temperature and the effect is more pronounced with higher the PSS content. If the
number density of mobile ions was thermally activated, then more and more Na
+
ions would become mobile with increasing temperature and thus contribute to the
long-range transport. This argument is reminiscent of the “weak electrolyte model”
put forward by Ravaine and Souquet [74] for explaining the ion transport in
inorganic glasses. On the other hand, the density of available pathways for the
ion transport could decrease if the chain conformation of the polyelectrolyte
network changed with temperature. Structural rearrangements and a higher local
mobility of chain segments could block the ways for the Na
+ ions, leading to an
increase in the characteristic mean square displacement.
PDADAMAC-rich PEC behave differently. In analogy to the arguments given
above, a negative α-value means that either the number density of mobile ions
decreases or the number of available pathways for the ions increases with increasing
temperature. Summerfield scaling of conductivity spectra retained for α ¼ 0 can
therefore be considered as a special case where neither the number density of mobile
ions nor the number of available ion pathways depend on temperature, or both effects
are present, but cancel out.
In Fig. 6, the spectral shape of PSS- and PDADMAC-rich PEC was shown
to differ significantly. The differences in the α-values found here are a further
indication for the existence of different structures in different kinds of PEC. One
possible explanation is that in PDADMAC-rich PEC the large Cl
À ions, being the
dominant species of small counterions, have to be hosted in the matrix. This will
lead to larger voids in the polyelectrolyte matrix in which the Cl
À ions are
embedded. The pathways for the ion transport of the diluted Na
+ ions will be
therefore completely different than in PSS-rich PEC, where Cl
À will be of very
minor importance. In the latter, PEC Na
+ ions might find a network of connected
pathways. A consistent picture about the ion transport arises with the assumption
that in all dried PEC alkali ions always govern the ion transport. In addition, we
assume for PDADMAC-rich PEC that all Na
+ ions are “dissociated” from their
counter charges (similar to a dilute solution of a weak electrolyte), implying that
they all contribute to the ion transport. As the number density of the Na
+ is low in
PDADMAC-rich PEC, the conductivity is very low. With increasing temperature,
however, more pathways become accessible for the sodium ions. The higher the
Na
+ concentration in the PSS-rich samples becomes, the more we have to consider
that the number density of mobile charge carries is thermally activated. The release
of more mobile Na
+ with increasing temperature then governs the temperature
dependence of the onset of conductivity dispersion.
5.3 The Time–Humidity Superposition Principle in PEC
Figures 14 and 21 show that an increase in RH has a similar effect on conductivity
spectra as an increase in temperature: the dc conductivity increases with RH and the
onset of dispersion is characterized by ν* shifts to higher frequencies. In contrast,
Ion Conduction in Solid Polyelectrolyte Complex Materials
129
number density of mobile ions was thermally activated, then more and more Na
+
ions would become mobile with increasing temperature and thus contribute to the
long-range transport. This argument is reminiscent of the “weak electrolyte model”
put forward by Ravaine and Souquet [74] for explaining the ion transport in
inorganic glasses. On the other hand, the density of available pathways for the
ion transport could decrease if the chain conformation of the polyelectrolyte
network changed with temperature. Structural rearrangements and a higher local
mobility of chain segments could block the ways for the Na
+ ions, leading to an
increase in the characteristic mean square displacement.
PDADAMAC-rich PEC behave differently. In analogy to the arguments given
above, a negative α-value means that either the number density of mobile ions
decreases or the number of available pathways for the ions increases with increasing
temperature. Summerfield scaling of conductivity spectra retained for α ¼ 0 can
therefore be considered as a special case where neither the number density of mobile
ions nor the number of available ion pathways depend on temperature, or both effects
are present, but cancel out.
In Fig. 6, the spectral shape of PSS- and PDADMAC-rich PEC was shown
to differ significantly. The differences in the α-values found here are a further
indication for the existence of different structures in different kinds of PEC. One
possible explanation is that in PDADMAC-rich PEC the large Cl
À ions, being the
dominant species of small counterions, have to be hosted in the matrix. This will
lead to larger voids in the polyelectrolyte matrix in which the Cl
À ions are
embedded. The pathways for the ion transport of the diluted Na
+ ions will be
therefore completely different than in PSS-rich PEC, where Cl
À will be of very
minor importance. In the latter, PEC Na
+ ions might find a network of connected
pathways. A consistent picture about the ion transport arises with the assumption
that in all dried PEC alkali ions always govern the ion transport. In addition, we
assume for PDADMAC-rich PEC that all Na
+ ions are “dissociated” from their
counter charges (similar to a dilute solution of a weak electrolyte), implying that
they all contribute to the ion transport. As the number density of the Na
+ is low in
PDADMAC-rich PEC, the conductivity is very low. With increasing temperature,
however, more pathways become accessible for the sodium ions. The higher the
Na
+ concentration in the PSS-rich samples becomes, the more we have to consider
that the number density of mobile charge carries is thermally activated. The release
of more mobile Na
+ with increasing temperature then governs the temperature
dependence of the onset of conductivity dispersion.
5.3 The Time–Humidity Superposition Principle in PEC
Figures 14 and 21 show that an increase in RH has a similar effect on conductivity
spectra as an increase in temperature: the dc conductivity increases with RH and the
onset of dispersion is characterized by ν* shifts to higher frequencies. In contrast,
Ion Conduction in Solid Polyelectrolyte Complex Materials
129