Brownian dynamics of polymer chains in membranes

Abstract

We present a theory of the Brownian dynamics of polymer chains embedded in two-dimensional hydrodynamic membranes. The excluded volume effect and both the intra- and interchain hydrodynamic interactions are included. We show that, in the dilute solution limit, the mean square displacement of a labeled monomer obeys the familiar diffusive law just as the center of mass of the whole chain. Furthermore, our calculations show that the interchain hydrodynamic interaction does not induce the screening of the hydrodynamic interaction to the leading order in concentration and that the mode dependence of the concentration- dependent relaxation times arises solely from the excluded volume effect. However, at very high concentrations, the square of the hydrodynamic screening length decays exponentially with concentration in membranes in contrast to an algebraic decay under isotropic conditions. In the screened regime, the effective viscosity of the membrane depends exponentially on the concentration demonstrating the absence of free-draining behavior at any concentration. These predicted dynamical properties of chains trapped in a membrane are in distinct contrast with the laws in three dimensions. © 1985 American Institute of Physics.