London dispersion constants

The Hamaker constant of any material depends on the number of atoms or molecules per unit volume q and the London dispersion constant... 

In this equation, AG°CS is taken to be negligible for p- and y-cyclodextrin systems and to be constant, if there is any, for the a-cyclodextrin system. The AG W term is virtually independent of the kind of guest molecules, though it is dependent on the size of the cyclodextrin cavity. The AG dw term is divided into two terms, AG°,ec and AGs°ter, which correspond to polar (dipole-dipole or dipole-induced dipole) interactions and London dispersion forces, respectively. The former is mainly governed by the electronic factor, the latter by the steric factor, of a guest molecule. Thus, Eq. 2 is converted to Eq. 3 for the complexation of a particular cyclodextrin with a homogeneous series of guest molecules ... 

With this basis, one gets for the constant in the London dispersion energy formula E = — j... 

A good start is the long and well-referenced review article Origins and applications of London dispersion forces and Hameker constants in ceramics by Roger J. 

The stability constant of complexes between /1-cyclodextrine and p-nitroaniline is higher than that of aniline because the resonace charge delocalization (and London dispersion interactions) is an important factor influencing the stability of these complexes62. This behaviour parallels that of corresponding phenols. 

The over-riding significance of gas-phase measurements is that in the gaseous state the contributions of electrostatic and even of London dispersion forces can be reasonably estimated this allows of more significant comparison with the observed AH values. At this point it may be appropriate to emphasize the variation in AH with the medium in which it is observed. If the free energy increase (AG) attending the dissociation of the dimer were to vary with the dielectric constant (D) according to... 

It should be noted that when replacing the London dispersive interactions term by other properties such as, for example, the air-hexadecane partition constant, by expressing the surface area in a more sophisticated way, and/or by including additional terms, the predictive capability could still be somewhat improved. From our earlier discussions, we should recall that we do not yet exactly understand all the molecular factors that govern the solvation of organic compounds in water, particularly with respect to the entropic contributions. It is important to realize that for many of the various molecular descriptors that are presently used in the literature to model yiw or related properties (see Section 5.5), it is not known exactly how they contribute to the excess free energy of the compound in aqueous solution. Therefore, when also considering that some of the descriptors used are correlated to each other (a fact that... 

Solutions of nonpolar solutes in nonpolar solvents represent the simplest type. The forces involved in solute-solvent and solvent-solvent interactions are all London dispersion forces and relatively weak. The presence of these forces resulting in a condensed phase is the only difference from the mixing of ideal gases. As in the latter case, the only driving force is the entropy (randomness) of mixing. In an ideal solution (AW, = 0) at constant temperature the free energy change will be composed solely of the entropy term ... 

There are two types of solute-solvent interactions which affect absorption and emission spectra. These are universal interaction and specific interaction. The universal interaction is due to the collective influence of the solvent as a dielectric medium and depends on the dielectric constant D and the refractive index n of the solvent. Thus large environmental perturbations may be caused by van der Waals dipolar or ionic fields in solution, liquids and in solids. The van der Waals interactions include (i) London dispersion force, (ii) induced dipole interactions, and (iii) dipole-dipole interactions. These are attractive interactions. The repulsive interactions are primarily derived from exchange forces (non bonded repulsion) as the elctrons of one molecule approach the filled orbitals of the neighbour. If the solute molecule has a dipole moment, it is expected to differ in various electronic energy states because of the differences in charge distribution. In polar solvents dipole-dipole inrteractions are important. 

See R. H. French, "Origins and applications of London dispersion forces and Hamaker constants in ceramics," J. Am. Ceram. Soc., 83, 2117-46 (2000) K. van Benthem, R. H. French, W. Sigle, C. Elsasser, and M. Rtihle, "Valence electron energy loss study of Fe-doped SrTiOs and a E13 boundary Electronic structure and dispersion forces," Ultramicroscopy, 86, 303-18 (2001), and the extensive literature cited therein. Energy E" in those papers is written as hco" here. 

These temporary dipoles last only a fraction of a second, and they constantly change yet they are correlated so their net force is attractive. This attractive force depends on close surface contact of two molecules, so it is roughly proportional to the molecular surface area. Carbon tetrachloride has a larger surface area than chloroform (a chlorine atom is much larger than a hydrogen atom), so the intermolecular London dispersion attractions between carbon tetrachloride molecules are stronger than they are between chloroform molecules. 

The chemical term AG9 is assumed to be a constant which applies for all species of a given heavy metal (e.g., Pb, PbOH, PbCl" ", etc.), and which takes into account effects such as those of Van der Waals and London dispersion forces which do not easily lend themselves to theoretical interpretation. 

For the substituted polysilylenes, (SiRR ) , the coupling constant can be varied systematically by changing the side groups (this change affects e and Vd via the backbone polarizability) or the solvent (this change affects Vj) via the London dispersion forces e is expected to be only weakly solvent dependent for nonpolar systems). Therefore, in principle, the three distinct phase behaviors predicted by the theory may be observed by judicious choice of polymer-solvent pairs. 

In the above isotherm equation, K is the equilibrium constant for the molecules (due to London dispersion interactions), while K is the equilibrium constant for the ions and has the form... 

The composite system of two different linear molecules has hence four independent elementary dipole dispersion constants, which in London form can be written as ... 

Considering several dipole excitations, we can write for the two dispersion constants in London form ... 

Table 4.3 N-term results for the Cn dipole dispersion constant and the Cg London dispersion coefficients for the H-H interaction...

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