Screening in Ionic Systems: Simulations for the Lebowitz Length

Abstract

Simulations of the Lebowitz length, $ξ_{\text{L}}(T,ρ)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $ρ\lesssim 4ρ_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $ξ_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $ρ> {1/10}ρ_c$ (with $ρ_c a^3 \simeq 0.08$). At highe r densities $ξ_{\text{L}}$ rises above the Debye length, $ξ_{\text{D}} \prop to \sqrt{T/ρ}$, by 10-30% (upto $ρ\simeq 1.3ρ_c$); the variation is portrayed fairly well by generalized Debye-Hückel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $ρ$ or fixed $T$, $ξ_{\text{L}}(T, ρ)$ remains finite with $ξ_{\text{L}}^c \simeq 0.30 a \simeq 1.3 ξ_{\text {D}}^c$ but displays a weak entropy-like singularity.