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1 NANOTRIBOLOGY OF POLYMER BRUSHES INVESTIGATED BY ATOMIC FORCE MICROSCOPY By FRANCIS TED J. LIMPOCO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009
2 2009 Francis Ted J. Limpoco
3 These efforts are dedicated to the memory of Francisco dela Cruz Limpoco (1908-1987) Not papers, not final philosophica l declarations, but love. not intellectual survival, but the su rvival of love. ~Paul Feyerabend
4 ACKNOWLEDGMENTS This adventure would not have reached this moment of achievement without the guidance, friendship, and generosity of a host of people. I am indebted, first and foremost, to Prof. Scott Perry, for his expert advice and mentorship, for opening opportunities for sc ientific growth, and for providing a collegial setting that encourag ed exploration. He has maintained clarity of thought when things got muddled, and a sustaine d focus towards the goal. I would always find insight whenever I sought his counsel. I am grateful to past and present colleague s, from the Chemistry Department of the University of Houston where this work bega n, to the Materials Sc ience and Engineering Department of the University of Florida where it has come to fruition: to Ian Laboriante and Xiaoping Yan for sharing their expertise on AFM; to Tim Fulghum and Derek Patton for teaching this polymer physical chemist skills in organic synthesis; to Mike Brady and Joelle Payne who taught me more than what I had taught them. I would like to thank, in particular, Prof. Gobet Advincula at UH for his collaboration in preparing surface-grafted polymers, Prof. Nick Spencer at ETH-Zrich for his groups collaboration with th e PEG brush systems, and Dr. Ben Smith, Lori Clark, and Joni Nattiel for making my transition to UF much smoother. To friends who have become truly an interim family here in the United StatesKata Santos, Chris Jamison, Chaitanya Danda, Faith Minglana, Imee Martinez, Adam Bordelon, Ben Raterman, Josh Lowitz, Jane and Bruce Young, Cr is Dancel, Joey Orajay, Biko EvaristI owe the flavor and texture of what could easily have been a bland graduate students life. To my mentors at the Ateneo de Manila Universit yAchoot Cuyegkeng, Toby Dayrit, Erwin Enriquez, Dr. Chua, the late Dr. Kapauan and Fr. SchmittI owe nothing less than philosophia the love of wisdom, and the desire for scholarship.
5 My family here and in the Philippines has b een a constant source of support: Tita Teming and John, Tita Auring, Tita Paking, Tito Chila, Lo la Thelma, Joanna and Bo, and my special brother Ian, whose indomitable joy of life sustains me. Even so, my profoundest gratitude goes to Nanay and Tatay for giving me a firm foundation, the c onfidence of love, and their unwavering faith.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............14 CHAPTER 1 INTRODUCTION..................................................................................................................16 Friction, Adhesion, and Wear: A Historical Perspective........................................................16 Modern Toolkit for the Micr oscopic Study of Friction..........................................................18 Atomic Force Microscopy...............................................................................................19 Contact Mechanics of Single Asperities..........................................................................21 Surface Force Apparatus.................................................................................................23 Surface Science at Ultrahigh Vacuum.............................................................................24 Molecular Dynamics Simulations...................................................................................24 Boundary Lubrication........................................................................................................... ..25 Biomimetic Lubrication with Polymer Brushes.....................................................................27 Biolubrication................................................................................................................. .27 Aqueous Lubrication.......................................................................................................28 Polymer Brushes..............................................................................................................29 Motivation for the Study....................................................................................................... ..31 Subjects Addressed............................................................................................................. ....32 2 INSTRUMENTAL METHODS.............................................................................................35 Atomic Force Microscopy......................................................................................................35 AFM Assembly...............................................................................................................35 Force-Distance Plots........................................................................................................37 Lateral Signal Detection..................................................................................................46 Friction-Load Maps.........................................................................................................47 Force Calibration.............................................................................................................51 Quartz Crystal Microbalance..................................................................................................60 Equivalent Circuit Model................................................................................................60 Acoustic Reflectometry...................................................................................................63 Ellipsometry................................................................................................................... .........64 X-ray Photoelectron Spectroscopy.........................................................................................69 Binding Energies.............................................................................................................71 Spectral Features.............................................................................................................74 Quantitation................................................................................................................... ..78
7 3 POLY(L-LYSINE)graft -POLY(ETHYLENE GLYCOL) BRUSHES.................................83 Introduction................................................................................................................... ..........83 Experiments.................................................................................................................... ........86 Preparation of PLLg -PEG Copolymers.........................................................................86 Measurement of PLLg -PEG Adsorption on Silica.........................................................87 AFM Friction Force Measurements................................................................................88 Results........................................................................................................................ .............91 Influence of Duration of Polymer Deposition.................................................................91 Influence of Polymer Architecture..................................................................................94 Adsorbed Mass, Grafting Ratio, and Film Thickness.....................................................97 Discussion..................................................................................................................... ........100 Influence of Duration of Polymer Deposition...............................................................100 Influence of Polymer Architecture................................................................................101 Conclusion..................................................................................................................... .......107 4 POLYSTYRENE BRUSHES...............................................................................................108 Introduction................................................................................................................... ........108 Experiments.................................................................................................................... ......112 Synthesis of Azochlor osilane Initiator..........................................................................112 Surface-Initiated Polymeriza tion (SIP) of Styrene........................................................114 Characterization of Surface Modifications....................................................................116 AFM Normal and Lateral Force Measurements............................................................117 QCM Solvent Uptake Measurements............................................................................119 Results........................................................................................................................ ...........121 Surface Characterization by XPS Analysis...................................................................121 Ellipsometric Film Thickness Measurements...............................................................124 Solvent Uptake and Dissipation Monitoring.................................................................125 Friction Force Response and Brush Swelling/Collapse................................................128 Discussion..................................................................................................................... ........133 Conclusion..................................................................................................................... .......135 5 POLY(ETHYLENE IMINE)graft -POLY(ETHYLENE GLYCOL) BRUSHES...............136 Introduction................................................................................................................... ........136 Experiments.................................................................................................................... ......141 Preparation of Polymer Br ush-Coated Interfaces..........................................................141 AFM Normal and Lateral Force Measurements............................................................146 QCM Solvent Uptake Measurements............................................................................148 Results and Discussion.........................................................................................................149 Effect of Solvent on Friction and Normal Force Responses.........................................150 Effect of Solvent on th e Relative Mass Uptake.............................................................156 Backbone Architecture and Fr iction Response Hysteresis............................................160 Conclusion..................................................................................................................... .......165
8 6 CONCLUSIONS AND FUTURE DIRECTIONS...............................................................167 Recapitulation................................................................................................................. ......167 Lubricity and Fouling Resistance.........................................................................................171 Further Research............................................................................................................... ....174 LIST OF REFERENCES.............................................................................................................180 BIOGRAPHICAL SKETCH.......................................................................................................199
9 LIST OF TABLES Table page 3-1 Summary of data for the thr ee PEG chain length series of PLL( x )g [ y ]-PEG( x ), varying in lysine/P EG grafting ratios ( y ); x and z are PLL and PEG average molecular weights in kDa, respectively.............................................................................99 3-2 Wet brush thickness ( hfilm) compared with brush thickne ss calculated from scaling laws ( h = Na1/3)..............................................................................................................103 4-1 Normalized frequency ( f / f ) and bandwidth ( / f ) shifts of PS-modified and blank quartz crystals under various solvent environments........................................................127 5-1 Contact angles of a piece of silicon wafer taken after each step in the cleaning procedure...................................................................................................................... ....144 5-2 Normalized frequency ( f / f ) and bandwidth ( / f ) shifts of a quart z crystal resonator under various solvent environments befo re (Blank) and after (Polymer) the adsorption of PEIg -PEG, and their respective differences ( )....................................159 5-3 Wet mass of PEIg -PEG adsorbed on a quartz crys tal resonator under different solvent environments, calculated from the differences in observed frequency shifts for the solvent before and after the adsorption of PEIg -PEG.........................................159
10 LIST OF FIGURES Figure page 1-1 Friction force image (20 20 ) of a tungsten tip slidi ng on graphite showing atomic stick-slip..................................................................................................................... ........20 1-2 Plot of contact area versus normal loa d, plotted in non-dimensional units, of a purely elastic Hertzian contact, and adhesive elastic cont act regimesDMT to JKR.................22 1-3 Stribeck curve, showing the different l ubrication regimes in terms of the effect of lubricant viscosity (), rotational velocity (, i.e., for a journal bearing), and pressure ( p ).........................................................................................................................26 1-4 Grafted chains in a good solvent at (l eft) low graft density or the mushroom regime, and at (right) high graft density or the brush regime.........................................30 2-1 The AFM assembly using an 8-sector piezo electric tube scanner to generate motions in the x -, y -, and z -directions, and a beam-deflecti on method for the deflection and torsion sensing of the cantilever........................................................................................36 2-2 Attractive and repulsive interactions between the tip and the substrate cause the cantilever to deflect down and up, respec tively, as load is applied. Frictional interactions cause it to twist opposite the vector of the force............................................38 2-3 Cantilever deformations are detected by the position-sensitive photodetector from changes in the equilibrium position at the center of four quadrants..................................38 2-4 Examples of force-distance plots, showing the loading (dashed) and unloading (solid) traces................................................................................................................. ......40 2-5 Force-distance plot of a 5-m glass colloidal probe impinging upon a substrate consisting of poly(ethylene oxide)block -poly(butylene oxide) adsorbed on a octadecyltrichorosilane (OTS )-modified silicon wafer.....................................................45 2-6 Normal and lateral signal images genera ted by rastering the tip across the sample 500 nm from left to right (trace) and vice-versa (retrace), as load is applied and removed.....49 2-7 Friction loops obtained from slices of the lateral signal tr ace (upper) and retrace (lower) images of Fig. 26 at increasing loads...................................................................50 2-8 Difference image, processed from Fi g. 2-6, between the lateral trace and retrace scans represents the vertical widths of the friction loops (Fig. 2-7) and relates to the friction force................................................................................................................. ......52
11 2-9 Friction-load maps of (top) a 5-m silica probe sliding on a bare and polymer-coated (hydroxypropyl-guar gum, HGuar) silicon wa fer under liquid, and (bottom) a sharp Si3N4 tip sliding on silicon wafer and highly or iented pyrolitic graphite (HOPG) in air............................................................................................................................ ...........53 2-10 Parallel beam cantilever indicating the relevant geometric dimensions that are important in force calibrations...........................................................................................55 2-11 Beam-bending method for determini ng the normal load force constant...........................55 2-12 Thermal power spectrum of a cantilever rated with a normal spring constant of 0.58 N/m and a resonance frequency of 40-75 kHz...................................................................57 2-13 Friction loops on flat, inclined, and d eclined surfaces at a given applied load.................59 2-14 Section of quartz crysta l showing the thickness-shear m ode of vibration (left); the Butterworth-van-Dyke equivalent circuit for a quartz crysta l between electrodes (right)........................................................................................................................ .........61 2-15 Conductance spectrum of an unloaded qua rtz crystal showing a peak (red) at its fundamental resonance frequency of 12 MHz, corresponding to a minimum in both electrical and mechanical impedance.................................................................................61 2-16 Linearly polarized light interacting with a reflective surface becomes elliptically polarized...................................................................................................................... .......65 2-17 Reflection and transmission on a single interface between vac uum and a material characterized by a complex refractive index, 2...............................................................65 2-18 Multiple reflections and transmissions of light on a double interface with complex refractive indices, 1 and 2..............................................................................................68 2-19 The XPS instrumentation, consisting of: a load-lock that prepares the sample to be introduced into the UHV chamber, an X-ray source with either Al or Mg anodes, a single crystal quartz monochromator, electr on focusing lens system, a hemispherical electrostatic anayzer, and the detect ion and data processing system.................................70 2-20 Atomic processes involved in photoe mission illustrated in terms of energy level diagrams for a conductor (top) and an insulator (bottom).................................................72 2-21 The XPS survey spectrum of a silicon wafer after exposure to oxygen plasma, showing the principal spectral features..............................................................................75 2-22 Detail of the XPS survey spectrum of silicon wafer from 970 to 450 eV, showing the O 1s photoelectron peak at 533 eV, and the inelastic scattering peak that continuously tails for 954 eV.............................................................................................75
12 2-23 Detail of the XPS survey spectrum of silicon wafer from 200 to 0 eV, showing the chemical shifts in the Si 2s and 2p peak s due to photoelectrons coming from the native oxide layer (~1.4 nm thick) an d the underlying elemental silicon..........................77 2-24 Detail of the XPS survey spectrum of silicon wafer from 1400 to 900 eV, showing the O KLL Auger lines at 1013 eV (KL1L1), 999 eV (KL1L2,3), and 978 eV (KL2,3L2,3)..........................................................................................................................77 2-25 Survey spectrum of poly(methylmeth acrylate) (PMMA) brush on a silicon wafer showing the C and O photoel ectron and Auger peaks due to the polymer, and the much attenuated signal from the silicon substrate.............................................................80 3-1 Structure of a PLLg -PEG copolymer consisting of a poly(L-lysine) backbone and randomly grafted poly(ethylene glycol) side chains..........................................................84 3-2 The PLL-g-PEG adsorption on metal oxide surfaces........................................................84 3-3 The AFM instrumentation..................................................................................................89 3-4 Scanning electron microscopy (SEM) images of a 5-m glass probe on a 0.58 N/mrated V-shaped cantilever that is typi cally used in the AFM friction force measurements................................................................................................................... ..92 3-5 Influence of polymer deposition time on the tribological behavior of PLL-g-PEG brushes........................................................................................................................ .......93 3-6 Friction versus decreasing lo ad plots for three series of PLLg -PEG polymers: (A) PLL(20)g -PEG( 2 ), (B) PLL(20)g -PEG( 5 ), (C) PLL(20)g -PEG( 10 ); in each series, the polymers vary only in lysine/PEG grafting ratios........................................................95 3-7 Plot of coeffici ent of friction versus L /2 RF, estimated from Eq. 3-6 and 3-7................105 3-8 Plot of adsorbed mass of human serum versus L /2 RF of PLLg -PEG chains adsorbed on Nb2O5 surface..............................................................................................105 4-1. Interfacial friction as a function of d ecreasing load for the contact between an SiO2 substrate coated with PLL(20)g [3.5]-PEG(5) and a 5-m SiO2 probe in different solvent environments.......................................................................................................109 4-2. Scheme for the preparation of PS brush on Si wafer surface..........................................113 4-3 The 1H NMR spectra taken from crude sample s tracking the transformation of the AIBN-type azo initiator...................................................................................................115 4-4 The QCM set-up for impedance analysis of a quartz crystal resona tor, consisting of a network analyzer, test fixt ure, and liquid flow cell.........................................................120
13 4-5 Survey XPS spectra of si licon wafer after cleaning with O2 plasma (bottom), grafting of the azo initiator (middle) and surface-initiated polymer ization of styrene (top)........122 4-6 High-resolution XPS spectrum of (top) the N 1s region after grafting the azo initiator, showing the nitrogen chemical sh ifts of the azo and the cyano groups, and (bottom) the C 1s region after surface-ini tiated polymerization of styrene, showing the shake-up satellite peak near the C 1s photoelectron peak due to the styrene aromatic ring.................................................................................................................. ..123 4-7 Fractional shifts in frequency ( f / f ) and bandwidth ( / f ) of (top) a blank and (bottom) a PS brush-modified quart z crystal resonator under 2-propanol, n -butanol, and toluene.................................................................................................................... ...126 4-8 Friction force versus normal load between a 5-m SiO2 probe on PS brush-modified (117.6-nm thick) Si wafer, under 2-propanol, n -butanol, and toluene............................130 4-9 AFM force versus z -piezo displacement plots of a 5-m SiO2 probe affixed on a cantilever ( kN=0.58 N/m, nominal value) in cont act against a PS brush-modified (117.6-nm thick) Si wafe r under (A) 2-propanol, (B) n -butanol, and (C) toluene..........131 5-1 Structure of polycation backbones in PEG-grafted copolymer systems..........................137 5-2 Flocculation models of PEI stabilized co lloids at different PEI charge densities...........137 5-3 Structure of PEIg -PEG that is scaled down to 20% of the size used in this study; the relative size of the PEG chai ns with respect to the PE I backbone, however remains the same....................................................................................................................... ....142 5-4 Friction force response as a function of normal load between symmetric tribointerfaces consisting of polymer-coated silicon wafer substrate and silica probe...151 5-5 Conformational structure of PEG in water......................................................................153 5-6 Force versus z -piezo displacement plots, under different solvent environments, of a silicon wafer substrate against a glass collo idal probe that were both coated with PEIg -PEG.......................................................................................................................155 5-7 Fractional shifts in frequency ( f / f ) and bandwidth ( / f ) under methanol, ethanol, 2-propanol, and aqueous HEPES solution of a quartz crystal resonator before and after the in situ adsorption of PEIg -PEG........................................................................158 5-8 Tribological behavior of asymmetric tribointerfaces consisting of PEIg -PEG-coated silicon wafer substrate a nd a bare silica probe.................................................................161 6-1 Force-displacement plots of a 5-m glass colloidal probe against a PLL(20)g [3.2]PEG(5)-coated silicon wafer substrate at di fferent temperatures as compared to a bare silicon wafer substrat e at ambient temperature........................................................178
14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NANOTRIBOLOGY OF POLYMER BRUSHES INVESTIGATED BY ATOMIC FORCE MICROSCOPY By Francis Ted J. Limpoco May 2009 Chair: Scott S. Perry Major: Chemistry We investigated lateral and normal forces be tween polymer brush-modified substrates and a silica colloidal probe by atomic force microscopy (AFM). Copolymers consisting of poly(ethylene glycol) gr afted onto linear poly(L-lysine) (PLLg -PEG) or branched poly(ethylene imine) (PEIg -PEG) represent brush systems that can be immobilized onto the oxide layer of silicon at physiological pH. In previous studies, such oxide surfaces coated with molecularly thin PLLg -PEG films exhibited reduced friction at th e nanoand macro-scale levels versus the uncoated surfaces. Furthermore, the friction response was f ound to be highly dependent on duration of deposition, with the most signif icant reduction coinciding with the equilibration of coverage. Interfacial friction was also found to be a func tion of polymer architect ureof both PEG chain length and grafting ratio (i.e., the molar ratio of lysine monomer to PEG chain). Reduction in friction is observed with the increase in PEG ch ain length, as well as in the molar ratio of PEG chain to lysine monomer. These effects can be ra tionalized in terms of th e spatial packing density of PEG on the surface and its conse quent conformational structure. Polymer brushes also exhibit tr ibological properties strongly dependent on solvent quality, thus providing a way to tailor the lubricity of contacting surfaces. Substr ates coated with PEG-
15 grafted brushes, representing hydrophilic systems, exhibit friction response that systematically vary with solvent quality, with friction increasi ng as the polarity of the solvent decreases. The opposite was observed for polystyrene covale ntly tethered on silicon wafers by direct surface initiated polymerization, forming a dense hydrophobic brush. Higher friction response was observed on a polystyrene brus h under polar alcohol solvents, that becomes vanishingly low when the solvent is switched to toluene, a good solvent. Complementary solvent uptake measurements with a quartz crystal microbalan ce (QCM) show relatively greater mass loading and increased plasticity under toluene compared to the alco hols. In both the hydrophobic and hydrophilic cases, the solvent-driv en switch in the polymer conf ormation, from an extended to collapsed state, moderates the tribology of these polymer brush systems.
16 CHAPTER 1 INTRODUCTION Friction, Adhesion, and Wear : A Historical Perspective Mechanical systems necessarily rely on the tr ansmission of loads between surfaces that move (roll, slide, approach and separate normally ) relative to each other . Tangential motions between surfaces are almost always accompanied by friction a resistance to motionthat results in the loss of some part of the energy of motion; normal appr oach and separation of surfaces may manifest adhesion interactions. Generall y, at least one half of the moving interface involves a solid body such that its wear the progressive loss of materialalso accompanies the effects of friction. In mechanical systems, thes e contacting surfaces are therefore the critical points where failure is most likely to occur [2, 3] The engineering aim, then, is to ensure the efficient transfer of mechanical power and th e prevention of catastroph ic breakdown by methods that minimize energy (frictional) and material (wear) dissipation. Tribology was formally defined as a field of study when in 1964 a Lubrication Engineering Workgroup was formed in Britain to assess the p resent position of lubr ication education and research . From the ensuing report (1966) by H. P. Jost, the neologism tribology emerged (coined from the classical Greek word for rubb ing) to mean the sc ience and technology of interacting surfaces in relative motion and of related subjects and practices , and to represent a more cohesive approach to the multidisciplinary investigation of friction, wear, and lubrication. Although examples of technological means to ge t around friction stretch back to antiquity, its first quantitative treatment was by Leonardo da Vinci (1452-1519) whose massive Codex Atlanticus contains the bulk of his tri bological studies . He anticipa ted the laws of friction that we later attribute to Guillaume Amontons (1663-1705) for the paper De la Resistance Cause dans les Machines (1699) ; stated in modern form, th ese are: (1) the force of friction is
17 directly proportional to the applied load; (2) the force of friction is inde pendent of the apparent area of contact. Da Vinci also introduced the concept of the coefficient of friction ( ) as the ratio of the force of friction ( FL) to the normal load ( FN). FLFN (1-1) That da Vinci arrived at a general friction coe fficient (for polished smooth surfaces) of 1/4, while Amontons reported it as 1/3, is in hindsi ght intriguing, especially given that his notebooks were inaccessible unti l recent times . Amontons, and later Charles-Augustin Coul omb (1736-1806), gave a purely mechanical account of friction, ascribing it to the roughness of the contacting surfaces and the force required either to lift interlocking asperiti es over each other or to elastically deform these during sliding motion . The coefficient of friction, in the firs t case, for example, would then be related only to the space-averaged sl ope of the asperities ( tan ) , which typically fall within 0-20 . Coulomb, however, in Thorie des machines simples (1785), also included an adhesive term ( FA) in the first use of the two-term friction equation. F L F A F N (1-2) In his consideration of st atic and kinetic friction, he stated what is now considered the third law of friction: kinetic friction is independent of s liding velocity. Adhesion, ne vertheless, was mostly neglected, as its dependence on contact area co ntradicted the known la ws of friction, and a thermodynamic account of friction (i.e., in terms of energy losses) had to wait until the nature of the real area of contact and the interactions between microscopic as perities was elucidated . While there is a long history of research on friction, the subject of wear has not been tackled until recently. Aside from the systematic studies of da Vinci on the wear behavior of materials, the vast majority of scientific output has been after WWII . Da Vinci observed that
18 wear is proportional to the load, and follows the main vector of the load. This anticipates the empirical rule (c. 1950s) by J. F. Archard that the wear volume is directly proportional to the load and the sliding distance and inversely proporti onal to the hardness of the softer of the two interacting surfaces. This applies to both adhesive and abrasive types of wear, even with their different underlying processes; other wear mechanisms include fatigue erosion and corrosion Modern Toolkit for the Microscopic Study of Friction Surfaces are generally rough on the microscopi c scale such that contact between them occurs only at their asperities. The real area of contact can be several orders of magnitude smaller than the apparent (or projected) area of contact [7, 8]. F. P. Bowden and D. Tabor assumed that the lateral force (friction) is proportional to this real contact area ( A ) and the shear strength () . F L A (1-3) High stresses induced at such small contact po ints would cause plastic deformation of the asperities akin to a local hardne ss test; the asperities are co mpressed such that the area of contact and the normal force (l oad) is related by the scratc h hardness or yield stress (yield) of the softer material: A FN/ yield . Amontons law (Eq. 1-1) is t hus recovered, and the coefficient of friction ( / yield) expressed simply in terms of well-known mechanical properties of materials [4, 7]. Even before this plowing account of friction, G. A. Tomlinson in 1929 revived the adhesion concept, and considered dry, sliding fric tion in terms of energy dissipation within force fields between molecules of opposing surfaces; force is necessary to overcome molecular adhesion such that both normal and lateral fo rces would linearly depend on the number of interacting molecules [4, 7, 10]. Lack of knowledge, however, about details of surface
19 deformation and intermolecular forces precluded qua ntitative treatment, and thus this molecular account remained largely conceptual and empirical . Within the last two decades, the emergence of proximal probes which afforded the facility to investigate forces and deformations with mo lecular resolution, along wi th the recruitment of ultrahigh vacuum (UHV) techniques in surface sc ience to exquisitely ch aracterize tribological interfaces, and the improvement in computational capacity and methods to simulate tribological processes, signaled the advent of nano tribology, representing a more intense inquiry into the molecular origins of friction, w ear, and lubrication [6, 7, 11-16]. Atomic Force Microscopy Almost from its invention in 1986 , the potential of atomic force microscopy (AFM) for lateral force sensing was imme diately exploited . The first lateral force images (Fig. 1-1) obtained with a fine tungsten tip sliding on the ba sal plane of graphite showed atomic stick-slip behavior  predicted by the Tomlinson mode l [7, 10]. Typically, AFM uses a small stiff probe (the tip) affixed to the end of a comp liant cantilever [6, 14, 19]. Commercially available tips generally consist of either silicon or silicon nitride, passivated with native oxide, and with a radius of curvature of 10-100 nm; cantilevers are made from th e same material, with normal spring constants of 0.01-100 N/m , and coated with reflective material (usually gold) to enable the use of the optical-lever method for nor mal deflection sensing . At moderate loads of tens of nanonewtons, the contact area between a tip-substrate pair of commensurate stiffness (e.g., E 150 GPa, =0.24 for Si3N4) would be in the order of tens of nm2, exerting pressures in the gigapascal range ; this configuration therefore represents a suitable model for a singleasperity contact. Al ternatively, glass ( E 72 GPa, =0.3) microspheres of 1-10 m radii are also used as probes [6, 19], providing minimi zed pressures in the megapascal range and
20 Figure 1-1. Friction force image (20 20 ) of a tungsten tip slidi ng on graphite showing atomic stick-slip. Contrast illustrates differences in friction, with bright re presenting relatively high friction. This left-to-right scan al so exhibits the transition from static to kinetic friction from the bright, distorted section on the left to the darker, periodic section on the right, respectively. Reproduced from reference  by permission of The American Physical Society.
21 contact areas in the order of hundreds of nm2, for more delicate substrat es such as organic thin films, polymers, and biological samples. Contact Mechanics of Single Asperities Bowden-Tabor theory assumes a direct re lationship between load and contact area ( A F N) that is inconsistent with the Hertzian continuum model for pur ely elastic contacting spheres (A FN 2/3) . Moreover, at small scales, e.g., si ngle asperities or AFM tips, the surfaceto-bulk ratio becomes significant such that adhesion due to attr active surface forces cannot be neglected and must be included in descriptions of the contact area . There are two limiting cases depending on the spatial range over which adhe sive forces take effect with respect to the range of elastic deformation. For strong adhesion, compliant materi als, and large tip radii, the contact area is described by the Johnson-Kendall-Roberts (J KR) model [14, 22]. The opposite limitweak adhesion, stiff materials, and sma ll tip radiiis described by the DerjarguinMller-Toporov (DMT) model [14, 23]. The more general Maugis-Dugdale (MD) model defines a transition parameter (3 / 2*) / ( E ) describing intermediate behavior between the DMT-toJKR limits (0.1 5) in terms of the ratio of the work of adhesion (surface energy per unit area, ) and the reduced elastic modulus ( E* ) of the contacting pair [21, 24, 25]. In practice, the Carpick-Ogletree-Salmeron (COS) transition parameter (0 1), an empirical approximation of the MD solution, can be used to fit measuremen ts of contact area and/ or friction as a function of normal load (Fig. 1-2) [21, 26]. Adhesion effectively increases the contact ar ea depending on whether the attractive force is short-range (JKR) or long-range (DMT ), giving rise to finite frictional interactions even at zero or negative normal loads. An assumption in th e application of these continuum models to
22 Figure 1-2. Plot of contact area versus normal lo ad, plotted in non-dimens ional units, of a purely elastic Hertzian contact, and adhesive el astic contact regimesDMT to JKR. The latter approaches the Hertz case in the limit y 0 (zero adhesion). Adapted from reference .
23 nanometer-scale single-asperity cont acts is the direct proportionality of friction and contact area, where shear strength is a consta nt independent of pressure (E q. 1-3) . Fundamentally, continuum mechanics represent the displacement of materials as c ontinuous (blurred) variations in strain fields, related to the internal stre ss simply by the bulk elastic modulus. Molecular simulations of atomically smooth (crystallin e), rough (amorphous), and terraced tips show profound differences in pressure distributi onsthe latter two e xhibiting discontinuous behaviorand suggest that contact areas and yi eld stresses are underestimated, while friction and contact stiffness are overestimated by contin uum theory . Friction between an AFM tip sliding on self-assembled monolayers (SAMs) al so manifests an atypi cal superlinear (vs. sublinear, Fig. 1-2) dependence on load that canno t be fit to any continuu m model, arising partly from the nonlinear stiffening of mo lecules comprising the SAMs . Surface Force Apparatus Surface force apparatus (SFA), developed in th e early 1970s, has been used extensively to measure normal forces  between two atomica lly smooth, curved mica sheets as a function of their separation in both ambient [29, 30] and liquid environments . In the late 1980s, an added lateral sliding mechanism also allowed th e measurement of shear forces under controlled compression/tension [22-34]. This tribo-SFA has been used to investigate friction and phase transitions in confined liquids (e.g., hydro carbon lubricants, surfactants, polymers) under boundary conditions [35-37] yielding insight into molecular mechanisms of boundary lubrication [38, 39]. The radius of curvature of the conf ining surfaces is typical ly 0.2-2 cm, while the maximum pressures at the contact area normally do not exceed 0.1 GPa . While the SFA has normal resolution in molecular dimensions, lateral resolution is on the order of micrometers; furthermore, the requirement for molecular smoothness limits the substrate material to mica .
24 Surface Science at Ultrahigh Vacuum An inherent difficulty in tribological resear ch, whether on the macro or micro scale, is that the object of study is always hiddenit is buried in the inters tices of the contact. Structural and compositional characterization of the interf ace can therefore be done only before and after sliding events. UHV (~10-10 Torr) methods developed in the 1960s to study surfaces , such as low-energy electron diffracti on (LEED) and X-ray photoelectron spectroscopy (XPS) [42-44], for example, have the ability to selectively interrogate only the very topmost layer (e.g., 2-5 nm deep) of atoms, providing surface specific in formation, respectively, on structure and composition. UHV environments also provide the ab ility to prepare surfaces with well-defined structures (via sputtering and annealing) and adsorbate coverage s (via dosing), and to maintain these in clean (or essentially an absence of ) atmosphere . Furthermore, tribological measurements under UHV (e.g., UHV-AFM) repr esent fundamental data that inform experimental investigations in realwe tting, passivating, corrosive, heterogeneous environments. Molecular Dynamics Simulations Complementing these developments in experi mental tools are adva nces in theoretical modeling of physical and chemical processes invo lved in friction. Growth in computing power enabled the simulation of elaborate systems cons isting of a multitude of discrete parts and degrees of freedom, asymmetries, nonlinearitie s, and complex intera ction potentials . Furthermore, friction generates heat: it is an i rreversible process not tractable to classical thermodynamic treatment [16, 46]. Molecular dynamics (MD) simu lations can follow the spatial and temporal evolution of such intricate systems with refined resolution by the direct numerical solution of the (quantum or classical) equations of motion . Video animation of particle trajectories permit us to virtually see what is happening in the buried sliding interface with
25 nanometer and femtosecond detail, revealing mo des of excitation and pathways of energy dissipation [11, 16]. Boundary Lubrication Interactions of load-bearing su rfaces are manifested macrosc opically as friction and wear. Lubrication is the process of re ducing friction and wear by the interposition of materials that modify the interaction between these load-bear ing surfaces [2, 47]. The main functions of a lubricant are: (1) to physically separate surfaces by in terposing a coherent, viscous film between them, and (2) to chemically modify the surface by a thin protective coating so that when solidsolid contact does occur, the formation of adhesi ve junctions between the underlying surfaces is minimized . Different operational regimes de pend on the minimum thickness of the lubricant film (hmin) relative to the heights of the surf ace asperities (root-mean-square roughness, Rq) of the contacting pair, or the ratio: hmin/ Rq1 2 Rq2 2 The most important development in tribology during the Industrial Revolution was the mathematical theory of fluid-film lubrication culminating in the work of O. Reynolds in 1886 that related the film thickness ( h0) to the lubricant viscosity (), pressure or load ( p ), and the relative velocity of the bearing surfaces ( U ) . Regimes of lubrication can thus be consid ered in terms of increasing severity of surface interactions as lubricant thickness decreases, and can be evaluated from the Stribeck curve (1902)a plot of the coefficien t of friction as a function of h0 U / p (Fig. 1-3) [3, 4, 48, 49]. In the hydrodynamic regime (A, Fig. 1-3), there is no contact between th e bearing surfaces as they are completely separated by a thin fluid film ( 5) [2, 3, 48, 49]. Effects of surface roughness become negligible, and the only resist ance to tangential motion is due to viscous losses in the lubricant. For a fluid with Newton ian rheology, the coefficient of friction would thus be related directly to its viscosity. As lubricant thickness decreases with higher pressures
26 Figure 1-3. Stribeck curve, show ing the different lubrication regi mes in terms of the effect of lubricant viscosity (), rotational velocity (, i.e., for a journal bearing), and pressure ( p ). See the text for the explanation of th e points A, B, C, and D on the curve. Adapted from reference .
27 and/or lower sliding velocities, mechanical interactions between surface asperities become prominent (1 5); traction is still mitigated by the bulk viscosity, but also by the elastic flattening of surface profiles [2, 3, 48, 49]. This mixed regime (A-B, Fig. 1-3) includes both this elasto-hydrodynamic (EHD) situ ation and the transition to bo undary lubrication. In the boundary regime (B-C or B-D, Fig. 1-3), the lubricant film is reduced to molecularly thin layers ( 1) that are only 1% of the mean rms height of the asperities. There is thus more extensive solidsolid contact leading to wear from the breaking of adhesive junctions and the plastic deformation of asperities , to higher coefficients of frictiontwo orders of magnitude more than the hydrodynamic minimum , and to the eventual breakdown of lubrica tion (scuffing). What governs lubrication in this regime is not bulk pr operties such as density nor viscosity, but the chemical composition of the boundary film and the substrate . This opens up the possibility of tailoring the chemistry, and thus th e lubricity, of th e tribointerface. Biomimetic Lubrication with Polymer Brushes Biolubrication Physiological tribosystems such as human di arthrodial joints exhibit strikingly low coefficients of friction. Bones that transmit lo ads have enlarged ends that form the bearing surfacethe shoulders and hips being spherical, while the elbows and knees, cylindrical contacts [3, 47, 50]. These bearing surf aces are overlaid with soft por ous articular cartilage a few millimeters thick and kept separated by a thin film of synovial fluid. This surface is considered rough by engineering norms (~1 m asperity heights), the synovial fluid only marginally more viscous than water, and the typical operationa l velocities low [3, 47, 50]. We would therefore expect high friction and wear, but actual ly observe low friction coefficients ( 0.001) even by hydrodynamic standards [3, 47, 50]. Moreover, thes e joints are expected to perform effectively
28 under high loads, at generally low sliding speeds for seventy to eighty years . Engineers looking at articular joints ex plain their remarkable performa nce by invoking a squeeze-film mechanism coupled with the elastic flatte ning of the compliant asperities [2, 3]. Aqueous Lubrication Another striking feature of physiological tribosystems is their reliance on aqueous lubrication , in contrast to the oiliness or lubricity requ ired by W. B. Hardy [3, 4] for boundary lubrication. Water has excellent heat tran sfer properties due to its high specific heat capacity, but has a low pressure -coefficient of viscosity ( in 0e p), which severely impairs its load-bearing capacity, especially in the EHD re gime . Despite this, water may be retained on the articular surface through lubricating glycopro teins with brush-like structures. Synovial fluid consists mainly of water and, among othe rs, hyaluronic acid and mi nor protein components such as lubricin (LGP-I) and superficial zo ne protein (SZP) ; hyaluronic acid, a polysaccharide, at the least imparts viscosity to the medium , while the glycoproteins are implicated in boundary lubrication . These m ucin-like proteins consist of a polypeptide backbone with anionic oligosaccharide side chains (bristles) that account for their extensive retention of water. Furthermore, brush-like pr oteoglycan aggregates are also embedded in the collagen fibers of cartilage forming a comple x fiber-reinforced composite, imparting it compressive stiffness from the drag of flui d expressed through ngs trm-sized pores, and enabling it active participation in it s own lubrication, e.g., in theo ries of weeping or boosted mechanisms [47, 50]. The resistance of water from being squeezed out of these brush-like molecules is therefore important in both the mechanical and tribological propert ies of articulating joints; they make aqueous lubrication possible despite the pre ssure-viscosity limitations of water. This idea
29 is invoked in devising analogous (b iomimetic) lubrication mechanisms for engineering systems, and informs the study of the solv ent-dependence of friction on synthetic polymer brush systems. Polymer Brushes Surfaces modified with physically and chemical ly grafted polymer brushes are predicted to exhibit novel properties in terms of their adhesion, lubrication, viscoelast icity, and wettability [54-60]. Moreover, complex architectures can be achieved which lead to exquisitely tailored surfaces that are responsive to their environmen t [61, 62], including solvent switchable diblock [63-68] and mixed brushes [69-78], nanopatterne d brushes from lithographic techniques [79-83] vertically segregated brushes [84, 85], Y-sh aped amphiphilic brushes [86, 87], and surfaceattached dendrimers with tunable in terfacial friction properties . The term polymer brush denotes chains of macromolecule s attached on a surface with only one or a few anchor points, and at high grafting densities, such that the chains are crowded and extend away from the surface . Such densely tethered polymers on surfaces are predicted to be highly extended in a good solvent and have been considered as novel boundary layer lubricants [89, 90]. In such systems, strong co mpression would tend to increase osmotic pressure within the brush, resulting in a tendency for th e chains to swell back and extend, effectively manifesting a repulsive interac tion and low friction [91, 92]. For a real chain following the statistics of a self-avoiding ra ndom walk, the Flory radius (RF) for the rms end-to-end distance in a dilute soluti on (assuming a good solvent) scales with the degree of polymerization (N) as RF aN (1-4) where a is the statistical segment length (e.g., monomer size) and is the size exponent in d dimensions (1 d 4): 3/(2d ). For example, in three dimensions, RFaN3/5 [93-95].
30 Figure 1-4. Grafted chains in a good solvent at (left) low graft de nsity or the mushroom regime, and at (right) high graft density or the b rush regime. Adapted from reference .
31 For chains anchored on a surface, the dist ance between graft points is defined as La 1/2 (1-5) where is the grafting density or th e fraction of grafted sites ( a2/ L2, 0 1). When 1 (maximum coverage), La, i.e., the shortest possible dist ance between graft points is the segment length. The conformation of a polymer brush is the result of a balance be tween the entropy of mixing which tends to swell the grafted chains, and elastic restoring forces which limit the swelling [90, 91, 95-97]. At low grafting density, th e distance between two anchor sites must be larger than the Flory radius [90, 91]. The power law for grafting density is therefore N 6/5; the polymer brush is mushroom-like with dime nsions close to the Flory radius or a free polymer in a dilute solution (Fig 1-4). At high grafting density ( 1or N 6/5), the distance between anchor points is much less than the Flory radius; the coils overlap and the polymer begins to extend [90, 91]. Onset of chain extension at N 6/5 represents the inception of the brush regime; the polymer can be view ed as a liner string of blobs (hard spheres) extending along normal to the wall, with the brus h height scaling more strongly with the degree of polymerization [90, 91]. h Na 1/3 (1-6) Motivation for the Study Nano-scale tribological investigation of polym er brushes is interesting in itself as a fundamental study of the nature of friction forces under boundary lubr ication conditions. Brush-like configurations of macromolecules attached to surf aces represent a model system where effects such as grafting density and solven t quality on the lubricity can be systematically characterized.
32 Problems of friction (where it is not wanted) and wear are al so pervasive technological and economic concerns, and become even more acu te under boundary conditions. Investigating the performance of relevant bearing surfaces (e.g., metal oxides) with physically and chemically attached polymer coatings contribute to the technological means of mitigating energy and material losses due to friction and wear. The grow ing trend towards device mi niaturization, as in the case of microelectromechanical systems (M EMS) , calls for novel boundary lubrication mechanisms as surface effects overtake volumetric effects as these devices continue to scale down in size. Aqueous boundary lubrication, made possible with polymer s possessing polar or ionic functionalities, may eventually find uses in the biomedical and food industries where biocompatibility and green technology are impor tant , and where these may be more appropriate than traditional oilbased lubricants [99, 100]; in th e case of poly(ethylene glycol), tribology could even be intimat ely linked with fouling resist ance . Finally, controlled techniques of direct polymerization on surfaces [102-105] open up the way to exquisitely tune the tribological properties of these surfaces or to create smart surfaces that adaptively respond to their changing environment. Subjects Addressed This dissertation reports the systematic inves tigation of lateral and normal forces between polymer brush-modified substrates and a silica colloidal probe by AFM. Molecularly thin films of polymer brushes were prepared and probed at velocities, forces, and length scales under boundary conditions employed in AFM. Frictional forces were continuously measured as a function of load as a feature of the tribol ogical system (e.g., polymer architecture or environmental conditions) was systematically adjusted. Furthermore, in order to make valid comparisons, the same tip/cantilever assembly was used in each case.
33 Copolymers consisting of poly(ethyleneg lycol) grafted onto linear poly(L-lysine) (PLL-gPEG) or branched poly(ethyleneimine) (PEI-g-PEG) represent brush systems that can be immobilized onto the oxide layer of silicon at physiological pH. In previous studies, such oxide surfaces coated with PLL-g-PEG films exhibited reduced fric tion at the nanoand macro-scale levels as compared to the uncoated surfaces [51, 106-108]. In Chapter 3, the friction response of PLL-g-PEG was further investigated as a function of the duration of deposition and of polymer architecture, i.e., of both PEG chain lengt h and grafting ratio (the molar ratio of L-lysine monomer to PEG chain). These effects were ration alized, using a scaling argument, in terms of the spatial packing density of PE G on the surface and its conse quent conformational structure. Polymer brushes also exhibit tr ibological properties strongly dependent on solvent quality, thus providing a way to tailor the lubricity of contacting surfaces. Substrates coated with PEGgrafted brushes, representing hydrophilic systems, have been known to exhibit friction response that systematically vary with solvent quality, with friction increasing as the polarity of the solvent decreases [92, 109, 110]. These results are complemented in Chapter 4 by demonstrating a similar general behavior: the increase in lubricity of a hydrophobic brush, this time, in a nonpolar solvent environment . Polystyr ene (PS) brushes were prepared on oxidepassivated silicon wafers by surface initiated poly merization; an azo-type free radical initiator was silanized and immobilized onto silicon wafe rs on which polystyrene was directly grown. Formation of the initiator film, and, subsequent ly, the polymer brush on the surface were tracked by XPS and by ellipsometry. Fricti on response of PS brushes were measured as a function of solvent environments exchanged in situ. Complementary solvent exchange measurements were performed with the quartz crys tal microbalance (QCM) with a PS brush modified-resonator to monitor relative mass uptake and dissipation.
34 PEI is an amino analogue of PEG, which, due to the tri-valence of nitrogen, is highly branched; this represents an alternative backbone architecture to PLL in PEG-grafted systems. In Chapter 5, the tribological behavior of the PEI-g-PEG system was characterized, using complementary AFM and QCM methods, to investig ate the influence of so lvent quality and of its branched architecture w ith respect to the linear PLL-g-PEG system. The main theme of this study addresses how the tribology of polymer brushes originates from the conformational changes driven by solvent-segm ent interactions (i n both hydrophilic and hydrophobic cases), and the architect ural features that dictate the organization and packing density of chains on the surface.
35 CHAPTER 2 INSTRUMENTAL METHODS Atomic Force Microscopy Atomic force microscopy (AFM) uses a tip/ cantilever assembly to probe the forces between an ultrafine tip and a sa mple substrate. It can track t opographic features by maintaining a constant repulsive force between the tip a nd sample during scanning by monitoring the normal deflection of the cantilever. The cantilever bends vertically in response to attractive and/or repulsive forces acting on the tip, with deflection from its equilibrium position being proportional to the normal load. Lateral forces ca n also be detected by m onitoring the twisting of the cantilever from its equilibrium position. The amount of torsion represents frictional force acting on the tip as it slides along the sample surface. Normal and lateral signals are monitored si multaneously by the AFM detection system so that load and friction data can be collected together in the form of a friction-load map [19, 112]. This provides information on the load dependence of friction that is central to the use of AFM in tribological research . This section describes the experiment al method and technical aspects of generating friction-load maps by AFM. AFM Assembly One possible AFM configuration consists of a sample sitting on a piezoelectric tube that permits it to be moved relative to a fixed tip pos ition (Fig. 2-1). For example, the tube can be sectioned into eight sectors: the t op four sectors for scanning in the x and y directions (+x, x, +y, y), the bottom four for offsetting the same. Wh en the scanning sectors all receive the same voltage, the tube will elo ngate or contract providi ng a scanning motion in the z direction; the inside of the tube may be used for the z-offset.
36 Figure 2-1. The AFM assembly usi ng an 8-sector piezoelectric tube scanner to generate motions in the x-, y-, and z-directions, and a beam-deflecti on method for the deflection and torsion sensing of the cantilever.
37 Forces at the tip and sample interface are detected using an optical beam-deflection method. A laser beam is reflected from the back of a flexible cantilever on which the probe is affixed, and focused onto a position-sensitive four-quadrant photodiode Local attractive and repulsive forces between the tip and the sample would cause the cantile ver to bend; frictional forces would cause it to twist (Fig. 2-2). The lase r beam acts as an optical (infinitely stiff) lever converting the small deflection/tors ional angles of the cantilever into measurable displacements of the spot location on the photodetector. Photodetector design enables the separate de tection of the normal deflection and lateral torsion of the cantilever, accomplished through th e simultaneous measurement of the reflected light intensity on all four quadran ts (Fig. 2-3). Normal signal (SN) is the net difference in photodiode voltage signal between th e top (T) and bottom (B) quadrants, S N ( S TL S TR) ( S BL S BR) (2-1) while the lateral signal (SL) is the net difference between the left (L) and right (R) quadrants, S L ( S TL S BL) ( S TR S BR). (2-2) Photodetector sensitivity (in units of V/m), obtained from the careful calibration of the piezo motions, and the cantilever force constants (in units of N/m) converts the voltage signals SN and SL into the corresponding force units. Force-Distance Plots Force-distance plots [113, 114] are obtained by monitoring the cantile ver normal deflection as the substrate is moved towards the fixed tip until contact is achieved, and then moved back until the tip detaches from the substrate. Th is is accomplished by modulating the scanning sectors of the piezoelectric tube simultaneously with a triangular vol tage in order to generate the vertical approach (positive voltage ramp) and retract (negative voltage ramp) motions. Initial
38 Figure 2-2. Attractive and repulsi ve interactions between the tip and the substrate cause the cantilever to deflect down and up, respectiv ely, as load is applied. Frictional interactions cause it to twist opposite the vector of the force. Figure 2-3. Cantilever deformations are detect ed by the position-sensi tive photodetector from changes in the equilibrium position at the cent er of four quadrants : top-left (TL), topright (TR), bottom-left (BL), bottom-right ( BR). Normal deflection is detected from the difference in signals of the top two a nd bottom two quadrants; torsion is detected from the difference in signals of the left two and right two quadrants. Slight rotation of the detector results in the coupling of SN and SL, which manifests in a non-zero SL during normal deflections.
39 z-position may be adjusted with the z-offset signal; the range of the distance traversed may be set by the application of a scaling factor to the modulating voltage. Measurement starts at a distance where ther e is no interaction be tween the tip and the substrate (Fig. 2-4A). Cantilever deflection is at its equilibrium positi on and the force-distance plot should be flat and zero, ex cept, that is, for the presence of artifacts. Under dry conditions, dielectric samples may develop unwanted electrost atic charge that may necessitate its grounding to remove the tip/sample bias. Oscillation may al so be observed in reflective samples (e.g., Si, Au, HOPG) due to the interference of the laser beam on the cantilever with its spill-over on the sample. This is easily confirmed for its waveleng th should relate to that of the laser and the refractive index of the medium ( oscillation laser/2 nmediu m ), and minimized by keeping the cantilever at a small angle [115, 116]. Finally, hydrodynamic drag may cause an offset in the zero-deflection part of the force-distance pl ot; this can be corrected by reducing the approach/retract velocities . As the tip/sample separation decreases during approach, attractive forces between them develop and register as a nega tive deflection (or bending down) of the cantilever; in the absence of surface charge, this force is due to van de r Waals interactions a nd has a characteristic distance-dependence ( r 6) [113, 114, 117, 118]. When the attr active force gradient exceeds the cantilever spring constant, inst ability causes an abrupt jump -to-contact [14, 113, 114]. Long-range repulsive forces are also observe d especially under wa ter due to its high dielectric constant [113, 114] (Fig 2-4C). This registers as a positive deflection (or bending up) of the cantilever, which may be overlayed with the van der Waals snap-in in the force-distance curve, or completely mask it . Surfaces under water are usually charged due to the ionization of acidic/basic groups or the adsorption of ions from solution; furthermore, the
40 (A) (B) Figure 2-4. Examples of force-di stance plots, showing the loadi ng (dashed) and unloading (solid) traces: (A) typical plot in air, showi ng jump-to-contact and adhesion/capillary hysteresis; (B) the same plot, but showing pi ezo hysteresis; (C) typi cal plot in water, showing long-range repulsion; (D) unloading plots of a rigid versus deformable surface; (E) typical plot on polymer co ated surface under liquid. Adapted from references [115-118].
41 (C) (D) Figure 2-4. Continued.
42 (E) Figure 2-4. Continued.
43 charging is balanced by an atmosphere of count erions of equal and opposite charge, forming an electrostatic double-layer. This electrostati c field decays exponen tially with distance (e r), and is screened in solutions of hi gh ionic strength, as described by the Derjarguin-Landau-VerweyOverbeek (DLVO) theory [113, 114, 119]. In addition short-range non-DLVO repulsive forces may also be observed near (1-3 nm) the surface associated with dehydration and changes in water structure (hydrogen-bonding network) in th e vicinity of charged surfaces [113, 114, 117]. In the contact regime, very strong repulsive forces ( r 12, due to Pauli exclusion) between electrons of the atoms of the tip and the substr ate dominate . If th e material is rigid, deformation will be negligible, and the amount of deflection will be linea r with respect to the piezo displacement; the slope of this region of the force-di stance curve corresponds to the stiffness or normal spring constant of the cantilever, according to Hookes Law. kN FN d (2-3) If significant deformation occurs, usually on the sample, the amount of deflection as the load is increased is also governed by the contact mechan ics (Hertz, JKR, DMT, Chapter 1) between the tip and the substrate  (Fig. 2-4D). During retraction, the cantilever deflection foll ows the reverse of the approach trace for an elastic contact; hysteresis would be observed if indentation occurs due to plastic deformation [120, 121]. In addition, for open-loop systems, where the piezo displacement is not tracked by feedback control, hysteresis woul d also be observed as an artif act due to the lag in the piezo response as the modulating voltage is reversed (Fig. 2-4B). After the cantilever returns to its equilib rium position (zero deflection), the tip may continue to adhere onto the s ubstrate even with sustained re traction (or the application of negative load) due to adhesive forces. This regist ers, again, as a negative cantilever deflection
44 an adhesion hysteresisusually much larger than the snap-in deflecti on [113, 114, 116]. When the pull-off force overcomes the adhesive intera ction, the tip detaches from the substrate, and the cantilever jumps back to its equilibrium position; this pull-off force is related to the work of adhesion of the tip/substr ate junction [113, 114]. Surfaces in air are usually also coated by an ul trathin film of water that contributes a much larger capillary component to the pull-off force. This is of course removed when working under water, except when adventitious hydrocarbons, this time, form the meniscus between the tip and substrate . Finally, surfaces coated with poly mers or decorated with binding sites manifest characteristic features that ar e consistent with stepwise disent anglement of polymer chains (at large retraction distances, Fig. 24E) or detachment of specific binding sites between the tip and substrate [122, 123]. As an example, Fig. 2-5 shows the normal load as a function of sepa ration distance in an aqueous buffered medium between a glass colloidal probe and a substrate consisting of a block copolymer adsorbed on an alkylsilane-modified s ilicon wafer. Contact point (zero separation) is taken to be the point of zero normal load (or zero deflection) after the initial snap-in, as in Fig. 24A. The plot illustrates the different interaction regimes between the probe and substrate as they are brought into contact (dashed curve) and then separated (solid curve): the instability snap-in when van der Waals attractive forces overcome the cantilever spring constant (see inset); plastic deformation of the polymer/OTS film; elastic contact with the stiff silicon wafer substrate; enormous adhesion forces between the probe and the alkylsilane SAMs, which is absent when the the same block copolymer is coated on a ba re silicon wafer substrate; extended polymer bridging at very long separation distances. This example demons trates the rich information obtained about the contact from a fairly simple and straightforward experiment.
45 -20 -10 0 10 20Normal Load (nN) 300 200 100 0 Separation Distance ( nm ) stiff, elastic Si substrate deformation of polymer/OTS film van der Waals snap-in adhesion to OTS SAMs polymer bridging Figure 2-5. Force-di stance plot of a 5-m glass colloidal probe impinging upon a substrate consisting of poly(ethylene oxide)-block-poly(butylene oxide) adsorbed on a octadecyltrichorosilane (OTS)-modified silicon wafer. The OTS forms a selfassembled monolayer (SAMs) on the substr ate by chemically bonding to the native oxide layer. Dashed curve represents th e approach trace while the solid curve represents the retract trace; inset: section of the approach trace near the contact point. 2.0 1.5 1.0 0.5 0.0nN 80 60 40 20 0 nm
46 Lateral Signal Detection For the typical microfabricated V-shaped can tilevers, the dimensions of the tip and cantilever are such that the lateral signal is about 20-80 times smaller than the normal signal . Care must therefore be taken in conditioning the AFM system to optimally detect the lateral signal [19, 124]. In the first place, the gain of the latera l signal channel must be set as high as possible, which is not necessarily the case in most commercial AFM units. Second, the laser spot must be aimed and focu sed near the end of th e cantilever furthest from the base, as this part of a V-shaped cantile ver twists more than any other part. Third, the reflected laser spot must be aimed at the center of the four-quadrant photodiode when the cantilever is at its equilibrium position. This is accomplished by mechanically moving the photodetector normally and laterally until the co rresponding signals are minimized. Any residual imbalance may be nulled out by fine electronic offset control. Fourth, cross-talk between the normal and la teral signal channels must be removed or minimized. Coupling of the signals may occur due to misalignment of the laser spot on the cantilever or small errors in photode tector orientation, e.g., it may be slightly rotated (Fig. 2-3). It may also be due to imperfections in the moun ting of the cantilever, or in the tip/cantilever fabrication itself, e.g., asymmetry in cantilever dimensions or tip placement thereon. Significant cross-talk may thus be removed by simply realig ning the laser or remounting the tip/cantilever assembly. A simple way of verifying decoupling is by obtaining force-distance plots, where normal and lateral signals are monitored as a function of tip-sample separation. When the cantileverlaser-photodetector system is prope rly aligned, there should ideally be no signal in the lateral channel of a force-distance plot, as the forces involved should only have vertical components. Cross-talk can then be compensated for by addi ng or subtracting a fraction of the normal signal
47 from the lateral signal until the latter is comple tely nulled out; this effectively rotates the detector electronically such that it is square d with respect to the normal and lateral spot displacements. Finally, before scanning, the slope must be corrected for samples that are not mounted perpendicular to the tip. This can cause a skew in the normal force image, as the tip would experience a higher load on one part of the scan area versus another. By summing a portion of the xand y-scan voltages into the z-scan voltage, the background sl ope can be compensated for electronically. This would add an average slope in the xand y-directions of the image, which, if opposite the background slope, would effectively nu llify it. Compensation can be adjusted in real-time by performing a line scan in the xand y-directions before obt aining a friction-load map. Lack of facility to compensate for the slope of the sample and the cross-talk between the normal and lateral signals still limits most comm ercial AFMs in performing quantitative friction force measurements. A small pitch, for example, can typically be corrected by software slopesubtraction without affecting the scaling of topographic data, but must be corrected in real-time for friction force measurements in order avoid of fsetting the friction loops. Furthermore, most commercial AFMs built for standard imaging mode s typically reduce the lateral signal gain and do not provide for lateral signal offsetting; this w ould blunt the lateral signal sensitivity that is critical in making precise friction force measurements. Friction-Load Maps Topography is usually obtained by rastering th e sample parallel to the long cantilever axis because this minimizes the twisting of the cantilever due to late ral forces. Conversely, friction images are best obtaine d by rastering the sample orthogona l to the long can tilever axis, as this mode is more sensitive to lateral forces.
48 A friction-load map is essentially a combina tion of a force-distance plot and a friction image. The sample is scanned laterally over a give n distance as the normal load is increased and then decreased [19, 112]. This is implemented by disabling y-scanning, and so the scanning is only in the x-direction (i.e., effectively a line scan). Afte r each trace and retrace cycle of the scan, the sample is moved incrementally in the z-direction, which is equivalent to an incremental change in normal load. This is accomplished by modulating the z-voltage of the piezoelectric tube with a triangular wave whose period is scal ed according the number of lines of the image. Therefore, in the first half of the image, the load is increased, until it reaches a maximum, and then it is decreased. This is done while the feedback is turned off, or its gain set to a minimum. Normal and lateral signal channels are r ecorded simultaneously during the scanning, generating two sets of 3-dimensional images: a pa ir of normal load (lef t and right trace) and a pair of lateral force (l eft and right trace) images (Fig. 2-6). The normal signal looks the same in the trace and retrace scans, as expected, and either one may be used for the friction-load map. Lighter color represents a more positive cantilever deflection, indicating a higher applied normal load. The lateral signal, however, exhibits opposite contrasts in the trace and retrace scans. This is due to the fact that friction acts as a restoring force that op poses the direction of motion, and therefore the lateral deflection will have opposite signs for the two directions. This is more clearly seen when a horizontal slice of the trace a nd retrace scans of the lateral images are plotted together (Fig. 2-7) (i .e., as a friction loop). Th e trace initially shows a regime of static friction (or st iction), a sharp increase where th e tip sticks to the sample, followed by a regime of kinetic friction as the tip slides over the sample. The same magnitude of lateral deflection is observed duri ng the retrace, as the sliding st ops and reverses direction, but with an opposite sign.
49 Figure 2-6. Normal and lateral signal images ge nerated by rastering the tip across the sample 500 nm from left to right (trace) and vice-versa (retrace), as load is applied and removed. Lateral images show contrast between the tr aces as the friction force vector is always opposite the direction of motion. (Note: the sample consists of a silicon wafer coated with hydroxypropyl-guar gum.)
50 -150 -100 -50 0 50 100Friction Response (mV) 500 400 300 200 100 0 x -Piezo Displacement ( nm ) 5 nN 10 nN 15 nN 20 nN 25 nN Figure 2-7. Friction loops obtained from slices of the lateral signal trace (upper) and retrace (lower) images of Fig. 2-6 at increa sing loads. Asymmetry may be due to misalignment of the laser spot or probe position on the cantilever; the offset may be due to a small sample slope.
51 Net friction is taken to be the half of the diffe rence of the forward and reverse traces of the friction loop. This is obtained by first taking the difference between the trace and retrace images of the lateral signal (Fig. 2-8). Each slice of th e lateral and normal signals are then averaged over the entire x-displacement. Although this may include the static regime, its width is small compared to the kinetic regime, and it is usually averaged-out. The friction-load map is then obtained by plotting friction (i.e., lateral signal difference) as a function of either increasing or decreasing load (Fig. 2-9), with the lateral signal finally halved in the process. The friction-load map shows the load dependence of kinetic friction for a particular tip-substrate pair [19, 112]. The slope of the friction load map is therefore the coefficient of friction. Force Calibration Normal (or lateral) signal is sometimes taken to also mean the normal (or lateral) force. Strictly speaking, the signal refers to the voltage outputs SN and SL of the photodetector that corresponds to certa in cantilever displacements. In order to report force units, the signals must first be converted to displacements using the can tilever/photodetectors optical lever sensitivity (sN or sL, in V/m units); the displacements are then converted to forces using the cantilevers force constants (kN or kL, in N/m units) . FN SN kNsNcos SN FL SL kLsL SL (2-4) The ratio of the cantilevers force constant a nd the optical lever sensitivity represents the calibration factors ( and ) that must be determined experimentally; the geometric term in accounts for the slight tilt (Fig. 210) of the cantilever with respect to the sample surface. Beam theory solves for the normal and lateral force constants in terms of the dimensions (L, w, t) and material properties (E, G) of the cantilever :
52 Figure 2-8. Difference image, processed from Fig. 2-6, between the lateral trace and retrace scans represents the vertical widths of the friction loops (Fig. 2-7) and relates to the friction force. As the normal load is the same for the trace and retrace scans, either one or the average may be used. Images ar e then averaged spa tially over the 500-nm x-displacement, and the friction-load map obtained from either the loading or unloading cycles. Lateral signal scale is 20 mV per division, while the normal force scale is 5 nN per division.
53 100 80 60 40 20Friction Response (mV) 30 25 20 15 10 5 0Normal Load ( nN ) Loading on Si-wafer Unloading on Si-wafer Loading on HGuar Unloading on HGuar 8 6 4 2 0Friction Response (mV) 60 40 20 0 -20Normal Load (nN) Loading on Si-wafer Unloading on Si-wafer Loading on HOPG Unloading on HOPG Figure 2-9. Friction-load maps of (top) a 5-m silica probe sliding on a bare and polymer-coated (hydroxypropyl-guar gum, HGuar) silicon wa fer under liquid, and (bottom) a sharp Si3N4 tip sliding on silicon wafer and highly or iented pyrolitic graphite (HOPG) in air. Frictional response here is given in units of lateral signal (mV), which may be converted into force units (nN) by proper calibration of the can tilevers torsional spring constant.
54 kN Et3w 4 L '3 kL Gt3w 3 L h2 (2-5) where E and G are the Youngs and shear moduli, respectively, and L is the length from the fixed end of the cantilever to the point where the tip is attached; in addition, the lateral force constant also depends on the height of the tip ( h ), which represents the lever arm of the torsional moment (Fig. 2-10). These force cons tants are related to the flexural and torsional stiffness of the cantilever by a scaling factor that ratios the length at which the load is applied ( L i.e., at the tip) to the total length of the cantilever ( L ) [125, 126]. kN kflexuralL L 3 kL ktorsionalh2 L L (2-6) Normal optical lever sensitivity ( sN) may be obtained by monitoring SN as a function of tipsample separation on a rigid substrate; in the ab sence of significant deformation, the cantilever deflection (and, thus, SN) would be equivalent to the piezos z -displacement. The manufacturers nominal value for the normal spring constant may then be used to set the force response of optical lever. This reported valueobtained analy tically (Eq. 2-5) from the elastic modulus of the material and the cantilever dimensions [ 127, 128]might vary as much as 50% from the actual value; the variability on the thickness, in particular, has a huge effect on the calculated normal spring constant (kN t3). In situ procedures may be used to calibrate th e cantilever normal spring constant: (1) calibrating the test cantilever against a referenc e cantilever of known fo rce constant [129, 130], (2) calculating the spring constant from the cantilevers resonance frequency and Q-factor obtained from its thermal noise spectrum [ 131], and (3) the Sader method based on the hydrodynamic damping of the cantileve r in a fluid medium [126, 132].
55 Figure 2-10. Parallel beam cantilever indicating the relevant geometric dimensions that are important in force calibrations. Figure 2-11. Beam-bending method for determ ining the normal load force constant: kref( zpiezo dtest)= ktest dtest.
56 In the first method, a deflection versus z -displacement plot is obtained between a test cantilever ( ktest) and a reference cantilever ( kref) of known spring constant that are in mechanical equilibrium: kref dref ktest dtest. Deflection of the reference cantilever is equal to the difference between the piezos z -displacement and the deflecti on of the test cantilever: dref zpiezo dtest (Fig. 2-11). From the slope (c dtest / zpiezo) of the deflection versus z displacement plot, the value of ktest (or kN) may thus be calculated as ktest kref((1 c )/ c ) . The test cantilever is usually mounted at a small angle ( 5o), such that its deflection is actually dtestcos . In the second method, the can tilever is modeled as a harmonic oscillator in thermal equilibrium with its environment; the cantilevers rms fluctuations in this thermal bath is characteristic of its stiffness . This thermal noise can be isolated in the frequency domain from the power spectrum, and fit with a Lorentzian line shape (Fig. 2-12); the integral of this peak ( P ) represents the rms fluctuations in the time domain, and can thus be used to estimate the normal spring constant from the equipartition theorem: kN kB T / P. Sader method similarly uses the unloaded (rad ial) resonance freque ncy of the cantilever (f) and quality factor ( Qf) from its fundamental flexural res onance in a fluid medium (e.g., air). Together with knowledge of its plan view dimensions ( w L of Fig. 2-10), the fl exural stiffness of the cantilever may be obtained: kflexural 0.1906 w2LQf f 2 f, i( f), where is the density of the fluid medium and f, i( f) is the imaginary component of the hydrodynamic function that depends on the viscosity () of the fluid medium . Lateral optical sensitivity ( sL) is not as straightforward to obtain. Often, it is simply assumed to be the slope of the static part of th e friction loop. This slope, however, is not just an effect of the lateral stiffness of the cantilever, but also that of the tip ( kL,tip) and the contact
57 Figure 2-12. Thermal power spectrum of a cantilever rated with a normal spring constant of 0.58 N/m and a resonance frequency of 40-75 kHz. The y -axis represents the intensity of the cantilever normal deflection in units of m / Hz Blue line indicates the Lorentzian fit of the fundamental frequency that is ac tually 57 kHz; the other peaks are higher overtones. The actual spring constant is 0.32 N/m, 44% lower than the nominal value.
58 (kL,contact) to which it is mechanically coupled: ktotal 1 kL 1 kL,tip 1 kL,contact 1 . If the lateral stiffness of the tip and the contact are much highe r than that of the cantilever, which is the case for glass colloidal probes due to their large contact areas, the last two terms drop out and the total slope approximates the lateral sensitivity of th e cantilever. For sharp tips, the lateral contact stiffness may be comparable to or less than that of the cantilever such that using the total slope would severely underestimate the cantilevers lateral stiffness  Recently, a method of measuring sN directly was reported for a colloidal probe that does not include sliding on a surface; this involved pressing the probes equator against the flat side of a freshly cleaved GaAs sample that has perfect 90 features on the 100 plane . A lateral signal vers us horizontal displacement plot is generated whose slope is directly the lateral optical sensitivity of the cantilever. Lateral force constants are usually not reporte d by the manufacturer and must be measured in situ [124, 126, 133]. The well-known Sader me thod has also been extended to the determination of the cantilevers torsional stiffness: ktorsional 0.1592 w4LQt t 2t, i( t) . Subscript t indicates that the properties so-label ed were obtained, this time, from the thermal noise spectrum of the cantilevers torsional vibrational mode. To relate this to the cantilevers lateral force constant, the tip height must also be known (Eq. 2-6). A method that bypasses the separate determinatio n of the lateral opti cal sensitivity and the lateral force constant is the wedge calibration method [124, 133] in which the normal and lateral signals are monitored while scanning on a sloped surface, e.g., reconstructed SrTiO3 or a silicon grating. This is based on the geometric relatio nship between the components of the normal and lateral forces as the probe slides over a substr ate with a known slope. Experimentally, what one measures are the load depe ndence of the half-width ( W ) and the offset ( ) of the friction loops,
59 Figure 2-13. Friction loops on flat, inclined, and declined surfaces at a given applied load. The half-width ( W ), representing the frictional response, only slightly varies, while the offset ( ), due to the surface tilt, varies s ubstantially. The load dependence of W and are used to determine the lateral force sensitivity of the cantilever. Adapted from .
60 representing, more or less, the cantilevers torsio nal sensitivity due to the frictional force and the slope, respectively (Fig. 2-13) . Static force analysis of the sliding, assuming JKR contact conditions for adhesive friction, leads to the instrument-dependent lateral force calibration factor (in N/V units) (Eq. 2-4). Tip calibration is not a trivial matter. At a mi nimum, the manufacturers quoted value for the normal force constant is used together with the uncalibrated lateral signal. In this case, the friction-load map is reported as a friction response versus normal load, indicating the relative nature of the data. This is valid for comparativ e studies in which the same tip is used throughout. When the tip is also calibrated for lateral sens itivity, friction force versus normal load may be plotted, and a true, unitless, coe ffiction of friction reported. Howe ver, due to other uncertainties, such as the actual tip radius, the application of a reported coefficient of friction measured by AFM remains quite limited. Quartz Crystal Microbalance Microgram mass measurement using the quart z crystal microbalance (QCM) is based on the piezoelectric effect; this is the ability of certain noncentros ymmetric crystals to generate electrical potential when subjec ted to mechanical stress, and vice-versa . When a periodic voltage source is applied to a quartz crystal pl aced between two electrode s, it can be made to mechanically oscillate. The thickness-shear vibra tional mode (Fig. 12-14) of an AT-cut quartz, for example, is sensitive to the ad dition or removal of mass [135, 136]. Equivalent Circuit Model A quartz crystal thus configured can be modeled as an equiva lent RLC circuit (Fig. 12-14): C is the motional capacitance corresponding to the stored energy of oscilla tion and related to the crystals mechanical elasticity; L is the motional inductance co rresponding to the inertial component of the oscillation and related to mass displacement during vibration; R is the motional
61 Figure 2-14. Section of quartz cr ystal showing the thickness-shear mode of vibration (left); the Butterworth-van-Dyke equivale nt circuit for a quartz crystal between electrodes (right). Adapted from [135-139]. Figure 2-15. Conductance spectrum of an unloaded quartz crystal showing a peak (red) at its fundamental resonance frequency of 12 MHz, corresponding to a minimum in both electrical and mechanical impedance. Load on the surface causes a phase shift (blue) that has both elastic ( f ) and dissipative ( ) features. Adapted from .
62 resistance corresponding to dissipative losses in the energy of oscillation; C0 is a shunt capacitance due to the electrodes and other support structures [ 135, 136]. A resonant or tuned circuit exhibits fundamental resonance at the frequency f0 (2LC ) 1, indicating that mass sensitivity is due to the perturbation in the mo tional inductance, and that upon addition of mass there would be a negative frequency shift. In practice, the change in mass m / mq is obtained from the fractional shift in frequency f / f 0 using the Sauerbrey equation, based on physical models in terms of the mechanical and dimensional properties of a quartz crystal [135-137]. f f0 m mq 2 f 0Zq m 2 f 0qq m (2-7) For a 5 MHz AT-cut crystal operating in the fundamental mode, the acoustic impedance ( Zq 8.8 106 kg/m2 s)from the crystals shear modulus ( q 2.947 1011 g/cm s2) and density ( q 2.648 g/cm3)gives a mass sensitivity factor ( Cf) of 56.6 Hz cm2/g [135-139]. f 2 f0 2qq m Cf m (2-8) Evenly distributed mass of 1 g/cm2 added to a quartz crystal would therefore cause a decrease in frequency of 56.6 Hz or by about 0. 001%. This is valid for masses added in air or vacuum. Under liquid, frequency sh ift is observed, even without mass loading, due to viscous damping; the Kanazawa equation relates th is frequency shift to the viscosity (l) and density (l) of the liquid medium . f f0 3llqq 1/2 (2-9)
63 Acoustic Reflectometry When considered as an acoustic reflectometer a quartz crystal resonator may be used to probe loads at the interface using impedance analysis of the elect rical conductance spectra [138, 139]. Impedance ( Z R i X ) is the sum of the resistive (real) and reactive (imaginary) components of an electrical circuit; conductance ( G ) is the real part of its admittance ( Y G iB ), which is the reciprocal of impedance. When the frequency of excitation driving a quartz crystal matches its acoustic resonance fr equency, the amplitude of deformation is enhanced; at the same time, the electrical impedance is minimum, and, conversely, the current (or conductance, G ) through the crystal res onator circuit reaches maximum. Resonance is therefore the condition when the complex impedance becomes zero. For an unloaded crystal, the shear wave propa gating to the surface is totally reflected; a load (e.g., a film) on the surface cau ses part of the propagating wave to interact with the film causing a delay in reflection (Fig. 2-15). Interference would therefor e create a phase shift in the total reflection amplitude of the acoustic wave and can be treated similarly to Fresnels equations for reflected light (see section on Ellip sometry below) [138, 139]. This phase shift corresponds to a complex frequency shift ( f *) that takes into account both the elastic and dissipative interactions of the quartz crystal with its environment (Fig. 2-15). f f f i f iZq Zs (2-10) Here, is the half-bandwidth shift, related to dissipation (D 2 / f ) and Zs is the load impedance at the quartz-sample interface. Note th at for electrical circuits, it is the elastic (reactive) components of impedan ce that are frequency dependent (imaginary), while that for mechanical circuits, it is the dissipative (viscous) components.
64 In the Sauerbrey limit, i.e., a thin rigid film in air or vacuum, there is no bandwidth shift, and the fractional frequency shift is si mply proportional to the mass loading ( m ) on the quartz crystal (Eq. 2-7) . Under liqui d loading, the load impedance ( Zs) would be the acoustic impedance of the liquid that depends on both its density and complex viscosity. f f0 iZq ill (2-11) This rearranges to a general Kanazawa equation, f f0 f0llqq 1/2( i 1), (2-12) which predicts that under liquid, the frequency shif t is simply the negative of the bandwidth shift [140, 141]. In other words, since there is no mass loading, the fre quency shift is onl y attributable to dissipative interaction with a Newtonian fluid. For a viscoelastic film, in the thin film limit, in contact with a liquid, the complex frequency shift includes both a Kanazaw a term and a Sauerbrey term . f f0 f0llqq 1/2( i 1) 2 f0qq m (2-13) In the thin film limit (Eq. 2-13), the freque ncy and bandwidth shifts are the sums of the Kanazawa and Sauerbrey contributions . The Sauerbrey contribution can thus be extracted from the observed frequency shift by the st raightforward subtraction of the Kanazawa contribution. Ellipsometry Nanometer thickness measurements by ellipsomet ry of ultrathin films coated on reflective surfaces is based upon the interaction of polarized light with the film/surface causing a shift in polarization from linear to ellipti cal (Fig. 2-16) [142, 143]. Elliptic ity of the reflected light is
65 Figure 2-16. Linearly polarized light interacti ng with a reflective surf ace becomes elliptically polarized. Adapted from . Figure 2-17. Reflection and transm ission on a single interface be tween vacuum and a material characterized by a complex refractive index, 2. Adapted from .
66 given by the two values measured in ellipsometry: which is related to the ratio of amplitudes of the parallel and perpendicular co mponents of the reflected light, and which is related to the phase difference between the incident and refl ected light. The amount of ellipticity induced depends on the optical constants of the su rface material, and also on its thickness ( d ). The electric vector of light can be described as the sum of co mponents that ar e parallel (p) and perpendicular (s) to the plane of incidence. When the pand s-comp onents are in-phase, the light is linearly polarized; when they are 90 out-of-phase, the light is circularly polarized; when the phase lag is between 0 to 90 the light is elliptically polarized. When an incident beam of light strikes a su rface, some of the light is transmitted through, and some reflected (Fig. 2-16). Transmitted light will have a different velocity from the incident light due to the materials refractive index ( n ), and its intensity will be attenuated according to the materials extinction coefficient ( k ); these two optical constants form the real and imaginary parts of the complex refractive index ( ). N n ik (2-14) Ellipsometry measures the reflected light. The ratio of the amplitude of the reflected light to the amplitude of the incident light is given by the Fresnel re flection coefficient ( r ), which is a function of the complex refractive indices ( 1 and 2) and the angles of reflection (1) and refraction (2). For the simplest case of a single in terface (Fig. 2-17), the Fresnel reflection coefficients for the pand s-co mponents are given by [142, 143]: r12 p N 2 cos 1 N 1 cos 2 N 2 cos 1 N 1 cos 2 r12 s N 1 cos 1 N 2 cos 2 N 1 cos 1 N 2 cos 2 (2-15)
67 For a double interface (e.g. a thin film, 1, on a substrate, 2), multiple internal reflection leads to an infinite series of transmitted and refl ected light (Fig. 2-18). This infinite series of multiple reflections converge into a total reflection coefficient ( R ) [142, 143], Rp r12 p r23 p ei21 r12 p r23 p ei2 Rs r12 s r23 s ei21 r12 s r23 s ei2 (2-16) where is the film phase thickness, while d is the film thickness: 2 d 2 cos 2. (2-17) Total reflection coefficients ( Rp and Rs), are derived from the experimental ellipsometric parameters, formally defined as: the angle whose tangent is the ratio of the magnitudes of the total reflection coefficients, and the change in phase between the sand p-components of the incident (1) and reflected light (2) [142, 143]. 1 2 (2-18) tan Rp Rs (2-19) and are related in the fundament al equation of ellipsometry by which is the complex ratio of the total reflection coefficients. Rp R s tan ei (2-20) Experimentally, and are determined by adjusting the sett ings of a polarizer on the incident beam, and an analyzer on the reflected beam to find a null; the settings of the polarizer and analyzer are mathematically related to the values of and
68 Figure 2-18. Multiple reflections and transmissi ons of light on a double interface with complex refractive indices, 1 and 2. Adapted from [142, 143].
69 X-ray Photoelectron Spectroscopy Surface chemical analysis by X-ray photoele ctron spectroscopy (XPS) is based on the photoelectric effect, which was first satisfactoril y explained by Einstein in 1905 (in one of his Annus mirabilis papers) following Plancks concep t of quantized energy . A photon impinging upon an atom may interact with an elec tron in its orbitals, tr ansferring energy and causing that electron to be emitted from th e atom. Photoemission will not occur if the frequency of the incident photon is not gr eater than a threshold value ch aracteristic of the element, regardless of the intensity of light; it is the number of emitte d electrons (photoelectrons) that depend on intensity, provided that the photons have the right energy . By the time an electron to which energy has been imparted r eaches the atoms edge and escapes into space ( ~ 10 6s), some of that energy has been lost in performing the escape; the kinetic energy ( EK) of the photoelectron is thus the exce ss above the threshold value, and is related to the energy of the exciting photon by the Einstein equation: E K h E B, (2-21) where EB is the threshold or binding energy . It is the kinetic energy of the photoelectron that is measured in XPS from which the binding en ergy is derived that is used in both qualitative and quantitative analyses [145-149]. Typical XPS instrumentation (Fig 2-19) has the sample introdu ced from a load-lock that is pumped down to 10-6 Torr before being shuttled to the UHV chamber maintained at 10-10 Torr . X-rays are generated from the fluorescence of the anode material, either Mg or Al, which are bombarded with electrons, thus producing the K emission lines of Mg (1253.6 eV) and Al (1486.6 eV), having widths of 0.7 and 0.85 eV. Ofte n, these lines are specif ically selected using a single crystal quartz monochromator via Bragg di ffraction. The X-ray source, monochromator,
70 Figure 2-19. The XPS instrumentation, consisting of : a load-lock that prepares the sample to be introduced into the UHV chamber, an X-ray source with either Al or Mg anodes, a single crystal quartz monochromator, electr on focusing lens system, a hemispherical electrostatic anayzer, and th e detection and data processing system. Adapted from .
71 and target sample are all placed relative to each other on a Rowland circle. Photelectrons accelerate from the sample surface into the spectrome ter chamber that consists of focusing lenses and a hemispherical analyzer that deflects the in coming electrons with an electrostatic field, thereby ordering them according to their kinetic energies. At the exit, the electrons are captured and counted by the detection system, and processe d to yield the photoelect ron spectruma plot of electron count rate (counts per second) versus bindi ng energy (1400 to 0 eV, for Al K). Binding Energies In the gas phase, the binding energy is identic al with the first ionization potential of an electron in a given orbital; in solids, an additional energythe work function ()must be accounted for in removing an electron from the surface . For conducting samples electrically grounded to the instrument (Fig. 2-20), the Fermi levels ( Efermi) of both sample surface and instrument should be the same; it is the highest occupied energy level or the edge of the conduction band [145, 146]. Spectrometer work function (spectro) is the difference between the Fermi level and the vacuum level ( Evac) that is due to a potential difference between the sample surface and the spectrometer chamber; this is determined beforehand, during calibration, and used as a constant correcti on factor. Binding energy, referenced against the Fermi level (zero EB at Efermi) is thus: E B h E K spectro. (2-22) For insulators, the sample surface would not be in electrical cont act with the instrument; as a result, they would have different Fermi levels, and the sample work function (sample) must be considered separately (Fig. 2-20) [145, 146]. More over, charging of the sample due to the loss of electrons necessitates a supply of free charge carrierselectron ne utralizer and ion gunthat
72 Figure 2-20. Atomic processes involved in photoemission illustrat ed in terms of energy level diagrams for a conductor (top) and an insu lator (bottom); the ope n circles represent vacancies left by a photoelectron. Energy di agrams on the right show how the binding energy ( EB) is related to the othe r energy quantities by conservation. Adapted from [145, 146, 150].
73 will counteract charge build-up; this compensating energy (neut) must therefore also be considered . E B h E K sample neut (2-23) In practice, however, inte rnal references are used to align the binding energy scale; for polymers and organics, for example, the C 1s peak for the C C or C H bonds is set to 285.0 eV, so that all other binding energies could be accurately determined relative to this . The simplest theoretical expl anation of binding energies is Koopmans theorem [145, 151157], which approximates the ionization potential as the negative of the orbital energy (k) from which the electron has been removed [145, 151-157] ; it is derived from a Hartree-Fock (HF) self-consistent field calcul ation of the ground state ( N )-electron system [145, 151, 154]. EB EN1 EN K (2-24) Binding energy is the difference between the final state of the system with N -1 electrons and the initial, neutral state, assuming that the orbitals do not change in the process (frozen-orbital approximation), i.e., the only pe rturbation is the loss of the electron . This neglects reorganization and correlation e ffects that account for 1-10% e rror in predicted binding energy values [148, 152, 157]. Upon the creation of a co re hole, the system responds (reorganizes) in order to shield or minimize the energy created by ionization [145, 155, 157]; this relaxation is a final-state effect that has a negative influence on the binding energy. Mean-field methods like Hartree-Fock also fundamentally ignore the influence of instanta neous, local Coulombic interactions (correlation) between electrons, which would have a positive effect on binding energy [153, 155, 157]. E B E HF E reorg E corr (2-25)
74 It is just fortuitous that the reorganization and correla tion effects offset each other such that the Hartree-Fock energy approaches the exact binding energy, but not in all cases [153, 155, 157]. Spectral Features The XPS spectrum is a plot of electron c ount intensity in term s of the number of photoelectrons detected per second versus binding energy in electronvolts (eV). What is actually measured are the electrons velocities, and the x -axis could alternately be expressed in terms of kinetic energy as there is a simple proportional ity between the two; bi nding energies, however, are more chemically meaningful [145, 146]. Typi cally, a wide scan or survey spectrum (Fig. 221) is first obtained, primarily to identify the photoelectron peaks for qualitative analyses, followed by a high-resolution scan of specific pe ak regions for quantitative analyses and for elucidating fine structures such as chemical shifts and multiplet splitting. The most prominent features in the spectrum are, of course, the photoelectron peaks [145, 158]. The survey spectrum of a clean silicon wa fer (Fig. 2-21), for example, shows pronounced peaks for the core electrons of Si (2s, 2p) a nd O (1s, 2s) due to the native oxide and the underlying elemental silicon; a small C 1s peak at tributed to adventiti ous hydrocarbons is also observed even after exposure to oxygen plasma. Photoelectron peaks are typically intense and narrow; the intrinsic peak width is due to th e core hole lifetime, which has a fundamental (Heisenberg) uncertainty; for C 1s, the intrinsic peak width is ~0.1 eV and has a Lorentzian lineshape . Instrumental fact ors may broaden this intrinsic peak width (~1 eV): the energy spread of the incident X-ray, the resolution of the electrostatic analyzer, the charging of the sample, and energy spread of the neutralizer. These contributions ar e additive and have a Gaussian lineshape . To the left of the main photoelectron peak at higher binding energies (lower kinetic energy), is a long inelastic scattering tail (Fig. 2-22) due to photoe lectrons that suffer energy
75 70x103 60 50 40 30 20 10 0Count Rate (c/s) 1400 1200 1000 800 600 400 200 0Binding Energy (eV) O KLL O 1s Si 1s Si 2p O 2s C 1s Figure 2-21. The XPS survey spectrum of a silicon wafer after exposure to oxygen plasma, showing the principal spectral features: the photoelectron pe aks of Si, C, and O, the Auger peaks of O, and the continuously decreasing background due to inelastic scattering. The exciting X-ray source was Al K ( h=1487 eV). 70x103 60 50 40 30 20 10 0Count Rate (c/s) 900 800 700 600 500Binding Energy (eV) O 1s photoelectron peak inelastic scattering Figure 2-22. Detail of the XPS survey spectrum of silicon wafer from 970 to 450 eV, showing the O 1s photoelectron peak at 533 eV, a nd the inelastic scattering peak that continuously tails for 954 eV (=1487 eV 533 eV). Inset adapted from . photoelectron inelastic scattering h
76 losses as they exit the sample (Fig. 2-22, inse t) [145, 158]. Reduction in kinetic energy due to these collision events is not di screte, hence, a long continuou s tail is observed from the photoemission kinetic energy (e.g., 954 eV=1487 eV 533 eV for O) to zero kinetic energy. Detail of the Si 2s and 2p photoelectron p eaks (Fig. 2-23) each show two overlapping peaks, respectively, that are ~4 eV apart. Phot oelectrons originating fr om oxidized Si from the thin passivating layer (~1.4 nm thick) exhibit a higher binding energy compared to those from the underlying elemental Si. As binding energi es are the difference between the initial ( N )electron state and the final ( N -1)-state (Eq. 2-24), a change in th e orbital energies of the initial state arising from differences in chemical environmentsan initial state effect would cause a change in the observed binding energy . In particular, bonding with more electronegative elements (e.g., oxidation) tends to lower the en ergy of the orbital stac k and would result in a chemical shift to higher binding energies as in the case of Si O versus Si Si. High-resolution scan of the Si 2p peak (Fig. 2-23, inset) further reveals fine structures that are 0.6 eV apart due to multiplet splitting [145, 158]. Si has two unpaired electrons on its valence 3p orbitals; removal of an electron from the 2p orbita ls would result in a multiplicity of either 3/2 or 1/2 on the ion due to spin-orbit coupling. Energy losses due to the interaction of the photoelectron with surfa ce electrons (e.g., conduc tion band in metals)or plasmon losses also appear about 20 eV higher [145, 158] than the ma in peaks in Fig. 2-23; these loss peaks are due to group oscillations in the conduction band and o ccur in well-defined quanta as successively smaller peaks. Finally, valence band photoemissions are also observed in Fig. 2-23 as low intensity peaks between 10-20 eV [145, 158]. The survey spectrum also includes peaks around 1000 eV due to the O KLL Auger photoemission (Fig. 2-24). Upon the creation of a core ho le due to X-ray excita tion, electrons in
77 20x103 15 10 5 0Count Rate (c/s) 200 150 100 50Binding Energy (eV) Si 2s (Si-Si) Si 2s (Si-O) Si 2p (Si-Si) Si 2p (Si-O) O 2s valence electrons plasmon losses plasmon losses Figure 2-23. Detail of the XPS survey spectrum of silicon wafer from 200 to 0 eV, showing the chemical shifts in the Si 2s and 2p peak s due to photoelectrons coming from the native oxide layer (~1.4 nm thick) and the underlying elemental silicon. Inset: highresolution spectrum of the Si 2p region, showing multiplet splitting. 15x103 10 5 0Count Rate (c/s) 1400 1300 1200 1100 1000 900Binding Energy (eV) KL1L1 KL1L2,3 KL2,3L2,3 Figure 2-24. Detail of the XPS survey spectrum of silicon wafer from 1400 to 900 eV, showing the O KLL Auger lines at 1013 eV (KL1L1), 999 eV (KL1L2,3), and 978 eV (KL2,3L2,3). Inset adapted from [146, 150]. 102eV 101 100 99 98 Si 2p3/2 Si 2p1/2 valence band conduction band Efermi Evac Auger electron K (1s) L1 (2s) L2,3 (2p)
78 higher orbitals (valence electrons) may relax to fill the vacancy and in the process also emit a secondary (Auger) electron [145, 158]. In the case of O KLL tr ansition, the initial vacancy occurs in the K-shell, while th e final double-vacancy occurs in the L-shell (Fig. 2-24, inset). Auger electrons have kinetic energies that are independent of th e exciting radiation (h ), and are distinguished from primary photoemissions by thei r shift in positions when the X-ray anode material is exchanged [145, 158]. In spectra obtained with Mg K (h 1254 eV), for example, the O KLL peaks appear between 750-800 eV. Quantitation Surface analytical techniques lik e XPS must be able to measure signals that come from 1015 atoms/cm2 on the surface in a background of 1022 atoms/cm3 in the bulk [159-161]. This necessitates UHV technologies that minimize the scattering of probed particles (electrons, photons, atoms) emerging from the sample material, especially as the size of the irradiated spot is decreased (<100 m) with the demand for increased lateral resolution (e.g., in imaging). Surface sensitivity in XPS additionally comes from the de pth of origin of the photoelectrons; while X-ray photons penetrate deep into the sa mple, the emitted electrons that do not suffer energy losses usually come from depths of 1-4 nm from the surface  Electrons deeper in the bulk are extinguished, or suffer losses due to inelastic collisions and do not contribute to the photoelectron peak (F ig. 2-22, inset). Information depth is the average distance normal to the surface from which a specified perc entage of the signal originates; sampling depth is defined as three times the inelastic mean free path (( EK)), which coincides with the information depth that accounts for 95% of signal . Tilting the sample with respect to the an alyzer such that the photoelectrons captured are those with take o ff angles that approach the grazing limit may
79 further enhance surface sensitivit y ; this method may also be used to characterize samples with vertical heterogeneity [162-164]. Fig. 2-25 shows the survey spectrum of a silicon wafer after the surface initiated polymerization of methyl methacrylate (CH2CH(CH3)(CO2CH3)). While the C and O photoelectron peaks from the polymer are the dominant features, signals from the silicon substrate still appear, albeit very attenuated. Ellipsometric thickness of the poly(methyl methacrylate) (PMMA) brus h was measured to be 53 17 nmmore than adequate to prevent photoelectrons from the substrate fr om escaping. The fact that Si photoelectrons are still detected shows that the film, with highly uneven thicknes s in the first place, is likely also patchy. Analysis of photoelectron peak intensities can reveal quantitative information about the sample. The intensity of a peak from an element depends on many factors: I kinstr T ( E K ) L ( ) n ( E K ) cos (2-26) where: kinstr is an instrumental factor which includes the X-ray flux, spot size, and acceptance angle, and is determined beforehand during calibration; T ( EK) is the transmission factor which depend on the efficiency of aspects of the spectro meter such as focusing lenses, energy analyzer, and detector; L () is the angular symmetry factor that takes into account the direction (or angle, ) of the orbitals with respect to the X-ray incident beam; is the photoionization cross-section that is related to the pr obability of photoemission; n is the atom number density on the surface; ( EK) is the inelastic mean fee path or the average distance trav ersed by an electron between inelastic collisions; cos is the term related to the take-off angle at which the photoelectrons leave the sample [145, 148]. In quantitative analysis we wish to establis h a relationship between the intensity in terms the area under the photoelectron peak and the mo lar concentration of the element within the
80 25x103 20 15 10 5 0Count Rate (c/s) 1400 1200 1000 800 600 400 200 0Binding Energy (eV) C KLL O KLL C 1s O 1s Si 2s Si 2p O 2s Figure 2-25. Survey spectrum of poly(methylme thacrylate) (PMMA) brush on a silicon wafer showing the C and O photoel ectron and Auger peaks due to the polymer, and the much attenuated signal from the silicon substrate. Inset: high-resolution spectrum of the C 1s region revealing the C C, C O, C =O chemical shifts. 290 288 286 284 282 C=O CC CO
81 sampled region. All the terms in Eq. 2-26 except n an be combined into an atomic sensitivity factor ( S ) that is characteristic of an element [145, 158]. I n S (2-27) Typically, however, it is not the absolute value of n that is determined but the relative atomic concentrations or the mole fractions ( xi) [145, 158]. x1 n1ni I 1 / S 1Ii/ Si (2-28) Published empirical sensitivity factors can be used provided that the instrument-dependent terms in S such as kinstr and T ( EK) have the same characteristics as th e one used for analysis [150, 158, 165]; moreover, the use of S provides semiquantitative results (10-20% error) provided that the sample is homogeneous and that the cross-sect ions do not vary much across the different chemical/oxidation states of the element. PMMA has a 5 C to 2 O ratio, or 71% C and 29% O atom number concentrations. Integration of the C 1s and O 1s peak areas of the survey spectrum (Fig. 2-25) gives 71.1% C and 28.9% O, within 0.3% error. Integration of the same peak regions in the high-resolution spectrum (not shown) gives 72.3% C and 27.7% O, within 4% error. It is often the case that peaks not fully resolv ed are encountered in analysis and must be deconvoluted in order to extract quantitative information. In such cases, a peak fitting procedure must be used in order to dise ntangle the contributions of the sub-peaks . First, a background correction is typically applied, of which the most developed procedure accounts for inelastic scattering [145, 166]. Second, a fitting function is selected depending on the type of peak broadening that dominates: Gaussian for peak widt hs due to purely instrumental resolution, and a mixture of Gaussian-Lorentzian for intrinsic resolution contributions as the instrumental resolution is improved (i.e., <1 eV) . Fina lly, fitting must be made consistent across
82 different chemical species by setting the same full-width-half-maximum (FWHM) height for the peak fits of the same element, i.e., the same photoemission statistics (c ross-sections, core hole lifetimes) are assumed. High-resolution spectrum of the C 1s peak regi on (Fig. 2-25, inset) shows three unresolved peaks that are due to the C chem ical shifts in PMMA: the peak fits at 285, 286, and 288.5 eV are attributed to C C, C O, and C =O. There are 3 C C, 1 C O, and 1 C =O species in the repeating unit of PMMA, corresponding to at omic concentrations of 60%, 20%, 20%, respectively. Integration of the peak fit curves gives 59.7% C C, 20.1% C O, and 20.2% C =O, respectively, within 1% error of the theoretical value.
83 CHAPTER 3 POLY(L-LYSINE)graft -POLY(ETHYLENE GLYCOL) BRUSHES Introduction Poly(L-lysine)graft -poly(ethylene glycol) (PLLg -PEG) is a member of a family of polycationic PEG-grafted copolymer s that have been shown to chemisorb on negatively charged surfaces, including various metal oxides, provi ding a high degree of resistance to protein adsorption [167-169]. As a result, PLLg -PEG-modified surfaces have received strong interest in a variety of applications in cluding sensor chips for bioaffi nity assays and blood-contacting biomedical devices [170, 171]. Similarly, exploi ting its spontaneous adsorption onto metal oxide surfaces, PLLg -PEG is expected to si gnificantly lubricat e these inte rfaces in physiological, aqueous environments by forming a boundary polyme r brush layer. In conjunction with protein resistance, the lubrication of meta l oxide surfaces is of great signifi cance in medical applications. The structure of PLLg -PEG (Fig. 3-1) consists of a poly(L-lysine) backbone with multiple poly(ethylene glycol) side chains grafted onto the backbone via am ino groups on a fraction of the lysine units; the remainin g free amino groups provide the pathwa y for electrostatic interaction of the PLL backbone with appropriately charged su rfaces . Under appr opriate conditions of pH and ionic strength, polycations such as PLL become positively charged and irreversibly adsorb onto negatively charged metal oxide su rfaces by electrostatic attraction (Fig. 3-2). In earlier nanotribological inve stigations [51, 109] using AFM, significant reduction in interfacial friction measured between silicon oxide (substrat e) and a sodium borosilicate microsphere (probe) were obser ved upon the adsorption of PLLg -PEG on either one or both sides of the interface, represen ting asymmetric and symmetric tribosystems, respectively. In addition, an investigation on PLLg -PEG polymers differing only in PEG side-chain length revealed that interfacial forces measured under aqueous conditions were reduced with increasing
84 H2N H N N H H N OH H2N H2N NH NH2 O O O O O O k n O j i Figure 3-1. Structure of a PLLg -PEG copolymer consisting of a poly(L-lysine) backbone and randomly grafted poly(ethylene glycol) side chains. In this scheme, ( k + j )/ j represents the grafting ratio the fraction of lysine un its to PEG side-chainsfor very large n Figure 3-2. The PLLg -PEG adsorption on metal oxide surfa ces. At appropriate pH and ionic strengths, PLL becomes positively charged and sticks to negatively charged oxide surfaces, with PEG presented as a brush outer-layer.
85 PEG chain length, indicating th at interfacial adhesion and fr iction can be modified through control of the polymer molecular structure . Macroscopic i nvestigations, using pin-on-disk and mini traction machines, also showed that the boundary-lubrication properties of aqueous buffer solutions were significan tly improved upon addition of PLLg -PEG, with, again, a strong dependence on polymer architecture [106, 107] At low sliding/rol ling velocities, PLLg -PEG performed as a boundary lubricati ng film, and, at intermediate to higher velo cities, also facilitated the entrainment of fluid that separa ted the contacting surfaces ; water alone would not be able sustain this, especially at low velocities, due to its low pressure-coefficient of viscosity and poor film-forming properties. We conducted a systematic investigation of the dependence of interfacial friction on the molecular architecture of PLLg -PEG-coated interfaces. As in previous investigations [51, 109], a sodium borosilicate microsphere attached to the end of an AFM cantilever was used as the probe to avoid substantial deformation of th e polymer layer that would occur under the high contact pressures common in the use of conventional (<100 nm radius) Si3N4 tips. Interfacial friction measurements were carried out on polyme r-coated oxide-passivated silicon substrates with the bare (polymer-free) microsphere probes while in a HEPES buffer solution. Three series of polymer samples, distinguished by the PEG molecular weight, were used in the present investigation; within each series, the polymer s differ only in the lysine/PEG ratio (i.e., the grafting ratio or the molar ratio of L-lysine-mers to PEG side-chains). Based on friction measurements on a series of silicon substrates with native oxide coated with PLLg -PEG that are varying only in grafting ratios, it was observed that the lysi ne/PEG fraction substantially influences the interfacial friction of these pol ymer-associated interfaces in a manner intimately
86 tied to the conformation of PEG side-chains extending into the solution. These results can be rationalized in terms of the PEG packing dens ity on the surface using scaling arguments. Experiments Preparation of PLLg -PEG Copolymers PLLg -PEG copolymers were prepared and char acterized by our collaborators at the Laboratory for Surface Science and Technology, Department of Materials, Swiss Federal Institute of Technology, ETH-Zrich. Polyme r substrates were designated as PLL( x )g [ y ]PEG( z ), where the copolymer consisted of a PLL backbone of molecular weight x kDa and a grafted PEG side-chain of molecular weight z kDa with a grafting ratio [(lysine-mers)/(PEG side-chains)] of y Synthesis followed a previously describe d method [167, 168]. Briefly, poly(L-lysine) hydrobromide (PLL-HBr, MW 20 kDa, Sigma, St. Louis, MO) was dissolved in 50 mM sodium borate buffer solution, followed by filter sterilization of the solution (0.22 m pore-size filter). The N -hydroxysuccinimidyl ester of methoxypoly(ethylene glycol ) propionic acid (SPA-PEG, Shearwater Polymers, Inc., AL) was then added to the dissolved PLL-HBr. The reaction was allowed to proceed for 6 h at room temperature, after which the reacti on mixture was dialyzed (SpectraPor, MW cutoff size 6-8 kDa, Spectrum, H ouston, TX) against deionized water for 48 h. The product was freeze-dried and stored at C. By varying the molecular weight and amount of the starting material (PLL-HBr and SPAPEG) as well as effectively controlling the reaction progress, a series of PLLg -PEG graft copolymers of varying PEG side chain length and grafting ratios were prepared. Detailed preparation procedures and analytical informa tion of the product obtained via this method have been reported elsewhere [167, 168].
87 In this study, three series of polymers synt hesized using different PEG molecular weights were used. The synthesis approach produced a series of polymers of the general composition: PLL(20)g -PEG(2), PLL(20)g -PEG(5), and PLL(20)g -PEG(10), with each series consisting of 3 or 4 polymer samples differing only in grafting ratio. Measurement of PLLg -PEG Adsorption on Silica Characterization of the adsorption of the PLLg -PEG copolymer seri es on oxidized silicon surfaces were likewise performed by our colla borators at ETH-Zrich, using their optical waveguide light mode spectrosc opy (OWLS) and quartz crystal microbalance with dissipation monitoring (QCM-D) set-up. These complement ary techniques measure the dry and wet masses adsorbed on oxide surfaces, respectively, allowing for the determination of the polymer and associated solvent mass contributions separately. The OWLS measurement was carried out on a BIOS-I instrument (ASI AG, Zrich, Switzerland) using a Kalrez (Dupont, Wilmington DE) flow-through cell with a volume of 16 L. Waveguide chips (MicroVacuum Ltd., Budape st, Hungary) consisted of a 1-mm thick glass substrate and a 200-nm thick Si0.75Ti 0.25O2 waveguiding layer at the surface; a silica layer (~12 nm) was sputter-coated on top of the wave guiding layer in a Leybold dc-magnetron Z600 sputtering unit. Coating conditions and the prin ciples of OWLS inves tigations have been described in detail elsewhere [172-174]. It is im portant to note that the surface-adsorbed areal mass density determined by OWLS is regarded as a dry areal mass density due to the fact that solvent molecules coupled to the polymer will not contribute to a change in its refractive index, and, thus, do not contribute to the detected adsorbate mass. Reported dry areal mass density ( mdry) represents the average of thr ee individual experiments; as th is technique is highly sensitive
88 (LOD 1 ng/cm2) and allows for direct online monitori ng of macromolecular adsorption , a measurement error of less than 1% is expected. The QCM-D measurements were performe d with a commercial quartz crystal microbalance with dissipation monitoring (Q-Sense, Gothenbu rg, Sweden) equipped with a home-built laminar flow cell with a glass window allowing visual monitoring of injection and exchange of liquids . Sensor crystals us ed in measurements were 5-MHz AT-cut quartz, sputter-coated with SiO2 (also Q-Sense). Details of this set-up and measurements have been reported elsewhere [92, 110]. The QCM-D response to mass uptake on the crystal oscillator is reflected in the changes in both the resonant frequency ( f0) and dissipation factor ( D ) at different overtone s. In contrast to OWLS, the QCM-D approach is sensitive to th e viscoelastic properties and density of any mass coupled to the mechanical oscilla tion of the crystal; in this case the adsorbed mass consists of the PLLg -PEG copolymer along with solvent molecu les associated with it. A Voigt-based model was used in the analysis (Q-tools, version 2.0.1) where th e adsorbed layer was represented by a homogeneous, viscoelastic film characterized by shear modulus (film), viscosity (film), density (film), and film thickness ( hfilm) [176-178]. AFM Friction Force Measurements AFM was used to probe friction forces at the interfaces of polymer-modified substrates under physiological pH solutions. The microscope (F ig. 3-3) was equipped with a liquid cell/tip holder (Digital Instruments, Sa nta Barbara, CA), and controlled by SPM 1000 electronics and software (RHK Technology, Inc., Troy, MI). The microscope makes use of a single-tube scanner, on which substrates ar e scanned with respect to a fi xed tip position, and a beamdeflection technique in which lig ht from a laser diode is reflected from the back of a
89 Figure 3-3. The AFM instrumentation. Top: AFMhead assembly with the liquid cell/tip holder for in situ solvent exchange during friction force measurements. Bottom: Connection diagram for the home-built AFM head controlled by AFM100/STM100 electronics from RHK.
90 microfabricated cantilever onto a four-quadran t photodetector. Great er details of this instrumental design have been reported previously [19, 112]. Deflection of the cantilever normal to the su rface served to mon itor surface topograghy and interfacial adhesion; torsion or twisting of th e cantilever was indicative of frictional forces at the tip-sample interface. Kinetic friction data we re acquired by monitoring the lateral deflection of the cantilever as a function of position across the sample surface and applied normal load; this was accomplished by rastering the sample in a line-scan mode while first increasing and then decreasing the applied load. During this procedur e, friction and normal forces were measured simultaneously with a scan speed of 1400 nm/s ove r a distance of 100 nm. Normal loads were determined from the cantilevers nominal spring constant (kN 0.58 N/ m manufacturers reported value) and direct measurements of samp le displacement. Friction forces were calibrated through an improved wedge cal ibration method [124, 133]. To prepare the polymer-coated si lica substrates, a given PLL( x )g [ y ]-PEG( z ) was first dissolved in 10 mM HEPES (4-[2-hydroxyethyl]p iperazine-1-[2-ethanes ulfonic acid], SigmaAldrich Inc., St. Louis, MO) at a concentrati on of 1.0 mg/mL; unless otherwise noted, HEPES solutions in this study were adjusted to pH 7. 4 with 1.0 M NaOH. Si (100) wafers, with their native oxide layer, were used as substrates. Prior to immobilization of PLLg -PEG onto the oxide surface, the wafers (0.5 cm 0.5 cm) were prep ared by sonication in toluene (2 min) and in 2propanol (10 min), extensively rinsed with ultrapure water (EM SCIENCE, Gibbstown, NJ), dried under a gaseous nitrogen flow, and exposed for 2 min to an oxygen plasma (PDC-32G, Harrick Scientific Corporation, Ossining, NY) Oxidized substrat es were immediately transferred to the PLLg -PEG/HEPES solution, a nd incubated there for 40 min. Polymer-coated substrates were then rinsed and stored in HEPES buffer solution (i n the absence of PLLg -PEG)
91 until used in AFM experiments. Prior to AFM measurements, the polymer-coated substrates were withdrawn from solution, rinsed with HEPES buffer and ultrapure (18 M ) water to remove any free PLLg -PEG, and then dried under a nitrogen flow. AFM measurements were carried out in aque ous HEPES solutions; th e composition of the liquid environment encompassing the tip/sample in terface was controlled by transferring aliquots of solution in and out of the liquid cell th rough the use of two 5-mL syringes. Sodium borosilicate microspheres (Novascan T echnologies, Inc., Ames, IA) with 5.1 m diameter affixed to the end of AFM cantilevers were us ed as bare sliding c ounterfaces against the polymer-coated silicon substrates (Fig. 3-4); these colloidal probes were rinsed with dilute HCl (pH 1) and exposed to oxygen plasma for 15 s in between measurements to remove any adhering polymer. Normal loads were limited in order to avoid wear of both tip and polymer-coated substrate; scan rates were set such that hydr odynamic (viscous) contri butions were reduced. Valid comparison of friction data was enabled by using the same tip/cantilever assembly throughout a series of friction m easurements, while systematica lly varying other parameters, such as PEG chain-length, grafting ratio, and de position time. Reported friction data represent the average of at least six results obtained at di fferent locations across the surface. Generally, the measurement of at least one tip/s ample condition was repeated at th e end of a series to ensure significant changes (wear) had not occurred du ring the course of measurements. Results Influence of Duration of Polymer Deposition Using the same microsphere/can tilever assembly throughout, the frictional properties of several PLL(20)g [3.5]-PEG(2)-coated silicon wafer substr ates were evaluated as a function of polymer deposition times: 0.5, 1, 5, 10, 30, and 60 min. Data of Fig. 35 portray the distinct influence of the duration of pol ymer deposition on interfacial friction, indicating that longer
92 Figure 3-4. Scanning electron mi croscopy (SEM) images of a 5-m glass probe on a 0.58 N/mrated V-shaped cantilever that is typi cally used in the AFM friction force measurements. Images courtesy of th e Tribology Laboratory, Mechanical and Aerospace Engineering, University of Florida.
93 10 8 6 4 2Friction Force (nN) 25 20 15 10 5 0Normal Load (nN) 30 sec 0 1 min 0 5 min 10 min 30 min 60 min 0.30 0.25 0.20 0.15Coefficient of Friction 60 50 40 30 20 10 0Adsorption Time (min) Figure 3-5. Influence of polym er deposition time on the tribologi cal behavior of PLL-g-PEG brushes. Top: Friction versus decreasing load plots of a bare sodium borosilicate microsphere against PLL(20)g [3.5]-PEG(2)-coated SiO2 substrates prepared at different polymer deposition times. Bottom: plot of the coeffici ent of friction (i.e., slope of the friction load pl ots) as a function of durati on of polymer deposition.
94 deposition times result in lower friction. This is reflected in the rapid redu ction in the coefficient of friction (Fig. 3-5, bottom), which is defined as the slope of the fricti on-load plot (Fig. 3-5, top). Within the first 5 min of deposition, the va lue of the coefficient of friction is reduced to 90% of that measured for the in terface consisting of a bare microsphere against bare oxidized silicon; this reduction in the coefficient of fr iction was observed to reach a steady-state value after 1 hr. Reduction in friction occu rring more slowly over the latter portion of this period likely entails the reorganization of the polymer brush at the substrate/solution interface. Influence of Polymer Architecture Interfacial friction was measur ed for the contact of a 5.1-m bare borosilicate probe sliding against oxidized silicon wafer substrat es coated with a series of PLLg -PEG polymer brushes of different PEG molecular weights an d lysine/PEG grafting ratios (F ig. 3-6). Three general effects of polymer architecture on interf acial friction are apparent. First, lower interfacial friction is observed for tribosystems with increased PE G molecular weight (side-chain length) for approximately the same grafting ratio within each series, as exhibited through the maximum friction forces measured at a given applied normal load. For example, at 30 nN load, the friction forces with respect to PEG molecu lar weight are in the order of: ~10 nN for PLL(20)g (5.7)PEG(2) > ~8 nN for PLL(20)g (5.2)-PEG(5) > ~6 nN for PLL(20)g (5.8)-PEG(10); this is in good agreement with prior reports for th is polymer brush system . Second, for each PLLg -PEG series, interfacial frict ion decreases with decreasing lysine/PEG grafting ratio, as evid enced through a reduction in both the magnitude of friction forces at a specific load and the coefficient of friction ( slope of the friction-load plot). For each series, the lowest coefficients of friction are observed for the lo west grafting ratio, corresponding to the greatest density of PEG chains grafted onto the PLL backbone.
95 20 15 10 5Friction Force (nN) 35 30 25 20 15 10 5 0Normal Load (nN) PLL(20)g [3.3]-PEG(2) PLL(20)g [5.7]-PEG(2) PLL(20)g [8.0]-PEG(2) PLL(20)g [14.2]-PEG(2)(A) Figure 3-6. Friction versus decreasing load plots for three series of PLLg -PEG polymers: (A) PLL(20)g -PEG(2), (B) PLL(20)g -PEG(5), (C) PLL(20)g -PEG(10); in each series, the polymers vary only in lysine/PEG graf ting ratios. All measurements have been performed using the same AFM micros phere/cantilever assembly for the asymmetrically coated (i.e., bare microsphe re/coated substrate) tribointerface. Negative normal loads correspond to adhesive forces existing between the polymer brush and the sodium borosilicate microsphere.
96 12 10 8 6 4 2Friction Force (nN) 30 20 10 0Normal Load (nN) PLL(20)g [3.5]-PEG(5) PLL(20)g [5.2]-PEG(5) PLL(20)g [8.0]-PEG(5) PLL(20)g [11.8]-PEG(5)(B) 8 6 4 2Friction Force (nN) 30 25 20 15 10 5 0Normal Load (nN) PLL(20)g [5.8]-PEG(10) PLL(20)g [7.6]-PEG(10) PLL(20)g [15.7]-PEG(10)(C) Figure 3-6. Continued.
97 Third, interfacial adhesion between the bare borosilicate microsphere and the adsorbed polymer film is reduced/eliminated at resp ectively lower grafting ratios and higher PEG molecular weights. For non-adhesive contacts, friction force is expect ed to be zero at zero normal load; adhesion increases the effective cont act area between the probe and substrate as a function of normal load, and results in finite contact areasand thus fi nite friction forcesat zero and negative normal loads, e.g., the y -intercept of the fricion-lo ad map linear fit would be non-zero. In the PLLg -PEG system, the friction-load plots approach the non-adhesive limit as the number and size of PEG chains increases. Adsorbed Mass, Grafting Ratio, and Film Thickness Table 3-1 summarizes the data for the coefficient of friction () versus PEG molecular weight ( z ) and lysine/PEG grafting ratio ( y ); additionally, the adsorpti on of PLL-g-PEG from an aqueous solution composed of the physiological buffer, HEPES (a good solvent), has been characterized in terms of the dry adsorbed mass ( mdry) and the wet mass, using OWLS and QCM-D, respectively. From mdry and the parameters of the polymer architecture ( x y z where the prime indicates unit conversion from kDa to g/mole), the PEG surface packing density (), or the number of PEG chains per unit area of substrate, may be calculated from: PEG chains PLL g PEG chain PLL g PEG chains unit area nm2 (3-1) where, PEG chains PLL g PEG chain x y MWtlysine (3-2) PLL g PEG chains unit area mdry NAMWtPLL g PEG 10 23g cm2ng nm2 (3-3)
98 MWtPLL g PEG z PEG chains PLL g PEG chain x '. (3-4) Effective solvated film thickness ( hfilm) can be estimated from the mechanical coupling of the wet mass of the solvated pol ymer with the quartz crystal resonator in QCM-D. Measured shifts in frequency and dissipation can be fit to a viscoelastic Voigt m odel to obtain the four unknown parameters (film, film, film, hfilm) using soft constraints, such as assuming the storage modulus is lower than the loss modulus (G<
99 Table 3-1. Summary of data for the th ree PEG chain length series of PLL( x )g [ y ]-PEG( x ), varying in lysine/P EG grafting ratios ( y ); x and z are PLL and PEG average molecular weights in kDa, respectively. Note: mdry, dry mass measured by OWLS; hfilm, thickness of the wet brush derived from the Voigt model; calculated PEG surface packing density (Eq. 3-1); coefficient of friction. Polymer Architecture y mdry hfilm PLL( x )g [ y ]-PEG( z ) (lysine/PEG)(ng/cm2) (nm-2) (nm) 3.3 75.183 0.18 5.91 0.20 .04 5.7 55.45 0.12 5.01 0.431 .005 8 .0 45.06 0.09 4.19 0.75 .03 PLL(20)g -PEG(2) 14.2 36.76 0.05 3.09 0.88 .04 3.5 147.57 0.16 11.18 0.199 .006 5.2 111.95 0.12 9.75 0.308 .006 8 .0 88.27 0.09 9.35 0.46 .02 PLL(20)g -PEG(5) 11.8 59.81 0.05 6.98 0.58 .03 5.8 133.76 0.07 15.6 0.162 .003 7.6 109.14 0.06 12.9 0.226 .001 PLL(20)g -PEG(10) 15.7 55.76 0.03 10.01 0.35 .01
100 Discussion Influence of Duration of Polymer Deposition The kinetics and thermodynamics of polyele ctrolyte adsorption on oxide surfaces have been extensively studied [179, 180]. In general, polyelectrolytes will adsorb spontaneously in order to neutralize charges on the surface. Initia l rate of adsorption is diffusion limited, and therefore a function of th e degree of swelling (size) of the polyelectrolyte in the bulk solution . Low ionic strengths preclude the screening of electrostatic interact ions, thus causing the polyelectrolytes to adsorb irreversibly; moreover, once on the surface, spreading and reconformation is slow resulting in dangli ng loops and tails as well as conformational heterogeneity and overcompensation of surface char ge . Adsorption of comb copolymers in particular has been studied usi ng self-consistent field methods . For comb copolymers with adsorbing backbones (e.g., a polye lectrolyte) and nonadsorbing teet h, the latter will tend to protrude into the solution to compensate for th e decrease in entropy resulting in confinement, and thus decrease the critical adsorption ener gy. Moreover, the volume fraction profiles of adsorbed comb copolymers with narrow spacing between the teeth are expected to exhibit brushlike behavior (Fig. 3-2). The adsorption performance of PLL-based pol ymers has also been studied, with PLLg PEG found to adsorb spontaneously from aqueous solution onto many oxide surfaces [167, 168]. Electrostatic interaction betw een cations on the PLL backbone and the negative charge on the oxide surface leads to strong at traction under appropriate solution conditions. In general, the pH of the medium must be above the isoelectric point (IEP) of the oxide, where it will be negatively charged, and below the p Ka of the primary amines on PLL, wh ere it will be positively charged . In the present study, the adsorption of PLL(20)g [3.5]-PEG(2) onto silica-passivated surfaces have been performed from 1.0 mg/mL po lymer solutions in 10 mM HEPES, adjusted to
101 the physiological pH (7.4); as the IEP of s ilica is ~2.0 [182, 183], its surfaces would be negatively charged, while the amino groups (p Ka ~10) would be positivel y charged, under these conditions. The kinetics of adsorption of PLLg -PEG has been previous ly reported from OWLS measurements for various oxide surfaces, including Nb2O5, Si0.4Ti0.4O2, TiO2 [167, 168]. It has been observed that adsorption takes place rapidl y and irreversibly, with 95% of the final adsorbed mass reached within the first 5 min, fo llowed by a stable plateau after 20 min. The plot of coefficient of friction versus deposition time in Fig. 3-5 (bottom) essentially tracks the OWLS kinetic plot, with 90% of the re duction in friction occu rring within the first 5 min, followed by a slow leveling off after 30 min. These fricti on measurements were performed using the same tip/cantilever assembly on samples prepared at different deposition times, in contrast to the OWLS measurements, which were performed continuously over time. The presence of a solvated polymer layer, es pecially the outer layer composed of water soluble, flexible PEG side-chains, proves to be favorable to the reduction in friction. The observed lubricity with duration of polymer deposition is therefor e a function of the development of this solvated polymer layer on the surface; not only is the coverage incr eased over time, but as discussed below, the increase in packing density drives the PEG chains to form more extended conformations as well. Influence of Polymer Architecture The time dependence of friction reduction with PLLg -PEG adsorption suggests that the frictional properties of these inte rfaces are closely re lated to the areal density of PEG chains immobilized near the surface. The comprehensive e ffect of this areal density is revealed through an analysis of the coupled contribution of PEG chain length and grafti ng ratio to interfacial friction. To determine the number density of PE G chains on the surface, it is assumed that the
102 PLL backbone lies nearly flat on the surface, and that the PEG chains are protruding into the solution in a brush-like fashi on, as predicted for comb copol ymers with adsorbing backbones and nonadsorbing teeth. Table 32 re-presents the data for the wet thickness of the polymer film ( hfilm) (from Table 3-1), comparing it w ith the theoretical thickness ( h ) predicted from brush scaling laws (Eq. 1-6) [90, 91]. It shows that th e wet film thickness extracted from the Voigt-fit of the QCM-D data for all polymer architectures fall within 12% of the values predicted by scaling theory, and establishes gr ounds for the following analysis. In bulk solution, the Flory radius ( RF) reflects the conformation of a linear polymer that follows the statistics of a self-avoiding random walk (Eq. 1-4); this is considered as its unperturbed dimension. Upon confinement to a su rface, adsorbed polymers can be described in the form a two-dimensional lattice with an average distance between graft points ( L ) which scales with the packing density () as L 1/2 (Eq 1-5 and Fig. 1-4). If L is greater than RF, the polymer molecules would maintain their unpert urbed dimension on the surface; however, when L becomes smaller than RF, adjacent polymer chains begin to overlap and assume more extended conformations due to repulsive (excluded volume) interactions [90, 91, 184]. The ratio of L to RF can be used to gauge the degree of extension of a polymer grafted ont o a surface [167, 185, 186]; it includes information about both the polymers dimensions and packing density For the series of PLLg -PEG polymers, the polymer dimension refe rred to would be that of the PEG sidechains ( R F z) that are expected to protrude perpen dicular to the surface, while the packing density will be closely rela ted to the grafting ratio ( y 1, Eq. 3-2). Estimates of the Flory radius can be made us ing an empirical equation derived from static light scattering experiments on PEG [185, 187], RF0.181 N0.58(nm), (3-6)
103 Table 3-2. Wet brush thickness (hfilm) compared with brush thickness calculated from scaling laws (h = Na1/3). Polymer Architecture y hfilmh PLL(x)-g[y]-PEG(z) (lysine/PEG)(nm) (nm) 3.3 5.91 4.66 5.7 5.01 4.03 8 .0 4.19 3.63 PLL(20)-g-PEG(2) 14.2 3.09 3.12 3.5 11.18 11.18 5.2 9.75 10.05 8 .0 9.35 9.08 PLL(20)-g-PEG(5) 11.8 6.98 7.75 5.8 15.6 17.27 7.6 12.9 16.01 PLL(20)-g-PEG(10) 15.7 10.01 12.38
104 where N is the degree of polymerization; from this equation, the unperturbed dimensions of the PEG side-chains of different mol ecular weights are estimated to be 1.65 nm for 2 kDa PEG, 2.82 nm for 5 kDa PEG, and 4.21 nm for 10 kDa PEG. The prefactor in the ab ove equation relates to the PEGs persistence length (a of Eq. 1-4), which in another work on the osmotic properties of PEG was reported to be ~0.35 nm . In turn the average grafting di stance can be estimated from the surface packing density assuming a hexa gonal close-packed lattice arrangement [185, 186]. L 4 3 1/41/21/2 (3-7) Table 3-1 presents values for which are equivalent to the number of PEG chains per unit area (in nm2), as calculated from the dry mass (mdry) of the PLL-g-PEG adsorbed on the surface from OWLS measurements, and the parameters (x, y, z) of the polymer architecture (Eq. 3-1 to 34); as such, L relates to both the lysine/PEG grafting ratio and how the PLL-g-PEG copolymer stacks side-by-side on the surface during adsorption. Based on these values, the coefficient of frictio n, determined from data in Fig. 3-6 and presented in Table 3-1, can be plotted as a function of L /2 R F, a parameter that expresses the relative degree of extension of the PEG brush on the surface in terms of its chain length and packing density (Fig. 3-7). L /2 R F values below 1 represent the regime where lateral interaction between PEG chains begins to occur and the polymer begins to ex tend relative to its unperturbed dimensions. At L / 2 R F values below 0.5, L R F, a condition under which, accor ding to scaling theory, strong extension begins to occur, and the adsorbed polymer switches from the mushroom to the brush regime [90, 91, 184]. The plot clea rly reflects a strong reduction in friction at the on set of strong
105 1.0 0.8 0.6 0.4 0.2 0.0Coefficient of Friction 2.0 1.5 1.0 0.5 0.0L /2 RF (10, 5.8) (5, 3.5) (10, 7.6) (2, 3.3) (5, 8.0) (10, 15.7) (10,5.2) (2, 14.2) (2, 8.0) (5, 11.8) (2, 5.7) Figure 3-7. Plot of coef ficient of friction versus L/2RF, estimated from Eq. 3-6 and 3-7. Data labels, (z, y), indicate the PEG molecular weight in kDa (z) and the lysine/PEG grafting ratio (y). Figure 3-8. Plot of adsorbed mass of human serum versus L/2RF of PLL-g-PEG chains adsorbed on Nb2O5 surface. Reproduced from  by pe rmission of The American Chemical Society.
106 segment extension (L / 2 R F 0.5) supporting the idea th at the conformational state of PEG chains strongly determines the lubricity to the PLL-g-PEG copolymer system. The strength of this claim is underscored by the extent of the data derived from a matrix of architectures varying in both PEG molecular weight and grafting density. Coefficien t of friction values of PLL-g-PEG polymers with 2 kDa PEG side chains are obser ved to lay slightly outside the predicted relationship between friction and strong extension; this result could be rationalized through a potential for closer proximity between PLL backbones with shorter PEG side-chains on the surface, thus resulting in a gr eater effective surface packi ng density and leading to an overestimation of L in these cases. In general, it is seen that brush architectures possessing longer PEG side-chains and lower grafting ratios (relatively more PEG chains attached to the PLL backbone) exhibit the lowest frictional forces. Finally, it is noteworthy to observe that this tribological behavior of the PLL-g-PEG systemnamely the drastic reduction in friction near L /2 R F 0.5exhibits a remarkably similar trend to that observed fo r the protein resistance of PLL-g-PEG-coated surfaces [167, 185] (Fig. 3-8). In general, reducti on in surface energy and increase d steric repulsion are known to enhance protein resistance; in addition, the amo unt of bound water at the interacting interface has also been considered for PLL-g-PEG-coated surfaces. Similarly, here, the reductions in friction observed for the series of thin polymer films, e ssentially equivalent in chemical composition at the sliding interface, suggest an im portant role of solvent molecule s. It is surmised that the conformational changes of the polym er associated with an extended or brush-like state in which water is effectively complexed also produces the observed low shear st rength at the sliding interface.
107 Conclusion Frictional properties of PLL-g-PEG-coated silicon oxide surfaces have been systematically studied by AFM, as a function of deposition time and polymer architecture, using a 5.1-m diameter silica probe under aqueous media at physiological pH. The most significant reduction in friction occurred w ithin the first 5 min of substrate exposure to the polymer solution; however, further reduction is obser ved with conformational reorganization of the polymer film. Friction between the polymer-coate d substrates and colloi dal probe was observed to systematically vary with polymer architec ture, specifically, the PEG chain length and the lysine/PEG grafting ratio; the coefficient of fr iction decreased with respect to increased PEG molecular weight and decreased lysine/PEG ratio. The general friction response of PLL-g-PEG as a function of polymer architecture has been ra tionalized in terms of th e spatial density of PEG side-chains on the substrate. This areal density has been characterized in terms of the distance between PEG chains on the surface (L), related to grafting ratio and coverage, and the Flory radius (RF) of side-chains, related to the PEG molecu lar weight. It was observed that a drastic reduction in friction occurred at L / 2 R F 0.5, at the point where brush scaling theory predicts the onset of strong segment extension occurs. This trend is analogous to the increase in protein resistance previously observed [167, 185] for PLL-g-PEG-coated surfaces within the same brush conformation regime.
108 CHAPTER 4 POLYSTYRENE BRUSHES Introduction The ability to modify surfaces with polyme rs is especially important in boundary lubrication where there is more extensive soli d-solid contact, leading to generally greater friction, adhesion, and wear  As lubricant thickness decreases to molecularly thin films, its physicochemical properties become more important than its bulk viscosity. Polymer brushes confined to surfaces are pred icted to be highly extended in a good solvent, making these potentially effective boundary layer lubricants [89, 90]. Increase in osmotic pressure within the brush during compression manifests in long-range repulsive interac tion as the chains swell back and extend, giving rise to low shear strengths and low friction [91, 92]. Metal oxide surfaces coated with mo lecularly thin layers of poly(L-lysine)-graftpoly(ethyleneglycol) (PLL-g-PEG) brushes have been demonstrat ed to exhibit reduced friction at the nanoand macroscale levels [51, 92, 109, 110]. More import antly, the lubricity of these hydrophilic films was found to be strongly dependen t on solvent quality, in both single and binary solvent systems, being reduced as the no n-polar character of the solvent increased [92, 110]. In single solvent systems (Fig 4-1, top), the rate at which interfacial friction changes as a function of applied normal load decreased as the solvent environment was exchanged in the order of increasing polarity from 2-propanol ethanol, methanol, and aqueous HEPES buffer (indicated as water in the Fig. 4-1, top) . This trend str ongly correlated with the observed increase in areal solvation (solvent mass per unit s ubstrate area) and in the solvent number density in the brush (number of solvent molecu les per ethylene glycol unit), measured by complementary OWLS and QCM-D techniques. Th ese observations were accounted for in terms of the Hansen solubility parameters that relate total cohesive energy dens ity to dispersion, polar,
109 Figure 4-1. Interfacial friction as a function of decreasing load for the contact between an SiO2 substrate coated with PLL(20)-g[3.5]-PEG(5) and a 5-m SiO2 probe in different solvent environments. Top: solvents of systematically varying polarity. Bottom: 2propanol/aqueous buffer binary solvent system of varying 2-propanol volume fraction. Note: c is the critical volume fraction (s ee text). Reproduced from  and  by permission of The American Chem ical Society (with annotations by this author).
110 and hydrogen-bonding component s; a strong correlation existed between areal solvation and the polar and hydrogen bonding interaction energi es, while there was no correlation with the dispersion energy. Less favorable solvent-segment interaction under poor solv ents resulted in the solvent being expunged more easily under compression, leading to a less fl uid-like interface with less mobile segments giving rise to higher shea r strengths and friction under these conditions. In binary solvent systems (Fig. 4-1, bottom) consisting of 2-propanol and aqueous HEPES buffer, the rate of change of interfacial friction with applied normal load increased as the volume fraction of 2-propanolthe less polar componenti n the solvent environments increased . Moreover, in this case, two distinct regimes we re observed: there was a slow increase in the coefficient of friction ( 0.1) below the critical volume fraction (c) of 0.85, after which, there was a rapid increase ( 0.25) within the narrow range of 15% increase in 2-propanol. This trend strongly correlated with the steep decline in areal solvation above c, ascribed to partial solvent demixing that created a differen tial in solvent composition across the interface: below c the brush was richer in water compared to the bulk due to enthalpically favorable interactions; above c this entropic discrepancy between brush and bulk could no longer be maintained such that sudden conformational collap se ensued with further increase in 2-propanol. Rapid increase in interfacial friction strongly correlated with this collapse transition above c that, again, gave rise to the loss of chain mob ility that was responsible for the low shear, liquidlike nature of the fully solvated interface. The work of this chapter  aims to complement these previous results by demonstrating a similar general behavi or: the increase in lubricity of a hydrophobic brush with increasing nonpolar character of the solvent envi ronment. Whereas preformed PLL-g-PEG bottle-brushes were attached to oxide surfaces via electrostatic interact ion by regulating the pH,
111 here, polystyrene brushes were covalently tether ed to oxide passivated silicon wafers by direct polymerization of styrene on its surface. Normal and shear forces have been previously measured with the surface force apparatu s (SFA) between mica surfaces b earing preformed polystyrene adsorbed via a terminal zwitterionic group [59, 188, 189]. Normal forces became repulsive at higher polymer adsorption and at higher shear rates [188, 189], while shear forces remained extremely weak in good solvent ov er a wide range of velocitie s . It has been shown, however, that high polymer brush densities could be achieved by direct polymerization from the surface rather than attachment of preformed pol ymers [54, 190, 191]; polymer attachment would be severely diffusion limited and sterically hi ndered compared to monomer attachment, thus discouraging the formation of tightly packed brushes. Surface-initiated polymerization (SIP), in general, repres ents a versatile method of tailoring the lubricity of surfaces over a wide range of polymer-solvent systems. In the past, this has been realized through the self-assembl y of initiators on the surface through: (a) the functionalization of surfaces with groups that ini tiators can afterwards at tach to , (b) the synthesis of asymmetric initiators with an anchoring functionality [190, 191, 193], or (c) a combination of both . This work takes the route of asymmetrically modifying the available 4,4-azobis(4-cynanovaleric aci d), an AIBN-type initiator, with a double bond f unctionality that could then be coupled with a monochlorosilane, t hus providing a path to tether it onto the silicon oxide substrate by a condensation reaction with the terminal hydroxy groups. The mechanism and kinetics of the surface-in itiated free-radical polymerizatio n of styrene has already been extensively studied ; in this study, the formation of the initiator monolayer, and, subsequently, the polymer brush on the surface were simply monitored by XPS and ellipsometry.
112 Nanoscale friction force measurements were performed on these systems with an AFM, using a 5-m SiO2 colloidal probe while systematica lly varying the environment from good (toluene) to poor (2-propanol and n-butanol) solvents, with respect to the molecular composition of the polystyrene brush. Relativ e solvent uptake and viscoelastic response of the brush system were monitored with a quartz crystal microbalance (QCM) for the solvent series, and correlated with the friction data. Experiments Synthesis of Azochlorosilane Initiator The surface attached free radical initiator wa s prepared by asymmetrically modifying 4,4azobis(4-cynanovaleric acid) thr ough the consecutive Steglich es terifications of the carboxy moieties , first with n-butanol, followed by allyl alcohol (F ig. 4-2). A solution was prepared consisting of 5.60 g (20 mmol) of the azo in itiator, 75 mg of 4-(dimethylamino)pyridine (DMAP), and 1.48 g (20 mmol) of n-butanol, in about 40 mL of dr y, distilled tetrahydrofuran (THF), and then cooled to ice bath temperatur e. To this, a 15-mL THF solution of 4.12 g (20 mmol) N,N-dicyclohexylcarbodiimide (DCC) was slowly dripped, and then stirred for 3 h at room temperature. Urea byproduct was removed by vacuum filtration thro ugh a membrane filter with a 0.10-m cut-off, and the filtrate reduced thr ough the removal of THF by rotavap below 40 C. This was then added to water, extracted with dichloromethane, washed with brine solution, and dried over magnesium sulfate. Dich loromethane was removed by rotavap below 40 C, and the residue further dried under vacuum overnight This procedure should give a statistical product (actual yield 78%) in wh ich one carboxy moiety is capped with a butyl group. Without further purifications, this crude product was used in the next step where the remaining carboxy moiety was esterified with an equimolar am ount of allyl alcohol by the same DCC/DMAP
113 O N N O CN CN O O Si O O CN O Si O nOH N N HO CN CN O O BuOH DCC, DMAP DCC, DMAP OH O N N O CN CN O O HSi(CH3)2Cl H2PtCl6O N N O CN CN O O Si Cl Si wafer Et3N, Toluene 1. Styrene, >60 oC 2. Soxhlet extraction with THF 1 2 3 4 Figure 4-2. Scheme for the preparation of PS brush on Si wafer surface: synthesis of the azochlorosilane initiator (product 2); immobilization of the initiator on the oxidized Si wafer surface (product 3); surface-initiated polymeri zation of styrene (product 4).
114 procedure to yield product 1 (actual yield 92%), introducing a double bond functionality to the azo initiator. This transformation was indicated by the appearance of vinyl 1H NMR shifts at 5.2, 5.3, and 5.9 ppm (Fig. 4-3). The 1H NMR data were acquired in CDCl3, on the General Electric QE-300 spectrometer, and processed using NUTS software (Acorn NMR, Inc., CA). This vinyl species allowed the addition of a chlorosilane group to the azo initiator by hydrosilation [190, 195], which then provided an anchor to the oxi de layer on a silicon wafer. Since chlorosilanes are very re active with moisture, all reactio ns were carried out in dry apparatus under a nitrogen atmosphere. A total of 5 mL of dimethyl monochlorosilane and a catalytic amount of hexachloroplat inic acid was added to product 1, which had been previously vacuum-dried overnight. The mixture was refluxed at 35 C for 3 h, and then left to stir at room temperature overnight. Excess dimethylmonochl orosilane was removed by rotavap below 40 C. The remaining product 2 was dissolved in a small amount of dry, distilled toluene, and then quickly filtered through magnesium sulfate to re move both trace moisture and platinum catalyst. Disappearance of the vinyl 1H NMR shifts, and the appearance of methyl proton shifts on Si around 0 ppm indicated the formation of 2 (Fig. 4-3). Surface-Initiated Polymerization (SIP) of Styrene Silicon wafers, cut into small strips, were cl eaned before use as follows: sonication in a dilute cleaning solution (Fisherbra nd Ultrasonic Cleaning Solution, Fisher Scientific) for 15 min, followed by ultrapure water (18.2 M) for 5 min, soaking in piranha solution (70:30 H2SO4/30%H2O2) for 30 min, and washing and sonicat ion in ultrapure water for 10 min. [Caution! Piranha solution is highly corrosive a nd oxidizing. Use splash goggles and latex gloves when handling.] After drying in the oven, the silic on wafer was cleaned in oxygen plasma
115 6 5 4 3 2 1 0 ppm a b c d e e f f e e g b c d e e f f e e h i i a b a c d e e f f e e k j l m m a b c f e d g (not shown)a b c f e d h i i a b, l c, k f e d, j m Figure 4-3. The 1H NMR spectra taken from crude sample s tracking the transformation of the AIBN-type azo initiator: (bottom) after the first Steglich esterification with n-butanol; (middle) after the second Steglich este rification with allyl alcohol (product 1), showing the vinyl prot on shifts (labeled i); (top) after the ch lorosilane addition by hydrosilation (product 2), showing the disappearance of the vinyl proton shifts, and the appearance of the methyl protons shifts on the silane (labeled m). O N N HO CN CN O O O N N O CN CN O O O N N O CN CN O O Si Cl
116 for 2 min, and placed flat at the bottom of a se ptum-sealed vial that was purged with nitrogen gas. Into this vial, dry, distilled toluene, and 0.1 mL each of triethylamine and the toluene solution of azochlorosilane 2 was added. The reaction was allowe d to run overnight, after which the azo-modified silicon wafer 3 was washed thoroughly with methanol. This azo-modified silicon wafer was placed in a reaction vessel that was charged with 10 mL of styrene monomer from which the inhibito r was previously removed with basic alumina. The system was degassed to remove oxygen by four successive freeze-pump-thaw cycles, and then allowed to polymeri ze with stirring at 60-75 C for 43 h. The reaction was terminated by exposure to air, and the PS-modified silicon wafer 4 was washed by Soxhlet extraction in THF for 44 h to remove any free polymer. A similar procedure was used to graft polys tyrene onto a QCM quart z crystal with a SiO2sputtered gold electrode face (Maxtek, Inc., CA). The quartz crystal was washed with 2propanol, and then plasma cleaned under oxygen for 200 s before use. Styrene monomer was degassed separately from the azo-modified quart z crystal to prevent it from fracturing under the freeze-pump-thaw regime. Finally, as the active ar ea on the quartz crystal consists of a complex multilayer (Ti/Au/Ti/SiO2), a separate azo-modified silicon wafer was included in the reaction vessel to carry out concurrent polymerization for thickness measurements. Total reaction time was 24 h, followed by 40 h of Soxhlet extraction in THF. Characterization of Surface Modifications Surface modifications on the silicon wafer we re monitored by ellipsometry and XPS. Thickness measurements were performed on th e Multiskop system (Optrel GmbH, Germany) equipped with a 632.8 nm He-Ne laser s ource at an incident angle of 60. Ellipsometric parameters and were recorded on at least three ar eas on the sample. Together with the
117 materials refractive index (n) and extinction coefficient (k), these values were used in a layer model to calculate an average film thickness. Analysis of the surface elemental composition was performed using a PHI Model 5700 Xray photoelectron spectrometer equi pped with a monochromatic Al K X-ray source (h = 1486.6 eV, 350.0 W) incident at 90 relative to the axis of a hemispherical energy analyzer. The spectrometer was operated at low (survey) reso lution with 187.85 eV pass energy, and at high resolution with 23.50 eV pass energy, with a photoelectron take off angle of 45 from the surface, and an analyzer spot diameter of 1.1 mm. Survey spectra were collected from 0 to 1400 eV, and the high-resoluti on spectrum was obtained in the C 1s, O 1s, and N 1s regions. The O 1s peak of the SiO2 signal (533 eV) was used as the bindi ng energy reference. All spectra were obtained at room temperature and at a base pressure of about 10-8 Torr. Atomic concentrations were estimated from peak areas and publishe d instrumental sensit ivity factors . AFM Normal and Lateral Force Measurements Friction force measurements were performed using a home-built AFM scan head equipped with a liquid cell/tip holder (Dig ital Instruments, CA), controlled by AFM100/STM100 feedback electronics and SPM32 software (RHK Technology, In c., MI) (Fig. 3-3). The microscope uses a single tube piezo to move the sample relative to a fixed tip position. Reflection of a laser beam from the back of the cantilever is detected by a four-quadrant photodi ode. Details of this assembly have been reported elsewhere [19, 112]. The tip consisted of a 5-m silica colloidal sphere affi xed to a cantilever (Novascan Technologies, IA); this sphere served as the counterface to the PS brush-modified silicon wafer surface. The tip was used as received, with the spherical shape of the probe validated by optical microscopy. Its surface roughness was not determin ed; however, valid comparisons of friction
118 measurements have been made po ssible with the use of the same tip on the same sample, with only the solvents exchanged in situ. Kinetic friction was measured by monitoring th e lateral deflection of the cantilever as a function of tip position during sliding and loadin g/unloading. This was im plemented by rastering the sample in a line-scan mode as the load wa s ramped up and then down, while simultaneously recording both normal and frictional forces. A single cantilever assembly was used for all of the measurements reported in this study. Normal loads were determined from th e cantilevers nominal spring constant (kN 0.58 N/ m manufacturers reported value) and direct measurements of sample displacement. Such a cantilever/microsphere assembly wo uld exert a pressure of 95.6 MPa at an applied load of 20 nN on a silicon surface, assuming a He rtzian contact area of ~210 nm2. Friction force response was taken to be the ha lf-difference of the la teral deflection signal on the photodetector of the forward and reverse traces (i.e., a friction loop). Lateral forces were calibrated by sliding the tip at given normal load set-points across a s ilicon grating with known slopes (TGF11, MikroMasch, Spain). Details of this procedure have been reported elsewhere . Measurements used a scan rate of ~1400 nm /s over a distance of 100 nm. Reported friction data represent the increasing normal load ramp, with maximum applied loads of less than 60 nN to avoid tip and sample wear. At least three acq uisitions over several regions on the sample were averaged, with offset tip positions falling within an area of 2500 nm2. Solvents were exchanged in the order of toluene, 2-propanol, and n-butanol, by transferring aliquots in and out of the liquid cell using two 5-mL syringes.
119 Topographic images for surface roughness analys is were obtained in AC mode using an MFP-3D atomic force microscope (Asylum Res earch, Santa Barbara, CA), using a cantilever with a nominal resonance frequency of 70 kH z (AC240TS, Olympus, Japan). Images were collected at 1-m2 scan sizes, at scan rates of 0.80 Hz, over a 100-m2 sampling area. Roughness analyses were performed using bui lt-in functions in MFP-3D based on the Igor Pro, Version 5.0 (WaveMetrics, Inc., OR) platform. QCM Solvent Uptake Measurements The QCM system used for solvent uptake measurements was assembled from SA250B-1 Network Analyzer and test fixture (Saunders and Associates, Inc., AZ), a liquid flow cell (Maxtek, Inc., CA), and QTZ control software (Resonant Probes GmBH, Germany) (Fig. 4-4). Resonators consisted of AT-cut quartz crystals, also from Maxtek Inc., with silica-sputtered gold electrodes, and a fundamental re sonance frequency of 5 MHz. Solvent exchange experiments were perf ormed on both blank and PS brush-modified quartz crystals. The blank quartz crystal was cleaned prior to use by sonication in acetone, 2propanol, and ultrapure water for 5 min each. It was then plasma cleaned for 1 min under O2/H2O2 process gas. The PS brush-modified quartz crystal was simply wa shed with 2-propanol and then dried in air prior to use. Quartz crystals were installed in the flow cell one day prior to making measurements to allow for the stress-relaxation of the Viton O-ring. Data were collected in air for 100 min prior to the firs t solvent injection to ensure the stabilization of the system. Data were then collected in 10-min intervals between each solvent exchange Reported frequency and bandwidth shifts represent the average of data collected over a period of 5 min.
120 Figure 4-4. The QCM set-up for impedance analysis of a quartz crystal res onator, consisting of a network analyzer, test fixt ure, and liquid flow cell.
121 Results Surface Characterization by XPS Analysis Covalent grafting of PS onto silicon wafers was followed by XPS analysis. Fig. 4-5 presents the XPS spectra after cl eaning with oxygen plasma, after gr afting of the azo initiator, and finally, after the surface-init iated polymerization of styrene. The XPS analysis on the clean silicon wafer was performed immediately followi ng plasma cleaning. Its survey spectrum (Fig. 4-5, bottom) includes peaks characteristic of silicon and oxygen (Chapter 2), while a small amount of adventitious carbon is also present. After the self-assembly of the azo initiator on the clean silicon wafer, characteristic peaks in the survey spectrum (Fig. 4-5, middle) for nitrogen (N 1s) and carbon (C 1s) appeared at 400 and 286 eV, respectively. High-reso lution spectrum of the N 1s re gion (Fig. 4-6, top) showed two overlapping peaks at 400.0 and 401.5 eV, assigne d to the chemical shifts of the cyano and azo groups , respectively. Relative atomic concentrations of carbon and nitrogen were calculated by integration of the peak areas, with intensities normalized according the particular elements sensitivity. The observed C:N atomic con centration ratio (84:16) correlates well with the composition of the grafted azo initiator 3 (i.e., 21 C atoms to 4 N atoms). In some measurements, 87% C was observed, due most pr obably to the presence of adventitious carbon. Oxygen in the azo initiator was not included in this analysis as its intens ity was convoluted with the large background signal of SiO2. After grafting polystyrene, the survey spectrum (Fig. 4-5, top), shows the absence of the characteristic silicon and oxygen peaks from SiO2, and any nitrogen peaks from unreacted initiator or the part that remains attached to the silicon wafer after its fragmentation. Highresolution analysis of the C 1s region (Fig. 46, bottom) revealed a la rge peak at 284.2 eV
122 1400 1200 1000 800 600 400 200 0 Binding Energy (eV) Si 2p Si 2s O 1s O KLL N 1s C 1s C KVV Si/SiO2 Figure 4-5. Survey XPS spectra of silicon wafer after cleaning with O2 plasma (bottom), grafting of the azo initiator (middle), and surfaceinitiated polymerization of styrene (top). O CN O Si O nO N N O CN CN O O Si O
123 2.0x104 1.8 1.6 1.4Count Rate (c/s) 410 405 400 395 Binding Energy (eV) N N C N N 1s region 1.5x104 1.0 0.5Count Rate (c/s) 300 295 290 285 280 Binding Energy (eV) shake-up sattelite peak C 1s region Figure 4-6. High-resolution XPS spect rum of (top) the N 1s region af ter grafting the azo initiator, showing the nitrogen chemical shifts of the azo and the cyano groups, and (bottom) the C 1s region after surface-initiated pol ymerization of styrene, showing the shake-up satellite peak near the C 1s photoelectron peak due to the styrene aromatic ring. O N N O CN CN O O Si O O CN O Si O n
124 characteristic of a hydrocarbon system, as well as a small satellite peak at 291.1 eV assigned to shake-up indicative of the styrene aromatic ring . Ellipsometric Film Thickness Measurements Ellipsometric measurements were performed after each stage in the modification of the silicon wafer in order to provide data for a layer model wherein th e thickness value of a previous layer was used as reference for calculating that of its succeeding layer . First, the average SiO2 layer of six different samples was determin ed to be 14 3 after plasma cleaning, calculated using the optical cons tants of the Si substrate ( N 0.8580 i0.018) and its oxide layer (n 1.4598). Next, the thickness of the azo initiator film was evaluated from six different samples to be 11 4 using a two-layer model; since the refractive inde x of this compound is not known, that for (3-aminopropyl)trimethoxysilane (n 1.424), commonly used in functionalizing silica surfaces, was used as a worki ng value. Finally, the thickness of the PS film (n 1.591) was evaluated using a three-layer model. The sample used in AFM friction force measurements was determined to have an averag e dry thickness of 117.6 0.6 nm, measured at five different areas on each of two different samples. The active area on the QCM crystal consisted of a complex multilayer of quartz/Ti/Au/Ti/SiO2, and as we did not have information about the thicknesses of the underlying layers, it was not possible to directly track modifications by ellipsometric layer modeling. Thickness of the PS film on the QCM crystal was therefore estimated from a silicon wafer on which concurrent polymerization was carried out in the same vessel. Average PS film thickness was evaluated to be 30 9 nm, measured at five different areas on the sample, being less than that of the AFM sample as a result of shorter reaction time. However, differences in the roughness, or root-mean-square (rms) height, of th e silica layer on the Si wafer (0.22 0.02 nm)
125 and on the QCM crystal (1.78 0.08 nm) may also contribute to discrepa ncies in the estimated PS thickness values. The rms height s were averages taken from 1-m2 AFM scan sizes at different locations within a 100-m2 area. Solvent Uptake and Dissipation Monitoring The quartz crystal resonator represents an acous tic reflectometer that may be used to probe loads on its surface from the phase shift in the reflection amplitude of shear waves propagating along its thickness [138, 139]. The frequency shift ( f) and the bandwidth shift () are the real and imaginary components of a complex frequency shift ( f *) that take into account both the elastic and dissipative interactions of the quartz crystal with its e nvironment, respectively (Eq. 210). In the Sauerbrey limit, i.e., a thin rigid film in air or vacuum, there is no bandwidth shift, and the fractional shift in frequency is simp ly proportional to the mass loading on the quartz crystal  (Eq. 2-8); under li quid, there is only a purely viscous load such that the frequency shift is the negative of the bandwidth shift as predicted by the general Kanazawa relation (Eq. 29 and 2-12) [140, 141]. For a viscoe lastic film in contact with a liquid, the complex frequency shift includes both a Kanazawa term and a Sauerbrey term [138, 141], such that, in the thin film limit, the frequency and bandwidth shifts ar e the sums of the Ka nazawa and Sauerbrey contributions (Eq. 2-13). In the present study, f and were monitored simultaneously as solvents were exchanged over a PS brush-modified versus a blank quartz crys tal resonator. In the blank, there was no mass loading, and therefore, the frequency shift appr oximated the bandwidth shift, but with opposite sign (Fig. 4-7, Table 4-1). However, for the PS-m odified quartz crystal, mass loading due to the solvent uptake in the polymer produced different readings. The Sauerbrey contribution can be
126 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 f / f (x 10-3) 3500 3000 2500 2000 1500 1000 500 0 0.25 0.20 0.15 0.10 0.05 0.00 / f (x 10-3) Blank 2-Propanol n -Butanol Toluene n -Butanol 2-Propanol Toluene 2-Propanol -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 f / f (x 10-3) 7000 6500 6000 5500 5000 4500 4000 0.25 0.20 0.15 0.10 0.05 0.00 / f (x 10-3) PS Brush-Modified Toluene Toluene n -Butanol 2-Propanol n -Butanol 2-Propanol 2-Propanol Figure 4-7. Fractional shifts in frequency ( f/f) and bandwidth (/f) of (top) a blank and (bottom) a PS brush-modified quart z crystal resonator under 2-propanol, n-butanol, and toluene.
127 Table 4-1. Normalized frequency ( f/f) and bandwidth ( /f) shifts of PS-modified and blank quartz crystals under various so lvent environments. Sauerbrey mass and dissipation are calculated from the difference. Average f/f (-3) Solvent PS modified Blank Difference Sauerbrey mass (g/cm2) 2-Propanol .1615 .1551 .0074 0.56 n-Butanol .1904 .1759 .0145 1.28 Toluene .1120 .0904 .0217 1.91 Average / f (-3) Solvent PS modified Blank Difference Dissipation (-3) 2-Propanol 0.2000 0.1959 0.0041 0.0067 n-Butanol 0.2205 0.2198 0.0006 .0002 Toluene 0.1855 0.1101 0.0754 0.1500
128 extracted from the observed frequency shift by th e subtraction of the Kanazawa contribution as determined from the blank. f Sauerbrey f observed f Kanazawa (4-1) Comparison of the blank and the PS-m odified normalized frequency shift ( f/f) data shows only small differences under 2-propanol and n-butanol. Under toluene, however, the PS-modified quartz crystal exhibits a consid erably more negative frequenc y shift. Using the Sauerbrey relation, areal mass densities representing the solvent uptake in the polymer brush were estimated from the differences in the frequenc y shifts between the PS-modified quartz crystal ( fobserved) and the blank ( fKanazawa). The PS brush shows a higher relative solvent uptake in toluene compared to the alcohols. Comparison of the normalized bandwidth shift (/f) data reveals that under 2-propanol and n-butanol, the PS-modified quartz crystal closely follows the Kanazawa condition, as in the blank (Fig. 4-7). Under toluene, however, the PS-modified crystal considerably departs from this condition, i.e., a dramatically higher bandwidth sh ift is observed than what is expected in the Kanazawa regime. This is attributed to a change in the viscoelastic behavior of the polymer film, becoming more lossy or plasticized as it swel ls upon solvation. These observations are consistent with the swelling behavior observed in the AFM force-displacement plots and the high lubricity of polymer brushes under good solvents. Friction Force Response and Brush Swelling/Collapse With the PS-modified silicon surface under a toluene solution, friction was measured by rastering the sample in a direction perpendicu lar to the cantilevers long axis while first increasing and then decreasing the normal load. Both the normal and lateral deflections of the
129 cantilever were simultaneously recorded, with friction data consisting of the lateral force response as a function of normal load. Fig. 4-8 shows representative friction for ce measurements for two poor solvents (2propanol and n-butanol) and a good solvent (toluene) of polystyrene; the solvents were exchanged in the order of toluene, 2-propanol, n-butanol. Valid comparison of the data was enabled through the use of the sa me tip throughout, at the same modest normal force range (<60 nN), and exchange of solvents in situ so that the tip probed the same small area. Under 2propanol and n-butanol, the slopes, which represent coe fficients of friction, are both around 0.16, with mean errors of 2 10-3, averaged from six different re gions. Under toluene, the plot illustrates a vanishingly low friction coefficient between the tip and PS brush, three orders of magnitude lower than those measured in 2-propanol and n-butanol, with a mean error of 3 10-4. These trends were likewise obtained with different PS-brush samples. Topographic images also reveal changes in surface roughness under the different solvent environments studied. In air, the rms height of the PS brush is 0.8 0.3 nm; this decreased to 0.19 0.05 nm in toluene, and increased to 5 2 nm in 2-propanol. The rms height averages were calculated from 1-m2 scan sizes obtained in different locations over a 100-m2 area. Although these changes ar e consistent with the observed friction response, quantitative correlation of these roughness and friction values is complicated by the 3 to 4 orders of magnitude difference in sampling frequency of the two measurement approaches, i.e., a tapping rate of ~70 kHz versus a rastering rate of 14 Hz, respectively, given the viscoelastic nature of the film. Normal force versus tip-displacement plots were also obtained at sing le points across the surface and in different solvents. Fig. 4-9 shows th e approach traces of the silica colloidal probe
130 6 5 4 3 2 1 0Friction Force (nN) 40 30 20 10 Normal Load (nN) Toluene n -Butanol 2-Propanol Figure 4-8. Friction force vers us normal load between a 5-m SiO2 probe on PS brush-modified (117.6-nm thick) Si wafer, under 2-propanol, n-butanol, and toluene. The plots are representative of at least five measurements at different areas of the sample, for each solvent.
131 15 10 5 0Normal Load (nN) 400 300 200 100 0 Displacement ( nm ) 2-Propanol(A) 15 10 5 0Normal Load (nN) 400 300 200 100 0 Displacement ( nm ) n -Butanol(B) Figure 4-9. AFM force versus z-piezo displacement plots of a 5-m SiO2 probe affixed on a cantilever (kN=0.58 N/m, nominal value) in co ntact against a PS brush-modified (117.6-nm thick) Si wafe r under (A) 2-propanol, (B) n-butanol, and (C) toluene. Differences in the approach and retract traces are due to piezo hysteresis.
132 15 10 5 0Normal Load (nN) 400 300 200 100 0 Displacement ( nm ) Toluene(C) Figure 4-9. Continued.
133 toward the PS brush sample under toluene, 2-propanol, and n-butanol. The approach and retract curves under toluene demons trate the elastic character of these brushes under this solvent. Slight differences in the normal forces in the approach a nd retract traces for a gi ven displacement arises as a result of piezo hysteresis. Two things are observed from these data: firs t, the contact point be tween the tip and the sample occurs at a much greater distance from the Si substrate under toluene as compared to being under the alcohol solvents. This is clear evidence that the polymer brush exists in an extended conformation under toluene, and conversely, in a relative ly collapsed state under the alcohols. Contact here is taken to be the poi nt of departure from an equilibrium cantilever deflection in the force-displacement plot. Second the shapes of the plots differ significantly indicating substantial differences in the contact mechanics of the brush under different solvents. The tip encounters a harder surface when pus hing against the PS brush under alcohol, and a softer surface when pushing against the same und er toluene. Under toluene, a good solvent for polystyrene, the polymer brush is heavily solvat ed and assumes an extended conformation; upon compression by the application of load, the solven t is slowly exuded from the polymer brush, a process that is reversed upon retraction of the tip. Discussion Nanometer scale measurements of interfacial friction for the contact of a colloidal SiO2 probe and polystyrene brushes clearly demonstrat e a strong dependence of friction on the solvent environment. This dependence is understood in terms of the influence of the solvent environment on the conformational state of the brusha claim consistently supported by the complimentary QCM and AFM force displacement da ta. Together, these measurements portray the significant swelling of th e brush structure upon exposure to a toluene solvent and the
134 corresponding collapse when exposed to 2-propanol and n-butanol solvents. These molecular scale conformational changes result from the resp ective intermolecular interactions between the polymer brush and solvent molecules, which can be rationalized th rough a three-component Hansen solubility parameter model [92, 199, 200]; this approach is commonl y used to predict the solubility of a polymer in a solvent . Solubility parameters effectively describe the cohesive energy of a solvent system and can be expressed in terms of the Hansen dispersion, polar, and hydrogen-bonding components of the net interaction energy. These can be used to derive a single value of H, the ratio of cohesive energy densities, which indicates a polymers re lative solubility in a given set of solvents. H represents the ratio of the overall difference in the Hansen parameters between solvent and polymer, and the maximum difference tolerated by th e polymer for solution to occur; it can also be used to estimate the Flory interaction parameter (12) for higher molecular weight polymers . Values of H for the solvents used in this st udy decrease in the order of 2-propanol ( H 1.66), n-butanol ( H 1.52), and toluene ( H 0.42), where a value less than 1 represents high affinity with polystyrene. Overall, they por tray greater intermolecular attractions between a nonpolar solvent (toluene) and a hydrophobic polymer such as polystyrene, relative to the latters interaction with polar solvents (2-propanol, n-butanol). These values are consistent with the measured trends in solvent uptake and brus h swelling, where solven t-polymer interactions drive the swelling of the brush and conformationa l changes depicted in AFM force-displacement curves. As described in previous wo rk considering the solvation of PLL-g-PEG in a range of solvents [92, 110], we conclude that such confor mations and favorable solv ent-brush interactions represent the necessary criteria for the low fric tion measured at highly solvated polymer brush
135 surfaces. In light of the results of prior studies [92, 110], the present report of low friction measured for a hydrophobic brush system in the presence of a nonpolar solvent clearly supports the general description of brush lubricity in these solvation terms. Conclusion Polystyrene brushes were prepared on oxide pa ssivated silicon surfaces by surface-initiated free-radical polymerization and inve stigated in a range of solvent environments. It was observed that the PS brush exhibited a relatively higher so lvent uptake in toluene compared to 2-propanol and n-butanol. In turn, PS brushes exhibited vanishingly low fric tion responses in toluene, a good solvent, versus 2-propanol and n-butanol. In force-displacement plots, contact was observed at relatively greater tip -substrate separations under tolu ene compared to the alcohols, supporting the idea of brush swelling. These st udies support the reliance of the frictional response of polymer brush-modified interfaces on the quality of the solvent environment and the resulting conformation of the brush structure.
136 CHAPTER 5 POLY(ETHYLENE IMINE)-graft-POLY(ETHYLENE GLYCOL) BRUSHES Introduction Poly(ethylene imines) (PEIs) are a class of polyelectrolytes that ar e broadly applied as adhesives, dispersion stabilizers, and thickeners [202-205]. They are particularly important in the paper industry where they serve as drainage and rete ntion aids for fines, fibe rs, and fillers. In this capacity, they serve to control flocculation by adsorbing onto mainly negatively charged particles in the stock suspension [202-206]. PEI is generally prepared from aziridine (or ethylene imine, EI) via a ring-opening polyaddition reaction, acid-cataly zed in aqueous solution [206, 207] While this represents the amino analogue of linear polyether poly(ethylene gl ycol) (PEG), the tri-valency of nitrogen, in contrast, makes it highly branchedw ith a 1:2:1 ratio of primary, secondary, and tertiary amino groups, respectively (Fig. 5-1). Le ss common linear (or crys talline) PEI can be prepared from the isomerization polymerization of unsubstituted 2-oxazoline, followed by the alkaline hydrolysis of poly(N-formylethylenimine) . The presence of an amino group for every two methylene groups in either branched or linear PEI confers a high charge density on the po lymer when fully protonated at low pH, which can be progressively reduced by titration with ba se [204-206]. This facility to tune the charge density of PEI by varying the pH has profound effects, for example, on the flocculation mechanism [202, 203, 206] (Fig. 5-2). At lower pH (4.5), or higher charge density, the polymer adsorbs strongly to colloidal particles as flat, patchy films, and flocculation occurs from the net attractive interaction arising from the mosaic of positive (polymer) and negative (particle) charges. At higher pH (7.0), or lower charge density, the polymer adsorbs more weakly, with
137 N H n N H N N H nH N O NH2 NH2 n NH2 nlinear poly(ethylene imine) branched poly(ethylene imine) poly(L-lysine) poly(allylamine) Figure 5-1. Structure of poly cation backbones in PEG-grafted copolymer systems: linear and branched poly(ethylene imine), poly(L-lysine), and poly(ally lamine). Amino groups represent sites for PEGy lation or protonation. Figure 5-2. Flocculation models of PEI stabilized colloids at differe nt PEI charge densities: (left) patch-charge model at high charge density, where PEI forms a flat, patchy film on the particle surface; (right) bridging model at lower charge density where PEI adopts a more extended form and spans acros s particles. Adapted from .
138 more loops and tails than trai ns, and flocculation occurs through the bridgi ng of extended polymer segments in between particles. Aside from being hydrogen acceptors, amino groups can also act as hydrogen donors, thereby conferring added complexity to PEI structures . The NH bond that exists in primary and secondary amino groups endows polya mines the ability to form inter-segment hydrogen bonds that are not possibl e in polyethers. Anhydrous linea r PEI, for example, forms a tight double-stranded helix with intermolecular NHN hydrogen bonds; adsorption of water replaces these with NHO and OHN hydrogen bonds producing planar-zigzag forms in the hydrates [209, 210]. Linear PEI thus undergoes water-induced phase transitions among four distinct types of crystalline hydr ates depending on the EI/water stoichiometry: anhydrate (1/0), hemihydrate (1/0.5), sesquihydrate (1/1.5), and di hydrate (1/2) . In contrast, high molecular weight branched PEI forms in soluble gels in water . PEGylated PEI has aroused vi gorous interest over the la st 15 years as non-viral transfection vectors in gene deliv ery systems. Owing to the high charge density of PEI, and its highly branched structure (25% co rnerstone amines) , it is able to effectively complex plasmid DNA [211-218], oligodeoxynucleotides (ODNs) [202, 219-222], and ribozymes [220, 222, 223] via charge coupling of ammonium groups in the polymer with phosphate groups in the nucleotides [216, 220, 222]. Its cat ionic nature also allows it to interact non-specifically with negatively charged proteoglycans expressed on cell surfaces , and with its high buffering capacity or so-called proton s ponge effect [211-213, 222], facilita tes its entry into cells during endocytosis, with protonation of the amines promoting its es cape from the endosomes . Charge neutralization upon complexation with nucl eotides, however, render the polyplexes less soluble [213, 216], while intravenous delivery leads to opsonizationinducing their eventual
139 removal by the immune system [212, 214, 215]and enzymatic degradation [219, 220]. Grafting PEG chains on PEI have been shown to mitigate these by serving as a highly watersoluble and protein-resistant she ll to the polyplex core [212-224], manifesting in reduced toxicity  and decreased attenuation of gene expression . PEGylation of polycations has been previously used as a strategy for coating negatively charged surfaces with a molecularl y thin film of PEG brushes w ith areal densities that produce protein resistant [167, 168, 185] and lubrici ous [51, 92, 106, 107, 109, 110] interfaces under aqueous environments. Poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG) consists of a poly(L-lysine) (PLL) backbone with multiple poly(e thylene glycol) side-chains grafted onto the backbone via amino groups on a fraction of the lysine units. The remaining free amino groups become positively charged and have been shown to irreversibly stick onto negatively charged surfaces such as the passivating oxide layers of metals under appropriate pH conditions. The resistance of these PLL-g-PEG-coated surfaces against non-speci fic protein adsorption as well as their tribology have been systematically studied in terms of polymer architecture [106, 167, 185], polymer deposition time , and solvent quality [ 92, 110]. It has been c onsistently shown that both protein resistance and bounda ry lubrication at equilibrium adsorption depends on the density of PEG chains on the surface, dictated by the PEG chain length and grafting ratio, and by the degree of extension of the PEG brushes, wh ich additionally depends on solvent quality [92, 110, 167, 185]. Polymer brushes that are highly extended in good solven ts are predicted to exhibit low shear strengths due to the fluid-like mobility of the chain segments, resistance to compression due to the rise in osmotic pressure when solvent is squeezed out, and steric repulsion due to the entropic penalty in reduci ng the chain segments conformational space.
140 The same considerations lie behind the modi fication of PEI with PEG chains for the purpose of creating efficient gene delivery agents. Poly(ethylene imine)-graft-poly(ethylene glycol) (PEI-g-PEG) provides an opportunity to i nvestigate the infl uence of backbone architecture and chemical structure on the tribol ogical properties of PEGgrafted systems. Like its PLL analogue, PEI-g-PEG is expected to adsorb onto ne gatively charged metal oxide surfaces when some of the amino groups are protonated, fo rming an ultrathin film in which PEG-brushes are exposed at the interface. PE I however is highly branched, wh ereas PLL is linear (Fig. 5-1), and would have a higher charge density than PLL when fully protonated due to the number density of amino groups in the polymer. These anchoring groups on PEI are also located on the main chain, while those for PLL stick out as pe ndant side-chains on a backbone that consists of charge-neutral peptide linkages. Furthermore, depending on the pH, the quality of PEI films may vary based on either the patch-charge or bridgi ng models of flocculation [202, 203, 206]. These differences are bound to influence the manner of adsorption of PEI-g-PEG onto metal oxide surfaces, the density of PEG chains created, a nd ultimately the tribology of the boundary film. The profound effect of backbone architecture has recently been reported for the linear poly(allylamine)-graft-poly(ethylene glycol) (PAAm-g-PEG) system . It was observed that despite the higher charge density of amino groups on its backbone, PAAm-g-PEG adsorbed to a lesser extent and lubricated less well than PLL-g-PEG with the same spacing in between PEG chains. It was hypothesized that the lesser num ber of anchoring points and longer distances between them conferred greater degrees of freed om to the PLL versus PAAm backbone (Fig. 51); this would facilitate the reconformation of chains on the surface that would accommodate their tighter packing and allow them to c onform to irregularities on real surfaces.
141 In this study, lateral and normal forces be tween the surface-bound, brush-like copolymer, PEI-g-PEG and a silica colloidal probe were inve stigated by atomic force microscopy (AFM), and related to the relative mass of solvent with in the polymer. The amount of solvent adsorbed within the PEI-g-PEG brush as a function of solvent polarity was detected using the quartz crystal microbalance (QCM). The specific copoly mer used in this study has a branched PEI molecular weight of 25 kDa, grafting ratio of 3.5 ethylene imine units per PEG side-chain, and PEG molecular weight of 4 kDa (Fig. 5-3). PEI-g-PEG was adsorbed onto an oxide passivated silicon wafer by exposure to the polymer solutio n created using a buffer (HEPES) adjusted to physiological pH. Frictional forces were measur ed by sliding the AFM co lloidal probe against the polymer-coated substrate as the polarity of the solvent was systematically varied (HEPES, methanol, ethanol, 2-propanol) in situ. Lateral and normal forces de tected between the colloidal probe and PEI-g-PEG were compared with those found between the same colloidal probe/cantilever assembly and PLL-g-PEG of similar backbone and side-chain molecular weights and grafting ratio. Fr iction forces were also mon itored under both symmetric and asymmetric interfaces in order to elucidat e conformational and bridging effects under the systematically varying solvent environments. This work aims to highlight the comparison between the tribological properties of PEI-g-PEG and PLL-g-PEG as a function of solvent quality that would shed light, specifically, on the influence of their backbone architectures. Experiments Preparation of Polymer Br ush-Coated Interfaces PEI-g-PEG was synthesized and characterized by SurfaceSolutionS GmbH (Zrich, Switzerland) following a modified pr ocedure for the synthesis of PLL-g-PEG [167, 168, 185], producing core-shell copolymers with branched PEI core and br ush-like PEG shell (Fig. 5-3). The product has a characteristic PEI molecular wei ght of 25 kDa, a graftin g ratio of 3.5 ethylene
142 N N N N N N HN NH N HN N N N NH N N N NH2 N N H N H N N N H2N N N H N N H H2N HN N H N NH NH HN H2N NH N NH2 N HN H N NH NH HN N N H HN HN NH2 HN N NH N H2N H2N NH2 H2N NH N N N HN HN N H2N NH N HN N HN NH2 HN N H2N H2N N N HN N NH2 NH NH HN HN NH2 NH2 NH NH2 H N HN H2N NH2 NH H N HN NH NH H2N NH H N N H H2N NH2 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O NH2 O O O O O O O O O O O Figure 5-3. Structure of PEI-g-PEG that is scaled down to 20% of the size used in this study; the relative size of the PEG chai ns with respect to the PE I backbone, however remains the same. The ethyl imine-to-PEG side-chain grafting ratio is more than twice that for the actual copolymer used, i.e., only 13 PEG chains were drawn instead of 30 for the sake of clarity in representing the structure two-dimensionally.
143 imine units/PEG side-chain, and a PEG molecu lar weight of 4 kDa, and is designated as PEI(25)-g[3.5]-PEG(4). Grafting ratio had been dete rmined by two methods: from the ratio of the integrated peaks of the 1H NMR chemical shifts of the te rminal methyl protons of PEG (OCH 3) and the methylene protons of the PEI residues (NCH 2CH 2), and from the C:N ratio from total elemental analysis. PLL-g-PEG was prepared and characterized by our collaborators at the Laboratory for Surface Science and Technology, Department of Materials, Swiss Federal Institute of Technology, ETH-Zrich, following a method [167, 168, 185] previously described in Chapter 3. This produced a bottle-brush copolymer with lin ear PLL backbone and PEG bristles (Fig. 3-1), having characteristic PLL molecula r weight of 20 kDa, grafting ra tio of 3.2 lysine units/PEG side-chain, and PEG molecular weight of 5 kDa, and designated thus as PLL(20)-g[3.2]-PEG(5). Substrates consisted of either of the above copolymers adsorbed onto the native oxide layer of silicon wafers from a pH-controlled solution. S ilicon (100) wafers were cleaved to appropriate size (approximately 0.3 cm 0.3 cm) for use as substrates, an d treated by the following cleaning procedure: 5 min sonication ea ch in acetone and 2-propanol, rins ing with ultrapure water (18.2 M), immersion in fresh piranha solution (70:30 H2SO4/30%H2O2) at 80 C for 10 min, copious rinsing with ultrapure water, drying under a ni trogen flow, and, finally, exposure to an O2/H2O2 plasma for 2 min (Table 5-1). [Caution! Piranha solution is highly corrosive and oxidizing. Use splash goggles and latex gloves when handling.] The substrate that had just been cleaned under these oxidizing conditions was immediately subm erged in a 0.25 mg/mL polymer solution in 10 mM HEPES buffer (4-[2-hydroxyethyl]p iperazine-1-[2-ethan esulfonic acid], pH 7.4) for 60 min. After the polymer-coated substrates were removed from solution, they were rinsed with HEPES buffer to remove unbound and multilayered polymers, and dried under a nitrogen flow. AFM
144 Table 5-1. Contact angles of a piece of silicon wafer taken after each step in the cleaning procedure Contact Angle Treatment 70 Si wafer as received Wiped with tissue Drying with N2 gas 73 Sonication with acetone Drying with N2 gas Note: residue from acetone 60 Sonication with 2-propanol Drying with N2 gas 53 Sonication with ultrapure water Drying with N2 gas 0 5 Piranha solution at 80 C Rinsed with ultrapure water Drying with N2 gas
145 experiments immediately followed deposition of th e polymer on the substrate to eliminate timedependent material transfer in the HEPES buffer solution. Similarly prepared PEI-g-PEG-coated silicon wafer substrates were analyzed by SurfaceSolutionS GmbH (Zrich, Switzerland) by X-ray photoelectron spectroscopy (XPS) and variable angle spectroscopic ellipsometry (VASE) The C:N atomic concentration ratio measured from XPS was 12-18% higher than what was f ound by total elemental an alysis, across several grafting ratios examined (2.5 to 10). This is cons istent with a layered st ructure in which the PEI backbone lies close to the surface, while the PEG side-chains are extended away from the surface, resulting in the attenua tion of the N signal. A previous study on the multilayer modeling of XPS data for PLL-g-PEG has demonstrated a similar laye red structure of the polymer film . Ellipsometric thic knesses of adsorbed PEI-g-PEG films after rinsin g ranged from 1.7-1.1 nm, decreasing with the ethylene imine/PEG grafting ratio, consistent with a higher electrostatic affinity of the PEI backbone to the substrate as more ami no groups become available with increased grafting ratio. These values changed very little (0.03 nm, maxi mum) after exposure of the PEI-g-PEG film to human serum, indicating ex cellent resistance to serum adsorption. A slightly modified procedure was used to coat a silica colloidal probe that served as the fixed counterface to the sliding silicon wafe r substrate. A silica microsphere of 5 m diameter, attached at the end of a co mpliant cantilever with 0.58 N/m normal spring constant (manufacturers nominal value, Novascan Technologies, Inc., Am es, IA), was used for this purpose. The probe/cantilever assembly was clean ed prior to AFM measurements by rinsing in 0.1 M HCl, then with ultrapure water, followed by exposure to O2/H2O2 plasma for only 15 s to avoid roughening of the surface. These were then kept in HEPES buffer, and only removed and dried with nitrogen before making measurements. For symmetric tribopairs, where the probe was
146 also coated with polymer, it was immersed right after plasma treatment in the polymer solution (0.25 mg/mL in 10 mM HEPES) and incubated there for 60 min. Upon withdrawal from the polymer solution, the probe was rinsed with HEPES buffer to remove unbound and multilayered polymer and dried under a nitrogen flow prior to use in AFM measurements. AFM Normal and Lateral Force Measurements Normal and lateral forces at the interface of polymer-modified SiO2 substrates and a bare or polymer-modified silica microsphere were monitored by AFM under liquid environments, with the use of a liquid cell/tip holder (Digital Instruments, Santa Barbara, CA). Movements of the substrate relative to the fixed probe in the x, y, and z directions were implemented with a single-tube piezoelectric scanner. Normal and lateral tip defl ections were detected by the displacement of a laser beamreflected off the back of the cantilever from the center of a four-quadrant photodiode. The AFM was cont rolled by AFM100/STM100 electronics and SPM32 software (RHK Technology, Inc., Troy, MI). This AFM assembly has been discussed in more detail previously [19, 112]. Kinetic friction was measured between the co lloidal probe and the modified substrate through the torsional bending of the cantilever as it slid orthogona l to its long axis during loading and unloading cycles; the load wa s monitored concurrently from the normal deflection of the cantilever. The half difference between the forw ard and reverse traces of the lateral signal (friction loop) represents the friction force response as a function of tip/substrate separation. In this work, a scan rate of approximately 2 m/s was used over a distance of 200 nm. Normal forces were detected as a functi on of the separation of probe and substrate by monitoring the deflection of the can tilever perpendicular to the surface. Starting at a distance of 200 nm from the substrate, the tip was brought into contact with th e substrate, pressed further,
147 and then retracted to the original position. This approach/retract cycle allows for the measurement of relative contact distance, contact stiffness, and adhesion forces, from the comparison of the onset of cantilever deflection, the slope of the contact region, and the hysteresis between the approach an d retract cycles of force-distan ce plots, respectively. In both friction-load and force-distance measurements, the normal load was monitored so as not to exceed 25 nN to preclude the possibility of tip and substrate damage or wear. In this study, five friction-load and forcedistance measurements were made at various locations on the substrate. The spot s were at the corners and center of a square with side length of 100 nm, such that all of the offset tip positions lay within an area of 10,000 nm2. Representative friction force res ponse data could thus be obtained based on an average slope that relates to the mean coefficient of friction in the five location-specific measurements. Solvents were exchanged in the liquid cel l by transferring sufficient volume s using two 5-mL syringes in the order of aqueous HEPES, methanol, ethano l, 2-propanol, followed by a repeat of HEPES, and which were allowed to equilibrate for 30 min before making the first measurement. In order to make valid comparisons, the same tip/cantilever assembly was used, and the solvents exchanged in situ, such that only solvent-dependent effects on the friction and normal force response were probed. W ith knowledge of the manufacturers nominal spring constant of the cantilever ( k N 0.58 N/m) loads were determined based on its deflection given a known substrate displacement during contact. Relative friction force response of the polymer-modified substrate in different solvent e nvironments was determined by m onitoring the photodiode lateral signal at increasing and decreasing normal loads.
148 QCM Solvent Uptake Measurements The QCM used in this work to measure relative solvent uptake consisted of SA250B-1 Network Analyzer and test fixture (Saunders and Associates, Inc., Phoenix, AZ), a liquid flow cell (Maxtek, Inc., Beaverton, OR), and Q TZ control software (Resonant Probes GmBH, Germany). Resonators used in the experiments we re AT-cut quartz crysta ls (also Maxtek) with silica-sputtered gold electrodes and a 5 MHz fundamental resonance frequency. Prior to measurements, the quartz crystals we re cleaned with the following procedure: sonication for 5 min each in acetone, 2-propanol, and ultrapure water, rinsing with ultrapure water in between, drying under a nitrogen fl ow, and finally plasma cleaning in an O2/H2O2 environment for 1 min. The quartz crystal was imme diately installed into the liquid flow cell that had been cleaned with 2-propanol and dried unde r nitrogen flow. The assembly was allowed to sit overnight to permit the stress relaxation of the Viton O-ring seal. Resonant peaks were selected in air from the maxima in the conducta nce spectrum at several overtone numbers, from which the reference frequencies (f) and bandwidths () were determined by fitting to a Lorentzian function. Data were then recorded in air for 60 min to ensure stabilization, after which solvents were injected in the order of methanol, ethanol, 2-propanol, and HEPES. These data represent the background from which so lvent mass uptake measurements on the polymercoated quartz crystal were to be compared. Deposition of PEI-g-PEG was performed in situ as 0.25 mg/mL PEI-g-PEG solution was injected into the liquid flow cell and allowed to adsorb onto the silica surface for 10 min, followed by a HEPES rinse to remove unbound and multilayered PEI-g-PEG. Solvent injection was then repeated in the same series as before, on the polymer-coated quartz crystal. Throughout the ex periment, solvents were exchanged in 10 min intervals during which data were collected; shifts in the frequency ( f) and bandwidths ()
149 from the reference values were calculated by aver aging the data over 5 min intervals after it had reached a plateau that repr esented the steady state. Solvent exchange on a blank quartz crysta l would cause a negative frequency shift proportional to the square roots of the viscosity and density of the liquid, according to the Kanazawa relation (Eq. 2-9) ; this re presents the dissipative interaction (D 2 / f ) of the resonator with a viscous fluid as can be seen in a positive shift in the bandwidth of the same magnitude. On a polymer-coated quartz crystal, the frequency shift includes, additionally, mass loading due to the mechanical coupling of the so lvent that is intimately associated with the polymer segments. In the thin film limit, this mass uptake can be extracted from the observed frequency shift by the arithmetic su btraction of the viscous load c ontribution as determined from the blank run. This wet mass ( f) can be used to compare the relative solvent uptake of the polymer under different solvent environments. Deta ils of this approach have been reported elsewhere [111, 141]. Results and Discussion Using complementary AFM and QCM techni ques, the solvent-dependent tribological properties of PEI-g-PEG-modified interfaces have been investigated through friction force measurements, and related to polymer brush ex tension through normal force measurements and adsorbed solvent mass within the brush. Solven t quality was systematically varied from good (HEPES buffer solution) to progressively worse as the polarity of the alcohol used decreased (methanol, ethanol, and 2-propanol). SiO2 was chosen as the material for both the surface and counterface due to the known el ectrostatically-driven adsorption of amine-based polycations such as PEI-g-PEG and PLL-g-PEG on its negatively charged surface exposed to physiological pH. A 5-m diameter sphere was chosen as the probe because it allows for small contact
150 pressures on the soft polymer thin film; typical AFM tips, with radii less than 100 nm, would have contact pressures in the gigapascal range, even at the moderate loads us ed in this study, that could damage the soft thin film upon contact. In the following sections the effect of solvent on the frictional and normal forces for a PEI-g-PEG-modified interface, compared with that modified with PLL-g-PEG, will be presented and discussed in terms of the polymer adsorption on the silica surface, the so lvent uptake within the brushes as a function of its quality, and the differences between symmetric and asymmetric tribointerfaces. Effect of Solvent on Friction and Normal Force Responses Sliding between polymer-coated interfaces cons isting of a silicon wafer substrate and a fixed colloidal microsphere while in contact al lowed the simultaneous de tection of normal and frictional forces from the cantilever deflection an d torsion, respectively. In this study, both the substrate and the microsphere were coated with the same graft-copolymer, representing a symmetric tribointerface. Measurements began 30 mi n after the exchange of each solvent to remove any kinetically driven variations due to di fferences in the solvation of the polymer brush. Use of the same AFM tip/cantilever a ssembly throughout and solvent exchange in situ allowed for the valid comparison of data. In Fig. 5-4 (top), the interfacial kinetic friction is plotted as a function of increasing load for the symmetric contact of a PEI(25)-g[3.5]-PEG(4)-modified probe and substrate in different solvent environments. The plot illustrates the progressive decrease in lubricity of the PEI-g-PEG film as the solvents are exchanged in the orde r of aqueous HEPES, methanol, ethanol, and 2propanol, with the final HEPES wash showing a retu rn to low friction res ponse. This is evident from the reduction in the load-dependence of fr iction (i.e., decrease in slope) as the medium changed from the least polar (2-propanol) to the most polar (aqueous HEPES) solvent. This is consistent with previous observations of th e solvent-dependence of friction between the
151 50 40 30 20 10 0Friction Response (mV) 20 15 10 5Normal Load (nN) HEPES pH 7.4 (1st) Methanol Ethanol 2-Propanol HEPES pH 7.4 (2nd) PEI(25)g [3.5]-PEG(4) 50 40 30 20 10 0Friction Response (mV) 20 15 10 5Normal Load (nN) PEI(25)g [3.5]-PEG(4) PLL(20)g [3.2]-PEG(5) Figure 5-4. Friction forc e response as a function of normal load between symmetric tribointerfaces consisting of polymer-coate d silicon wafer substrate and silica probe. Top: PEI-g-PEG under different solvent environments. Bottom: comparison of PEI-gPEG and PLL-g-PEG under HEPES buffer adjusted to pH 7.4
152 symmetric interface consisting of silicon substr ate and glass colloidal probe coated with PLL(20)-g[3.5]-PEG(5) [92, 109]. As a control, fricti on as a function of normal load was also measured using the same tip/cantilever assembly in a similar symmetric interface coated with PLL-g-PEG of component molecular weights and grafting ratio co rresponding to that of PEI-gPEG (Fig. 5-4, bottom). The plot shows an almost identical load dependence of friction, which is vanishingly low under aqueous HEPES for both copol ymers with differing anchoring backbones. Both copolymers are expected to adsorb favorab ly onto a silica substrat e through the protonation of amino groups at physiological pH, such that the backbone (PEI or P LL) would lie near the surface while the PEG chains extend away forming a brush-like outer layer. Solvent-dependence of friction arises from the relative affinity of different solvents to PEG. Mller et al. demonstrated a strong correla tion between the areal so lvation (solvent mass per unit substrate area) and the Hansen polar and hydrogen-bonding solubility parameters for PLL-g-PEG, while there was an absence of systematic dependency on the dispersion parameter, for the same series of solvents used in this st udy ; these parameters are empirical predictors of a polymers solubility in a given solvent. They also calc ulated an average of 14 water molecules associated with each ethylene glycol unit, compared to 0.8 for 2-propanol, the worst solvent in the series. PEG is actually an amphiphilic molecule that is soluble in both water and organic solvents due to the fact that the conformation around the freely rotating CC bond units determine their polarity: the gauche form produces a net dipole moment, while the anti form does not (Fig. 5-5A) [226-232]. A nonpolar environmen t thus favors anti conformations making the polymer more rodlike, while a polar environm ent induces gauche kinks. Moreover, when the solvent is water, the distance between adjacent oxygen atoms in the gauche form would be commensurate with the OHO distance in liquid water allowing PEG to participate in its
153 O O O O O O O O gauche conformeranti conformer (A) (B) Figure 5-5. Conformational stru cture of PEG in water. (A) Newman (top) and Sawhorse (bottom) projections of the CC unit of PEG showing the gauche and anti conformers; (B) helical c onformation of PEG (black bonds) caged by a network of water molecules (white bonds). Reproduced from  by permission of The Royal Society of Chemistry.
154 hydrogen-bonding network (Fig. 5-5B) [226, 233]. Hartree-Fock calculations show that the strength of hydrogen-bonding betw een oligoethylene glycol strands and water is strongly dependent on its conformation [101, 234]. The he lical structure (through gauche kinks) is particularly predicted to adsorb water strongly forming a monolayer that can act as a nucleation template. Favorable association of water molecules with PEG through hydrogen-bonding, compared with segment-segment interactions, drive the polymer chains to extended conformations in an aqueous environment that lead to the mechani cal conditions that account for the reduction in friction observed in highly extended polymer boundary layers: high compressive strengths and low shear strengths. This is clearly seen in th e normal load plots as a function of separation distance between the substrate and pr obe symmetrically coated with PEI-g-PEG (Fig. 5-6). The approach trace under HEPES shows a longrange repulsive force extending beyond 200 m down to ~100 m, followed by a strong rise in normal force at 110 m interpreted as the start of the compressive regime; by contrast, compression starts at around 60 m under the alcohols. It takes almost twice the displacement to compress the PEI-g-PEG brush under the HEPES buffer compared to the alcohols to attain the same ma ximal normal force of 20 nN. This demonstrates that the polymer brush is in a more extended state under HEPES compared to the alcohols and that the water molecules are more resistant from being squeezed out of the brush than the alcohol molecules. Comparison of the approach and retract tr aces generally shows the compression to be elastic, with negligible a dhesion hysteresis under the alc ohols and only a minor one under HEPES. Offset between the approa ch and retract traceswhere the approach is steeper than the retract curveis mainly attributed to piezo hysteresis characteristic of open-loop control
155 15 10 5 0Normal Load (nN) 150 100 50 0 Displacement (m) HEPES Methanol Ethanol 2-Propanol Approach Trace(A) 15 10 5 0Normal Load (nN) 150 100 50 0 Displacement (m) Retract Trace HEPES Methanol Ethanol 2-Propanol(B) Figure 5-6. Force versus z-piezo displacement plots, under different solvent environments, of a silicon wafer substrate against a glass colloid al probe that were both coated with PEI-g-PEG: (top) approach and (bottom) retract traces.
156 systems. Plots of friction response as a functi on of decreasing load (not shown) show zero friction response at zero a nd negative loads confirming the absence of adhesion. Friction-load plots in Fig. 5-4 (top) also show a more pronounced superlinearity compared to similarly prepared PLL-g-PEG interfaces under the same solvent series [92, 109], indicating a more drastic change in shear sti ffness regimes with increasing loads. Friction response does not rise above the noise level until about 5 nN of normal load had been applied, while the approach traces of the force-displ acement plots (Fig. 5-6, top) already indicate significant compression in the brush at these load s. Drobek et al. have shown with the surface force apparatus (SFA) that for PLL(20)-g[3.5]-PEG(5) symmetrically coated onto mica sheets, significant interpenetration of the polymer brushes occur (28% of brush length) before repulsive forces are detected . Given that in AFM pr essures are even an or der of magnitude higher than in SFA, that no frictional forces are detect ed until 5 nN attests to the fluidity of these polymer brushes giving rise to th e low shear stiffness observed at the slow sliding velocities employed in AFM. Effect of Solvent on the Relative Mass Uptake Detection of changes in mass a nd dissipation of energy in the PEI-g-PEG film in different solvent environments was monitored by following th e shifts in frequency and bandwidth of the resonance peak of a quartz crystal resonator co ated with the polymer. This was accomplished by fitting the conductance (G) spectrum to a Lorent zian function to obtain the position of the maximum (resonance frequency, f) and the width at half the peak height (bandwidth, ); the shifts reported are offset relative to the peak parameters taken in air. In this study, solvents were first exchanged in the order of methanol, ethanol, 2-propanol and HEPES over a blank quartz crystal with an active area consisting of a silica-sputtered gold electrode; PEI-g-PEG was then
157 introduced as a HEPES solution and allowed to adsorb onto the silica overlayer, followed by a wash of polymer-free HEPES to remove loosel y-bound material, and then an exchange of the same solvent series as in the blank run. Shifts in frequency and bandwidth, normali zed over the fundamental frequency, were tracked over time (Fig. 5-7), with the solven ts being exchanged in approximately 10-min intervals. Data averaged over 4 min, prior to th e next solvent injection, when the system has attained steady state, are displa yed in Table 5-2. In the blank, the quartz crystal resonator is mainly de-tuned by viscous damping from its in teraction with the flui d medium. The general Kanazawa equation (Eq. 2-12) predicts that the shifts in frequency and bandwidth, representing real and imaginary parts, respectiv ely, of a complex phase shift in shear oscillation, should be the same magnitude but opposite in si gn. Data presented in Table 52 for the blank shows that the quartz crystal resonator used in this experiment indeed approxim ates this behavior; departure from this condition may arise due to the roughne ss of the active area that may provide cavities that could trap solvent molecules enhancing th eir inertial coup ling with the resonator . Immobilization of polymer on the surface would cause a shift in frequency due to the mass loading on the quartz crystal from the polymer, as well as solvent molecules that are intimately associated with it. Furthermore, the bandwidth shift would reflect changes in the energy dissipation as the resonator is also mechanically coupled to a visc oelastic layer. Differences in frequency and bandwidth shifts for each solvent in the series before and after the immobilization of PEI-g-PEG show a systematic trend with respect to solvent quality. First, as the solvent polarity decreases, it becomes a better solvent for PEI-g-PEG, as manifested in more negative frequency shifts that indicate higher mass loading ( m f ) on the crystal as more solvent molecules become affiliated with the polymer. Table 5-3 shows the values of the wet masses of
158 -0.20 -0.15 -0.10 -0.05 f / f (x 103) 0.20 0.15 0.10 0.05 f (x 103) Methanol Ethanol 2-Propanol HEPES PEIgPEG HEPES (1st rinse) HEPES (2nd rinse) Methanol Ethanol 2-Propanol Figure 5-7. Fractional shifts in frequency ( f/f) and bandwidth (/f) under methanol, ethanol, 2propanol, and aqueous HEPES solution of a qua rtz crystal resonator before and after the in situ adsorption of PEI-g-PEG.
159 Table 5-2. Normalized frequency ( f/f) and bandwidth (/f) shifts of a quartz crystal resonator under various solvent environmen ts before (Blank) and after (Polymer) the adsorption of PEI-g-PEG, and their respective differences (). Average / f (-3) Average f / f (-3) Solvent Blank Polymer / f Blank Polymer f / f HEPES (1st rinse) 0.1500 0.1569 0.0049 0.1441 0.1619 0.0178 Methanol 0.0926 0.0999 0.0053 0.0658 0.0733 0.0075 Ethanol 0.1370 0.1400 0.0010 0.0987 0.1036 0.0049 2-Propanol 0.1899 0.1921 0.0002 0.1542 0.1573 0.0031 HEPES (2nd rinse) 0.1570 0.0050 0.1639 0.0198 Table 5-3. Wet mass of PEI-g-PEG adsorbed on a quartz crystal resonator under different solvent environments, calculated from the differences in observed frequency shifts for the solvent before and after the adsorption of PEI-g-PEG. Solvent Wet Mass (g/cm2) HEPES (1st rinse) 1.39 Methanol 0.68 Ethanol 0.39 2-Propanol 0.28 HEPES (2nd rinse) 1.58
160 the polymer converted from f/f using the Sauerbrey equation (E q. 2-7). Increase in mass for aqueous HEPES is especially more drasticmore than 200% than that for methanol, the most polar alcohol solvent. This observation is consistent with the exceptional affinity of water for PEG segments, owing primarily to its ability to participate in hydroge n-bonding networks, as well as its fluctuating dipole moments that attune to its environment. Second, the rise in the solvent uptake in the PEI-g-PEG brush is accompanied by an increase in the bandwidth shift that indicates an increase in dissipation (D 2 / f ) or a decrease in the Q-factor of the polymercoupled resonator. Solvent molecules generally act as plasticizers that interrupt segment-segment interactions with more favorable segment-solven t interactions, causing the polymer to swell and its chains to begin to flow; such a swollen, vi scous film would thus be expected to enhance damping on the quartz crystal. Interes tingly, the bandwidth shift of PEI-g-PEG under methanol is slightly higher than that under HEPES; this could mean that the PEG chains under water make these more conformationally restrictedgiven its hydrogen-bonding cagecompared to being solvated with methanol. This could explain why the friction response under methanol did not rise above the noise level until 10 nN of load had been applied, despite being less solvated than being under water (Fig. 5-4, top). PEG chains under meth anol being thus more fluid-like accounts for the low shear stiffness observed below 10 nN. A bove this, the extent of compression would have caused substantial methanol to be squeezed outas it has less affinity than watergiving rise to the incipient detection of friction. Backbone Architecture and Fr iction Response Hysteresis Normal and lateral forces were also measured between asymmetric tribointerfaces consisting of a PEI-g-PEG-coated silicon wafer and a bare 5-m glass colloidal probe. Fig. 5-8 shows the friction force response pl otted against the applied normal load for this asymmetric
161 100 80 60 40 20 0Friction Response (mV) 20 15 10 5 0Normal Load (nN) HEPES pH 7.4 (1st) Methanol Ethanol 2-Propanol HEPES pH 7.4 (2nd) PEI(25)g [3.5]-PEG(4) 20 15 10 5 0Normal Load (nN) 400 300 200 100 0 Displacement (m) PEI(25)g [3.5]-PEG(4) Figure 5-8. Tribolog ical behavior of asymmetric tribointerfaces consisting of PEI-g-PEG-coated silicon wafer substrate and a bare silica probe. Top: friction force response as a function of increasing normal load under different solvent environments. Bottom: force versus z-piezo displacement plot under HE PES buffer solution at pH 7.4.
162 interface as the solvent is exchanged according to the series: aqueous HEPES, methanol, ethanol, 2-propanol, and HEPES. The plot illustrates a similar trend in the load dependence of friction with respect to solvent quality, i.e., the slope of the curves decrease as the solvent is replaced with a more polar one. Furthermore, the magnitude of the friction response for a given applied load is higher for this asymmetric versus symmet ric (Fig. 5-4, top) tribointerface; the friction response under 2-propanol, for example, is more th an twice at the maximum load of ~20 nN here compared to the symmetric case. This is consiste nt with previous observa tions of higher friction for asymmetrically coated PLL-g-PEG tribopairs: in both cases wh ere either the probe  or the substrate [92, 109] is coated with PLL-g-PEG, the magnitude of friction force was higher for the same applied load relative to the symmetri cally coated tribopair. Fo r asymmetric interfaces, the polymer brush would be rubbing agains t a rigid wall/ball consisting of SiO2, whereas it would encounter another soft and spongy polymer brush in symmetrically coated interfaces. In PLL-g-PEG systems negligible bridging a nd entanglement were observed in both triboconfigurations, and the shapes of their plots looked similar sugge sting analogous underlying friction mechanisms at work . An important difference in the tribological properties of thes e PEG-grafted systems is the hysteresis observed in the friction response of PEI-g-PEG under HEPES. Solvent washes begin with HEPES buffer at pH 7.4, followed by the alc ohol series, and finally a repeat of the HEPES wash; this tests for the reversibility of the stre tch-collapse transition of the polymer chains that account for the friction response. In PLL-g-PEG systems, the friction response is completely reversible [92, 109], while PEI-g-PEG shows gross hysteresis be tween the initial and final HEPES washes (Fig. 5-8, top). This can be accounted for by the difference in backbone
163 architecture of the two PEG-gr afted polymer systems that lead to their distinct adsorption behavior. At low pH conditions, PEI is expected to adsorb strongly onto negatively charged surfaces by coulombic interactions. However, due its branched structure, the charges are concentrated in a smaller volume, such that the surface charge is quickly overcompens ated, thus creating a repulsive barrier to further polymer adsorption [2 35]. This results in planar patch-charges on the surface consistent with the fl occulation model under these conditions [202, 203, 206]. At higher pH, PEI has lower charge density, adopting a more compact conformation, but forms a thicker film on the surface as more polymer molecules ar e required to reverse th e surface charge . Moreover, adsorption studies of high molecula r weight, hyperbranched PEI (750 kDa) have shown a monotonic increase in adso rption onto silicon wafers with pH, with a maximum at pH 10.5; increasing the ionic strength also had a si milar effect . Incr ease in adsorption with charge neutralization or screen ing indicated the strong non-coulom bic affinity of PEI onto silica surfaces. Furthermore, flocculation models pr edict bridging interactions becoming more important at higher pH as the polymer would have more dangling loops and tails than trains due to the reduction in charged anchoring groups [202, 203, 206, 236]. In this study, the adsorption of PEI-g-PEG and the subsequent tr ibological characterization of the polymer-coated substrate were carried out at pH 7.4 a nd an ionic strength of around 10 mM. Under these neutral pH conditions, the copo lymer backbone would exist as a relatively thick film with protruding loops and tails due to the lowered charge density. These dangling backbone segments could act as bridges thr ough coulombic and non-coulombic interactions between the polymer-coated substrate and the bare colloidal probe; the net attractive interaction would result in higher adhesion and thus a higher fr iction force response. The plot of normal load
164 as a function of probe/substrate separation (Fig. 5-8, bottom) indeed shows features that are characteristic of extensive polymer bridging in the retr act trace up to 200 m from the contact point; the friction-load plot of the first HEPES wash (Fig. 5-8, top) also depict a finite friction response at zero normal load that in dicates adhesive interaction. As the tip is run-in, material would transfer from the substrate to the probe, eventually creating a symmetric tribointerface. PEI has been known to form unstable films, requiring crosslinking with glutaraldehyde to pr event their desorption from pack ing materials in ion-exchange columns ; the transfer of PEI between mica sheets in SFA experiments have also been documented . The dehydration of the PEI-g-PEG with the successive alcohol washes may also induce some of the dangling amino groups to finally anchor onto the substrate. Control experiments showed a reduction in friction response after an ethanol rinse, which remained the same even after the probe/cantilever assemb ly was removed and cleaned with 0.1 M HCl followed by O2/H2O2 plasma to remove any polymer material that fouled the probe. In the PLL-g-PEG system, it has been shown th at changing the length of the PLL backbone from 20 to 350 kDa causes an order of magn itude increase in the coefficient of friction in the mini-traction machine (MTM) . In co ntrast to AFM measurements, MTM operates in the mixed sliding/rolling contact regime where ve locity dependent viscous effects are included. Nevertheless, the difference in the friction res ponse was attributed to unbound PLL chain in the fluid film resulting in a high resistance to shear . This has been rationalized as a consequence of the persistence length of the backbone, such that th e longer backboned PLL-gPEG would tend to loop away from the surface instead of adsorbing flat as in the case of the 20 kDa PLL [225, 237]. The 20 kDa PLL backbone is s ecured near the surfa ce while the PEG side
165 chains are presented as the topmost layer, accounting for the negligible bridging and entanglements in these systems. In contrast, PEI-g-PEG of similar backbone molecula r weight will have a more threedimensional structure upon adsorption to the surface under the same environmental conditions owing to PEIs extensive branching. This lead s to bridging and subse quent fouling of the colloidal probe after being run-in during the fi rst HEPES rinse, thus forming a symmetrical tribointerface. In addition, reconformation due su ccessive alcohol washes, l eads to a more stable polymer film with the PEI backbone firmly anchor ed on the substrate, while the PEG brushes are presented as the top layer. These effects re asonably explain the relatively reduced friction response observed in the final HEPES wash, whic h is corroborated by th e absence of hysteresis in the symmetrically coated probe and subs trate pair depicted in Fig. 5-4 (top). Conclusion Tribological properties of PEI-g-PEG, a surface-bound, brush-like copolymer, were investigated as a means to decrease the norma l and shear forces experienced between a silica colloidal probe and an oxide surface. PEI-g-PEG was adsorbed from solution onto oxidepassivated silicon surfaces through both coul ombic and non-coulombic interactions under physiological pH to form molecularly thin f ilms appropriate for AFM study. Lateral force measurements detected vanishingly low fricti on in aqueous HEPES, a good solvent, while friction was found to increase for the alcohols as the solvent polarity decreased (methanol, ethanol, 2-propanol). Solvent-dependent fricti on response observed in AFM experiments was corroborated by relative mass upt ake measurements using QCM. Greater mass uptake and higher dissipation in the PEI-g-PEG brush were seen under HEPE S buffer solution compared to the alcohols. Normal force-displacement relationshi ps also revealed an increased film thickness for the PEI-g-PEG brush under HEPES buffer solution as the incipient compressive regime
166 corresponded to a greater separation distance between the probe and substrate under HEPES versus the alcohols. These observa tions consistently por tray the dependence of brush lubricity on the favorable solvent-segment interactions that produce highly solvated chains with extended conformations. Friction force measurements of symmetric (PEI-g-PEG-coated substrate and probe) and asymmetric (PEI-g-PEG-coated substrate versus bare prob e) interfaces demonstrated differences in the solvent-dependent friction response due to bridging effects presen t between the brush and unmodified probe in the asym metric interface. Comparison of the friction response of PEI-gPEG and PLL-g-PEG brushes under HEPES buffer soluti on revealed vanishingly low friction forces for both systems, even though there were significant differences in molecular architecture. In PEI-g-PEG, however, hysteresis was observed in th e friction response due to bridging effects and subsequent fouling of the bare collo idal probe, which was absent in PLL-g-PEG systems and in the symmetric PEI-g-PEG tribointerface. Thes e effects were attributed to the more threedimensional structure of PEI due to its extens ive branching, demonstrating the effects of backbone architecture on the tribol ogy of PEG-grafted systems.
167 CHAPTER 6 CONCLUSIONS AND FUTURE DIRECTIONS Recapitulation This dissertation describes th e tribology of polymers confined to surfacesforming brushlike structuresat length scales, forces, and ve locities employed in atomic force microscopy (AFM). The probe/cantilever assembly represente d a force sensor that could measure the load dependence of friction, as it slid across a polymer brush-coated substrate, from the simultaneous detection of normal and lateral displacements and the determination of the respective spring constants. This study demonstrated how the fr iction response of polymer brushes was governed by architectural features that determined the p acking density of brush segments on the surface, and by the solvent environment that regulated th eir conformational state. Three model systems were hereby characterized: poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG), polystyrene (PS), and poly(ethylene imine)-graft-poly(ethylene glycol) (PEI-g-PEG). Interfacial friction between a silica colloid al sphere and a PLL-g-PEG-coated silicon wafer substrate was shown to depend on the polymer deposition time and architecture. PLL-gPEG spontaneously adsorbs onto the passivating oxide layer of silicon from a buffer solution at physiological pH due to electr ostatic attraction between prot onated amino groups on the PLL backbone and deprotonated silanol groups on silica. Drastic reduc tion in friction was observed within 5 min of substrate exposure to the polymer solution corres ponding to steady state coverage previously observed using spectroscopi c methods; a subsequent slower reduction over an hour was interpreted in terms pol ymer reconformation on the surface. Friction response at equilibrium adsorption was also observed to systematically depend on polymer architecture: it decrea sed with respect to increasing PEG chain length and decreasing lysine/PEG grafting ratio. These observations were rationaliz ed in terms of the PEG packing
168 density on the surface using scaling arguments where brush extension is characterized in terms of the ratio of the grafting distance (L), which depends on the grafting ratio and coverage, and the unperturbed radius of the polymer in a good solvent (RF), which scales with molecular weight. When the grafting distance is much larger than the polymers unperturbed radius, its dimensions approximate RF, assuming a flat, mushroom-like conf ormation; when the grafting distance is much smaller than the unperturbed radius, segmen ts of adjacent chains begin to overlap and assume brush-like conformations due to excluded volume effects. Drastic reduction in friction was observed at around L R F when scaling theory predicts the onset of strong segment extension occurs. An analogous maximal protein resistance has been previously observed in PLL-g-PEG systems around the same brush conformation regime. Substrates coated with PEG-grafted copolymer s that form brush like structures represent hydrophilic systems which have been shown to exhibit friction responses that systematically vary with solvent quality. It has been previously shown that PLL-g-PEG-coated inte rfaces exhibit a load dependence of friction that decreases as the solvent is exchanged from the least polar (alcohol) solvent to the most pol ar (aqueous) solvent. This behavi or was strongly correlated to the amount of solvent associated with the polymer, and rationalized in terms of the polar and hydrogen-bonding Hansen solubility parameters representing solvent-segment interaction energies. Complementary studies on PS brushes demonstr ated this to be a general tribological behavior, i.e., that an increase in lubricity was observed for a hydrophobic brush, this time, in a nonpolar solvent environment. In contrast to PLL-g-PEG that spontaneously coats silicon oxide surfaces as preformed bottle-brushes, PS brushe s were directly grown on silicon oxide surfaces by surface-initiated free-radical polymerization usi ng silane chemistry. It was observed that PS
169 brushes exhibited a relatively higher solvent uptake in toluene, a good nonpolar solvent, compared to the more polar alcohols; in turn, PS brushes also exhibited vanishingly low friction response in toluene compared to the alcohols. Normal force measurements as a function of approach displacement also showed contact at greater probe-substrate separations under toluene compared to the alcohols, indicating a more ex tended brush conformation. Dramatically higher dissipation was also observed by QCM under toluene that denote a more damped viscoelastic response as the polymer became more plasticized and fluid upon wetting by a favorable solvent. These observations coincided with the lower ratio of cohesive energy density between polystyrene and toluene compared with the alcoho ls, which reflected the difference in the overall Hansen parameters between polymer and solvent, and hence, their relative affinities. Highly extended conformations of mobile chain segm ents in a good solvent thus represented the necessary criteria for the low friction observed in these polymer brush systems. PEI is an amino analogue of PEG, which, due to the tri-valency of nitrogen, is commonly available as a highly branched polymer. It repr esents an alternative to PLL in PEG-grafted systems, and afforded the opportunity to investigate the influence of backbone architecture and chemical structure on the tribology of these systems. PEI-g-PEG, like PLL-g-PEG, is also expected to spontaneously adsorb onto silica subs trates via electrostatic attraction. PEI, however, represents a branched backbone architecture compared to linear PLL, and a more densely charged structure owing to the smalle r size of its repeating units. Anchoring amino groups in PEI also lie on the main chain, while they are penda nt side-chains on the PLL backbone that consists of charge-neutral peptide linkages. These differe nces are expected to influence the adsorption and conformation of PEG-grafted copolymers on surf aces, and hence, their tribological behavior. Poly(allylamine)-graft-poly(ethylene glycol) (PAAm-g-PEG) for example has recently been
170 shown to exhibit reduced adsorption and lubricity compared to PLL-g-PEG of commensurate PEG spacing on the backbone. The observation was expl ained in terms of the rigidity of PAAm backbone compared to PLL that permitted the la tter to freely reconf orm more on the surface allowing for tighter packing a nd acquiescence to irregularities. Load dependence of friction showed the same systematic dependence to solvent environment for PEI-g-PEG as for PLL-g-PEG, i.e., the friction response decreased while solvent uptake increased as th e polarity of the solvents changed from relatively nonpolar (alcohols) to polar (aqueous) so lvents. This was supported by c ontact at higher probe-substrate separations under aqueous buffer compared to the alcohols in normal force versus displacement plots. Furthermore, PEI-g-PEG and PLL-g-PEG of comparable component molecular weights and grafting ratios showed almost identical friction force responses under aqueous buffer solution. However, in asymmetric tribopairs, where a bare glass colloidal probe was rubbed against a polymer-coated substrate, gross hysteresis was observed for PEI-g-PEG between the first and last aqueous buffer washes (with alcohols of decreasing polarity in between), i.e., the friction response was high in the initial buffer washcom parable to that for the relatively nonpolar alcoholsfollowed by the typical low friction observ ed for the aqueous buffer in the final wash. PEI has been known to form unstable films on the surface, especially at relatively higher pH (e.g., 7) where flocculation due to polymer bridgi ng takes place, and have been observed to foul the counterface in SFA measurements. Thus, the hystersis observed could be rationalized in terms of bridging interactions between the polyme r-coated substrate and the bare glass colloidal probe, as evidenced in features on the force-disp lacement plots consistent with this, which were absent in the PLL-g-PEG system. As the tip was run-in, mate rial transferred from the substrate to
171 the probe, eventually creating a symmetric interface; also, the dehydration of the PEI-g-PEG film with the successive alco hol washes may have induced some dangling amino groups to eventually anchor onto the substrate. Such events r easonably explained the hysteresis observed in asymmetric PEI-g-PEG tribointerfaces, and were corrobor ated by the absence of such hysteresis in symmetrically coated systems. In li ght of the recent consideration of PAAm-g-PEG systems, this study reinforced the importance of the back bone architecture and chemical structure on the quality of PEG-grafted films formed on th e surface, and hence, on their tribology. Lubricity and Fouling Resistance Tribological investigations of PEG-coated surfaces were originally spurred by the resistance of such surfaces to non-specific prot ein adsorption. Blood contacting devices such as medical implants and intravenous mandrins and ca theters are prone to th e adhesion of proteins on their surfaces that trigger a cascade of events that may eventually induce thrombosis [238, 239]. Protein build-up on contact lenses (e.g., lyso zyme from the tear film ) is a common cause of eye discomfort that may also lead to microbi al infection and allerg ic reaction . That coatings with PEG-based polymers not only resu lts in fouling resistance, but also in the concomitant creation of highly lubricious surfaces therefore leads to synergistic benefits, for example, in the reduction of fluid drag, and in the creation of a boundary lubricant layer on loadbearing metal implants and in the interface between the contact lens and the eye. The ultimate (i.e., equilibrium) amount of protein adsorbed on a polymer brush-coated substrate is determined by the enthalpic balance between protein-substrate interactions (assumed to be attractive), and polymer-protein and proteinprotein interactions (ass umed to be repulsive) [238, 241]. If there is significant polymer-substrat e attraction, there will also be an additional enthalpic cost in desorbing polymer segments. Th ere is also an unfavorable loss of entropy in inserting a protein on a polymer brush-coated surf ace that arises from the loss of conformational
172 freedom of chain segments that are thus forced to extend due to excluded volume effects (steric repulsion) [101, 238, 241, 242]. Similarly, there is a penalty in compressing the polymer brush that comes from the resistance of solvent from being squeezed out, thus countering the entropy of mixing (osmotic repulsion) [101, 242]. Protein adsorption isotherms fr om single-chain mean field (SCMF) calculations show that the amount of adsorbed protein is determined by surface coverage of the polymer, i.e., the density of segments close to the substrate [238, 241]. This is the free energy barrier that determines the equilibrium adsorption. The intera ction potential between proteins and the grafted polymer layer, however, is found to be strongly dependent on the polymer film thickness. Thus, while grafting density exerts thermodynamic control over th e amount of proteins adsorbed, the molecular weight assumes kinetic control by modulating th e repulsive interac tion with proteins before they fall into th e attractive potential well associated with adsorp tion on the substrate [238, 241]. The calculated shape of the steric repul sion between a lysozyme and a PEG-grafted substrate, for example, exhibits a maximum [ 238, 241]. Also, the observation that even SAMs with only two ethylene glycol un its (i.e., approaching the pers istence length of the polymer) prevent protein adhesion [238, 243] can be acco unted for, thermodynamically, by the very high densities achievable from small-molecule self-assembly. In addition to this physical description of fouling resistan ce, there exists an account that regards the chemical details of the system [101, 233]in particular, the abili ty of water, the ubiquitous biological medium, to form hydrogen bonds that are unusually strong intermolecular interactions ( H 23.3 kJ/mol ) with specific orientation-dependence (OO length < 3.10 HOH angle >146 [245, 246], K J/mol 37.2 S ). Water is capable of being both an electron-donor (Lewis base) a nd electron-acceptor (Lew is acid), and can be on either end of a
173 hydrogen bond. Surfaces capable of Lewis acid-base interactions modify the local density and orientation of water molecules: the density increa ses due to tight binding of water to the surface, while its orientational informa tion is also propagated to adjo ining water molecules [101, 233]. Disruption of hydrogen bonds in the hydration layer near surfaces with prevalent Lewis acid or base moieties is the origin of the so-called hydration forces. Conventional DLVO theory, in considering exclusively electrosta tic and van der Waals contributions predicts only an adhesive minimum near surfaces, while experimental force plots of plasma treated hydrophilic surfaces in water actually exhibit a repulsive interaction at distances <5 nm that is accounted for by acidbase forces . In light of this, the PEG pol ymer can be considered as a Lewis base-rich system that will exhibit very str ong interaction with water . Furthermore, the gauche conformation that gives rise to its helical structure registers with the orientational requirements in the hydroge n-bonding network of water [101, 233]. The OO separation in PEG is 2.88 commensurate with the OO distance of 2.85 for hydrogen bonds in water . In contrast to PEG or poly(ethylene oxide) (CH2CH2O), closely related polymers such as poly(methylene oxide) (CH2O), poly(acetaldehyde) (CH2(CH3)O), and poly(propylene oxide) (CH2CH2CH2O) are not soluble in water at room temperature . Therefore, the ability of PEG to maximize the acid-base forces is also invoked as a chemically specific account of its ability to present a repulsi ve barrier to protein adhesion. The ability of PEG SAMs, for example, to prevent protein adhesi on can alternatively be explained in terms of hydration forces arising from the profusion of Lewis base sites on these surfaces [101, 243]. These studies on the nanotribology of polyme r-grafted surfaces probed by a colloidal sphere/cantilever assembly at the boundary lubric ation regime pointed to the related origins of lubricity and fouling resistance of polymer brushe s in a good solvent. Systematic investigations
174 of the friction force response of PLL-g-PEG systems showed a si milar dependence on PEG molecular weight and lysine/PEG grafting ratios that were an alogous to their resistance to protein adsorption in terms of how these influen ced the PEG packing density and film thickness on the surface. While dense, thick brush segm ents thermodynamically and kinetically limited protein adsorption, they also pr esented surfaces that were highly resistant to compression due to osmotic repulsion, and that have low shear strengths due to the hi ghly fluctuating, solvated chain segments (at least at the sliding velocities employed in AFM), which accounted for their vanishingly low friction response. The exceptiona l ability of PEG to retain water due to hydrogen bonding enhanced the repuls ive barrier to protein adhesi on, while also maintaining a boundary fluid layer (or water cloud ) on the surface that prevente d solid-solid contact between tribopairs that was not pos sible with water alone due to its low pressure-coefficient of viscosity. Finally, that the same phenome non of low friction response was observed for hydrophobic brushes in nonpolar solvents demonstrated that highly extended chain segments in a good solvent was a general requirement for produc ing lubricious surfaces from polymer brush systems. Further Research There remain several outstanding questions that need to be resolved with regards to the tribology of PEG-grafted systems investigated in this dissertation. This study mainly addressed the systematic dependence of polymer brush tribology in term s of polymer architecture and solvent quality. The composition of the aque ous solvent environment from which PLL-g-PEG and PEI-g-PEG were adsorbed onto metal oxide surf aces, and in which their friction response were tested, entailed maintaining the pH at 7.4 and the salt concentr ation at around 10 mM through the use of a buffer. These conditions were favorable to the adsorption and stabilization of the polymer brushes on the su rface of metal oxides via electrostatic attr action by creating a pH
175 environment that was above the isoelectric point of the metal oxide and below the pKa of the amino groups on the backbone, and ionic strengths th at would exempt the sc reening of charges. More importantly, these were typical physiological conditions under which these polymers were targeted to perform in engineering applications. It is clear however that the pr operties of these copolymer system s are also sensitive to their acid/base and salt environments, and it would be interes ting to systematically investigate the effects of pH and ionic strength on their tribological behavior not only in order to further unravel the physico-chemical basi s of their lubricity, but also in light of their potential applications in non-biological environments, e.g., in the food industry. The behavior of polyelectrolytes in solution is know n to be highly dependent on pH and ionic strength. The pH of the buffer solution dictate the degree of protona tion of the amino groups on the PLL and PEI backbones, and thus the resulti ng charge density on the polymer, which in turn influences its conformation and adsorption characteristics. High charge density, for example, would result in a more extended conformation in solution owing to repulsion of chain segments, and produce flat, patch-charge films on surfaces due to the ra pid overcompensation of the surface charges upon adsorption. High charge density on the polymer can also be dissipated through screening with counterions by increasing the io nic strength of the solution. Thus, the amount of PEI, for example, that adsorbs onto the native oxide of silicon increases with increasing pH (or ionic strength) as the charge density decreases (or is screened) and non-coulombic interactions with the surface dominate with less hindrance from electrostatic repulsion . To complicate matters further, the charge density/screening on the substrates surface is also modified by the pH/ionic strength to an extent no t necessarily the same as that of the polymer. It would be interesting to disentangle the contributions of these convoluted effects on the tribological
176 behavior of PLL-g-PEG and PEI-g-PEG, which may involve performing the polymer adsorption at different sets of conditions from those used in the testing of the polymer friction response. In contrast to the charged PLL and PEI bac kbones, the neutral PEG bristles should not be as sensitive to changes in pH environments. Sol ubility of PEG in water, however, is known to be influenced by salt concentration. Phase diagrams of aqueous solutions of PEG exhibit both an upper and lower critical solution temperatures (UCST and LCST, respectively) of the closedloop type, which means that the UCST occurs above the LCST, and in between them (i.e., within the loop) exists a miscibility gap [249, 250]. The UCST is related to the theta-condition of ideal polymer solutions, where the enthalpy of mixing is positive such that the solubility increases with increasing temperature  Phase separation at LCST, speci fically in phase diagrams of the closed-loop type, is accounted for by active groups in one molecule polarizing those of another, thus producing strong in teractions; the enthalpy of mixi ng is negative such that the solubility actually increases with decreasing temperature [249, 251]. In aqueous PEG solutions, these strong polarizing interact ions are, of course, due to hydrogen-bonding which is not addressed by usual solution thermodynamics [1 01, 233, 252-255]. At low temperatures, there is favorable excess enthalpy from the ether-wat er hydrogen bonding, a nd unfavorable excess entropy from the structure of the water of hydra tion around the ether units. As the temperature is increased there is a stronger rise in excess fr ee energy due to the breaking of the ether-water hydrogen bonds that is not matched by the modest gain in entropy from disrupting the water structure , resulting in the observed cloud point in aqueous PEG solutions at relatively elevated temperatures. The LCST of aqueous PEG solutions are known to vary systematically with molecular weight and salt concentrations. The LCST of a 5 kDa polymer for example is around 135 C,
177 while that for a 7,000 kDa polymer is around 95 C; above 50 kDa and 0.3 %(w/w), the precipitation temperature is neither sensitive to molecular weight nor concentration, i.e., the lower part of the closed-loop phase diagram flatte ns out . The LCST also decreases linearly with increasing salt concentration, such that the degree of its con centration dependence is determined primarily by the nature of the anion rather than, say, the ionic strength . The LCST of PEG in aqueous KI, for example, remains almost the same at ~100 C even with a change in salt concentration of 0. 1 to 1 M, while it reduces to ~50 C under the same change in aqueous KF; in contrast, th e salting out effect of K2SO4 and MgSO4 are almost the same. This salting out behavior follows the well-known Hofm eister series, which accounts for the salting out of proteins in terms of the ability of the anions to disrupt the water stru cture. The LCST of PEG is also insensitive to pH, for example, until above pH 10 where it begins to decrease drastically in proportion to the hydroxide i on concentration. Given the pres ent knowledge of the dependence of PEG lubricity on its stretch-collapse transi tion as moderated by solvent quality, it would be interesting to systematically investigate its tribology by induci ng conformational collapse with appropriate salts at the lower te mperature limit of solubility. Fig. 6.1 for example shows the force plots of a 5-m glass colloidal probe against a PLL(20)-g[3.2]-PEG(5)-coated silicon wafer substrate at different temperatures, compared with a bare silicon wafer substrate at ambient temper ature. The solution is buffered at pH 7 with sodium phosphate, which is known to decrease th e LCST of 4,000 kDa PEG to between 45 to 50 C . Preliminary results show an a pparent brush collapse between 35 to 45 C that is consistent with a phase transition. AFM force m easurements at elevated temperatures, however, are complicated by the layered construction of the cantilever used, composed of Si3N4 coated with gold that serves as a reflective mirror in the optical detection system. The incompatibility of
178 20 15 10 5 0Normal Load (nN) 120 100 80 60 40 20 0 Approach Displacement (nm) Bare Silicon 27.9 oC 35.0 oC 45.0 oC 55.0 oC Figure 6-1. Force-displacement plots of a 5-m glass colloidal probe against a PLL(20)-g[3.2]PEG(5)-coated silicon wafer substrate at diffe rent temperatures as compared to a bare silicon wafer substrate at ambient temperature.
179 the coefficients of thermal expansion of the two materials causes the cantilever to curl up as the temperature is increased, resulting in the drif t of the equilibrium cantilever position. The more serious challenge is, again, disentangling thes e temperature and salt effects on the PEG brushes that are confounded with their effects on the anchoring backbone polymers. These proposed research underscore the impor tance in understanding th e physico-chemical properties of molecularly tailored lubricants, such as the polymer brushes investigated in this study, which perform under boundary conditions. They also highlight the central place of AFM in the toolkit of modern tribological research in elucidating these properties with its ability to employ and detect forces and disp lacements at nanoscale resolutions.
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BIOGRAPHICAL SKETCH Francis Ted J. Limpoco was born in Manila, Philippines, to Rogelio C. Limpoco and Lucia J. Josue. He attended primary and secondary sch ools at La Salle Green Hills, run by the Brothers of the Christian Schools, where he finished as class valedictorian in 1987. Thereafter, he obtained his Bachelor of Scien ce degrees in chemistry (1991) and in computer engineering (1993), at the Jesuit-run Ateneo de Manila University, where he received the Bank of the Philippine Islands Science Award, given to the top three graduating science students. While finishing his second b achelor degree, he began te aching in the Chemistry Department at the Ateneo in 1992, becoming an Instructor in 2001 upon receiving his Master of Science in chemistry. He worked on the tougheni ng mechanisms in biominerals and specialized in the thermal analyses of polymers. Between 1994-1998 he also worked as a technical sales engineer for Handelshaus Consult Philippines, a family business concern, and trained in Germany and Italy on CAD/CAM system s in garment manufacturing. In the Fall 2004, he relocated to the United States to be gin his doctorate studies in chemistry at the University of Houston in Texa s, working in the fiel ds of surface science, nanotribology, and biomimetic lubrication, under the direction of Scott S. Perry. In 2006, he moved with his professor to th e Department of Materials Science and Engineering at the University of Florida where he continued to pursue his Ph.D. in chemistry.