Polyelectrolyte solutions, mode coupling

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]... 

Borsali, R., Vilgis, T. A., and Benmonna, M., Viscosity of weakly-charged polyelectrolyte solutions the mode-mode coupling approach. Macromolecules, 25, 5313-5317 (1992). 

The coupling theory described above is pertinent to only the fast mode where Df decreases with an increase in c. Furthermore, the counterion coupling theory (Muthukumar 1997) predicts that Df is independent of Cp in salt-free dilute and semidilute polyelectrolyte solutions, consistent with Figure 7.5a. The superfast mode mentioned above is not yet measurable in experiments with polyelectrolytes. The slow mode appearing for Cp/Cs > 1 may be attributed to temporary clustering of polyelectrolyte chains and its full understanding is yet to be reached. 

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

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