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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 |
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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 ak(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 ak(t) satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of ak(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, ak(t) takes the modified scaling form and the system can eventually evolve to a steady state.
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Received: 02 November 2010
Revised: 20 February 2011
Accepted manuscript online:
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PACS:
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68.43.Jk
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(Diffusion of adsorbates, kinetics of coarsening and aggregation)
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82.20.-w
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(Chemical kinetics and dynamics)
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89.75.Da
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(Systems obeying scaling laws)
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| Fund: 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). |
Cite this article:
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 2011 Chin. Phys. B 20 086801
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