Anisotropy molecular shape

Another important application of perturbation theory is to molecules with anisotropic interactions. Examples are dipolar hard spheres, in which the anisotropy is due to the polarity of tlie molecule, and liquid crystals in which the anisotropy is due also to the shape of the molecules. The use of an anisotropic reference system is more natural in accounting for molecular shape, but presents difficulties. Hence, we will consider only... 

The prime requirement for the formation of a thermotropic liquid crystal is an anisotropy in the molecular shape. It is to be expected, therefore, that disc-like molecules as well as rod-like molecules should exhibit liquid crystal behaviour. Indeed this possibility was appreciated many years ago by Vorlander [56] although it was not until relatively recently that the first examples of discotic liquid crystals were reported by Chandrasekhar et al. [57]. It is now recognised that discotic molecules can form a variety of columnar mesophases as well as nematic and chiral nematic phases [58]. 

As has been noticed by Gelbart and Gelbart [7], the predominant orientational interaction in nematics results from the isotropic dispersion attraction modulated by the anisotropic molecular hard-core. The anisotropy of this effective potential comes from that of the asymmetric molecular shape. The coupling between the isotropic attraction and the anisotropic hard-core repulsion is represented by the effective potential... 

The previous approach is valid as long as the molecular reorientation can be described by a single correlation time. This excludes molecules involving internal motions and/or molecular shapes which cannot, to a first approximation, be assimilated to a sphere. Due to its shape, the molecule shown in Figure 15 cannot evidently fulfil the latter approximation and is illustrative of the potentiality of HOESY experiments as far as carbon-proton distances and the anisotropy of molecular reorientation are concerned.45 58... 

Just because a molecule is long, narrow, and meets the requirement of geometric anisotropy docs not ensure that it will have a liquid crystal phase. The particular phase structure that occurs in a compound, i.e.. smectic, nematic, or chiral nematic, not only dc >cnds on the molecular shape hut is intimately connected with the strength and position of the polar or polarizable groups within the molecule, the overall polarizability of the molecule, and the presence ol chiral centers. 

The electrostatic part, Wg(ft), can be evaluated with the reaction field model. The short-range term, i/r(Tl), could in principle be derived from the pair interactions between molecules [21-23], This kind of approach, which can be very cumbersome, may be necessary in some cases, e.g. for a thorough analysis of the thermodynamic properties of liquid crystals. However, a lower level of detail can be sufficient to predict orientational order parameters. Very effective approaches have been developed, in the sense that they are capable of providing a good account of the anisotropy of short-range intermolecular interactions, at low computational cost [6,22], These are phenomenological models, essentially in the spirit of the popular Maier-Saupe theory [24], wherein the mean-field potential is parameterized in terms of the anisometry of the molecular surface. They rely on the physical insight that the anisotropy of steric and dispersion interactions reflects the molecular shape. 

Recently, the surface tensor model has been used together with the dielectric continuum model to calculate the orientational order parameters of solutes in nematic solvents [8,9,27], Figure 2.32 shows the theoretical results for anthracene and anthraquinone in nematic solvents with different dielectric anisotropy. Considering only the surface tensor contribution, positive Szz and Sxx and negative are obtained, with Szz > Sxx > Syy. This corresponds to what could be expected on the basis of the molecular shape the long axis (z) is preferentially aligned with the director, and the normal to the... 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

As to infrared spectroscopy - and the same holds good for other spectral ranges -the orientational order is readily observable in form of dichroism Being related to the molecular shape, the molecular polarizability is anisotropic as well. By the alignment of the molecules this anisotropy is transferred to the sample, however damped due to the imperfect order as described by the order parameters. As a consequence, the dielectric function and furthermore the (complex) refractive index are anisotropic, so that eventually (linear) dichroism and birefringence occur. 

There exists also a theory of Maier and Saupe (A , 47) which takes into account the stability of aligned molecules, for instance in the nematic state, due to the anisotropy of the dispersion forces. The Flory theory covers this as well, but in addition it takes into account two further effects anisotropy of the molecular shape, and the influence of that anisotropy on molecular packing. The separability of factors in equation (1) has been well justified by subsequent results (48), (Flory, P.J. private communication to W.Brostow, August 20, 1985). The Flory theory has been applied, among others, to ternary systems of the type rigid rod polymer... 

As discussed earlier, structural anisotropy is paramount in importance when considering the intermolecular interactions necessary to promote mesomorphism. The structural anisotropy is related to the molecular shape and we shall now endeavour to investigate its effect upon the mesomorphic properties of several complexes. In several instances we have discussed N, Sa and Sc phases arising from calamitic molecules, and in later sections we shall discuss disc-like molecules exhibiting columnar mesophases. Unfortunately such rigid definitions of molecular... 

The field of soft condensed matter/complex systems spans a seemingly diverse spectrum, including isotropic liquids with short-range order at the one end, and liquid crystals with long-range order in their anisotropic phases, often called mesophases, at the other [2-4]. Anisotropy in molecular shape plays a crucial... 

Molecular shape anisotropy plays a very important role in determining whether or not liquid crystal phases will be formed, and indeed, when they are formed, which particular modification will be generated in preference to other mesophases [3, 4]. Molecules that form liquid crystals are usually carbon based, but they need not be. They often have preferred shapes, based on rods, bananas, boards or discs. In the following account, the properties of some unusual rod-like organic systems which have asymmetric structures thereby making them optically active and chiral will be described. In particular, the unusual self-organizing properties and the structures of the frustrated phases of the (R), (S), and racemic forms of 1-methylheptyl 4 -(4-n-... 

As mentioned in the preceding section, the anisotropy in the molecular shape influences significantly HTP of chiral compounds. Thus, to discuss the structural effect on the photochemical change in HTP, the molecular aspect ratio, LjD, was estimated with MOPAC/PM3 method. The molecular aspect ratios of the chiral azobenzene compounds in their isomeric states are given in Table 10.3. The data reveal that HTP of the chiral azobenzene compounds in both the isomeric states... 

This relationship is modified by two constants the molecular shape factor/ (a function of the molecular dimensions) and the boundary coefficient C, which takes into account the interaction between the solvent and the solute. In principle, two-photon fluorescence anisotropy decays in isotropic media should yield the same diffusion times as for single photon excitation, but with significantly increased initial fluorescence anisotropy this can be seen in Figure 11.17, which compares single- and two-photon anisotropy decays for the fluorescent probe rhodamine 6G in ethylene glycol. Rotational drflusion times for small molecular probes vary from nanoseconds to hundreds of picoseconds for isotropic rotational drflusion in low viscosity solvents. 

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