Orientation dependent energy

Orientational energy from this source provides the basis for the Maier and Saupe theory asymmetry of molecular shape and its influence on molecular packing in the fluid are not taken into account. Consequently, in order to reconcile this theory with experiments, it has been necessary to postulate unreasonably large orientation-dependent energies and, by implication, excessively large value of Aa... 

Thus, kT is the orientation-dependent energy Soriem due to interactions between a segment and its neighbors in the perfectly ordered (vj/ = 0 and s = 1) neat fluid. The characteristic temperature is related to Aa according to... 

The orientation-dependent energy for the system as a whole, obtained as the averaged sum of the mean field interactions of all segments, is... 

As predicted by Flory, the critical aspect ratio of rod molecules for thermotropic liquid crystallinity is 6.4 [2,3]. However, in this prediction, the influence of temperature was not considered. The temperature effect was included in the form of an orientationally dependent energy function in more recent development of the Flory lattice model [3]. For LMWLCs, the aspect ratio is defined as Ljd, in which L is the length and d is the diameter of the molecule. For LCPs, the aspect ratio is replaced by persistence ratio through replacing molecule length L by persistence length q [3],... 

The electric quadrupole interaction Eirises from the orientation dependent energy of the non-spherical nucleus in the gradient of the electrostatic field at the nuclear site. In quantum-mechanical terms, the quadrupole interaction energy, E q of (18.41) becomes the quadrupolar hamiltonian operator S qI... 

There has been considerable elaboration of the simple Girifalco and Good relationship, Eq. XII-22. As noted in Sections IV-2A and X-6B, the surface ftee energies that appear under the square root sign may be supposed to be expressible as a sum of dispersion, polar, and so on, components. This type of approach has been developed by Dann [70] and Kaelble [71] as well as by Schonhom and co-workers (see Ref. 72). Good (see Ref. 73) has preferred to introduce polar interactions into a detailed analysis of the meaning of in Eq. IV-7. While there is no doubt that polar interactions are important, these are orientation dependent and hence structure sensitive. 

Crystals have spatially preferred directions relative to their internal lattice structure with consequences for orientation-dependent physico-chemical properties i.e., they are anisotropic. This anisotropy is the reason for the typical formation of flat facetted faces. For the configuration of the facets the so-called Wullf theorem [20] was formulated as in a crystal in equihbrium the distances of the facets from the centre of the crystal are proportional to their surface free energies. ... 

Cottrell, A.H., 1996, Point defects in Al-Ni-Cu alloys based on the NiAl phase, Intermetallics, 4 1 Leapman, R.D., and Silcox, J.,1979, Orientation dependence of core edges in electron energy loss spectra from anysotropic materials, Phys. Rev. Lett., 42 1361. 

In this case the interaction between neighbouring molecules is not only stronger but also orientation dependent. The mean statistical energy of dipole-dipole interactions 0dd also decreases with r 6, but depends on i2 (p dipole moment) according to 3>... 

The EM method has been tested on the inert gases and a range of small molecules and gives good agreement with experimental results in almost all cases.17 This method will be discussed further in relation to the orientation dependence of the electron impact ionization cross section in a later section. The semiempirical polarizability method described below was developed to calculate and to use it with the amax values obtained from this method in order to calculate the energy dependence of the cross section. 

Saini S, Srinivas G, Bagchi B (2009) Distance and orientation dependence of excitation energy transfer from molecular systems to metal nanoparticles. J Phys Chem B 113 1817-32... 

Rotationally mediated trapping is important. The coupling between rotational and kinetic energy arises from the orientational dependence of the attractive portion of the potential. 

Despite the orientational dependence of the sticking probability, at low incident kinetic energies all molecules are reoriented into favorable binding orientations during the collision. However, they might not actually stick. 

Our goal in this work is to understand the process of energy loss suffered by protons when they collide with water, and by which modes energy is transferred to the target. In particular, we are interested in the orientational dependence of the stopping power. 

The phenomenon of the orientation dependent surface free energy of metals is theoretically and experimentally well established [1-4]. An example from the experimental work of Heyraud and Metois for Pb is shown in fig. 1 [5]. Here the relative anisotropy of y(0) is derived from the ECS of Pb particles on graphite measured by scanning electron... 

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