126.96.36.199 The Maugis model of solids adhesion
The Maugis mechanics  (1992) is the most composite and accurate approach. It can be applied to any system (any materials) with both high and low adhesion. The amount of adhesion is determined by parameter :
where – interatomic distance.
DMT and JKR models are extreme cases of the Maugis mechanics corresponding to different parameters . For the stiff materials (DMT) , for compliant materials (JKR) .
Fig. 1a. Applicability of the Maugis model.
Fig. 1b. Plot of the force vs. the penetration depth.
The Maugis model assumes that the molecular attraction force acts within a ring zone at the contact area border. The Maugis correction to the Hertz problem solution is expressed implicitly via parameter :
where – tip curvature radius, – contact area radius, – effective Young's modulus , – work of adhesion (see chapter 188.8.131.52).
Both JKR model and Maugis mechanics adopt originally the existence of hysteresis during the approach-retraction cycle. It is assumed that during the cantilever approach the attraction force arises sharply at the moment of touching, then the system proceeds from point 0 into point 1 (Fig. 2). During the cantilever retraction the system "describes" the other path 1-2 until the jump out of the contact occurs 2-3.
Fig. 2. Plot of the force vs. the penetration depth for Maugis model at approach-retraction cycle.
The loop 0-1-2-3 in the plot means that to separate the probe from the sample some work must be done which is equal to the loop square. This is the work of adhesion .
- Maugis D.J., J. Colloid. Interface Sci. 150, 243 (1992).