Critical micelle concentration in three-dimensional lattice models of amphiphiles

Amphiphilic molecules with hydrophobic tails and hydrophilic heads form micelles of various shapes and sizes above a minimum threshold concentration known as the critical micelle. concentration (CMC). The CMC as wen as the size and the shape of the aggregates formed depend on various factors, e.g., the length of the amphiphiles, their internal rigidity, and temperature. In this letter we report the results of a detailed investigation of the dependence of the CMC on temperature for different lattice models of the amphiphilic self-assembly. Ensuring that the CMC can be unambiguously associated with a peak in the heat capacity as a function of the amphiphilic concentration, we show that for the amphiphiles of different lengths and head-to-tail ratios, the CMC decreases rapidly as a function of the chain length, consistently with the experimental results. However, for a given chain length, different lattice models predict that the CMC is always an increasing function of temperature. We point out that these lattice models, although widely used, are inadequate to explain the decrease of the CMC with temperature, seen experimentally for non-ionic surfactants.