On the DMT theory

The frequent claim that the Tabor parameter mu governs the transition from the DMT theory to the JKR theory is investigated. The change from the simple surface force law sigma similar to A/h(3) of the DMT theory to the Lennard-Jones law sigma similar to A/h(3)-B/h(9) of the MDT theory and the numerical solutions is noted, and the 'adhesive force' is evaluated for both laws. Except in the limit of zero Tabor parameter, when the Derjaguin theories reduce to the rigid-sphere model, the predictions are consistently worse than assuming the sphere to be rigid. A 'semi-rigid' sphere model is proposed, which correctly describes the asymptotic behaviour as mu -> 0, but leaves a considerable gap before the JKR theory can be applied.