Bond fluctuation model of polymers in random media

Conventional descriptions of polymers in random media often characterize the disorder by way of a spatially random potential. When averaged, the potential produces an effective attractive interaction between chain segments that can lead to chain collapse. As an alternative to this approach, we consider here a model in which the effects of disorder are manifested as a random alternation of the Kuhn length of the polymer between two average values. A path integral formulation of this model generates an effective Hamiltonian whose interaction term (representing the disorder in the medium) is quadratic and nonlocal in the spatial coordinates of the monomers. The average end-to-end distance of the chain is computed exactly as a function of the ratio of the two Kuhn lengths for different values of the frequency of alternation. For certain parameter values, chain contraction is found to occur to a state that is chain length dependent. In both the expanded and compact configurations, the scaling exponent that characterizes this dependence is found to be the same