I-N transition

TTF-CA more ionic, increasing q up to 0.7. The space group of the I-phase is Pn with two equivalent donor-acceptor dimers related by a glide plane with a ferroelectric arrangement (see Fig. 6.33(b)). Further examples of mixed-stack organic CT materials exhibiting N-I transitions are tetramethylbenzidine-TCNQ (Tn-i — 205 K) (Iwasa et al, 1990) and DMTTF-CA (Tn-i 65 K) (Aoki et al, 1993). 

The switching or memory phenomena induced by electric field application or photo irradiation have been studied on Mott insulators, charge ordered insulators, and N-I transition systems and were found to be fast phase transitions in general. For the former two systems, the phase transitions caused a pronounced change in reflectance and conductivity from insulating to metallic features. The third system also exhibited a change in conductivity and dielectric response connected with the transports of solitons and/or domain walls, dynamic dimerization, and... 

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. 

What does your best value for the exponent j8 indicate about the nature of the critical behavior underlying the N-I transition (mean-field second-order or tricritical) Note that /3 and P describe the temperature variation of the nematic order parameter S, which is a basic characteristic of the liquid crystal smdied. Thus, the same j8 and P values could have been obtained from measurements of several other physical properties, such as those mentioned in the methods section. 

Schematic parabolic band structure for CdSe, which has a band gap of 1.75 eV. The conduction band is labeled C, and several valence bands (V,) are shown. The filled and open circle symbols indicate the position of quantized k values mr/ai allowed for the / = 1 and n = 2 states of an NC with radius a. The solid arrow shows the / = 1 transition in which an electron is excited and a hole is created (open circle). The dashed arrow shows how the position of this n = i transition would change for a nanocrystal of smaller radius 32- (Adapted from Ref. 7.) This simple diagram is for the cubic zinc blend structure the hexagonal wurtzite structure has a small gap k= 0 between the and V2 bands.

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).

The nematic to isotropic transition of rigid rods in solution is of the first order. If the axial ratio L/D is great, the concentration of rods 4> D/L 1, even at the N — I transition, meets the condition of the second virial approximation. 

When the N — I transition occurs, the critical volume fractions in the nematic and isotropic phase are respectively... 

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. 

It is illustrated that the N-I transition is of first order. Experimentally, the latent entropies of small molecular mass liquid crystals, AE(TC), are very diverse, ranging from 1.25 to 7.55 J/mol. K. Most fall in the range of 2.50-3.35 J/mol.K. The Maier-Saupe prediction for the latent entropy at transition is in reasonable agreement with experiments. 

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. 

Figure 2.36 is a phase diagram for Vb = 1.1 and vc = 1.2, i.e., det(r>) <0. This is where the network is more strongly nematic than the pure solvent. Since vc > Vb, dilution initially stabilizes the nematic phase of the network. Thus, N-I coexistence initially extends upwards from T = 1.1, 4> = 1.0 (the N-I transition of the neat network) as in Figure 2.36(b). As dilution... 

Interestingly, if in a sample there coexist a crystalline phase and a monotropic-nematic phase, on heating of the two-phase sample there should give rise to a DSC curve which shows a peak of N-I transition on the lower temperature side of the melting temperature because Tn-i is lower than Tc-i- Such a DSC curve (Figure 4.25) was indeed observed when we were studying a low mass monotropic-nematic compound (4.5). 

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