High-Pressure Crystallization of Glass-Forming Liquids …
47
thermodynamic pathway. For example, a systematic slowing down of the crystallization rate is observed when lowering the temperature at a fixed pressure, or increasing
pressure at a fixed temperature (Fig. 14a). Interestingly, considering changes of the
liquid’s density ρ along different iso-lines, it turns out that when keeping the same
time scale of the molecular movements (isochrone) changes in the crystallization
rate are relatively very small.
Intuitively, the thermodynamic driving force is expected to vary freely along
isochrone. However, it is remarkable that μ (calculated using Eq. 4) changes only
very little when increasing temperature and pressure while controlling the time scale
of the molecular motions (see Fig. 14b). This surprising finding indicates that both
fundamental factors governing the crystallization progress are in some way connected
(or sense each other) even though only one of them is being explicitly controlled.
Same like with isochrones, we can also look in the T-p (T-ρ) space for iso-μ
lines. While moving along such lines the contribution coming from the thermodynamic driving forces towards crystallization should be under control. Along iso-(
lines, the crystallization behavior of the supercooled liquid is expected to be driven
primarily by the molecular mobility factor, while under isochronal conditions by
the thermodynamic factor. Such experiments were performed for indomethacin (see
Fig. 15). The results of the crystallization kinetic studies have led to a quite interesting
0
50
100
150
200
250
-5.4
-4.8
-4.2
-3.6
1.28
1.30
1.32
1.34
-5.4
-4.8
-4.2
-3.6
log 10 (τ α /s)=-3
Δμ=14 J/g
T=368 K
T=391 K
p=10 MPa
p=75 MPa
log
10
(k/s
-1
)
pressure (MPa)
iso-k
iso-k
(b)
log 10 (τ α /s)=-3
Δμ=14 J/g
T=368 K
T=391 K
p=10 MPa
p=75 MPa
log
10
(k/s
-1
)
ρ (g/cm
3
)
(a)
Fig. 15 Changes of the crystallization rate k as a function of a pressure and b density along different
iso-lines for indomethacin. Adapted with permission from [62]. Copyright (2016) American
Chemical Society
47
thermodynamic pathway. For example, a systematic slowing down of the crystallization rate is observed when lowering the temperature at a fixed pressure, or increasing
pressure at a fixed temperature (Fig. 14a). Interestingly, considering changes of the
liquid’s density ρ along different iso-lines, it turns out that when keeping the same
time scale of the molecular movements (isochrone) changes in the crystallization
rate are relatively very small.
Intuitively, the thermodynamic driving force is expected to vary freely along
isochrone. However, it is remarkable that μ (calculated using Eq. 4) changes only
very little when increasing temperature and pressure while controlling the time scale
of the molecular motions (see Fig. 14b). This surprising finding indicates that both
fundamental factors governing the crystallization progress are in some way connected
(or sense each other) even though only one of them is being explicitly controlled.
Same like with isochrones, we can also look in the T-p (T-ρ) space for iso-μ
lines. While moving along such lines the contribution coming from the thermodynamic driving forces towards crystallization should be under control. Along iso-(
lines, the crystallization behavior of the supercooled liquid is expected to be driven
primarily by the molecular mobility factor, while under isochronal conditions by
the thermodynamic factor. Such experiments were performed for indomethacin (see
Fig. 15). The results of the crystallization kinetic studies have led to a quite interesting
0
50
100
150
200
250
-5.4
-4.8
-4.2
-3.6
1.28
1.30
1.32
1.34
-5.4
-4.8
-4.2
-3.6
log 10 (τ α /s)=-3
Δμ=14 J/g
T=368 K
T=391 K
p=10 MPa
p=75 MPa
log
10
(k/s
-1
)
pressure (MPa)
iso-k
iso-k
(b)
log 10 (τ α /s)=-3
Δμ=14 J/g
T=368 K
T=391 K
p=10 MPa
p=75 MPa
log
10
(k/s
-1
)
ρ (g/cm
3
)
(a)
Fig. 15 Changes of the crystallization rate k as a function of a pressure and b density along different
iso-lines for indomethacin. Adapted with permission from [62]. Copyright (2016) American
Chemical Society