N-I transition temperature

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. 

Figure 1. Plot of K-N and N-I transition temperatures versus the number of methylene units in the aliphatic segment.

Figure 4. Crystal-isotropic (k-i), crystal-nematic (k-n), and nematic-isotropic (n-i) transition temperatures as a function of mole fraction of -(Cl ) q- spacer pertaining to the series of MBPE-8,10 copolyethers, containing methylbiphenyl ethane mesogen and randomly distributed -(CH,)0- and -(CH,).n- spacers (adapted from ref. 15).

Equation 2.71 is the self-consistency equation for S. S depends on the combination ksT/a only, shown in Figure 2.15, and thus is a function of temperature and the coupling constant a. As ksT/a = 0.22019, a nematic to isotropic transition occurs. The temperature Tc is the N-I transition temperature at which S jumps from 0.4289 to zero. 

The application of the Maier-Saupe theory to the polymer system results in the nematic to isotropic (N-I) transition temperature, Tc, the order... 

Wang (1995a) calculated the N-I transition temperature, the critical order parameter and the latent entropy at transition according to the model... 

At the N-I transition, the free energy is the same for both isotropic and nematic phases with different order parameters, 0 and Sc. Thus the N-I transition temperature is obtained as... 

Figure 2.19. N-I transition temperature Tc against the chain length L. (From Wang Warner, 1986.)...

Figure 2.20. N—I transition temperature Tc against the molecular weight. (From Blumstein et al. 1984.)...

In the second-order approximation of the free energy, above T, Sa and Sb are both zero. Below T, the order parameters are non-zero. At T, the quadratic terms vanish. This formula illustrates the pseudo-second-phase-transition temperature vs. the molecular parameters that shows the same shapes as those of the numerical calculations of the N-I transition temperature Tc, mentioned above. 

At low temperatures the nematic gel coexists with excess solvent, i.e., the i-N biphasic coexistence. Above the triple point TJ, excess solvent coexists with an isotropic gel, i.e., the i-I coexistence. Also, above this temperature, the isotropic and the nematic phases of a gel can coexist, i.e., I-N phases. Beyond the phase gap, a single nematic phase exists. The I-N region terminates at the = 1 axis. This is at T the N-I transition temperature of the undiluted network which, in turn, is close to Tni, the transition temperature of the uncrosslinked polymer melt from which the network derives. The nematic order is not expected for any 4> for T above. This is the limit of stability for even the undiluted case. 

The G-SmA-N-I transition temperatures of syndiotactic poly(6-[4 -(4"- -bu-toxyphenoxycarbonyl)phenoxyl)phenoxy]-hexyl methacrylate prepared by aluminum porphyrin initiated polymerizations also level off at approximately 25 repeat units [91]. Similarly, the glass and nematic-isotropic transition temperatures of poly[6-(4 -methoxy-4"- Z-methylstilbeneoxy)hexyl methacrylate] prepared by group transfer polymerization become independent of molecular weight at approximately 20 repeat units [48]. Both polymethacrylates reach the same transition temperatures as the corresponding polymers prepared by radical polymerizations, which have nearly identical tacticities. 

The extent of correlation between repeating units is dependent on molecular mass entropy of isotropization and nematic order parameter at the l/N transition both increase rapidly with molecular mass, before leveling off. The N/I transition temperature T l also follows a similar trend, leveling off at Mn 10,000. As a result of this molecular mass dependence of Tni> a N+I biphase is observed in polydisperse samples. 

The N -> I transition temperature alternates in a regular manner, the degree of alternation diminishing as n is increased. This is observed with the melting temperature of the normal alkanes and is attributed to the packing effects of the terminal methyl groups. 

The introduction of dye molecules into the liquid crystalline host does not change the majority of the properties of the host, provided that not too much dye is introduced (not more than 1-2%). The N I transition temperature of the liquid crystal, the viscous and elastic properties, the electrical conductivity (provided the dye is not ionic and does not contain ionic impurities), the dielectric permittivities, (provided the dye molecule does not have a large dipole moment), and even the refractive indices all remain the same. The only significant change in the properties of the crystal is the appearance of absorption bands in the visible region of the spectrum and a slight increase in viscosity [151]. 

Figure 2. Change in the N-I transition temperature with the electric field in (1) 5-CB and (2) 6-CB [17]. A double logarithmic scale is used.

To use the model to predict other properties of liquid crystal dimers, for example, the N-I transition temperature and the temperature dependence of the order parameter it is necessary to make an additional approx-imation. This is to relate the strength parameter Xa for a mesogenic group to the orientational order of the nematic mesophase. By analogy with the Maier-Saupe theory [63] and the extension of this to multicomponent mixtures [68] it is assumed that... 

It is often argued that it is the shape anisotropy which is largely responsible for liquid crystal formation. Two methods have been proposed to introduce this view into the calculation of the interaction tensor for each conformer. In one it is assumed that the tensor is proportional to the moment of inertia tensor which is readily calculated from a knowledge of the molecular geometry [75]. However, it is found that this paramet-rization results in too great a dependence of the N-I transition temperature on the molecular length [76]. This observation was partly responsible for the development of the surface tensor model [77]. In this the interaction tensor is defined in irreducible form as... 

Our aim here is not to make a detailed comparison of the various parametrizations which have been proposed for the potential of mean torque. Instead we wish to illustrate the nature of the results which can be obtained with models which include all of the conformations for the dimer, suitably weighted [78]. The calculations proceed in an analogous manner to the generic model for example to determine the N-I transition temperature it is necessary to determine when the molar Helmholtz free energy of the isotropic phase... 

The results of these calculations for the N-I transition temperature based on the continuous torsional model are shown in Fig. 26 for the methylene linked cyanobiphenyl dimers with the spacer containing from 3 to 18 atoms. For ease of comparison, the transition temperatures have been scaled with the value for the sixth member of the homologous series. The results reveal that the alternation in is rapidly attenuated with increasing spacer length and that for spacers containing more than about 11 atoms, the alternation in Tn-i is essentially... 

One typical example of model LCP is PSHQ9, poly[(phenylsulfonyl)-p-phenylene nonanemethylene bis(4-oxybenzoate)] [54], whose chemical structure is depicted in Figure 11.2. This is a main-chain LCP, which has a glass transition temperature Tg of 84 ° C, and a nematic-to-isotropic (N-I) transition temperature Tm of 162 °C. This polymer has only nematic phase at temperatures between and Tni-... 

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