Viscosity in concentrated solutions

Graessley, W.W., Hazleton,R.L., Lindeman,L.R, The shear-rate dependence of viscosity in concentrated solutions of narrow-distribution polystyrene. Trans. Soc. Rheol. 11,267-285 (1967). 

Fox TG, Flory PJ (1948) Viscosity-molecular weight and viscosity-temperature relationships for polystyrene and polyisobutylene. J Am Chem Soc 70(7) 2384-2395 Freed KF, Edwards SF (1974) Polymer viscosity in concentrated solutions. J Chem Phys 61(9) 3626-3633... 

W. W. Graessley, R. L. Hazleton, and L. R. Lindeman, The Shear Rate Dependence of Viscosity in Concentrated Solutions of Narrow Distribution Polystyrene Trans. Soc. Rheol. 11, 267-285 (1967). 

At even higher molecular weights and concentrations, the viscosity in concentrated solutions and melts goes from a linear to a 3.4 power dependence on M [Eq. (20) Eigure 13.21]. 

Dynamical Viscosity of Polymer Solutions, J. Chem. Phvs 61. 1189-1202 (1974) K.F. Freed and S.F. Edwards, "Polymer Viscosity in Concentrated Solutions, J. Chem. Phvs.. 61. 3626-3633 (1974). 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

The instrument constant B can be determined by measuring the t in two fluids of known density. Air and water are used by most workers (22). In our laboratory we used seawater of known conductivity and pure water to calibrate our vibrating flow systems (53). The system gives accurate densities in dilute solutions, however, care must be taken when using the system in concentrated solutions or in solutions with large viscosities. The development of commercial flow densimeters has caused a rapid increase in the output of density measurements of solutions. Desnoyers, Jolicoeur and coworkers (54-69) have used this system to measure the densities of numerous electrolyte solutions. We have used the system to study the densities of electrolyte mixtures and natural waters (53,70-81). We routinely take our system to sea on oceanographic cruises (79) and find the system to perform very well on a rocking ship. 

If one follows the solution viscosity in concentrated sulfuric acid with increasing polymer concentration, then one observes first a rise, afterwards, however, an abrupt decrease (about 5 to 15%, depending on the type of polymers and the experimental conditions). This transition is identical with the transformation of an optical isotropic to an optical anisotropic liquid crystalline solution with nematic behavior. Such solutions in the state of rest are weakly clouded and become opalescent when they are stirred they show birefringence, i.e., they depolarize linear polarized light. The two phases, formed at the critical concentration, can be separated by centrifugation to an isotropic and an anisotropic phase. A high amount of anisotropic phase is desirable for the fiber properties. This can be obtained by variation of the molecular weight, the solvent, the temperature, and the polymer concentration. 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

Aqueous solutions of magnesium nitrate are appreciably denser and more viscous than water. Table II illustrates data (9) On the densities (in g/ml) of concentrated solutions at high temperatures. Figure 2 illustrates the viscosity variations in concentrated solutions (9). 

A further depolarizing factor is introduced in concentrated solutions of given viscosity ). The empirical relationship found by Sveshnikov and Feofilov is... 

Variations in the temperature coefficient of viscosity with solvent, which have also been presented as evidence of association in concentrated solutions (135,143), could be similarly related to differences in Ta among the solutions. When free draining behavior is a possibility, the relative viscosities in different solvents should be compared at the same value of Co f°r the mixtures (that is, at constant free volume rather than at constant temperature). In any case, it is clear that a very well planned series of experiments is necessary in order to test for the existence of additional specific effects such as association. These comments are not meant to suggest that association can not occur at moderate concentrations. Indeed, the existence of association in various forms of polymethyl methacrylate seems well established (144). The purpose is rather to advocate that less specific causes be eliminated before association is inferred from viscosity measurements alone. 

The reduced shear rate / retains a meaning over the entire range of concentration, becoming / = [r/] t]sMy/RT at infinite dilution and / =rj0My/cRT in concentrated solutions, where t]0 > t]s. The corresponding reduced viscosities are [t/]/M0 and Reduced plots remove most of the observed variation among systems (Figs. 8.4-8.7), and simplify the empirical examination of residual... 

Fig. 8.15. Viscosity vs shear rate in concentrated solutions of narrow distribution polystyrene The solvent in n-butyl benzene, the concentration is 0.300 gm/ml and the temperature is 30° C. The symbols are O for M = 860000 and for M = 411000 at low shear rates (155) and at high shear rates (346). The solid line for M= 860000 is the master curve for monodisperse systems from Graessley (227). The solid line for M=411000 is the master curve from Ree-Eyring (341). Either master curve fits data for both molecular weights...

Bueche,F. Viscosity of polymers in concentrated solutions. 3. Chem. Phys. 25, 599-600 (1956). 

Bueche,F. Viscosity of polymers in concentrated solution, J. Chem. Phys. 25, 599-600 (1956). See also Bueche,F. Viscosity of molten branched polymers and their concentrated solutions. J. Chem. Phys. 40,484-487 (1964). 

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