Modes of counterion density fluctuations and counterion-mediated attractions between like-charged fluid membranes

Counterion-mediated attractions between like-charged fluid membranes are long ranged and nonpairwise additive at high temperatures. At low temperatures, however. they are pairwise additive, and decay exponentially with the membrane separation. Using a simple model for the electrostatic attraction between like-charged surfaces, we show that the nature of these attractions is determined by the dominant modes of fluctuations in the density of counterions. While the nonpairwise additive interactions arise from long-wavelength fluctuations and vanish at zero temperature, the short-ranged pairwise additive interactions arise from short-wavelength fluctuations and are stronger at low temperatures.