Statistical thermodynamics of curvature elasticity in surfactant monolayer films: A molecular approach

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Abstract
A statistical thermodynamictheory is developed to study curvature elastic properties of self‐assembled monolayer films formed by nonionic surfactants at the interface between water and oil domains in microemulsions. A mean‐field approximation to the conformational entropy is obtained by sequential placement of chain segments on a lattice, such that bond‐correlated excluded volume effects are properly incorporated. The resulting free energy is minimized at zero lateral (osmotic) pressure with respect to a set of layer‐ and orientation‐dependent statistical weights, from which the splay and Gaussian bending elastic moduli, spontaneous curvature, molecular area, and chain segment distributions are predicted. Calculations are reported for monolayers comprised of a single surfactant and for mixtures of surfactants of different lengths and stiffness. We examine the origins of the significant differences between our predictions and those of Szleifer et al. In particular, for self‐assembledmonolayers, we find that the bending moduli of mixtures of chains of different lengths are not lower than those of a single‐component monolayer with a surfactant of corresponding number‐average length. The approach to long‐chain behavior of the elastic moduli is predicted to occur for chains much longer than those normally used experimentally as nonionic surfactants. However, extrapolation of our predictions to this limit yields power‐law exponents very similar to those predicted by Wang and Safran.