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 non-pairwise additive at high temperatures. At zero temperature, however, they are pairwise additive and decay exponentially with the membrane separation. Here we show that the nature of these attractions is determined by the dominant modes of fluctuations in the density of counterions. While the non-pairwise 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. 
Bae-Yeun Ha (SFU)