Reduced viscosity vs. concentration

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.

Fig. 1. Representative plots of the reduced viscosity vs concentration for polyelectrolytes and non-polyelectrolytes...

Figure 11. Reduced viscosity vs. concentration relationships of PS and sulfonated polystyrene with different sodium sulfonate levels in tetrahydrofuran. (Reproduced with permission from reference 114. Copyright 1982 Wiley.)...

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. 

Viscosity measurements were also performed to complement the DLS data. The [r ] values for the zwitterionic samples are considerably higher than those for the amine-capped samples and the reduced viscosity vs concentration plots are not always... 

Figure 4, Reduced viscosity vs. concentration (A) polymer 4b in Hp (B) Na salt of polymer 4b in 5% NaCl aqueous solution (C) polymer 4a in HjO at 30° C...

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity vs. concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

Fig. 3.6. Reduced viscosity vs concentration profile from n-Cg HRAM 1.0,1.25 mol % hydrophobe compared with HP AM. Reprinted with permission from Ref. 9...

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. 

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

FIG. 9.14 Reduced viscosity (104 cmVg) plots of poly(N-butyl-4-vinylpyridinium) bromide vs. concentration (104 g/cm3) with various concentrations of added sodium chloride (mol/l). After Eisenberg and Pouyet, 1954. 

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. ...

FIGURE 9.5 Zero shear rate reduced viscosity (r sp0/c) vs. concentration of sodium pectate at various NaCl concentrations 1-7 0, 0.2, 0.4, 1.0, 2.5, 5.0 and 50 mM. From Pals and Hermans (1952), with permission of Elsevier Applied Science. 

Another characteristic type of viscosity behavior of polyelectrolytes is the effect of added simple salts on the viscosity [16]. The polyelectrolytes used were poly(styrene-co-4-vinylpyridine) (90/10) quatemized with /(-butyl-bromide, and the solvent was nitromethane. The added salt was tetra-butyl-ammonium bromide, which was easily dissolved in nitromethane. A small amount of added salt (10 M) produces a maximum in the viscosity curve (psp/c vs. c), and as more simple salts are added the reduced viscosity further reduces. When the added salt concentration is 0.1 N, the reduced viscosity is about the same as that of the parent polymer. This phenomenon is explained in terms of the screening effect by simple salts of electrostatic interactions among fixed ions [1,2]. 

Viscometric characterisation of the dispersions was carried out to further reveal differences in particle properties. Figure 2 shows the typical concentration vs reduced viscosity plots for the four varieties. The intercept represents the intrinsic viscosity that is related to the average size of the particle. 

The modified titration curves of the fractionated (MA-St)n aqueous NaCl at various ionic strengths from 0.009 to 0.27 resembled the potentiometric behaviors of the maleic acid copolymer with n-butyl vinyl ether and poly(methacrylic acid) in aqueous salts. There was no precipitation or turbidity in the deionized polymer solution, except in aqueous NaCl of 0.27 M. The conformational transition from the compact to extended coil form was seen in diagp ams of the intrinsic viscosity vs. qp and the reduced viscosity in the range 0.1 < aj < 0.4 was independent of polymer concentration. Both the potentiometric and viscometric titration data showed that the pH-induced conformational transition of (MA-St)n in aqueous NaCl is due to intramolecular interaction. The unperturbed molecular dimensions were calculated from the viscosity data and the acid compact form of this copolymer was found to be not so compact as the conformations of globular proteins. Dilatometry did also indicate existence of the transition,and the transition was observed in aqueous solutions of various salts chlorides, bromides, perchlorates and thiocyanates of Na" ", K" ", Rb" ", Cs" " and... 

Figure 9. Reduced viscosity Tired vs weight fraction for mixtures of i-l/a-1 PMMA fs-l/a-l PMMA in toluene at 25 C D = 0.01 s l. Total polymer concentration c = 1.0 g/dl.

Figure 37. Reduced viscosity-concentration piot for a typical associating polymer vs.a nonassociating polymer. C is the overlap concentration [97].

FIG. 16.18 Non-Newtonian viscosity ratio for solutions of narrow molecular weight distribution polystyrenes in n-butyl benzene, plotted vs. reduced shear rate q/q0, where qa, equal to the reciprocal of the characteristic time constant Tn, is chosen empirically for each solution. The data were obtained for molecular weights ranging from 160 to 2400 kg/mol and for concentrations ranging from 0.255 to 0.55 g/ml at temperatures from 30 to 60 °C.The full line is calculated with the aid of Eqs. (16.52)—(16.55). From Graessley, Hazleton and Lindeman (1967). Courtesy Society of Rheology. 

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