Adsorption at structured interfaces

Consider the case of sticky spheres The sticky potential has the form 

The Langmuir adsorption sites can be represented by a collection of sticky sites of the same form as was suggested by Baxter. Only that now we do not have a sphere covered uniformly by a layer of glue, but rather a smooth, hard surface with sticky points, which represent adsorption sites where actual chemical bonding takes place. For a regular crystal lattice face, Eq.(1.136) has to be changed to 

Here z is the distance to the contact plane, which is at a distance aj2 from the electrode, and R y) is the position of a point on the planar surface at z. In 

are natural numbers, and ai.aj are lattice vectors of a lattice A(s) on the surface at z.The lattice of sticky adsorption sites at the electrode surface is 

A(-(7/2). The requirement of point adsorption sites rather than extended regions around the sites is not essential to our discussion. It is clear that phase transitions will occur even in smooth surfaces, simply because the two dimensional gas does undergo such phase transitions. Less localized forms of the adsorption potential can be includes as long as the soft potential does not overlap neighboring sites. The model as it stands includes every interaction of the adsorbed atoms The solvent mediated potentials of mean force as well as the quantum effects at metallic surfaces 

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