A two-dimensional gas of interacting electric dipoles with hard cores: Van der Waals isotherms and their possible application in lipid phase transitions

Abstract

We calculate the thermodynamic properties of a two-dimensional fluid of hard disks with embedded dipoles. Our attention is centered on the isotherms in the neighborhood of the critical point. Evaluating the canonical partition function by the "factor cluster expansion", we exhibit the Van der Waals loops obtained considering the exact two-body clusters and the "hard core" contribution of the three-body clusters. The Van der Waals isotherms can be scaled as universal functions of the parameter λ=p²/4πεr ³₀ kT, where p, r₀, ε, are the dipole moment, hard core radius, and permittivity which characterize the interaction. The model is applied to the lipid phase transition found in natural and synthetic membranes. The typical critical parameters (T_c≈300K, π_C≈50 dyne/cm) reflect a physically reasonable value for the dipole moment of a polar head group of a lipid but a much-too-small value for the hard core radius.