Van der Waals force London

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

Adhesion of particles Small particles experience adhesion forces, allowing them to attach to surfaces. These forces may be made up from surface tension of liquid films, or London (Van der Waals) forces. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

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. 

In the concentrated environment of electroplating baths, the diffusiophoretic force is the only force that can counteract the attractive London-van der Waals force. An appreciable diffusiophoretic force is, however, only present in binary electrolytes. In practice, particles are codeposited from supported electrolytes. In supported electrolytes, the diffusiophoretic force is absent, and Valdes model predict that under... 

We often use the term dispersion force to describe these attractions. Some texts prefer the term London-van der Waals forces. 

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. 

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. 

London-van der Waals forces generally are multipole (dipole-dipole or dipole-induced dipole) interactions produced by a correlation between fluctuating induced multipole (principal dipole) moments in two nearly uncharged polar molecules. Even though the time-averaged, induced multipole in each molecule is zero, the correlation between the two induced moments does not average to zero. As a result an attractive interaction between the two is produced at very small molecular distances. 

The repulsive force depends on the double layer potential and thickness, the particle radius and the dielectric constant of the medium, whereas the attractive force arises from retarded London/van der Waals forces. 

The influence of the electric potential of the surface of the drops was shown by Watanabe and Gotoh (W3) for the case of mercury droplets in aqueous solutions. In the case of oil drops in water the electric double layer is in the water phase, which makes possible a real interaction between the double layers of the two drops that approach each other. In the case of water drops in an oil phase, however, the electric double layers are on the inside of the drops, so that the interaction of these layers when two drops approach each other is much smaller [see Sonntag and Klare (S5)], which means that the potential barrier is much smaller or may even be absent, and the attraction by London-van der Waals forces predominates. This at least is a first explanation of why systems in which water is the dispersed phase show much higher interaction rates than systems in which oil is the dispersed phase. 

For a typical experimental hydrosol critical coagulation concentration at 25°C of 0.1 mol dm-3 for z = 1, and, again, taking if/d = 75 mV, the effective Hamaker constant, A, is calculated to be equal to 8 X 10 20 J. This is consistent with the order of magnitude of A which is predicted from the theory of London-van der Waals forces (see Table 8.3). 

The stability of latexes during and after polymerization may be assessed at least qualitatively by the theoretical relationships describing the stability of lyophobic colloids. The Verwey-Overbeek theory (2) combines the electrostatic forces of repulsion between colloidal particles with the London-van der Waals forces of attraction. The electrostatic forces of repulsion arise from the surface charge, e.g., from adsorbed emulsifier ions, surface sulfate endgroups introduced by persulfate initiator, or ionic groups introduced by using functional monomers. These electro-... 

There also exist dispersion, or London-van der Waals forces that molecules exert towards each other. These forces are usually attractive in nature and result from the orientation of dipoles, and may be dipole-dipole (Keesom dispersion forces), dipole-induced dipole (Debye dispersion forces), or induced dipole-induced dipole... 

Electrostatic interactions occur between the ionic head groups of the surfactant and the oppositely charged solid surface (head down adsorption with monolayer structure) [56]. Acid-base interactions occur due to hydrogen bonding or Lewis acid-Lewis base reactions between solid surface and surfactant molecules (head down with monolayer structure) [57]. Polarisation of jt electrons occurs between the surfactant head group which has electron-rich aromatic nuclei and the positively charged solid surface (head down with monolayer structure) [58]. Dispersion forces occur due to London-van der Waals forces between the surfactant molecules and the solid surface (hydrophobic tail lies flat on the hydrophobic solid surface while hydrophilic head orients towards polar liquid) [59]. 

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

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