London Forces or London Dispersion Forces

Overview of bond length

When two atoms form a covalent bond, the distance between their centres is called bond length. Bond order is determined by the number of bonds, based on the number of electrons. The bond length and bond order are inversely related to each other. Bond length is generally measured on a picometre scale. Based on the number of electrons involved in bonding, bond order can be 1,2 or 3, implying that it is a single, double, or triple, respectively. This means that 2, 4, or 6 electrons are involved in bonding.

London Dispersion Forces 

Non-polar molecules also show similar behaviour. We know that all substances, noble gases included, exist in solid and liquid states in certain conditions. This indicates that there must be some sort of intermolecular interaction which cannot be assigned to simple electrostatic attractions or forces. 

These interactions were called dispersion forces. German physicist Fritz London discovered these forces. In 1930, he proposed that when temporary fluctuations in the distribution of electrons occur within atoms and non-polar molecules, it leads to the production of temporary instantaneous dipole moments, which produce attractive forces called London dispersion forces between non-polar substances.

We can understand it by assuming that electrons of an atom are usually symmetrically distributed around the nucleus. There are some instances in which atoms can momentarily develop a non-symmetric distribution of electrons, producing a temporary dipole formation. This instantaneous dipole can distort the electronic cloud of the neighbouring atom, causing a dipole to be formed in it. Because of this phenomenon, interatomic attraction happens, which is weak and short-lived.

If solid has to be produced from these interactions, the motions of the atoms have to be significantly reduced. This can explain the low freezing points of noble gases. As the atomic mass and atomic number increase, the number of electrons increases, so there is a higher chance of producing momentary dipoles. In other words, we can say that larger atoms having many electrons display higher polarisability as compared to smaller atoms. Thus, the London forces’ importance greatly increases with atomic size.

The induced dipole moment’s strength μ, is directly proportional to the electric field’s strength, E. This implies that if strength of electric field is high, it will cause greater distortions and larger interaction:

            μ= ∝E

where, μ= dipole moment that was induced,

            ∝= polarizability, and

            E= electric.field.

Examples of London Dispersion Forces

London Dispersion Forces can be seen in non-polar molecules like Halogens

F2, Cl2, Br2, I2

Energy of interaction

London proved that we can calculate the potential energy of 2 molecules that are uncharged (or of 2 identical atoms) using the following formula:

                     V11 =-34∝2I/r6

The above equation can be slightly changed in case of non-identical atoms or molecules:

                     V12 = -3/2 (I1I2/I1+I2)(∝1∝2/r6)

Where, I= first ionisation energy of every molecule,

              ∝= polarizability, and

               r= distance or separation between molecules or bond length.

From here it can be seen that the attractive energy due to the temporary dipole falls off as 1/r6. This implies that if we double the distance (or bond length) the attractive energy decreases by 26 or 64-fold.

So, we can say that the dispersion forces depend on molecular size, number of electrons, distance between the atoms (or bond length) as well as shape of molecule.

Molecular size and number of electrons

Larger and heavier atoms and molecules can exhibit stronger dispersive forces as compared to smaller and lighter ones. In a larger atom or molecule, the valence electrons are farther from the nucleus as compared to smaller atoms. 

Consequently, they are less tightly held and hence can form temporary dipoles easily. The ease with which distortion of electron distribution can happen is known as polarisability. Hence, London forces are stronger between easily polarised molecules, and weaker between molecules not easily polarised.

Molecular shape

The magnitude of dispersion forces is also affected by the shapes of molecules. This can be understood by considering the example of neopentane and n-pentane. 

n-pentane molecules are somewhat cylindrical. Their shape allows them to come in contact with each other effectively compared to partially spherical neopentane molecules.

This is why neopentane is a gas, while n-pentane is a liquid, as the London dispersion force is stronger in n-pentane than in neopentane.

Conclusion

Intermolecular forces are responsible for holding molecules together in a liquid or solid. These forces are comparatively weaker and electrostatic in nature. In the case of molecules having a net dipole moment, dipole-dipole interactions can be seen. 

Fritz London explained the attractive forces in the case of non-polar molecules. He

proposed that a temporary fluctuation in electronic distribution within atoms or molecules leads to the formation of a temporary dipole, which, in turn, can induce a dipole in the neighbouring atom or molecule. This produces London dispersion forces. These forces are dependent on size, the shape of the molecule, the number of electrons, and the distance between atoms or bond length