Anisotropic dispersion interaction

Both theoretical approaches qualitatively describe the "thermotropic" and "lyotropic" liquid crystalline state of rod-like molecules ( see also D.B. DuPre, R. Parthasarathy, this book). Combination of both theories (Flory, Ronca)(7) slightly improves the predictions compared to the experimental findings. Anisotropic dispersion interactions and/or anisometric molecular shape can thus be the basis for explaining theoretically the appearance of "lyotropic" and "thermotropic" liquid crystalline phases. 

Expansion coefficients of the anisotropic dispersion interaction in the series of Legendre polynomials P/(cosy) were evaluated using the method of Reduced Spectra of Oscillator Forces (RSOF) by Meyer et al [6] and the relevant calculations of the dynamic fragment polarizabilities [7]... 

Figure 20. Phase diagram for the right-handed system 3Cl-CTC/EMMAc. Experimentally determined phase boundaries O theory of Warner and Flory with anisotropic dispersion interaction and an aspect ratio of x=20 . Vp, Vp volume fraction of the polymer in the isotropic and anisotropic phase at equilibrium, respectively (adapted from [11]).

PVT analysis presented in this chapter has revealed that main-chain LCs resemble monomer LCs in many thermodynamic characteristics. In addition to the conventional anisotropic dispersion interactions and steric repulsions, however, special attention is required for the effect of the nematic conformation of the spacer on the molecular... 

Hohm U (1994) Dispersion of polarizability anisotropy of H2, O2, N2O, CO2, NH3, C2H6, and cyclo-C3H6 and evaluation of isotropic and anisotropic dispersion-interaction energy coefficients. Chem Phys 179 533-541... 

The ab initio potentials used in solid nitrogen are from Refs. [31] and [32]. They have been respresented by a spherical expansion, Eq. (3), with coefficients up to = 6 and Lg = 6 inclusive, which describe the anisotropic short-range repulsion, the multipole-multipole interactions and the anisotropic dispersion interactions. They have also been fitted by a site-site model potential, Eq. (5), with force centers shifted away from the atoms, optimized for each interaction contribution. In the most advanced lattice dynamics model used, the TDH or RPA model, the libra-tions are expanded in spherical harmonics up to / = 12 and the translational vibrations in harmonic oscillator functions up to = 4, inclusive. 

Judged from the above experimental results the anisotropic dispersion interaction seems to accouht successfully for the average solute orientation at least for aromatic solute molecules. It should be emphasized, however, that the applicability of the dipolar approximation adopted in the simple Maier and Saupe theory is questionable. This approximation has been made responsible for the failure of this simple theory to account in a quantitative way for the observed temperature dependence of the order in nematic phases [120]. In an attempt to overcome these difficulties a number of authors improved the Maier and Saupe theory. 

Hard-core repulsion between anisotropic molecules, discussed in the previous subsection, can be the driving force of the I-N transition in lyotropic systems. In contrast, in thermotropic liquid crystals the transition occurs at some particular temperature and therefore some attraction interaction must be involved. The corresponding molecular theory, based on anisotropic dispersion interactions, was proposed by Maier and Saupe[ll, 12]. 

The more serious problem in the original Maier-Saupe theory is related to the choice of the anisotropic dispersion interaction potential (Eq. 27) (see the detailed discussion... 

In principle, a combination of short range repulsive forces and anisotropic dispersive interactions between mesomorphic molecules is sufficient to understand their selforganization in mesophases [1]. This basic approach is used for theoretical descriptions of mesomorphic states, especially for their simulations by molecular dynamics or Monte Carlo calculations of systems composed of idealized particles. Even on this simplified level, realistic pair potentials constitute one of the crucial problems. 

First, it is important to appreciate that all liquid crystal mesophases exist due to non-covalent interactions between molecules, namely the anisotropic dispersion forces mentioned earlier. However, this section will address more specific non-covalent interactions that have been used either to induce liquid-crystalline behaviour or to generate a new species that is liquid crystalline. 

A highly anisotropic polarisability is required in order to enhance intermolecular dispersive interactions. This is favoured by the presence of easily polarisable groups and permanent dipoles. 

Wormer PES, Hettema H, Thakkar AJ (1993) Intramolecular bond length dependence of the anisotropic dispersion coefficients for H2-rare gas interactions. J Chem Phys 98 7140-7144... 

In this equation, viscosity is independent of the degree of dispersion. As soon as the ratio of disperse and continuous phases increases to the point where particles start to interact, the flow behavior becomes more complex. The effect of increasing the concentration of the disperse phase on the flow behavior of a disperse system is shown in Figure 8-41. The disperse phase, as well as the low solids dispersion (curves 1 and 2), shows Newtonian flow behavior. As the solids content increases, the flow behavior becomes non-Newtonian (curves 3 and 4). Especially with anisotropic particles, interaction between them will result in the formation of three-dimensional network structures. These network structures usually show non-Newtonian flow behavior and viscoelastic properties and often have a yield value. Network structure formation may occur in emulsions (Figure 8-42) as well as in particulate systems. The forces between particles that result in the formation of networks may be... 

The correlation contributions are of secondary importance. They primarily include the weakly anisotropic dispersion term (cf. Fig. 6) and a smaller but much more anisotropic electrostatic correlation term. In the PES modeling, the latter may be safely absorbed in the total electrostatic interaction. 

From the theory of London dispersion interactions as extended by Inura and Okano > and otherto include anisotropic interactions, one may estimate CT 0.05. Values of T evaluated on this basis according to Eq. (19) are compared in Table 4 with those deduced from the transition temperatures T j, the axial ratios x, and the function shown in Fig. 9. The agreement is quite satisfactory. The values... 

The molecular DFT approach derives an expression J-c[p] expanding the anisotropic excess parts of the perturbative pair interaction potentials into spherical harmonics. That way the inclusion of the anisotropic dispersion and quadrupolar interactions succeeds [7]. 

So far only the minimal multipole moments and their contribution to the j, a., and (t2) values have been considered. However, they are not the only manifestations of the degeneracy in the characteristics of the absorption and Raman spectra under consideration. For instance, an important additional contribution to the torque can arise because of the anisotropy of the dispersion interaction between the molecules owing to the nonzero matrix elements of the anisotropic components of the polarizability tensor, i.e., the anisotropy of the cubic symmetry molecules in degenerate states. 

In the theory of electric properties of molecular systems in degenerate electronic states some unsolved problems remain. First, the problem of intermolecular interactions considering the degeneracy of the electronic states of the interacting molecules has not been solved completely. In this case, besides the lowering of the multipolarity of the interaction described in this paper, one can expect an essential contribution of anisotropic induction and dispersion interactions to different virial correction to the equations of state, refraction, and other electric characteristics of matter. 

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