MECHANICS OF ADHESION - Nanoindentation with Biological Applications - page 96

1 and the probe and surface are at the quiescent point at which
the surface interaction and spring equilibrium positions coincide: the tip
is on the surface. Further decreases in s beyond this point lead to the
repulsive force of the tip-surface interaction perturbing the tip to an
equilibrium position z ∗

z ∗ / z 0 =

s and the perturbations can be large as z ∗ / z 0 1 . > ≈

Hence for s / z 0

> 1 , the tip is experiencing an adhesive interaction and

for s / z 0 1 , the tip is experiencing an indentation interaction. Note that

the z -position of the inflection point of the total force F curve in Fig. 4-9
remains invariant with changes in s . In fact, the derivatives at all
locations on this curve are invariant with s and variations in s simply lead
to vertical translations of this curve. This is a consequence of the
linearity of the probe spring; similar derivative invariance was observed
in the earlier considerations of the logarithmic potential for the same
reason.
The separation of the adhesive and indentation interactions at the
quiescent point is made clear in Fig. 4-10 , which plots the force-actuator
position behavior as observed at the boundaries of the system for the
k S

<

1.3 k 2 system above—this is what would be observed in a typical
atomic force microscopy (AFM) experiment. Note that in this case the
perceived shape of the force interaction is distorted from that given in
Figs. 4-7 and 4-9 by the addition of the displacement of the spring. As
noted in Chapter 2 , for most macroscopic indentations, nanoindentation
of engineering materials with diamond probes, and force spectroscopy
using stiff atomic force microscope cantilevers,

=

k and thus k

S 0

k k and the sequence above occurs during a contact. In fact, k S is
usually so large that the adhesive approach segment is not even observed
as shown in Fig. 4-10 for the case k S

S 2

100 k 2 —this is what is observed in
a typical nanoindentation experiment. Also shown in Fig. 4-10 is a
magnification of the response around the quiescent point for the
k S

=

100 k 2 case; the maximum adhesive force exerted by the surface on
the tip is identical to that exerted in the k S

=

1.3 k 2 case, but is negligible
relative to the force exerted during the subsequent indentation process.
The very stiff probe, however, contributes negligibly to the displacement
of the system and thus the perceived force interaction between the tip and

=