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A. Nogales et al.
distribution function, respectively. The last term corresponds to the contribution
of the dc electrical conductivity, σ dc , whose exponent is related to the conduction
mechanism [18]. The average relaxation time (τ max ) value of the distribution can be
calculated as follows:
τ max =
1
2π F max
= τ HN
sin
bπ
2 + 2c
−
1
b
sin
bcπ
2 + 2c
1
b
(2)
where F max is the frequency at which the maximum in dielectric loss appears, and
τ HN is the central relaxation time of Eq. 1. A satisfactory description of the evolution
of the segmental relaxation with crystallization time based on the HN formalism
can be achieved considering separately the contribution of the different components
present in the dielectric loss spectra as described by the dashed lines in Fig. 4. In
general these include a dc conductivity and a β-relaxation contribution at lower and
higher frequencies, respectively, in addition to the two α-relaxations [15, 16, 35, 37].
In Fig. 5 (left panel) the evolution with crystallization time of the different dielectric
magnitudes has been represented for the data corresponding to Fig. 4. Figure 5a
shows the WAXS patterns during crystallization revealing the appearance of Bragg
maxima associated to the crystalline phase as crystallization time increases. An estimation of the crystallinity degree (X c ) in the sample can be obtained by considering
the ratio of Bragg reflections contribution to the total scattered intensity [32, 35,
Fig. 5 HN equation parameters resulting from the fitting of the dielectric data of Fig. 3 for the
α (•) and α (◯) relaxations as a function of crystallization time. (ε) dielectric strength, (b and
c) shape parameters, (log 10 τ max ) relaxation time of maximum loss and (X c ) crystallinity degree.
Dashed lines in b correspond to the contribution of the different β 1 and β 2 processes described by
two independent Cole-Cole processes. The continuous line is the total fit considering the additive
contribution of both processes. “Adapted with permission from ref. [35]. Copyright (2020) Elsevier.”
A. Nogales et al.
distribution function, respectively. The last term corresponds to the contribution
of the dc electrical conductivity, σ dc , whose exponent is related to the conduction
mechanism [18]. The average relaxation time (τ max ) value of the distribution can be
calculated as follows:
τ max =
1
2π F max
= τ HN
sin
bπ
2 + 2c
−
1
b
sin
bcπ
2 + 2c
1
b
(2)
where F max is the frequency at which the maximum in dielectric loss appears, and
τ HN is the central relaxation time of Eq. 1. A satisfactory description of the evolution
of the segmental relaxation with crystallization time based on the HN formalism
can be achieved considering separately the contribution of the different components
present in the dielectric loss spectra as described by the dashed lines in Fig. 4. In
general these include a dc conductivity and a β-relaxation contribution at lower and
higher frequencies, respectively, in addition to the two α-relaxations [15, 16, 35, 37].
In Fig. 5 (left panel) the evolution with crystallization time of the different dielectric
magnitudes has been represented for the data corresponding to Fig. 4. Figure 5a
shows the WAXS patterns during crystallization revealing the appearance of Bragg
maxima associated to the crystalline phase as crystallization time increases. An estimation of the crystallinity degree (X c ) in the sample can be obtained by considering
the ratio of Bragg reflections contribution to the total scattered intensity [32, 35,
Fig. 5 HN equation parameters resulting from the fitting of the dielectric data of Fig. 3 for the
α (•) and α (◯) relaxations as a function of crystallization time. (ε) dielectric strength, (b and
c) shape parameters, (log 10 τ max ) relaxation time of maximum loss and (X c ) crystallinity degree.
Dashed lines in b correspond to the contribution of the different β 1 and β 2 processes described by
two independent Cole-Cole processes. The continuous line is the total fit considering the additive
contribution of both processes. “Adapted with permission from ref. [35]. Copyright (2020) Elsevier.”