Langmuir monolayers: structures and phase transitions

Abstract

This paper briefly reviews information recently obtained from grazing incidence X-ray diffraction studies of the structures of the several phases in the high-surface-density region of an amphiphile monolayer on water. We also present a new theory, based on a density functional formalism, for the transition between untilted (hexagonal) and tilted (distorted hexagonal) phases in these monolayers. We find that in the region from 0 to ca. 0.5 rad tilt angle the tilted states are thermodynamically more stable (ca. 0.2–2.0 k_BT per segment lower in free energy) than the untilted state, so that the monolayer, when expanded, always adopts the value of tilt angle determined by the area per molecule. Eventually, for large tilt, say e.g. > 0.6 rad, the chemical potential of the monolayer increases as the tilt increases. There is, then, a minimum of the free energy versus tilt angle for which the constraint derived from the area per molecule is effectively relieved. We find that an incompressible monolayer has a small change in average density and a large change in area per molecule across the transition. Conversely, a monolayer with large compressibility has a large density change and a small change in area per molecule across the transition. Our analysis correctly reproduces the principal features of the observed phase transitions. We speculate on the nature of ‘island phases’ and the relation of these to the close-packed phases of the monolayer.