Article,
Dynamic Scaling in the Kinetics of Clustering
Physical Review Letters, 54 (13): 1396--1399 (April 1985)
DOI: 10.1103/physrevlett.54.1396
Abstract
In irreversible aggregation processes without a gelation transition the cluster size distribution approaches a scaling form, ck(t)∼s-2φ(k/s). Usking Smoluchowski's coagulation equation we determine the exponents in the mean cluster size s(t)∼tz (t→∞) and in the small- and large-x behavior of the scaling function φ(x). Depending on certain characteristics of the coagulation coefficients, φ(x)∼x-τ (x→0) or φ(x)∼exp(-xμ) (x→0) with μ some negative constant. In aggregation processes with gelation a similar scaling form is obtained as t approaches the gel point.
