Van der Waals force

Source: Wikipedia, the free encyclopedia.

Rainwater flux from a canopy. Among the forces that govern drop formation: Van der Waals force, surface tension, cohesion, Plateau–Rayleigh instability.
Microfiber cloth makes use of van der Waals force to remove dirt without scratches.[1]

In

ionic or covalent bonds, these attractions do not result from a chemical electronic bond;[2]
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

molecular dipoles
whose rotational orientations are dynamically averaged over time.

Definition

Van der Waals forces include attraction and repulsions between

ionic bonding in that they are caused by correlations in the fluctuating polarizations of nearby particles (a consequence of quantum dynamics[6]
).

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,

intermolecular forces
have several possible contributions:

  1. A repulsive component resulting from the Pauli exclusion principle that prevents close contact of atoms, or the collapse of molecules.
  2. Attractive or repulsive
    Keesom interaction or Keesom force after Willem Hendrik Keesom
    .
  3. Induction (also known as
    Peter J. W. Debye
    .
  4. 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

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. Random thermal motion can disrupt or overcome the electrostatic component of the van der Waals force but the 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 (

E. M. Lifshitz.[13][14] A more general theory of van der Waals forces has also been developed.[15][16]

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

hydroxyl group
dominate other weaker van der Waals interactions. In higher molecular weight alcohols, the properties of the nonpolar hydrocarbon chain(s) dominate and determine their solubility.

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

sublimation heat
is a measure of the dispersive interaction.

Van der Waals forces between macroscopic objects

For

Hamaker[19][full citation needed] (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules[20][full citation needed
] as the starting point) by:

 

 

 

 

(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

Langbein derived a much more cumbersome "exact" expression in 1970 for spherical bodies within the framework of the Lifshitz theory[25][full citation needed] while a simpler macroscopic model approximation had been made by Derjaguin as early as 1934.[26][full citation needed
] Expressions for the van der Waals forces for many different geometries using the Lifshitz theory have likewise been published.

Use by geckos and arthropods

Gecko climbing a glass surface

The ability of

spatulae, or microscopic projections, which cover the hair-like setae found on their footpads.[27][28]

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

contact electrification), not van der Waals or capillary forces.[36]

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

References

  1. ^ Woodford, Chris (2 July 2008). "How do microfiber cloths work? | The science of cleaning". Explain that Stuff. Retrieved 11 February 2022.
  2. ^ Garrett, Reginald H.; Grisham, Charles M. (2016). Biochemistry (6th ed.). University of Virginia. pp. 12–13.
  3. .
  4. .
  5. ^ 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. .
  6. .
  7. .
  8. .
  9. .
  10. .
  11. .
  12. ^ "New way to levitate objects discovered". Science Daily. 6 August 2007.
  13. S2CID 463815
    .
  14. .
  15. .
  16. .
  17. .
  18. ^ H. C. Hamaker, Physica, 4(10), 1058–1072 (1937)
  19. ^ London, F. Transactions of the Faraday Society 33, 8–26 (1937)
  20. S2CID 250790137
    .
  21. .
  22. .
  23. ^ E. M. Lifshitz, Soviet Physics—JETP, 2, 73 (1956)
  24. ^ D. Langbein, Physical Review B, 2, 3371 (1970)
  25. ^ B. V. Derjaguin, Kolloid-Zeitschrift, 69, 155–164 (1934)
  26. PMID 19656797
    .
  27. .
  28. ^ Steenhuysen, Julie (8 October 2008). "Gecko-like glue is said to be stickiest yet". Reuters. Retrieved 5 October 2016.
  29. ^ Quick, Darren (6 November 2011). "Biologically inspired adhesive tape can be reused thousands of times". New Atlas. Retrieved 5 October 2016.
  30. PMID 21865250
    .
  31. .
  32. .
  33. .
  34. .
  35. . 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.
  36. .
  37. .

Further reading

External links