The viscosity slope constant k′, i.e., \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\lim }\limits_{c \to 0} \frac{{d\left( {{{\eta _{sp} } \mathord{\left/ {\vphantom {{\eta _{sp} } c}} \right. \kern-\nulldelimiterspace} c}} \right)}}{{dc}}\frac{1}{{[\eta ]^2 }} $\end{document}, is shown to be of increasing significance in polymer science as a molecular‐weight‐independent criterion of solvent power and as a parameter sensitive to various changes in polymer structure, such as long‐chain branching. Ideally, it is a dimensionless parameter, independent of molecular size, which arises only from the mutual hydrodynamic interaction of polymer molecules and depends, therefore, on the intrinsic flexibility of the polymer chain and on the polymer density in the coiled molecule. In real systems, however, other interactions may contribute, sometimes very significantly, to k′. For such real systems, the general expression: is suggested. In ternary systems, polymer–polymer–solvent, ideal expressions for ηsp/c and k′ are developed, that for k′ being: It is proposed that deviations from ideal behavior so defined are due to nonhydrodynamic polymer‐polymer interactions and might be used to detect and measure the strength of such interactions. Some preliminary data for the system polystyrene–poly(methyl methacrylate)–m‐xylene are presented and discussed.
The .Sourness of Acids 2347 corresponding runs without catalysts total yields of 83 and 33% of the symmetrical isomers were obtained. These experiments show that these catalysts have no influence on either the total yield or the total yields of the symmetrical isomers. This is presumably due to the fact that because of the more elevated temperature required for this reaction, the stannic chloride and the iodine monochloride are volatilized and lost from the reaction mixtures despite the presence of a condenser.
By emulsion polymerization at 55°C., samples of styrene‐divinylbenzene copolymer were prepared, whose content of divinylbenzene varied from 0 to 0.150%. Measurements of intrinsic viscosity and of the slope constants β and k′ were made, at 25.0°C. in butanone and in benzene, of these samples and of fractions obtained from them by fractional precipitation. In both solvents the intrinsic viscosity of unfractionated polymer was at a maximum at a divinylbenzene content of about 0.005% and k′ was at a maximum at about 0.10%. Since the gel point was also in the neighborhood of 0.10%, it is concluded that a maximum in k′ is a better indication of the gel point than a maximum in [η]. As with linear polymers, [η] was smaller and k′ larger in the poorer solvent. For the higher fractions of a given lightly cross‐linked sample, k′ increased with increasing intrinsic viscosity, deviating progressively more from the value (0.40 in butanone) characteristic of the low fractions and of linear polystyrene. This progressive deviation appeared to begin at an intrisic viscosity which for different samples decreased with increasing proportion of divinylbenzene. These effects are accounted for qualitatively in termas of Baker's “microgel” concept and the effects of the two solvents on the dissolved molecules and dispersed microgel particles.
The variation with shear of the concentration dependence of the reduced viscosity was studied in the system polystyrene‐toluene at 20, 40, and 60°C. The slope constant k′ was determined at constant shear stress k′T and at constant shear rate k′D; k′T was found to increase, k′D to decrease, with increasing shear. Alternatively, the concentration dependence was expressed in terms of Peterlin's effective viscosity. For this system the effective viscosity at constant shear stress was independent of shear but the effective viscosity at constant shear rate decreased with shear. The decrease in k′D, and in effective viscosity at constant shear rate with shear are attributed to molecular entanglement and an explanation is proposed for the observed differences in behaviour at constant shear stress and constant shear rate. In appendices a new formula for the calculation of viscosity ratios from the relative flow times is derived, and a procedure is outlined to compute intrinsic viscosities and limiting slope constants that will be free from absorption effects.
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