Coherent approach to critical demixing in strongly coupled binary ionic mixtures. I. Weak electron-ion coupling and stability requirements.

Abstract

We analyze the minimal conditions required to build up a coherent and neutral-like description of critical phenomena in strongly coupled binary mixtures of pointlike positive charges. One is thus led to bridge the gap between the microscopic approach dealing with the divergence of the ionic structure factors ${S}_{\ensuremath{\alpha}\ensuremath{\beta}}$(k) in the k\ensuremath{\rightarrow}0 limit and the thermodynamic one deduced as usual from the Gibbs free-energy function. We emphasize the fundamental role played by the electronic polarization. Namely, modeling the plasma in the so-called polarized binary ionic mixture which accounts for the electronic density fluctuations through a static dielectronic function \ensuremath{\epsilon}(k), we show that the ionic mixture may be properly described as a mixture of ``pseudoatom'' if \ensuremath{\epsilon}(k) fulfills the compressibility sum rule while the weak electron-ion coupling hypothesis is assumed to be valid. Conversely, the binary ionic mixture model, with no electronic polarization at all, appears to be inappropriate to the microscopic approach, as a consequence of the rigid character of the electron background.