Localization of a polymeric manifold in quenched random media

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Abstract
We present a replica calculation and obtain analytically the size of a polymer chain with excluded volume interactions in quenched random media. We show that the size of the polymer is shrunk as the density of the impurities constituting the random medium is increased. We demonstrate that this is a general phenomenon. There are three regimes depending on the strength of the impurity density v. In the weak impurity density regime the polymer obeys the self-avoiding statistics with its gyration radius R depending on its typical length L according to R∼L(D+2)/(d+2), where D is the dimension of the polymer and d is the space dimension. In the intermediate regime the polymer is in the unperturbed state where R∼L(2−D)/2. In the third regime of localization occurring for sufficiently large v, R∼v−(2−D)/[4D−(2−D)d] in the absence of three-body interactions and R∼v−1/d LD/d in the presence of strong three-body effects. We examine the effect of long-range interactions of the type w‖r‖−α between the segments of the polymer separated by r on the localization and find that the polymer collapse is suppressed for realistic impurity densities [v<wR(d−α)/2].

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