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The transition of spherical to rod-like micelles is studied in a lattice model for amphiphiles using the single chain mean-field ͑SCMF͒ theory and grand-canonical Monte Carlo ͑GCMC͒ simulations. A linear combination of the free energy of spherical and infinite cylindrical geometries is assumed in the SCMF theory to estimate the free energy of rod-like micelles. The SCMF theory finds that the symmetric H 4 T 4 amphiphile at a dimensionless temperature scale, T*, of T*ϭ6.5 favors the formation of spherical micelles at all investigated overall amphiphile concentrations. On the other hand, the asymmetric H 3 T 6 amphiphile at T* between 8.5 and 12.5 starts by forming spherical micelles ͑first cmc) at low overall amphiphile concentrations and then forms rod-like micelles ͑second cmc) as the overall amphiphile concentration increases. The GCMC simulations also find that the symmetric H 4 T 4 amphiphile forms spherical micelles while the asymmetric H 3 T 6 amphiphile tends to form rod-like micelles. The second cmc is found to increase with increasing T* whereas it decreases with increasing tail length. Our results are in good qualitative agreement with experimental observations.

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A single-chain mean-field theory is used to predict the properties of binary surfactant solutions including the critical micelle concentration (cmc). In particular, the cmc of two symmetric nonionic amphiphiles is calculated as a function of temperature in order to analyze the validity of the ideal mixing assumption, often employed in the mass action model. On comparing against literature Monte Carlo results for the same lattice model we find that although it is applicable at low temperatures and hence cmcs at low amphiphile concentrations, at higher temperatures it becomes necessary to correct for the nonideal mixing of the free chain-free chain bulk interaction. We find that a simplistic model taking into account only the repulsive interaction is sufficient to restore the excellent quantitative agreement found between a single-chain mean-field theory calculations and literature molecular simulation results at the low temperature limit.