Long-range potential dispersion

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

All of the classical force fields used in the study of ionic liquids contain elements of the Tosi-Fumi potential model. Like Eq. (4.2-1), these force fields are all pairwise additive, meaning that the energy and force on an atom can be found by summing all its interactions with its neighbors. In addition, the force fields all contain a Coulomb term that accounts for electrostatic interactions, a short-range repulsive term and one or more long-range attractive (dispersion) terms. 

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

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... 

The interaction parameters for the water molecules were taken from nonempirical configuration interaction calculations for water dimers (41) that have been shown to give good agreement between experimental radial distribution functions and simulations at low sorbate densities. The potential terms for the water-ferrierite interaction consisted of repulsion, dispersion, and electrostatic terms. The first two of these terms are the components of the 6-12 Lennard-Jones function, and the electrostatic term accounts for long-range contributions and is evaluated by an Ewald summation. The... 

If the structure is decided by an effective potential ues (r), it was demonstrated in the mean spherical approximation (MSA) that the direct correlation function c(r) should rapidly approach — pMerr (r) for large r (see Section IE). According to Reatto and Tau [131], this relationship, which is asymptotically exact for large distance and low density, holds quite well when the long-range dispersion term of the AS potential, - Cg / r6, and the AT triple-dipole potential, < m3 (r) > (8n/3)vp/r6, are considered, so that the direct correlation function reads... 

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