Chemistry Reference
In-Depth Information
time can be obtained by
fitting to theoretical models such as the Kohlrausch
-
Williams
-
Watts (KWW) equation [38].
4.3 DIELECTRIC RELAXATION METHODS
Dielectric relaxation spectroscopy (DRS) allows for the investigation of molecular
motion in solids [39]. In DRS, electric dipoles within a molecule are perturbed from their
equilibrium con
field is removed, the
relaxation back to equilibrium of the electric dipoles within the molecules is monitored
via the electric susceptibility. The rate at which the electric dipoles relax depends on the
extent to which the local electric dipole-dependent transitions are modulated by the
molecular motion. The experiment reports on the mole fraction of dipole reorientation at
the measurement frequency, which is often in the MHz to GHz range. Relaxation in DRS
has some parallels with nuclear spin relaxation measured by solid-state NMR, mainly in
the use of similar spectral density functions to explain relaxation phenomena, although
the techniques measure different phenomena [40]. Although DRS has not been widely
applied in studies of amorphous solid dispersions, the closely related technique of
thermally stimulated current (TSC) spectroscopy, also referred to as thermally stimulated
depolarization current (TSDC) spectroscopy, has been applied in several studies [41,42].
TSDC is a method that can be used to study low-frequency molecular motions in the
frequency range of 10
3
to 10
5
Hz [43]. TSDC is able to better resolve lower frequency
relaxation mechanisms as a function of temperature than DRS [44]. A TSDC experiment
results in a thermogram with peaks corresponding to the depolarization current intensity
as a function of temperature [41]. Sharper peaks tend to correspond to
guration by an external electric
field. When the
α
-relaxation, while
β
-relaxation peaks tend to be broad and cover a wider temperature range [43]. Special-
ized thermal windowing (or thermal cleaning) experiments can be used to con
rm
α
-relaxation processes [42]. Thermal windowing allows for observation of a distribution
of temperature-dependent relaxation times, in contrast to the single average value
generally available from other techniques [42]. Kinetic parameters obtained from
TSDC experiments can be used to probe molecular mobility below
T
g
. An extensive
study of dispersions containing 10
60% (w/w) of a small-molecule drug with PVP was
performed using TSDC [41,42]. The amorphous drug showed two events in the TSDC
spectrum, while DSC could only observe one thermal event. Analysis of pure PVP with
an average molecular weight of 40 kDa (commonly known as
-
grade) by TSDC
showed two distinct motional modes, a higher temperature mode assigned to
“
K30
”
α
-relaxation
processes near to
T
g
and a lower temperature motional mode (at 132.3
C) assigned to
°
β
-processes that involve localized, noncooperative motional processes with weak
interactions between nearby atoms and correspondingly low activation enthalpies [42].
4.4 MOISTURE SORPTION METHODS
Amorphous materials tend to exhibit increased hygroscopicity relative to crystalline
solids, as water can be absorbed into their internal structure in addition to being adsorbed
on particle surfaces [45]. Many of the commonly used polymers in amorphous solid
