Phase transitions nematic- smectic

In the nematic phase, one can induce macroscopic orientation by controlling the surface boundary conditions. However, because nematic ordering is the result of a spontaneously broken symmetry, fluctuations of the director n are a soft mode. Indeed a macroscopically oriented nematic phase is much more turbid than a macro-scopically oriented smectic-A phase because of light scattering from orientational fluctuation domains. The layered structure of the smectic-A phase suppresses these orientational fluctuations, and it is this coupling that affects the character of the transition (see [5] for a broad survey of such phase transitions). However, smectic phases exhibit one-dimensional orientational order, characterized by the Landau-Peierls fluctuation of the layer spacing [6, 7]. As a result, the essential features needed to capture the NA transition are ... 

As one example. Figure 10.4 shows results obtained with octyl-cyanobiphenyl (8CB, Hi7C8(C6H4)2CN). At high temperature, 8CB is an isotropic liquid. When it is cooled slowly to 40.5 °C, the material becomes a nematic liquid crystal, where the molecules align and show a preferred orientation. Cooling further to 33.5 C, 8CB undergoes a phase transition from smectic to nematic, where in addition to the orientational order the molecules form a layered structure. 8CB forms solid crystals when the temperature is reduced below 21.5 °C. When confined between two... 

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

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. 

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. 

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] ... 

The compound in Fig. 3b exhibits two smectic phases (Sm and Sm ) in addition to nematic, whereas the compound in Fig. 3a exhibits only a nematic phase. The substitution of an alkoxy for an alkyl tail is known to shift phase transition temperatures considerably. In the cyano-biphenyls (Fig. 4), substitution of an alkoxy tail raises the melting point from 24 to 48 °C and T from 35 to 68 °C [22]. 

In 1978, Bryan [11] reported on crystal structure precursors of liquid crystalline phases and their implications for the molecular arrangement in the mesophase. In this work he presented classical nematogenic precursors, where the molecules in the crystalline state form imbricated packing, and non-classical ones with cross-sheet structures. The crystalline-nematic phase transition was called displacive. The displacive type of transition involves comparatively limited displacements of the molecules from the positions which they occupy with respect to their nearest neighbours in the crystal. In most cases, smectic precursors form layered structures. The crystalline-smectic phase transition was called reconstitutive because the molecular arrangement in the crystalline state must alter in a more pronounced fashion in order to achieve the mesophase arrangement [12]. 

With increasing temperature, phase transitions occur, including ciystalline to smectic C to smectic A to nematic to isotropic, or crystalline to nematic to isotropic. These examples demonstrate that not all possible transitions neeessarily oceur. Depending on the number of mesophases occurring, thermotropic mono-, di-, tri-, or tetramorphism may be distinguished. 

It may be asserted that the fundamental reason arises from the fact that, while parallel arrangements of anisotropic objects lead to a decrease in orientational entropy, there is an increase in positional entropy. Thus, in some cases, greater positional order will be entropically favorable. This theory therefore predicts that a solution of rod-shaped objects will undergo a phase transition at sufficient concentration into a nematic phase. Recently, this theory has been used to observe the phase transition between nematic and smectic-A at very high concentration (Hanif et al.). Although this model is conceptually helpful, its mathematical formulation makes several assumptions that limit its applicability to real systems. 

Turning to the low temperature transition of the homopolymer of PHBA at 350 °C, it is generally accepted that the phase below this temperature is orthorhombic and converts to an approximate pseudohexagonal phase with a packing closely related to the orthorhombic phase (see Fig. 6) [27-29]. The fact that a number of the diffraction maxima retain the sharp definition at room temperature pattern combined with the streaking of the 006 line suggests both vertical and horizontal displacements of the chains [29]. As mentioned earlier, Yoon et al. has opted to describe the new phase as a smectic E whereas we prefer to interpret this new phase as a one dimensional plastic crystal where rotational freedom is permitted around the chain axis. This particular question is really a matter of semantics since both interpretations are correct. Perhaps the more important issue is which of these terminologies provides a more descriptive picture as to the nature of the molecular motions of the polymer above the 350 °C transition. As will be seen shortly in the case of the aromatic copolyesters, similar motions can be identified well below the crystal-nematic transition. 

An exception to the rule that lowering the Iciiiperaiure cutises transitions to phases with increased order sometimes occurs for polar compounds w hich form the smectic l. phase (a layered structure formed by molecular dimers). Decreasing the temperature cutises u transition front nematic to smectic. 1,.,. but a further lowering of the temperature produces J transition back to the nematic phase tcalled the reentrant nematic phase). Electric or magnetic fields also may induce mesomorphic phase transitions. 

The systematic synthesis of non amphiphilic l.c.-side chain polymers and detailed physico-chemical investigations are discussed. The phase behavior and structure ofnematic, cholesteric and smectic polymers are described. Their optical properties and the state of order of cholesteric and nematic polymers are analysed in comparison to conventional low molar mass liquid crystals. The phase transition into the glassy state and optical characterization of the anisotropic glasses having liquid crystalline structures are examined. 

In Table 9a the phase transitions of two arbitrarily selected systems are compared, where the length of the free substituent A is varied. For the poly(methacrylate) No. 1 and the poly(siloxane) No. 3 nematic phases are observed which become smectic... 

Figure 3. Liquid-crystal textures of the methyl-substituted model ester viewed through crossed polarizers, a, Smectic C-to-nematic transitional phase and b, smectic mosaic texture at 160 °C. Original magnification, 320x.

Depending on temperature, transitions between distinct types of LC phases can occur.3 All transitions between various liquid crystal phases with 0D, ID, or 2D periodicity (nematic, smectic, and columnar phases) and between these liquid crystal phases and the isotropic liquid state are reversible with nearly no hysteresis. However, due to the kinetic nature of crystallization, strong hysteresis can occur for the transition to solid crystalline phases (overcooling), which allows liquid crystal phases to be observed below the melting point, and these phases are termed monotropic (monotropic phases are shown in parenthesis). Some overcooling could also be found for mesophases with 3D order, namely cubic phases. The order-disorder transition from the liquid crystalline phases to the isotropic liquid state (assigned as clearing temperature) is used as a measure of the stability of the LC phase considered.4... 

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