CELLS AND MEMBRANES - Nanoindentation with Biological Applications - page 338

14

12

10

8

A

6

B

4

C

2

O

D

0

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Punch Displacement, ω 0 = w 0 / b

Figure 10-8. Delamination trajectory ABCD with “pull-off ” at C. The curves show
different pre-stress on the sample membrane.

Generalized intersurface forces with finite and non-zero magnitude
and range can be incorporated into the adhesion model in the form of a
square well using the Barenblatt-Dugdale-Maugis cohesive zone theory.
The short range force discussed above corresponds to the Johnson-
Kendall-Roberts (JKR) limit, while the situation with infinite range but
vanishing magnitude is referred to the Derjaguin-Muller-Toporov (DMT)
limit. The lengthy and mathematically involved JKR to DMT transition
for membrane adhesion is not given here but only the qualitative
discussion. 25
At mechanical equilibrium with a non-zero load and fully developed
cohesive zone, the membrane profile can be divided into three regions
( Fig. 10-9 ): (i) within the contact circle ( r c ), the membrane is in
intimate contact with the substrate; (ii) the inner cohesive annulus ( c <
r c s ), the uniform intersurface force, F s , acts as the membrane-substrate

separation falls within the force range ( w w s ); and (iii) the outer

annulus ( c s < r < a ), intersurface interaction vanishes.