The Nonpolar van der Waals Attraction Forces

The attraction forces which act most frequently in physical adsorption are the nonpolar van der Waals forces. Since London (23) described the close connection between their nature and the cause of optical dispersion, they may also be called dispersion forces. The main contribution to the nonpolar van der Waals forces arises from the interaction of continually changing inducing dipoles and induced dipoles. The interaction energy of a pair of atoms due to this contribution is inversely proportional to the sixth power of the distance  

The constant C depends on the properties of the atoms. London (23) derived the following approximation for C  

Other approximations for C have been derived of these we shall mention only 

Apart from the term in Eq. (7) there are other contributions toward the nonpolar van der Waals interaction energy arising from the interaction of continually changing quadrupoles with dipoles and quadrupoles with quadrupoles. The total expression should, therefore, be written as 

In numerical calculations of adsorption energies, however, expression (7) is mostly used. It is assumed that the two last terms of Eq. (11) are counterbalanced by the contribution of the repulsion forces (see Sec. IV,4). Expression (7) gives the interaction energy between two atoms. In order to evaluate the adsorption energy, the interaction energies of the adsorbed atom with all individual atoms of the adsorbent should be calculated and added together. This addition is allowed, as the dispersion forces are, at a first approximation, additive. If a molecule instead of an atom is adsorbed, the summation should be made for all atoms of the molecule. In the latter case we may sometimes expect deviations from the additive law. Many molecules show different polarizabilities in different directions. If the position of an adsorbed molecule is fixed, the angles of its various axes of polarizability with respect to the surface enter into the calculations (25). If, however, the molecule rotates freely, which is often the case in physical adsorption, this correction is not necessary. 

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