Electrostatic potential long-range

The above provides a means of showing how the total excess charge on the solution side of the interface q the excess charge due to cations F+ and the excess charge due to anions F, vary with potential in a solution of fixed concentration of electrolyte. On the basis of this approach to the electrocapillary curves it has been shown that the Gibbs surface excess for cations is due solely to electrostatic forces (long-range coulombic), and this is reflected in the fact that the electrocapillary curves for different cations and... 

In Chapter 2 the curve of Fig. 7 was introduced, to show the mutual potential energy arising from short-range forces in contrast to that arising from long-range electrostatic forces. To account for the existence of molecules and molecular ions in solution, we need the same curve with the scale of ordinates reduced so as to be comparable with those of Fig. 

Figure 2. The electrostatic potential energy for atoms with half charges of opposite signs for the different methods of long range truncation.

Therefore, we predict that for a system with any finite misfit, a uniform film with a thickness greater than several monolayers is not the equilibrium state the system can lower the chemical potential by the formation of clusters. Clusters will form on either the bare substrate (Volmer-Weber mode any finite misfit with WKl and large misfits if W >1) or on a few layers of uniform film (Stranski-Krastanov mode up to moderate misfits with W>1). This will be true for any system without long-range (e.g. electrostatic) forces. 

Note that, due to their infinite-range character, pure Coulombic potentials can actually lead to significant bond non-additivity for any proposed separation into bonded and nonbonded units. This reflects the fact that classical electrostatics is oblivious to any perceived separation into chemical units, because all Coulombic pairings (whether in the same or separate units) make long-range contributions to the total interaction energy. 

---