The Isotropic to Nematic Phase Transition

Some important observations, which should apply de facto to many nematic systems containing dispersed nanoparticles, particularly those with metal or semiconductor cores, were reported in 2006 by Prasad et al. [297]. The authors found that gold nanoparticles stabilized with dodecanethiol decreased the isotropic to nematic phase transition of 4-pentyl-4 -cyanobiphenyl (5CB) almost linearly with increasing nanoparticle concentration (x p) and increased the overall conductivity of these mixtures by about two orders of magnitude. However, the anisotropy of the electric conductivity (Act = [Pg.349]

The isotropic-to-nematic transition is determined by the condition [1 — (2/3)TBBWBB/k T] = 0 whereas the spinodal line is obtained when the denominator of XAA is equal to zero. These conditions are evaluated in the thermodynamic limit (Q = 0) in Fig. 7 for a Maier-Saupe interaction parameter Web/I bT = 0.4xAb and for NA = 200, N = 800, vA = vB = 1. When the volume fraction of component A(a) is low, the isotropic-to-nematic phase transition is reached first whereas at high < >A the spinodal line is reached first. In the second case, the macromolecules do not have a chance to orient themselves before the spinodal line is reached. This RPA approach is a generalization of the Doi et al. [36-38] results (that were developed for lyotropic polymer liquid crystals) to describe thermotropic polymer mixtures. Both approaches cannot, however,... 

Are all quantitative predictions of the thermodynamics of liquid crystals correct. If not stop here. The reason for this step is that die theory (Flory-Huggins lattice model) also predicts the occurrence of the isotropic to nematic phase transition in liquid crystals. If the theory had predicted correctly the properties of glasses but had failed for liquid crystals we would have had to abandon it, especially since in both cases the cause of the transition is ascribed to the vanishing of the configurational entropy. Alternatively the correctness of the prediction for liquid crystals argues for the correctness of the prediction for glasses. Since we have not been stopped by steps 3 and 4 we proceed to step 5. 

In conclusion, it appears that the conformational selection taking place at the isotropic to nematic phase transition is such that torsion angles close to 0° or to 180° are favored in all cases, while the exact results obtained for each system depend on the interplay of this tendency and of the intrinsic conformational preferences prescribed by E. The general finding that torsion angles close to 0° or to 180° are favored in... 

Calculations based on the full size distribution, Xj(Q), are tedious. A number of authors therefore replace Xj(f2) by Xl(Q), where L is a mean aggregate length. Using this monodispersity assumption in conjunction with Onsager s trial function approach Odijk [58] has investigated the effect of micellar flexibility on the isotropic-to-nematic phase transition in solutions of linear aggregates. Oz. is modeled in terms of the simple d = 1-model discussed above. In addition... 

The inequality / i / 2 however, which is here postulated in order to explain the experiments, also has an intuitive physical meaning Near Tc an in-plane compressional flow (V v ) can cause (in-plane) BOO much more efficiently than an elongational flow across the layers (V V ). By this description the observed anisotropy of sound anomalies is traced back to the anisotropy of the coupling between in-plane and across-plane flow to BOO. The situation is somehow reminiscent of pre-transitional effects near the isotropic to nematic phase transition, where shear flow can cause nematic ordering. Of course, the picture given here has to be corroborated by additional experiments (currently under way) testing the full 0- and o r-dependence of Eq.(4). 

In the case of the higher temperature crystallization, as will be shown in Sect. 4, the theory of Doi et al. is applicable without doubt since the primary phase separation involves the transition from the isotropic to nematic phase, but in the case of the glass crystallization near Tg described above its applicability is unclear since the observed data may correspond to the secondary phase separation. However, if the secondary phase separation occurs, the primary phase separation must have proceeded prior to that. In a rapidly quenched glass even if the primary phase separation had already taken place, it would be still incomplete, so that it will re-start by heating. 

Solutions of poly(l,4-phenylene-2,6-benzobisthiazole), PBT, exhibit an isotropic to nematic phase transition in a variety of solvents including methane sulfonic acid, MSA, chlorosulfonic acid, CSA, and poly phosphoric acid, PPA (1-4). In the latter case the transition occurs over a range of water -P2O5 compositions. In these acids the polymer, with repeating unit... 

The Nematic - Isotropic Phase Transition. For nematic solutions kept free from moisture, the phase transformations described in the preceding were not observed, but the nematic phase could be reversibly transformed to the isotropic phase over a temperature interval Tj - Tj lOK. For the sample with w = 0.041, this transition occurred over the range T = 92 C to Tj = 101 0. For temperatures between T and Tj, the sample was biphasic, with the isotropic and nematic phases coexisting. This behavior is similar to that observed in previous studies, in which Tj - Tj is observed to be independent of w over a range of w for which Tj increases with increasing w (3,4). 

The isotropic-to-nematic transition is defined by the characteristic equation Det M = 0 (where Det represents the determinant of a matrix). If the Van der Waals interactions were turned off (W0 = 0) so that only nematic interactions are left, then M would be the denominator of X so that X would blow up for this condition (Det M = 0). Above certain critical values of Wj s the blend forms the nematic phase. As in the case of purely flexible mixtures, the spinodal condition is ... 

Figure 20. (a) Orientational correlation time t in the logarithmic scale as function of the inverse of the scaled temperature, with the scaling being done by the isotropic to nematic transition temperature with Ti-N. For the insets, the horizontal and the vertical axis labels read the same as that of the main frame and are thus omitted for clarity. Along each isochor, the solid line is the Arrhenius fit to the subset of the high-temperature data and the dotted line corresponds to the fit to the data near the isotropic-nematic phase boundary with the VFT form, (b) Fragility index m as a function of density for different aspect ratios of model calamitic systems. The systems considered are GB(3, 5, 2, 1), GB(3.4, 5, 2, 1), and GB(3.8, 5, 2, 1). In each case, N = 500. (Reproduced from Ref. 136.)... 

The transition from isotropic to nematic phase is characterized by formation of molecular orientation with respect to director n We may characterize it by order parameter Z (Figure 17). 

Starting from the isotropic phase, where the molecules have all three degrees of freedom, cooling will increase the density and rotation about the long axis becomes restricted. Series of models have been developed that consider the density of liquid in terms of the restriction of the order.These theories identify a critical density at which the isotropic to nematic transition would be predicted. Constraint of the molecule in terms of its rotation about the long axis defines the nematic phase. If now the translational freedom is restricted and layered alignment is imposed on the molecules, then smectic order is created. The smectic phase can still retain disorder in rotational freedom about the short axis. Loss of this final degree of freedom will lead to the creation of a erystalline ordered structure. This simple approach provides a description for the isotropic nematic smectic crystalline transitions. 

The difference between mechanisms 1 and 2 is illustrated in Figure 14 schematizing the transition from isotropic to nematic phase for molecularly dispersed rodlike polymers (Figure 14(a)), for closed (Figure 14(b)), and open (Figure 14(c)) supramolecular assemblies. Whereas molecular and closed supramolecular polymers are just oriented in the nematic phase, in the case of open SPs development of orientation is simultaneous with an enhancement of polymerization [5]. 

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