Theta solvent molecular weight scaling

Fig. 5.9. Comparison of extinction angle curves of high molecular weight fractions of polystyrene and cellulose tricarbanilate, using linear scales and reduced shear rate For data on polystyrene Taps. No. 5 and solvents see Table 3.2. (n) Taps. No. 5 in methyl (4-bromo-phenyl carbinol) at 18° C (theta-temperature), (V) the same at 50° C, (o) Taps. No. 5 in monobromo benzene at 25° C, ( ) cellulose tricarbanilate M = 720,000 in benzophenone at 55° C (jy = 4.70 cps) and (a) at...

Both the scaling with co and the proportionality constant, V3, are confirmed by experimental data (see Fig. 3-13). The lines in Fig. 3-13 are proportional to G and G" — computed in the nondraining limit. The agreement with data for a polystyrene of high molecular weight (M = 860,000) in theta solvents is excellent. In addition to its agreement with experimental data, the predictions of Zimm theory are supported by molecular dynamics simulations (Pierleoni and Ryckaert 1991 DUnweg and Kremer 1991). 

Comparison of experiment versus a scaling analysis according to Eq. (1.100) indicates that hard-sphere scaling works reasonably well for theta and subtheta conditions [Simha, 1952 Simha and Chan, 1971 Utracki and Simha, 1981], but breaks down for good solvents. For these systems, a molecular weight-dependent scaling concentration can be defined of the form [Utracki and Simha, 1963 Simha and Somcynsky, 1965]... 

The grouping in the parenthesis of Equation 10.10 can be related to the characteristic ratio and is nearly independent of the polymer molecular weight the dependence of intrinsic viscosity on solvent quality is therefore proportional to the product aM. In theta solvents, a is unity (the intrinsic viscosity scales with and in good solvents a is proportional to (the intrinsic viscosity scales with M ). Comparison with Equation 10.1 suggests that the Mark-Houwink parameter should lie in the range 0.5 expansion factor if theta conditions for the polymer solution are known. 

The classical method to determine and a of a given polymer is as follows. First, prepare fractions of different molecular weights either by synthesis or by fractionation. Next, make dilute solutions of different concentrations for each fraction. Measure the viscosity of each solution, plot the reduced viscosity as a function of polymer concentration, and estimate [17] for each fraction. Plot [17] as a function of the molecular weight in a double logarithmic scale. This method has been extensively used to characterize polymer samples because the exponent a provides a measure of the chain rigidity. Values of a are listed in Table 3.2 for some typical shapes and conformations of the polymer. The value of a is around 0.7-0.8 for flexible chains in the good solvent and exceeds 1 for rigid chains. In the theta solvent, the flexible chain has a = 0.5. 

Fig. 3. Intrinsic viscosities of polystyrene fractions plotted against their molecular weights on logarithmic scales in accordance with Eq. (14). The upper set of data was determined in benzene, a good solvent for this polymer. The lower set of data was determined in cyclohexane at the Theta point. The slopes of the lines are a = 0.75 and 0.50, respectively. From the results of A1tares, Wyman and Allen.

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