Lattice models of amphiphile and solvent mixtures.

Materials based on amphiphilic molecules have a wide range of industrial applications and are of fundamental importance in the structure of many biological systems. Their importance derives from their behaviour as surface-active agents in solubilization applications and because of their ability to form systems with varying degrees of structural order such as micelles, bilayers and liquid crystal phases. The nature of the molecular ordering is of importance both during the processing of these materials and in their final application. A Monte Carlo simulation of a three dimensional lattice model of an amphiphile and solvent mixture has been developed as an extension of earlier work in two dimensions. In the earlier investigation the simulation was carried out with three segment amphiphiles on a two dimensional lattice and cluster size distributions were determined for a range of temperatures, amphiphile concentrations and intermolecular interaction energies. In the current work, a wider range of structures are observed including micelles, bilayers and a vesicle. The structures are studied as a function of temperature, chain length, amphiphile concentration and intermolecular interaction energies. Clusters are characterised according to their shape, size and surface roughness. A detailed temperature-concentration phase diagram is presented for a system with four segment amphiphiles. The phase diagram shows a critical micelle concentration (c.m.c) at low amphiphile concentrations and a transition from a bicontinuous to lamellar region at amphiphile concentrations around 50%. At high amphiphile concentrations, there is some evidence for the formation of a gel. The results obtained question the validity of current models of the c.m.c. The Monte Carlo simulations require extensive computing power and the simulation was carried out on a transputer array, where the parallel architecture allows high speed. The development of a suitable parallel algorithm is discussed. A mean field model of a bilayer is presented which has similar interaction potentials as the Monte Carlo model. The ordering of the bilayer is examined as a function of chain length, bilayer thickness, temperature and inter molecular interaction energies. In this approximation a phase transition to the ordered bilayer is observed.