The Nematic-Smectic A Transition

The liquid-crystal transition between smectic-A and nematic for some systems is an AT transition. Depending on the value of the MacMillan ratio, the ratio of the temperature of the smectic-A-nematic transition to that of the nematic-isotropic transition (which is Ising), the behaviour of such systems varies continuously from a k-type transition to a tricritical one (see section A2.5.91. Garland and Nounesis [34] reviewed these systems in 1994. 

Fig. 10. The dependence of the transition temperatures on the number of carbon atoms, m, in the terminal chains for the m.040.m series [37]. Melting points are denoted by O, indicates nematic-isotropic transitions, smectic A-isotropic transitions, 0 the smectic C-isotropic transition, the smectic A-nematic transition, A smectic B-smectic A transitions, + smectic F-smectic A transitions, x smectic F-smectic C transitions and A smectic C-smectic A transitions. Cr Crystal SmA smectic A N nematic SmB smectic B I isotropic SmF smectic F SmC smectic C...

Fig. 5.2.8. Temperature dependence of the orientational order parameter s determined by quadrupolar splitting measurements for CBOOA. The inset shows the discontinuity in slope at the smectic A-nematic transition. (After...

Sied, M.B. Lopez, D.O. Tamarit, J.L.I. Bario, M. Liquid crystal binary mixtures 8CB + 80CB Critical behaviour at the smectic a—nematic transition. Liq. Cryst. 2002,29,57-66. 

The Landau-de Gennes theory for the nematic isotropic transition can be extended to the smectic A-nematic transition. The order parameter for this transition is rl), the amplitude of the density wave describing the formation of layers in the smectic A phase. Since the difference between a value of rlr and -Irlrl only amonnts to a shift of one half layer spacing in the location of all the layers (and therefore no change in the free energy per nnit volume), the expansion in terms of powers of rlr can only contain even powers. Hence the free energy per unit volume in the smectic A phase can be written as... 

The Maier-Saupe theory can also be extended to describe the smectic A-nematic transition in what is called McMillan s model. Two order parameters are introduced into the mean-field potential energy function, the usual orientational order parameter S and an order parameter a related to the amplitude of the density wave describing the smectic A layers,... 

In the McMillan model, the smectic A-nematic transition can be continuous or discontinuous. If a is less than 0.7, then o decreases to zero continuously and S is continuous at the smectic A- nematic transition. If a is between 0.7 and 0.98, then a jumps to zero discontinuously and S has a small discontinuity at the smectic A-nematic transition. When a is greater than 0.98, the smectic phase transforms directly into the isotropic phase with discontinuities in both order parameters. So just as in the extended Landau-de Geimes theory for the smectic A phase, a tricritical point is predicted at a=0.7, which corresponds to a ratio in the smectic A—nematic transition temperature to the nematic-isotropic transition temperature of 0.87. A great deal of experimental work has been done on the smectic A-nematic transition, and the results seem to indicate that the tricritical point occurs when the ratio of the two transition temperatures is significantly larger than 0.87. 

H. Birecki, R. Schaetzing, F. Rondelez, J. D. Litster, Light scattering of a Smectic-A phase near the Smectic-A-Nematic transition, Phys. Rev. Lett. 1976, 36, 1376-1379. 

In some compounds (usually the lower members of a homologous series), the transition to the Nd phase takes place directly from the crystal, while in others (the higher members of the series) it takes place via a columnar phase (Table 2) [31, 32]. The trend is somewhat analogous to the behaviour of the smectic A-nematic transition for a homologous series, and as will be discussed in Sec. 3 this trend can be explained by an extension of the McMillan model of the A-N transition to systems of discotic molecules. There is also X-ray evidence of skew cybotactic groups in the Np phase prior to the transition to the D, phase, very much like the situation seen near a nematic-smectic C transition [34]. 

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