Phase Diagram of a Lattice Model for Ternary Mixtures of Water, Oil, and Surfactants
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Phase diagram of a lattice model for ternary mixtures of water, oil, and surfactants Mohamed Laradlji, Hong Guo, Martin Grant and Martin J. Zuchkermann,
Centre for the Physics of Materials and Department of Physics, McGill University, 3600 Rue University, Montreal, Quebec, Canada H3A 2T8 Abstract Large scale Monte-Carlo simulations have been performed on a lattice model for a three component system of water, oil, and surfactants to obtain the phase equilibria and scattering behavior for a wide range of temperatures and chemical potentials. We observed that this model has a rich phase behavior, namely a water-oil phase coexistence, a microemulsion phase , a lamellar phase, and a square phase. This phase diagram is consistent with experiments, and is in qualitative agreement with a model of Gompper and Schick [ Phys. Rev. Lett. 62, 1647 (1989)].
Introduction Amphiphilic surfactants lead to many interesting structures when mixed with water and oil, due to their anisotropic molecular structure with a polar head which prefers to be in contact with water, and a hydrophobic tail which likes oil'. This molecular nature allows surfactants to microphase separate water and oil into small and coherent regions, since they screen the repulsive interaction between water and oil, which would lead to a complete phase separation in the absence 2 of surfactants . For extremely small surfactant concentrations, a two-phase coexistence of water and oil is usually observed. A microemulsion phase is usually obtained for higher surfactant concentrations. In spite of the disordered character of microemulsions, water and oil remain separated within a few hundreds of Angstromss by surfactant monolayers, but are uncorrelated at large distances. For small water volume fractions as compared to that of oil (or vice versa), a microemulsion is formed of globules of water in oil (or vice versa). However, for comparable" volume fractions of water and oil, a microemulsion usually has a bicontinuous structure. In the last case, small angle neutron scattering experiments show a well defined peak in the water-water 3 structure factor at a wave number q > 0, corresponding to the average distance between like domains. It is also observed that the position of the peak increases as the surfactant concentration increases, which is simply due to the increase in the interfacial film where surfactants are present. As the surfactant concentration is fu~rther increased, surfactant monolayers become stiff leading to the formation of liquid crystalline phases, such as lamellar, cubic, and hexagonal structures, which usually have quasi-long range order. 4 Both phenomenological and lattice gas models have been proposed to study these systems , and most of them were treated via mean-field approximations, in which fluctuations were ignored. In this paper, we show that the fluctuations are important in these ternary mixtures, especially for the microemulsion, where water, oil and surfactant density profiles exhibit strong spatial fluctuations, and that more accurate me
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