W. Richard Bowen and Nidal Hilal 4

252 9. APPLICATION OF ATOMIC FORCE MICROSCOPy
Surface profile from primary scan
FIguRE 9.3 Interleaved scanning wherein the force modulation scan uses the predetermined
sample height.
to oscillate by (i) the influence of an external driving force (such as a
magnetic field), (ii) vibrating the sample using an electromechanical
oscillator, (iii) mounting the cantilever on a secondary piezoceramic oscillator
or (iv) modifying the primary piezoceramic scanner voltage. The
preferred method may be influenced by the apparatus and the desired
frequency range, as some oscillators exhibit mechanical resonances and
produce excessive acoustic interference, the latter problem is likely to be
more pronounced when the sample is contained in a small liquid cell.
A wide range of modulation frequencies and experimental methods have
been employed, ranging from a few hertz to several megahertz, and
although the basic excitation principle is retained, the analytical methods
vary significantly. For example, atomic force acoustic microscopy
(AFAM) employs excitation frequencies to several megahertz in order to
elicit sample-specific, frequency-dependent spectra derived from contact
measurements [60, 61].
9.3 DynAMIC MoDuLATIon STuDIES on
ConFInED FLuIDS
For those studies where the viscoelastic response is of interest,
attempts are made to relate the deflection amplitude and phase of the
cantilever to the dynamic complex modulus G*(�) of the material. In
standard rheometry, a sample subjected to a sinusoidally varying shear
stress will respond with a sinusoidally varying shear strain, and the
mechanical characteristics of the sample may then be described by the
complex modulus as given by
�( �)
G*( �)
�
ε( �)
(9.1)