Most of biologically relevant macromolecules or particles in soft-matter systems are charged and repel each other with screened electrostatic forces. On the other hand, complex solvents in biological systems may induce effective attraction between macromolecules.
I will present generic lattice models for systems containing particles interacting with short-range attraction and long- range repulsion (SALR)potentials, and describe results obtained in one dimension and in two dimensions on a triangular lattice. In both cases, the ground state was found analytically and phase diagram was determined in Mean Field approximation. Moreover, in one dimension the equation of state and the correlation function were calculated exactly, and the two dimensional model was studied be means of Monte Carlo simulations (Metropolis algorithm). The phase behaviour of the model is very rich. When the repulsion is sufficiently strong, periodic ordering of self-assembled
clusters or stripes is obtained for some range of thermodynamic states. We find coexistence of ordered phases with the same symmetry but different degree of order, and reentrant melting upon decreasing temperature or increasing density. Finally, I will describe effects of confinment on the ordered structure.
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