Correct Phase-Diagrams of Liquid-Crystals Reported To Exhibit the (Nonexistent) Incommensurate Smectic-A Phases

Three different incommensurate phases predicted by the phenomenological theory of frustrated smectics were reportedly found in mixtures of DB80CN and 80BCAB and DB,OCN and 80CB. The results of our high-resolution X-ray diffraction study of these materials show that these phases are, indeed, coexistences of two or more smectic-A phases. The correct phase diagrams of the two systems are found to be in excellent agreement with the phenomenological models. At this time, there remain no known materials that exhibit an incommensurate smectic-A phase. Materials with a large electric-dipole moment along the long molecular axis have been known [ 1,2] to exhibit rich smectic-A polymorphism. Phenomenological theories [3-61 have been remarkably successful in understanding the formation of nearly ten frustrated smectic liquid-crystal phases. These theories invoke two order parameters to account for the two density modulations that exist in these phases. One of the density modulations results from the layered structure of the smectic phases, while the second one arises from the dipole pairing of the molecules. A large number of smectic-A phases are naturally predicted on the basis of relative amplitudes and periodicities of the two modulations and the directions of corresponding wave vectors relative to each other. In the simplest monolayer smectic-A, (A,) phase, there is no significant dipole pairing and the layer spacing, d, is equal to the molecular length 1. The bilayer smectic-A2 (A2) phase, with two modulations of periodicities 1 and 21, is formed when antiparallel molecules form pairs of length 21. However, if the molecules form pairs with a significant length-wise overlap, the partial bilayer smectic-Ad (Ad) phase with layer spacings of 1’ and 21’(1 < 21’ < 21) is formed. Three incommnsumte smectic-A phases were also predicted [3-61. The wave vectors of the two density modulations in these phases are collinear but incommensurate, i.e. the ratio of their wave numbers is not a rational fraction. The incommensurate smectic-Ail (Ai1) and smectic-Aiz (Aiz) phases form when the order parameter coupling is weak. In the Ail and Ai2 phases, molecular orderings similar to the AI and Ad and the Az and Ad phases, respectively, 136 EUROPHYSICS LETTERS interpenetrate on the microscopic scale. In the strong-coupling limit, lock-in regions similar to the A2 phase are separated by soliton regions in which the two modulations are out of phase with each other. This is known as the incommensurate soliton or Ai, phase. The binary mixtures of (A) 4-n-octyloxyphenyl-4'-cyanobenzoyloxybenzoate (DB80CN) and 4-n-octyloxybenzoate-4'-cyanoazobenzene (80BCAB) were reported [7] to exhibit all three incommensurate phases. Dotted lines in fig. la) represent the phase diagram reported in ref.[7]. The positions of X-ray diffraction peaks and their temperature dependence in these incommensurate phases were, apparently, in accordance with the theory. The Ai, phase gave rise to diffraction peaks at 2q0, q f f , and q s ( = 2q0 q"), in excellent agreement with the theory. A second system (B), mixtures of 4-n-heptyloxyphenyl-4'-cyanobenzoyloxybenzoate (DB,OCN) and 4-octyloxy-4'-cyanobiphenyl (80CB), had also been reported [8,9] to exhibit the Ai2 phase. The phase diagram calculated for this system from an extension[lO] of the original phenomenological model[5] was strikingly similar to that obtained experimentally [SI. Very recently, we have applied high-resolution X-ray diffraction to further investigate the structure of these phases. Our results have revealed[ll] that the Ail and Ai, phases of system A are coexistences of the Ad and A I and the A d , A I , and A2 phases, respectively. The Ai2 phase of system B was found [12] to be a coexistence of the Ad and A2 phases. Here, we present evidence that the Ai2 phase of system A is also a coexistence of the Ad and A2 phases.