SmA Phase

In the smectic Aj (SmA ) phase, tlie molecules point up or down at random. Thus, tire density modulation can be described as a Fourier series of cosines ... 

To completely specify the orientational ordering, the complete set of orientational order parameters, P/,L = 0,2,4.. ., is required. Only the even rank order parameters are non-zero for phases with a symmetry plane perjDendicular to the director (e.g. N and SmA phases). 

This transition is usually second order [18,19 and 20]. The SmC phase differs from the SmA phase by a tilt of the director with respect to the layers. Thus, an appropriate order parameter contains the polar (0) and azimuthal ((]i) angles of the director ... 

Obviously 9 =0 corresponds to the SmA phase. This transition is analogous to the nonnal-superfluid transition in liquid helium and the critical behaviour is described by the AT model. Further details can be found elsewhere [18, 19 and 20]. 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

McMillan s model [71] for transitions to and from tlie SmA phase (section C2.2.3.2) has been extended to columnar liquid crystal phases fonned by discotic molecules [36, 103]. An order parameter tliat couples translational order to orientational order is again added into a modified Maier-Saupe tlieory, tliat provides tlie orientational order parameter. The coupling order parameter allows for tlie two-dimensional symmetry of tlie columnar phase. This tlieory is able to account for stable isotropic, discotic nematic and hexagonal columnar phases. 

Fig. 8 Optical micrograph of a a nematic phase, b a SmA phase (reproduced with kind permission of the American Chemical Society) and c a SmC phase (reproduced with kind permission of the copyright owner, D.W. Bruce)... 

A different mechanism is that of charge transfer, of which there are many examples based, in particular, on metallomesogens [14]. In these cases, mesophases can be induced by adding the electron-poor TNF (2,4,7-trinitro-9-fluorenone) and Fig. 9 shows Pd mesogen 4, which shows a particular type of SmA phase when TNF is added [15]. 

Fig. 9 The two components that form a charge-transfer complex, which exhibits the biaxial SmA phase...

However, the hydrogen-bonded mesogens that are of most interest in the context of this article are those elaborated initially by Kato and Frechet in the early 1990s [24-33]. In this approach, a pyridine, which may or may not have liquid crystal properties, was hydrogen bonded with a 4-substituted benzoic acid to form a new species with its own, distinct mesomorphism. For example, complex 9 shows a SmA phase that persists to 238 °C (n = 2, m = 4), while its free component pyridine is nematic to 213 °C the component benzoic acid is also nematic (as the H-bonded dimer) to 147 °C (although note that the notional monomer would not be liquid crystalline). 

The liquid crystal properties of the complexes were characterised using polarised optical microscopy and showed a nematic phase for n = 4 and 6 and a SmA phase for n = 6, 8, 10 and 12. The mesophases were monotropic for n = 4 and 6 and enantiotropic for the others the progression from a nematic phase for shorter chain lengths to SmA at longer chain lengths is quite typical for simple, polar mesogens. 

Examination of the thermal behaviour showed that with three exceptions, all complexes showed a monotropic SmA phase with in almost all cases, melting being observed between 88 and 99 °C, with clearing between 82 and 89 °C. Of the three exceptions, 15-6,8 and 15-8,10 showed no liquid crystal phase at all, while 15-12,6 showed an additional monotropic nematic phase. A curious feature of these complexes is the apparent insensitivity of the melting and clearing points to both n and m. 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

The close compounds bearing three aromatic rings (two of them related by an ester bridge as part of an isocyanide promesogen, Figure 7.7) also show an SmA phase... 

Complexes with the simplest alkoxyphenylisocyanide and several halides are prepared by metathetical reactions of [AuCl(CNR)] with KX salts (Figure 7.19) [17]. The chloro-derivatives (n > 4) andthebromo-complexes (n > 6) display SmA phases. However, the ligands and the iodo-complexes are not liquid crystals. The transition temperatures decrease in the order Cl > Br > I, according to the decrease in polarity of the Au—X bond. It is important to note that the coordination of a very simple non-mesomorphic isocyanide (only one alkoxy chain and one aromatic ring) to Au—Cl allows the formation of a quite ordered and stable smectic mesophase. 

By the same procedure are obtained the corresponding biphenyl isocyanide derivatives (Figure 7.20) [18]. Now, the free isonitriles are already liquid crystals displaying nematic and SmA phases with a short range of existence at moderate temperatures (40-85 °C), while the complexes show a marked increase in the melting points and also an expansion ofthe range of existence of the mesophase (up to 140 °C N and SmA phases). The exception is the shortest iodo-derivative, which is not a mesogen. Most of the complexes decompose into the isotropic state (above 220 °C). The biphenyl moiety increases the polarizability anisotropy compared to the phenyl and hence facilitates liquid crystal behavior. 

Similar compounds to those shown in Figure 7.25 have been prepared with a different mesomorphic isocyanide (Figure 7.27) [15]. All of them are mesogens and exhibit short-range SmA mesophases, except the perfluorophenylpyridine derivative, which shows an SmA phase in the range 87.4-215 °C. This much longer... 

The complexes bearing one chiral substituent display a smectic A mesophase when the non-chiral chain is long, or an enantiotropic cholesteric and a monotropic SmA phase for shorter alkoxy chains. A TGBA phase is observed for the derivative which contains the chiral isocyanide combined with the diethyloxy, when the SmA to cholesteric transition is studied. The compound with two chiral ligands shows a monotropic chiral nematic transition. When this compound is cooled very slowly from the isotropic liquid it exhibits blue phases BP-III, BP-II, and BP-I. 

Electroclinic effect118,119 Close to the phase transition from the tilted SmC phase to the orthogonal SmA phase the tilt angle becomes soft (soft mode). Consequently, one can realize faster switching times than in SSFLC and DHF cells. 

For these compounds the packing of the molecules also depends strongly on the details of the molecular structure (see Fig. 9) and on the delicate balance between segregation and optimized space filling. For example, for the SmA phases of the 4-substituted ethers 15b (4-N02) and 16b (4-CN) the dll ratio is around 1.7 and an antiparallel partial bilayer arrangement with interdigitated aromatics was proposed (see Fig. lib) [113]. However, for the SmA phases of the 1,3-substituted ethers 15a... 

It should also be noted that the stability of the distinct mesophases can be quite different. It seems that there is a significant effect of molecular shape and topology, stabilizing SmA phases in the system 41/43 and Colhex phases in the system 35/37. In addition, the mesophase stability is often reduced close to the transition to another mesophase (see Fig. 15). Hence, the order-disorder temperatures can only be roughly estimated based on segmental solubility parameters [24, 25]. 

Compounds like 88 (Fig. 25a), in which the Rp-segments are decoupled from the rod-like core by longer aliphatic spacers, can be regarded as polyphilic ABC molecules which are expected to lead to triply segregated smectic phases as shown in Fig. 19c. However, in compound 88, for example, the SmA-phase is composed of only two sets of distinct sublayers, though there are three mutually incompatible... 

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