Isotropic-nematic theory

Analytical approaches to understanding the effect of molecular flexibility on orientational order have concentrated on both the isotropic-nematic and the nematic-smectic transition [61, 62] and mean field theory has shown that cholesteric pitch appears not to depend on the flexibility of the molecule [63]. 

The SD is a phase separation process usually occurring in systems consisting of more than two components such as in solutions or blends. However, in the present case the system employed is composed of one component of pure PET. In this case, what triggers such an SD type phase separation Doi et al. [24, 25] proposed a dynamic theory for the isotropic-nematic phase transition for liquid crystalline polymers in which they showed that the orientation process... 

Kinetics of isotropic-nematic phase transition of liquid crystals (Doi s theory)... 

The coagulation process can now be considered in perspective of a ternary polymer-solvent-nonsolvent system, A schematic ternary phase diagram, at constant temperature, is shown in Figure 8. The boundaries of the isotropic and narrow biphasic (isotropic-nematic) regions are based on an extension of Flory s theory ( ) to a polymer-solvent-nonsolvent system, due to Russo and Miller (7). These boundaries are calculated for a polymer having an axial ratio of 100, and the following... 

Utracki and Lyngaae-Jprgensen [2002] observed several common aspects of exfoliated CPNCs and liquid-crystal polymers (LCPs). Similar six-phase structures are predicted for CPNCs and observed in LCPs isotropic, nematic, smectic-A, columnar, house of cards, and crystal [Porter and Johnson, 1967 Balazs et al., 1999 Ginzburg et al., 2000]. These phases in CPNCs originate in a balance between the thermodynamic interactions, clay concentration, and platelets orientation, while in LCPs they depend mainly on temperature. Since it is more difficult on the one hand to prepare disk-shaped than rigid-rod molecules, and on the other to develop flow theory for LCPs with disk moieties, the number of publications on the latter systems is small [Ciferri, 1991]. 

Fig. 3.6. A set of AFM experimental force curves, obtained during the approach of surfaces at different temperatures, just above the isotropic-nematic phase transition. The pronounced pull-in step corresponds to the capillary condensation. The inset shows the experimentally determined D, T) phase diagram for B,CB together with the results of the LdG theory, indicated by the solid line.

The full lines in Fig. 3.8 are best fits to the presmectic interaction, based on the LdG theory [22,24] with an addition of the van der Waals force [2,14]. Just like in previous nematic cases, the mesoscopic LdG theory superbly describes the structural force between the surfaces. The fitting of the measured presmectic forces to the theory allows for the determination of many important surface parameters, that are difficult to obtain using other methods. For example, the amplitude of the smectic order at the surface and the smectic correlation length can be obtained directly. For 8CB on silanated glass, one obtains a typical surface smectic order parameter iPfi which is of the order of 0.1 and the smectic correlation length y, which is in perfect agreement with X-ray data of Davidov et al. [25]. In addition to that, it has been observed that the smectic order is coupled to the nematic order and this amplifies the presmectic interaction close to the isotropic-nematic phase transition [23]. 

Ericksen proposed a theory for fluids such as nematic liquid crystals which could become anisotropic during flow. By assuming symmetry around the director, the expression for the stress tensor was somewhat simplified. We compare here briefly Ericksen s transversely isotropic fluid theory with the transient behavior observed for thermotropic copolyesters of PHB/PET. 

Liquid crystals manifest a number of transitions between different phases uprm variation of temperature, pressure or a craitent of various compounds in a mixture. All the transitions are divided into two groups, namely, first and second order transitions both accompanied by interesting pre-transitional phenomena and usually described by the Landau (phenomenological) theory or molecular-statistical approach. In this chapter we are going to consider the most important phase transitions between isotropic, nematic, smectic A and C phases. The phase transitions in ferroelectric liquid crystals are discussed in Chapter 13. 

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 transition from water to ice at 1 atmosphere pressure is a first-order transition, and the latent heat is about 100 J/g. The isotropic-nematic transition is a weak first-order transition because the order parameter changes discontinuously across the transition but the latent heat is only about 10 J/g. De Gennes extended Landau s theory into isotropic-nematic transition... 

R. M. Homreich, Landau theory of the isotropic-nematic critical point, Phys. Lett., 109A, 232 (1985). 

De Gennes used Landau theory to describe the isotropic-nematic transition. In his theory, he used a scalar order parameter S defined by... 

The concept potential of mean force was used by Onsager [3] in his theory for the isotropic-nematic phase transition in suspensions of rod-like particles. Since the 1980s the field of phase transitions in colloidal suspensions has shown a tremendous development. The fact that the potential of mean force can be varied both in range and depth has given rise to new and fascinating phase behaviour in colloidal suspensions [4]. In particular, stcricaUy stabilized colloidal spheres with interactions close to those between hard spheres [5] have received ample attention. 

Scaled Particle Theory of the Isotropic-Nematic Transition... 

We now compare experimental results on the isotropic-nematic transition in mixed suspensions of colloidal rods and polymer with the theory presented in the previous sections. 

Later, Burning and Lekkerkerker [37] observed isotropic—nematic phase separation in a dispersion of sterically stabilized boehmite rods, which approximate hard rods, in cyclohexane. Buitenhuis et al. [43] studied the effect of added 35 kDa polystyrene (/ g = 5.9nm) on the hquid crystal phase behaviour of sterically stabilized boehmite rods with average length L = 1.1 nm and average diameter D = ll.lnm in ortho-dichlorobenzene. Different phase equihbria were observed. Two biphasic equilibria dilute isotropic phase Ij + nematic N, concentrated isotropic phase I2 + nematic N and a triphasic equilibrium 1 -F I2 + N (see photo. Fig. 6.20). In this system the boehmite rods are quite polydisperse. Therefore comparison with theory should be done with an approach including polydisperse rods. We further note no li +12 coexistence was observed experimentally but... 

The resulting phase diagram is shown in Fig. 12. We can identify a type of phase diagram predicted from the theory for intermediate stiffnesses. We do not see a coexistence between two nematic states as was predicted for very large stiffness and also no liquid-gas coexistence a lower densities. The liquid-gas coexistence point seems to be buried within the two-phase region of the isotropic-nematic transition and we have indications [23] that it may become observable when we slightly reduce the intrinsic chain stiflhiess. 

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