Free-Energy Increment of Multilayer Membrane System Due to Membrane–Membrane Interaction Potentials: Analysis Based on the Intermembrane Distance Distribution Function

Abstract

The free energy increment due to the membrane–membrane interaction potentials in a multilayer fluid membrane system is investigated. We propose an expression of the free energy increment Δ f per unit volume in terms of the intermembrane distance distribution function. The analytic expression of the intermembrane distance distribution function is derived by the Monte Carlo calculation. It is found that Δ f behaves as Δ f ρ4 for the low membrane density ρ for short-range interaction systems. For short-range repulsive interactions, we have a rigorous inequality Δ f < c4ρ4, where \(c_{4}\) is a positive constant. On the basis of the Δ f behavior, the universal and nonuniversal properties of the free energy of the membrane system are discussed.