Rosenbluth chain cluster growth in the study of micelle self-assembly

A Rosenbluth algorithm [J. Chem. Phys. 23, 356 (1955)] for enumerating clusters of chains is presented. The method is used to undertake a direct enumeration of the cluster partition function for small clusters in a three-dimensional lattice model of a binary mixture of amphiphile and solvent. In this model, the amphiphiles are represented as connected chains on a lattice, with vacant sites representing the solvent. The results from the Rosenbluth method are compared with those obtained by Metropolis Monte Carlo simulations which allow free self-assembly of clusters. The agreement between the two methods allows an unambiguous identification of the packing entropy associated with micelle self-assembly. Results are presented for unbranched chains having two head and four tail segments (H2T4) and also four head and four tail segments (H4T4). Although the cluster enumeration method described in this paper has been developed for micellar systems, it will have applications in a variety of areas including nucleation and percolation.