Chemistry Reference
In-Depth Information
where either temperature
T
is lowered suf
to something close to
10
8
sor
T
g
is raised relative to
T
with the addition of other amorphous solids having
greater
T
g
values, as with API-polymer amorphous dispersions (to be discussed
subsequently). It would also be bene
ciently to increase
τ
cial if these other amorphous solids, such as
polymers, could act as speci
c crystallization inhibitors.
Studies dealing with crystallization of organic molecules from the amorphous state
in the absence of any solvent have shown that the classical picture of homogeneous
nucleation and crystal growth from the liquid state can serve as a useful conceptual
model [28]. Here, it is assumed that molecules in the liquid state under certain conditions
must first undergo spontaneous nucleation, the formation of aggregates or nuclei
consisting of a few hundred molecules, followed by the growth of macroscopic-size
crystallites. The major thermodynamic factor driving nucleation and crystal growth is the
free energy difference per unit volume between molecules in the amorphous state and
those of the crystal,
G
v
, as depicted in Figure 1.14. However, the formation of nuclei
requires phase separation to occur with the creation of new surfaces between the nuclei
and amorphous matrix, a process that is thermodynamically unfavorable. Because of this,
when nuclei form there must be an increase in free energy
Δ
Δ
G
s
, which for a spherical
nucleus of radius
r
can be described as
r
2
Δ
G
s
4
π
σ
;
(1.11)
where
σ
is the surface free energy per unit area of surface (the surface tension in liquids)
r
2
is the surface area. Thus, the overall free energy of homogeneous nucleation,
and 4
π
Figure 1.14.
Schematic representation of the energetics associated with crystallization from
the amorphous state.
