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Methods for Structural and Chemical Characterization of Nanomaterials 127

consisting of two side-by-side photodiodes. The difference between the
two photodiode signals indicates the position of the laser spot on the
detector and thus the angular deflection of the tip. Because the tip-to-
detector distance generally measures thousands of times the length of
the cantilever, the optical lever greatly magnifies the motions of the
tip. Because of the approximately 2000-fold magnification in the meas-
ured deflection, the optical lever detection can theoretically obtain a
14 1/2
noise level as low as 10 m/Hz .
The advantage of the AFM/STM over electron microscopes is that
it is possible to measure in the z-axis in addition to both the x-axis and
y-axis. In this way it is possible to get a three-dimensionally resolved
image of a surface. Furthermore, using the AFM it is possible to meas-
ure interfacial forces between surfaces in both gaseous and liquid
environments. For example, Brant et al. [2002 and 2004] used an
AFM to characterize the surface morphology of water-treatment mem-
branes and to subsequently measure the interfacial forces between the
membrane surface and various nanoparticles. This information may
then be used to either optimize or prevent particle attachment to a
given surface as in groundwater transport processes or engineered
systems.
Although originally conceived as an imaging device, because the oper-
ating principle of the AFM is based on the measurement of force between
a small tip and a surface with piconewton sensitivity, this method can also
be used to characterize interactions between surfaces and nanomaterials.
Force is measured by recording deflection of the free end of a cantilever
as its fixed end approaches and is subsequently retracted from a sample
surface. The interaction force occurring between the AFM probe and the
sample surface is then calculated according to Hooke’s law (F 5 k z )
where F is the force; k is the cantilever spring constant; and z is the ver-
tical deflection of the cantilever. A positive vertical deflection indicates
repulsion while a negative one indicates attraction. Figure 4.14 represents
a typical force curve generated by an AFM, where force is plotted as a func-
tion of separation distance (h). Initially the colloid probe is far from the
sample surface and no force is detected (a). As the probe approaches the
surface it encounters some type of force (repulsive or attractive) before con-
tacting the surface (b). The probe is then pressed against the sample sur-
face until a preset loading force is reached, and then the probe is retracted
(c). The pull-off force is measured as the force required to separate the two
surfaces (maximum negative deflection) (d) and is used to approximate
the strength of adhesion between the two surfaces.
A significant advantage of the AFM over other force measuring tech-
niques, is its ability to operate in either air or water [33]. AFM force
measurements may be carried out using either a standard silicon nitride
tipped cantilever or a probe with attached material such as a colloid or