Free energy profiles for penetration of methane and water molecules into spherical sodium dodecyl sulfate micelles obtained using the thermodynamic integration method combined with molecular dynamics calculations.

The free energy profiles, ΔG(r), for penetration of methane and water molecules into sodium dodecyl sulfate (SDS) micelles have been calculated as a function of distance r from the SDS micelle to the methane and water molecules, using the thermodynamic integration method combined with molecular dynamics calculations. The calculations showed that methane is about 6-12 kJ mol(-1) more stable in the SDS micelle than in the water phase, and no ΔG(r) barrier is observed in the vicinity of the sulfate ions of the SDS micelle, implying that methane is easily drawn into the SDS micelle. Based on analysis of the contributions from hydrophobic groups, sulfate ions, sodium ions, and solvent water to ΔG(r), it is clear that methane in the SDS micelle is about 25 kJ mol(-1) more stable than it is in the water phase because of the contribution from the solvent water itself. This can be understood by the hydrophobic effect. In contrast, methane is destabilized by 5-15 kJ mol(-1) by the contribution from the hydrophobic groups of the SDS micelle because of the repulsive interactions between the methane and the crowded hydrophobic groups of the SDS. The large stabilizing effect of the solvent water is higher than the repulsion by the hydrophobic groups, driving methane to become solubilized into the SDS micelle. A good correlation was found between the distribution of cavities and the distribution of methane molecules in the micelle. The methane may move about in the SDS micelle by diffusing between cavities. In contrast, with respect to the water, ΔG(r) has a large positive value of 24-35 kJ mol(-1), so water is not stabilized in the micelle. Analysis showed that the contributions change in complex ways as a function of r and cancel each other out. Reference calculations of the mean forces on a penetrating water molecule into a dodecane droplet clearly showed the same free energy behavior. The common feature is that water is less stable in the hydrophobic core than in the water phase because of the energetic disadvantage of breaking hydrogen bonds formed in the water phase. The difference between the behaviors of the SDS micelles and the dodecane droplets is found just at the interface; this is caused by the strong surface dipole moment formed by sulfate ions and sodium ions in the SDS micelles.