Mean-field theory of concentrated polyelectrolyte solutions: Statics and dynamics

Abstract

This paper discusses the static and dynamic properties for ‘‘reasonable’’ charged polyelectrolyte chains (f${\mathrm{\phi }}^{\mathrm{*}}$, where ${\mathrm{\phi }}^{\mathrm{*}}$ is the ‘‘overlap’’ concentration) with and without added salt on the basis of the Edwards-Hamiltonian formalism. In this formalism the hydrodynamical effects are neglected. Expressions for the free energy F, the osmotic pressure Π, the structure factors ${\mathit{S}}_{\mathit{i}\mathit{j}}$(q), the charge fluctuations ${\mathit{S}}_{\mathrm{CF}}$(q), the screened potentials ${\mathit{U}}_{\mathrm{scr}}$(q) for polyions and counterions, and the radius of gyration ${\mathit{R}}_{\mathit{g}}$ are derived. As for the dynamics of such systems, two relaxation modes characterize the intermediate scattering function S(q,t). The first mode represents the standard diffusion and is identified as being the cooperative diffusion frequency. It increases with the polyelectrolyte concentration φ and with the degree of ionization f [${\mathit{D}}_{\mathit{c}}$(f)>${\mathit{D}}_{\mathit{c}}$(f=0)] and is independent of the Debye screening parameter ${\mathrm{\kappa }}^2$. The second process presents a nonzero frequency at ‖q‖=0 and is called the ‘‘plasmon’’ mode. The variation with polyelectrolyte concentration φ, degree of ionization f, counterion concentration ${\mathrm{\phi }}_{\mathit{i}}$, and wave vector q is presented in a systematic way for all measurable quantities. We also present some remarks regarding the statics and dynamics of neutral and polyelectrolyte mixtures in solution.