Viscosity polyelectrolyte dynamics

Although the theory of polyelectrolyte dynamics reviewed here provides approximate crossover formulas for the experimentally measured diffusion coefficients, electrophoretic mobility, and viscosity, the validity of the formulas remains to be established. In spite of the success of one unifying conceptual framework to provide valid asymptotic results, in qualitative agreement with experimental facts, it is desirable to establish quantitative validity. This requires (a) gathering of experimental data on well-characterized polyelectrolyte solutions and (b) obtaining the relationships between the various transport coefficients. Such data are not currently available, and experiments of this type are out of fashion. In addition to these experimental challenges, there are many theoretical issues that need further elaboration. A few of these are the following ... 

Table 2 Dynamic viscosity of different polyelectrolyte sodium salts in aqueous dispersions...

Tj max increases [19] linearly with M. An increase in the salt concentration moves Umax toward higher c so that c ax c, and it drastically lowers the value of Analogous to the viscosity behavior, the dynamic storage and loss moduli also show [22] a peak with c. The unusual behavior at low c where the reduced viscosity increases with dilution in the polyelectrolyte concentration range between and c, along with the occurrence of a peak in the reduced viscosity versus c, has remained as one of the most perplexing properties of polyelectrolytes over many decades. 

Dilute polyelectrolyte solutions, such as solutions of tobacco mosaic virus (TMV) in water and other solvents, are known to exhibit interesting dynamic properties, such as a plateau in viscosity against concentration curve at very low concentration [196]. It also shows a shear thinning at a shear strain rate which is inverse of the relaxation time obtained from the Cole-Cole plot of frequency dependence of the shear modulus, G(co). 

Polyelectrolyte behavior is exhibited by solutions of SPS in DMF, Fig. 12. At low polymer concentrations, the viscosity Increases as a result of repulsion between the unshielded anions, which Increases the hydrodynamic volume of the polymer. The structure of SPS in DMF solutions as determined by static and dynamic light scattering is also discussed in the chapter by Hara and Wu. 

Some of the relevant questions primarily motivated by scientific interest are the following. How is the size of a polyelectrolyte affected by molecular weight, intrinsic stiffness, solvent quality, or ionic strength Which observables are well characterized by coarse-grained quantities such as a linear charge density, and which depend on chemical details How are dynamic quantities like viscosity or electrophoretic mobility related to static properties of poly electrolytes ... 

All of the observations made for random ionomer nonaqueous (polar) solutions parallel those for polyelectrolyte aqueous solutions the difference is only quantity, not the quality. These include upturn in a viscosity curve, negative angular dependence at low concentration and positive dependence at higher concentration in Zimm plots, appearance of two modes in dynamic scattering, and a drop in conductance. 

Fujita and coworkers [79] smdied fluorescently labeled polyoxyethylene chains and found a good correlation between the concentration dependence of the friction coefficient evaluated from the anisotropy measurements and from the macroscopic viscosity. Fujita developed the fi ee-volume theory which describes reasonably well the concentration dependence of in the whole concentration region, [80] but it does not enable prediction of the parameters at a molecular level. Hyde et al. [81] used the Fujita theory for fairly successful interpretation of the experimental data. An interesting paper has been published by Viovy and Moimerie [82]. The authors studied concentrated solutions of anthracene-labeled polystyrene in toluene. They found good correlation of the local dynamics with the viscosity in the range of high concentrations and made one very important observation the local dynamics are unaffected by the overlap of the polymer chains that occurs at concentrations higher than c (concentration of the first overlap—see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions ). 

The best approach is, therefore, to compare the results of simulations made at different length scales with real measurements to determine the validity of the approach since the causes for changes in e.g. viscosity can be caused by changes in local interaction energy or with the PE structure or both [103]. In this section, the results of computer simulations with relation to the PE structure, complex formation and dilution behavior are summarized. The focus lies on molecular dynamics simulations since Monte Carlo simulations [102, 113] are discussed in detail in chapter Thermodynamic and Rheological Properties of Polyelectrolyte Systems . 

---