Cooperative diffusion in weakly charged polyelectrolyte solutions

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Abstract
We study the dynamics of concentration fluctuations of a weakly charged polyelectrolyte solution in the limit where they are controlled by hydrodynamic interactions. We find three relaxation modes: a plasmon mode corresponding to the fast relaxation of charge fluctuations; a diffusive mode involving mainly the motion of the small ions (salt and counterions) to restore the ‘‘Donnan equilibrium,’’ and a slower cooperative diffusion mode corresponding to the breathing motion of the polyelectrolyte chains and ions. In the limit where the electrostatic effects are dominant, at zero wave vector, the cooperative diffusion constant has a nonmonotonic variation with the monomer concentration. Contrary to what happens in neutral polymer solutions, in the limit of low ionic strength, it decreases with the monomer concentration in agreement with recent experimental observations of Schosseler et al. on gels.The cooperative diffusion constant as a function of wave vector shows a minimum for a wave vector corresponding approximately to the peak in the structure factor.

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