Phase transitions in liquid crystals

7 PHASE TRANSITIONS IN LIQUID CRYSTALS 5.7.1 Nematic-Smectic a Transition 

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. 

When a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These pretransitional fluctuations were called cybotactic clusters in the early literature (Fig. 5.21). Regardless of a physical picture of such fluctuations, it has been observed that the cluster size grows as the transition is approached. Furthermore, these clusters are anisotropic, being elongated along the director. They also grow faster along this direction as the transition is approached from above. 

One of the most important theories for the nematic-smectic A phase transition is the Landau-de Gennes model. Another is the McMillan model, which was discussed in Section 5.5.2. The Landau-de Gennes theory is applied in the case of a second-order phase transition by combining a Landau expansion (Section 1.5) for the free energy in terms of an order parameter for smectic layering with the elastic energy of the nematic phase (Eq. 5.19). A suitable order parameter for the smectic structure allows both for the layer periodicity and the fluctuations of layer position (r)  

Using this order parameter, the free energy density in the nematic phase close to a transition to the smectic phase can be shown to be given by 

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Barois P 1992 Phase transitions in liquid orystals introduotion to phase transition theories Phase Transitions In Liquid Crystals ed S Martelluooi and A N Chester (New York Plenum)... 

For some recent reviews, see (a) De Jeu WFi (1992) In Martelucci S, Chester AN (eds) Phase transitions in liquid crystals. Plenum Press, New York, chaps 1-3 (b) Osipov MA (1998) In Goodby J, Demus D (eds) Handbook of liquid crystals, 2nd edn, Wiley-VCH, Berlin... 

Image Amplification by Means of Photochemically Triggered Phase Transition in Liquid Crystal... 

V. Molinier, P. J. J. Kouwer, Y. Queneau, J. Fitremann, G. Mackenzie, and J. W. Goodby, A bilayer to monolayer phase transition in liquid crystal glycolipids, J. Chem. Soc., Chem. Commun. (2003) 2860-2861. 

S. Kurihara, T. Ikeda, and S. Tazuke, Photochemically induced isothermal phase transition in liquid crystals. Effect of interaction of photoresponsive molecules with matrix mesogens, Mol. Cryst. Liq. Cryst. 178, 117-132(1990). 

PHOTOREACTIONS INDUCING PHASE TRANSITION IN LIQUID CRYSTALS... 

Photoinduced Phase Transition in Liquid Crystals (S. Tazuke and S. Kurihara)... 

One of the most active areas of research in the statistical mechanics of interfacial systems in recent years has been the problem of freezing. The principal source of progress in this field has been the application of the classical density-functional theories (for a review of the fundamentals in these methods, see, for example, Evans ). For atomic fluids, such apphcations were pioneered by Ramakrishnan and Yussouff and subsequently by Haymet and Oxtoby and others (see, for example, Baret et al. ). Of course, such theories can also be applied to the vapor-liquid interface as well as to problems such as phase transitions in liquid crystals. Density-functional theories for these latter systems have not so far involved use of interaction site models for the intermolecular forces. 

K. L. Savithramma, in Theoretical studies on order and phase transitions in Liquid Crystals , thesis, Mysore University, India (1982). 

Are all quantitative predictions of the thermodynamics of liquid crystals correct. If not stop here. The reason for this step is that die theory (Flory-Huggins lattice model) also predicts the occurrence of the isotropic to nematic phase transition in liquid crystals. If the theory had predicted correctly the properties of glasses but had failed for liquid crystals we would have had to abandon it, especially since in both cases the cause of the transition is ascribed to the vanishing of the configurational entropy. Alternatively the correctness of the prediction for liquid crystals argues for the correctness of the prediction for glasses. Since we have not been stopped by steps 3 and 4 we proceed to step 5. 

Cladis, P.E. Re-entrant phase transitions in liquid crystals. In Demus, D., Goodby, J., Gray, G.W., Spiess, H.-W., Vill, V. (eds.) Physical Properties of Liquid Crystals, pp. 289-303. Wiley-VCH, Weinheim (1999)... 

Martelucci, S. and Chester, A.N. (eds) (1992) Phase Transitions in Liquid Crystals (New York Plenum Press). 

The observed nonlinearity mechanism can be used hereafter to investigate the effect of impurities on the character of phase transitions in liquid crystals, inasmuch as the experiments afford a unique possibility of controlling the impurity density. To realize such investigations it is necessary to explain the form of the photoconformation transformations of mesogenic molecules. Once the intermolecular order parameter responsible for the change of the refractive index is determined, dynamic holography methods can be... 

R. Shashidhar, in Phase Transitions in Liquid Crystals, S. Martellucci and A. N. Chester, eds., Plenum Press, New York, London, 1992, p. 245. 

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