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/u1)λ-1 exp ( — λu/u1). 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 (p0) and the density of cross-linked units per unit dose (q0). s+√s = p0/q0 + 1/q0u1r. 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 p0, q0 and the corresponding G values are deduced. It is found, in the case of polyethylene, that q0 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 q0 are also observed for polyvinyl acetate and polyvinyl chloride.