2.2.7.2 The DMT model of solids adhesion

The DMT model [1, 2] (Derjagin, Muller, Toropov – 1975) is applied to tips with small curvature radius and high stiffness. It is assumed that deformed surfaces geometry differs not much from that given by the Hertz problem solution. Consideration of the Van der Waals forces acting along the contact area perimeter results in an additional probe-sample attraction which weakens forces of elastic repulsion.

Fig. 1a.  Applicability of the DMT model.

Fig. 1b.  Plot of the force vs. the penetration depth.

The relation between the pressure and the penetration depth is as follows:

,

(1)

where – tip curvature radius, – contact area radius, – effective Young's modulus, , – work of adhesion (see chapter 2.2.7.1).

References.

1. Derjaguin B.V., Muller V.M., Toropov Yu.P., J. Colloid. Interface Sci. 53, 314 (1975).
2. Derjuguin B.V., Churayev N.V., Muller V.M. Surface forces. – Moscow: Nauka Publ. 1985 (in Russian)