Session L45: Friction and Brushes

Velcro$^{\mbox{{\textregistered}}}$ as a Mesoscopic Model System for Stick-Slip Motion

The Amontons-Coulomb (AC) laws of friction, established during the 18$^{th}$ Century, serve to explain many of the phenomenological observations of friction in the macroscopic world. The AC laws for friction do not adequately explain certain systems, which undergo stick-slip motion, however. The hook-and-loop system (Velcro), in particular, exhibits easily observed stick-slip motion. Velcro evinces clear evidence of stick-slip dynamics that is independent of sliding velocity in accordance with Coulomb but, the maximum static friction force $F_s^{\max } $ and kinetic friction $F_k $ are keenly dependent on ``area of contact'' (hook number) in contrast to accepted law, but consistent with recent studies of frictional dynamics in nanoscopic systems. Both the $F_s^{\max } $ and $F_k $ as a function of area follow power law dependences with an exponent of approximately 2/3. Moreover, the fluctuations of the kinetic friction $F_k $ also follow a power law dependence with an exponent of approximately 1/2 in accordance with random walk theory. On the other hand, the $F_s^{\max } $ and $F_k $ both follow a linear dependence with applied load in accordance with the classical theory of AC.   

The Use of Microscale Geometry to Tailor Stimulus-Responsive Surface Friction

The capability to tailor stimulus-responsive surface friction, including sensitivity profile, range, temporal response and deformation mechanisms, holds great potential for an array of engineering and biomedical applications. In this study, the pH-dependent friction of layer-by-layer assemblies of poly(allylamine hydrochloride) and poly(acrylic acid) (PAH/PAA) were quantified for structures of a continuous planar film and anisotropic microtube forests via lateral force microscopy. By comparing experiments to microstructure-specific finite element modeling, a mechanistic change from surface adhesion-dominated friction ($\mu $=0.11) to viscoelasticity-governed shear (=0.017) was predicted upon ionic crosslink density reduction of PAH/PAA from pH 5.5 to 2.0 for the film (6.5$\times $ decrease). The responsiveness of $\mu $ was further tuned by the tube forest geometry to be 3.5$\times $. At pH 5.5, $\mu $ (=0.094) was lower than the film due to discrete tube bending/buckling and smaller tip-sample interface stress. At pH 2.0, $\mu $ (=0.027) was higher because of inter-tube contact and weaker substrate effect. This study provides an excellent platform to quantitatively access and design dynamic substrates with tailorable stimulus-responsive surface friction.   

Viscous friction of hydrogen-bonded matter

Amontons' law successfully describes friction between macroscopic solid bodies for a wide range of velocities and normal forces. For the diffusion and forced sliding of adhering or entangled macromolecules, proteins and biological complexes, temperature effects are invariably important and a similarly successful friction law at biological length and velocity scales is missing. Hydrogen bonds are key to the specific binding of bio-matter. Here we show that friction between hydrogen-bonded matter obeys in the biologically relevant low-velocity viscous regime a simple equations: the friction force is proportional to the number of hydrogen bonds, the sliding velocity, and a friction coefficient $\gamma_{\rm HB}$. This law is deduced from atomistic molecular dynamics simulations for short peptide chains that are laterally pulled over hydroxylated substrates in the presence of water and holds for widely different peptides, surface polarities and applied normal forces. The value of $\gamma_{\rm HB}$ is extrapolated from simulations at sliding velocities in the range from $v=10^{-2}$ m/s to 100 m/s by mapping on a simple stochastic model and turns out to be of the order of $\gamma_{\rm HB} \simeq 10^{-8}$ kg/s. 3 hydrogen bonds act collectively.   

Molecular mechanisms of friction at soft polymer interfaces

Polymer molecules strongly anchored to a solid substrate and interdigitated into bulk crosslinked elastomer have been shown recently to efficiently promote adhesion and friction between substrate and elastomer. Concerning friction, the regime of low surface coverage in surface anchored chains has been fully and quantitatively accounted for by the pull off mechanisms, where individual chains are dynamically extracted from the elastomer. Then, the stretching energy of these chains dominates the friction losses. We focus here on the dense surface coverage regime. We present systematic experiments performed on the polydimethylsiloxane (PDMS) - silica system, and determine molecular weight and sliding velocity dependences of the friction stress. We show that the friction is dominated by the shear thinning of the grafted layer confined between the elastomer and the substrate, and responding to the shear solicitation like a melt, but with very long relaxation times. We also show that the friction stress appears highly sensitive to the molecular organization inside the surface anchored polymer layer, comparing end grafted and strongly adsorbed layers having otherwise the same molecular characteristics (molecular weight of the chains, and thickness of the surface anchored layer).   

Frictional properties of the end-grafted polymer layer in presence of salt solution

We have studied the frictional behaviour of grafted poly[2-(dimethylamino)ethyl methacrylate] (PDMAEMA) films using friction force microscopy (FFM). The films were prepared on native oxide-terminated silicon substrates using the technique of atom transfer radical polymerization (ATRP). These brushes had constant grafting density (1.18 nm2), and of a thickness of $\sim$66 nm, as measured by ellipsometry. We show that single asperity contact mechanics (Johnson-Kendall-Roberts (JKR) and Derjaguin-M\"uller-Toporov (DMT) models) as well as a linear (Amontons) relation between applied load and frictional load all apply to these systems depending on the concentration of salt and the nature of the FFM probe. Measurements were made using gold-coating and polymer functionalized silicon nitride triangular probes. Polymer functionalized probe included growth the PDMAEMA with same method on tips. The frictional behaviour are investigated between PDMAEMA and gold coated and PDMAEMA tips immersed in different concentrations of KCl, KBr and KI.   

Nanofluidity of Polymer Melt: Two velocity hydrodynamics

According to the traditional macroscopic theory, the flow of the entangled polymer melt is associated with the relaxation processes in the network of entanglements. Each entanglement is formed by polymer chains, and these chains are moving randomly along their reputation tubes. Because of this random motion of polymers each entanglement has a finite lifetime. The lifetime is equal to the time needed for a polymer to leave its original tube. We should point out, that the motion of individual polymer chain in a tube is assumed to be completely random (diffusive). It means, that according to traditional theory, in average there is no systematic displacement of polymers with respect to the network of entanglements. The local polymer flow velocity in this theory is just the instant local velocity of individual entanglements forming this network. But the drift of individual polymers provides additional mechanism of a flow of a polymer melt, which becomes dominant at small scale. We suggest two velocity hydrodynamic equations which describe combined contribution of these two mechanisms. For illustration of this method we solve the problem of mobility of a small particle in a polymer melt.   

Poly(ethylene oxide) Chains Are Not ``Hydrophilic'' When They Exist As Polymer Brush Chains

By using a combined experimental and theoretical approach, a model poly(ethylene oxide) (PEO) brush system, prepared by spreading a poly(ethylene oxide)-poly($n$-butyl acrylate) (PEO-PnBA) amphiphilic diblock copolymer onto an air-water interface, was investigated. The polymer segment density profiles of the PEO brush in the direction normal to the air-water interface under various grafting density conditions were determined from combined X-ray and neutron reflectivity data. In order to achieve a theoretically sound analysis of the reflectivity data, we developed a new data analysis method that uses the self-consistent field theoretical modeling as a tool for predicting expected reflectivity results for comparison with the experimental data. Using this new data analysis method, we discovered that the effective Flory-Huggins interaction parameter of the PEO brush chains is significantly greater than that corresponding to the theta condition, suggesting that contrary to what is more commonly observed for PEO in normal situations, the PEO chains are actually not ``hydrophilic'' when they exist as polymer brush chains, because of the many body interactions forced to be effective in the brush situation.   

Tunable Surface Properties from Bioinspired Polymers

Tunability of surface properties is of importance for a variety of coating applications, including antifouling coatings. We have investigated the surface properties of polypeptoids, a class of non-natural biomimetic polymers based on an N-substituted glycine backbone, that combine many of the advantageous properties of bulk polymers with those of synthetically produced proteins, including controllable chain shape, sequence, and self-assembled structure. We demonstrate the influence of the amount and sequence of hydrophobic monomers in a predominantly hydrophilic peptoid chain on surface properties. Especially the surface reconstruction behavior of block copolymers of these amphiphilic polypeptoids with polystyrene upon contact with water will be addressed. It has been found that surface reconstruction of peptoid chains that contain a sequence of only three fluorinated monomers and up to forty-two hydrophilic monomers occurs within seconds, whereas reorganization of surfaces containing five fluorinated monomers was an order of magnitude slower. Surfaces with higher fluorine content also showed lower settlement of spores of the green algae Ulva.   

Concentration Fluctuations of a Semidilute Polymer Solution in Good Solvent Near a Repulsive Surface

The concentration profile of a semidilute polymer solution in good solvent near a repulsive surface has been previously calculated.\footnote{J.~F.~Joanny, L.~Leibler, P.-G.~de Gennes, J. Polym. Sci. 17, 1073 (1979)} In this work we consider fluctuation corrections to the mean field concentration profile in the presence of a repulsive surface using the Cahn-Hilliard square-gradient approach extended to polymer interfaces. Our results predict that at strongly repulsive surfaces, a polymer in good solvent exhibits concentration fluctuations associated with the surface in addition to fluctuations of the bulk polymer solution. We compare our predictions with current experiments which have measured fluctuations in the concentration of interphase chromatin (DNA with its associated proteins) inside the nucleus of mammalian cells \textit{in vivo} using ultrafast high space resolution spinning disc confocal microscopy.   

Kinetics of Polymer Interfacial Reaction

Germanium crystals modified with high quality azide functional monolayers are used to directly monitor in situ the kinetics of interfacial ``click'' reactions with complementary alkyne end-functional poly(n-butyl acrylate) (PnBA) and polystyrene (PS) by attenuated total reflectance infrared spectroscopy (ATR-IR). In the presence of copper (I), the azide-modified Ge substrates react quantitatively with PnBA and PS via a 1,3-dipolar cycloaddition reaction. Time-resolved ATR-IR measurements show two regimes of kinetic behavior, as predicted by theory. In the first regime the rate is rapid and is controlled by diffusion of the polymer through the solvent, scaling with the square root of time. The rate slows considerably in the second regime, limited by penetration of the reacting polymer through the covalently bound polymer brush layer, scaling with the natural logarithm of time. The influence of polymer size and solvent quality are reported.   

Influence of Substrate Surface Energy on the Morphological Evolution of PS/PMMA Blend Thin Films

In this study, the morphological evolutions of PS/PMMA blend thin films are systematically characterized during thermal annealing on both preferential and non-preferential surfaces. The evolution of phases on preferential surfaces was dictated by the preferential wetting of the components, and the coarsening process of the PMMA domains. PS droplets with high spatial correlation were formed in a moderately asymmetric PS/PMMA blend because of PS dewetting via a controlled nucleation mechanism. In contrast, a more asymmetric blend evolved into PS droplets via a random nucleation process, such that the PS droplets did not exhibit spatial correlation and had a broad size distribution. The morphological evolution of the blends on relatively non-preferential surfaces was also dictated by domain coarsening, but proceeds without the formation of PMMA wetting layer. As a result, a diverse set of non-equilibrium, micro- and nanoscale morphologies were observed.