Thermodynamical, structural, and clustering properties of a microemulsion model

Skaf, Munir S.; Stell, George
November 1992
Journal of Chemical Physics;11/15/1992, Vol. 97 Issue 10, p7699
Academic Journal
A lattice version of the microemulsion model introduced by A. Ciach, J. Ho\ye, and G. Stell [J. Phys. A 21, L111 (1989)] (CHS) is studied within a mean-field approximation. In the absence of (orientational) surfactant–surfactant interactions, an exact integration of the amphiphiles’ orientational degrees of freedom in the CHS model yields an effective spin-one Hamiltonian with multibody, temperature-dependent interactions between particles, closely resembling the model introduced by M. Schick and W. H. Shih [Phys. Rev. Lett. 59, 1205 (1987)] and subsequently studied by Gompper and Schick. The phase diagram for the CHS effective Hamiltonian on a two-dimensional lattice is calculated at a mean-field level. Comparisons with selected results from Schick’s model are then discussed. The calculated structure functions are in qualitative agreement with experimental results, showing a structural evolution from water-in-oil, to bicontinuous, to oil-in-water microemulsions as the water-to-oil concentration ratio is varied. The symmetric (ρW=ρO) subspace of the disordered phase of both models is then investigated using a percolation theory previously introduced by the authors. In both models the bicontinuous microemulsion phase is identified as a region of the phase diagram where the three molecular species are simultaneously percolating. Finally, the percolation threshold lines are investigated, for both models, as functions of their energy couplings. We find, again, similar behavior for the CHS effective Hamiltonian and Schick Hamiltonian. However, the thresholds are found to be more sensitive to the amphiphilic strength of the surfactant in the former.


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