INDENTATION AND ADHESION AT SMALL LENGTH SCALES - Nanoindentation with Biological Applications - page 31

tip end of the cantilever to displace and deflect relative to the actuator
end. A beam of light from a laser source is reflected from the back of the
cantilever and collected by a split photodiode detector; deflection of the
cantilever by tip-surface interaction-induced bending moments causes
movement of the beam spot at the detector and thus changes in
photodiode output. Geometrical optics allows the cantilever deflection to
be determined from the photodiode output and cantilever mechanics
enable the deflection to be related to the tip-end displacement, and thus,
from the cantilever stiffness, the force between the tip and surface. Once
again, although the indentation apparatus controls the position of the
probe at the built-in actuator end, the displacement of the tip relative to
the surface is not the same as that imposed by the indenter on the probe
as a whole. The imposed probe displacement and the tip reaction
displacement are related by the stiffness of the cantilever between the tip
and the actuator and the tip-surface interaction stiffness. Mechanically,
however, the IIT and AFM geometries are equivalent: The probe consists
of the tip + spring in series.
As before, from a thermodynamic perspective, the probe + surface
comprises the system under consideration and the microscope indenter is
the environment. Here we will take the boundaries of the system to be
the interface between the sample surface and the microscope platform
and the interface between the cantilever and the actuator. The size of the
system, quantified by distance between these two interfaces, s , is
imposed by the actuator, which, along with the microscope frame, is well
approximated as rigid for typical AFMs. The load, F , conjugate to the
actuator displacement, is that inferred from the photodetector “load cell”
after a calibration that includes the cantilever stiffness and the
microscope optics geometry. As before, there is an internal tip-surface
separation variable, w , and the deformation response of the cantilever is
quantified by the internal cantilever displacement, ( s − w ). There is a
much greater recognition in AFM studies that the underlying ( F , w )
contact relationship is significantly mediated by the ( F , s w ) cantilever

spring relationship to determine what is observed in terms of ( F , s ). This
is because there is a much greater range of probe spring constants
available for AFM studies through selection of the cantilever material
and geometry.

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