Dispersion interaction orientation-dependence

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. 

This dispersion interaction must be added to the dipole-dipole interactions between molecules, such as HCl, NH3 and H2O which have a permanent dipole, fi. The magnitude of die dipole moment depends on tire differences in electronegativity of the atoms in the molecule. Here again, the energy of interaction varies as (orientation effect). 

A quantitative model for repulsion and dispersion interactions has been derived by Amovilli and Mennucci [21] based on the theory of weak interactions [22], Cavitation is strictly empirical in this context since it does not depend on the molecule but only on the cavity shape and on the environment it will have an indirect effect on properties only by contributing to the determination of the preferred molecule-interface orientation. 

If one or both of the molecules in an interacting pair lacks a centre of symmetry, e.g. CH4 -CH4, Ar- 014, or Ar- -cyclopropane, there is, in addition to the dispersion energy terms in ET, an orientation-dependent contribution that varies as R. It could be significant for coupling the translation and rotation in gases and liquids and for the lattice energy of solids. ... 

Theoretical formulations of reorganization in the course of electron-transfer processes have undergone a number of advances in recent years. The relative importance of various solvent contributions (including translational as well as orientational response, and inductive and dispersion as well as elecrostatic interactions) can depend strongly on the polarity (i.e., dipolar, higher multipolar, or nonpolar) as well as other molecular features of the solvent [21, 47-49]. Molecular-level perspectives on solvent response are of great utility in helping to parameterize effective cavity models (e.g., in conjunction with conventional [50] or spatially nonlocal [47] dielectric models). Additivity relationships traditionally assumed to pertain to sol-... 

The interaction of the carbon dioxide molecule with the sieve includes electrostatic, induction, dispersion, and repulsion contributions. The CO2 molecule was assumed to be capable of free rotation, so that the directional interactions could be averaged over all orientations using a Boltzmann weighting factor (JJ) this causes the electrostatic ion-quadrupole interaction to depend on the temperature. Mean values were used for the polarizability (a), the diamagnetic susceptibility (x), and the equilibrium radius of the CO2 molecule. Using vector summation for the total electric field at the CO2 molecule, the total potential, c(r), at a given position r is given by ... 

Fig. 1. Orientational dependence of the dispersion (multipole) interaction energy between two pyra-zine molecules at R = lOa (from ref. ). Different 2 -pole contributions to eqn. (21) are labelled by (Ij Iglg) quadratic terms 1 = 1, lg = 1 mixed pole terms 1 + 1 or lg + i ...

The van der Waals forces represent an averaged dipole-dipole interaction, which is a superposition of orientation interactions (between two permanent dipoles, Keesom 1913), induction interaction (between one permanent dipole and one induced dipole, Debye 1920) and dispersion interaction (between two induced dipoles, London 1930). The interaction between two macroscopic bodies depends on the geometry of the system (see Fig. 3). For a plane-parallel film with uniform thickness, h, from component 3 located between two semi-infinite... 

Although, PHB and PHBV polymers are generally considered as hydrophobic polymers according to lordanskii and co-workers (lordanskii, 1999), it seems that bacterial polymers slightly interacts with water molecules explaining the water sorbed concentration inside the film. This hydrophilic character is a function of the ratio between dispersive interactions (hydrophobic effect) and hydrophilic interactions (polar and electrostatic effects) and depends on the morphology and degree of orientation of the aiusotropic units inside film. The presence of imperfect crystallites inside polymer may result in the formation of sites (essentially accessible carbonyl moieties) for the absorption of water molecules. 

The internal pressure primarily responds to rupture of London dispersion and dipole-dipole interactions, whereas the ced also includes breaking of the less distance- and orientation-dependent H-bond interactions. For water the ced is extremely high but the... 

Judged from the above experimental results the anisotropic dispersion interaction seems to accouht successfully for the average solute orientation at least for aromatic solute molecules. It should be emphasized, however, that the applicability of the dipolar approximation adopted in the simple Maier and Saupe theory is questionable. This approximation has been made responsible for the failure of this simple theory to account in a quantitative way for the observed temperature dependence of the order in nematic phases [120]. In an attempt to overcome these difficulties a number of authors improved the Maier and Saupe theory. 

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