Relationships between Parameters in the Mark

Houwink Equation II.

Abstract

Following the treatment of Kamide and Kawai (J. Chem. High Polymer, Japan, 20, 512 (1963)), theoretical relationships between the parameters K_m and a in the Mark-Houwink equation [r]=K_mM^a have been derived by the use of the treatments of Flory and Fox (FF), Kurata and Yamakawa (KY) and Fixman (Fi). Combination of the FF and Fi treatments leads to:
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and of the KY and Fi treatments to:
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where K is the Flory constant and M₀ a parameter of the molecular weight range for which the values of K_m and a apply. Experimental data for poly (methyl methacrylate), polystyrene, poly (vinyl acetate), atactic polypropylene and isotactic polypropylene are in good agreement with these relationships which also provide a means of evaluating K from values of K_m and a for good solvents.
The relationships are not, however, applicable to cellulose derivatives. For these, deviations of values predicted by theoretical treatments or combinations of them from those obtainedexperimentally follow the order: FF>KY-KSR>KY-Fi>FF-KSR>FF-Fi where KSR refers to the treatment of Kurata, Stockmayer and Roig.
It is shown that d log K_M/da><0 for a><a^* where a^* is the value of a at d log K_M/da=0 and depends on M₀ but not on K. Since no experimental data have shown d log K_M/da to be greater than zero, the treatments considered may only apply, at best, to cases where 0.5<a<a^*. Because of this, the Flory-Fox treatment, even if a<0.8, cannot interpret the experimentaldata in terms of only volume effects and, even if a<1.0, the Kurata-Stockmayer and Stookmayer-Fixman treatments may be inapplicable in certain cases.