Static properties of polymer chains in porous media

The static properties of a polymer molecule in a porous medium are investigated. The porous medium is simulated using a site percolation model in which the various sites are occupied (or unoccupied) randomly. A freely jointed chain is allowed to move in continuous space between the obstacles. Effects of excluded volume interactions between the links have also been studied. Using a generalized Flory theory, we have shown that, when the strength of disorder is large enough, the mean square end-to-end distance scales as N2ν, where N is the number of links in the chain, and ν takes on a value different from that for a free chain. Under these conditions, the polymer assumes a compact, globule-like conformation. For sufficiently large N, the Flory theory gives ν=1/(d+2) for freely jointed chains and ν=1/d for chains with excluded volume. Various correlation functions such as the distribution of the end-to-end distance and density profile of monomers with respect to the center of mass of the chain have been computed using Monte Carlo simulations. These results are interpreted using scaling concepts and an approximate variational theory based on replica methods. The limitations of the replica variational theory are assessed by an application to the directed polymer in a quenched random environment. We have also studied the shape fluctuations that the polymer molecule undergoes in the random environment. It is argued that these shape fluctuations are relevant to the transport mechanism of polymers in random media. The results obtained for the porous media are contrasted with those found for polymers in media where the obstacles are arranged in a regular manner.