W. Richard Bowen and Nidal Hilal 4

180 6. NANOSCALE ANALySIS Of PHARMACEUTICALS by SCANNINg PRObE MICROSCOPy
measurements more typically measured on a micron or greater scale to
determine elastic modulus and hardness [29]. There are, however, a number
of limitations of the AFM data that must first be considered. First,
as standard AFM cantilevers are typically very flexible (so that they are
sensitive to nanoNewton forces), they are incapable of deforming surfaces
beyond approximately 10 GPa elastic modulus. Second, unlike a
traditional indenter, an AFM probe does not approach or deform a surface
completely normal to that surface, because of the need to have the
lever at a slight angle to ensure that the probe apex contacts the sample
first. This causes lateral deformation errors in the data, which are only
negligible with relatively small indent depths.
Despite these issues, many groups have employed AFM to determine the
elastic, inelastic and hardness properties of materials. Such deformation
behaviour of pharmaceutical ingredients is known to affect pharmaceutical
processes such as milling and compaction [30–33]. To date, most
reported pharmaceutical examples of this approach have used a modified
AFM equipped with a relatively large probe with well-defined
geometry and a much stiffened spring that supports this probe [30,
34, 35]. Typically, in these methods, material parameters are extracted
from load-displacement unloading curves using approaches outlined by
Oliver and Pharr [36]. Recently, Ward and co-workers [37] have utilised
a sharp AFM probe and normal cantilevers to record nanomechanical
measurements on sorbital samples to quantitatively distinguish between
amorphous and crystalline domains through Young’s modulus measurements.
Figure 6.4 shows images and typical force distance curves
obtained from crystalline and amorphous sorbitol regions and a control
of a hard, non-indenting silicon substrate. To determine the nanoindentation
of the probe tip into the sorbitol sample as a function of load,
the force distance curves from the sorbitol sample and the control hard
substrate were compared. When comparing the amorphous and the
crystalline regions, it is the amorphous region that provided the greater
deflection of the tip (indicating the softer material and greater indentation)
at the given applied loads [37]. In this approach, a comparison of
the gradients of the contact region of the force distance curves between
a hard non-deformable reference surface and the sample can provide the
relative stiffness of a surface [38]. By applying the Hertz model [39] to
the nanoindentation data, a quantitative value of the Young’s modulus of
the surfaces can be obtained. The Hertz model describes the elastic deformation
of two homogenous surfaces under an applied load and is often
used to model AFM data since it requires little knowledge of parameters
such as surface energy. The first step in modelling the data is to compare
force distance curves recorded on the sample and an ideally hard reference
(glass surface) to determine the indentation (�) of the probe into the
sample as a function of load. The contact regions of the curves are overlaid
such that zero force is equal to zero indentation.