The moment sum-rules for ionic liquids at criticality

TL;DR

This paper examines the behavior of charge-charge sum-rules in ionic liquids at criticality, highlighting the failure of the second-moment sum-rule and the validity of the fourth-moment sum-rule through theoretical discussion and simulation comparison.

Contribution

It provides a critical analysis of the sum-rule behaviors at criticality, especially explaining the failure of the second-moment sum-rule and the applicability of the fourth-moment sum-rule.

Findings

Second-moment sum-rule fails at criticality in symmetric ionic liquids.

Fourth-moment sum-rule remains valid at criticality.

Simulation results support the theoretical analysis.

Abstract

We discuss the first three well known moment charge-charge sum-rules for a general ionic liquid. For the special symmetric case of the Restricted Primitive Model, Das et al. [Phys. Rev. Lett. 107, 215701 (2011)] has recently discovered, through Monte Carlo simulations, that the Stillinger-Lovett or second-moment sum-rule fails at criticality. We critically discuss a possible explanation for this unexpected behavior. On the other hand the fourth-moment sum-rule turns out to be able to account for the results of the simulations at criticality.