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Gas-liquid critical parameters of asymmetric models of ionic fluids

The effects of size and charge asymmetry on the gas-liquid critical parameters of a primitive model (PM) of ionic fluids are studied within the framework of the statistical field theory based on the collective variables method. Recently, this approach has enabled us to obtain the correct trends of the both critical parameters of the equisize charge-asymmetric PM without assuming ionic association. In this paper we focus on the general case of an asymmetric PM characterized by the two parameters: hard-sphere diameter-, $λ=σ_{+}/σ_{-}$ and charge, $z=q_{+}/|q_{-}|$, ratios of the two ionic species. We derive an explicit expression for the chemical potential conjugate to the order parameter which includes the effects of correlations up to the third order. Based on this expression we consider the three versions of PM: a monovalent size-asymmetric PM ($λ\neq 1$, $z=1$), an equisize charge-asymmetric PM ($λ=1$, $z\neq 1$) and a size- and charge-asymmetric PM ($λ\neq 1$, $z=2$). Similar to simulations, our theory predicts that the critical temperature and the critical density decrease with the increase of size asymmetry. Regarding the effects of charge asymmetry, we obtain the correct trend of the critical temperature with $z$, while the trend of the critical density obtained in this approximation is inconsistent with simulations, as well as with our previous results found in the higher-order approximation. We expect that the consideration of the higher-order correlations will lead to the correct trend of the critical density with charge asymmetry.