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# London Dispersion Interactions

The attractive forces that exist between molecules are known as intermolecular forces. These include ionic interactions, dipole-dipole interactions and dispersion or London dispersion forces. Dipole-dipole interactions and dispersion forces are weaker than thermal energy (2.4 kJ/mole) at room temperature and are referred to as Van der Waals Force. The London dispersion force is the weakest intermolecular force. It is a temporary attractive force that results when the electrons in two adjacent atoms occupy positions that make the atoms form temporary dipoles.

### Introduction

Unequal sharing of electrons causes rapid polarization and counter-polarization of the electron cloud forming short lived dipoles. These dipole interact with the electron clouds of neighboring molecules forming more dipoles. The attractive interaction of these dipole are called dispersion or London Dispersion forces. These forces are weaker than other intermolecular forces. They do not extend over long distances. The strength of these interactions within a given molecule depends directly on how easily the electrons in the molecules can move (i.e., be polarized). Large molecules in which the electrons are far from the nucleus are relatively easy to polarize and therefore possess greater dispersion

If it were not for dispersion forces, the noble gases would not liquefy at any temperature since no other intermolecular force exists between the noble gas atoms. The low temperature at which the noble gases liquefy is to some extent indicative of the magnitude of dispersion forces between the atoms. Electron distribution around an atom or molecule can be distorted. This distortion is called the polarizability.

### Polarizability

The polarizability is used to describe the tendency of molecules to form charge separation. Induced dipole occurs when a molecule with an instantaneous dipole induces a charge separation on other molecule. The result is a dipole-dipole attraction. The strength of the induced dipole moment, $$\mu$$, is directly proportional to the strength of the electric field, $$E$$ with a proportionality constant  $$\alpha$$ called the polarizability. The strength of the electric field causes the distortion in the molecule. Therefore, greater the strength of the electric field, the greater the distortion, and result to a larger polarizability:

$$\mu = \alpha'{E}$$

where,

• $$\mu$$ = the induced dipole moment
• $$\alpha$$ = the polarizability
• $$E$$ = the electric field

### Dipole-dipole attraction

Dipole molecules tend to arrange their positive end towards the negative ends of neighboring dipole molecules (see polar molecules and dipole moments).

### Interaction Energy

Interaction energy can be approximated using the London formula. A German physicist, Fritz London proved that potential energy of two uncharged molecules or identical atoms can be measured by following equation:

$$V = -\dfrac{3}{4} \dfrac{\alpha_2I}{r^6}$$

Above equation is used as mention below for nonidentical atoms or molecules 1 and 2

$$V = -\dfrac{3}{2} \dfrac{I_1I_2}{I_1 + I_2} \dfrac{\alpha _1' \alpha _2'}{r^6}$$

with

### Example

Using the formal equation, calculate the potential energy (V) between two Ar atoms separated by 4.0 Armstrong in air. (Answer=-0.77 KJ/mol)

### References

1. Atkins, Peter and Julio de Paula. Physical Chemistry for the Life Sciences. Oxford, UK: Oxford University Press. 2006. pg 466-467.
2. Garrett, Reginald H. and Charles M. Grisham. Biochemistry 3rd edition. United Stated of America: Thomson Brooks/Cole. 2005. pg 13.
3. Harwood, William S., Herring, Geoffrey F., and Ralph H. Petrucci. General Chemistry: Principles and Modern Applications 8th edition. Upper Saddle River, New Jersey. 2002. pg 497-499.
4. Chang, Raymond. Physical Chemistry for the Biosciences. University Science Books. 2005. pg 497-498.

### Contributors

• Ryan Ilagan (UCD)

16:50, 10 Jul 2014

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