Smectic A phases

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

The smectic A phase is a liquid in two dimensions, i.e. in tire layer planes, but behaves elastically as a solid in the remaining direction. However, tme long-range order in tliis one-dimensional solid is suppressed by logaritlimic growth of tliennal layer fluctuations, an effect known as tire Landau-Peierls instability [H, 12 and 13]... 

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... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

Figure C2.2.9. Polygonal domains of focal conics in a smectic A phase confined between parallel plates.

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. 

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

The nematic to smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is tire simplest example of a phase transition characterized by tire development of translational order [88]. Experiments indicate tliat tire transition can be first order or, more usually, continuous, depending on tire range of stability of tire nematic phase. In addition, tire critical behaviour tliat results from a continuous transition is fascinating and allows a test of predictions of tire renonnalization group tlieory in an accessible experimental system. In fact, this transition is analogous to tire transition from a nonnal conductor to a superconductor [89], but is more readily studied in tire liquid crystal system. 

Wlren a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These fluctuations were called cybotactic clusters in tire early literature. Regardless of tire physical picture of such fluctuations. 

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] ... 

McMillan W L 1971 Simple molecular model for the smectic A phase of liquid crystals Phys.Rev A 4 1238-46... 

Flard spherocylinders (cylinders witli hemispherical end caps) were studied using computer simulations [118]. In addition to a nematic phase, such particles also display a smectic-A phase, in which tire particles are arranged in liquid-like layers. To observe tliis transition, ratlier monodisperse particles are needed. The smectic-A phase was indeed observed in suspensions of TMV particles [17]. 

The positional order of the molecules within the smectic layers disappears when the smectic B phase is heated to the smectic A phase. Likewise, the one-dimensional positional order of the smectic M phase is lost in the transition to the nematic phase. AH of the transitions given in this example are reversible upon heating and cooling they are therefore enantiotropic. When a given Hquid crystal phase can only be obtained by changing the temperature in one direction (ie, the mesophase occurs below the soHd to isotropic Hquid transition due to supercooling), then it is monotropic. An example of this is the smectic A phase of cholesteryl nonanoate [1182-66-7] (4), which occurs only if the chiral nematic phase is cooled (21). The transitions are aH reversible as long as crystals of the soHd phase do not form. 

No coherent threadline could be maintained and the extmdate flew off the windup as short, brittle, crystalline lengths. Not until many years later did other workers show that this polymer on cooling exhibits a mesophase transition directly from the isotropic melt to a smectic A phase. Good sources of information on Hquid crystals and Hquid crystal polymers are available (212—216). 

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. 

FIG. 32 Textures of Sodium Pentadecane 1-Sulfonate, (a), Crystalline phase at 80°C (b), smectic B phase at 113°C (c), smectic A phase at 250°C. Sample window 1.4 mm2, crossed Nicols. 

Fig. 7. Snapshots from a smectic-A phase of liquid crystal dimer molecules composed of two Gay-Berne mesogens linked by a flexible alkyl chain. Data from [112] supplied by Dr M R Wilson, University of Durham...

The two singlet distribution functions are not in themselves sufficient to characterise the order in a smectic A phase because there is, in general, a correlation between the position of a molecule in a smectic layer and its orientation. We need, therefore, the mixed singlet distribution function P(z,cos ) which gives the probability of finding a particle at position z and at an orientation P with respect to the director [18,19]. At the level of description provided by the order parameters it is necessary to introduce the mixed order parameter... 

Although the common nematic and smectic A phases have uniaxial symmetry, the molecules that form them are not cylindrically symmetric, although they... 

Fig. 19. A snapshot of a configuration showing a surface-induced smectic A phase near a smooth wall for the GB(3.0, 5.0, 2, 1) mesogen...

The nematic phase of all the compounds CBn is characterized by a coherence length of about 1.4 times the elongated structure of the molecule. Based on this behaviour local associations in form of dimers with cyano-phenyl interactions were postulated. For the smectic A phase a partial bilayer arrangement of the molecules (SAd) is most likely. But there are also example for the smectic A phase with a monolayer (Sai) or a bilayer (Sa2) arrangement of the molecules as well as a commensurate structure A large number of X-ray measurements were carried out in the liquid crystalline state to clear up the structural richness and variability (see Chap. 2, this Vol. [52]). 

Hartung and Rapthel [64] described the crystal structure of the mesogenic 2-methylthio-5-(4 -n-butyloxyphenyl)-pyrimidine which forms a monotropic smectic A phase. The chemical structure of this compound is presented in Fig. 5. The compound crystallises in the triclinic space group PI with two molecules per unit cell. The molecules adopt a fully stretched and nearly planar form. The pyrimidine ring is nearly planar. The dihedral angle between the phenyl and the pyrimidine rings is 22.7°. The molecules are arranged parallel to each other. 

C = crystalline phase N = nematic phase Sa = smectic A phase Sb = smectic B phase I = isotropic phase. 

Ito et al. [152] described the crystal structure of 4-[(S)-2-methylbutyl]phe-nyl 4 -hexylbiphenyl-4-carboxylate which shows a smectic A phase and a cholesteric phase. The molecules are arranged in a tilted smectic-like layer structure. Within the layers, the long molecular axes are tilted (30°). However, the compound exhibits no smectic C phase. 

An orthogonal layered structure in the solid state of rod-like molecules is the exception rather than the rule. Therefore, there is no conclusive evidence that a tilted layer structure in the solid state melts to a tilted smectic phase. In other words, if we consider the solid state as precursor for the type of the liquid crystalline state, no real precursor for an orthogonal fluid smectic phase would exist. As demonstrated in Fig. 19, the compound B-A for example exhibiting a smectic A phase has a tilted layer structure in the solid state. 

Smectic A and C phases are characterized by a translational order in one dimension and a liquid-like positional order in two others. In the smectic A phase the molecules are oriented on average in the direction perpendicular to the layers, whereas in the smectic C phase the director is tilted with respect to the layer normal. A simple model of the smectic A phase has been proposed by McMillan [8] and Kobayashi [9] by extending the Maier-Saupe approach for the case of one-dimensional density modulation. The corresponding mean field, single particle potential can be expanded in a Fourier series retaining only the leading term ... 

A lattice model of uniaxial smectics, formed by molecules with flexible tails, was recently suggested by Dowell [29]. It was shown that differences in the steric (hard-repulsive) packing of rigid cores and flexible tails - as a function of tail chain flexibility - can stabilize different types of smectic A phases. These results explain the fact that virtually all molecules that form smectic phases (with only a few exceptions [la, 4]) have one or more flexible tail chains. Furthermore, as the chain tails are shortened, the smectic phase disappears, replaced by the nematic phase (Fig. 1). 

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