Dispersion forces, London theory

Van der Waals force Also called intermolecular forces, secondary valence forces, dispersion force, London dispersion force, or van der Waals attraction. It is an attractive force between two atoms or non-polar molecules, which arise because a fluctuating dipole moment in one molecule induces a dipole moment in the other, and the two dipole moments then interact. They are somewhat weaker than hydrogen bonds and far weaker than inter-atomic valences. Information regarding their numerical values is mostly semi-empirical, derived with the aid of theory from an analysis of physical and chemical data. 

Kristyan, S., Pulay, P., 1994, Can (Semi)Local Density Functional Theory Account for the London Dispersion Forces , Chem. Phys. Lett., 229, 175. 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

Mahanty, J., and Ninham, B. W., Dispersion Forces, Academic Press, New York, 1976. (An advanced monograph on dispersion forces. Discusses topics such as London and Lifshitz theories.)... 

Whereas many scientists shared Mulliken s initial skepticism regarding the practical role of theory in solving problems in chemistry and physics, the work of London (6) on dispersion forces in 1930 and Hbckel s 7t-electron theory in 1931 (7) continued to attract the interest of many, including a young scientist named Frank Westheimer who, drawing on the physics of internal motions as detailed by Pitzer (8), first applied the basic concepts of what is now called molecular mechanics to compute the rates of the racemization of ortho-dibromobiphenyls. The 1946 publication (9) of these results would lay the foundation for Westheimer s own systematic conformational analysis studies (10) as well as for many others, eg, Hendrickson s (11) and Allinger s (12). These scientists would utilize basic Newtonian mechanics coupled with concepts from spectroscopy (13,14) to develop nonquantum mechanical models of structures, energies, and reactivity. 

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). 

In conclusion, we suggest that the ion dispersion forces were ignored by most (but by no means all) electrolyte theories mainly because they are important only for separations between ions smaller than about 5 A, and the interactions at these distances are not well-known. It is hard to believe that at these distances the interactions can be accurately described by a sum between a hard-wall repulsion, a Coulomb interaction, and a London attraction. Even if the latter would be true, a correction in the local dielectric constant (because of incomplete screening by water molecules) would render again the van der Waals interactions negligible, up to distances of the order of ion diameters. 

Types ionic, covalent, metallic, hydrogen bonding, van der Waals theory (including London dispersion forces)... 

Kristyan S, Pulay P (1994) Can (semi)local density-functional theory account for London dispersion forces, Chem Phys Lett, 229 175-180... 

Dispersion. Dispersion or London-van der Waals forces are ubiquitous. The most rigorous calculations of such forces are based on an analysis of the macroscopic electrodynamic properties of the interacting media. However, such a full description is exceptionally demanding both computationally and in terms of the physical property data required. For engineering applications there is a need to adopt a procedure for calculation which accurately represents the results of modem theory yet has more modest computational and data needs. An efficient approach is to use an effective Lifshitz-Hamaker constant for flat plates with a Hamaker geometric factor [9]. Effective Lifshitz-Hamaker constants may be calculated from readily available optical and dielectric data [10]. 

For the substituted polysilylenes, (SiRR ) , the coupling constant can be varied systematically by changing the side groups (this change affects e and Vd via the backbone polarizability) or the solvent (this change affects Vj) via the London dispersion forces e is expected to be only weakly solvent dependent for nonpolar systems). Therefore, in principle, the three distinct phase behaviors predicted by the theory may be observed by judicious choice of polymer-solvent pairs. 

Physical adsorption is a universal phenomena, producing some, if not the major, contribution to almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley (1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. 

O. A. von Lilienfeld, I. Tavernelli, U. Rothhsberger, and D. Sebastiani (2004) Optimization of Effective Atom Centered Potentials for London Dispersion Forces in Density Functional Theory. Phys. Rev. Lett. 93, p. 153004... 

Dispersion forces are often called London forces, after the German-born physicist Fritz London (1900-1954). He initially postulated their existence in 1930, on the basis of quantum theory. 

The role of the medium, in which contacting and pull-off are performed, has been mentioned but not considered so far. However, the surroundings obviously influence surface forces, e.g., via effective polarizability effects (essentially multibody interactions e.g., by the presence of a third atom and its influence via instantaneous polarizability effects). These effects can become noticeable in condensed media (liquids) when the pairwise additivity of forces can essentially break down. One solution to this problem is given by the quantum field theory of Lifshitz, which has been simplified by Israelachvili [6]. The interaction is expressed by the (frequency-dependent) dielectric constants and refractive indices of the contacting macroscopic bodies (labeled by 1 and 2) and the medium (labeled by 3). The value of the Hamaker constant Atota 1 is considered as the sum of a term at zero frequency (v =0, dipole-dipole and dipole-induced dipole forces) and London dispersion forces (at positive frequencies, v >0). 

Fortunately, most organic solvents are nonpolar and therefore their intermolecular forces are weak London or dispersion forces. Hildebrand used the term "regular solutions" to describe solutions of nonelectrolytes and their nonpolar solvents. Additional theories on the solubility of polymers were developed by Flory ( ) and Huggins O). Probably the most important publications leading to the practical use of solubility theories by polymer scientists were those published by Burrell in 1955 ( ) and 1966 ( ). Modifications in the Hildebrand solubility parameter concept for regular solutions to account for larger intermolecular forces were made by Liebermann ( ), Crowley (.7), Hansen and Beerbower ( ) and Nelson et al. (9). 

Lattice theories [37] enable one to consider nonspecific physical forces (e.g., molecular dipole moments, induction effects, and London dispersion forces) and have been applied successfully to model nonideality in a wide range of mixtmes. Guggenheim [43] was the first to develop a quasichemical theory using lattice models. Wilson [44], Renon and Prausnitz [45], Abrams and Prausnitz [46], and Vera et al. [47] modified it for nomandom mixtures. Panayiotou and Vera... 

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