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The van der Waals equation is an equation of state that can be derived from a special form of the potential between a pair of molecules (hard-sphere repulsion and R^-6 van der Waals attraction).

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:

• permanent dipole–permanent dipole forces
• permanent dipole–induced dipole forces
• instantaneous induced dipole-induced dipole (London dispersion forces).

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 alcohols, the properties of the polar hydroxyl group dominate the weak intermolecular forces of van der Waals. In higher 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.

Contents 1 Definition 2 London dispersion force 3 Relation to the Casimir effect 4 Use by animals 5 Nanotechnology 6 Notes 7 Sources

[edit] 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: 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), and, finally some use the term "van der Waals force" solely as a synonym for the London/dispersion force. So, if you come across the term "van der Waals force", it is important to ascertain what the author means by it.

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.

See this URL for an introductory description of the van der Waals force (as a sum of attractive components only).

[edit] 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 temporary multipoles in molecules without permanent multipole moments. London dispersion forces are also known as dispersion forces, London forces, or induced dipole–dipole forces.

London forces can be exhibited by nonpolar molecules because electron density moves about a molecule probabilistically (see quantum mechanical theory of dispersion forces). There is a high chance that the electron density will not be evenly distributed throughout a nonpolar molecule. When electrons are unevenly distributed, a temporary multipole exists. This multipole will interact with other nearby multipoles and induce similar temporary polarity in nearby molecules. London forces are also present in polar molecules, but they are only a small part of the total interaction force.^{[citation needed]}

Electron density in a molecule may be redistributed by proximity to another multipole. Electrons will gather on the side of a molecule that faces a positive charge and will retreat from a negative charge. Hence, a transient multipole can be produced by a nearby polar molecule, or even by a transient multipole in another nonpolar molecule.

In vacuum, London forces are weaker than other intermolecular forces such as ionic interactions, hydrogen bonding, or permanent dipole-dipole interactions.^{[citation needed]}

This phenomenon is the only attractive intermolecular force at large distances present between neutral atoms (e.g., a noble gas), and is the major attractive force between non-polar molecules, (e.g., nitrogen or methane). Without London forces, there would be no attractive force between noble gas atoms, and they wouldn't exist in liquid form.

London forces become stronger as the atom or molecule in question becomes larger. This is due to the increased polarizability of molecules with larger, more dispersed electron clouds. This trend is exemplified by the halogens (from smallest to largest: F₂, Cl₂, Br₂, I₂). Fluorine and chlorine are gases at room temperature, bromine is a liquid, and iodine is a solid. The London forces also become stronger with larger amounts of surface contact. Greater surface area means closer interaction between different molecules.

[edit] Relation to the Casimir effect

The London-van der Waals forces are related to the Casimir effect for dielectric media, the former the microscopic description of the latter bulk property. The first detailed calculations of this were done in 1955 by E. M. Lifshitz.^[2]

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.

[edit] Use by animals

The ability of geckos to climb on sheer surfaces has been attributed to van der Waals force.^[3] A recent study suggests that water molecules of roughly monolayer thickness (present on all surfaces) also play a role.^[4] Nevertheless, a gecko can hang on a glass surface using only one toe. Efforts continue to create a synthetic "gecko tape" that exploits this knowledge. So far, research has produced some promising results — early research yielded an adhesive tape^[5] product, which only obtains a fraction of the forces measured from the natural material, and new research^[6] is being developed with the goal of featuring 200 times the adhesive forces of the natural material. Researchers at Rensselaer Polytechnic Institute and the University of Akron announced in a paper published in the June 18–22, 2007 issue of the Proceedings of the National Academy of Sciences that they have created a synthetic “gecko tape” with four times the sticking power of a natural gecko foot.^[7]

Researchers at Stanford University and Carnegie Mellon University recently developed a gecko-like robot which uses synthetic setae to mount walls.^[8]

On October 9th 2008, the discovery of a new type of dry glue designed to mimic gecko feet was announced. The glue is 10 times stickier than the gravity-defying lizards, and three times stickier than other gecko-inspired glues. Liming Dai of the University of Dayton said "It's the stickiest dry glue yet". ^[9]

[edit] Nanotechnology

DARPA (Defense Advanced Research Projects Agency) is also currently working on this technology to enable a soldier to scale a wall at .5 m/s. This project is named Z-Man. Experiments are currently underway to develop nano-adhesives using the van der Waal effect. Researchers at the University of Akron, in the US, have created a material made of columns of nanotubes rooted in pieces of flexible polymer. The nanotubes were grown on a silicon base and then transferred to the polymer to provide a flexibe base, similar to a gecko's foot. When dried, the polymer holds the silicon base, which in turn, holds the nanotubes.

Using this technique, an adhesive tape has been developed that sticks four times better than a gecko's foot. Particularly effective has been a checkerboard carpet of this material, which can be peeled and re-adhered repeatedly without weakening.^[10]

[edit] Notes

[edit] Sources

• 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

v • d • e Chemical bonds "Strong" Covalent bonds & Antibonding Sigma bonds: 3c-2e  · bent bond  · 3c-4e (Hydrogen bond, Dihydrogen bond, Agostic interaction) · 4c-2e Pi bonds: π backbonding · Conjugation · Hyperconjugation · Aromaticity · Metal aromaticity Delta bond: Quadruple bond · Quintuple bond · Sextuple bond Coordinate covalent bond · Hapticity Ionic bonds Cation-pi interaction · Salt bridge Metallic bonds Metal aromaticity "Weak" Hydrogen bond Dihydrogen bond · Dihydrogen complex · Low-barrier hydrogen bond · Symmetric hydrogen bond · Hydrophile Other noncovalent van der Waals force · Mechanical bond · Halogen bond · Aurophilicity · Intercalation · Stacking · Entropic force · Chemical polarity other Disulfide bond · Peptide bond · Phosphodiester bond Note: the weakest strong bonds are not necessarily stronger than the strongest weak bonds