Coordination number statistics of cluster formation

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.