EXACT RESULTS AND MEAN-FIELD APPROXIMATION FOR A MODEL OF MOLECULAR AGGREGATION

We present a simple one-dimensional model with molecular interactions favoring the formation of clusters with a defined optimal size. Increa sing the density, at low temperature, the system goes from a nearly id eal gas of independent molecules to a system with most of the molecule s in optimal clusters, in a way that resembles the formation of micell es in a dilution of amphiphilic molecules, at the critical micellar co ncentration. Our model is simple enough to have an exact solution, but it contains some basic features of more realistic descriptions of amp hiphilic systems: molecular excluded volume and molecular attractions which are saturated at the optimal cluster. The comparison between the exact results and the mean field density functional approximation sug gests new approaches to study the more complex and realistic models of micelle formation; in particular it addresses the long-standing contr oversy surrounding the separation of internal degrees of freedom in th e formulation of cluster association phenomena. (C) 1997 American Inst itute of Physics. [S0021-9606(97)51747-8].