The London-van der Waals Forces

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 

Illustration of the dispersion (induced dipole-induced dipole) forces. Large dots represent nucleus smaller dots are the electrons and 5+ and S- indicate the net local charges due to the asynunetric distortions of the atoms. 

Entropic confinement forces occur at ultrathin ( 5 nm) surfactant films and between bilayers in solution. They are mainly responsible for the stability observed in so-called Newton black soap films. It arises from the steric repulsion occurring when adsorbed layers overlap. These forces operate by various modes, like undulation, peristaltic fluctuations, or by head-group overlap.  

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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. 

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. 

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-... 

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... 

Casimir, H.B.G. Polder, D. The influence of retardation on the London-van der Waals forces. Physical Review 1948, 73, 360-372 Overbeek, J.T.G. The interaction between colloidal particles. 

In this chapter, we consider Brownian diffusion, sedimentation, migration in an electric Reid, and thermophoresis. The last term refers to particle movement produced by a temperature gradient in the gas. We consider also the London-van der Waals forces that are important when a particle approaches a surface. The analysis is limited to particle transport in stationary —that is. nonllowing— gases. I ransporl in flow systems is discussed in the chapters which follow. 

Chu. B. (1967) Molecular forces Based on the Baker Lectures of Peter J. W. Debye. Wiley-Inierscience, New York. This smal I, concisely written book reviews the origins of the London-van der Waals forces and derives expressions for the interaction energy between bodies under the influence of these forces. 

Casimir H B G and Polder D 1948 The influence of retardation on the London-van der Waals forces... 

They arise because of a transient polarization of the atom or molecule which will act on the surroundings to produce spontaneous fluctuations elsewhere. The causes of such interaction have been extensively reviewed by Kauz-mann and Jehle The electromagnetic properties of van der Waals forces were first shown by London in 1930 and are frequently referred to as the London-van der Waals forces. The extension of the theory of van der Waals attractive forces from the atomic or microscopic scale to bulk powders on the macroscopic scale was first carried out by Lifshitz in 19SS (ref. 16). 

Fig. 22. Illustrating the London-Van der Waals forces between an atom and an Infinitely large plate of thickness c .

The influence of the medium through which the forces are t lansmitted may be roughly taken into account by dividing the constant A found in this way by the square of the refractive index, as the London-Van der Waals force is essentially of an electric nature. But as we are not fully informed as to the exact values of the London-VanderWaals constants, we shall leave this point out of the discussion for the present. 

If we consider the picture of the London-Van Der Waals forces as given above, viz., as an attraction between the temporary dipole of one atom and the dipole induced by it of the second atom, the finite velocity of propagation of electromagnetic actions causes the induced dipole to be retarded against the inducing one by a time equal to rn/c (if r is the distance between the two atoms and n the refractive index of the medium for the frequency coupled with the temporary dipole). The reaction of the induced dipole on the first one again is retarded by the same time, and if in this total time-lag of 2rn/c the direction of the first dipole is altered by 90 ", the force exerted is exactly nullified, and by a change of 180 " even reverted from an attraction into a repulsion. 

If we call the frequency of the motion of electrons in the atom V, the wavelength connected with it l, the first zero of the London-Van Der Waals force wifi be reached at a distance r —, time-lag. velocity = 1/8 v. cjn = a/8. 

A is of the order of 1000 A, so r is of the order of 10 cm. This means that beyond this distance the London-Van Der Waals force is practically non-existant. 

We believe, however, that for the principal aspect of the question, and the determination of the order of magnitude, the above suffices. The consequences of this cutting off of the London-.Van Der Waals forces are unimportant for small particles ( 10 ) where these forces do not, anjrway, reach Farther than 10 cm. The influence in the case of large particles (10 and larger) will be discussed in Chapter XII, 5. 

Very recently Casimir and Polder succeeded in giving an exact quantum mechanical -description of the influence of the retardation effects on the London-Van Der Waal s-forces. They found, in fair accord with what was expected by the semi- classical reasoning given above, that a significant reduction of the London-Van Der Waals force between two atoms is felt for distances larger than A/3. When the distance is very large the L o n d o n-energy is proportional to 1/r, instead to 1/r as is found when no account is taken of the retardation. 

As in part II, we shall assume also in this part that the attraction between coUoidal particles is entirely based upon the London-Van der Waals forces. Hamaker showed how the London-Van der Waals interaction between two spherical particles may be found from the interaction b etween the elements of these spheres. His expression for the energy of attraction Va) runs, using our symbols,... 

It may seem strange at first sight that W can be smaller than 1, as is shown in the figures. This means, however, that the flocculation is more rapid than when no forces act between the particles. W < 1 means that the stability is diminished by attractive forces, viz. the London -Van der Waals forces, which act practically unhampered by the repulsion for large concentrations of electrolyte or for small surface potentials (Fig. 47 resp. Fig. 48). 

As in Part It, we have hitherto neglected the influence of the secondary minimum in the potential curves situated at comparatively large values of s, where the London-Van der Waals force again surpasses the repulsion. As already pointed... 

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