Anisotropic crystals, additive effects

An important addition compared to previous models was the parameterization of the internucleosomal interaction potential in the form of an anisotropic attractive potential of the Lennard-Jones form, the so-called Gay-Berne potential [90]. Here, the depth and location of the potential minimum can be set independently for radial and axial interactions, effectively allowing the use of an ellipsoid as a good first-order approximation of the shape of the nucleosome. The potential had to be calibrated from independent experimental data, which exists, e.g., from the studies of mononucleosome liquid crystals by the Livolant group [44,46] (see above). The position of the potential minima in axial and radial direction were obtained from the periodicity of the liquid crystal in these directions, and the depth of the potential minimum was estimated from a simulation of liquid crystals using the same potential. 

Banes and Hailer [81] studied the effect of fluoride addition on the size and morphology of apatite crystals in close-to-physiological conditions. These authors in particular reported that fluoride uptake was accompanied by some anisotropic growth of the apatite crystals the width and/or thickness of the crystals increased with F uptake while no noticeable change in length was observed. In addition, LeGeros et al. [66] pointed out the decrease in calcium deficiency linked to a progressive fluoride incorporation. 

In much of the above analysis, the relative magnitude of the surface and bulk contribution to the nonlinear response has not been addressed in any detail. As noted in Section 3.1, in addition to the surface dipole terms of Eq. (3.9), there are also nonlocal electric-quadrupole-type nonlinearities arising from the bulk medium. The effective polarization is made of a combination of surface nonlinear polarization, PNS (2co) (Eq. (3.9)), and bulk nonlinear polarization (Eq. (3.8)) which contains bulk terms y and . The bulk term y is isotropic with respect to crystal rotation. Since it appears in linear combination with surface terms (e.g. Eq. (3.5)), its separate determination is not possible under most circumstances [83, 129, 130, 131]. It mimics a surface contribution but its magnitude depends only upon the dielectric properties of the bulk phases. For a nonlinear medium with a high index of refraction, this contribution is expected to be small since the ratio of the surface contribution to that from y is always larger than se2(2co)/y. The magnitude of the contribution from depends upon the orientation of the crystal and can be measured separately under conditions where the anisotropic contribution of vanishes. 

If monomeric liquid crystals are polymerised, the polymers also show in many cases the liquid-crystalline effects. In addition, their viscosity during flow is unexpectedly low in the anisotropic phase state. 

The big difference between normal isotropic liquids and nematic liquids is the effect of anisotropy on the viscous and elastic properties of the material. Liquid crystals of low molecular weight can be Newtonian anisotropic fluids, whereas liquid crystalline polymers can be rate and strain dependent anisotropic non-Newtonian fluids. The anisotropy gives rise to 5 viscosities and 3 elastic constants. In addition, the effective flow properties are determined by the flow dependent and history dependent texture. This all makes the rheology of LCPs extremely complicated. 

The most important difference between particles inside the bulk and in the interfacial layer comes from the surrounding environment of the particles the particles inside the bulk are in an isotropic environment, while those in the interface are in an anisotropic environment thus, in the interlayer, the forces between the particles are unbalanced. To reduce the resulting surface pressure, some additional processes occur that must be taken into account. On clean surfaces (for example, on a solid surface in vacuum), these processes are the bond-length contraction or relaxation and reconstruction of the surface particles (Somorjai 1994). It results in significantly reduced spacing between the first and second layers compared to the bulk. The perturbation caused by this movement propagates a few layers into the bulk. The other effect is that the equilibrium position of the particles changes that is the outermost layers can have different crystal structure than the bulk. This phenomenon is the reconstruction. 

Because the diffraction experiment involves the average of a very large number of unit cells (of the order of 10 in a crystal used for X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the average atom. In addition, if an atom moves from one disordered position to another, it will be frozen in time during the X-ray diffraction experiment. This means that atomic motion and spatial disorder are difficult to separate from each other by simple experimental measurements of intensity falloff as a function of sm6/X. For this reason, atomic displacement parameter is considered a more suitable term than the terms that have been used historically, such as temperature factor, thermal parameter, or vibration parameter for each of the correction factors included in the structure factor equation. A displacement parameter may be isotropic (with equal displacements in all directions) or anisotropic (with different values in different directions in the crystal). 

---