A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered (O) and disordered (D) forms of water are treated as two components, and we assume that the density of the D component is larger. The density of the sample is determined by the fraction of cells occupied by the O and D forms of water. Due to the larger density of the D state, the strength of the van der Waals (vdW) interactions increases in the direction O-O

We show that amphiphilic and colloidal systems with competing interactions can be described by the same Landau-Brazovskii functional. The functional is obtained by a systematic coarse-graining procedure applied to systems with isotropic interaction potentials. Microscopic expressions for the coefficients in the functional are derived. We propose simple criteria to distinguish the effective interparticle potentials that can lead to macro-or microsegregation. Our considerations concern also charged globular proteins in aqueous solutions and other system with effective short-range attraction long-range repulsion interactions.

We present a method for the generation of periodic embedded surfaces of nonpositive Gaussian curvature and multiply continuous phases. The structures are related to the local minima of the scalar order parameter Landau-Ginzburg Hamiltonian for microemulsions. In the bicontinuous structure the single surface separates the volume into two disjoint subvolumes. In some of our phases ͑multiply continuous͒ there is more than one periodic surface that disconnects the volume into three or more disjoint subvolumes. We show that some of these surfaces are triply periodic minimal surfaces. We have generated known minimal surfaces ͑e.g., Schwarz primitive P, diamond D, and Schoen-Luzatti gyroid G and many surfaces of high genus. We speculate that the structure of microemulsion can be related to the high-genus gyroid structures, since the high-genus surfaces were most easily generated in the phase diagram close to the microemulsion stability region. We study in detail the geometrical characteristics of these phases, such as genus per unit cell, surface area per unit volume, and volume fraction occupied by oil or water in such a structure. Our discovery calls for new experimental techniques, which could be used to discern between bicontinuous and multiply continuous structures. We observe that multiply continuous structures are most easily generated close to the water-oil coexistence region.