Viscosity vs. polymer concentration

Figure 3. Reduced viscosity vs polymer concentration plots for a diblock polymer and homopolystyrene sulfonates.

Figure 31.3 Viscosity vs. polymer concentration of PES-NMP dopes and critical concentration (Chung et al., 1997).

Viscosity data are reported in Table I for a number of the polysaccharide derivatives in 5% LiCl/N,N-dimethylacetamide solutions. At low concentrations of polymers, an upward curvature in the DSp/c (reduced viscosity) vs c (concentration) plot was observed. Additionally, nonlinear increases in solvent viscosity were observed for increased lithium ion concentrations in the absence of polymer. Therefore, reduced viscosities at 0.25 dl/g are reported. 

An important dimensionless relationship between viscosity and concentration was found by Papkov et al. (1974) and reproduced in Fig. 16.30, where the variation of viscosity with polymer concentration for different molecular weights, expressed as intrinsic viscosities, is shown (left). The reduced viscosity t]/if vs. the reduced concentration c/c is shown on the right. The viscosity of the solution jumps down rapidly above the critical concentration as the nematic mesophase forms. The dimensionless relationship is remarkable. The relationship between the viscosity at the maximum and the intrinsic viscosity (see inset) appears to be r/max = 5.5b/]1 5, where rj is expressed in Ns/m2 and [77] in m3/kg. 

Fig. 13. Reduced viscosity w. polymer concentration and dynamic elastic modulus vs. polymer concentration relationships. Left reduced viscosity measured at a shear rate of 3.4 sec. ...

The peak in the plot of viscosity vs. surfactant concentration in general occurs in the vicinity of the CAC. Here, the composition of the mixed HM-polymer-surfactant micelles changes strongly with concentration to become dominated by the surfactant thus, the cross-linking effect is lost. 

Figure 4. Low-shear viscosity of PPTA solutions in 100% sulfuric acid vs polymer concentration. Note the conspicuous maximum in the viscosity prior to the onset of the formation of the anisotropic phase. Polymer inherent viscosity was 2.7 dl/g. Data from Jingsheng et al. (13).

Fig. 3. Solution viscosity vs concentration for ethylene oxide polymers (10). The molecular weight of the polymer is indicated on each curve. The dependence of the intrinsic viscosity [Tj] on molecular weight M for these polymers can be expressed by the Mark-Houwink relationship ...

Fig. 56. Dependence of Mwof the microgels on the polymer yield in the anionic polymerization of EDMA in toluene by n-BuLi [254] (see Figure 53 caption for the reaction conditions). Reduced viscosity vs concentration of microgels a) Composition (mol %) N,N -methyl-enebisacrylamide (55%), methacrylamide (33%), methacrylic acid (2%), methacrylamido acetaldehyd-dimethylacetal (10%),measured at 20 °C in water, b) Composition (mol %) 1,4-DVB (35%), propenic acid amide-2-methyl-N-(4-methyl-2-butyl-l,3-dioxolane prepared by emulsion copolymerization and measured in dimethylformamide.

Solvent viscosity vs, concentration plots for cellulose dissolved in TFA-CH2CI2 (70/30, v/v) do not exhibit a maximum (1I,S1) in contrast to the typicid behavior of polymer liquid crystal solutions. This same behavior is exhibited by other cellulose-solvent systems (52,fiQ). Conio et al. (59) si gest that due to the close proximity of the cholesteric mesophase to its solubility limit, it is only observed in a metastable condition. 

Fig. 3. Solution viscosity vs concentration for ethylene oxide polymers (10). The molecular weight of the polymer is indicated on each curve.

The authors observed that the formation of aggregates of polyazophenylene is very dependent on the flexibility of the polymer matrix. Poly(azophenylene-b-styrene) fails to exhibit both a maximum in their viscosity vs concentration functions and also an U V maximum at 580 nm. In contrast, the flexible diene matrix favours aggregation, and the resulting, strong intermolecular n-electron interactions lead to a considerably... 

According to Cardenas and O Driscoll [39], there exist two populations of macroradicals, of a polymerization degree greater and smaller than a certain critical size Pc. Pc is defined by a bend in the plot of log tj (system viscosity) vs. log DP (degree of polymerization of the dissolved polymer). With increasing concentration and chain length of the polymer, the importance of poly-... 

Still, there is the most interesting phenomenon that the cationic polymer poly(iV-hexadecyl-/V,/V-dimethy-N-vinylbenzyl ammonium chloride) 28 exhibits very low reduced viscosities but does not show polyelectrolyte behaviour in aqueous solution [103, 292] the plot of reduced viscosity vs concentration is strictly linear, and is insensitive to added salt (Fig. 20). Importantly, this head type vinyl polymer without main chain spacer is not water-soluble and thus not a true polysoap, but forms only metastable aqueous solutions (see Sect 2.2.4). Similar results were reported for alkylated poly(vinylimidazoles) such as 26 [347], It may be speculated that such solutions represent rigid molecular latexes rather than flexible polymeric micelles , and further studies on such systems would be most interesting. 

Figure 1. Experimental viscosity ratio vs. volume fraction polymer concentration effects. (Reproduced with permission from reference 19. Copyright 1992 Society of Petroleum Engineers.)...

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

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