Chemistry Reference
In-Depth Information
function of time were quite complex for the different systems examined, suggesting that a
more detailed examination of the mechanism of the turbidity evolution could yield
additional insight into the role of the polymers. There are also a number of studies that
have speci
cally probed the impact of polymers on both crystal nucleation and growth
and examples will be discussed in the following sections.
5.6.2.2 Impact of Polymers on Crystal Nucleation.
rst-
order phase transition that involves the formation of a new phase from a supersaturated
solution. According to classical nucleation theory, the nucleation rate
J
is given by the
following expression [2,138]:
Nucleation is a
;
B
ln
2
S
J
A
exp
(5.13)
where
A
and
B
are constants for a given system at a particular temperature and
S
is the
supersaturation ratio equal to
c
/
c
∗
, where
c
is the actual solution concentration and
c
∗
is
the saturation solubility in the medium of interest. The exponent
B
/ln
2
S
represents the
energy barrier for nucleation. Equation 5.13 clearly shows that the nucleation rate is
highly sensitive to the supersaturation and, therefore, when evaluating the crystallization
tendency of supersaturated solutions generated from amorphous solid dispersions, it is
very important to have knowledge of the extent of the supersaturation of the solution.
Because it is very dif
cult to measure the nucleation rate directly, induction time
measurements are typically used to evaluate the impact of additives on nucleation.
The experimentally observed induction time is the time taken for the system to nucleate
and also includes the additional time taken for the material to grow to a detectable size.
The induction time is typically regarded as being inversely proportional to the nucleation rate.
Nucleation rates are notoriously sensitive to experimental factors, including volume of the
test solution, the presence of impurities, and stirring rate. Therefore, when comparing
the impact of different polymers on the nucleation behavior, it is important not only to compare
systems at the same supersaturation but also to maintain similar experimental conditions.
Polymers have been shown to have very dramatic effects on nucleation rates;
however, not all polymers are equally effective and the most effective polymer can vary
from compound to compound. The impact of polymers on the induction times of
celecoxib, efavirenz, and ritonavir was studied at the supersaturation expected to be
generated by dissolution of the amorphous form [139]. The induction times in the
presence of low concentrations of polymers (5 ppm) increased by a factor of at least 2 and
up to a factor of 5 in the presence of the most effective polymers. For ritonavir and
efavirenz, the best polymers were similar for the two compounds; however, for
celecoxib, different polymers were found to be effective at modifying the nucleation
behavior. The effectiveness of the various polymers appeared to depend on the
hydrophobicity of the polymer relative to that of the drug. A strong dependence of
the induction time on supersaturation was also observed in the presence of HPMC for
celecoxib. At the highest supersaturation measured, the induction time for crystallization
was about 20 min in the presence of the polymer, compared with less than 5min in the
absence of the polymer. However, when the supersaturationwas halved, no crystallization
