Charge and Density Fluctuations Lock Horns : Ionic Criticality with Power-Law Forces

Abstract

How do charge and density fluctuations compete in ionic fluids near gas-liquid criticality when quantum mechanical effects play a role ? To gain some insight, long-range ${\Phi }_{\pm \pm }^{\mathcal{L}}/r^{d+\sigma }$ interactions (with $\sigma >0$), that encompass van der Waals forces (when $\sigma =d=3$), have been incorporated in exactly soluble, $d$-dimensional 1:1 ionic spherical models with charges $\pm q_0$ and hard-core repulsions. In accord with previous work, when $d>\min \{\sigma ,2\}$ (and $q_0$ is not too large), the Coulomb interactions do not alter the ($q_0=0$) critical universality class that is characterized by density correlations at criticality decaying as $1/r^{d-2+\eta }$ with $\eta =\max \{0,2-\sigma \}$. But screening is now algebraic, the charge-charge correlations decaying, in general, only as $1/r^{d+\sigma +4}$; thus $\sigma =3$ faithfully mimics known \textit{non}critical $d=3$ quantal effects. But in the \textit{absence} of full ($+,-$) ion symmetry, density and charge fluctuations mix via a transparent mechanism: then the screening \textit{at criticality} is \textit{weaker} by a factor $r^{4-2\eta }$. Furthermore, the otherwise valid Stillinger-Lovett sum rule fails \textit{at} criticality whenever $\eta =0$ (as, e.g., when $\sigma >2$) although it remains valid if $\eta >0$ (as for $\sigma <2$ or in real $d\le 3$ Ising-type systems).

8 pages, in press in J. Phys. A, Letters to the Editor

References in corpus (2)

• Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte
• Ionic criticality : an exactly soluble model

Cited by in corpus (2)

• Screening in Ionic Systems: Simulations for the Lebowitz Length
• Criticality in multicomponent spherical models : results and cautions