always present. Assume that the pair potential between two atoms or small molecules is purely attractive and of the form w = -C/rn, where C is a constant for interaction energy, decided by the molecule's property and n = 6 for van der Waals attraction. With another assumption of additivity, the net interaction energy between a molecule and planar surface made up of like molecules will be the sum of the interaction energy between the molecule and every molecule in the surface body. So the net interaction energy for a molecule at a distance D away from the surface will therefore be where w(r) is the interaction energy between the molecule and the surface, is the number density of the surface, z is the axis perpendicular to the surface and passesding across the molecule, with z = D at the point where the molecule is, and z = 0 at the surface, x is the axis perpendicular to the z axis, with x = 0 at the intersection. Then the interaction energy of a large sphere of radius R and a flat surface can be calculated as where W(D) is the interaction energy between the sphere and the surface, is the number density of the sphere. For convenience, Hamaker constant A is given as and the equation becomes With a similar method and according to Derjaguin approximation, the van der Waals interaction energy between particles with different shapes can be calculated, such as energy between two spheres: sphere and surface: two surfaces: per unit area. Double layer force A surface in a liquid may be charged by dissociation of surface groups (e.g. silanol groups for glass or silica surfaces) or by adsorption of charged molecules such as polyelectrolyte from the surrounding solution. This results in the development of a wall surface potential which will attract counterions from the surrounding solution and repel co-ions. In equilibrium, the surface charge is balanced by oppositely charged counterions in solution. The region near the surface of enhanced counterion concentration is called the electrical double layer (EDL). The EDL can be approximated by a sub-division into two regions. Ions in the region closest to the charged wall surface are strongly bound to the surface. This immobile layer is called the Stern or Helmholtz layer. The region adjacent to the Stern layer is called the diffuse layer and contains loosely associated ions that are comparatively mobile.