Theory of Gel—Dose Curves for Polymers Undergoing Simultaneous Crosslinking and Scission

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Abstract
Computer calculations of the fraction of gel as a function of radiation dose have enabled tables to be constructed of the relation between gel fraction and number of crosslinks for various initial weight to number average molecular weight ratios and for a number of different ratios of chain scissions to crosslinks. The theory is based on the Wesslau molecular-weight distribution function and the results are in much better agreement in the case of many polymers than are the theoretical calculations of Inokuti based on a normalized Poisson distribution equation or the theory of Charlesby—Pinner based on a random molecular-weight distribution. It is shown that the initial slope of the (s+s1/2)-vs-(rg/r) curve is more helpful in many cases in determining the ratio of scissions to crosslinks than is the intercept at infinite dose. Indications of the breadth of the initial molecular weight distribution can also be obtained from the initial slope.