LATTICE MODEL OF SELF-ASSEMBLY

A microscopic lattice model of two-component mixtures of water and amphiphile is introduced. The model is defined on a simple cubic lattice, the vertices of which are occupied by Ising and Heisenberg degrees of freedom which model water- and amphiphile-filled cubes. The orientations of the lipid molecules are described by the directions of the Heisenberg spin-vectors. Microscopic interactions between two water-filled cubes, two lipid-filled cubes, or a water- and a lipid-filled cube are related to the coupling constants of the model. In this paper we discuss the zero-temperature states of the model and, for some parts of the parameter space, these are explicitly constructed from local octahedral clusters of the cubic lattice. We then introduce a mean-field theory that preserves the full symmetry of the Hamiltonian, and thereby construct the global phase diagrams for different choices of the coupling parameters. In the conclusions to our paper we comment on other theoretical methods of solution being applied to the present Hamiltonian. © 1990 American Institute of Physics.