A trapped polymer chain in random porous media

Abstract

Dynamic and static properties of a polymer chain without self-excluded volume, which performs Brownian motion between randomly distributed impenetrable fixed obstacles, have been investigated by Monte Carlo simulations and analyzed by scaling considerations. The mean square radius of gyration 〈S2〉, the center-of-mass diffusion coefficient D, and the longest relaxation time τ are functions of x=(1−p)(N)1/2 for all chain lengths N and porosities p above the percolation threshold. Simulations have been performed for x≲10. With increasing x the radius of gyration exhibits a crossover from Gaussian statistics 〈S2〉∼N to a collapsed state where 〈S2〉 is independent of N. This phenomenon is attributed to the effects of both the lack of self-excluded volume and the presence of an effective self-attractive potential arising from random repulsion between polymer and the solid particles of the medium. The strong dependency upon chain length of D∼N−2.9±0.3 and τ∼N4.0±0.4 is conjectured to result from randomly distributed bottlenecks and traps in the porous solid. If these local constraints are released by arranging the obstacles in a periodic array, familiar reptation dynamics and 〈S2〉∼N are observed.