Smectic-Nematic-Isotropic Phase Separations

Mean field theories can also be extended to the phase behavior of smectic A liquid crystal and flexible polymer blends [63, 70-74] by combining the Flory-Huggins theory for isotropic mixing and Kobayashi-McMillan theory [32, 75] for smectic A ordering of liquid crystals. 

Y = 2exp[—(fo/d)], which can be vary between 0 and 2 and increases with increasing chain length of alkyl end-chains of nematogens. The smectic condensation is more favored for larger values of y. The smectic A order parameter can be calculated by  

We have an isotropic phase with S = t) = 0, a nematic phase with S 0,r = 0, and a smectic A phase with S / 0, r 0. The equilibrium distribution function/(z, Q) is 

96 [33]. Reprinted with permission from Reference [33], Copyright (1998) American Institute of Physics. 

Combining the Flory-Hu jns theory for an isotropic mixing and a free energy for other liquid crystalline phases opens up the possibility of extending the theory to describe other Uquid crystalline phases such as smectic C. Such mean field theories have been appUed to phase diagrams of colloidal solutions [35], crystal and liquid crystal mixtures [82], and colloid and Uquid crystal mixtures [83]. 

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Examples of these formulations are systems based on a difunctional LC epoxy monomer (diglycidyl ether of 4-4 -dihydroxy-Q -methylstilbene), cured with methylene dianiline (Ortiz et al., 1997). The generation of liquid-crystalline microdomains (smectic or nematic) in the final material required their phase-separation before polymerization or at low conversions. This could be controlled through the initial cure temperature. Values of GIc, (kJm-2) were 0.68 (isotropic), 0.75 (nematic), and 1.62 (smectic). The large improvement produced by the smectic microdomains was attributed to an extensive plastic deformation. 

The pre-smectic oscillatory interaction was first observed in an AFM force experiment in the isotropic phase of a liquid crystal 8CB [23] and is shown in Fig. 3.8 for different temperatures close to the isotropic-nematic phase transition. The oscillatory force decays gradually with increasing separation, the range of the force is equal to the smectic correlation length inside the isotropic phase. 

No phase separation was observed when an isotropic monomer was polymerized to a nematic or smectic polymer. The nematic or smectic polymers are soluble in the isotropic monomer. When a certain conversion is obtained, a phase transition from isotropic to nematic or smectic phase takes place. This phase transition, caused by variation of the mole fraction of the monomer and the polymer, is comparable with a phase transition caused by varying the temperature at constant composition. 

The thermodynamic parameters, measured at various temperatures for the isotropic, nematic, or smectic phase of a liquid crystalline stationary phase, are related to changes in the ability of a solute to interact with the solvent. Several theoretical treatments, including the refined infinite dilution solution model [453, 480, 481] and the lattice model [455,456], have been postulated for the general interpretation of the thermodynamic parameters in terms of the retention and selectivity parameters in gas chromatographic separations. However, attempts to correlate the thermodynamic quantities with specific solute-solvent interactions remain qualitative. Nevertheless, a few general observations can be noted. Upon cooling from an isotropic phase into a liquid crystalline phase, the values of decrease and those of 7 increase. Plots of Vg or 7 versus temperature show discontinuities at phase transition temperatures. The activity coefficient of any solute in an anisotropic environment (Ya) is found to be more positive (and typically, 7r>l) than in its isotropic phase (7i°°). This trend in is a reflection of vari-... 

Transitions with the participation of liquid crystals sometimes show characteristic phenomena. If a nematic modification turns to a smectic A or smectic C phase, transient stripes in the form of a myelinic texture (also called chevron texture or striated texture) are often visible. Typically for the polyester prepared from di-w-propyl-/ -terphenyl-4,4" carboxylate and tetramethylene glycol, the nematic phase separates from the isotropic liquid on cooling in droplets which coalesce and form large domains. Cooling of the threaded-schlieren texture produces a transition to the smectic A phase this change is characterized by transition phenomena, mostly stripes, which broaden into larger areas ( transition bars ). 

Binary mixtures of a flexible polymer and a low molecular weight liquid crystalline molecule, or a rigid rod-like molecule, are of interest because of their important technological applications in high modulus fibers, nonlinear optics, and electro-optical devices. These blends are basic materials for recent new technologies of liquid crystal displays [1,2], The performances of these systems are closely related to phase separations and conformations of polymer chains dissolved in a liquid crystalline phase. One of the main problems is to examine the location of various phases such as isotropic, nematic, and smectic phases, depending on temperature and concentration. To understand the thermodynamics and thermal instability of these blends, it is important to consider the co-occurrences between liquid crystalline ordering and phase separations. 

Therefore we again obtain the first order transition for jAi — Ci >0 and second order for IB jA2 — Ci < 0 and a tricritical point for IB /Ai — C =0. The tricritical point (TCP) is located in the continuous phase transition line separating the nematic and smectic A phases [12], see a phase diagram schematically shown in Fig. 6.12. Such a point should not be confused with the triple point common for the isotropic, nematic and SmA phases. In Fig. 6.12, for homologues with alkyl chains shorter than l , the N-SmA transition is second order and shown by the dashed curve. With increasing chain length the nematic temperature range becomes narrower (like in Fig. 6.1) and, at TCP, the N-SmA transition becomes first order (solid curve). 

Fig. 19 shows the temperature dependence of the retention times of p- and m-xylene in 4,4 -dihexyloxyazoxybenzene. Good separation is observed both in the nematic (125 to 80°C) and in the smectic phase (T < 80°C). At the isotropic-to-nematic transition the retention time decreases in a small temperature interval (125—120°C). Such a behavior is expected according to rule 1 and has been observed in many cases [134, 128]. It should be emphasized that the drop in Vg at the isotropic-to-nematic transition takes place over a rather broad temperature range (that is 5°C), rather than sharply. This has been attributed to pretransitional effects [134]. 

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