W. Richard Bowen and Nidal Hilal 4

248 9. APPLICATION OF ATOMIC FORCE MICROSCOPy
the Hertz model (i.e. sphere against sphere compression) for non-adhesive
systems. Furthermore, the Hertz model is readily adapted to provide
idealised descriptions of geometries such as conical tips compressing flat
substrates [28].
Notwithstanding the fact that AFM is routinely used in studies where
elastic deformations are satisfactorily described by idealised models – a
limitation of the use of AFM in many rheological experiments, particularly
those involving fluids, is the assumed description of both the geometry
and the flow field contained within.
Therefore, for the AFM-based study of fluids, the use of colloid probes
[29] has proved to be of considerable benefit. Colloid probes (which are
fabricated by attaching a colloid sphere to the underside of an AFM cantilever)
have found favour in several different research areas including the
drainage of thin films [30], interfacial forces [31], mechanical properties
of cells [32–34], lubrication theory [35] and the deformation of colloidal
droplets [36, 37] to name but a few.
As has been alluded to previously, the successful use of AFM in
microrheological and tribological studies is facilitated by the ability to
describe force through the deflection and known spring constant of the
cantilever. However, the topographical imaging capability of an AFM has
been used as a component part of some studies. The imaging capabilities
of an AFM have been used to measure the biaxial extensional deformation
involved in the industrially important process of bubble inflation [38].
In this method the force-measuring capabilities of the AFM are not fully
exploited, instead the AFM is used to measure the radius of curvature of
microbubbles produced by inflating a thin polymer film, which is adhered
to a porous silicon substrate. A similar approach is used to study the surface
properties of polymers by using an AFM to measure the embedding
rate of nanoparticles at temperatures near to the glass transition temperature
of the polymer [39].
Considering force measurement, one technique of particular relevance
to tribology and lubrication studies is lateral force measurements in friction
force microscopy (FFM) [40–44], which considers the torsion of a cantilever
arising from frictional forces generated between a scanning tip and a surface.
As lateral perturbations are caused by both frictional forces and surface
features, it is informative to consider the local surface topography. The influence
of surface features upon the lateral deflection becomes apparent if the
surface is scanned in opposing directions, as a topography-induced torsional
response is dependent upon the scan direction (the torsion is reversed)
whereas the lateral deflection arising from the effect of the frictional component
will remain unchanged (Figure 9.1).
The beneficial application of microrheometry as an adjunct to traditional
bulk rheometry is demonstrated by the application of AFM force
studies (including dynamic FFM, [45]) to adhesive materials. For example,