Theory of the mechanical degradation of polymers in solution by stirring. Size distribution after random scission

Abstract

Cutting is performed at random on an arbitrary set of threads of sizes all greater than a predetermined length, a. The threads are cut at random until all become smaller than a, thus giving a distribution of sizes from zero to a. No thread will be cut further if its size is smaller than a. The size distribution is shown to be uniform. A more complicated case is considered in which pieces are cut at random until all are smaller than a but greater than m, such that m < 1 2 a . This case yields a final distribution which is uniform on [m, a-m], and decreases monotonically on [a-m, a]. The theory is applied to the scissions of polymers in solution by high speed stirring. Other possible applications are also discussed.