Kinetics of heterogeneous nucleation for low mean cluster populations

The process of nucleation is normally described using rate equations for the mean populations of molecular clusters. This approach can be justified for cases where these mean populations are large. However, it may be unsuitable in the case of heterogeneous nucleation on small particles if the mean populations are of the order of unity or less. In such a case, considering the average populations might be erroneous since the statistical fluctuations in the molecular populations should be taken into account. Here a stochastic treatment of heterogeneous nucleation kinetics is presented that is described by a set of master equations, and a modified expression for the nucleation rate has been deduced. Furthermore, a numerical method for solving the stochastic system has been examined, and the results show that the rate of nucleation can differ greatly from that obtained with the traditional kinetics.