Two computational methods for describing size selected nanocluster growth and obtaining accurate cluster size distributions

Describing nanocluster growth and obtaining size distributions of clusters near kinetically determined metastable states is a computationally difficult problem because of the slow convergence of size distributions near the metastable state. In this work, we examine the size selected growth of nanoclusters in such situations by using a mesoscopic reaction kinetic model (RKM), and introduce two effective computational schemes for describing the size selection and obtaining size distributions. The first method is based on the particle coalescence method (PCM), where the configuration space of clusters is sampled by using the rejection-free Bortz–Kalos–Lebowitz algorithm. The second method is based on direct numerical integration of the RKM by using the transformation referred to as the master equation discretization (MED) scheme. We compare the computational reliability of the PCM and RKM discretization methods in a typical case of 2D-nanocluster growth with size dependent energetics and show that both of these approaches allows us to study in detail the evolution of the size distribution in all stages of the growth.