Van der Waals dispersion

Good, van Oss, and Caudhury [208-210] generalized this approach to include three different surface tension components from Lifshitz-van der Waals (dispersion) and electron-donor/electron-acceptor polar interactions. They have tested this model on several materials to find these surface tension components [29, 138, 211, 212]. These approaches have recently been disputed on thermodynamic grounds [213] and based on experimental measurements [214, 215]. 

The measurement of surface forces out-of-plane (nonual to the surfaces) represents a central field of use of the SFA teclmique. Besides the ubiquitous van der Waals dispersion interaction between two (mica) surfaces... 

There are numerous techniques which provide information related to the surface energy of solids. A large array of high-vacuum, destructive and non-destructive techniques is available, and most of them yield information on the atomic and chemical composition of the surface and layers just beneath it. These are reviewed elsewhere [83,84] and are beyond the scope of the present chapter. From the standpoint of their effect on wettability and adhesion, the property of greatest importance appears to be the Lifshitz-van der Waals ( dispersion) surface energy, ys. This may be measured by the simple but elegant technique of... 

The concept of adsorption potential comes from work with high-purity, synthetic microporous carbon, which relies solely on van der Waals dispersive and electrostatic forces to provide the energy for adsorption. The polymeric microporous adsorbents that operate solely through van der Waals dispersive and electrostatic forces often cannot provide the surface potential energy needed to trap compounds that are gases under ambient conditions, and for very volatile compounds the trapping efficiency can be low for similar reasons. 

In molecular crystals, there are two levels of bonding intra—within the molecules, and inter—between the molecules. The former is usually covalent or ionic, while the latter results from photons being exchanged between molecules (or atoms) rather than electrons, as in the case of covalent bonds. The hardnesses of these crystals is determined by the latter. The first quantum mechanical theory of these forces was developed by London so they are known as London forces (they are also called Van der Waals, dispersion, or dipole-dipole forces). 

Table A.4.1 Attractive Forces at Interfaces-surface Energy, y, and London-van der Waals Dispersion Force Component of Surface Energy, y(L) a>...

London-van der Waals forces, which are multipole interactions produced by correlation between fluctuating induced multipole moments in two nearly uncharged polar molecules. These forces also include dispersion forces that arise from the correlation between the movement of electrons in one molecule and those of neighboring molecules. The van der Waals dispersion interaction between two molecules is generally very weak, but when many groups of atoms in a polymeric structure act simultaneously, the van der Waals components are additive. 

FIG. 10.7 Direct measurements of van der Waals dispersion forces. The measurements correspond to the force between two flat (mica) surfaces separated by a distance d. The line shown is the theoretical expression for unretarded van der Waals force. The figure shows that the unretarded expression describes the measurements sufficiently accurately for d about 6.5 nm or less. (Redrawn with permission of J. N. Israelachvili and G. E. Adams, J. Chem. Soc., Faraday Trans. 1, 78, 975 (1978).)... 

The model of Girifalco, Good, and Fowkes has been extended to other interactions. For example, if we assume that the surface energies are the sum of van der Waals (dispersive) and polar interactions, one often uses the equation [272]... 

Curve P represents the physical interaction energy between M and X2. It inevitably includes a short-range negative (attractive) contribution arising from London-van der Waals dispersion forces and an even shorter-range positive contribution (Born repulsion) due to an overlapping of electron clouds. It will also include a further van der Waals attractive contribution if permanent dipoles are involved. The nature of van der Waals forces is discussed on page 215. 

Clarke and co-workers developed a model to calculate the thickness of the amorphous film observed in polycrystalline ceramics.37,38 The model is based on a force balance between an attractive van der Waals dispersion force that acts across the grain boundaries, any capillary forces present, and repulsive disjoining forces (such as steric forces and electrical double-layer forces) in the amorphous film.37,38 The repulsive steric force is based on the... 

Van der Waals postulated that neutral molecules exert forces of attraction on each other which are caused by electrical interactions between dipoles. The attraction results from the orientation of dipoles due to any of (1) Keesom forces between permanent dipoles, (2) Debye induction forces between dipoles and induced dipoles, or (3) London-van der Waals dispersion forces between fluctuating dipoles and induced dipoles. (The term dispersion forces arose because they are largely determined by outer electrons, which are also responsible for the dispersion of light [272].) Except for quite polar materials the London-van der Waals dispersion forces are the more significant of the three. For molecules the force varies inversely with the sixth power of the intermolecular distance. 

Figure S.3 Potential energies of interaction between two colloidal particles as a function of their distance of separation, for electrical double layers due to surface charge (VolK London-van der Waals dispersion forces (V ), and the total interaction (VT). From Schramm [426], Copyright 2003, Wiley.

It is true that all molecular and atomic forces ultimately find their root in the mutual behavior of the constituent parts of the atoms, viz., the nuclei and the electrons. They may theoretically all be derived from the fundamental wave equations. It is, however, convenient, as in other branches of physics and chemistry, to treat the various forms of mutual interaction of atoms as different forces, acting independently. We shall therefore follow the usual procedure and treat such forces as the nonpolar van der Waals (dispersion) forces, the forces of the electrostatic polarization of atoms or molecules by ions or by dipoles, the mutual attraction or repulsion Coulomb forces of ions and of dipoles, the exchange forces leading to covalent bonds, the repulsion forces due to interpenetration of electronic clouds, together with the Pauli principle, etc., all as different, independently acting forces. 

For van der Waals (dispersion) interactions, the polarizabilities of the sorbate molecule and the atoms on the sorbent surface are both important (see Eq. (9)). For electrostatic interactions, for a given sorbate molecule, the charges and van der Waals radii of the surface atoms are important. The roles of these parameters are discussed separately. 

B. M. Axilrod and E. Teller, "Interaction of the van der Waals type between three atoms," J. Chem. Phys., 11, 299-300 (1943) see also the pedagogical article by C. Farina, F. C. Santos, and A. C. Tort, "A simple way of understanding the non-additivity of van der Waals dispersion forces," Am. J. Phys., 67, 344-9 (1999) for the step from two-body to three-body interactions. 

Interactions between crossed cylinders of mica in air, uncoated or coated with fatty acid monolayers, are described in J. N. Israelachvili and D. Tabor, "The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm," Proc. R. Soc. London Ser. A, 331, 19-38 (1972). An excellent review of this and related work is given in J. N. Israelachvili and D. Tabor, Van der Waals Forces Theory and Experiment, Vol. 7 of Progress in Surface and Membrane Science Series (Academic Press, New York and London, 1973). Later reconciliation of theory and experiment required taking note of cylinder radius L. R. White, J. N. Israelachvili, and B. W. Ninham, "Dispersion interaction of crossed mica cylinders A reanalysis of the Israelachvili-Tabor experiments," J. Chem. Soc. Faraday Trans. 1, 72, 2526-36 (1976). 

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