Microscopic or Hamaker Approach

As derived above, the potential energy of the van der Waals interaction between two molecules A and B is given by 

The minus sign arises because it is an attractive force. Cab is a material specific constant and equal to Qotai in Eq. (2.22). It sums up contributions of all three dipole-dipole interactions. 

In order to determine the interaction between macroscopic solids, in the first step we calculate the van der Waals energy between molecule A and an infinitely extended body with a planar surface made of molecules B. This is also relevant in understanding the adsorption of gas molecules to surfaces. We sum up the van der Waals energy between molecule A and all molecules in solid B. Practically, this is done by integration of the molecular density Qg over the entire volume of the solid  

we already see a remarkable property of macroscopic van der Waals forces the energy of a molecule and a macroscopic body decreases less steeply than the energy between two molecules. Instead of the dependence, the energy falls off 

In the second step, we calculate the van der Waals energy between two infinitely extended solids that are separated by a parallel gap of thickness D. Therefore, we use Eq. (2.26) and integrate over all molecules in solid A  

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