Abstract
The statistical methodology of population balance (PB) has been applied in order to predict the effects of cross-linking and chain-scissioning induced by ionizing radiation on the distribution of molecular weight between cross-links (MWBC) of a siloxane-based elastomer. Effective molecular weight distributions were extracted from the quantification of residual dipolar couplings via multiple quantum nuclear magnetic resonance (MQ-NMR) measurements and are taken to reflect actual MWBC distributions. The PB methodology is then applied to the unirradiated MWBC distribution and considers both chain-scissioning and the possibility of the formation of three types of cross-links: random recombination of scissioned-chain ends (end-linking), random covalent bonds of free radicals on scissioned-chain ends (Y-cross-linking), and the formation of random cross-links from free radicals on side groups (H-cross-linking). The qualitative agreement between the statistical modeling approach and the NMR data confirms that it is possible to predict trends for the evolution of the distribution of MWBC of polymers under irradiation. The approach described herein can also discern heterogeneities in radiation effects in different structural motifs in the polymer network.
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