Kinetics of catalytically activated aggregation–fragmentation process

doi:10.1088/1674-1056/20/8/086801

中国物理B ›› 2011, Vol. 20 ›› Issue (8): 86801-086801.doi: 10.1088/1674-1056/20/8/086801

Kinetics of catalytically activated aggregation–fragmentation process

林振权¹, 高艳², 王海锋², 薛新英²

(1)Department of Physics, Wenzhou University, Wenzhou 325027, China; (2)Key Laboratory of Ecophysics and Department of Physics, College of Science, Shihezi University, Shihezi 832003, China

收稿日期:2010-11-02 修回日期:2011-02-20 出版日期:2011-08-15 发布日期:2011-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10275048 and 10875086) and by the Science Foundation of Shihezi University (Grant No. RCZX200745).

Kinetics of catalytically activated aggregation–fragmentation process

Gao Yan(高艳)^a), Wang Hai-Feng(王海锋)^a)†, Lin Zhen-Quan(林振权)^b), and Xue Xin-Ying(薛新英)^a)

^a Key Laboratory of Ecophysics and Department of Physics, College of Science, Shihezi University, Shihezi 832003, China; ^b Department of Physics, Wenzhou University, Wenzhou 325027, China

Received:2010-11-02 Revised:2011-02-20 Online:2011-08-15 Published:2011-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10275048 and 10875086) and by the Science Foundation of Shihezi University (Grant No. RCZX200745).

摘要/Abstract

摘要： We propose a catalytically activated aggregation—fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of species A will fragment into two smaller clusters under the catalysis of C clusters. By means of mean-field rate equations, we derive the asymptotic solutions of the cluster-mass distributions a_k(t) of species A, which is found to depend strongly on the competition between the catalyzed aggregation process and the catalyzed fragmentation process. When the catalyzed aggregation process dominates the system, the cluster-mass distribution a_k(t) satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of a_k(t) breaks down completely and the monodisperse initial condition of species A would not be changed in the long-time limit. In the marginal case when the effects of catalyzed aggregation and catalyzed fragmentation counteract each other, a_k(t) takes the modified scaling form and the system can eventually evolve to a steady state.

关键词: aggregation, fragmentation, catalytically activated reaction, rate equation

Abstract: We propose a catalytically activated aggregation—fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of species A will fragment into two smaller clusters under the catalysis of C clusters. By means of mean-field rate equations, we derive the asymptotic solutions of the cluster-mass distributions a_k(t) of species A, which is found to depend strongly on the competition between the catalyzed aggregation process and the catalyzed fragmentation process. When the catalyzed aggregation process dominates the system, the cluster-mass distribution a_k(t) satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of a_k(t) breaks down completely and the monodisperse initial condition of species A would not be changed in the long-time limit. In the marginal case when the effects of catalyzed aggregation and catalyzed fragmentation counteract each other, a_k(t) takes the modified scaling form and the system can eventually evolve to a steady state.

Key words: aggregation, fragmentation, catalytically activated reaction, rate equation

中图分类号: (Diffusion of adsorbates, kinetics of coarsening and aggregation)

68.43.Jk

82.20.-w (Chemical kinetics and dynamics) 89.75.Da (Systems obeying scaling laws)

高艳, 王海锋, 林振权, 薛新英. Kinetics of catalytically activated aggregation–fragmentation process[J]. 中国物理B, 2011, 20(8): 86801-086801.

Gao Yan(高艳), Wang Hai-Feng(王海锋), Lin Zhen-Quan(林振权), and Xue Xin-Ying(薛新英). Kinetics of catalytically activated aggregation–fragmentation process[J]. Chin. Phys. B, 2011, 20(8): 86801-086801.

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Kinetics of catalytically activated aggregation–fragmentation process

Kinetics of catalytically activated aggregation–fragmentation process

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