Molecular liquids intermolecular, orientational

Maier and Saupe [13] developed a statistical theory to describe the liquid crystalline state and the molecular ordering for the nematic phase. In analogy to the treatment of ordering phenomena in ferromagnetics or ferroelectrics, this theory describes the intermolecular orientational forces by a mean field method. Each individual molecule feels a nematic potential D = f (0, S, V) which depends on the momentaneous angle 6 between its long axis and the optic axis, the order parameter S and the molar volume V. S is then given by... 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

The anisotropy of the liquid crystal phases also means that the orientational distribution function for the intermolecular vector is of value in characterising the structure of the phase [22]. The distribution is clearly a function of both the angle, made by the intermolecular vector with the director and the separation, r, between the two molecules [23]. However, a simpler way in which to investigate the distribution of the intermolecular vector is via the distance dependent order parameters Pl+(J") defined as the averages of the even Legendre polynomials, PL(cosj r)- As with the molecular orientational order parameters those of low rank namely Pj(r) and P (r), prove to be the most useful for investigating the phase structure [22]. 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

There are a number of possible explanations for the formation of more than one photodimer. First, due care is not always taken to ensure that the solid sample that is irradiated is crystallographically pure. Indeed, it is not at all simple to establish that all the crystals of the sample that will be exposed to light are of the same structure as the single crystal that was used for analysis of structure. A further possible cause is that there are two or more symmetry-independent molecules in the asymmetric unit then each will have a different environment and can, in principle, have contacts with neighbors that are suited to formation of different, topochemical, photodimers. This is illustrated by 61, which contrasts with monomers 62 to 65, which pack with only one molecule per asymmetric unit. Similarly, in monomers containing more than one olefinic bond there may be two or more intermolecular contacts that can lead to different, topochemical, dimers. Finally, any disorder in the crystal, for example due to defective structure or molecular-orientational disorder, can lead to formation of nontopochemical products in addition to the topochemical ones formed in the ordered phase. This would be true, too, in those cases where there is reaction in the liquid phase formed, for example, by local melting. 

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. 

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