Crystallization, anisotropic interactions

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... 

Hu W, Frenkel D (2005) Polymer crystallization driven by anisotropic interactions. Adv Polym Sci (in this volume)... 

The classical cholesteric phase materials show only a weak anisotropic interaction with electric fields and hence are of limited use in electro-optical response applications. Cholesteric phases for these outlets are consequently produced by adding chiral dopants to nematic liquid crystals. 

The critical densities for the formation of the electronic polaronic crystals depend on the effective volume occupied by the doped charge carriers. The anisotropic interactions between the doped charge carriers produce the stripe or checkboard phases [15-16],... 

Hu, W. and Frenkel, DPolymer Crystallization Driven by Anisotropic Interactions. Vol. 191, pp. 1-35. 

On the other hand, when rotational motion is slow, or when the symmetry of the complex is less than cubic, as in Mn2+ complexes with macromolecules, Au)Xr is often greater than one, the anisotropic interactions are incompletely averaged and EPR spectra similar to those for randomly oriented solid samples are observed. In these cases the spectra depend upon the angular relationships between the magnetic field vector and the crystal field axis of the ion. Moreover, when the symmetry of the manganese ion complexes deviate greatly from cubic, the EPR spectra depend upon the sharing of spectral intensity between the normal and forbidden (AMS = + 1, Amp = + 1) transitions. 

Two ions are well-known for their highly anisotropic properties. Firstly, in the rare-earth family, Dy3+ which has a 6H15/2 ground state. The spin-orbit interaction is stronger than the crystal field effects. The ratio J /J can be of the order of 100 (Jj. = 0), gjj = 20 and gi = 0 this is practically an ideal case. Secondly, in the transition element series, the ion Co2+ is also characterized by anisotropic interactions (either in the tetrahedral or octahedral coordination), the anisotropy being however lower than in the case of Dy3+. J /J is about 0.5 for this ion. Some Fe2+ compounds also display a behavior approximating to the Ising model. 

When the sample is allowed to equilibrate in a strong static magnetic field, the direction of B0 defines the z axis, and all the anisotropic interactions discussed earlier in this chapter are displayed. Many commercially important materials are liquid crystals, as are biological membranes, and NMR can be used to investigate their structures. In addition, small molecules that would tumble randomly in an isotropic solvent are impeded in a liquid crystal solvent to the extent that they, too, display anisotropic interactions. However, the order parameter for such a small molecule is usually much less than the maximum values of + 1 or — y2. Typically, values of S 0.1 are observed for molecules dissolved in... 

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