Polyelectrolyte configuration in a disordered medium

We consider the configuration of a linear polyion embedded in a disordered medium with quenched fluctuations in the density of ionic sites that comprise the disorder. Expressions for the disorder-averaged interactions among the polyion beads are derived. The problem of polyion structure in a quenched disordered medium is thus reduced to that of a self-interacting polymer with adjusted pair potentials among its units. This class of problems is solvable by existing theories for polymer and polyelectrolyte configuration. We analyze the problem using the Feynman-Bogoliubov variational method with a Gaussian reference Hamiltonian and compare the results of this approach with those of Monte Carlo simulations performed using the same disorder-averaged pair potentials. At all conditions, the charged disorder leads to a contraction of the polymer, the effect being strongly dependent on the quenching temperature and the concomitant permittivity of the disorder which effectively determine the magnitude of the potential fluctuations in the system. At high disorder strength, the scaling characteristic of a self-avoiding chain is retained for shorter polyions. For sufficiently long polymers, however, the size of the polymer coil becomes almost independent of the degree of polymerization N. The transition between the two regimes takes place at the degree of polymerization at which the characteristic distance among the beads, measured in terms of the radius of gyration Rg, reaches the distance rmin corresponding to the minimum of the effective disorder-averaged pair potential among the beads.