Energy and size fluctuations of amphiphilic aggregates in a lattice model

We have studied the self-assembly of amphiphiles over wide ranges of temper ature and concentration using Monte Carlo simulation of a lattice model int roduced by Care. A new feature that we have observed is that for all the co ncentrations studied, the specific heat exhibits a peak as a function of te mperature. The physical origin of this peak can be traced back to energy fl uctuations occurring at the onset of micelle formations and can be used to characterize the critical micelle concentration (CMC). Our observations (i) that the temperature dependence of the specific heat fits rather well with the Schottky-type specific heat of a degenerate two-level system and (ii) that there is the simultaneous appearance of a knee in the cluster distribu tion function (CDF) explain the underlying physics of identifying the CMC w ith the appearance of this knee in the CDF, as proposed by Nagarajan and Ru ckenstein. We show that the various moments of the cluster distribution fun ctions can be expressed solely in terms of the second moment as predicted b y a mean-field theory of Blankschtein, Thurston, and Benedek. We also calcu late the fluctuation in the amphiphilic aggregate sizes and relate our simu lation results to those from a simple but exactly soluble model proposed by Israelachvili.