150
K. Adrjanowicz and R. Richert
Abbreviations
BDS Broadband dielectric spectroscopy
ε ∞
High-frequency limit dielectric constant
ε s
Static dielectric constant
J
Nucleation rate
MWS Maxwell–Wagner–Sillars
PC
Propylene carbonate
RMS Root mean square
T g
Glass transition temperature
T m
Melting temperature
TTT Time-temperature-transformation
u
Crystal growth rate
VEC Vinyl ethylene carbonate
1 Introduction
Crystallization is an important aspect in designing materials and understanding their
behavior [1–4]. It is a process that can prevent glass formation, the transition to
the amorphous solid that forms by cooling a supercooled liquid to below the glass
transition temperature T g . In some cases, crystallization can also be driven to lead to
different polymorphs, i.e., different crystal structures of the same chemical compound
which will have different properties. Tailoring the outcome of a crystallization
process or preventing it altogether is usually done by modifying the temperature
T, its rate of change q = dT /dt, or by applying pressures beyond the ambient level.
This work is concerned with how a static electric field influences the crystallization
outcome.
For understanding the process of crystallization, it is important to realize that two
separate steps are involved: nucleation and crystal growth. For typical molecular
materials, the nucleation rate J(T ) and the crystal growth rate u(T ) can follow very
different patterns on the temperature scale, as indicated in Fig. 1.
According to the standard Gibbs theory of nucleation, a critical nucleus size is
required before further growth remains a thermodynamically favored process [5].
The difference in the chemical potentials μ between melt and crystal phase, μ
= μ
melt
− μ
crystal , determines the thermodynamic driving force for crystallization,
with μ
crystal < μ
melt for temperatures T < T m . According to this classical theory of
homogeneous nucleation, the free energy involved in forming a nucleus is the sum of
a volume term, −Vρρμ, and a surface term, Aσ. For a spherical nucleus with volume
V = 4πr
3 /3 and surface area A = 4πr
2 , the free energy as a function of radius r is
G = 4πr
2
σ − 4πr
3
ρρμ/3. The barrier to nucleation, G max , then controls the
nucleation rate J, and this maximum of G is reached when the radius equals its
critical value r c = 2σ /ρρμ, where dG/dr = 0, see Fig. 2. In this framework, it
K. Adrjanowicz and R. Richert
Abbreviations
BDS Broadband dielectric spectroscopy
ε ∞
High-frequency limit dielectric constant
ε s
Static dielectric constant
J
Nucleation rate
MWS Maxwell–Wagner–Sillars
PC
Propylene carbonate
RMS Root mean square
T g
Glass transition temperature
T m
Melting temperature
TTT Time-temperature-transformation
u
Crystal growth rate
VEC Vinyl ethylene carbonate
1 Introduction
Crystallization is an important aspect in designing materials and understanding their
behavior [1–4]. It is a process that can prevent glass formation, the transition to
the amorphous solid that forms by cooling a supercooled liquid to below the glass
transition temperature T g . In some cases, crystallization can also be driven to lead to
different polymorphs, i.e., different crystal structures of the same chemical compound
which will have different properties. Tailoring the outcome of a crystallization
process or preventing it altogether is usually done by modifying the temperature
T, its rate of change q = dT /dt, or by applying pressures beyond the ambient level.
This work is concerned with how a static electric field influences the crystallization
outcome.
For understanding the process of crystallization, it is important to realize that two
separate steps are involved: nucleation and crystal growth. For typical molecular
materials, the nucleation rate J(T ) and the crystal growth rate u(T ) can follow very
different patterns on the temperature scale, as indicated in Fig. 1.
According to the standard Gibbs theory of nucleation, a critical nucleus size is
required before further growth remains a thermodynamically favored process [5].
The difference in the chemical potentials μ between melt and crystal phase, μ
= μ
melt
− μ
crystal , determines the thermodynamic driving force for crystallization,
with μ
crystal < μ
melt for temperatures T < T m . According to this classical theory of
homogeneous nucleation, the free energy involved in forming a nucleus is the sum of
a volume term, −Vρρμ, and a surface term, Aσ. For a spherical nucleus with volume
V = 4πr
3 /3 and surface area A = 4πr
2 , the free energy as a function of radius r is
G = 4πr
2
σ − 4πr
3
ρρμ/3. The barrier to nucleation, G max , then controls the
nucleation rate J, and this maximum of G is reached when the radius equals its
critical value r c = 2σ /ρρμ, where dG/dr = 0, see Fig. 2. In this framework, it