First-order nematic-isotropic phase

These theories all pr>edict a first order nematic-isotropic phase transition, and a weakly temperature dependent order parameter. In rigid rod Maier-Saupe theory, the order parameter is given by the angle of the rod to the direction 0" prefered orientation... 

In the previous chapters we have seen how an anisotropic, attractive interaction between the molecules of the form P2(cos O12) can give rise to a first-order nematic-isotropic phase transition. The origin of the anisotropy lies in the fact that almost all the liquid-crystal molecules are elongated, rod-like, and fairly rigid (at least in the central portion of the molecule). It is clear, however, that besides the anisotropic attractive interaction there must also be an anisotropic steric interaction that is due to the impenetrability of the molecules. 

A novel variation of this technique (62) involves depression of the first-order, nematic-isotropic melting transition of A(-(p-ethoxybenzylidene)-p-ra-butylaniline. Polystyrene and poly(ethylene oxide) are soluble in both phases, and Mn values of up to 10 have been studied. 

Equations (40) and (41) describe the first order nematic-isotropic transition. At high temperatures Eq. (40) has only the isotropic solution 5=0. At f-0.223 two other solutions appear. One of them is always unstable but the other one does correspond to the minimum of the free energy F and characterizes the nematic phase. The actual nematic-isotropic phase transition takes place when the free energy of the nematic phase becomes equal to that of the isotropic phase. This happens at f = Tn i=0.220. At the transition temperature the order parameter 5=0.44. 

We will discuss nematic ordering in polymer systems and we start with solutions of rigid rods as the simplest system in which isotropic-nematic transition occurs. Solutions of a flexible polymer and a nematic low molecular liquid crystal display at low polymer content, when cooled down from the isotropic phase, segregation into a nematic and an isotropic phase. At higher polymer content, the solution decays first in two isotropic phases, one rich in polymer, and the other poor in polymer. Further cooling leads to separation of the latter in a nematic phase very poor in polymer and the isotropic phase rich in polymer. This is sketched schematically in Figure 19. Phase behavior of the indicated type was observed in EBBA (/ -ethoxy benzylidene- w-4- -butylaniline) mixed with polystyrene (Ballauf, 1986 Lee et al., 1994) and with poly(ethylene oxide) (Kronberg et al., 1978). 

Techniques.—A novel method for the determination of the number average molar mass (M ) is reported by Kronberg and Patterson, based on the observation that polystyrene and poly(ethylene oxide) are soluble in the nematic and isotropic phases of the liquid crystalline iV-(/>-ethoxybe zylidene)/ n-butylanaline. Presence of a polymer depresses the first-order nematic-Tsotropic melting transition, by decreasing the nematic order, and as liquid crystals tend to exhibit large values of the cryoscopic constant, molar masses of up to 10 may be studied with some accuracy. 

It is natural to ask what effect, if any, the steric interaction might have on the nematic-isotropic phase transition. Onsager recognized that a system of hard rods, without any attractive interaction, can have a first-order transition from the isotropic phase to the anisotropic phase as tbe density is increased. To see how this can come about, we note that in a gas of hard rods there are two kinds of entropy. One is the entropy due to the translational degrees of freedom, and the other is the orientational entropy. In addition, there is a coupling... 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

In Fig. 4 the experimental isobaric volume temperature curve of the 1-l.c. 4-hexyloxybenzoic acid 4 -hexyloxyphenylester is shown, which possesses a nematic phase 37,38). Two phase transformations are indicated by the jumps of the V—T curve the isotropic to nematic and, at lower temperatures, the nematic to crystalline transformation. As well known, both transformations are of first order and obey the Clausius-Clapeyron equation. 

To check the phase transformation isotropic -> nematic, the validity of the Clausius Clapeyron equation is examined. It has been shown 38), that within the experimental error the results fulfill Eq. 1 in analogy to the low molar mass l.c. The phase transformation isotropic to l.c. is therefore of first order with two coexisting phases at the transformation point. Optical measurements on the polymers confirm these thermodynamical measurements (refer to 2.3.1.3). 

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