The Nematic-Isotropic Transition

The liquid-crystal transition between smectic-A and nematic for some systems is an AT transition. Depending on the value of the MacMillan ratio, the ratio of the temperature of the smectic-A-nematic transition to that of the nematic-isotropic transition (which is Ising), the behaviour of such systems varies continuously from a k-type transition to a tricritical one (see section A2.5.91. Garland and Nounesis [34] reviewed these systems in 1994. 

NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Liquid crystalline solutions as such have not yet found any commercial uses, but highly orientated liquid crystal polymer films are used to store information. The liquid crystal melt is held between two conductive glass plates and the side chains are oriented by an electric field to produce a transparent film. The electric field is turned off and the information inscribed on to the film using a laser. The laser has the effect of heating selected areas of the film above the nematic-isotropic transition temperature. These areas thus become isotropic and scatter light when the film is viewed. Such images remain stable below the glass transition temperature of the polymer. 

Note 2 For rod-like molecules, the order parameter of the effective molecular symmetry axis at the nematic-isotropic transition is about 0.3 and can increase to about 0.7 in the... 

Rather more surprisingly, there is evidence that even with a fixed rigid-rod length the nematic-isotropic transition temperature can depend upon molecular weight, although to a much lesser extent than in the cases already considered. Thus in the polymer XI the transition temperature rose from 135.5 °C to 165 °C as M was increased from 4,000 to 20,000 62). 

Figure 2.32 Order parameters calculated for (a) anthracene and (b) anthraquinone dissolved in nematics with different dielectric anisotropy [9]. For the case Ae > 0, the results obtained in the absence of induction effects are also shown (dotted line). The temperature dependence of the dielectric anisotropy is taken into account, with the values eNI = 10.2, AeN/ = 8 and eNI = 5.2, AeN/ = —0.5 for the two cases at the nematic-isotropic transition. Atomic charges in absolute value greater than 0.1 are shown (in e units). The y axis is perpendicular to the molecular plane.

Typical data obtained on 5CB in the nematic-isotropic transition region. The sample is first heated from the nematic into the isotropic phase and then cooled back into the nematic. Note that the detector voltage is independent of temperature and is near zero when Tis above the N-I transition temperature. The sUghtly larger values observed at the minima for the nematic phase result from some residual ellipticity of the beam if the first polarizer and the n director are not oriented at exactly 45 degrees. 

The homopolymer showed an enantiotropic nematic mesophase, whereas the diblock copolymer generated microphase-separated lamellae, in which the SCLCP block possessed a nematic-isotropization transition similar to the homopolymer (Table 17). Upon heating, the nematic microphase decreased continuously in the nematic phase from 38.5 nm to 27 nm and showed a constant value of about 26 nm after the nematic-isotropization transition. Therefore, materials in which these block copolymers are macroscopically aligned are expected to show reversible contraction in one dimension, making this polymer system an interesting candidates for an artificial muscle or actuator. 

It was shown by Helfrich that at temperatures shghtly above the nematic-isotropic transition temperature, a field induced phase transition from isotropic to nematic can be observed by applying an electric field. According to a thermodynamic consideration, the shift in the transition temperature caused by the electric field E is given by... 

Figure 2.9 Temperature-dependence of the axial ratio f = bx/d of Kuhn length bf to molecular diameter d for poly(hexylisocyanate) (PHIC) in toluene (O) and tetrahydrofuran ( ) and for hydroxypropylcellulose (HPC) in dimethylacetamide (A). Here is the transition temperature from the nematic or chiral nematic to the isotropic phase in the melt. The lines fit the expression

PHIC extrapolate to roughly 6.7, which is close to the value predicted by the Flory theory in the melt. This suggests that even for bulk HPC, the nematic-isotropic transition is driven primarily by excluded-volume, or packing, effects and only secondarily by anisotropic van der Waals interactions. The temperature dependence of the axial ratio could be incorporated into the Maier-Saupe potential by suitably adjusting the temperature dependence of the coefficient 17ms-... 

The degree of orientational order in a uniaxial nematic is given by the order parameter S, defined by Eq. (2-3). S is zero in the isotropic state, and it approaches unity for hypothetically perfect molecular alignment (i.e., all molecules pointing in the same direction). In single-component small-molecule nematics, such as MBBA, S varies with temperature from 5 0.3 at Tni, the nematic-isotropic transition temperature, to S 0.7 or so at lower... 

Change in selectivity from H2O selective to ethanol selective at the nematic-isotropic transition temperature... 

We are mainly concerned with domain properties well below the nematic-isotropic transition. We concentrate on the interaction between the glass-like properties of random nematics (specifically irreversibility and dependence of final behavior on initial conditions) and the long-range order properties of the final equilibrium or metastable state (specifically the question of whether the final state is LRO, QLRO or SRO). Specifically we are seeking to resolve the puzzle of when and how QLRO or SRO develops in these systems. 

Like ebulliometry, the cryoscopic method is also limited to relatively low-molecular-weight polymers with up to 50,000. A newer variation of this method involves the solute-induced depression of the nematic-isotropic transition temperature for a liquid crystal solvent such as p-azoxyanisole [2]. This technique appears to be particularly convenient for high-molecular-weight polymers and may be applicable for M values as high as 10 . 

As the temperature reaches the clear point Tc or isotropization temperature Ti, S jumps abruptly down to zero. The phenomenon implies that the nematic-isotropic transition is of first order. 

The conclusions are dependent on the shape of rigid rods and hence the second virial coefficient. Thus, the concentration difference and the critical order parameter differ at the nematic — isotropic transition for different shapes of rods. 

It should be pointed out that to meet the second virial approximation, molecules must have a large L/D so that at the transition the solution is dilute. For molecules of axial ratio less than 10 the theory does not work well. In addition, the Onsager value of the density difference at the nematic — isotropic transition is greater than the experimental data. 

The nematic-isotropic transition occurs when the free energies of the nematic and the isotropic phases are equal, i.e.,... 

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