahead of the contact ( ) in Figures 4.13A and C) has features that are characteristics of both the PnBMA and PnPMA surfaces as well as interfaces with sapphire. Since there is no contact interface here, these spectral features are generated at an off critical angle [137,180]. The contributions from the Si (CH 3 ) 2 groups of the PDMS segments are expected at 2906 cm 1 (symmetric, r + PDMS ) and at 2962 cm 1 (asymmetric, r PDMS ). At these interfaces, the PDMS peaks are not resolved because they overlap with the higher intensity peaks of the methacrylate ester side chains. Based on these arguments, the structure of the PDMS exhm /PnBMA and PDMS exhm /PnPMA contact interfaces (before sliding) are similar to the PnBMA and PnPMA surfaces before contact. As explained before, it was not possible to acquire a complete spectrum during sliding and instead we have monitored the intensity of selected vibrations from the interface as a function of time (Figures 4.19B and D). Figure 4.19B shows the I PnBMA Symm I PnBMA Fr /I PnBMA Symm and IPnBMA Fr as a function of time. The ratio of the average intensities,, during slidin (at the plateau) is The same ratio is 0.97 and 0.85 for the PDMS exhm /PnBMA interface before and after sliding, respectively. The similarity between these three numbers indicate that there is very small difference, if any, in the spectral features of the PDMS exhm /PnBMA interface before contact, after 197

220 contact and during sliding. Consequently, we can argue that neither adhesion nor friction affects the molecular structure of PnBMA ester side chains as expected for a liquid-like surface. In the case of PDMS exhm /PnPMA interface, a peak ratio analysis can not be used to evaluate the molecular structure of the contact and sliding interface because the contact interface after sliding in Figure 4.19C shows the emergence of a strong CH 2 asymmetric peak. A similar behavior was observed at the PnPMA surface after sliding (Figures 4.18B). This is a clear evidence of an irreversible restructuring induced by the sliding of the PDMS exhm elastomer on the PnPMA surface. The same restructuring may be taking place at the PnBMA surface but due to the mobility of the surface groups it will not be observable in the time frame of the SFG experiments. So far, we have analyzed the SFG spectral features of the PDMS exhm /PnBMA and PDMS exhm /PnPMA interfaces upon contact and during sliding. The SFG signals are a function of both the number density and the average orientation of the molecules at the interface. Therefore, the SFG intensity can change while maintaining the same spectral features in the SFG spectra depending on the distribution of the surface molecules. In order to evaluate the SFG intensities, we can compare the SFG spectra of PDMS exhm /PnBMA with that of PnBMA surface as well as the SFG spectra of PDMS exhm /PnPMA with that of PnPMA surface. However, this would require the correction of the spectra in terms of different incident angles and refractive indices which involves various assumptions. 198

221 SFG Intensity (a.u.) A. PVNODC B. PnBMA C. PnPMA Wavenumber (cm -1 ) Figure 4.20: Comparison of the SFG intensity of the r + vibrations at incident angle of 12 (open symbols) for A) PDMS exhm /PVNODC, B) PDMS exhm /PnPMA, and C) PDMS exhm /PnPMA interfaces with that at incident angle of 42 (filled symbols). 199

222 Another way of analyzing the average molecular orientation is to take advantage of the SFG measurements at the PVNODC surface and PDMS exhm /PVNODC interface. We have already shown that the PVNODC side chains do not restructure upon mechanical contact with PDMS exhm lenses and PVNODC has a similar refractive index as PnBMA and PnPMA. Therefore, we have compared the SFG intensity of the methyl r + vibration of the side chains at two incident angles, 42 (filled symbols) for surface and 12 (open symbols) for PDMS exhm /PVNODC (Figure 4.20A), PDMS exhm /PnBMA (Figure 4.20B), and PDMS exhm /PnPMA (Figure 4.20C) interfaces. The SFG intensity is about three times weaker at 12 for the PDMS exhm /PVNODC interface than that at 42. This is due to the partial loss of the SFG output signal at this interface because the conditions are not ideal for the total internal reflection to take place. Mainly, the refractive index of PDMS exhm is only slightly less than that of PVNODC and thus some portion of the incident beams can penetrate through the interface. Based on this observation the intensity of the PnBMA and PnPMA r + peaks are expected to decrease by three times in the absence of restructuring. However, the SFG intensity at 12 for the PDMS exhm /PnBMA interface is nine times and for the PDMS exhm /PnPMA is six times lower than that at 42. This clearly indicates that there is a significant reduction in the average orientation of the methyl groups upon contact with the PDMS exhm surface. Similar to the PDMS exhm /PS interface, this change in orientation can be interpreted as a signature of local interdigitation. As a reminder, all three of these interfaces have 200

223 comparable friction and adhesion forces. Since the SFG spectra for the PnBMA surface before and after sliding are similar (Figure 4.12), the local interdigitation upon contact is reversible. On the other hand, the PnPMA surface exhibits irreversible restructuring upon sliding as evident from the emergence of the CH 2 asymmetric peak (Figure 4.19C and Figure 4.18B). Based on these observations, the molecular changes at the PnBMA and PnPMA surfaces upon contact and sliding are the origin of higher friction forces compared to that at the PDMS exhm /PVNODC interface. In conclusion, we have observed change in the orientation of the PnBMA and PnPMA methyl groups of the ester side chains similar to that of the PS phenyl groups. Therefore, this also indicates local interpenetration at the contact interface of PDMS exhm with liquid-like PnBMA and glassy PnPMA. The changes are reversible for PnBMA and irreversible for PnPMA. The friction and adhesion behaviors of PDMS exhm elastomer on PnBMA and PnPMA surfaces are similar to those on PS surface. Shortly, the interpenetration was not resolved by adhesion measurements and the shear stresses are a factor of four higher than that of PDMS exhm /PVNODC interface. This supports our hypothesis that regardless of the T g a local interpenetration exists at the contact interface of elastomers with glassy as well as liquid-like polymers which causes energy dissipation during sliding and is the reason behind higher friction forces compared to that on crystalline polymers. However, it is not clear at this point why the molecular changes of different polymer chains that have different chemical structure and chain mobility are affecting the shear stress values 201

224 in a similar fashion. If the interaction between the elastomer and polymer surfaces are originated from only van der Waals forces and the depth of penetration is similar, then the energy spent to pull the elastomer groups out of the local penetration may be similar resulting in comparable shear stresses. Then, a quantitative analysis of the PDMS exhm /PnBMA and PDMS exhm /PnPMA interfaces similar to that of the PDMS exhm /PS interface may provide a better explanation once an SFG spectra in SPS polarization can be obtained. It is also not clear why the changes in orientation of the PnPMA methyl groups are irreversible but those of the PS phenyl groups are reversible even though both are in a glassy state at T R. Characterizing the molecular structure of the elastomer contact interfaces with various other polymers may improve our understanding in this matter. Above all, the main unknown is the quantitative relation of molecular changes with friction and adhesion. We hope that these studies and more to come can be helpful in improving theories that can build this relationship. 4.3 Synthetic Gecko Foot-hairs from Multiwalled Carbon Nanotubes The mechanism that allows a gecko lizard to climb any vertical surface and hang from a ceiling with one toe has attracted considerable interest and awe for over two millennia. Recent studies have discovered that the gecko s ability to defy gravity comes from its remarkable feet and toes [148]. Each five-toed foot is covered with microscopic elastic hairs called setae. The ends of these hairs split into spatulas which 202

225 come in contact with the surface and cause enough intermolecular (van der Waals, (VdW)) forces to hold them in place. Similarly, the same VdW forces act between our two hands when held together but they do not stick to each other. The reason is that the roughness of our hands prevents them to come close to each other at separations relevant for VdW forces. On the other hand, based on the gecko s foot anatomy, if our hands were made up of elastic tiny structures that were able to deform or bend at different length scales in accordance with the contact surface and correct for the roughness then perhaps our hands could also adhere to surfaces we touch. This achievement is not far behind. There have been recent attempts to fabricate surface patterns with polymers to mimic the structure of setae and spatulas [152,153]. However, these synthetic systems are not comparable to nature s precision. The gecko s foot-hairs have the proper aspect ratio, thickness, stiffness, and structure to adhere to any type and shape of surface with enough density to provide high adhesion forces. Here, we report a novel structure based on multiwalled carbon nanotubes (MWNT) constructed on polymer surfaces with strong nanometer level adhesion that can serve as dry adhesives similar to or stronger than gecko foot-hairs. The first step of our approach involves the growth of micron MWNT on quartz or silicon substrates through chemical vapor deposition [190]. A gaseous mixture of ferrocene (0.3g) as a catalyst source and xylene (30mL) as a carbon source is heated to above 150 and passed over the substrate for 10 min which is heated to 800 in a quartz tube furnace. The MWNT grows selectively on the 203

226 oxide layer with controlled thickness and length. The oxide layer of the substrate can be patterned by photolithography followed by a combination of wet and/or dry etching in order to create various patterns of MWNT [191]. The scanning electron microscope (SEM) image of typical MWNT grown on silicon is shown in Figure 4.21a. These tubes are vertically aligned with a typical diameter of 10-20nm and length of 65 ñm. The samples, with the MWNT side facing up, are then gently dipped in a beaker containing methyl methacrylate monomer (60 ml) and were polymerized using a 2,2 -azobisisobutyronitrile initiator (0.17gr) and 1-decanethiol chain transfer agent (30 ñl) in a clean room. After the completion of polymerization in a water bath at 55 for 24h, the samples are taken out by breaking the beaker. The MWNT are completely embedded and stabilized in the PMMA matrix. The PMMA-MWNT sheets are peeled off from the silicon substrates forming a very smooth surface. The MWNT were exposed from the silicon-facing side of the PMMA matrix by etching the top 25 ñm with a good solvent (acetone or toluene) for 50 mins and subsequently washed with deionized water for 10 mins. The exposure length of the MWNT can be controlled by varying the solvent etching time. As a control, blank PMMA films prepared with the same procedure are etched with solvent and observed to maintain a very smooth surface. Figure 4.21b shows MWNT brushes on PMMA films. Any pattern [191] of MWNT on silicon can be exactly transferred on the top of the polymer surface. The brushes are mostly aligned vertically and in general forms into entangled 204

227 bundles ( 50 nm diameter) due to the solvent drying process. This creates surface roughness which in turn enhances the adhesion as shown below. Figure 4.21: Scanning electron microscope images of vertically aligned multiwalled carbon nanotube structures: (left) grown on silicon by chemical vapor deposition ( 65 ñm long), (right) transferred into PMMA matrix and then exposed on the surface ( 25 ñm) after solvent etching with a rate of 0.5 µm/min. The adhesive behavior of the MWNT brushes are measured with a Digital Instruments Nanoscope IIIa multimode scanning probe microscope (SPM). SPM has been used before as a powerful technique for measuring mechanical and interfacial properties of carbon nanotubes [ ]. Standard rectangular silicon probes (MikroMasch) with typical radius of curvature < 10 nm and spring constant of 3.5 N/m (with an accuracy of 10% according to manufacturer specifications) are used 205

228 in the measurements. Representative SPM images for vertically and horizontally aligned nanotubes are shown in Figures 4.22A and b, respectively. These are consistent with the SEM image in Figure 4.21B. Scans are performed at 0.5Hz scan rate and with tapping mode in order to prevent irreversible displacements and deformations. Force-distance curves are obtained between the brushes and silicon probe under ambient conditions where a hysteresis loop (pull-off) corresponds to adhesion forces and elastic properties [197]. A typical loading/unloading curve is given in Figure 4.22C. The curve shows weak repulsive forces upon approach and high adhesion upon retraction. The loading regime of the curve exhibits a change in slope 90nm (Figure 4.22C) after the probe makes contact with the surface of the brush sample. Considering the sparse structure of the topmost part and highly elastic nature of carbon nanotubes this complete length can be taken as an approximation for the maximum penetration depth. At the slope change the probe touches a denser part or compresses the bundles that are in contact. The penetration depth is different at different points on the brush surface due to the roughness mentioned before. The lowest penetration depth is observed when the nanotube bundles are aligned vertical and densely packed or lie flat on the surface, which also corresponds to the lowest adhesion forces (shown in Figures 4.22 B and D). On the other hand, higher depths and adhesion forces are observed where the bundles are disordered and entangled creating surface roughness and providing penetration space for the probe. In these rough regions the adhesion forces exhibits a larger distribution in pull-off forces due 206

229 TM Deflection (nm) C unloading loading Tip Displacement (nm) TM Deflection (nm) D Loading Unloading Tip Displacement (nm) TM Deflection (nm) E loading 0 unloading Tip Displacement (nm) Figure 4.22: Topography and force measurement of multiwalled carbon nanotube brushes on PMMA with scanning force microscope (SPM). A) and B) show real SPM height images taken by tapping mode for vertically and horizontally aligned MWNT, respectively. The bars represents 5 ñm and 150 nm, respectively. C) shows a typical deflection-versus-displacement curve during a step loading/unloading cycle with high hysteresis loop. The silicon probe on approach sticks to the nanotubes (triangle) and requires a pull-off force to detach the probe from the surface (filled circles), D) The deflection-versus-displacement curve from Figure 2b with negligible adhesion, and E) with double pull-offs. 207