Dynamics of a polymer chain confined in a membrane

TL;DR

This paper develops a comprehensive Brownian dynamics model for Gaussian polymer chains in membranes, analyzing how confinement and hydrodynamics influence their diffusion, relaxation, and structure, revealing Zimm-like and Rouse-like behaviors depending on geometry.

Contribution

It introduces a full hydrodynamics theory for polymers in membranes, deriving mobility tensors and analyzing dynamics in different geometries with new diffusion expressions.

Findings

Diffusion coefficient derived for free membrane geometry.

Large polymer size exhibits Zimm-like behavior in free membranes.

Relaxation times are Rouse-like in sandwiched membrane geometry.

Abstract

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded volume interactions on the polymer relaxation time.