Modulated structures in Langmuir monolayers and in smectic films

Modulated structures have been observed in nonchiral systems such as Langmuir monolayers and freely suspended smectic films, and a mechanism involving spontaneous chiral symmetry breaking has recently been suggested to account for the occurrence of these structures. We study a simple model corresponding to this mechanism in the mean-field approximation. We find that the model exhibits two uniaxially modulated phases (the director field is colinear or noncolinear) and a vortex-lattice phase, in addition to the two uniform ordered phases (one chiral and one nonchiral) and the disordered phase. The high-temperature transition from the uniform nonchiral phase to the noncolinear uniaxial phase is found to be of third order; it belongs to a peculiar, intermediate class of transitions that has previously been suggested to occur in chiral systems. The low-temperature transition from the noncolinear uniaxial phase to the uniform chiral phase is second order, but also peculiar, because the wave number vanishes linearly at the transition; the modulated phase just above the transition is best described as a spatially varying commensurate phase with walls. {} 1996 The American Physical Society.