Dynamics of polyelectrolyte solutions

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Abstract
We have derived a theory of dynamics of dilute and semidilute polyelectrolyte solutions by explicitly considering triple screening associated with electrostatic, excluded volume, and hydrodynamic interactions. The three screening lengths corresponding to these interactions are coupled among themselves differently at different polyelectrolyte (c) and salt (cs) concentrations. We have derived expressions for the self-translational diffusion coefficient D, electrophoretic mobility μ, coupled diffusion coefficient Df, and the viscosity η of the solution by accounting for the coupling between electrostatics and hydrodynamics. In infinitely dilute solutions, we show that Zimm dynamics is applicable and D∼1/Rg, μ∼M0, and η−η0∼cRg3/M for all values of cs, where Rg and M, respectively, are the radius of gyration and molecular weight of the polyelectrolyte and η0 is the solvent viscosity. Df is derived to be M0 at low cs and to approach D at higher cs. As the polyelectrolyte concentration is increased to semidilute conditions, excluded volume and hydrodynamic interactions get progressively screened. In the Rouse regime, where hydrodynamic interaction is screened and entanglement effects are weak, we have derived expressions for the various transport coefficients. In this regime, at low cs, D∼c0M−1, Df∼c0M0, μ∼c0M0, and η−η0∼cM; at high cs, D∼c−1/2M−1, Df∼c/(c+2cs), μ∼c−1/2M0, and η−η0∼c5/4M. The crossover formulas between these asymptotic laws with numerical prefactors are derived. We have demonstrated that the Rouse law applicable to semidilute unentangled polyelectrolyte solutions at low cs is the empirical Fuoss law. The slow diffusion coefficient observed in light scattering studies of polyelectrolyte solutions is attributed to the emergence of an effective attractive interaction between similarly charged segments of topologically correlated objects such as polyelectrolytes at sufficiently high c and low cs. The consequences of entanglements at very high polyelectrolyte concentrations are briefly mentioned. The theoretical formulas derived here are in qualitative agreement with all known phenomenological results of polyelectrolyte dynamics, and some fresh predictions are made.