Please wait a minute...
Chinese Physics, 2005, Vol. 14(8): 1676-1682    DOI: 10.1088/1009-1963/14/8/038

Aggregate growth driven by monomer transfer

Ke Jian-Hong (柯见洪), Zhuang You-Yi (庄友谊), Lin Zhen-Quan (林振权)
School of Physics and Electronic Information,Wenzhou Normal College, Wenzhou 325027, China
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 μνak(t) takes the scaling form only in the case of μ<ν and μ+ν<2. As for the case with μ+ν>2 (μν) 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.
Keywords:  kinetic behaviour      aggregate growth      scaling law      rate equation  
Received:  28 September 2004      Revised:  14 December 2004      Accepted manuscript online: 
PACS:  82.20.Pm (Rate constants, reaction cross sections, and activation energies)  
  82.30.Hk (Chemical exchanges (substitution, atom transfer, abstraction, disproportionation, and group exchange))  
  82.70.-y (Disperse systems; complex fluids)  
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

[1] Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence
Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Chin. Phys. B, 2022, 31(9): 093101.
[2] Pump pulse characteristics of quasi-continuous-wave diode-side-pumped Nd:YAG laser
Zexin Song(宋泽鑫), Qi Bian(卞奇), Yu Shen(申玉), Keling Gong(龚柯菱), Nan Zong(宗楠), Qingshuang Zong(宗庆霜), Yong Bo(薄勇), and Qinjun Peng(彭钦军). Chin. Phys. B, 2022, 31(5): 054208.
[3] Studies on aluminum powder combustion in detonation environment
Jian-Xin Nie(聂建新), Run-Zhe Kan(阚润哲), Qing-Jie Jiao(焦清介), Qiu-Shi Wang(王秋实), Xue-Yong Guo(郭学永), and Shi Yan(闫石). Chin. Phys. B, 2022, 31(4): 044703.
[4] Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy
Zeyu Zhang(张泽宇), Qiang Zhang(张强), and Wenbo Mi(米文博). Chin. Phys. B, 2022, 31(4): 047305.
[5] Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear
Zhi-Gang Zhou(周志刚), Yi-Min Jiang(蒋亦民), Mei-Ying Hou(厚美瑛). Chin. Phys. B, 2017, 26(8): 084502.
[6] Equivalent electron correlations in nonsequential double ionization of noble atoms
Shansi Dong(董善思), Qiujing Han(韩秋静), Jingtao Zhang(张敬涛). Chin. Phys. B, 2017, 26(2): 023202.
[7] Studies on convergence and scaling law of Thomson backscattering spectra in strong fields
Han-Zhang Xie(谢含章), Chun Jiang(蒋纯), Bai-Song Xie(谢柏松). Chin. Phys. B, 2017, 26(12): 124101.
[8] An equivalent circuit model for terahertz quantumcascade lasers: Modeling and experiments
Yao Chen (姚辰), Xu Tian-Hong (徐天鸿), Wan Wen-Jian (万文坚), Zhu Yong-Hao (朱永浩), Cao Jun-Cheng (曹俊诚). Chin. Phys. B, 2015, 24(9): 094208.
[9] Scaling law of single ion-atom impact ionization cross sections of noble gases from He to Xe at strong perturbative energies
Ren Ping-Yuan (任屏源), Zou Xian-Rong (邹贤容), Shao Jian-Xiong (邵剑雄), Wang Shi-Yao (王诗尧), Zhou Man (周满), Zhou Wang (周旺), Yang Ai-Xiang (杨爱香), Yan Peng-Xun (闫鹏勋), Chen Xi-Meng (陈熙萌). Chin. Phys. B, 2015, 24(6): 063402.
[10] A fractal approach to low velocity non-Darcy flow in a low permeability porous medium
Cai Jian-Chao (蔡建超). Chin. Phys. B, 2014, 23(4): 044701.
[11] 227-W output all-fiberized Tm-doped fiber laser at 1908 nm
Hu Zhen-Yue (胡震岳), Yan Ping (闫平), Xiao Qi-Rong (肖起榕), Liu Qiang (柳强), Gong Ma-Li (巩马理). Chin. Phys. B, 2014, 23(10): 104206.
[12] A theoretical and experimental investigation of an in-band pumped gain-switched thulium-doped fiber laser
Zhou Ren-Lai (周仁来), Ju You-Lun (鞠有伦), Zhao Jie (赵杰), Yang Chao(杨超), Wang Yue-Zhu(王月珠). Chin. Phys. B, 2013, 22(6): 064208.
[13] Degradation behaviors of high power GaN-based blue light emitting diodes
Zhong Can-Tao (钟灿涛), Yu Tong-Jun (于彤军), Yan Jian (颜建), Chen Zhi-Zhong (陈志忠), Zhang Guo-Yi (张国义). Chin. Phys. B, 2013, 22(11): 117804.
[14] Calculation of the photoelectron spectra under the scaling transform
Ye Hui-Liang (叶会亮), Wu Yan (吴艳), Zhang Jing-Tao (张敬涛), Shao Chu-Yin (邵初寅). Chin. Phys. B, 2013, 22(1): 013207.
[15] Fluctuations in airport arrival and departure traffic: A network analysis
Li Shan-Mei (李善梅), Xu Xiao-Hao (徐肖豪), Meng Ling-Hang (孟令航 ). Chin. Phys. B, 2012, 21(8): 088901.
No Suggested Reading articles found!