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The Maugis mechanics [1]
(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  :
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(1) |
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)  .
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| 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 2.2.8.1).
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.
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| 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 .
References.
- Maugis D.J., J. Colloid. Interface Sci. 150, 243 (1992).
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