42
K. Adrjanowicz
For dimethyl phthalate, the initial and final state points are, (T 0 = 308 K, p 0 =
0.1 MPa) and (T c = 283 K, p c = 100 MPa), respectively. As can be seen, the latter one
is located in the undercooled liquid state, but far above the glassy state. Crystallization
progress at a given (T c , p c ) conditions were followed with the use of the dielectric
spectroscopy. The results presented in Fig. 10 demonstrate changes in the real part
of complex dielectric permittivity at 2 kHz that accompanies crystallization progress
for the investigated sample at (T c , p c ) approached either via pathway 1 or 2. As can be
seen, at the initial stages no changes in the value of ε
as a function of time is observed
in both cases. Then, after some time, ε
starts to decrease. This effect is as due to a
reduction in the number of actively reorientating dipoles as crystallization proceeds.
Interestingly, we found that the crystallization behavior of dimethyl phthalate at (T c ,
p c ) depends strongly on the chosen path. Firstly, we note that the crystallization halftime, t 1/2 , defined as a time when changes in crystallinity reach 50% is much shorter
for pathway 1. As we get t 1/2 ∼ = 27 min for path 1, and t 1/2 ∼ = 51 min for path 2.
A clear difference is also observed in the induction period, t ind , which is related to
the nucleation process. Formally, t ind is composed of three parts: the relaxation time
required for a system to achieve quasi-steady-state conditions, the time needed to
form stable nuclei and the time for nuclei to grow to detectable size [75]. In our case,
the first and third components remain exactly the same. Therefore, the differences
in the induction time at (T c , p c ) conditions, as due to the choice of the different
thermodynamic path, must be related to the nucleation time.
Lastly, we also note differences in the value of the dielectric permittivity for the
fully crystallized sample. The sample which approaches crystallization conditions
via pathway 1 has a slightly higher value of the dielectric constant than for path
2. This suggests that in the first case there should be a more irregular alignment
of the molecules within the crystalline structure which changes polarization and
affect the dielectric response of the material. This supposition was also verified with
the use of molecular dynamics simulations for a Lennard-Jones system (the results
are presented in Fig. 11) and demonstrates that it is statistically more probable to
get uniformly formed crystalline material with denser structure when isothermal
compression (80%) is chosen rather than isobaric cooling (65%).
To conclude, crystallization is T-p path-dependent meaning that the way of moving
in the phase diagram to reach the final state point might itself affect the overall crystallization behavior of the glass-forming liquid at a selected (T c , p c ) point. The
results of this study indicate also that the path-dependent effect arises mostly from
the changes at the very early stages of the crystallization process (the number and
size of the initial clusters). Moreover, it was found that the choice of a particular thermodynamic pathway to reach the final (T c , p c ) point might affect also the crystalline
structured of obtained material, leading to denser and ordered structure or either less
dense with a more random arrangement. Thus, the crystallization tendency of various
materials on increased pressure can be tuned depending on the chosen path. Although
demonstrated here differences in the overall crystallization times for isobaric cooling
and isothermal compression takes only minutes, we suppose that more pronounced
effects should be observed at a higher temperature and in the gigapascal regime where
the changes in the density of the liquid will be more pronounced. The results presented
K. Adrjanowicz
For dimethyl phthalate, the initial and final state points are, (T 0 = 308 K, p 0 =
0.1 MPa) and (T c = 283 K, p c = 100 MPa), respectively. As can be seen, the latter one
is located in the undercooled liquid state, but far above the glassy state. Crystallization
progress at a given (T c , p c ) conditions were followed with the use of the dielectric
spectroscopy. The results presented in Fig. 10 demonstrate changes in the real part
of complex dielectric permittivity at 2 kHz that accompanies crystallization progress
for the investigated sample at (T c , p c ) approached either via pathway 1 or 2. As can be
seen, at the initial stages no changes in the value of ε
as a function of time is observed
in both cases. Then, after some time, ε
starts to decrease. This effect is as due to a
reduction in the number of actively reorientating dipoles as crystallization proceeds.
Interestingly, we found that the crystallization behavior of dimethyl phthalate at (T c ,
p c ) depends strongly on the chosen path. Firstly, we note that the crystallization halftime, t 1/2 , defined as a time when changes in crystallinity reach 50% is much shorter
for pathway 1. As we get t 1/2 ∼ = 27 min for path 1, and t 1/2 ∼ = 51 min for path 2.
A clear difference is also observed in the induction period, t ind , which is related to
the nucleation process. Formally, t ind is composed of three parts: the relaxation time
required for a system to achieve quasi-steady-state conditions, the time needed to
form stable nuclei and the time for nuclei to grow to detectable size [75]. In our case,
the first and third components remain exactly the same. Therefore, the differences
in the induction time at (T c , p c ) conditions, as due to the choice of the different
thermodynamic path, must be related to the nucleation time.
Lastly, we also note differences in the value of the dielectric permittivity for the
fully crystallized sample. The sample which approaches crystallization conditions
via pathway 1 has a slightly higher value of the dielectric constant than for path
2. This suggests that in the first case there should be a more irregular alignment
of the molecules within the crystalline structure which changes polarization and
affect the dielectric response of the material. This supposition was also verified with
the use of molecular dynamics simulations for a Lennard-Jones system (the results
are presented in Fig. 11) and demonstrates that it is statistically more probable to
get uniformly formed crystalline material with denser structure when isothermal
compression (80%) is chosen rather than isobaric cooling (65%).
To conclude, crystallization is T-p path-dependent meaning that the way of moving
in the phase diagram to reach the final state point might itself affect the overall crystallization behavior of the glass-forming liquid at a selected (T c , p c ) point. The
results of this study indicate also that the path-dependent effect arises mostly from
the changes at the very early stages of the crystallization process (the number and
size of the initial clusters). Moreover, it was found that the choice of a particular thermodynamic pathway to reach the final (T c , p c ) point might affect also the crystalline
structured of obtained material, leading to denser and ordered structure or either less
dense with a more random arrangement. Thus, the crystallization tendency of various
materials on increased pressure can be tuned depending on the chosen path. Although
demonstrated here differences in the overall crystallization times for isobaric cooling
and isothermal compression takes only minutes, we suppose that more pronounced
effects should be observed at a higher temperature and in the gigapascal regime where
the changes in the density of the liquid will be more pronounced. The results presented