Nematic potential

Here Wgn are the coefficients of the expansion of the electrostatic free energy, which can be obtained from the free energy Wfl(li), according to Equation (2.269). T2n are the irreducible spherical components of the (second rank) surface tensor, which describe the anisometry of the molecular shape, and can be calculated in the form of integrals over the molecular surface [25]. Given the nematic potential the distribution function... 

The distribution of orientations can, in principle, be computed theoretically from a nematic potential that expresses the influence of one rod s orientation on that of its neighbors. 

An alternative nematic potential due to Maier and Saupe (1958, 1959, 1960) is perhaps more appropriate for thermotropic nematics. The Maier-Saupe potential is given by... 

The first two terms in this expression for the stress tensor are elastic terms due to Brownian motion and the nematic potential, respectively. The last term is a purely viscous term produced by the drag of solvent as it flows past the rod-like molecules [see Eq. (6-36)]. is a drag coefficient, which for modestly concentrated solutions is predicted to follow the dilnte-solution formula (Doi and Edwards 1986 see Section 6.3.1.4) ... 

Figure 3 Schematic Phase diagram in flow-rate and nematic potential for the three molecular flow behaviours of sheared liquid crystals...

With either nematic potential, the equilibrium orientation distribution T eq( ) can be computed via a self-consistency condition, and the isotropic-to-nematic transition has been analyzed in terms of nematic strength parameters. ... 

The Doi theory captures the molecular viscoelasticity of LCP, i.e., the relaxation of the orientation distribution under flow. But it completely ignores distortional elasticity and is limited to monodomains. The assumption of spatial uniformity underlies all its key elements the nematic potential, the kinetic equation, and the elastic stress tensor. Therefore, its successes are restricted to situations where distortional elasticity is insignificant. 

Maier and Saupe, in their well-known molecular-statistical theory, described the intermolecular orientational forces by a mean field method. The Maier-Saupe theory successfully predicts the relationship between the molecular orientation parameter S and the nematic potential D as a function of temperature [10,14]. 

Fig. 7.16 A mechanical model that helps to understand the process of retardation or acceleration of molecular rotation in the nematic potential slow hindered rotation of molecule at the angles fs tc/2 (a), fast accelerated rotation about long molecular axes at the angles d 0 or 7C (b) and quite fast molecular precession within small 3-angles (c)...

It is instructive to compare the ratio an/aj 1.5 for ionic processes with a much higher ratio ajj,/a 10 — 10 for the conductivity due to dielectric losses. In the first case, the orientational nematic potential Wn does not influence the translational motion of ions and cj /a L. In the secmid case, the losses eJJ come in from the field induced alignment of the lOTigitudinal molecular axes against the potential barrier and dramatically depend on Wn whereas losses e" caused by molecular rotation about the longitudinal molecular axes are independent of Therefore, ratios e"n/ "j. (and are very large. 

The initial configurations exhibit a random orientation of the liquid crystal distributed uniformly over the unit three-dimensional sphere. The system is equilibrated in the isotropic phaae at the nematic potential U = 2 for a time t = 20r (r = l/(6i3 A(l -17/3)) is a characteristic relaxation time). The system is then quenched into the nematic phase at 17 = 6. 

A detailed description of the molecular motions in the Maier-Saupe potential disturbed by the electric probe field has been done by Martin and co-workers. These authors obtained the numerical solutions for the relaxation times T and Tj and for polarization. They found that the relaxation process measured at nUE geometry is slowed down with respect to the Debye-type motion in the isotropic phase, whereas the second relaxation process connected with the molecular reorientations around the long axes (nlE geometry) becomes faster in the presence of the nematic potential, that is, gn > 1 and < 1. 

Figure 3. Retardation factor gj = T as function of the nematic potential barrier parameter cr = q/RT according to Meier et al, Eq. (26) (broken line), and Coffey et a 146 150 gq 27) (dashed line) and exact solution (solid line). (Reprinted with kind permission from the authors and the editor of Liq. Crystals.)...

The alkylcyanobiphenyls are specially suited for the investigation of the dielectric relaxation because the two main modes of dipole relaxation are well separated. The hindered rotation about the short molecular axis is shifted to relatively low frequencies conveniently accessible in impedance bridge measurements. This relaxation process is coupled to the strength of the nematic potential q, which should be sensitive to a variation of the intermolecular distance. Hence a strong pressure dependence is expected for this relaxation process. 

As outlined in Section II.B, Maier and Saupe have introduced the nematic potential q, which is a measure of the average strength of interaction between molecules treated as rigid bodies. However, the information about the values of the nematic potential is rather scarce. It can be determined from the deuterium NMR spectra and from... 

Figure 23. Comparison of the retardation factors gj and corresponding nematic potential q values obtained for 5PCH at different conditions. [Crosses, Meier-Saupe Eq. (26) other symbols, Coffey et al. Eq. (27).]...

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