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The story of coulombic critiality

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Abstract

Recent experiments on phase separation and criticality in ionic fluids are reviewed briefly. The data suggest a sharp distinction betweensolvophobic criticality, displayed by nonionic fluids and some electrolytes, that is associated with Ising-like exponents, β≅0.325, γ≅1.239, and ν≅0.631, andCoulombic (orionic)criticality characterized by classical, van der Waals exponents, β=0.5, γ=1, and ν=0.5. Only experiments on the sodium-ammonia system seem to straddle this dichotomy: they show crossover from classical to Ising behavior close toT c at a characteristic crossover scalet x=|Tx−Tc|/Tc. A range of theoretical issues thus raised is discussed, including other conceivable options (spherical model, tricriticality, etc.). Attention is drawn to Nabutovskii's work and various scenarios are illustrated with the aid of schematic phase diagrams containing multicritical points that could, in principle, separate two distinct universality classes of electrolyte criticality. The advantages of examining a basic four-state lattice model that allows for ionic association-dissociation, etec., are reviewed. The issue of the existence, location, and nature of the long-heralded but still elusive gas-liquid transition and critical point in the continuum restricted primitive model (hard spheres carrying charges +q and −q) is taken up in further detail. Earlier theoretical work and recent Monte Carlo simulations are summarized. In an effort to obtain a physically transparent, semiquantitative description, the work of Debye and Hückel and its subsequent elaboration via Bjerrum's concept of bound ion paris is revisited and seen to predict phase separation and criticality. Recent work by Levin and the author is described which repairs serious defects of the earlier theories by including the interaction of the ion-pair dipoles with the screening ionic fluid, following Debye-Hückel methods. The resulting mean field theory agrees quite well with the simulations and appears to embody the most crucial physical effects. However, the role of critical fluctuations, the related interplay of the charge and density correlation functions, the likelihood of Ising-like behavior, and the associated crossover scalet x remain important unsettled questions. An Appendix presents a critique of arguments by Stell to the effect that the restricted primitive model should display Ising behavior and that 1/r 4 effective interactions might be significant.

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  1. Institute for Physical Science and Technology, University of Maryland, 20742, College Park, Maryland, USA

    Michael E. Fisher

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This article is based on a lecture delivered at the First Lars Onsager Symposium held at the Norwegian Institute of Technology, Trondheim, Norway, 2–4 June 1993.

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Fisher, M.E. The story of coulombic critiality. J Stat Phys 75, 1–36 (1994). https://doi.org/10.1007/BF02186278

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