Concentration dependence, mode coupling viscosity

A simple theory of the concentration dependence of viscosity has recently been developed by using the mode coupling theory expression of viscosity [197]. The slow variables chosen are the center of mass density and the charge density. The final expressions have essentially the same form as discussed in Section X the structure factors now involve the intermolecular correlations among the polyelectrolyte rods. Numerical calculation shows that the theory can explain the plateau in the concentration dependence of the viscosity, if one takes into account the anisotropy in the motion of the rod-like polymers. The problem, however, is far from complete. We are also not aware of any study of the frequency-dependent properties. Work on this problem is under progress [198]. 

The concentration dependence of the viscosity of polyelectrolyte solutions has been discussed by several authors [Cohen et al., 1988 Cohen and Priel, 1990 Borsali et al., 1992, 1994 Antonietti et al., 1997]. Several groups [Borsali et al 1992, 1994 Antonietti et al., 1997] have used the mode-mode coupling approximation of Hess and Klein [1983]. In the weakly charged polyelectrolyte limit, the latter formulation leads to an expression for the time-dependent viscosity of the form [Borsali et al., 1992]... 

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

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