Anisotropic dispersion potential

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]. 

A new empirical potential for water has been developed using spectroscopic data, which is able to model condensed water with good accuracy.483 The potential is referred to as the VRT(ASP-W)III potential (the third fitting of the Anisotropic Site Potential with Woemer dispersion to Vibration-Rotation Tunnelling data). It give excellent results for vibrational properties of water clusters up to (H20)6, but unlike earlier spectroscopically derived potentials also models the liquid state well. MC simulations are used to study the liquid state properties. It is noted that this potential only partly accounts for many-body interactions (the induction term) and the simulations do not include... 

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... 

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. 

The starting point for a theory of the anisotropic intermolecular interaction in liquid crystals is the Maierand Saupe theory [114,115,116,118].This theory is based on the assumption that the intermolecular interaction potential in nematic liquid crystals is determined primarily by Lx)ndon dispersion forces. The effective anisotropic potential U of a molecule C in the anisotropic dispersion field generated by its oriented neighbors s is calculated by averaging the pair potential between two molecules C and s over all orientations of the solvent molecules s and over all... 

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. 

We consider first the Maier-Saupe tlieory and its variants. In its original foniiulation, tills tlieory assumed tliat orientational order in nematic liquid crystals arises from long-range dispersion forces which are weakly anisotropic [60, 61 and 62]. However, it has been pointed out [63] tliat tlie fonii of tlie Maier-Saupe potential is equivalent to one in... 

A rigorous treatment of dispersion in soils is beyond the scope of this book. However, some qualitative discussion is warranted because of the potential and existing problems already described. Two ntain problems arise bceause dispersion in soil (or land) is anisotropic (i.e., it varies with direction) and the penneability is not only a variable but also att unknown. 

As has been noticed by Gelbart and Gelbart [7], the predominant orientational interaction in nematics results from the isotropic dispersion attraction modulated by the anisotropic molecular hard-core. The anisotropy of this effective potential comes from that of the asymmetric molecular shape. The coupling between the isotropic attraction and the anisotropic hard-core repulsion is represented by the effective potential... 

The above potential neglects a number of effects, such as anisotropic polarizability of the surface atoms, three-body terms, substrate mediated dispersion energy, and so forth. To better represent experiment and detailed anisotropic calculations [69], a modified form of the truncated Fourier expansion (6) is considered [67,68], namely... 

A liquid crystal is a general term used to describe a variety of anisotropic structures formed by amphiphilic molecules, typically but not exclusively at high concentrations. Hexagonal, lamellar, and cubic phases are all examples of liquid crystalline phases. These phases have been examined as drug delivery systems because of their stability, broad solubilization potential, ability to delay the release of encapsulated drug, and, in the case of lamellar phases, their ability to form closed, spherical bilayer structures known as vesicles, which can entrap both hydrophobic and hydrophilic drug. This section will review SANS studies performed on all liquid crystalline phases, except vesicles, which will be considered separately. Vesicles will be considered separately because, with a few exceptions, generally mixed systems, vesicles (unlike the other liquid crystalline phases mentioned) do not form spontaneously upon dispersal of the surfactant in water and because there have been many more SANS studies performed on these systems. 

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