Treating the two particles as infinitely large flat plates, then the attraction per unit surface area becomes (forces between macroscopic bodies e.g. particles is the sum of the interactions with all the molecules in the bodies).
A is Hamaker constant and has a value ranging from 10-20-10-19 J (2.5kT-25kT, k is Boltzman constant, D is the separation distance, a is the particle size)
Note, the potential energy falls off much more slowly (1/D2).