Charge fluctuations and correlation lengths in finite electrolytes

Fluctuations of the charge Q(Lambda) inside a subdomain Lambda embedded in an electrolyte contained in a finite cubical box of dimensions L X L X L with periodic boundary conditions are investigated. When A is an L X L "slab" of width W, asymptotically exact expressions for the mean-square fluctuation < Q(Lambda)(2)> are obtained in terms of the Lebowitz length xi(L)(T,rho) and of the "true" or asymptotic screening/decay length xi(Z,infinity)(T,rho) together, when the charge correlation decay is oscillatory, with the characteristic wavelength lambda(Z)(T,rho). In finite systems, the normalized charge fluctuations exhibit threefold scaling behavior in the ratios xi(Z,infinity)/W, W/lambda(Z), and W/L. This enables one to estimate all the correlation lengths away from criticality quite precisely from finite-size grand canonical Monte Carlo simulations. The results for xi(Z,infinity), lambda(Z), and xi(L) are presented for the restricted primitive model or hard-sphere 1:1 electrolyte for densities rho less than or similar to 1.3 rho(c), and T greater than or similar to 4T(c). The fitted values compare favorably with the expectations of generalized Debye-Hijckel theory [Lee and Fisher, Europhys. Lett. 39, 611 (1997)]; specifically, if xi(D)alpha(T/rho)(1/2) is the Debye length, we find xi(Z,infinity) < xi(D)< xi(L), although, since ion-pairing is neglected, the charge oscillations set in only for densities similar to 1.9 times larger than predicted.