Abstract
The “tree-like model” proposed by Flory-Stockmayer is regarded as a standard statistics of polymer distribution and gelation. By the use of probability generating functions (pgf), “cascade theory” greatly reduces the burden of combinatorial calculation of the tree-like model; it allows the systematic formulation of simultaneous equation of polymer distribution and enable us to calculate the required statistical parameters without explicit expressions of the distribution. The interpretations of rudimentary knowledge of pgf, formulations, derivations, and calculations of cascade theory are shown. Some examples of formulation are illustrated, which include simultaneous equation of vectorial pgf and formulae concerning the average degree of polymerization, gelation point, and distribution of the degree of polymerization in the addition polymerization of diepoxides with diamines. The theoretical progresses of cascade theory are briefly reviewed. Cascade theory has the simplicity of use and possibilities of growing to the practical tool for experimental study.
