Anisotropic molecules

It is occasionally desirable to retain a small proportion of molecular orientation, in order to quantitate the dipolar interactions present, whilst minimizing their contribution to the linewidth. Partial orientation may be achieved by using a nematic solvent. In large, magnetically anisotropic molecules it may occur naturally at the highest magnetic fields. 

Thennotropic liquid crystal phases are fonned by anisotropic molecules witli long-range orientational order and in many types of stmcture witli some degree of translational order. The main types of mesogen are Arose tlrat are rodlike or calamitic and Arose Arat are disclike or discotic. 

Thennotropic liquid crystal phases are fonned by rodlike or disclike molecules. However, in the following we consider orientational ordering of rodlike molecules for definiteness, although the same parameters can be used for discotics. In a liquid crystal phase, the anisotropic molecules tend to point along the same direction. This is known as the director, which is a unit vector denoted n. 

London23 has treated the case of the attractive force between anisotropic molecules on the dipole-dipole interaction basis as well as on the monopole basis mentioned above. The small anisotropy found for the chlorine atom makes the dipole-dipole formulation appropriate. For the symmetrical orientation in the Cl2 molecule the London formula is... 

It is not possible to predict from the related crystal structure alone whether the compound will melt to a liquid crystalline phase or not, because the anisotropic molecules (calamitic and discotic ones) form in favourable anisotropic packing. As a rule long shaped rod-like molecules quite often possess a layered arrangement in the solid state regardless of whether the compound is mesogenic or not. 

As indicated, the power law approximations to the fS-correlator described above are only valid asymptotically for a —> 0, but corrections to these predictions have been worked out.102,103 More important, however, is the assumption of the idealized MCT that density fluctuations are the only slow variables. This assumption breaks down close to Tc. The MCT has been augmented by coupling to mass currents, which are sometimes termed inclusion of hopping processes, but the extension of the theory to temperatures below Tc or even down to Tg has not yet been successful.101 Also, the theory is often not applied to experimental density fluctuations directly (observed by neutron scattering) but instead to dielectric relaxation or to NMR experiments. These latter techniques probe reorientational motion of anisotropic molecules, whereas the MCT equation describes a scalar quantity. Using MCT results to compare with dielectric or NMR experiments thus forces one to assume a direct coupling of orientational correlations with density fluctuations exists. The different orientational correlation functions and the question to what extent they directly couple to the density fluctuations have been considered in extensions to the standard MCT picture.104-108... 

The excitation spectrum proves even more useful near the surface. Since anisotropic molecules at the surface of a liquid tend to orient relative to the surface tangent, one might expect the excitation spectrum to be sensitive to such orientation. For example, suppose we take the extreme case in which molecules at the surface are oriented with their transition moments perpendicular to the surface tangent. Then the only field component which can excite these molecules is the radial field at the surface. When one recalls that only the N type vector field has radial components, one expects that a calculation of the excitation spectrum of such a molecular layer will yield half as many resonant features as shown in Figure 8.4. Indeed this is the case. Figure 8.7 shows the calculated surface average of the square modulus of the radial component of the local electric field, < E er 2>J, where sr is the radial unit vector. 

Liquid crystals are materials that exist in a state that is intermediate between a liquid state and a solid. They are formed by anisotropic molecules, known as calamitic molecules, which are long and narrow, i.e. have a large length-to-breadth ratio. These rod shaped molecules orientate themselves in different ways as they change from the crystalline to the liquid state at different temperatures, existing in the smectic and nematic phases, as shown in Figure 5.1. 

Let the coordinate system be such as that given in Figure 4. IS. The electric vectors of a plane polarized radiation vibrate along OZ in the ZX plane and OX is the direction of propagation of the plane polarized wave. When a solution of anisotropic molecules is exposed to this plane polarized radiation, the electric vector will find the solute molecules in random orientation. Only those molecules absorb with maximum probability which have their transition moment oriented parallel to OZ (photoselection). Those molecules which are oriented by an angle 6 to this direction will have their absorption probability reduced by a factor cos 6, and the intensity of absorption by cos2 6. Finally, the molecules oriented perpendicular to the electric vector will not absorb at all. These statements are direct consequences of directional nature of light absorption... 

Finally, since the long-range transfer probabilities are all, to some degree, dependent on mutual orientation of donor and acceptor, it is necessary to retain the facility to average over all orientations. Further attention is given in Chap. 5 to rotational effects during reactions between anisotropic molecules in solution. In Chap. 5, Sect. 4.2, the experimental evidence currently available indicates that molecules re-orient more rapidly than they react. 

Samson and Deutch [258] and Hess [259a] have also discussed the reaction of anisotropic molecules, though only Hess considered rotational relaxation effects. No studies have used the experimentally measured values of rotational relaxation times, which may be 1.5—10 times faster than the Debye equation, eqn. (108), predicts. The theory of Sole and Stockmayer [256] will underestimate the rate of chemical reactions when rotational relaxation is faster than they assumed. 

Molecular type and arrangement deduced from anisotropic properties of crystals. It is evident that, in dealing with crystals of unknown structure, the anisotropic properties may often be used to give direct information about the general shajJe of the molecules or polyatomic ions in the crystals and the way in which the molecules or ions are packed. A strongly anisotropic crystal must contain strongly anisotropic molecules or polyatomic ions packed in such a way that the anisotropies of the different molecules or ions do not neutralize each other, and a consideration of the properties of the crystal in all direc-... 

Anisotropic potentials. The anisotropy of the interaction potentials may be taken into account in the computation of spectral moments. For the zeroth and first moments, the anisotropy of the interaction affects the pair distribution function, g(R,Qi,Q2), which thus becomes dependent on the orientations of molecules 1 and 2. A perturbation treatment based on the assumption of small anisotropy was given later for an estimate of the effects of the anisotropy of H2-He and H2-H2 pairs [293], Moments of more strongly anisotropic molecules (N2, CO2) were recently considered [67, 122],... 

Other difficulties are owing to the influence of the solvent. With stiff and bulky chains the so-called micro-form-effect becomes of importance, when the refractive index increment differs considerably from zero (7). In this case the random link approximately acts like a cylinder of length A and with a refractive index different from that of the solvent. Another effect occurs in good solvents which consist of anisotropic molecules. These molecules become oriented along the polymer chain, considerably contributing to its anisotropy [Frisman, Dadivanyan and Dyuzhev (752)]. In this way, the determination of the eigen anisotropy of weekly anisotropic polymer chains becomes rather doubtful. 

Silver nitrate in ammoniacal solution may be completely reduced to silver by aqueous arsenious oxide. The reduction is hindered by the presence of ammonium sulphate, owing to the decrease in concentration of the hydroxyl ions 5 neutral salts such as sodium sulphate or sodium nitrate have no effect. Similarly, auric chloride may be reduced to gold.6 At 20° C. an aqueous solution of vitreous arsenious oxide reacts 4 to 5 times as rapidly as an aqueous solution of the octahedral form 7 the greater rate of dissolution in water of the former variety has been mentioned (p. 137), but from supersaturated solutions of the two forms there is no appreciable difference in the rates of deposition. The explanation of the inferior reducing power of the crystalline variety may be that there exist anisotropic molecules which only slowly lose their anisotropic properties. An ammoniacal solution of arsenious oxide heated with cupric sulphate in a sealed tube at 100° C. causes reduction... 

For C70 the phase diagram is more complicated. Because of the anisotropic molecules it should contain at least three phases, with free molecular rotation at high temperature, uniaxial rotation at intermediate temperatures, and frozen rotation or... 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

Keyes T, Kivelson D, McTague JP. Theory of k-independent depolarized Rayleigh wing scattering in liquids composed of anisotropic molecules. J Chem Phys 1971 55 4096-4100. 

The calculation of G for the anisotropic molecule leads to C a313, thus V ( /03-... 

Since their discovery in the nineteenth century [1], hquid crystals have fascinated scientists due to their unusual properties and their wide range of potential apphcations, especially in optoelectronics. LC systems can be divided into two categories thermotropic LC phases and lyotropic LC phases. Thermotropic LC systems result from anisotropic molecules or molecular parts (so called mesogens or mesogenic moieties, respectively), and form hquid crystalline phases between the soHd state and the isotropic hquid state, where they flow like liquids but possess some of the characteristic physical properties of crys-... 

Figure 8 Illustration of a magnetically anisotropic molecule. Its energy depends on its orientation relative to the applied magnetic field, Bq. Thus, it will preferentially adapt orientations with lower energies. (Adapted from Bertini, Luchinat, Parigi and Pierattelli. 2005 Wiley-VCH)...

For the case of anisotropic dipolar oscillators, the dispersional forces have been discussed by London and De Boer. On neglecting the anisotropy of electron oscillation frequency, the dispersional energy of interaction between two anisotropic molecules becomes, in a dipole-dipole approximation > ... 

Other Contributions to the Kerr Constant. In the case of naturally anisotropic molecules, the deviation tensor df in the expansion (195) does not vanish, causing a cross-effect as well as higher-order fluctuational effects to appear, in addition to the previous angular correlation effect (I77a). The cross-effect appears owing to co-operation between molecular angular correlations-the first term of equation (195) and the translational fluctuations described by the second term of (195). We shall consider this effect in the next subsection. 

The clasdcal fundamentals of the theory of the Kerr effect are due to Voigt in terms of dectron theory of the atom as an anharmonic oscillator and to Langevin in terms of statistical optical reorioitation of anisotropic molecules in a static dectric fidd. Buckingham proposed a theory and method of measurement of the optical birefringence induced by the gradient of a static electric field permitting the determination of electric quadrupole moments. 

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