Van der Waals forces theory

ISRAELACHVILI, J.N. and TABOR, D., van der Waals forces theory and experiment , in CADENHEAD, D.A. and DANIELLI, J.F. (editors), Progress in Surface and Membrane Science, 7, 1-55, Academic Press (1973)... 

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). 

The second part, Computation, advises the user on algorithms as well as ways to convert experimental data into grist for the computational mill. It includes an essay on the physics of dielectric response, the aspect of van der Waals force theory that needlessly daunts potential users. 

Israelaehvili JN, Tabor D (1973) Van der Waals forces theory and experiment. In Danielli JR Rosenberg MD, Cadenhead DA (eds) Progress in surface and membrane science, Vol 7. Academic, New York, p 1... 

J.N. Israelachvili, D. Tabor "Van der Waals Forces Theory and Experiment", in Progress in Surface and Membrane Science, Vo1.7, ed. by D.A. Cadenhead, J.F. Danielli, M.D. Rosenberg (Academic Press, New York 1.973)... 

Inumaru K., Nakajima H., Ito T., Misono M. Porous aggregates of unidirectionaUy oriented (NH4)3PWi2O40 microcrystallites Epitaxial self-assembly. Chem. Lett. 1996 7 559-560 IsraeladiviH J.N., Tabor D. The measurement of van der Waals disprasion forces in the range 1.5-130 nm. Proc. Roy. Soc. (London) A 1972 331 19-38 Israelachvih J.N., Tahor D. van der Waals forces Theory and expaiment. Prog. Surf. Membr. Sd. 1973 7 1-55... 

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

With the reader bearing in mind this framework, the Lifshitz theory of van der Waals interactions can readily be understood. According to the Lifshitz theory, van der Waals forces arise from the absorption of photons of frequency tu by a material with a complex dielectric constant... 

Based on the application of the established theory of colloid stability of water treatment particles [8,85-88], the colloidal particles in untreated water are attached to one another by van der waals forces and, therefore, always tend to aggregate unless kept apart by electrostatic repulsion forces arising from the presence of electrical charges on the particles. The aggregation process... 

In this theory, the adhesion is due to electrostatic forces arising from the transfer of electrons from one material of an adhesive joint to another. Evidence in support of this theory includes the observation that the parts of a broken adhesive joint are sometimes charged [48]. It has been shown that peeling forces are often much greater than can be accounted for by van der Waals forces or chemical bonds. 

Refinements in the theory of interparticle long-range van der Waals forces (the Landau-Lifshitz theory) are within reach. New techniques are now available for measuring the complex dielectric constants of various media required for the implementation of that theory. 

The surface force apparatus (SFA) is a device that detects the variations of normal and tangential forces resulting from the molecule interactions, as a function of normal distance between two curved surfaces in relative motion. SFA has been successfully used over the past years for investigating various surface phenomena, such as adhesion, rheology of confined liquid and polymers, colloid stability, and boundary friction. The first SFA was invented in 1969 by Tabor and Winterton [23] and was further developed in 1972 by Israela-chivili and Tabor [24]. The device was employed for direct measurement of the van der Waals forces in the air or vacuum between molecularly smooth mica surfaces in the distance range of 1.5-130 nm. The results confirmed the prediction of the Lifshitz theory on van der Waals interactions down to the separations as small as 1.5 nm. 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

Van der Waals forces are derived from the energy of interaction between two molecules, Vss. These can be derived from London s theory as follows ... 

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. 

A 2D soft-sphere approach was first applied to gas-fluidized beds by Tsuji et al. (1993), where the linear spring-dashpot model—similar to the one presented by Cundall and Strack (1979) was employed. Xu and Yu (1997) independently developed a 2D model of a gas-fluidized bed. However in their simulations, a collision detection algorithm that is normally found in hard-sphere simulations was used to determine the first instant of contact precisely. Based on the model developed by Tsuji et al. (1993), Iwadate and Horio (1998) incorporated van der Waals forces to simulate fluidization of cohesive particles. Kafui et al. (2002) developed a DPM based on the theory of contact mechanics, thereby enabling the collision of the particles to be directly specified in terms of material properties such as friction, elasticity, elasto-plasticity, and auto-adhesion. 

Y.. Dappe, M.A. Basanta, F. Flores, J. Ortega, Weak chemical interaction and van der Waals forces between graphene layers A combined density functional and intermolecular perturbation theory approach, vol. 74, p. 205434-9, 2006. 

---