3-POINT EXTENSION HYPERNETTED CHAIN, CONVENTIONAL HYPERNETTED CHAIN, AND SUPERPOSITION APPROXIMATIONS - NUMERICAL RESULTS FOR THE FORCE BETWEEN 2 PLATES

The conventional hypernetted chain/mean spherical (HNC/MS) equation and a superposition approximation to the Born-Green-Yvon (BGY) equation are derived and numerically solved for the force between two charged plates immersed in a primitive model electrolyte or a point-ion electrolyte. The results are compared to the force calculated through the three-point extension to the HNC/MS approximation. The force between two hard plates, immersed in a hard-sphere fluid, is also calculated with these three theories. Excellent agreement is found among the three theories for the force between two hard uncharged plates. For charged plates, the agreement goes from good to total disagreement, depending on the plate potential and/or electrolyte concentration. While the three theories predict attractions between the plates, the conventional HNC/MS and BGY equations predict a nonexistent attraction at low electrolyte concentration. The corresponding conventional method and superposition approximation method calculations of the force between two plates immersed in a point-ion solution are in surprisingly good agreement with the Verwey-Overbeek results, when the potential on the plates is low,and/or the electrolyte concentration is high. © 1990 American Institute of Physics.