MOLECULAR ORIENTATIONAL VIBRATIONS IN MONOLAYER SYSTEMS

Elementary excitations in dense (solid-phase) monolayer systems-molecu lar orientational vibrational modes-are studied. The hydrophilic heads of the amphiphilic molecules are assumed to be fixed and form a certa in lattice, and the hydrophobic alkane chains are modeled as rigid rod s that can rotate freely around the fixed heads. Both a simple one-dim ensional chain and a two-dimensional model are investigated. The molec ular orientational vibrational modes show a universal, unusual frequen cy gap at k=0 except at the upright-tilted phase transition point. Thi s frequency gap is explained by a lack of ''translational'' symmetry i n these oscillator systems. The disappearing of this frequency gap, wh ich indicates softening of the vibrational mode, is responsible for th e upright-tilted phase transition. An analytical method capable of cal culating a wide range of physical quantities, such as the tilt angle, the orientational correlation function, and the specific heat, has bee n worked out accompanying the exploration of the molecular orientation al vibrational modes. The results agree with those from the Monte Carl o simulation well.