Mathematical modeling of distributive properties of linear homo- and copolymer subjected to scission

Previous results concerning the modeling of scission of linear homopolymer chains are reviewed and new approaches are proposed, extending to length distributions for chains with different numbers of scission points and to copolymer chains. Analytical solutions for random and parabolic scission of a uniform population of polymer chains are compared and extended with solutions from a numerical scheme using Chebyshev polynomials (PREDICI®), giving rise to interesting conclusions concerning the relative lengths of the 3 different types of chains. The outcomes were applied to a reaction system with recombination of chain fragments, yielding an analytical solution of the 2-dimensional population balance problem in chain length and numbers of combination points. As regards copolymer scission an exact equation and a simple approximation for the fragment length distribution has been obtained based on all possible configurations of sequences of unbroken bonds between two types of monomer units. Scission of weaklinks could also be successfully treated using the simple approximation based on a copolymer composition weighted average scission probability.