Kinetic Behavior of Exchange-Driven Growth with Catalyzed-Birth Processes

• Published in: Communications in theoretical physics 2006-12, Vol.46 (6), p.1113-1120, Article 1113
• Main Author: WANG Hai-Feng LIN Zhen-Quan KONG Xiang-Mu
• Format: Article
• Language: English
• Subjects: 交换-驱动生长; 催化出生过程; 动力学行为; 聚合过程; 速率方程
• ISSN: 0253-6102
• DOI: 10.1088/0253-6102/46/6/029

Two catalyzed-birth models of n-species （n ≥ 2） aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Ak^m and Af^m of the same species with the rate kernels Km（k,j）= Kmkj （m = 1, 2,... ,n, n ≥ 2）, and aggregates of A^n species catalyze a monomer-birth of A^l species （l = 1, 2 , n - 1） with the catalysis rate kernel Jl（k,j） -Jlkj^v. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution ak^l（t） of A^l species depends crucially on the value of the catalysis rate parameter v： （i） ak^l（t） obeys the conventional scaling law in the case of v ≤ 0, （ii） ak^l（t） satisfies a modified scaling form in the case of v 〉 0. In the second model, the mechanism of monomer-birth of An-species catalyzed by A^l species is added on the basis of the first model, that is, the aggregates of A^l and A^n species catalyze each other to cause monomer-birth. The kinetic behaviors of A^l and A^n species are found to fall into two categories for the different v： （i） growth obeying conventional scaling form with v ≤ 0, （ii） gelling at finite time with v 〉 0.