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In
molecular physics Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, m ...
, the van der Waals force is a distance-dependent interaction between
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s or
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s. Unlike ionic or
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between ato ...
s, these attractions do not result from a chemical electronic bond; 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 Johannes Diderik van der Waals (; 23 November 1837 – 8 March 1923) was a Dutch theoretical physicist and thermodynamicist famous for his pioneering work on the equation of state for gases and liquids. Van der Waals started his career as a sch ...
, the van der Waals force plays a fundamental role in fields as diverse as
supramolecular chemistry Supramolecular chemistry refers to the branch of chemistry concerning chemical systems composed of a discrete number of molecules. The strength of the forces responsible for spatial organization of the system range from weak intermolecular forces ...
,
structural biology Structural biology is a field that is many centuries old which, and as defined by the Journal of Structural Biology, deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every le ...
,
polymer science Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines includ ...
,
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal ...
,
surface science Surface science is the study of physical and chemical phenomena that occur at the interface of two phases, including solid– liquid interfaces, solid– gas interfaces, solid–vacuum interfaces, and liquid– gas interfaces. It includes th ...
, and
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...
. It also underlies many properties of
organic compounds In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
and
molecular solid A molecular solid is a solid consisting of discrete molecules. The cohesive forces that bind the molecules together are van der Waals forces, dipole-dipole interactions, quadrupole interactions, π-π interactions, hydrogen bonding, halogen bo ...
s, including their
solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
in polar and non-polar media. If no other
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
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 cloud In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any sp ...
s. The van der Waals forces are usually described as a combination of the London dispersion forces between "instantaneously induced
dipole In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system ...
s",
Debye force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. ...
s between permanent dipoles and induced dipoles, and the
Keesom force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. a ...
between permanent molecular dipoles whose rotational orientations are dynamically averaged over time.


Definition

Van der Waals forces include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces. They differ from
covalent A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
and ionic bonding in that they are caused by correlations in the fluctuating polarizations of nearby particles (a consequence of
quantum dynamics In physics, quantum dynamics is the quantum version of classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of quantum mechanics. Quantum dynamics is releva ...
Chapter 6 Electromagnetic Radiation in an Absorbing Medium). The force results from a transient shift in electron density. Specifically, the electron density may temporarily shift more greatly to 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. 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). Van der Waals forces are often among the weakest chemical forces. For example, the pairwise attractive van der Waals interaction energy between H atoms in different H2 molecules equals 0.06 kJ/mol (0.6 meV) and the pairwise attractive interaction energy between O atoms in different O2 molecules equals 0.44 kJ/mol (4.6 meV). 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 to ~15 times the value of the individual pairwise interatomic interactions (excluding covalent bonds). The strength of van-der-Waals bonds increases with higher
polarizability Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of all matter, considering that matter is made up of elementar ...
of the participating atoms. For example, the pairwise van der Waals interaction energy for more polarizable atoms such as S atoms in H2S and sulfides exceeds 1 kJ/mol (10 meV), and the pairwise interaction energy between even larger, more polarizable Xe atoms is 2.35 kJ/mol (24.3 meV). 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 betweeen 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 and on the order of 32 kJ/mol (330 meV) for high-melting Pt, which is about one order of magnitude stronger than in Xe due to the presence of a highly polarizable
free electron gas Free electron in physics may refer to: *Electron, as a free particle *Solvated electron *Charge carrier, as carriers of electric charge *Valence electron, as an outer shell electron that is associated with an atom *Valence and conduction bands, as a ...
. 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 An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. a ...
have several possible contributions: # A repulsive component resulting from the
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formula ...
that prevents close contact of atoms, or the collapse of molecules. # Attractive or repulsive
electrostatic Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for ...
interactions between permanent charges (in the case of molecular ions), dipoles (in the case of molecules without inversion centre),
quadrupole A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...
s (all molecules with symmetry lower than cubic), and in general between permanent
multipole A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Similarly ...
s. These interactions also include
hydrogen bond In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a l ...
s, cation-pi, and
pi-stacking In chemistry, pi stacking (also called π–π stacking) refers to the presumptive attractive, noncovalent pi interactions ( orbital overlap) between the pi bonds of aromatic rings. However this is a misleading description of the phenomena sinc ...
interactions. Orientation-averaged contributions from electrostatic interactions are sometimes called the Keesom interaction or Keesom force after Willem Hendrik Keesom. # Induction (also known as polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced multipole on another. This interaction is sometimes called Debye force after Peter J.W. Debye. # Dispersion (usually named London dispersion interactions after
Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces ( London dispersion forces) are today ...
), 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 Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
(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 The Lennard-Jones potential (also termed the LJ potential or 12-6 potential) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studie ...
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 In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pre ...
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 Evgeny Mikhailovich Lifshitz (russian: Евге́ний Миха́йлович Ли́фшиц; February 21, 1915, Kharkiv, Russian Empire – October 29, 1985, Moscow, Russian SFSR) was a leading Soviet physicist and brother of the physicist ...
. A more general theory of van der Waals forces has also been developed. The main characteristics of van der Waals forces are: * They are weaker than normal covalent and ionic bonds. * Van der Waals forces are additive 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 In chemistry, a hydroxy or hydroxyl group is a functional group with the chemical formula and composed of one oxygen atom covalently bonded to one hydrogen atom. In organic chemistry, alcohols and carboxylic acids contain one or more hydroxy ...
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.


London dispersion force

London dispersion forces, named after the German-American physicist
Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces ( London dispersion forces) are today ...
, are weak
intermolecular force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. ...
s that arise from the interactive forces between instantaneous multipoles in molecules without permanent
multipole moments A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Similarly ...
. In and between organic molecules the multitude of contacts can lead to larger contribution of dispersive attraction, particularly in the presence of heteroatoms. London dispersion forces are also known as '
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
forces', 'London forces', or 'instantaneous dipole–induced dipole forces'. The strength of London dispersion forces is proportional to the polarizability of the molecule, which in turn depends on the total number of electrons and the area over which they are spread. Hydrocarbons display small dispersive contributions, the presence of heteroatoms lead to increased LD forces as function of their polarizability, e.g. in the sequence RI>RBr>RCl>RF. In absence of solvents weakly polarizable hydrocarbons form crystals due to dispersive forces; their sublimation heat is a measure of the dispersive interaction.


Van der Waals forces between macroscopic objects

For
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena a ...
bodies with known volumes and numbers of atoms or molecules per unit volume, the total van der Waals force is often computed based on the "microscopic theory" as the sum over all interacting pairs. It is necessary to integrate over the total volume of the object, which makes the calculation dependent on the objects' shapes. For example, the van der Waals interaction energy between spherical bodies of radii R1 and R2 and with smooth surfaces was approximated in 1937 by Hamaker (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules as the starting point) by: 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 ''R''1, ''R''2, and ''r'' (the distance between the surfaces): \ z = R_ + R_ + r. The van der Waals ''
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
'' between two spheres of constant radii (''R''1 and ''R''2 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,\ F_(z) = -\fracU(z). This yields: In the limit of close-approach, the spheres are sufficiently large compared to the distance between them; i.e., \ r \ll R_ or R_, so that equation (1) for the potential energy function simplifies to: with the force: The van der Waals forces between objects with other geometries using the Hamaker model have been published in the literature. 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 many-body interactions and retardation. A more rigorous approach accounting for these effects, called the " macroscopic theory" was developed by
Lifshitz Lifshitz (or Lifschitz) is a surname, which may be derived from the Polish city of Głubczyce (German: Leobschütz). The surname has many variants, including: , , Lifshits, Lifshuts, Lefschetz; Lipschitz ( Lipshitz), Lipshits, Lipchitz, Lips ...
in 1956. Langbein derived a much more cumbersome "exact" expression in 1970 for spherical bodies within the framework of the Lifshitz theory while a simpler macroscopic model approximation had been made by Derjaguin as early as 1934. Expressions for the van der Waals forces for many different geometries using the Lifshitz theory have likewise been published.


Use by geckos and arthropods

The ability of
gecko Geckos are small, mostly carnivorous lizards that have a wide distribution, found on every continent except Antarctica. Belonging to the infraorder Gekkota, geckos are found in warm climates throughout the world. They range from . Geckos a ...
s – which can hang on a glass surface using only one toe – to climb on sheer surfaces has been for many years mainly attributed to the van der Waals forces between these surfaces and the spatulae, or microscopic projections, which cover the hair-like
seta In biology, setae (singular seta ; from the Latin word for "bristle") are any of a number of different bristle- or hair-like structures on living organisms. Animal setae Protostomes Annelid setae are stiff bristles present on the body. ...
e found on their footpads. A later study suggested that capillary adhesion might play a role, but that hypothesis has been rejected by more recent studies. A recent study has however shown that gecko adhesion to smooth Teflon and
polydimethylsiloxane Polydimethylsiloxane (PDMS), also known as dimethylpolysiloxane or dimethicone, belongs to a group of polymeric organosilicon compounds that are commonly referred to as silicones. PDMS is the most widely used silicon-based organic polymer, as its ...
surfaces is mainly determined by electrostatic interaction (caused by
contact electrification Contact electrification is a phrase that describes a phenomenon whereby surfaces become electrically charged, via a number of possible mechanisms, when two or more objects come within close proximity of one another. When two objects are "touched" ...
), not van der Waals or capillary forces. There were efforts in 2008 to create a dry glue that exploits the effect, and success was achieved in 2011 to create an adhesive tape on similar grounds. In 2011, a paper was published relating the effect to both velcro-like hairs and the presence of lipids in gecko footprints. Among the
arthropod Arthropods (, (gen. ποδός)) are invertebrate animals with an exoskeleton, a segmented body, and paired jointed appendages. Arthropods form the phylum Arthropoda. They are distinguished by their jointed limbs and cuticle made of chiti ...
s, 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.


In modern technology

In May 2014,
DARPA The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the A ...
demonstrated the latest iteration of its "Geckskin" technology by having a 100 kg researcher (saddled with 20 kg of recording gear) scale an glass wall using only two climbing paddles. Tests are ongoing, but DARPA hopes one day to make the technology available for military use, giving soldiers
Spider-Man Spider-Man is a superhero appearing in American comic books published by Marvel Comics. Created by writer-editor Stan Lee and artist Steve Ditko, he first appeared in the anthology comic book ''Amazing Fantasy'' #15 (August 1962) in the Si ...
-like abilities in urban combat.


See also

* Arthropod adhesion *
Dispersion (chemistry) A dispersion is a system in which distributed particles of one material are dispersed in a continuous phase of another material. The two phases may be in the same or different states of matter. Dispersions are classified in a number of dif ...
*
Gecko feet The feet of geckos have a number of specializations. Their surfaces can adhere to any type of material with the exception of Polytetrafluoroethylene, Teflon (PTFE). This phenomenon can be explained with three elements: * Foot structure * Structure ...
*
Lennard-Jones potential The Lennard-Jones potential (also termed the LJ potential or 12-6 potential) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studie ...
* Noncovalent interactions *
Synthetic setae Synthetic things are composed of multiple parts, often with the implication that they are artificial. In particular, 'synthetic' may refer to: Science * Synthetic chemical or compound, produced by the process of chemical synthesis * Synthetic o ...
* Van der Waals molecule *
Van der Waals radius The van der Waals radius, ''r'', of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, ...
*
Van der Waals strain Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals rep ...
*
Van der Waals surface The Van der Waals surface of a molecule is an abstract representation or model of that molecule, illustrating where, in very rough terms, a surface might reside for the molecule based on the hard cutoffs of Van der Waals radii for individual at ...
* Wringing of gauge blocks used in machining


References


Further reading

* * **English translation: * * * * **English translation: * * *


External links

* An introductory description of the van der Waals force (as a sum of attractive components only) * TED Talk on biomimicry, including applications of van der Waals force. * {{Authority control Intermolecular forces
Force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...