MECHANICS OF ADHESION - Nanoindentation with Biological Applications - page 95

Figure 4-9. The variations in the net force (solid line) with tip position for combined Mie
(M) and harmonic (S) interactions (dotted lines) between a probe tip and a surface as an
actuator moves the probe towards the surface. The probe spring stiffness is super-critical
such that a stable equilibrium position of the tip is possible for all imposed probe
positions. The values are normalized using the characteristic values ( Eqs. 4-22 a nd 4-25 ).

For s / z 0 = 2.5, the attractive force of the tip-surface interaction
perturbs the tip to an equilibrium position z ∗

< s (the F = 0 position in
Fig. 4-9) , but the perturbation is not large. As s is decreased to s / z 0 = 1.5,
the surface attraction becomes greater and the separation between the
imposed probe position and the tip position becomes greater; in fact
z ∗ / z 0 ≈ 1 under these conditions. As s is decreased even further, the tip
position remains almost invariant as z ∗ / z 0 1 , until at s / z 0 = 1.0, →