Isotropic potentials, orientational

Thus Q = K — K implies that Q = k — k. In other words, Q is the momentum transfer to the electron. If we assume that there is no particular orientation of the perturber during the collision we can replace U (fi, fi, p) by the isotropic potential U(fi, fi, p). With this approximation in Eq. (11.5) we recognize the Bom approximation to the electron scattering amplitude... 

Poniewierski and Stecki [245] combined hard Onsager spherocylinders with an attractive Maier-Saupe type quadrupolar potential. The Lenard-Jones interaction potential often used in isotropic phases with a repulsive term proportional to and an attractive part proportional to r" depends only on the intermolecular distances r, and is therefore not suited to the description of anisotropic fluids. A modification of this isotropic potential that accounts for the relative orientations of anisotropic particles has been proposed by Berne and Pechukas... 

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

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... 

Figure I. Schematic representation of statistical orientational distribution functions in isotropic (I) and nematic (N) potentials. Dashed curves depict adjusted distributions under electric field poling.

In the positive branch of the i/V graph, anodic dissolution process will remove material from silicon crystals. The conditions for optimal etching of silicon have been extensively explored for micromachining or surface polishing in the fabrication of electronic devices. Most generally, the etch rate of silicon in HE solutions is isotropic among the various crystalKne orientations. The etch rate of silicon at room temperature at the open-circuit potential (OCP) is very low, on the order of 10 nm s , which is equivalent to 100 nA cm , in aqueous HE solutions. 

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