Packing of hydrocarbon chains and symmetry of condensed phases in Langmuir monolayers

We compare the packing characteristics of alkyl chains in Langmuir monolayers of nonchiral and racemic compounds as determined from available grazing incidence X-ray diffraction data. The analysis demonstrates a gradual change of the projected unit cell dimensions from those of a hexagonal packing of hydrocarbon chains, characteristic of high-temperature monolayer phases, to one of two more dense rectangular packing modes with the projected unit cell dimensions 5.0 x 7.5 Angstrom(2) and 4.4 x 8.7 Angstrom(2), characteristic of low-temperature phases. The 5.0 x 7.5 Angstrom(2) unit cell incorporates the well-known herringbone arrangement, with an ideally 90 degrees dihedral angle between the planes of carbon backbone chains. The 4.4 x 8.7 Angstrom(2) cell, almost never observed in 3D structures, is characterized by a 40 degrees dihedral angle. We characterize the packing modes by lattice energy calculations. The distribution of the projected unit cell dimensions for the various Langmuir monolayers reveals no discontinuity in the local molecular order between crystalline phases and mesophases. The local symmetry of the molecular packing, as determined from the X-ray data, is compared with the symmetry deduced from the Landau theory of phase transitions. The symmetry of the local order in the mesophases is not maintained on the long-range length scale. We show that two phases of the same local molecular arrangement, a herringbone-ordered two-dimensional crystal and the corresponding one-dimensional mesophase, possess mutually orthogonal directions of glide symmetry.