中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1676-1682.doi: 10.1088/1009-1963/14/8/038
柯见洪, 庄友谊, 林振权
Ke Jian-Hong (柯见洪), Zhuang You-Yi (庄友谊), Lin Zhen-Quan (林振权)
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.
中图分类号: (Rate constants, reaction cross sections, and activation energies)