Calculating van der Waals Forces Between Macroscopic Bodies

6 CALCULATING VAN DER WAALS FORCES BETWEEN MACROSCOPIC BODIES 

The strategy for scaling up the van der Waals attraction to macroscopic bodies requires that all pairwise combinations of intermolecular attraction between the two bodies be summed. This has been done for several different geometries by Hamaker. We consider only one example of the calculations involved, namely, the case of blocks of material with planar surfaces. This example serves to illustrate the method and also provides a foundation for connecting van der Waals forces with surface tension, the subject of the next section. 

We assume the ring is located a distance f inside the surface of the block then 

6 Schematic illustration of interactions (a) interaction between a molecule and a block of material and (b) interaction between two blocks of material. (Redrawn with permission from P. C. Hiemenz, J. Chem. Educ., 49, 164 (1972). 

Therefore the integration of Equation (56) over the block gives 

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Hamaker (1932) and de Boer (1936) calculated van der Waals forces between macroscopic bodies using the summation method. 

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