COMMENT ON THE TILTING TRANSITION IN LANGMUIR MONOLAYERS

We report a calculation of the free energy difference between a reference monolayer, in which the amphiphile molecules are vertical and arranged in a hexagonal lattice, and the derivative monolayer, in which the amphiphile molecules are tilted and arranged in a distorted hexagonal lattice. For the case that the interaction between amphiphile molecules, and that between an amphiphile molecule and the surface, are described by a Lennard-Jones interaction per unit length, it is found that a tilted state of the monolayer is stable only if the ratio of the amphiphile chain-surface to amphiphile chain-amphiphile chain interactions exceeds a critical value. When the area per molecule and temperature are the same, a monolayer with molecules tilting toward their nearest neighbors has a larger tilt angle and lower free energy than a monolayer with molecules tilting between the nearest neighbors.