W. Richard Bowen and Nidal Hilal 4

250 9. APPLICATION OF ATOMIC FORCE MICROSCOPy
to either the probe or the sample substrate and observing the amplitude
and phase response of the cantilever when the probe is either in contact
with the surface of the material or is in close proximity to a surface
with an intervening fluid layer. Although many forms of the modulation
technique have been employed to characterise predominantly elastic
materials, comparatively few AFM studies use superimposed modulation
to study confined liquids.
Various terms are used to describe dynamic modes of operation
although many of the reported modes are essentially similar in design.
Tapping mode (or intermittent contact) imaging is perhaps the most familiar
dynamic AFM technique. In tapping mode the cantilever is oscillated
at or near its resonance frequency such that when the tip interacts with the
sample surface, the amplitude and phase response will change. In response
to this deviation, a feedback loop adjusts the height of cantilever above the
surface to achieve a constant vibration amplitude. Phase contrast images
obtained from tapping mode studies are routinely discussed in terms of
the perceived damping effects induced by the elasticity or compliance of
the sample surface. Most commonly, qualitative interpretation of the phase
data may be used to discern areas of varying stiffness. FMM is essentially
a dynamic mode of operation in which the tip and substrate interact under
conditions of a constant (average) force such that the amplitude of the
cantilever oscillation varies about a nominal set point. Modulated force
experiments are often performed at a single point upon the surface, and
for the case of intervening liquids, the amplitude and phase are often monitored
as a function of probe to surface distance.
Considering predominantly elastic surfaces, FMM is often used to
generate surface images, which are generally referred to as either ‘elasticity
maps’ or ‘viscoelasticity maps’, depending upon the interpretation
of the force data. The fundamental approach employs single-point force
modulation [59] in which an ‘AC modulation’ is superimposed upon
either the probe or the sample during a ‘DC’ (i.e. force–distance) experiment.
If the modulation frequency is sufficiently high, the technique may
be employed while scanning a surface and is a complementary approach
to point-wise force mapping [28].
The basic method and interpretation is considered by Maivald et al.
(1991) [52] who exploit variations in local surface elasticity to provide a
basis for image contrast in inhomogeneous materials. The probe is scanned
across the surface with the feedback loop maintaining contact with a
(nominal) constant cantilever deflection and therefore a constant applied
force. If the sample is caused to oscillate a small distance �z 1 in the direction
normal to the surface, the undulating motion of the surface produces
a corresponding superimposed deflection of the cantilever �z 2. For an
infinitely hard sample, the deflection of the cantilever will be such that
�z 1 � �z 2, whereas in the case of softer samples the sample surface will