Screening in Ionic Systems: Simulations for the Lebowitz Length

Abstract

Simulations of the Lebowitz length, ${\xi }_{\text{L}}(T,\rho )$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $\rho \lesssim 4{\rho }_c$ 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 ${\xi }_{\text{L}}$. 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 $\rho >1/10{\rho }_c$ (with ${\rho }_c{a}^3\simeq 0.08$). At highe r densities ${\xi }_{\text{L}}$ rises above the Debye length, $ξ_{\text{D}} \prop to \sqrt{T/ρ}$, by 10-30% (upto $\rho \simeq 1.3{\rho }_c$); the variation is portrayed fairly well by generalized Debye-Hückel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $\rho$ or fixed $T$, ${\xi }_{\text{L}}(T,\rho )$ remains finite with ${\xi }_{\text{L}}^c\simeq 0.30a\simeq 1.3{\xi }_{\text{D}}^c$ but displays a weak entropy-like singularity.

4 pages 5 figures

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