Anisotropic dispersion

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. 

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... 

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. 

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. 

The higher terms describe more complicated fluctuations. For polyatomic molecules, the dispersion coefficients depend on orientation, and for noncentro-symmetric molecules, there are anisotropic dispersion coefficients of odd powers, starting at However, the average of the Cy coefficient over all orientations is zero, if all orientations have equal weight. 

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]. 

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]... 

The extent of exfoliation and dispersion of the clay platelets in a nanocomposite where the polymer matrix is reinforced by highly anisotropic dispersed silicate plateletes [19] are affected critically by the kinetic barriers in these systems. In this example, kinetic barriers often have the detrimental effect of not allowing the most favorable morphology to be attained. 

Nucker et al. [8.16] first reported anisotropic dispersion of the free carrier plasmon in Bi2Sr2CaCu20g. Here, we will only discuss the anisotropic dispersion of the insulator case not only because of its simplicity but also for the subsequent understanding of the insulator-to-metal transition in the normal state of these compounds that occurs with doping. 

As mentioned above, the liquid-crystal state exists between the solid and liquid states and is stabilized by the presence of intermolecular, anisotropic dispersion forces that result from the anisotropic nature of the molecules that form the phases. Thus, rod-like molecules are much longer than they are broad and, hence, possess one unique, long axis. Similarly, disk-like molecules are rather flat and, hence, possess one, unique short axis (Figure 2). 

The exact nature of the intermolecular forces need not be specified for the development of the theory. However, in their original presentation Maier and Saupe assumed that the stability of the nematic phase arises from the dipole-dipole part of the anisotropic dispersion forces. The second order perturbed energy of the Coulomb interaction between a pair of molecules 1 and 2 is given by... 

Generally speaking, compounds exhibiting the Sc phase have transverse components of permanent electric dipole moments. A number of molecular statistical models (including hard rod theories for systems composed of oblique cylinders) have been developed. " Goossens " has proposed a model composed of ellipsoidal molecules with attractive interactions arising from anisotropic dispersion forces as well as permanent quadrupole moments. His calculations show that the interaction between the permanent quadrupole moments can produce a tilting of the molecules, but a detailed comparison of the predictions with experimental data has yet to be made. 

Various models proposed may not account for all these experimental facts. The Keating [20] and Bottcher [21] evaluation does not account for such a variety of behavior. Goossens [22] proposed the chiral nematic structure as the result of an anisotropic dispersion energy between chiral mesogens, and predicts for thermotropic LCs a pitch that is essentially independent of temperature. Lin-Liu et al. [23] developed a theory that accounts for all the above-stated temperature effects. The temperature dependence of the pitch is determined by the shape and position of the intermolecular potential as a function of the intermolecular twist... 

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... 

The papers presented in this symposium give some indication of the wide variety of polymers which are now known to form liquid crystalline phases Polymeric liquid crystals are usually classified according to the mesophase structure e g., nematic, cholesteric, smectic A, etc ). However, these classes are quite broad For example, the cholesteric lyotropic phases formed by synthetic polypeptides in suitable solvents differ markedly from the cholesteric thermotropic phases formed from silicone polymers with cho-lesteryl ester side chains. In particular, the driving forces behind the formation of the mesophases are quite different for these two examples, being essentially due to chain stiffness in the first case and to anisotropic dispersion force interactions in the second case It may therefore be useful to classify polymeric liquid crystals according to the polymer chain structure ... 

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... 

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