Phase transitions nematic-hexagonal

Figure 19.3. The time evolution of the morphology of an A3B7 surfactant melt, as predicted by dissipative particle dynamics [84], Mean field theory predicts the correct equilibrium hexagonal phase but does not provide any insights into how this equilibrium morphology is reached. The simulations showed that the dynamics of ordering is determined by the percolation of tubes, subsequently destabilized by a nematic or smectic phase transition and also that hydrodynamic effects are important in reaching equilibrium for this system. See the insert showing the colored figures for a better view.

POM characterization revealed that Poly-2 has a batonnet-like texture from 125 to 94 °C and a fan-shaped texture from 94 to 80 °C during the cooling process. On the other hand, Poly-3 has a sandy texture from 142 to 112 °C and a batonnet-like texture from 112 to 93 °C during the cooling process. XRD measurements revealed that Poly-2 has a discotic nematic (No) phase at higher LC temperatures and a discotic lamellar (Dl) phase at lower LC temperatures. Poly-3 showed a Nq phase and a hexagonal columnar (CoL) phase at higher and lower LC temperatures, respectively. The phase transition temperatures of Poly-2 and Poly-3 are summarized in Table 11.2. 

FIGURE 45 5,5 -Substituted 2,6-6w(l-ethyl-benzimidazol-2-yl)pyridines and their transition temperatures (in °C). Abbreviations Cr = crystalline phase, SmC = smectic C phase, SmA = smectic A phase, N = nematic phase. Col/, = hexagonal columnar phase, I = isotropic liquid. 

Fig. 9 Left panel-, time autoCF of the central torsion of T6 in the smectic (590 K), nematic (650 K) and isotropic (685 K) phase inset shows the Arrhenius plot of the trasional correlation time, with different regimes observed in the smectic (circles) and nematic-isotropic (squares) phases [2]. Right panel time autoCF of molecular axes for alkoxy-substilnted phthalocyanines in the rectangular (300 K) and hexagonal (425 K) columnar phase inset shows an Arrhtmius plot of the correlation times for the in-plane rotation, revealing the phase transition at about 330 K. Reprinted with permission from [34]. Copyright 2009 American Chemical Society...

McMillan s model [71] for transitions to and from tlie SmA phase (section C2.2.3.2) has been extended to columnar liquid crystal phases fonned by discotic molecules [36, 103]. An order parameter tliat couples translational order to orientational order is again added into a modified Maier-Saupe tlieory, tliat provides tlie orientational order parameter. The coupling order parameter allows for tlie two-dimensional symmetry of tlie columnar phase. This tlieory is able to account for stable isotropic, discotic nematic and hexagonal columnar phases. 

If the concentration of surfactant becomes high enough, surfactant structures often develop long-range order, and hence they become liquid crystalline. They are lyotropic liquid crystals, because the transition to the liquid-crystalline state is induced by concentration changes. Surfactant solutions can form nematic and smectic-A liquid-crystalline phases analogous to those discussed in Chapter 10. In addition, hexagonal and cubic phases are common in surfactant solutions. 

For example, for n = 12, two transitions within the liquid crystalline region are observed from a nematic columnar phase (Ncoi) to a hexagonal columnar lattice (Dh) and then finally to a rectangular lattice (Dr). The X-ray diffraction data on benzimi-dazolium salts have also been reported [40], and indicate a switch from a lamellar... 

Fig. 6.2.1. Theoretical plot of the reduced transition temperature against the model parameter a showing the hexagonal, nematic and isotropic phase boundaries. All the transitions are of first order.

FIGURE 17.17 Phase diagram obtained from mean-field theory by Knaapila et al. for the molecular weight dependence of the thermal transition from a hexagonal ordered phase and a nematic mesophase in the PF2/6 polyfluorene polymer. (Adapted from Knaapila, M., et aL, Phys. Rev. E, 71, 2005. With permission.)... 

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