The London-van der Waals Dispersion Force

Although arising from complex quantum-mechanical factors, dispersion forces have several easily understood characteristics, such as the following  

They have a relatively long range of action compared to covalent bonds, their effect in some cases extending to a range of 10 nm or more. 

They may be attractive or repulsive, depending on the situation, and generally do not adhere to simple power laws with respect to their dependence on separation distances. 

They are nonadditive, in that the interaction between any two atoms or molecules will be affected by the presence of other nearby atoms and molecules. 

The dispersion force is basically quantum mechanical in nature because it involves interactions between rapidly fluctuating dipoles resulting from the movement of the outer-valence-shell electrons of an atom or molecule. Rigorous derivations, therefore, can become quite complex and will serve little useful purpose in the present discussion. The interested reader is referred to the works cited in the Bibhography for further enlightenment. 

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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. 

The molecular component of the disjoining pressure, IIm(/i), is negative (repulsive). It is caused by the London-van der Waals dispersion forces. The ion-electrostatic component, IIe(/i), is positive (attractive). It arises from overlapping of double layers at the surface of charge-dipole interaction. At last, the structural component, IIs(/i), is also positive (attractive). It arises from the short-range elastic interaction of closed adsorption layers. 

The London-van der Waals dispersion forces have long been recognized as being important in thin liquid films. These forces have been calculated for different surfaces by pairwise smnmation of the individual dispersion... 

Disjoining pressure is a macroscopic pressure correction accounting for long-range intermolecular interactions (of. Deryagin, 1955). For most common solid-liquid interactions, such as the London-van der Waals dispersion forces, the disjoining pressure has the following form ... 

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. 

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.

L) values for water and mercury have been determined by measuring the interfacial tension of these liquids with a number of liquid-saturated hydrocarbons. The inteimolecular attraction in the liquid hydrocarbons is entirely due to London-van der Waals dispersion forces for all practical purposes. Yjd was derived from contact angle measurements. 

Adsorption by Dispersion Forces. Occurs via London-van der Waals dispersion forces acting between adsorbent and adsorbate molecules (Figure 2-9). Adsorption by this mechanism generally increases with an increase in the molecular weight of the adsorbate and is important not only as an independent mechanism, but also as a supplementary mechanism in all other types. For example, it accounts in part for the pronounced ability of surfactant ions... 

Bowling [1988] describes van der Waals forces in the following way. At absolute zero temperature solids can exhibit local electric fields and above this temperature additional contributions come from the excitation of the atoms and molecules making up the solid material. Van der Waals forces include forces between molecules possessing dipoles and quadrapoles produced by the polarisation of the atoms and molecules in the material. These dipoles and quadrapoles may be present naturally or by induced polarity. Non-polar attractive forces may also be present. The non-polar van der Waals forces may also be referred to as London-van der Waals dispersion forces because London associated these forces with the cause of optical dispersion, i.e. spontaneous polarisation [Com 1966]. Such dispersion forces will make the major contribution to the intermolecular forces, except where the opportunity to polarise is small and the dipole moment is large. 

London-van der Waals dispersion forces V ) and the total interaction (Vf). (Adapted from Schramm [15]. Copyright (2003), reproduced with permission of John Wiley Sons, Inc)... 

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. 

Ionic species can induce a dipole in a nonpolar molecule over a short range. London forces exist between instantaneous and induced dipoles, and are operative between all bodies when they are close together. For molecular systems they are also commonly called van der Waals attractive forces after the Dutch physicist (J.D. van der Waals) who described these forces as being active in crystals [65]. The London/van der Waals force is also frequently referred to as the dispersion force and is important in the solution phase. 

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). 

Further developments with this model were to a large extent initiated by Fowkes ), who started from the assumption that the molecular forces, determining Y could be split up into components, of which only the London-van der Waals or dispersion forces had enough range to penetrate into an adjoining phase. For these forces the Berthelot principle would hold, so in (2.11.16] the geometric mean only involves the dispersion contributions to y and he replaced [2.11.17] by... 

Hamaker Constant In the description of the London-van der Waals attractive energy between two dispersed bodies, such as particles. The Hamaker constant is a proportionality constant characteristic of the internal atomic packing and polarizability of the particles. Also termed the van der Waals-Hamaker constant. See also Dispersion Forces. 

J. N. Israelachvili, The calculation of van der Waals dispersion forces between macroscopic bodies, Proc. Royal Soc. (London) 331A 39 (1972). See also Chap. 7 in J. Mahanty and B. W. Ninham, Dispersion Forces. Academic Press, London, 1976. 

Table I reports the values of the static (Agt) and dispersive (Ajisp) parts of the Hamaker constant of silica in water, calculated from Equation (2). The corresponding values for TiOa, a typical electrocratic colloidal oxide, are also included for comparison, which is probably the key to an explanation of the special behavior of the silica hydrosols. These data show that the Hamaker constant of Si02 is approximatively 35 times smaller than that of Ti02. Thus, the attraction energy between two silica particles is 35 times smaller than that between two Ti02 particles of the same size. This weakness of the attraction energy enhances the role of the afore-mentioned structural forces, which are strongly dominated by the London-van der Waals attraction in the case of Ti02.

Interparticle forces are a determinant factor for most properties of dispersions, including rheological behavior. They are produced by the molecular forces on the surfaces of the particles, due to their nature or to adsorbed molecules, that modify the interface. These are electrical forces arising from charges on the particles and London-van der Waals attraction forces. The role of these forces on suspension stability has been extensively study and is known as the DLVO theory. In addition, sterical forces encountered on dispersions stabilized with nonionic species also exert an important influence on rheological behavior. The nature of these forces will not be considered since they are matters of discussion in Chapters 1-4. However, from a rheological point of view it is impwtant to understand how these factors modify the flow characteristics of dispersions. 

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