Interactions between Surfaces and Particles

The above discussion centered on the forces controlling the interactions between two isolated atoms or molecules. For multiunit systems it is assumed that the units interact mutually according to the Lennard-Jones potential, and that the total interaction is the sum of all individual interactions. For the repulsive term, it is common to neglect the repulsive component for units in one bulk phase and consider only repulsion between opposing surfaces. 

Mathematically, the simplest situation to analyze is that involving two hard, flat, effectively infinite surfaces separated by a distance, //, in a vacuum. The free energy of attraction per unit area in such a case is approximated by 

In most practical instances, it is safe to neglect all of the higher terms. 

Because interactions between surfaces fall off much more slowly with distance than those for individual atoms or molecules, the retardation effect mentioned above becomes more significant. However, while the retardation effect is important in quantitative theoretical discussions of surface interactions, from a practical standpoint, it is still relatively insignificant compared to other factors. 

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