Symmetrical Molecule with Central Forces

In order to simplify the presentation only axially symmetric molecules are considered in detail. This restriction is not altogether necessary as other systems can be treated by similar methods with very similar results. In the next section a general method of separating the intermolecular field into a central-force part and directional terms of various angular symmetries is described. Simple models such as dipole-dipole forces to represent interactions between polar molecules correspond to particular terms of this expansion. The additional free energy due to the directional part of the field can then be estimated by a perturbation method, provided that the additional field is not too large. The method is applicable at any density and enables approximate theories of monatomic systems to be extended so as to apply to more realistic intermolecular fields. 

We consider a macroscopic sample of a simple fluid in thermodynamic equilibrium with its surroundings at the absolute temperature T. The simple fluid sample consists of a number, N, of (identical) spherically symmetric molecules, held in a rigid container of volume V, which interact with pairwise central forces. Thus the mutual forces between two molecules centered at and are derivable from a potential which is a function of the distance — r — r ) between the centers of the two... 

Although certain of the above-mentioned theories are moderately successful in representing the experimental data of CF4 -t- CH and other fluorocarbon + hydrocarbon mixtures, experimental values of and x are required. At present there is no satisfactory method of obtaining these parameters a priori. Scott, in his 1958 review, considered the various possible factors that could lead to a weakening of the unlike interactions in such mixtures. He concluded that the three most significant were the presence of non-central forces, differences in ionization potential, and differences in size of the two component molecules. The use of the Kihara potential together with the Hudson and McCoubrey rule takes account of all these effects and thus the undoubted success of the Knobler treatment is not surprising. Criticisms could be levelled at his use of a spherically symmetric potential for substances such as n-hexane but the use of a more realistic potential such as the Kihara line-core potential is hardly justified until reliable experimental values for the ionization potentials of the fluorocarbons become available. 

Consider a fluid of molecules Interacting with pair additive, centrally symmetric forces In the presence of an external field and assume that the colllslonal contribution to the equation of motion for the singlet distribution function Is given by Enskog s theory. In a multicomponent fluid, the distribution function fi(r,Vj,t) of a particle of type 1 at position r, with velocity Vj at time t obeys the equation of change (Z)... 

LB films of five new hybrid dimethyidioctadecylammonium/heteropolyanions DODA/HPA (HPA=[PZ(H20)M0 03,], Z=Co, Cu, Mn, Zn, Ni) were prepared and characterized by it-A isotherms, UV-Vis absorption spectra, IR spectra, small-angle X-ray diffraction (SAXD), and atomic force microscope (AFM). The results show that these compounds have good film-forming property on the air-water interface. The collapse pressure of LB films is 28.7-37.5mN/m. The area per molecule is 28.18-49.07 nm mol". The LB films have lamellar structures in which the monolayers of the heteropolyanions alternate with bilayers of DODA to form centrally symmetrical LB films. 

The aim hae is to take a microscopic view of an ion inside a solvent. The central consideration is that ions orient dipoles. The spherically symmetrical electric field of the ion may tear water dipoles out of the water lattice and make them point (like compass needles oriented toward a magnetic pole) with the appropriate charged end toward the central ion. Hence, viewing the ion as a point charge and the solvent molecules as electric dipoles, one obtains apicture of ion-dipole forces as the principal source of ion-solvent interactions. 

The energy along the reaction path has a double-well shape, with two symmetrical minima that are due to the strong ion-molecule polarization force and a central barrier to atom exchange. The structme at the barrier corresponds to a planar CH3 group. The reaction therefore proceeds through a Walden inversion, Figme 5.21. 

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