Smectic A and

In the smectic-A phase the molecules are oriented on average in a direction perpendicular to the layers, whereas in the smectic-C phase the director is tilted with respect to the layer normal. The tilted smectic-C phase has been compared to superfluid helium, and the smectic A-smectic C transition is predicted to exhibit critical behavior similar to that of helium. 

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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. 

Detailed x-ray diffraction studies on polar liquid crystals have demonstrated tire existence of multiple smectic A and smectic C phases [M, 15 and 16]. The first evidence for a smectic A-smectic A phase transition was provided by tire optical microscopy observations of Sigaud etal [17] on binary mixtures of two smectogens. Different stmctures exist due to tire competing effects of dipolar interactions (which can lead to alternating head-tail or interdigitated stmctures) and steric effects (which lead to a layer period equal to tire molecular lengtli). These... 

Leadbetter A J 1979 Structural studies of nematic, smectic A and smectic C phases The Moiecuiar Physics of Liquid Crystais ed G R Luckhurst and G W Gray (London Academic)... 

Thermotropic liquid-crystalline properties of different metal alkanesulfonates are studied by microscopy and X-ray diffraction [59]. Sodium soaps show smectic polymorphism of smectic A and smectic B phases. Ammonium soaps only show smectic A phases but polymorphism in the crystalline state. Calcium soaps show columnar mesophases. In Figs. 32 and 33 some textures and x-ray diffraction patterns are depicted. 

The distribution of the intermolecular vector is also of value in distinguishing between smectic A and smectic B phases with the latter having long range bond orientational order [23, 24]. At the local level we can define a bond orientational order parameter, PeCn) for molecule i at position q by [25]... 

Fig. 8. The distance dependence of the bond orientational correlation function gs (r ) found for the mesogen GB(4.4, 20.0, 1, 1) in the smectic A (.) and the smectic B (—) phases...

The dimer model proposed by Wilson [83] was found not to exhibit a nematic phase but smectic A and B phases and so, although semi-realistic features are included, the model is not able to reproduce the behaviour of real dimers such as the a,co-bis(4 -cyanobiphenyl-4-yloxy) [87], which exhibit nematic phases, although liquid crystal dimers exhibiting smectic phases are also known [88]. In these simulations, the GB-GB interaction appears to be too strong and so the system forms a smectic phase in which the GB and LJ units... 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

Smectic A and smectic C mesophases characterised by anti-parallel (SmA2, SmAj, and SmC2, SmCj) and random (SmAi and SmCi) alignments of the molecular dipoles within the layer thickness in Fig. 10. 

Note 3 Two TGBA structures are possible in one, the number of blocks corresponding to a rotation of the layer normal by 2ti is an integer, while in the other, it is a non-integer. Note 4 A TGBA is found in a phase diagram between smectic A and chiral nematic mesophases or between a smectic A mesophase and an isotropic phase. 

On passing from the least ordered smectic A phase down to the more ordered crystal H and K phases the layer planes tend to sharpen up. In the smectic A and C phases the layers are therefore very diffuse, and can be thought of as one-dimensional density waves relative to the director. Thus, locally these two phases are very similar in structure to the nematic phase. 

The smectic state, apart from exhibiting a rich variety of modifications, is also thermodynamically ordered. Thus, there is a well-defined sequence of phases formed on cooling from the isotropic liquid. For instance, the following transition sequence would be observed for a ferrocene liquid crystal exhibiting enantiotropic smectic C, smectic A and nematic phases ... 

Within a smectic layer, a state of order called hexatic can exist that is intermediate between the liquid order of the smectic A, and the crystalline order of crystalhne smectic B. This state of order characterizes the hexatic smectic-B phase. Flexatic order consists of long-range bond orientational order, but no long-range positional order. This is illustrated... 

Fig. 10 Schematic of the molecular packing arrangement in the smectic A and smectic C phases of a dendron, 14, based on the 4-alkoxy-4 -cyanbiphenyl moiety...

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