Catalysisdriven aggregate growth
Abstract
We propose twospecies catalysisdriven aggregation models in which coagulation of one species occurs only in the presence of another species (the catalyst). By means of generalized Smoluchovski rate equations, we study the kinetics of the system with the rate kernel K_{A}(i; j; l) vprop l^{ugr}, at which two A clusters of size i and j bond together under the catalytic action of a B cluster of size l. The results show that the cluster mass distribution of species A obeys a conventional scaling law in the ugr geq 0 case while it may satisfy the modified scaling form in other cases. Moreover, it is found that the scaling exponents are nonuniversal and dependent on the value of index ugr in most cases. On the other hand, we also investigate the scaling behaviour of the mutually catalysisdriven aggregate growth. For the system with the rate kernel K_A(i;j;l) \propto l^{\upsilon_1} and K_B(i;j;l) \propto l^{\upsilon_2} , its kinetics depends crucially on the values of the indices ugr_{1} and ugr_{2}. Either species scales according to the conventional or modified form in most cases; while the system may undergo a gelation transition in some special cases.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2004
 DOI:
 10.1088/03054470/37/13/004
 Bibcode:
 2004JPhA...37.3967K