A theoretical study of structure and thermodynamics of fluids with long-range competing interactions exhibiting pattern formation

We study the structure and phase behavior of a model fluid with competing short-range attraction and long-range repulsion, constituted by hard spheres interacting by means of two opposite Kac potentials. We use, to this purpose, a thermodynamically self-consistent integral equation approach developed by one of the authors [J.-M. Bomont and J.-L. Bretonnet, J. Chem. Phys. 119, 2188 (2003)], which proven accurate in predicting the properties of other competing fluids. We choose the potential parameters in such a way that, upon appropriate thermodynamic conditions, the fluid displays microphase separation terminating, at sufficiently low temperatures, with a phase transition into an ordered-pattern fluid. The propensity toward the pattern formation is indicated by long-wavelength, slowly decaying oscillations in the pair correlation function, and by the presence of a sharp peak in the structure factor S(q) at a small but finite wavevector q(c). The limits of stability of the micro-separated phase are identified by a drastic, diverging-like, increase of S(q(c)) as the temperature drops. The behavior of S(q) in the disordered-pattern phase suggests that different morphologies of the ordered patterns should be expected, depending on the ratio between the strengths of competing interactions. The structural predictions are confirmed, at the thermodynamic level, by the change of sign observed in the "residual multi-particle entropy," according to the one-phase ordering criterion developed by Giaquinta and Giunta [Physica A 187, 145 (1992)], and by the trend shown by the chemical potential. Our self-consistent approach succeeds in describing the thermodynamic regime where the phase transition occurs, whereas, as reported in the literature, other sophisticated schemes within the same theoretical framework generally fail; reasons of this outcome and putative remedies are discussed.