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In physical chemistry, the van der Waals force (or van der Waals interaction), named after Dutch scientist Johannes Diderik van der Waals, is the attractive or repulsive force between molecules (or between parts of the same molecule) other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral molecules.[1] The term includes:

It is also sometimes used loosely as a synonym for the totality of intermolecular forces. Van der Waals forces are relatively weak compared to normal chemical bonds, but play a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. Van der Waals forces define the chemical character of many organic compounds. They also define the solubility of organic substances in polar and non-polar media. In low molecular weight alcohols, the properties of the polar hydroxyl group dominate the weak intermolecular forces of van der Waals. In higher molecular weight alcohols, the properties of the nonpolar hydrocarbon chain(s) dominate and define the solubility. Van der Waals forces grow with the length of the nonpolar part of the substance.

## Definition

Van der Waals forces include attractions between atoms, molecules, and surfaces. They differ from covalent and ionic bonding in that they are caused by correlations in the fluctuating polarizations of nearby particles (a consequence of quantum dynamics).

Intermolecular forces have four major contributions. In general an intermolecular potential has a repulsive component (which prevents the collapse of molecules because as entities move closer to one another these repulsions dominate). It also has an attractive component, which, in turn, consists of three distinct contributions:

1. The electrostatic interactions between charges (in the case of molecular ions), dipoles (in the case of molecules without inversion center), quadrupoles (all molecules with symmetry lower than cubic), and in general between permanent multipoles. The electrostatic interaction is sometimes called the Keesom interaction or Keesom force after Willem Hendrik Keesom.
2. The second source of attraction is induction (also known as polarization), which is the interaction between a permanent multipole on one molecule with an induced multipole on another. This interaction is sometimes measured in debyes after Peter J.W. Debye.
3. The third attraction is usually named after Fritz London who himself called it dispersion. This is the only attraction experienced by non-polar atoms, but it is operative between any pair of molecules, irrespective of their symmetry.

Returning to nomenclature, different texts refer to different things using the term "van der Waals force". Some texts mean by the van der Waals force the totality of forces (including repulsion); others mean all the attractive forces (and then sometimes distinguish van der Waals-Keesom, van der Waals-Debye, and van der Waals-London); finally, some use the term "van der Waals force" solely as a synonym for the London/dispersion force.

All intermolecular/van der Waals forces are anisotropic (except those between two noble gas atoms), which means that they depend on the relative orientation of the molecules. The induction and dispersion interactions are always attractive, irrespective of orientation, but the electrostatic interaction changes sign upon rotation of the molecules. That is, the electrostatic force can be attractive or repulsive, depending on the mutual orientation of the molecules. When molecules are in thermal motion, as they are in the gas and liquid phase, the electrostatic force is averaged out to a large extent, because the molecules thermally rotate and thus probe both repulsive and attractive parts of the electrostatic force. Sometimes this effect is expressed by the statement that "random thermal motion around room temperature can usually overcome or disrupt them" (which refers to the electrostatic component of the van der Waals force). Clearly, the thermal averaging effect is much less pronounced for the attractive induction and dispersion forces.

The Lennard-Jones potential is often used as an approximate model for the isotropic part of a total (repulsion plus attraction) van der Waals force as a function of distance.

Van der Waals forces are responsible for certain cases of pressure broadening (van der Waals broadening) of spectral lines and the formation of van der Waals molecules. The London-van der Waals forces are related to the Casimir effect for dielectric media, the former being the microscopic description of the latter bulk property. The first detailed calculations of this were done in 1955 by E. M. Lifshitz.[2][3]

## Calculation

$F(r)= \frac{\lambda}{r^s} - \frac{\mu}{r^t}$

## London dispersion force

London dispersion forces, named after the German-American physicist Fritz London, are weak intermolecular forces that arise from the interactive forces between instantaneous multipoles in molecules without permanent multipole moments. London dispersion forces are also known as dispersion forces, London forces, or induced dipole–dipole forces.

## Use by animals

Gecko climbing glass using its natural setae

The ability of geckos - which can hang on a glass surface using only one toe - to climb on sheer surfaces has been attributed to van der Waals force,[4][5] although a more recent study suggests that water molecules of roughly monolayer thickness (present on virtually all natural surfaces) also play a role.[6] Efforts continue to create a dry glue that exploits this knowledge.

## Footnotes

1. ^ International Union of Pure and Applied Chemistry (1994). "Van der Waals forces". Compendium of Chemical Terminology Internet edition.
2. ^ IE Dzyaloshinskii, EM Lifshitz, LP Pitaevskii: GENERAL THEORY OF VAN DER WAALS' FORCES
3. ^ For further investigation, one may consult the University of St. Andrews' levitation work in a popular article: Science Journal: New way to levitate objects discovered, and in a more scholarly version: New Journal of Physics: Quantum levitation by left-handed metamaterials, which relate the Casimir effect to the gecko and how the reversal of the Casimir effect can result in physical levitation of tiny objects.
4. ^ http://www.clemson.edu/newsroom/articles/2009/august/geckos.php5
5. ^ Kellar Autumn; Metin Sitti ; Yiching A. Liang; Anne M. Peattie; Wendy R. Hansen; Simon Sponberg; Thomas W. Kenny; Ronald Fearing; Jacob N. Israelachvili; Robert J. Full. Evidence for van der Waals adhesion in gecko setae. Proceedings of the National Academy of Sciences of the USA 2002, 99, 12252–12256. doi:10.1073/pnas.192252799
6. ^ G. Huber, H. Mantz, R. Spolenak, K. Mecke, K. Jacobs, S. N. Gorb, and E. Arzt. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements. Proceedings of the National Academy of Sciences of the USA 2005, 102, 16293–16296. doi:10.1073/pnas.0506328102

## References

• Iver Brevik, V. N. Marachevsky, Kimball A. Milton, Identity of the Van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence, hep-th/9901011
• I. D. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, Usp. Fiz. Nauk 73, 381 (1961)
• English translation: Soviet Phys. Usp. 4, 153 (1961)
• L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, 1960, pp. 368–376.
• Mark Lefers, "Van der Waals dispersion force". Holmgren Lab.
• E. M. Lifshitz, Zh. Eksp. Teor. Fiz. 29, 894 (1955)
• English translation: Soviet Phys. JETP 2, 73 (1956)
• Western Oregon University's "London force". Intermolecular Forces. (animation)
• J. Lyklema, Fundamentals of Interface and Colloid Science, page 4.43