Polyelectrolyte solution, viscosity

It was found earlier by experiment and theory that the viscosity intrinsic of polyelectrolyte solutions is nearly linear with the reciprocal square root of the ionic strength over a certain range, such as... 

Theoretical treatment of the viscosity-concentration relationship for polyelectrolyte solutions would involve both the cumbersome statistics of highly elongated chains beyond the range of usefulness of the Gaussian approximation and the even more difficult problem of their electrostatic interactions when highly charged. There appears to be little hope for a satisfactory solution of this problem from theory. Fuoss has shown, however, that experimental data may be handled satisfactorily through the use of the empirical relation ... 

The reduced viscosity of a polyelectrolyte solution at the monomer concentration c is defined by... 

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 ... 

The crossover between the Kirkwood-Riseman-Zimm behavior and the Rouse behavior requires a better understanding, in terms of the contributing factors for the occurrence of a maximum in the plot of reduced viscosity against polyelectrolyte concentration at low salt concentrations. A firm understanding of the structure factor of polyelectrolyte solutions at concentrations comparable to the overlap concentration is necessary. 

In the mucosal environment, effects of salt, pH, temperature, and lipids need to be taken into consideration for possible effects on viscosity and solubility. A pH range of 4-7 and a relatively constant temperature of 37°C can generally be expected. Observed solution properties as a function of salt and polymer concentration can be referred to as saline compatibility. Polyelectrolyte solution behavior [27] is generally dominated by ionic interactions, such as with other materials of like charge (repulsive), opposite charge (attractive), solvent ionic character (dielectric), and dissolved ions (i.e., salt). In general, at a constant polymer concentration, an increase in the salt concentration decreases the viscosity, due to decreasing the hydrodynamic volume of the polymer at a critical salt concentration precipitation may occur. 

Polyelectrolyte complexation in aqueous solution between PEI and PMAA has been studied through viscometry, conductometry, potentiometry, and IR spectroscopy [90]. Upon addition of increasing concentrations of PMAA to an aqueous PEI solution, viscosity dropped suddenly around a 1 to 4 ratio of PMAA to PEI because of the complexation and subsequent coiling of the complexed chains. Reduced viscosity then rose past this ratio indicating that the stoichiometry of the complex occurs in a 1 4 (PMAA groups PEI groups) formation. Conductance and titration experiments agreed with this theory. The... 

The viscosity of xanthan solutions is also distinct from that of flexible polyelectrolyte solutions which generally shows a strong Cs dependence [141]. In this connection, we refer to Sho et al. [142] and Liu et al. [143], who measured the intrinsic viscosity and radius of gyration of Na salt xanthan at infinite dilution which were quite insensitive to Cs ( > 0.005 mol/1). Their finding can be attributed to the xanthan double helix which is so stiff that its conformation is hardly perturbed by the intramolecular electrostatic interactions. In fact, it has been shown that the electrostatic persistence length contributes only 10% to the total persistence length even at as low a Cs as 0.005 mol/1 [142]. Therefore, the difference in viscosity behavior between xanthan and flexible polyelectrolyte... 

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). 

The viscosity of a linear polyelectrolyte solution depends on the conformation of the molecules, which in turn is affected by intramolecular electrostatic interactions between charged segments located along the polymer backbone, but the interactions in systems of charged polyelectrolytes are still far from being understood. The study on the solution property of cyclic polyelectrolyte is of interest, since the chain expansion of a cyclic... 

In general, the viscosity r] of an aqueous polyelectrolyte solution is a complicated function of... 

Fixation of hydrophilic units as side-groups of a hydrophobic macromolecular chain leads to water-soluble polysoaps [205], exhibiting a similar diversity of self-organized structures like the monomeric analogues. A detailed review can be found in [206]. In contrast to polyelectrolytes and ionomers described above, the association of the amphiphilic groups of polysoaps occurs preferentially intramolecularly. As a consequence the solution viscosity remains low, even for highly concentrated solutions [207] and no critical micelle concentration (CMC) can be found up to extreme dilutions [208,209]. 

Tam, K. C. and Tiu, C. 1993. Improved correlation for shear-dependent viscosity of polyelectrolyte solutions. J. Non-Newtonian Fluid Mech. 46 275-288. 

Similar solution behavior was reported(9-11) for sulfonate ionomers. Rochas eit al. (9) observed a polyelectrolyte effect for acrylonitrile-methallylsulfonate copolymers in DMF. Lundberg and Phillips(10) studied the effect of solvents, with dielectric constants ranging from c 2.2 to e 46.7, on the dilute solution viscosity of the sulfonic acid and Na-salt derivatives of sul-fonated polystyrene (SPS). For highly polar solvents such as DMF and dlmethylsulfoxide (DMSO, e 46.7) they observed a polyelectrolyte effect, but for relatively non-polar solvents such as THF and dioxane (c = 2.2) no polyelectrolyte effect was observed. Like Schade and Gartner, these authors concluded that polar solvents favor ionization of the metal sulfonate group while non-polar solvents favor ion-pair interactions. 

Because of strong interactions in polyelectrolyte solutions without added salt, the use of the well-known Stokes-Einstein relation for free particle diffusion D = kBT/6Trr)Rh, where 17 is viscosity and Rh is hydrodynamic radius, is rather limited. Even at very low concentrations, where intermo-lecular interactions can be neglected due to large intermolecular separations, the friction factor contains in addition to the Stokes-Einstein contribution /SE = 67717/4 also a contribution from electrolyte dissipation, so that the total friction factor / = /SE + /eidiS, where the electrolyte dissipation term reflects the retardation of the polyion motion due to the instantaneous distortion of the surrounding ion atmosphere as the polyion moves through the solvent [27,28],... 

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