Chemistry Reference
In-Depth Information
amorphous forms (
G
a
!
c
), and the activity of the amorphous solute saturated with water
(exp
I
a
2
), as shown in the following equation:
Δ
exp
Δ
G
a
!
c
RT
C
amorphous
C
eq
exp
Ia
;
(6.4)
where
R
is the gas constant,
T
is the temperature in Kelvin, and exp
I
a
2
and
Δ
G
a
!
c
can be estimated using the methods presented in Refs [55
57], respectively. The
theoretical enhancement in solubility can be several orders of magnitude [45]. However,
when comparing predicted solubility values for several amorphous drugs with exper-
imentally reported values in the literature, there is typically a poor correlation. This
inconsistency has been attributed, in part, to the rapid crystallization to a lower solubility
drug form from the amorphous material upon contact with dissolution
-
fluids or
crystallization from the supersaturated solution generated upon dissolution of the
amorphous solid [45,48].
Crystallization from solution is a two-part process by which crystals are formed.
It involves nucleation and growth, and both processes require a thermodynamic driving
force to occur. This thermodynamic driving force is created by the presence of a
supersaturated solution. The driving force for crystallization is the difference in chemical
potential (
Δ
μ
) of a molecule in the supersaturated and saturated solution [58]:
;
c
c
0
Δ
μ
kT
ln
(6.5)
where
k
is the Boltzmann constant,
T
is the absolute temperature,
c
is the solute concentration, and
c
0
is the equilibrium solute concentration at equilibrium temperature
T
0.
For dilute solutions, the supersaturation ratio
S
is given by the ratio of concentra-
tions [59]:
c
c
0
:
S
(6.6)
The magnitude of
S
is an important factor in determining how long supersaturation
can be maintained. A system is always stable (i.e., no crystallization will occur) when
c
c
0
<
0; the concentration is
above the equilibrium solubility and an increase in bioavailability can be observed since
spontaneous crystallization is improbable. Under these conditions, nucleation, precipi-
tation, deposition, and growth of a new phase are possible. Spontaneous nucleation
occurs when
c
c
0
0. It is possible to prolong the metastable state using certain
additives [58]. This observation is of great interest since it means that the solution
concentration can be increased and maintained with a low risk of crystallization. Guzmán
0. A system is considered to be metastable when
c
c
0
>
