A lattice model of the micellar phase of an amphiphile and solvent mixture in the quasi-chemical approximation

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Abstract
A lattice model of an amphiphile-solvent system with nearest-neighbour interactions is studied in the quasi-chemical approximation. The interaction potential is expressed in terms of a tail-solvent, a head-solvent and a head-head interaction. The results derived apply to the monomeric and micellar phases of this system. Expressions are obtained for the chemical potentials of the amphiphile and the solvent in terms of the interaction parameters, the lengths of the molecules and the coordination number of the lattice. These are evaluated numerically and used to determine the critical temperature, the critical volume fraction of the amphiphile and the temperature-composition curves. It is found that increasing the solvophilic nature of the head segment leads to an asymmetrical temperature-composition curve which is identified as being characteristic of micelle formation in this model. The head-head repulsion is found to have limited effect upon the critical properties of the model in the micellar region. This is interpreted as supporting Menger's suggestion (1979) that the micelle is a 'porous cluster'.

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