Tuning structure and mobility of solvation shells surrounding tracer additives

Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings

We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.

Impact of solvent granularity and layering on tracer hydrodynamics in confinement

Classic hydrodynamic arguments establish that when a spherical tracer particle is suspended between parallel walls, tracer-wall coupling mediated by the solvent will cause the tracer to exhibit position-dependent diffusivity. We investigate how the diffusivity profiles of confined tracers are impacted by the diameter size-ratio of the tracer to solvent: starting from the classic limit of infinite size-ratio (i.e., continuum solvent), we consider size-ratios of four or less to examine how hydrodynamic predictions are disrupted for systems where the tracer and solvent are of similar scale. We use computer simulations and techniques based on the Fokker-Planck formalism to calculate the diffusivity profiles of hard-sphere tracer particles in hard-sphere solvents, focusing on the dynamics perpendicular to the walls. Given wall separations of several tracer diameters, we first consider confinement between hard walls, where anisotropic structuring at the solvent lengthscale generates inhomogeneity in the tracer free-energy landscape and undermines hydrodynamic predictions locally. We then introduce confining planes that we term transparent walls, which restrict tracer and solvent center-accessibilities while completely eliminating static anisotropy, and reveal position-dependent signatures in tracer diffusivity solely attributable to confinement. With or without suppressing static heterogeneity, we find that tracer diffusivity increasingly deviates on a local basis from hydrodynamic predictions at smaller size-ratios. However, hydrodynamic theory still approximately captures spatially-averaged dynamics across the pores even for very small tracer-solvent size-ratios over a wide range of solvent densities and wall separations.