Chinese Physics, 2006, Vol. 15(8): 1896-1902    DOI: 10.1088/1009-1963/15/8/045
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# Aggregation processes with catalysis-driven monomer birth/death

Chen Yu(陈玉), Han An-Jia(韩安家), Ke Jian-Hong(柯见洪), and Lin Zhen-Quan(林振权）
School of Physics and Electronic Information,Wenzhou University, Wenzhou 325027, China
Abstract  We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the help of species B. The system with the size-dependent monomer birth/death rate kernel $K(i,j) = Jij^v$ is then investigated by means of the mean-field rate equation. The results show that the kinetic scaling behaviour of species A depends crucially on the value of the index $v$. For the model with catalysis-driven monomer birth, the cluster-mass distribution of species $A$ obeys the conventional scaling law in the $v \leq 0$ case, while it satisfies a generalized scaling form in the $v > 0$ case; moreover, the total mass of species A is a nonzero value in the $v < 0$ case while it grows continuously with time in the $v \geq 0$ case. For the model with catalysis-driven monomer death, the cluster-mass distribution also approaches the conventional scaling form in the $v < 0$ case, while the conventional scaling description of the system breaks down in the $v \geq 0$ case. Additionally, the total mass of species A retains a nonzero quantity in the $v < 0$ case, but it decreases to zero with time in the $v \geq 0$ case.
Keywords:  kinetic behaviour      cluster growth      scaling law      rate equation
Received:  16 December 2005      Revised:  24 February 2006      Accepted manuscript online:
 PACS: 82.70.-y (Disperse systems; complex fluids) 82.20.Pm (Rate constants, reaction cross sections, and activation energies) 82.30.-b (Specific chemical reactions; reaction mechanisms)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10305009 and 10275048) and the Zhejiang Provincial Natural Science Foundation, China (Grant No 102067).