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RENORMALIZATION GROUP TREATMENT OF ENTROPIC INTERACTIONS IN LAMELLAR PHASES

Abstract
Functional renormalization group is applied to study entropic interactions in lamellar phases consisting in a stack of tensionless fluid membranes. This approach allows to recover Helfrich's formula for the steric free energy of a layer per unit area f(d) = c_∞(k_BT)²/κd² (where d is the mean distance between layers) and to estimate analytically the universal coefficient c_∞. Our estimate c_∞ .0810 is much closer to the estimates extracted from Monte Carlo simulations c_∞ ≈ .106 than to the original estimate of Helfrich c_∞ = 3π² / 128.