Volume 116, Number 2, October 2016
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||23 November 2016|
Coordination number statistics of cluster formation
1 Department of Chemistry, Physical and Theoretical Chemistry Laboratory - South Parks Road, Oxford, OX1 3QZ, UK
2 School of Materials, University of Manchester - Manchester, M13 9PL, UK
Received: 24 June 2016
Accepted: 3 November 2016
We establish a direct relation between the distribution of coordination numbers for individual particles and the mean cluster size using simple statistical considerations. We test our probabilistic theory against an experimental model system of superparamagnetic colloidal particles, which form chain-like clusters upon the application of an external magnetic field. We find that the experimental cluster size distribution is well described by a shifted geometric distribution, consistent with a Smoluchowski aggregation scheme. Computer simulations of an atomistic model show that ordering of the positions of the particles prior to aggregation alters the cluster size distribution. These simulations corroborate the validity of our coordination number statistics approach to aggregation processes and demonstrate that the cluster formation process can be interpreted as a compound Poisson process.
PACS: 82.70.Dd – Colloids / 83.80.Gv – Electro- and magnetorheological fluids / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2016
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