Nematic systems, theory

Luckhurst G R 1985 Molecular field theories of nematics systems composed of uniaxial, biaxial or flexible molecules Nuclear Magnetic Resonance of Liquid Crystals ed J W Emsiey (Dordrecht Reidel)... 

In a weak flow field, Eq. (64) can be rewritten in a form similar to that for the direct n appearing in Leslie and Ericksen s phenomenological theory [160—163] for nematic systems. Thus, we have... 

All the above theories are derived for rigid rod nematic liquid crystal systems. The rheological behavior of chiral nematic liquid crystals is more complex and less understood than that of nematic systems. Rey introduced a model based on rigid rod chiral nematic liquid crystals to describe permeation shear flow and small amplitude oscillatory shear flow. The model can predict some common phenomena of chiral nematic liquid crystals, e.g., the three-region... 

For nematic LCs, theory predicts a characteristic dispersion law Tiz(coo) oc [36, 37]. This is exactly what we observe for the monomeric 8 and dimeric systems 7. Although a somewhat higher exponent is evaluated for the polymers 4, there is no doubt that collective order fluctuations occur in these systems, likewise [174]. 

The chemical shifts allowed the local order parameters to be computed which indicated the uniaxial to biaxial nematic phase transition. The nematic phase of a deuterated fiuorenone nematogen has been studied by NMR and X-ray and evidence for biaxial order close to its glass transition temperature has been inferred. The possible symmetries of the biaxial nematic phase have been examined based on experimental results and it is concluded that a monoclinic symmetry rather than an orthorhombic symmetry that is more likely to be the cause for the observed phase biaxiality in thermotropic bent-core and calamitic-tetrapode nematic systems. Density functional theory has been employed in a detailed conformational study of a bent-core mesogen The chemical shielding... 

Ronca G, Yoon D (1984) Theory of nematic systems of semiflexible polymers. II. Chains of finite length in the bulk. J Chem Phys 80(2) 925-929... 

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... 

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... 

It may be asserted that the fundamental reason arises from the fact that, while parallel arrangements of anisotropic objects lead to a decrease in orientational entropy, there is an increase in positional entropy. Thus, in some cases, greater positional order will be entropically favorable. This theory therefore predicts that a solution of rod-shaped objects will undergo a phase transition at sufficient concentration into a nematic phase. Recently, this theory has been used to observe the phase transition between nematic and smectic-A at very high concentration (Hanif et al.). Although this model is conceptually helpful, its mathematical formulation makes several assumptions that limit its applicability to real systems. 

The virial expansion has enjoyed greater appeal, especially as applied to lyotropic systems. Onsager s classic theory rests on analysis of the second virial coefficient for very long rodlike particles. It was the first to show that a solution of hard, asymmetric particles such as long rods should separate into two phases above a threshold concentration that depends on the axial ratio of the particles. One of these phases should be anisotropic (nematic), the other completely isotropic. The former is predicted to be somewhat more concentrated than the latter, but it is the alignment (albeit imperfect) of the solute molecules that is the predominent distinction. The phase separation is a consequence of shape asymmetry alone intervention of intermolecular attractive forces is not required. 

Similar results have been obtained by Bianchi, Ciferri and Tealdi for the system DMAc, 3% LiCl/PBA/X-500 the lattermost designation denotes the polymeric terephthalamide of p-aminobenzhydrazide which occurs as a random coil in solution. Their experimental results are shown in Fig. 7. In confirmation of Aharoni s results and of theory as well, the X-500 component is not detectable in the nematic phase. The close resemblance of Figure 7 to th6 theoretical diagram shown in Figure 6 is evident. 

While the possibility of this dispersion of micro-domains of the nematic phase in an isotropic phase cannot be dismissed, concrete evidence for morphologies of this kind in nematogenic copolymers is not prominently in evidence. The longer sequences of rigid units undoubtedly are responsible for promotion of liquid crystallinity but, as theory suggests they appear to be uniformly dispersed Sequences of units that include many flexible members and hence are not rodlike may assume a role analogous to that of the solvent in a lyotropic system The nematic copolymer should, on this basis, consist of a single phase. 

The theory for various molecular dynamics simulation algorithms for the calculation of transport coefficients of liquid crystals is presented. We show in particular how the thermal conductivity and the viscosity are obtained. The viscosity of a nematic liquid crystal has seven independent components because of the lower symmetry. We present numerical results for various phases of the Gay-Berne fluid even though the theory is completely general and applicable to more realistic model systems. 

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