Van der Waals force
In
they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanishes at longer distances between interacting molecules.Named after Dutch physicist Johannes Diderik van der Waals, the van der Waals force plays a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. It also underlies many properties of organic compounds and molecular solids, including their solubility in polar and non-polar media.
If no other force is present, the distance between atoms at which the force becomes repulsive rather than attractive as the atoms approach one another is called the van der Waals contact distance; this phenomenon results from the mutual repulsion between the atoms' electron clouds.[3]
The van der Waals forces
Definition
Van der Waals forces include attraction and repulsions between
The force results from a transient shift in electron density. Specifically, the electron density may temporarily shift to be greater on one side of the nucleus. This shift generates a transient charge which a nearby atom can be attracted to or repelled by. The force is repulsive at very short distances, reaches zero at an equilibrium distance characteristic for each atom, or molecule, and becomes attractive for distances larger than the equilibrium distance. For individual atoms, the equilibrium distance is between 0.3 nm and 0.5 nm, depending on the atomic-specific diameter.[7] When the interatomic distance is greater than 1.0 nm the force is not strong enough to be easily observed as it decreases as a function of distance r approximately with the 7th power (~r−7).[8]
Van der Waals forces are often among the weakest chemical forces. For example, the pairwise attractive van der Waals interaction energy between H (hydrogen) atoms in different H2 molecules equals 0.06 kJ/mol (0.6 meV) and the pairwise attractive interaction energy between O (oxygen) atoms in different O2 molecules equals 0.44 kJ/mol (4.6 meV).[9] The corresponding vaporization energies of H2 and O2 molecular liquids, which result as a sum of all van der Waals interactions per molecule in the molecular liquids, amount to 0.90 kJ/mol (9.3 meV) and 6.82 kJ/mol (70.7 meV), respectively, and thus approximately 15 times the value of the individual pairwise interatomic interactions (excluding covalent bonds).
The strength of van-der-Waals bonds increases with higher polarizability of the participating atoms.[10] For example, the pairwise van der Waals interaction energy for more polarizable atoms such as S (sulfur) atoms in H2S and sulfides exceeds 1 kJ/mol (10 meV), and the pairwise interaction energy between even larger, more polarizable Xe (xenon) atoms is 2.35 kJ/mol (24.3 meV).[11] These van der Waals interactions are up to 40 times stronger than in H2, which has only one valence electron, and they are still not strong enough to achieve an aggregate state other than gas for Xe under standard conditions. The interactions between atoms in metals can also be effectively described as van der Waals interactions and account for the observed solid aggregate state with bonding strengths comparable to covalent and ionic interactions. The strength of pairwise van-der-Waals type interactions is on the order of 12 kJ/mol (120 meV) for low-melting Pb (lead) and on the order of 32 kJ/mol (330 meV) for high-melting Pt (platinum), which is about one order of magnitude stronger than in Xe due to the presence of a highly polarizable free electron gas.[12] Accordingly, van der Waals forces can range from weak to strong interactions, and support integral structural loads when multitudes of such interactions are present.
More broadly,
- A repulsive component resulting from the Pauli exclusion principle that prevents close contact of atoms, or the collapse of molecules.
- Attractive or repulsive Keesom interaction or Keesom force after Willem Hendrik Keesom.
- Induction (also known as Peter J. W. Debye.
- Dispersion (usually named London dispersion interactions after Fritz London), which is the attractive interaction between any pair of molecules, including non-polar atoms, arising from the interactions of instantaneous multipoles.
Hereby, different texts may refer to a different spectrum of interactions using the term "van der Waals force". Typically, contributions (1) and (4) are considered as van-der-Waals forces, excluding effects from permanent multipoles as described in (2) and from permanent polarization in (3). However, some texts describe the van der Waals force as 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).
All intermolecular/van der Waals forces are
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 (
The main characteristics of van der Waals forces are:[17]
- They are weaker than normal covalent and ionic bonds.
- The Van der Waals forces are additive in nature, consisting of several individual interactions, and cannot be saturated.
- They have no directional characteristic.
- They are all short-range forces and hence only interactions between the nearest particles need to be considered (instead of all the particles). Van der Waals attraction is greater if the molecules are closer.
- Van der Waals forces are independent of temperature except for dipole-dipole interactions.
In low molecular weight alcohols, the hydrogen-bonding properties of their polar
Van der Waals forces are also responsible for the weak hydrogen bond interactions between unpolarized dipoles particularly in acid-base aqueous solution and between biological molecules.
London dispersion force
Van der Waals forces between macroscopic objects
For
-
(1)
where A is the Hamaker coefficient, which is a constant (~10−19 − 10−20 J) that depends on the material properties (it can be positive or negative in sign depending on the intervening medium), and z is the center-to-center distance; i.e., the sum of R1, R2, and r (the distance between the surfaces): .
The van der Waals force between two spheres of constant radii (R1 and R2 are treated as parameters) is then a function of separation since the force on an object is the negative of the derivative of the potential energy function,. This yields:
-
(2)
In the limit of close-approach, the spheres are sufficiently large compared to the distance between them; i.e., or , so that equation (1) for the potential energy function simplifies to:
-
(3)
with the force:
-
(4)
The van der Waals forces between objects with other geometries using the Hamaker model have been published in the literature.[21][22][23]
From the expression above, it is seen that the van der Waals force decreases with decreasing size of bodies (R). Nevertheless, the strength of inertial forces, such as gravity and drag/lift, decrease to a greater extent. Consequently, the van der Waals forces become dominant for collections of very small particles such as very fine-grained dry powders (where there are no capillary forces present) even though the force of attraction is smaller in magnitude than it is for larger particles of the same substance. Such powders are said to be cohesive, meaning they are not as easily fluidized or pneumatically conveyed as their more coarse-grained counterparts. Generally, free-flow occurs with particles greater than about 250 μm.
The van der Waals force of adhesion is also dependent on the surface topography. If there are surface asperities, or protuberances, that result in a greater total area of contact between two particles or between a particle and a wall, this increases the van der Waals force of attraction as well as the tendency for mechanical interlocking.
The microscopic theory assumes pairwise additivity. It neglects
Use by geckos and arthropods
The ability of
There were efforts in 2008 to create a dry glue that exploits the effect,[29] and success was achieved in 2011 to create an adhesive tape on similar grounds[30] (i.e. based on van der Waals forces). In 2011, a paper was published relating the effect to both velcro-like hairs and the presence of lipids in gecko footprints.[31]
A later study suggested that capillary adhesion might play a role,[32] but that hypothesis has been rejected by more recent studies.[33][34][35]
A 2014 study has shown that gecko adhesion to smooth Teflon and
Among the arthropods, some spiders have similar setae on their scopulae or scopula pads, enabling them to climb or hang upside-down from extremely smooth surfaces such as glass or porcelain.[37][38]
See also
- Arthropod adhesion
- Cold welding
- Dispersion (chemistry)
- Gecko feet
- Lennard-Jones potential
- Noncovalent interactions
- Synthetic setae
- Van der Waals molecule
- Van der Waals radius
- Van der Waals strain
- Van der Waals surface
- Wringing of gauge blocks
References
- ^ Woodford, Chris (2 July 2008). "How do microfiber cloths work? | The science of cleaning". Explain that Stuff. Retrieved 11 February 2022.
- ^ Garrett, Reginald H.; Grisham, Charles M. (2016). Biochemistry (6th ed.). University of Virginia. pp. 12–13.
- ISBN 9780470399545.
- OCLC 226037727.
- ^
Abrikosov, A. A.; Gorkov, L. P.; Dzyaloshinsky, I. E. (1963–1975). "6: Electromagnetic Radiation in an Absorbing Medium". Methods of Quantum Field Theory in Statistical Physics. ISBN 978-0-486-63228-5.
- S2CID 52088903.
- OCLC 534717.
- S2CID 235823673.
- PMID 23276161.
- ISSN 0002-7863.
- ISSN 1932-7447.
- ^ "New way to levitate objects discovered". Science Daily. 6 August 2007.
- S2CID 463815.
- .
- S2CID 64619547.
- OCLC 912437861.
- PMID 26083908.
- ^ H. C. Hamaker, Physica, 4(10), 1058–1072 (1937)
- ^ London, F. Transactions of the Faraday Society 33, 8–26 (1937)
- S2CID 250790137.
- ISBN 978-0-12-375181-2.
- ISBN 978-0-521-83906-8.
- ^ E. M. Lifshitz, Soviet Physics—JETP, 2, 73 (1956)
- ^ D. Langbein, Physical Review B, 2, 3371 (1970)
- ^ B. V. Derjaguin, Kolloid-Zeitschrift, 69, 155–164 (1934)
- PMID 19656797.
- PMID 12198184.
- ^ Steenhuysen, Julie (8 October 2008). "Gecko-like glue is said to be stickiest yet". Reuters. Retrieved 5 October 2016.
- ^ Quick, Darren (6 November 2011). "Biologically inspired adhesive tape can be reused thousands of times". New Atlas. Retrieved 5 October 2016.
- PMID 21865250.
- PMID 16260737.
- .
- PMID 20952618.
- PMID 20920615.
- PMID 25008078.
We have demonstrated that it is the CE-driven electrostatic interactions which dictate the strength of gecko adhesion, and not the van der Waals or capillary forces which are conventionally considered as the main source of gecko adhesion.
- S2CID 250841250.
- PMID 21593034.
Further reading
- Brevik, Iver; Marachevsky, V. N.; Milton, Kimball A. (1999). "Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of These Phenomena to Sonoluminescence". Physical Review Letters. 82 (20): 3948–3951. S2CID 14762105.
- Dzyaloshinskii, I. D.; Lifshitz, E. M.; Pitaevskii, Lev P. (1961). "Общая теория ван-дер-ваальсовых сил" [General theory of van der Waals forces] (PDF). Uspekhi Fizicheskikh Nauk (in Russian). 73 (381).
- English translation: Dzyaloshinskii, I. D.; Lifshitz, E. M.; Pitaevskii, L. P. (1961). "General theory of van der Waals' forces". .
- Landau, L. D.; Lifshitz, E. M. (1960). Electrodynamics of Continuous Media. Oxford: Pergamon. pp. 368–376.
- Langbein, Dieter (1974). Theory of Van der Waals Attraction. Springer Tracts in Modern Physics. Vol. 72. New York, Heidelberg: Springer-Verlag.
- Lefers, Mark. "Van der Waals dispersion force". Life Science Glossary. Holmgren Lab. Archived from the original on 24 July 2019. Retrieved 2 October 2017.
- Lifshitz, E. M. (1955). "Russian title is missing" [The Theory of Molecular Attractive Forces between Solids]. Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki (in Russian). 29 (1): 94.
- English translation: Lifshitz, E. M. (January 1956). "The Theory of Molecular Attractive Forces between Solids" (PDF). Soviet Physics. 2 (1): 73. Archived from the original (PDF) on 13 July 2019. Retrieved 8 August 2020.
- "London force animation". Intermolecular Forces. Western Oregon University.
- Lyklema, J. Fundamentals of Interface and Colloid Science. p. 4.43.
- Israelachvili, Jacob N. (1992). Intermolecular and Surface Forces. ISBN 9780123751812.
External links
- Senese, Fred (1999). "What are van der Waals forces?". Frostburg State University. Retrieved 1 March 2010. An introductory description of the van der Waals force (as a sum of attractive components only)
- "Robert Full: Learning from the gecko's tail". TED. 1 February 2009. Retrieved 5 October 2016. TED Talk on biomimicry, including applications of van der Waals force.
- Wolff, J. O.; Gorb, S. N. (18 May 2011). "The influence of humidity on the attachment ability of the spider Philodromus dispar (Araneae, Philodromidae)". Proceedings of the Royal Society B: Biological Sciences. 279 (1726): 139–143. PMID 21593034.