Monte Carlo lattice simulation of amphiphilic systems in two and three dimensions

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Abstract
Microstructures such as 2D micelles (in two dimensions) and lamellar arrays, cylinders, and spheres (in three dimensions) are allowed to self-assemble via Monte Carlo simulation of an idealized lattice model for amphiphile–oil–water systems. Energies, free energies, equilibrium phase diagrams, and solution microstructures are estimated by Monte Carlo sampling of configuration space. In two dimensions (2D) at a temperature at which oil units have only a 3% solubility in the water phase, amphiphile at 20% concentration solubilizes any ratio of oil and water into a single phase and at lower concentrations produces phases with ultralow interfacial tension between them. As expected, in 3D solubilization is weaker and interfacial tensions higher than in 2D at comparable temperatures. Nevertheless, 3D systems containing the longest amphiphile (four head and four tail units) shows ordered solution structures, such as micelles at modest amphiphile concentration and periodic lamellar and cylindrical structures at high amphiphile concentration that are analogous to those of diblock polymers mixed with low molecular weight homopolymers.

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