Abstract We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel $K(i,j;l)\propto l^{\nu}$ and the catalysis-fragmentation rate kernel $F(i,j;l)\propto l^{\mu}$ , where l is the size of the catalyst aggregate, and $\nu$ and $\mu$ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters $\nu$ and $\mu$ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters $\nu$ and $\mu$, but also depend on the values of these two parameters. When $\nu> \mu$ and $\nu\geqslant 0$, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution ak(t) obeys the conventional or generalized scaling law; when $\nu<\mu$ and $\nu \geqslant 0$ or $\nu>0$ but $\mu \geqslant 0$, the catalysis-fragmentation process may play a dominating role and ak(t) approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ak(t) obeys a modified scaling law.
Received: 20 March 2010
Revised: 03 August 2010
Accepted manuscript online:
PACS:
82.65.+r
(Surface and interface chemistry; heterogeneous catalysis at surfaces)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104).
Cite this article:
Li Xiao-Dong(李晓东), Lin Zhen-Quan(林振权), Song Mei-Xia(宋美霞), and Ke Jian-Hong(柯见洪) Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours 2010 Chin. Phys. B 19 128201
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
