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

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Enthalpic Interactions and Solution Behaviors of Solvent-Free Polymer Brushes

We performed molecular dynamics simulations to characterize the role of enthalpic interaction in impacting the static and dynamic properties of solvent-free polymer brushes. The intrinsic enthalpic interaction in the simulation was introduced using different attraction strengths between distinct species. Two model systems were considered: one consisting of binary brushes of two different polymer types and the other containing a mixture of homopolymer brushes and free molecules. In the first system, we observed that, when two originally incompatible polymers were grafted to opposing surfaces, the miscibility between them was significantly enhanced. A less favorable intrinsic enthalpic interaction in the brushes resulted in a more stretched chain configuration, a lower degree of inter-brush penetration, and faster segmental relaxation. In the second system, we characterized the solvent capacity of the homopolymer brushes from variations in the energy components of the system as a function of the number of free molecules. We determined that molecular absorption was driven by the release of the entropic frustration for the grafted chains in conjunction with the chemical affinity between the solutes and polymers. The solute distribution function within the inter-wall space showed that solute-polymer mixing in the middle of the gap occurred preferentially when the enthalpic interaction was more favorable. When this was not the case, absorption was predominantly localized near the grafting surface. From the mean square displacement of the solute, we found that the brush profiles restrained the molecular diffusion perpendicular to the grafting wall; the weaker the attraction from the brush, the higher the solute mobility.

Structural and Dynamical Coupling in Solvent-Free Polymer Brushes Elucidated by Molecular Dynamics Simulations

We investigate the chain configuration and segmental dynamics in interacting solvent-free polymer brushes using molecular dynamics simulations. The brush systems are designed to mimic the interstitial space between a pair of neighboring polymer-grafted nanoparticles in solvent-free nanoparticle-organic hybrid materials. Each brush consists of uniformly grafted chains formed by a given number of monomer beads. In monodisperse systems, two opposing brushes have the same chain length and grafting density. In mixed conditions, we consider binary systems with two surfaces being separately grafted with polymers of distinct chain lengths at different grafting densities as well as bidisperse systems with polymers of two different lengths being tethered to the surfaces at a fixed grafting density. We demonstrate that the brush configuration and interpenetration are both governed by the need that monomer beads have to uniformly fill the space. For systems with longer chain lengths and/or higher grafting densities, the larger interwall separation yields more stretched brush conformations and reduced extents of interbrush mixing. As a result, the polymer configurational entropy is generally decreased and the segment-to-segment relaxation dynamics is slowed down accordingly. The grafting of chains at a high density not only makes the relaxation dynamics deviate from the standard Rouse prediction but also leads to distinct relaxation times for the free and tethered segments. The more slowly relaxing tethered segments play a more important role in determining the overall end-to-end fluctuations. Moreover, the two distinct relaxation processes are consistent with the two-stage decay in the Rouse mode fluctuation autocorrelation function. In the presence of brush bidispersity, the collaboration between polymers of different lengths is evidently observed in the brush profiles. The variations of the chain configuration for the two polymers are complementary, and the associated relaxation dynamics of the two species are significantly coupled.

Polymer Brush Friction in Cylindrical Geometries

Polymer brushes are outstanding lubricants that can strongly reduce wear and friction between surfaces in sliding motion. In recent decades, many researchers have put great effort in obtaining a clear understanding of the origin of the lubricating performance of these brushes. In particular, molecular dynamics simulations have been a key technique in this scientific journey. They have given us a microscopic interpretation of the tribo-mechanical response of brushes and have led to the prediction of their shear-thinning behavior, which has been shown to agree with experimental observations. However, most studies so far have focused on parallel plate geometries, while the brush-covered surfaces might be highly curved in many applications. Here, we present molecular dynamics simulations that are set up to study the friction for brushes grafted on the exterior of cylinders that are moving inside larger cylinders that bear brushes on their interior. Our simulations show that the density distributions for brushes on the interior or exterior of these cylinders are qualitatively different from the density profiles of brushes on flat surfaces. In agreement with theoretical predictions, we find that brushes on the exterior of cylinders display a more gradual decay, while brushes on the interior of cylinders becomes denser compared to flat substrates. When motion is imposed, the density profiles for cylinder-grafted brushes adapt qualitatively differently to the shear motion than observed for the parallel plate geometry: the zone where brushes overlap moves away from its equilibrium position. Surprisingly, and despite all these differences, we observe that the effective viscosity is independent of the radius of the brush-grafted cylinders. The reason for this is that the viscosity is determined by the overlap between the brushes, which turns out to be insensitive to the exact density profiles. Our results provide a microscopic interpretation of the friction mechanism for polymer brushes in cylindrical geometries and will aid the design of effective lubricants for these systems.