Chemistry Reference
In-Depth Information
modulation, such as the use of stochastic temperature modulation, have been developed
to address situations where this assumption is not met [24]. Instead of a slow sinusoidal
temperature change, in these methods a stochastic (or random) series of step changes is
impressed upon a linear temperature ramp.
MDSC measurements of
T
g
are commonly used to assess miscibility of amorphous
solid dispersions. Observation of a single
T
g
by MDSC is consistent with the presence of
a homogeneous, miscible dispersion. In Figure 4.1a, a
T
g
measurement was performed
using MDSC on three amorphous solid dispersions of tenoxicam:
L
-arginine in poly-
vinylpyrrolidone (PVP). All three of the dispersions show a single
T
g
, in agreement with
other data showing miscibility at the molecular level [25]. In contrast, the observation of
two
T
g
values by MDSC is indicative of phase separation. In Figure 4.1b, two
T
g
values
are observed by MDSC analysis for dispersions of dextran and PVP that are consistent
with the
T
g
values observed for the individual amorphous components [26]. The
observation of
T
g
by MDSC can be challenging in some polymer systems that do
not exhibit a clear
T
g
even in the pure polymer, such as in hydroxypropylcellulose
(HPC) [27]. In dispersions, the potential occurrence of amorphous nanosuspensions also
presents a challenge to MDSC analysis. Detection of a
T
g
event by MDSC for a particular
amorphous domain generally requires a domain size of approximately 30 nm or
greater [26,28].
The
T
g
values measured by DSC and MDSC can be empirically interpreted to
compare the properties of different amorphous solid dispersions.
T
g
values are generally
increased by the presence of stronger intermolecular forces such as hydrogen bonding
and van der Waals forces. This is related to the effect noted earlier, wherein near to
T
g
molecules and polymers overcome intermolecular forces and begin to move past one
another and exhibit liquid-like motion. Beyond this qualitative interpretation, quantita-
tive models are also available and are widely used in the study of amorphous solid
dispersions. One of the most common quantitative models for
T
g
involves the Gordon
-
Taylor (GT) equation [29]. The GT equation predicts the
T
g
of an amorphous binary
mixture (such as a drug and a polymer) from the properties of the individual amorphous
components. The GT equation assumes that the free volumes of both components are
additive and that no speci
c interactions occur between the two components. The free
volume is the volume available in the solid to permit motion of nearby atoms [11]. Under
these assumptions, the
T
g
can be predicted as
w
1
T
g
;
1
K
GT
w
2
T
g
;
2
w
1
K
GT
w
2
T
g
;
mix
;
(4.2)
where
w
1
and
w
2
are the weight fractions of each component and
T
g,1
and
T
g,2
are the
glass transition temperatures of each component. The constant
K
GT
is given by
K
GT
ρ
1
Δ
α
2
ρ
2
Δ
α
1
;
(4.3)
where
Δ
α
2
are the change
in thermal expansivity of
T
g
of each component. The true densities are commonly
ρ
1
and
ρ
2
are the true densities of each component and
Δ
α
1
and
