INDENTATION AND ADHESION AT SMALL LENGTH SCALES - Nanoindentation with Biological Applications - page 33

between cantilever spatial displacement and angular deflection; the
photodiode senses deflection, but the linear relation allows a simple
relation between diode output and load). The contact displacement is still
given by

F
k a

w = (2-15)

and for the load and contact stiffness here gives w = 1 nm.
The very small, atomic-scale contact displacement above ( w d here)

and the similarity of the cantilever spring stiffness to the characteristic
bond stiffness ( k S ≈ k bond in AFM) suggest that other small-scale effects
may influence AFM contacts. That is, the effects of interatomic forces
may play a role in determining AFM contact behavior in addition to,
perhaps even dominating, the effects of interatomic stiffness; the small
scales may introduce a significant adhesion component into the nature of
the contact as distinct from the purely indentation behavior considered
above. To examine this, consider the surface interaction force between
the surface and the probe at the characteristic maximum bond force

≈

F a, surface F max, bond ( a / d ) 2 (2-16)

Using the values of F max, bond , a , and d above gives F a, surface 100 μN,

which is much greater than the above contact force of F = 10 N. This

calculation suggests that forces associated with surface interactions will
definitely be comparable to forces associated with bulk deformation at
AFM contacts; AFM contacts will have strong adhesion character.
It might be argued that the above calculation assumes ideal solid-like
(primary) bonding between the materials forming the contact and that,
even if the materials are identical as assumed here, this is unlikely to
occur between typical uncleaned surfaces in air at typical contact time
scales (

μ

1 s ). This is true, although such a calculation certainly pertains
for cleaned surfaces in ultra-high vacuum. However, surface interactions
arising from secondary bonding between the materials will also lead to
adhesive effects at small contacts. Secondary bonding influences,
particularly those arising from van der Waals interactions, are pervasive
between surfaces in close proximity (separations of

≈

≈ d ). Such influences
are typically an order of magnitude weaker than those of primary