Polymers in a disordered environment

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Abstract
A polymer chain in equilibrium in a disordered environment is studied using a Flory theory and by mapping the problem onto random walks in an environment with traps. The asymptotic behaviour of the size of the polymer, R, as a function of the number of monomers, N, is obtained. If the disorder is weak in comparison with the self-repulsion of the chain, the self-avoiding random walk result is found. The random environment leads to effective attractive forces which, for sufficiently strong disorder, lead to the collapse of the chain. The properties of the collapsed chain depend upon the type of disorder and on the self-repulsion of the chain. If the self-repulsion increases sufficiently fast as the density increases then the collapsed chain has a finite density (N/Rd to constant as N to infinity ); otherwise several other interesting scaling forms are possible.
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