Microscopic approach of Hamaker between parallel slab surfaces

4 Microscopic approach of Hamaker between parallel slab surfaces 

Equation (548) can also be re-derived if we consider the unit area of a thin sheet of molecules having a thickness of dx and % away from the surface of a second slab (1), and similar to the derivation of Equation (528), we can write for the same kind of interacting materials 

In practice, Equation (549) can be used when D is very small compared with the lateral dimensions of the slab. When Equations (536) and (549) are combined, we have 

The term An can be used instead of Au in Equation (550) if the surfaces of two slabs of different materials interact with each other. If the slabs are not very thick, having a thickness of A, and A2, then the dispersion interaction potential can be given as 

If the thickness of the slabs Ai and A2 is very large, so that Ai, A2 — then we obtain 

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