Dispersion force Potential

It is interesting to compare the results of the simple and the accurate classical collision theories in the case of an atom-atom (or radical-radical) recombination reaction governed by an attractive dispersion-force potential... 

Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

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... 

Sorption of nonionic, nonpolar hydrophobic compounds occurs by weak attractive interactions such as van der Waals forces. Net attraction is the result of dispersion forces the strength of these weak forces is about 4 to 8 kj/mol ( 1 2 kcal/mol). Electrostatic interactions can also be important, especially when a molecule is polar in nature. Attraction potential can develop between polar molecules and the heterogeneous sod surface that has ionic and polar sites, resulting in stronger sorption. 

FIG. 1 The mean force potential acting between colloidal species, /3fV (r), in adsorbed colloidal dispersion. In parts (a) and (b) the matrix density is taken as negligibly small, = 10 and = 0.193, respectively. In both parts, the evolution of the mean force potential with solvent density is shown p = 0.2, 0.3 and 0.4 (solid, dashed, and dotted lines, respectively). In part (c) the evolution of the PMF on matrix density is presented. The solvent density is held constant, p =0.3 the matrix density is Pmcr = 0.193, 0.386, and 0.772 (dotted, dashed, and solid lines, respectively). The diameter of the matrix species is = 7.055. The density of colloids is Pcg] = 10 , with Uc = 5, in all the cases in question. 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

The elution of compounds on GC columns is a complex process related to the volatility of the compound, which results from its boiling point, and the chemical interactions between the compound and the stationary phase. These interactions are typically those which arise from polar-polar interactions, dispersion forces, dipole-dipole interactions, and so forth. Collectively, they are described by the term the chemical potential, Ap.°, which derives from the potential for the compound to... 

Instead of the hard-sphere model, the Lennard-Jones (LJ) interaction pair potential can be used to describe soft-core repulsion and dispersion forces. The LJ interaction potential is... 

To represent the elasticity and dispersion forces of the surface, an approach similar to that of Eqs. (3) and (4) can be taken. The waU molecules can be assumed to be smeared out. And after performing the necessary integration over the surface and over layers of molecules within the surface, a 10-4 or 9-3 version of the potential can be obtained [54,55], Discrete representation of a hexagonal lattice of wall molecules is also possible by the Steele potential [56], The potential is essentially one dimensional, depending on the distance from the wall, but with periodic variations according to lateral displacement from the lattice molecules. Such a representation, however, has not been developed in the cylindrical pore... 

Phthalocyanines have attracted particular attention as potential surface modifiers due to their stability and tendency to form ordered structures directed by dispersion forces. They are inherently host-guest structures with a readily interchangeable coordinating metal ion, which in the solid state results in a tunable bandgap. At a surface, in addition to possibly interesting electronic... 

Potential functions for the interaction energies due to repulsive and to dispersion forces between two atoms as a function of the interatomic distance... 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

The Smoluchowski-Levich approach discounts the effect of the hydrodynamic interactions and the London-van der Waals forces. This was done under the pretense that the increase in hydrodynamic drag when a particle approaches a surface, is exactly balanced by the attractive dispersion forces. Smoluchowski also assumed that particles are irreversibly captured when they approach the collector sufficiently close (the primary minimum distance 5m). This assumption leads to the perfect sink boundary condition at the collector surface i.e. cp 0 at h Sm. In the perfect sink model, the surface immobilizing reaction is assumed infinitely fast, and the primary minimum potential well is infinitely deep. 

Figure 4. Potential energy diagrams for a pair of particles with on the left, a steric barrier (V ) and dispersion force attraction (V.) and on the right, with electrostatic repulsion (V ) added. Reproduced with permission from Ref. (13).Copyright 1980, Butterworths.

G. C. Lie and E. Clementi, Study of the structure of molecular complexes XII Structure of liquid water obtained by Monte Carlo simulation with the Hartree-Fock potential corrected by inclusion of dispersion forces, J. Chem. Phys. 62 2195 (1975). 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

The model presented here develops these ideas and introduces features which make the calculation of mixture properties simple. For a polar fluid with approximately central dispersion forces together with a strong angle dependent electrostatic force we may separate the intermolecular potential into two parts so that the virial coefficients, B, C, D, etc. of the fluid can be written as the sum of two terms. The first terms B°, C°, D°, etc, arise from dispersion forces and may include a contribution arising from the permanent dipole of the molecule. The second terms contain equilibrium constants K2, K, K, etc. which describe the formation... 

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