[show abstract][hide abstract] ABSTRACT: Effective attraction between like-charged walls mediated by counterions is studied using local molecular field (LMF) theory. Monte Carlo simulations of the "mimic system" given by LMF theory, with short-ranged "Coulomb core" interactions in an effective single particle potential incorporating a mean-field average of the long-ranged Coulomb interactions, provide a direct test of the theory, and are in excellent agreement with more complex simulations of the full Coulomb system by Moreira and Netz [Eur. Phys. J. E 8, 33 (2002)]. A simple, generally applicable criterion to determine the consistency parameter sigma(min) needed for accurate use of the LMF theory is presented.
[show abstract][hide abstract] ABSTRACT: A simple model used to explore the interaction between like-charged macroions as mediated by intervening counterions is treated with local molecular field theory (LMF). LMF has recently been extended to general Coulombic systems by splitting the Coulomb potential 1/r into a short-ranged core that can be explicitly simulated and a long-ranged portion treated using a mean field approach; the potential separation is determined by a physically-relevant spacing parameter sigma. Here we show that LMF can treat the two-wall model system surprisingly well using an analytical Poisson-Boltzmann type technique. Also, combining self-consistent solution of LMF with simulation of the short-ranged core particles using the minimum image convention yields even more accurate results without using costly and complex Lekner or Ewald sums.
[show abstract][hide abstract] ABSTRACT: Structural and thermodynamic properties of ionic fluids are related to those of a simpler ``mimic'' system with short ranged intermolecular interactions in a spatially varying effective field by use of Local Molecular Field (LMF) theory, already successfully applied to nonuniform simple fluids. By consistently using the LMF approximation to describe only the slowly varying part of the Coulomb interaction, which we view as arising from a rigid Gaussian charge distribution with an appropriately chosen width $\sigma$, exceptionally accurate results can be found. In this paper we study a uniform system of charged hard spheres in a uniform neutralizing background, where these ideas can be presented in their simplest form. At low densities the LMF theory reduces to a generalized version of the Poisson-Boltzmann approximation, but the predicted structure factor satisfies the exact Stillinger-Lovett moment conditions, and with optimal choice of $\sigma$ the lowest order approximation remains accurate for much stronger couplings. At high density and strong couplings the pair correlation function in the uniform mimic system with short ranged interactions is very similar to that of the full ionic system. A simple analytic formula can then describe the difference in internal energy between the ionic system and the associated mimic system.