Analysis of the solubility behaviour of irradiated polyethylene and other polymers

Abstract

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.