First-order nematic-isotropic phase transition

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. 

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. 

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. 

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... 

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). 

The first important characteristic is that living systems are liquid crystalline. Liquid crystals are orientationally ordered molecular liquids. When a molecular liquid is in the isotropic liquid state (which models the primordial soup), it has neither translational nor orientational order. At the phase transition to the nematic state, the most basic liquid crystal transition, the system selects a special direction for long-range orientational order. This direction is called the director and denoted by a unit vector, n. By selecting a special direction, the nematic breaks the continuous rotational symmetry of the isotropic liquid. A phase boundary intervenes between the nematic and the isotropic liquid when they coexist. 

A similar analysis can be made for the Landau free energy of a weakly first-order phase transition, for example the nematic-isotropic transition exhibited by some liquid crystals (Section 5.7.1). The free energy (Eq. 1.13), is supplemented by an additional cubic term C T)xlr if the transition is first order. The first-order nature of the transition can be confirmed by calculating the entropy density change at the transition, which turns out to be... 

First, the phase transitions of liquid crystals in microcavities of submicrometer size are strongly affected by finite size effects. The nematic-to-isotropic phase transition, for instance, has been shown to become continuous [105, 106, 111]. This phenomenon can be explained by Landau-type models [105-107, 111, 114, 115]. The same effect of a continuous nematic-to-isotropic transition was also observed in bulk liquid single crystal elastomers [116, 117] (see Chap. V of Vol. 3 of this Handbook), whereas the corresponding linear polymer shows a discontinuity of the order parameter at the phase transition. For the elastomers, both a confinement due to the crosslinking and an internal mechanical field, resulting from a second crosslinking performed under mechanical stress, may explain the continuous character of the nematic-to-isotropic transition. 

Figure 1. Phase diagram of the uniaxial and biaxial nematic phases as predicted by the microscopical theories (N(. calamitic nematic N, biaxial nematic and Nj discotic nematic). In the case of systems of hard rectangular plates, the parameter a is the shape anisotropy of the elementary units (i.e., the width to length ratio of the rectangles). In the case of mixtures of rodlike and disk-like particles, x is the relative concentration of the disk-like particles. The first order transition to the isotropic phase is marked as a dashed line. The second order N -Nb phase transitions are represented with solid lines (from [8, 13]).

Close to the phase transitions point (such as the weak first-order isotropic to nematic transition or the second-order nematic to smectic transition), the order of the low-temperature phase occurs transiently in the finite small size of fluctuations, which is called cybotactic clusters. When the correlation length of the fluctuation increases towards the transition point, the relaxation time diverges. For example, near the nematic-smectic phase transition point, it can be seen that the correlation length becomes longer towards the transition point by X-ray diffraction experiments (Fig. 10.21). In addition, the increase of the relaxation time of the fluctuations can be measured using dynamic light scattering method, which wiU be introduced in detail in Sect. 10.4.3.2. 

A-nematic phase transition (SNT) is of second order, while the NIT is of first order. In Figure 2.16b, the smectic order parameter discontinuously drops to zero with increasing <)> and the SNT is of first order. In Figure 2.16c, the nematic phase disappears and we only have the first-order smectic A-isotropic phase transition (SIT). Owing to McMillan theory for a pure nematogen (<)> = 0), the SNT should be second order for Tsf /T j < 0.87 and first order for larger values of 7 /T j, where shows the SNT temperature of a pure nematogen. 

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). 

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