Critical charge and density coupling in ionic spherical models

Abstract

We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions GNN and GZZ on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive non-ionic interactions. Near criticality, GNN and GZZ are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum-rule, which characterizes a conducting fluid, is violated at criticality in non-symmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semi-classically by incorporating algebraically decaying interactions, GZZ decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.

Algebraic infection of charge correlations at the ionic critical point

“…[7] Such simulations show the violation of the Stillinger-Lovett second moment sum rule on the one hand, and the divergence of the fourth moment of S(r) on the other hand: these facts will be taken as starting inputs in our improved BGY analysis. This provides the exponent s of the 1∕r s -decay of S(r) with 5 + 𝜂 ≤ s ≤ 6 + 𝜂, in agreement with heuristic estimations [24] inferred within a completely different approach from ours.…”

Algebraic infection of charge correlations of a classical electrolyte at the critical point of the liquid-gas transition

“…Including the refined three-body decays in the analysis of Section V A, one finds that S(r) indeed decays as 1/r 6+η when r → ∞. Furthermore, it turns out that such decay has been independently obtained in [23] within a completely different approach. Accordingly, the 1/r 6+η -decay of S(r) appears as a quite robust prediction, despite it is not yet rigorously established.…”

Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations

“…Early researches − show that electrolyte solutions have a “classical” criticality with β ≈ 0.5 (see Figure b). This claim has proved unreliable because of the difficulty to measure the data or inappropriate treatment of theory in the near-critical region . Further theoretical and experimental studies show that the criticality in electrolyte solution is still Ising-like. , A direct explanation is that Debye screening of ions gives an effective short-range interaction.…”

“…This claim has proved unreliable because of the difficulty to measure the data or inappropriate treatment of theory in the near-critical region . Further theoretical and experimental studies show that the criticality in electrolyte solution is still Ising-like. , A direct explanation is that Debye screening of ions gives an effective short-range interaction. In the near-critical region, charge and density fluctuations of long wavelengths are of primary importance.…”