INDENTATION AND ADHESION AT SMALL LENGTH SCALES - Nanoindentation with Biological Applications - page 36

for indentation contact of very soft or compliant materials), the
oscillations become larger and slower, 34 kHz , and

very easily measured. If the stiffness of the probe spring is increased, the
amplitude of oscillation clearly decreases, and this is the case with
typical nanoindentation systems; the amplitude of tip oscillation is
negligible and usually undetectable. (The larger probe stiffness is
compensated by the larger probe mass to give comparable resonant
frequencies; for the steel probe considered above the probe resonant
frequency is about 140 kHz. Dynamic properties of nanoindenters,
however, are typically limited by the smaller resonant frequencies of the
instrument as a whole, typically much less than 1 kHz).
Variations in tip-resonance oscillation amplitude and frequency will
also occur if the stiffness experienced by the tip is changed not by
change in probe spring stiffness but by the superposition of a contact
stiffness field. For indentation-like contacts, in which the tip is
deforming the surface, the total stiffness experienced by the tip is greater
than the probe stiffness and the resonant frequency will be greater than
the free resonance; this is the basis for contact-resonance AFM methods
of modulus mapping of surfaces. For adhesive-like contacts the total
stiffness experienced by the tip can decrease significantly in attractive
surface force fields, leading to large decreases and increases in resonant
frequency and thermal amplitude, respectively; this is the basis for
dynamic stiffness field (and, by integration, force field) AFM force
spectroscopy. In many cases, the stiffness field experienced by the tip
can vanish completely and such instability points are the basis for
adhesion measurements.

a S 0.6 nm and

ω S

5. Contact Responses of Biological Materials
It is important to note that many, if not most, biological materials will
have Young's moduli significantly less than the 100 GPa material
considered here as an example (in fact this value approaches that for the
mineral apatite, the stiff constituent of bones and teeth). Taking 100 MPa
as a representative value gives a contact stiffness for a 100 nm radius
contact of about 20 N m −1 and thus 1 μ N is required to create 50 nm of