Attractions Between Like-Charged Walls Via Local Molecular Field Theory

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.