Modelling of the changes in the molar mass distribution function of a polymer caused by random scission of the polymer chains - an update

There are diverse models available for describing the change of molar mass distribution of nitrocellulose. These consider averaged values or even the full development of molar mass distribution. At increased temperatures the degradation described by reactions of first order dominates but at moderate ones re-polymerisation might play some role. In two kinetic approaches the combined mechanisms are considered: (I) chain scission by bond splitting between chain unit only and chain re-polymerisation; (II) chain splitting by decomposition of single chain elements and chain re-polymerisation. The change of the molar mass distributions caused by such reactions can also be described by sets of differential equations for discrete distribution. A formulation for continuous distribution functions was suggested earlier, but it was not yet verified to be a solution of the related integro-differential equation. A derivation of the solution is found by Laplace Transformation which provides the same results as obtained for discrete distributions and their generalizations by limiting processes.