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 LxLxL with periodic boundary conditions are investigated. When Lambda is an LxL "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 , Wlambda_{Z} , and WL . 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, similar1.3rho_{c} and T greater, similar4T_{c} . The fitted values compare favorably with the expectations of generalized Debye-Hückel theory [Lee and Fisher, Europhys. Lett. 39, 611 (1997)]; specifically, if xi_{D} proportional, variant(Trho);{12} 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 approximately 1.9 times larger than predicted.
Kim
Young C
YC
Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Fisher
Michael E
ME