AbstractWe 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.
Received: 28 September 2004
Revised: 14 December 2004
Accepted manuscript online:
PACS:
82.20.Pm
(Rate constants, reaction cross sections, and activation energies)
Fund: 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).
Cite this article:
Ke Jian-Hong (柯见洪), Zhuang You-Yi (庄友谊), Lin Zhen-Quan (林振权) Aggregate growth driven by monomer transfer 2005 Chinese Physics 14 1676
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