Friction and Relaxation Dynamics of Highly Extended Polymer Brush Melts under Compression and Shear

Correlation between viscoelastic response and frictional properties of hydrated zwitterionic polymer brush film in narrowing shear gap

HYPOTHESIS

A hydrated 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer brush exhibits exceptional lubricity. This lubrication mechanism has traditionally been attributed to either the inherent fluidity of the brush or the water film that forms owing to its hydrophilic nature. Given previous findings that the frictional properties of the MPC polymer brush film show load dependence, we hypothesize that the lubrication mechanism can be elucidated by examining the shear gap (varies owing to the load) dependence of the brush's viscoelastic response.

EXPERIMENTS

MPC polymer brush films with different thicknesses were prepared. Their viscoelastic responses were evaluated across different shear gap widths, and the frictional properties were subsequently compared across states with distinct viscoelastic behaviors.

FINDINGS

The observed shear viscoelasticity demonstrated a clear gap dependence that correlated with frictional attributes. Our data suggests that the lubrication mechanism shifts based on the shear gap. Specifically, two states exhibited low coefficients of friction: one where the osmotic pressure supports the load while allowing flexible deformation of the brush film, and the other where the brush film undergoes compression and transitions to a fully elastic state.

Surface Forces Characterization of Concentrated PMMA Brush Layers under Applied Load and Shear

Concentrated polymer brushes (CPBs) are known to exhibit excellent lubrication properties. However, the frictional behaviors of CPBs vary, depending on their preparation and operating conditions. In order to understand such complicated properties, it is necessary to determine their structures and correlate them with their properties, during shear motion. In this study, we employed surface forces and resonance shear measurement (RSM) as well as refractive index measurement using fringes of equal chromatic order (FECO) for studying the structure of the CPBs of poly(methyl methacrylate) (PMMA) in toluene. The obtained elastic (ks) and viscous (bs) parameters based on the RSM for the PMMA-PMMA were higher than those obtained for PMMA-silica over the entire distance range. With the increasing shear amplitude on the PMMA-PMMA under an applied load, the bs value first increased and then decreased while the ks value monotonically decreased. These behaviors were consistent with those of the thicker CPBs reported in a previous paper (Soft Matter, 2019). Thus, the dynamics of the CPBs under the applied load and shear were not dependent on the thickness of the polymer brushes in this case. The density distribution of the swollen PMMA brushes along the distance in the thickness direction of the brush layer was estimated by using the measured refractive index values, showing that the fraction of the PMMA brushes in the outer region from the surface (20% in the thickness) was ca. 10%. This lower density region near the surface of the swollen CPBs enabled them to interpenetrate with each other. Changes in the refractive index value under shear were observed, indicating that the interpenetrated PMMA chains were pulled out with increasing shear amplitude. These results demonstrated that broader applications of CPBs are possible by regulating the friction between them under different operating conditions, even for usually lubricious CPBs.

Lubrication in polymer-brush bilayers in the weak interpenetration regime: Molecular dynamics simulations and scaling theories

We conduct molecular dynamics (MD) simulations and develop scaling laws to quantify the lubrication behavior of weakly interpenetrated polymer brush bilayers in the presence of an external shear force. The weakly interpenetrated regime is characterized by 1<d_{g}/d_{0}<2, where d_{g} is the gap between the opposing surfaces (where the brushes are grafted) and d_{0} is the unperturbed brush height. MD simulations predict that in the shear thinning regime, characterized by a larger shear force or a large Weissenberg number (W), R_{g}^{2}∼W^{0.19} and η∼W^{-0.38}, where R_{g} is the chain extension in the direction of the shear and η is the viscosity. These scaling behaviors, which are distinctly different from that witnessed in strongly compressed regime (for such a regime, characterized by d_{g}/d_{0}<1, R_{g}^{2}∼W^{0.53}, and η∼W^{-0.46}), match excellently with those predicted by our scaling theory.

Polyelectrolyte brush bilayers in weak interpenetration regime: Scaling theory and molecular dynamics simulations

We employ molecular dynamics (MD) simulations and develop scaling theories to quantify the equilibrium behavior of polyelectrolyte (PE) brush bilayers (BBLs) in the weakly interpenetrated regime, which is characterized by d_{0}<d_{g}<2d_{0}, where d_{g} is the gap between the opposing plates where the PE brushes are grafted and d_{0} is the unperturbed height of a PE brush grafted at a single plate. Scaling predictions establish that, for the weakly interpenetrated osmotic PE BBLs δ∼N^{1/2}(2-d_{g}/d_{0})^{1/2} (where δ is the interpenetration length and N is the number of Kuhn segments in PE brush). MD simulations excellently recover this dependence of δ on N and the extent of interpenetration (quantified by d_{g}/d_{0}). These predictions, unlike the existing studies, establish a finite interpenetration for all values of d_{g}/d_{0} as long as d_{g}<2d_{0}. Finally, we quantify the monomer and counterion concentration distributions and point out that these two distributions may quantitatively deviate from each other at locations very close to the channel centerline, where the interpenetration-induced monomer concentration can be significantly low.

Compression of polymer brushes in the weak interpenetration regime: scaling theory and molecular dynamics simulations

We employ scaling theory and Molecular Dynamics (MD) simulations to probe the compression of the semi-dilute polymer brush bilayers (BBLs) in the weak interpenetration (IP) regime. Such a regime is characterized by two layers of interacting polymer brushes grafted on opposing planar surfaces having a separation d_g, such that d₀ < d_g < 2d₀, with d₀ being the unperturbed brush height. Currently, scaling theories are known for polymer BBLs with a much larger degree of IP (i.e., d_g < d₀) - in such regimes, the brush height can be quantified by the corresponding IP length δ. On the other hand, we show that in the weak IP regime, the brush height is not solely dictated by δ. We develop new scaling theories to show that δ in this weak IP regime is different from that in the strong IP regime. Secondly, we establish that the compressed brush height in this weakly IP regime can be described as d ∼ N^χ with χ < 1 and varying monotonically with d_g/d₀. MD simulations are carried out to quantify δ and χ and the results match excellently with our new scaling theory predictions. Finally, we establish that our scaling theory can reasonably predict the experimentally witnessed variation of the interaction energy dictating the compressive force between the interpenetrating brushes in this weakly IP regime.

Grafting density dominant glass transition of dry polystyrene brushes

The effects of the grafting densities (σ_p), molecular weights (M_n) and thicknesses of dry polystyrene (PS) brushes on their glass transition temperature (T) were investigated by ellipsometry. The results show that T strongly depends on the grafting density of the PS brushes. The T of the PS brushes with σ_p > 0.30 increases with decreasing M_n (or brush thickness) and is mainly dominated by entropic effects, in which the grafted chains are highly extended along the film thickness direction resulting in a sharp reduction in configurational entropy. The T of PS brushes with σ_p < 0.30 decreases with decreasing M_n (or brush thickness) which is mainly dominated by surface effects. For intermediate-density brushes (σ_p = 0.30), T becomes independent of M_n or brush thickness. The reason for this grafting density dependence of T is attributed to the transition of the PS brush conformation from mushroom-to-brush.

Polymer-brush lubrication: a review of recent theoretical advances

This review compiles recent theoretical advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biological problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equilibrium and out-of-equilibrium situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromolecular inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative analytical approaches, experiments and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using molecular dynamics simulations.

Calf serum constituent fractions influence polyethylene wear and microbial growth in knee simulator testing

Calf serum lubricants consisting of various polypeptide constituent fractions are routinely used in knee wear simulators as part of the standardized test protocol. Three calf sera (bovine, new-born and alpha) were diluted as per the recommendation of ISO 14243-3 and used in displacement-controlled knee wear simulators to investigate their effects on polyethylene wear. Biochemical analyses included measuring total polypeptide degradation, electrophoretic profiles and low-molecular weight polypeptide concentrations to elucidate their involvement in the wear process. The effects of the various calf sera constituent fractions on microbial growth were also explored. The polyethylene wear rates and the results from the biochemical analyses for the three calf serum lubricants were all found to be statistically significantly different from each other. The lubricant derived from the alpha-calf serum was closest in constituent fractions to human synovial fluid. It also showed the lowest polyethylene wear rate (14.38 ± 0.85 mm3/million cycles) and the lowest amount of polypeptide degradation (7.77 ± 3.87%). Furthermore, the alpha-calf serum lubricant was associated with the least amount of change in the electrophoretic profile, the least change in low-molecular weight polypeptide concentration, and the lowest microbial growth in the presence of sodium azide (a microbial inhibitor conventionally used in implant wear testing). Replacing sodium azide with a broad spectrum antibiotic-antimycotic eradicated the microbial growth. Some speculation was entertained regarding the effect of alpha-calf serum on colloid-mediated boundary lubrication. Based on the results, it was recommended that ISO 14243-3 be modified to include guidelines on calf serum constituent fractions that would favour using alpha-calf serum in order to improve the fidelity of the simulation in knee implant wear testing.

Commissioning of a displacement-controlled knee wear simulator and exploration of some issues related to the lubricant

A six-station displacement-controlled knee simulator with separately controlled left (L) and right (R) banks (three wear implants per bank) was commissioned for a total of three million cycles (Mc) following ISO 14243-3. A commissioning protocol was applied to compare the polyethylene wear among the six wear stations by exchanging the implants between wear stations. Changes in lubricant characteristics during wear testing, such as polypeptide degradation, low-molecular-weight polypeptide concentration, and possible microbial contamination were also assessed. The total mean wear rate for the implants was 23.60 ± 1.96 mm3/Mc and this was of a similar magnitude to the mean wear rate for the same implant tested under similar conditions by DePuy Orthopaedics Inc. (Warsaw, IN). Repeated run-in wear was observed when the implants were exchanged between wear stations, suggesting that implants should be subjected to the same wear station throughout the duration of a wear test. The total polypeptide degradation for the implants measured 30.53 ± 3.96 per cent; the low-molecular-weight polypeptide concentration of the “used” lubricant for implants (0.131 ± 0.012 g/L) was 3.3 times greater than the mean polypeptide concentration of the fresh, “unused” lubricant (0.039 ± 0.004 g/L). This increase in low-molecular weight polypeptide concentration was suggested to be attributable to protein shear in the articulation of the implant, the circulation of the lubricant, and some proteolytic activity. Sodium azide was ineffective in maintaining a sterile environment for wear testing as a single, highly motile Gram-negative micro-organism was identified in the lubricant from wear tests.

Normal and frictional forces between surfaces bearing polyelectrolyte brushes

Normal and shear forces were measured as a function of surface separation, D, between hydrophobized mica surfaces bearing layers of a hydrophobic-polyelectrolytic diblock copolymer, poly(methyl methacrylate)- block-poly(sodium sulfonated glycidyl methacrylate) copolymer (PMMA- b-PSGMA). The copolymers were attached to each hydrophobized surface by their hydrophobic PMMA moieties with the nonadsorbing polyelectrolytic PSGMA tails extending into the aqueous medium to form a polyelectrolyte brush. Following overnight incubation in 10 (-4) w/v aqueous solution of the copolymer, the strong hydrophobic attraction between the hydrophobized mica surfaces across water was replaced by strongly repulsive normal forces between them. These were attributed to the osmotic repulsion arising from the confined counterions at long-range, together with steric repulsion between the compressed brush layers at shorter range. The corresponding shear forces on sliding the surfaces were extremely low and below our detection limit (+/-20-30 nN), even when compressed down to a volume fraction close to unity. On further compression, very weak shear forces (130 +/- 30 nN) were measured due to the increase in the effective viscous drag experienced by the compressed, sliding layers. At separations corresponding to pressures of a few atmospheres, the shearing motion led to abrupt removal of most of the chains out of the gap, and the surfaces jumped into adhesive contact. The extremely low frictional forces between the charged brushes (prior to their removal) is attributed to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments.