Vander Vaal Forces

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Van der Waals force

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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 sum of the attractive or repulsive

forces 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:

force between two permanent dipoles (Keesom force)

force between a permanent dipole and a corresponding induced dipole (Debye force)

force between two instantaneously induced dipoles (London dispersion force)

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-London forces grow

with the length of the nonpolar part of the substance.

Contents

1 Definition

2 London dispersion force

3 Van der Waals forces between macroscopic objects

4 Use by animals

5 References

6 Further reading

7 External links

[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[2]).

Intermolecular forces have four major contributions:

1. A repulsive component resulting from the Pauli exclusion principle that prevents the

collapse of molecules.

2. Attractive or repulsive electrostatic interactions between permanent 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 Keesominteraction or Keesom force after Willem Hendrik Keesom.

3. 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.

4. Dispersion (usually named after Fritz London), which is the attractive interaction

between any pair of molecules, including non-polar atoms, arising from the

interactions of instantaneous multipoles.

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).

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 themicroscopic description of the latter bulk property. The first detailed calculations of this were

done in 1955 by E. M. Lifshitz.[3][4]

[edit] London dispersion force

Main article: 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. These forces dominate the

interaction of non-polar molecules, and also play a less significant role in Van der Waals

forces than molecules containing permanent dipoles or ionized molecules. London dispersion

forces are also known as dispersion forces, London forces, or instantaneous dipole – induced

dipole forces. They increase with the molar mass, causing a higher boiling point especially

for the halogen group.

[edit] Van der Waals forces between macroscopic objects

For macroscopic 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 R 1 and R 2 and with smooth

surfaces was approximated in 1937 by Hamaker [5] (using London's famous 1937 equation for

the dispersion interaction energy between atoms/molecules[6] 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 R1, R2, and r (the distance

between the surfaces): .

In the limit of close-approach, the spheres are sufficiently large compared to the distance

between them, i.e. , so that equation (1) for the potential energy

function simplifies to:

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:

The van der Waals forces between objects with other geometries using the

Hamaker model have been published in the literature.[7][8][9]

From the expression above, it is seen that the van der Waals force decreases with

decreasing particle size (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 easily 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 in 1956.[10]

Langbein derived a much more cumbersome "exact" expression in 1970 for spherical bodies within the framework of the Lifshitz theory[11] while a simpler

macroscopic model approximation had been made by Derjaguin as early as

1934.[12] Expressions for the van der Waals forces for many different geometries

using the Lifshitz theory have likewise been published.

[edit] Use by animals

Gecko climbing glass

The ability of geckos – which can hang on a glass surface using only one toe – to

climb on sheer surfaces has been attributed to the van der Waals forces between

these surfaces and the spatula (plural spatulae), or microscopic projections, which

cover the hair-like setae found on their footpads.[13][14] A later study suggested

that capillary adhesion might play a role,[15] but that hypothesis has been rejected

by more recent studies.[16] [17] [18] There were efforts in 2008 to create a dry glue

that exploits the effect.[19] In 2011, a paper was published relating the effect to

both velcro-like hairs and the presence of lipids in gecko footprints.[20]

INTERMOLECULAR BONDING - VANDER WAALS FORCES

This page explains the origin of the two weaker forms ofintermolecular attractions - van der Waals dispersion forces anddipole-dipole attractions. If you are also interested in hydrogenbonding there is a link at the bottom of the page.

What are intermolecular attractions?

Intermolecular versus intramolecular bonds

Intermolecular attractions are attractions between onemolecule and a neighbouring molecule. The forces of attractionwhich hold an individual molecule together (for example, thecovalent bonds) are known as in t ramolecular attractions.These two words are so confusingly similar that it is safer toabandon one of them and never use it. The term"intramolecular" won't be used again on this site.

All molecules experience intermolecular attractions, although in

some cases those attractions are very weak. Even in a gas likehydrogen, H2, if you slow the molecules down by cooling thegas, the attractions are large enough for the molecules to sticktogether eventually to form a liquid and then a solid.

In hydrogen's case the attractions are so weak that themolecules have to be cooled to 21 K (-252°C) before theattractions are enough to condense the hydrogen as a liquid.Helium's intermolecular attractions are even weaker - themolecules won't stick together to form a liquid until thetemperature drops to 4 K (-269°C).

van der Waals forces: dispersion forces

Dispersion forces (one of the two types of van der Waals forcewe are dealing with on this page) are also known as "Londonforces" (named after Fritz London who first suggested how theymight arise).

The origin of van der Waals dispersion forces

Temp orary f luctuat ing dipoles

Attractions are electrical in nature. In a symmetrical moleculelike hydrogen, however, there doesn't seem to be any electrical

distortion to produce positive or negative parts. But that's onlytrue on average.

The lozenge-shaped diagram represents a small symmetricalmolecule - H2, perhaps, or Br2. The even shading shows that onaverage there is no electrical distortion.

But the electrons are mobile, and at any one instant they might

find themselves towards one end of the molecule, making thatend -. The other end will be temporarily short of electrons andso becomes +.

Note: (read as "delta") means "slightly" - so + means "slightlypositive".

An instant later the electrons may well have moved up to theother end, reversing the polarity of the molecule.

This constant "sloshing around" of the electrons in the moleculecauses rapidly fluctuating dipoles even in the most symmetricalmolecule. It even happens in monatomic molecules - moleculesof noble gases, like helium, which consist of a single atom.

If both the helium electrons happen to be on one side of theatom at the same time, the nucleus is no longer properlycovered by electrons for that instant.

How temp orary dipoles give rise to intermo lecular

attract ions

I'm going to use the same lozenge-shaped diagram now torepresent any molecule which could, in fact, be a much morecomplicated shape. Shape does matter (see below), but keeping

the shape simple makes it a lot easier to both draw the diagramsand understand what is going on.

Imagine a molecule which has a temporary polarity beingapproached by one which happens to be entirely non-polar justat that moment. (A pretty unlikely event, but it makes thediagrams much easier to draw! In reality, one of the molecules islikely to have a greater polarity than the other at that time - andso will be the dominant one.)

As the right hand molecule approaches, its electrons will tend tobe attracted by the slightly positive end of the left hand one.

This sets up an induced dipo le in the approaching molecule,which is orientated in such a way that the + end of one isattracted to the - end of the other.

An instant later the electrons in the left hand molecule may wellhave moved up the other end. In doing so, they will repel theelectrons in the right hand one.

The polarity of both molecules reverses, but you still have +attracting -. As long as the molecules stay close to each otherthe polarities will continue to fluctuate in synchronisation so thatthe attraction is always maintained.

There is no reason why this has to be restricted to twomolecules. As long as the molecules are close together this

synchronised movement of the electrons can occur over huge

numbers of molecules.

This diagram shows how a whole lattice of molecules could beheld together in a solid using van der Waals dispersion forces.An instant later, of course, you would have to draw a quitedifferent arrangement of the distribution of the electrons as theyshifted around - but always in synchronisation.

The strength of dispersion forces

Dispersion forces between molecules are much weaker than thecovalent bonds within molecules. It isn't possible to give anyexact value, because the size of the attraction variesconsiderably with the size of the molecule and its shape.

How m olecular size affects the strength of the disp ersion

forces

The boiling points of the noble gases are

helium -269°C

neon -246°C

argon -186°C

krypton -152°C

xenon -108°C

radon -62°C

All of these elements have monatomic molecules.

The reason that the boiling points increase as you go down thegroup is that the number of electrons increases, and so alsodoes the radius of the atom. The more electrons you have, andthe more distance over which they can move, the bigger thepossible temporary dipoles and therefore the bigger thedispersion forces.

Because of the greater temporary dipoles, xenon molecules are"stickier" than neon molecules. Neon molecules will break awayfrom each other at much lower temperatures than xenonmolecules - hence neon has the lower boiling point.

This is the reason that (all other things being equal) biggermolecules have higher boiling points than small ones. Biggermolecules have more electrons and more distance over whichtemporary dipoles can develop - and so the bigger moleculesare "stickier".

How m olecular shape affects the strength of the dispersion

forces

The shapes of the molecules also matter. Long thin moleculescan develop bigger temporary dipoles due to electron movementthan short fat ones containing the same numbers of electrons.

Long thin molecules can also lie closer together - these

attractions are at their most effective if the molecules are reallyclose.

For example, the hydrocarbon molecules butane and 2-methylpropane both have a molecular formula C4H10, but theatoms are arranged differently. In butane the carbon atoms arearranged in a single chain, but 2-methylpropane is a shorterchain with a branch.

Butane has a higher boiling point because the dispersion forcesare greater. The molecules are longer (and so set up biggertemporary dipoles) and can lie closer together than the shorter,fatter 2-methylpropane molecules.

van der Waals forces: dipole-dipole interactions

Warning! There's a bit of a problem here with modern syllabuses.The majority of the syllabuses talk as if dipole-dipole interactions werequite distinct from van der Waals forces. Such a syllabus will talk aboutvan der Waals forces (meaning dispersion forces) and, separately,dipole-dipole interactions.

All intermolecular attractions are known collectively as van der Waalsforces. The various different types were first explained by differentpeople at different times. Dispersion forces, for example, weredescribed by London in 1930; dipole-dipole interactions by Keesom in1912.

This oddity in the syllabuses doesn't matter in the least as far asunderstanding is concerned - but you obviously must know what yourparticular examiners mean by the terms they use in the questions.Check your syllabus.

If you are working to a UK-based syllabus for 16 - 18 year olds, butdon't have a copy of it, follow this link to find out how to get one.

A molecule like HCl has a permanent dipole because chlorine ismore electronegative than hydrogen. These permanent, in-builtdipoles will cause the molecules to attract each other rathermore than they otherwise would if they had to rely only ondispersion forces.

Note: If you aren't happy about electronegativity and polar molecules, follow this link before you go on.

It's important to realise that all molecules experience dispersionforces. Dipole-dipole interactions are not an alternative todispersion forces - they occur in addition to them. Moleculeswhich have permanent dipoles will therefore have boiling pointsrather higher than molecules which only have temporary

fluctuating dipoles.

Surprisingly dipole-dipole attractions are fairly minor comparedwith dispersion forces, and their effect can only really be seen ifyou compare two molecules with the same number of electronsand the same size. For example, the boiling points of ethane,CH3CH3, and fluoromethane, CH3F, are

Why choose these two molecules to compare? Both haveidentical numbers of electrons, and if you made models youwould find that the sizes were similar - as you can see in thediagrams. That means that the dispersion forces in bothmolecules should be much the same.

The higher boiling point of fluoromethane is due to the largepermanent dipole on the molecule because of the highelectronegativity of fluorine. However, even given the largepermanent polarity of the molecule, the boiling point has onlybeen increased by some 10°.

Here is another example showing thedominance of the dispersion forces.

Trichloromethane, CHCl3, is a highly polarmolecule because of the electronegativity ofthe three chlorines. There will be quitestrong dipole-dipole attractions between onemolecule and its neighbours.

On the other hand, tetrachloromethane, CCl4, is non-polar. Theoutside of the molecule is uniformly - in all directions. CCl4 hasto rely only on dispersion forces.

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Next: Complementarity Up: Protein surfaces and binding Previous:

Hydrophobic interactions Contents

Electrostatic interactions

Hydrogen bonds, salt bridges and van der Waals also provide attractive

forces between molecules. Hydrogen bonds between protein and ligand

can be more favourable than between protein and solvent[Fersht,

1987], and although they are not found in large numbers in all

interfaces, they make an important contribution to the binding energy

of association. Hydrogen bonds via water molecules trapped in theinterface are also commonly observed. Hydrogen bonds and salt-

bridges are thought to confer specificity to interactions due to their

dependence on the precise location of participating atoms[Fersht,

1984,Fersht, 1987].

Van der Waals interactions occur between all neighbouring atoms in

structures and interfaces, but are not significantly different to those

made by the same atoms with solvent. Thus a requirement exists for

the atoms in the interface to be at least as densly packed as in bulk

solvent; implying shape complementarity as discussed in the following

section.

Copyright Bob MacCallum - DISCLAIMER: this was written in 1997

and may contain out-of-date information.

So which has the highest boiling point? CCl4 does, because it isa bigger molecule with more electrons. The increase in thedispersion forces more than compensates for the loss of dipole-dipole interactions.

The boiling points are:

CHCl3 61.2°C

CCl4 76.8°C

Vander Vaal Forces

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