Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours

• Published in: Chinese physics B Vol. 19; no. 12; pp. 559 - 570
• Main Author: 李晓东 林振权 宋美霞 柯见洪
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2010
• Subjects: 催化聚合; 动力学模型; 动力学行为; 广义标度律; 碎裂过程; 聚集行为
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/12/128201

We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.