Smectic A-nematic phase transition

Garland C W and Nounesis G 1994 Critical behavior at nematic-smectic-A phase transitions Phys. Rev. E 49 2964-71... 

The Maier-Saupe tlieory was developed to account for ordering in tlie smectic A phase by McMillan [71]. He allowed for tlie coupling of orientational order to tlie translational order, by introducing a translational order parameter which depends on an ensemble average of tlie first haniionic of tlie density modulation noniial to tlie layers as well as / i. This model can account for botli first- and second-order nematic-smectic A phase transitions, as observed experimentally. 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

In the framework of irreversible thermodynamics (compare, for example, [31, 32]) the macroscopic variables of a system can be divided into those due to conservation laws (here mass density p, momentum density g = pv with the velocity field v and energy density e) and those reflecting a spontaneously broken continuous symmetry (here the layer displacement u characterizes the broken translational symmetry parallel to the layer normal). For a smectic A liquid crystal the director h of the underlying nematic order is assumed to be parallel to the layer normal p. So far, only in the vicinity of a nematic-smectic A phase transition has a finite angle between h and p been shown to be of physical interest [33],... 

To extract concrete predictions for experimental parameters from our calculations is a non-trivial task, because neither the energetic constant B nor the rotational viscosity yi are used for the hydrodynamic description of the smectic A phase (but play an important role in our model). Therefore, we rely here on measurements in the vicinity of the nematic-smectic A phase transition. Measurements on LMW liquid crystals made by Litster [33] in the vicinity of the nematic-smectic A transition indicate that B is approximately one order of magnitude less than Bo. As for j we could not find any measurements which would allow an estimate of its value in the smectic A phase. In the nematic phase y increases drastically towards the nematic-smectic A transition (see, e.g., [51]). Numerical simulations on a molecular scale are also a promising approach to determine these constants [52],... 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model... 

Bouwman W G and de Jeu W H 1992 3D XY behavior of a nematic-smectic A phase transition confirmation of the de Gennes model Phys.Rev.Lett 68 800-3... 

Garland, C.W. and Noimesis, G. (1994) Critical Behavior of the Nematic-Smectic A Phase Transitions. Physical Review E, 49,2964-2971. 

Garland CW, Nounesis G (1994) Critical-behavior at nematic smectic - a phase-transitions. Phys Rev E 49 2964-2971... 

Kss axe found [6.28] to diverge in the nematic phase as the temperature approaches a nematic-smectic A phase transition. In cholesteric phases, all deformations are allowed, but Kss is larger than 22-... 

The nematic-smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is the simplest example of a phase transition characterized by translational order. Experiments indicate that it can be first order or more usually continuous, depending on the range of stability of the nematic phase. The critical behaviour that results from a continuous transition is fascinating and allows a test of predictions of the advanced theories for critical phenomena, in an accessible experimental system. In fact, this transition is analogous to the transition from a normal conductor to a superconductor, but is more readily studied in the liquid crystal system. 

High-resolution x-ray scattering and heat capacity experiments have been used to investigate the critical behaviour near the nematic-smectic A phase transition. 

It is also possible to use turbidity measurements to evaluate elastic constants (Fig. 5, though elastic constants measured in this way for alkylcyanobiphenyls (nCBs) [25] and mixtures [26] are consistently higher than those determined by Frederiks transition studies. Hakemi [27] measured j, 22 and 33 for 8CB (octylcyano biphenyl) close to the nematic-smectic A phase transition and deduced a value of the critical exponent from the divergence of 22 and 33. 

In a recent work, isotropic-nematic-smectic A phase transitions in thermotropic liquid crystals were also induced by applying an electric field [140]. The liquid crystal investigated (a mixture of 8CB and lOCB) showed a first order isotropic to smectic A transition. When in the isotropic phase and near the spontaneous transition temperature, a field-induced first order transition was observed from a paranematic to a nonspontaneous nematic phase. For higher values of the applied electric field, another first order transition occurred from the nonspontaneous nematic to a phase exhibiting the same order as a smectic A phase. A phenomenological Landau-de Gennes model has been developed to describe these transitions [141],... 

S. Sprunt, L. Solomon, J. D. Litster, Equality of X-ray and light scattering measurements of coherence lengths at the nematic-smectic-A phase transition, Phys. Rev. Lett. 1984, 53, 1923. 

W. Doane, S. Parker, B. Cvilk, D. L. Johnson, and D. L. Fishel, Possible Second-Order Nematic-Smectic-A Phase Transition, Phys. Rev. Lett., 28, p. 1694 (1972). 

Martinoty P, GaUani J, Collin D (1998) Hydrodynamic and nonhydrodynamic behavior of layer-compression modulus B at the nematic-smectic- A phase transition in 80CB. Phys Rev Lett 81 144... 

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