46
K. Adrjanowicz
2.4 Changing Crystallization Behavior of Glass-Forming
Liquids by Moving Along Different Iso-Lines
As already demonstrated, in T-p space of glass-forming liquid, we can find state
points along which the time scale of the cooperative molecular movements remains
the same. In practice, this implies that the changes in the crystallization behavior of
investigated materials comes exclusively due to the variation of the thermodynamic
factor. However, one can also look at this aspect from a much broader perspective
and investigate the crystallization tendency of glass-forming liquids along different
iso-lines among which isobars and isotherms are the easiest to approach from the
experimental point of view (e.g., no need to perform prior high-pressure dielectric
studies).
Figure 14a presents changes in the crystallization rate as a function of pressure
or either density for racemic ketoprofen and its methylated derivative (no possibility
of h-bonding). It can be seen that each crystallization line (i.e., isobar, isochrone,
isotherm) spans in the two-dimensional T-p space differently, signifying that the crystallization tendency of the studied liquids can be modified by choosing an adequate
Me-RS-ketoprofen, isochrone log 10 (τ α /s)≅-5.7
Me-RS-ketoprofen, isotherm T=304 K
Me-RS-ketoprofen, isobar p=0.1 MPa
RS-ketoprofen, isochrone log 10 (τ α /s)≅-6.0
RS-ketoprofen, isobar p=0.1 MPa
0 50 100 150 200 250 300 350
-6
-5
-4
-3
1.04
1.08
1.12
-6
-5
-4
-3
0 50 100 150 200 250 300 350
0
10
20
30
40
1.04
1.08
1.12
0
10
20
30
isobar
is
o
t
h
e
r
m
iso chr one
log (k/s
-1
)
p (MPa)
is o t h e r m
isobar
log (k/s
-1
)
ρ (g/cm
3 )
iso ch ron e
isochrone
isobar
is o th e rm
i s o t h e r m
Me-RS-ketoprofen, isochrone log 10 (τ α /s)≅-5.7
Me-RS-ketoprofen, isobar p=0.1 MPa
Me-RS-ketoprofen, isotherm T=304 K
RS-ketoprofen, isochrone log 10 (τ α /s)≅-6.0
Δμ (kJ/mol)
p (MPa)
isochrone
isobar
(a)
(b)
Δμ (kJ/mol)
ρ (g/cm
3 )
Fig. 14 Changes in the crystallization rate constant k a and a thermodynamic driving force towards
crystallization b as a function of pressure and density (insets) along different iso-lines for
ketoprofen and methyl ketoprofen (in the form of racemic mixtures). Re-adapted with permission
from [66]. Copyright (2016) American Chemical Society
K. Adrjanowicz
2.4 Changing Crystallization Behavior of Glass-Forming
Liquids by Moving Along Different Iso-Lines
As already demonstrated, in T-p space of glass-forming liquid, we can find state
points along which the time scale of the cooperative molecular movements remains
the same. In practice, this implies that the changes in the crystallization behavior of
investigated materials comes exclusively due to the variation of the thermodynamic
factor. However, one can also look at this aspect from a much broader perspective
and investigate the crystallization tendency of glass-forming liquids along different
iso-lines among which isobars and isotherms are the easiest to approach from the
experimental point of view (e.g., no need to perform prior high-pressure dielectric
studies).
Figure 14a presents changes in the crystallization rate as a function of pressure
or either density for racemic ketoprofen and its methylated derivative (no possibility
of h-bonding). It can be seen that each crystallization line (i.e., isobar, isochrone,
isotherm) spans in the two-dimensional T-p space differently, signifying that the crystallization tendency of the studied liquids can be modified by choosing an adequate
Me-RS-ketoprofen, isochrone log 10 (τ α /s)≅-5.7
Me-RS-ketoprofen, isotherm T=304 K
Me-RS-ketoprofen, isobar p=0.1 MPa
RS-ketoprofen, isochrone log 10 (τ α /s)≅-6.0
RS-ketoprofen, isobar p=0.1 MPa
0 50 100 150 200 250 300 350
-6
-5
-4
-3
1.04
1.08
1.12
-6
-5
-4
-3
0 50 100 150 200 250 300 350
0
10
20
30
40
1.04
1.08
1.12
0
10
20
30
isobar
is
o
t
h
e
r
m
iso chr one
log (k/s
-1
)
p (MPa)
is o t h e r m
isobar
log (k/s
-1
)
ρ (g/cm
3 )
iso ch ron e
isochrone
isobar
is o th e rm
i s o t h e r m
Me-RS-ketoprofen, isochrone log 10 (τ α /s)≅-5.7
Me-RS-ketoprofen, isobar p=0.1 MPa
Me-RS-ketoprofen, isotherm T=304 K
RS-ketoprofen, isochrone log 10 (τ α /s)≅-6.0
Δμ (kJ/mol)
p (MPa)
isochrone
isobar
(a)
(b)
Δμ (kJ/mol)
ρ (g/cm
3 )
Fig. 14 Changes in the crystallization rate constant k a and a thermodynamic driving force towards
crystallization b as a function of pressure and density (insets) along different iso-lines for
ketoprofen and methyl ketoprofen (in the form of racemic mixtures). Re-adapted with permission
from [66]. Copyright (2016) American Chemical Society