中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1676-1682.doi: 10.1088/1009-1963/14/8/038

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Aggregate growth driven by monomer transfer

柯见洪, 庄友谊, 林振权   

  1. School of Physics and Electronic Information,Wenzhou Normal College, Wenzhou 325027, China
  • 收稿日期:2004-09-28 修回日期:2004-12-14 出版日期:2005-07-13 发布日期:2005-07-13
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10305009 and 10275048)and the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067).

Aggregate growth driven by monomer transfer

Ke Jian-Hong (柯见洪), Zhuang You-Yi (庄友谊), Lin Zhen-Quan (林振权)   

  1. School of Physics and Electronic Information,Wenzhou Normal College, Wenzhou 325027, China
  • Received:2004-09-28 Revised:2004-12-14 Online:2005-07-13 Published:2005-07-13
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10305009 and 10275048)and the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067).

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摘要： We propose a solvable aggregate growth model with the rate kernel K(i;j;l)∝ iμ jν lvarpi (varpi ≥ 0), at which a monomer transfers from the A aggregate of size i to the A aggregate of size j only with the help of a B aggregate of size l. By means of the mean-field rate equation approach, we obtain the analytical solutions of the aggregate size distributions in several different cases. For a symmetrical system with μ=ν, the aggregate size distribution ak(t) approaches the conventional scaling form in the μ <3/2 case; while for an asymmetrical system with μ\neq ν, ak(t) takes the scaling form only in the case of μ < ν and μ +ν <2. As for the case with μ+ν>2 (μ＜ν) or μ>3/2 (μ = ν), the system may have a gelationlike transition. Moreover, we also study the kinetic scaling behaviour of the model with the generalized kernel K(i;j;l)～(iμ jν+iνjμ) lvarpi. The aggregate size distribution obeys a scaling law only in the μ+ν< 3 case; while in other cases, the system may undergo a gelationlike transition after a sufficiently long time.

关键词: kinetic behaviour, aggregate growth, scaling law, rate equation

Abstract: We propose a solvable aggregate growth model with the rate kernelK(i;j;l)∝iμjνl? (??0), at which a monomer transfers from the A aggregate of size i to the A aggregate of size j only with the help of a B aggregate of size l. By means of the mean-field rate equation approach, we obtain the analytical solutions of the aggregate size distributions in several different cases. For a symmetrical system with μ = ν, the aggregate size distributionak(t) approaches the conventional scaling form in the μ<3/2 case; while for an asymmetrical system with μ≠ν, ak(t) takes the scaling form only in the case of μ<ν and μ+ν<2. As for the case with μ+ν>2 (μ≠ν) or μ>3/2 (μ = ν), the system may have a gelationlike transition. Moreover, we also study the kinetic scaling behaviour of the model with the generalized kernelK(i;j;l)~(iμjν+iνjμ)l?. The aggregate size distribution obeys a scaling law only in the μ+ν<3 case; while in other cases, the system may undergo a gelationlike transition after a sufficiently long time.

Key words: kinetic behaviour, aggregate growth, scaling law, rate equation

中图分类号:  (Rate constants, reaction cross sections, and activation energies)

  • 82.20.Pm
82.30.Hk (Chemical exchanges (substitution, atom transfer, abstraction, disproportionation, and group exchange)) 82.70.-y (Disperse systems; complex fluids)