Isotropic-nematic

Camp P J, Mason C P, Allen M P, Khare A A and Kofke D A 1996 The isotropic-nematic transition in uniaxial hard ellipsoid fluids coexistence data and the approach to the Onsager limit J. Chem. Phys. 105 2837-49... 

Figure C2.2.2. Isotropic, nematic and chiral nematic phases. Here n denotes tire director. In tire chiral nematic phase, tire director undergoes a helical rotation, as schematically indicated by its reorientation around a cone.

Disc-like particles can also undergo an Onsager transition—here tire particles fonn a discotic nematic, where tire short particle axes tend to be oriented parallel to each other. In practice, clay suspensions tend to display sol-gel transitions, witliout a clear tendency towards nematic ordering (for instance, [22]). Using sterically stabilized platelets, an isotropic-nematic transition could be observed [119]. 

Let us enter the world of liquid crystals built by the purely entropic forces present in hard body systems. The phase diagram of hard spherocylinders (HSC) shows a rich variety of liquid crystalline phases [71,72]. It includes the isotropic, nematic, smectic A, plastic, and solid phases [73]. In a plastic crystal the particle centers lie on lattice sites, but the orientations of the... 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

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]. 

Berardi et al. [66] have also investigated the influence of central dipoles in discotic molecules. This system was studied using canonical Monte Carlo simulations at constant density over a range of temperatures for a system of 1000 molecules. Just as in discotic systems with no dipolar interaction, isotropic, nematic and columnar phases are observed, although at the low density studied the columnar phase has cavities within the structure. This effect was discovered in an earlier constant density investigation of the phase behaviour of discotic Gay-Berne molecules and is due to the signiflcant difference between the natural densities of the columnar and nematic phases... 

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)... 

Fig. 32 The calculated strength of PpPTA yarns as a function of the concentration. The isotropic-nematic concentration is indicated by cni... 

Fig. 8. Isotropic-nematic transformation of a hyperbranched polyether as described by Per-cec et al. [34,35]...

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... 

Chen s analysis is more accurate than the procedure in which the Onsager trial function is used with a(N) given by Eq. (18), but it is very involved to carry through. On the other hand, the Onsager trial function procedure is simple enough for practical purposes. As shown in Appendix A, it predicts the isotropic-nematic phase boundary concentrations that can be favorably compared with those by Chen s procedure. 

The Gaussian trial function for f(a) used by Odijk [6] is mathematically simpler than Onsager s and allows p to be expressed by the leading term of Eq. (22) and ct(N) to be derived analytically. However, it becomes less accurate as the orientation gets weaker. As shown in Appendix A, its use leads to the isotropic-nematic phase boundary concentrations largely different from those by Chen s method and hence is not always relevant for quantitative discussion. 

Chen [47] calculated the isotropic-nematic phase boundary concentrations using not any trial function but f(a) determined by an numerical-iteration procedure. This method is more rigorous than the one resorting to a trial... 

The distribution of chain sequence extension, calculated by using RIS models, is compared with isotropic-nematic transition characteristics for a number of thermotropic polymers comprising rigid groups connected by polymethylene spacers. The distribution depends strongly not only on the odd-even character of the number of methylene units of the spacers, but also on the specific groups (or atoms connected at the ends of polymethylene spacers. 

Values of enthalpy and entropy change at isotropic-nematic transitions... 

To check the phase transformation isotropic -> nematic, the validity of the Clausius Clapeyron equation is examined. It has been shown 38), that within the experimental error the results fulfill Eq. 1 in analogy to the low molar mass l.c. The phase transformation isotropic to l.c. is therefore of first order with two coexisting phases at the transformation point. Optical measurements on the polymers confirm these thermodynamical measurements (refer to 2.3.1.3). 

A) Onsager s rigid-rod model (1949) was the first correct model of an athermal Isotropic —> Nematic phase transition. It is a relatively simple model that predicts phase transitions. It is based on excluded volume between two rigid rods, which reads... 

---