A MOLECULAR-MODEL FOR TILTING PHASE-TRANSITIONS BETWEEN CONDENSED PHASES OF LANGMUIR MONOLAYERS

A model of interacting rigid rods is proposed to describe tilting phase transitions in monolayers of freely rotating long-chain molecules with hexatic in-plane order. The model takes into account steric repulsion and van der Waals attraction between neighboring rods as well as the orientational entropy of individual rods, all within a mean field approximation limited to the unit cell. Two variants of the model are proposed, with different constraints on the polar molecular headgroups. In the first, the headgroups are grafted to a hexagonal close-packed (hcp) lattice, and in the second, the headgroup lattice deforms to accommodate to the tilt. For the monolayer on a solid substrate, tilt has two opposing actions on the internal energy. The decrease in the distance between rods acts to reduce the interaction energy, while the decrease in the overlapping length of the rods acts to increase it. As the area per molecule increases, the competition between these two effects drives the first-order phase transition U (untilted molecules) --> NNN (collective tilt of the molecules in the direction of the next-nearest neighbor). This transition is present for both the fixed and the deformable lattices. For the monolayer on the water surface, the molecular tilt is accompanied by an increasing contact of the polar heads with the water. In this case, the effective interaction potential appears to be temperature dependent and under some circumstances can result in the first-order phase transition being replaced by a second-order one (U --> NN) with the collective tilt in the direction of the nearest neighbor. The results obtained with the help of this model are compared with computer simulations and with experiment.