Effects of counterion size on the attraction between similarly charged surfaces

Interaction between similarly charged surfaces can be attractive at high electrostatic coupling constants Xi = l(B)Z(2)/mu GC, where l(B) is the Bjerrum length, mu GC the Gouy-Chapman length, and Z the valency of counterions. While this effect has been studied previously in detail, as a function of surface charge density and valency of the pointlike counterions, much less is known about the effect of counterion size. We apply the Wang-Landau sampling Monte Carlo (MC) simulation method to compute the free energy F as a function of the scaled distance between the plates (D) over tilde = D/mu GC for a range of Xi and scaled counterion radii (R) over tilde = R/mu GC. We find that for large Xi and small ion radius, there is a global equilibrium distance (D) over tilde = (D) over tilde (eq) = 2(1 + (R) over tilde), correctly giving the expected value at the point counterion limit. With increasing (R) over tilde the global minimum in F((D) over tilde) changes to a metastable state and finally this minimum vanishes when (R) over tilde reaches a critical value, which depends on Xi. We present a state diagram indicating approximate boundaries between these three regimes. The Wang-Landau MC method, as it is applied here, offers a possibility to study a wide spectrum of extended problems, which cannot be treated by the use of contact value theorem. (C) 2010 American Institute of Physics. [doi:10.1063/1.3506896]