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The equation for the sol fraction ( s ) of a cross-linked polymer network becomes readily tractable when applied to special cases of the generalized distribution function n( u ) = C ( u/u 1 ) λ -1 exp ( — λu/u 1 ). For values of λ = ∞, 1 and 0 respectively, this function yields the uniform distribution, the exponential distribution and a hypothetical pseudo-random distribution. Assuming that cross-linking and fracture occur at random and in proportion to the radiation dose, simple expressions are derived relating sol fraction to radiation dose ( r ) for each of the three distributions. The most useful of these is the relation involving the fracture density per unit dose ( p 0 ) and the density of cross-linked units per unit dose ( q 0 ). s +√ s = p 0 / q 0 + 1/ q 0 u 1 r . This holds strictly for exponential distributions, whether or not main-chain fracture occurs simultaneously with cross-linking, and also holds at high doses for the other distributions considered, providing that cross-linking is accompanied by fracture. This treatment is applied to experimental results on low-density and high-density polyethylenes, polyvinyl acetates, polyvinyl chloride, polypropylene and polyalkyl acrylates. The relevant radiation parameters p 0 , q 0 and the corresponding G values are deduced. It is found, in the case of polyethylene, that q 0 is, within experimental error independent of the molecular weight, degree of branching or crystallinity, but is affected by the presence of air. Similar values of q 0 are also observed for polyvinyl acetate and polyvinyl chloride.

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When subjected to the effect of ionizing radiation, such as atomic pile radiation or gamma radiation, cellulose is rapidly degraded into a powdery material. A theoretical treatment shows that if the effect of radiation is to cause fracture at random in the main chain, the relation between intrinsic viscosity [η] and radiation dose R should be of the form: where R0 is a “virtual” radiation dose needed to produce the initial number‐average molecular weight from a chain of infinite molecular weight. The published data of Saeman, Millett, and Lawton have been used to verify this formula, which leads to a relationship between [η] in cupriethylenediamine and viscosity‐average molecular weight Mv: with α = 0.71. The constant K has been evaluated by comparison with data given by Gralen, but is less accurately known. It is deduced that one million roentgen results in fracture of 0.16% of the monomer units in the main chain. The decomposition of carbohydrates under radiation, which occurs at the same time as main chain fracture, can be explained on the assumption that approximately one monomer unit is decomposed per main chain fracture. The study of intrinsic viscosity of irradiated polymers appears to offer an accurate means of evaluating α in the usual formula for intrinsic viscosity [η] = KMα.

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