Adhesion at single point contacts.

With the advent of the Surface Force Apparatus (SFA) in which contact is between atomically smooth cleaved mica, and the Atomic Force Microscope (AFM), where an ultrasharp stylus is loaded against a plane, it is for the first time possible to study the behaviour of a single, well-defined, contact area. But because of the difficulties of the experiments, it is of great importance to study the contact mechanics of adhesive contacts in order to provide the experimenter with a theoretical background to help in interpreting the measurements. For many years the only theory available was the one developed by Johnson, Kendall & Roberts (JKR theory) in studying rubber/glass contacts. This allows for the influence of the surface energy of the solids in increasing the area of contact above the Hertzian value, and good agreement has been found with the observed contact areas. But because it is based on surface energy rather than surface forces, it is unable to deal with surfaces approaching each other, and already experiencing attractive forces while still out of contact: or with the 'jumping-on' of contacts, already observed in the rubber/glass experiments, and an important feature of SFA experiments. Three models based on surface forces are described here. One involves full numerical calculations for a particular law of surface force: the other two are analytical models based on greatly simplified laws of force. The Maugis model takes the surface force to be a constant when the gap between the surfaces is positive but less than a critical value h(c), and to be zero for larger gaps: when the gap falls to zero the normal elastic laws apply. An alternative model, based directly on Hertz theory, is introduced here, and the results of all the models compared.