Path-integral approach to a polymer chain in random media with long-range disorder correlations

In this paper we consider the model of a flexible polymer chain embedded in a quenched random medium with long-range disorder correlations. Using the Feynman path integral approach we show that for the case of long-range quadratic correlations, we obtain an analytical result. The result is (R-2) = 2b(2) root 3(pi)(3/2)xi(5)/2 rho N Delta b(2) tanh N/2 root 2 rho N Delta b(2)/3(pi)(3/2)xi(5), where (R-2) is the mean square end-to-end distance of the polymer chain, is the correlation length of disorder, A is an unknown parameter, b is the Kuhn step length, p is the density of random obstacles and N is the number of links. It is shown that for a polymer chain in a random media with long-range quadratic correlations, where p is not too high, the behavior of the polymer chain is like that of a free chain. This result agrees with the calculation using the replica method. However, in a medium where p is very high, the variation of the mean square end-to-end distance with disorder and its distance depending on p are found in our approach.