SCALING THEORY FOR MULTIPOLYMER COAGULATION

We study the scaling behavior of the n-tuple coalescence process, described by the generalized Smoluchovski equations (GSE). It is found that, for a specific class of homogeneous reaction kernels, the cluster size distribution approaches a scaling form, ck(t)s-2(k/s), with the mean cluster size behaving as s(t)tz as t. The dynamic exponent z and the small- and large-x behaviors of the scaling function (x) are derived from the GSE. For large x, it is found that (x)Ax-e-ax (x) [=+(n-1)], which is valid for all gelling and nongelling coagulation kernels with <1. While for small x, (x)x- or (x)exp(-x) with <0, depending on certain characteristics of the coagulation kernels. © 1994 The American Physical Society.