permittivity, ε
0 , which is connected to the imaginary part of the complex conductivity
σ
00 via ε
0 (ν) ¼ σ
00 (ν)/(2πνε 0 ).
It was shown that the shape of the complex conductivity spectra of the
investigated PEC systems can be divided into two classes: those with x > 0.50
and those with x 0.50 [47]. In Fig. 6a it is obvious that, for comparable dc
conductivities, the dispersive regime begins earlier on the frequency scale for PEC
with x > 0.50 than for the other PEC. In all materials with x > 0.50, a “shoulder”
occurs in the conductivity spectra, roughly between 0.1 kHz and 10 kHz.
An analogous behavior is hardly detectable for x 0.50. The real part of the
permittivity shows higher values, and ε
0 decays more rapidly with increasing
frequency, for x > 0.50 than for x 0.50. An analysis of the exact shape of the
real part of the dynamic conductivity will be described in Sect. 3.4.
3.2 Temperature Dependence of the DC Conductivity of PEC
The dc conductivities can be extracted from Nyquist plots of the complex impedance
by fitting parameters of a model equivalent circuit to the data. The equivalent circuit
always consists of a parallel connection of an Ohmic resistance and a constant phase
element [40]. The same dc values are also obtained by identifying the conductivity
values of the low-frequency plateau with the dc conductivity. This extraction of dc
conductivities from the spectra of dried PEC is straightforward because electrode
polarization effects are almost absent.
In a typical experimental procedure, conductivity spectra were measured during
two subsequent heating and cooling cycles. In the first cycle, the sample was cooled
down to about À90
C. After that the temperature was increased up to 200
C in
steps of 10
C. Then, the samples were kept at 200
C for about 3 h and cooled down
stepwise by 10
C to the lowest temperature at which the conductivity could still be
determined. These measurements are termed “first measurement series.” In a
second measurement series, the sample was first heated to 300
C and, after a
prolonged isothermal heat treatment of more than 6 h, the temperature dependence
of the complex conductivity was measured by decreasing the temperature stepwise
by 10
C. Arrhenius plots of the ionic conductivity of a PEC with x ¼ 0.70 obtained
from both series are shown in Fig. 7. The upper straight line shown in this figure
corresponds to the conductivity before annealing the sample at high temperatures
and it obeys the Arrhenius law. Strong deviations from Arrhenius behavior start
above 25
C. This temperature is consistent with DSC data obtained for a first
heating, which were interpreted as a loss of water [40]. The loss of water continues
until 200
C is reached.
The conductivity observed during cooling down from 200
C is also Arrheniustype; however, it is three orders of magnitude lower than the conductivity of the
samples before drying. In passing, one notes that in contrast to the huge discrepancy
of the ionic conductivity values of “humid” and “dried” NaPSS/PDADMAC PEC,
the activation enthalpy of the conductivity is almost identical. The latter finding is
Ion Conduction in Solid Polyelectrolyte Complex Materials
109
0 , which is connected to the imaginary part of the complex conductivity
σ
00 via ε
0 (ν) ¼ σ
00 (ν)/(2πνε 0 ).
It was shown that the shape of the complex conductivity spectra of the
investigated PEC systems can be divided into two classes: those with x > 0.50
and those with x 0.50 [47]. In Fig. 6a it is obvious that, for comparable dc
conductivities, the dispersive regime begins earlier on the frequency scale for PEC
with x > 0.50 than for the other PEC. In all materials with x > 0.50, a “shoulder”
occurs in the conductivity spectra, roughly between 0.1 kHz and 10 kHz.
An analogous behavior is hardly detectable for x 0.50. The real part of the
permittivity shows higher values, and ε
0 decays more rapidly with increasing
frequency, for x > 0.50 than for x 0.50. An analysis of the exact shape of the
real part of the dynamic conductivity will be described in Sect. 3.4.
3.2 Temperature Dependence of the DC Conductivity of PEC
The dc conductivities can be extracted from Nyquist plots of the complex impedance
by fitting parameters of a model equivalent circuit to the data. The equivalent circuit
always consists of a parallel connection of an Ohmic resistance and a constant phase
element [40]. The same dc values are also obtained by identifying the conductivity
values of the low-frequency plateau with the dc conductivity. This extraction of dc
conductivities from the spectra of dried PEC is straightforward because electrode
polarization effects are almost absent.
In a typical experimental procedure, conductivity spectra were measured during
two subsequent heating and cooling cycles. In the first cycle, the sample was cooled
down to about À90
C. After that the temperature was increased up to 200
C in
steps of 10
C. Then, the samples were kept at 200
C for about 3 h and cooled down
stepwise by 10
C to the lowest temperature at which the conductivity could still be
determined. These measurements are termed “first measurement series.” In a
second measurement series, the sample was first heated to 300
C and, after a
prolonged isothermal heat treatment of more than 6 h, the temperature dependence
of the complex conductivity was measured by decreasing the temperature stepwise
by 10
C. Arrhenius plots of the ionic conductivity of a PEC with x ¼ 0.70 obtained
from both series are shown in Fig. 7. The upper straight line shown in this figure
corresponds to the conductivity before annealing the sample at high temperatures
and it obeys the Arrhenius law. Strong deviations from Arrhenius behavior start
above 25
C. This temperature is consistent with DSC data obtained for a first
heating, which were interpreted as a loss of water [40]. The loss of water continues
until 200
C is reached.
The conductivity observed during cooling down from 200
C is also Arrheniustype; however, it is three orders of magnitude lower than the conductivity of the
samples before drying. In passing, one notes that in contrast to the huge discrepancy
of the ionic conductivity values of “humid” and “dried” NaPSS/PDADMAC PEC,
the activation enthalpy of the conductivity is almost identical. The latter finding is
Ion Conduction in Solid Polyelectrolyte Complex Materials
109