What is the key difference between sphere-sphere interaction and sphere-plate interaction in calculation of XDLVO theory?
Hi Ma,
In the standard approximations it is the way the attractive and repulsive forces scale that is different. For example, the attractive portion (van der Waals force) is described by a Hamaker constant, A, which is not different for any geometry. However, the way this Hamaker A is used is different. The attractive van der Waals force may be calculated for a sphere-sphere interaction as
F = -A/(6L2) (R1R2/(R1+R2))
where L is the distance between spheres 1 and 2 of radii R1and R2, respectively.
For a sphere-plate interaction, on the other hand, the force is
F = -AR/(6L2)
where R is the radius of the sphere. So you see it is simply the scaling that is different. The same sort of scaling applies to the repulsive electrostatic forces. I suggest reading chapter 13 and 14 of Israelachvili's "Intermolecular and surface forces", 2011 (3rd ed.).
Hope this helps!
Quinn
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