Energy and size fluctuations of amphiphilic aggregates in a lattice model

We have studied the self-assembly of amphiphiles over wide ranges of temperature and concentration using Monte Carlo simulation of a lattice model introduced by Care. A new feature that we have observed is that for all the concentrations studied, the specific heat exhibits a peak as a function of temperature. The physical origin of this peak can be traced back to energy fluctuations 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 distribution function (CDF) explain the underlying physics of identifying the CMC with the appearance of this knee in the CDF, as proposed by Nagarajan and Ruckenstein. We show that the various moments of the cluster distribution functions can be expressed solely in terms of the second moment as predicted by a mean-field theory of Blankschtein, Thurston, and Benedek. We also calculate the fluctuation in the amphiphilic aggregate sizes and relate our simulation results to those from a simple but exactly soluble model proposed by Israelachvili.