more strongly as ν*(T). Considering a log–log plot of the normalized conductivity
versus normalized frequency, the straight line connecting the onset frequencies will
then have a slope exceeding one. The same holds true for all other straight lines
connecting other characteristic points defined via σ
0 (ν n ,T) ¼ nσ dc (T). This behavior
has been discussed above for the temperature-dependent spectra of dried xNaPSS
(1 À x) PDADMAC PEC with an excess of NaPSS.
These principles derived for temperature-dependent conductivity spectra will
now be transferred to the humidity-dependent scaling of σ(ν,RH). Here, the
conductivity can be written very generally as:
σðν; RHÞ ¼ N v ðRHÞ Á μðν; RHÞ Á q:
(12)
Assuming that, like in the temperature case, the mobility at short and long time
scales, μ(ν n ,RH), is “activated” in the same way as the onset frequencies, then the
Summerfield-type of scaling found experimentally implies that the number density
of mobile ions does not depend on RH. In analogy to the temperature-dependent
conductivity spectra of other ion-conducting materials showing Summerfield
scaling, the only effect of humidity is to increase the ionic mobility. The finding
of a constant number density in the RH-dependent conductivity spectra as deduced
above is in contrast to the temperature dependence of similar NaPSS/PDADAMAC
complexes with an excess of NaPSS, where the number density of mobile Na
+ ions
seems to increase with temperature [41, 47]. This means that although there
are strong similarities between the influence of temperature and RH on the ion
dynamics, these influences are not completely identical. In completely dry polyelectrolyte complexes, some bound Na
+ ions are released to take part in the
conduction process when the temperature is raised [41]. By contrast, an increase
in humidity does not change the number density of mobile ions. The reason for this
could be that even at a RH of 29%, the lowest value employed, the complexes have
already absorbed an amount of water sufficient for hydrating all Na
+ ions, which
can then contribute to the ion transport. During long-range transport, the hydrated
Na
+ ions (which stay in the vicinity of not intrinsically compensated polyanion
charges) move to other negative counter sites that are temporally accessible, while
always avoiding other Na
+ ions of same charge. This thermally activated process is
speeded up with increasing water content according to Eq. (10), while the number
of mobile cations remains the same.
However, this special type of Summerfield-type RH-dependence in ionconducting materials is not necessarily a general finding. It is well known that
some materials have conductivity spectra that obey the TTSP with temperature
-independent spectral shapes of the conductivity, but nevertheless deviate from
Summerfield scaling [41, 44, 71, 76, 77]. In these materials, the shape of the
conductivity spectra is found to be independent of temperature (TTSP fulfilled),
but the slope of the line connecting the onset frequencies in a plot of log (σ
0 T) versus
log(ν) differs from one, in most cases exceeding one. As explained in [41, 71], the
latter effect can be explained by a number density of mobile ions that increases
with temperature. Analagous deductions can also be made on the basis of the
Ion Conduction in Solid Polyelectrolyte Complex Materials
133
versus normalized frequency, the straight line connecting the onset frequencies will
then have a slope exceeding one. The same holds true for all other straight lines
connecting other characteristic points defined via σ
0 (ν n ,T) ¼ nσ dc (T). This behavior
has been discussed above for the temperature-dependent spectra of dried xNaPSS
(1 À x) PDADMAC PEC with an excess of NaPSS.
These principles derived for temperature-dependent conductivity spectra will
now be transferred to the humidity-dependent scaling of σ(ν,RH). Here, the
conductivity can be written very generally as:
σðν; RHÞ ¼ N v ðRHÞ Á μðν; RHÞ Á q:
(12)
Assuming that, like in the temperature case, the mobility at short and long time
scales, μ(ν n ,RH), is “activated” in the same way as the onset frequencies, then the
Summerfield-type of scaling found experimentally implies that the number density
of mobile ions does not depend on RH. In analogy to the temperature-dependent
conductivity spectra of other ion-conducting materials showing Summerfield
scaling, the only effect of humidity is to increase the ionic mobility. The finding
of a constant number density in the RH-dependent conductivity spectra as deduced
above is in contrast to the temperature dependence of similar NaPSS/PDADAMAC
complexes with an excess of NaPSS, where the number density of mobile Na
+ ions
seems to increase with temperature [41, 47]. This means that although there
are strong similarities between the influence of temperature and RH on the ion
dynamics, these influences are not completely identical. In completely dry polyelectrolyte complexes, some bound Na
+ ions are released to take part in the
conduction process when the temperature is raised [41]. By contrast, an increase
in humidity does not change the number density of mobile ions. The reason for this
could be that even at a RH of 29%, the lowest value employed, the complexes have
already absorbed an amount of water sufficient for hydrating all Na
+ ions, which
can then contribute to the ion transport. During long-range transport, the hydrated
Na
+ ions (which stay in the vicinity of not intrinsically compensated polyanion
charges) move to other negative counter sites that are temporally accessible, while
always avoiding other Na
+ ions of same charge. This thermally activated process is
speeded up with increasing water content according to Eq. (10), while the number
of mobile cations remains the same.
However, this special type of Summerfield-type RH-dependence in ionconducting materials is not necessarily a general finding. It is well known that
some materials have conductivity spectra that obey the TTSP with temperature
-independent spectral shapes of the conductivity, but nevertheless deviate from
Summerfield scaling [41, 44, 71, 76, 77]. In these materials, the shape of the
conductivity spectra is found to be independent of temperature (TTSP fulfilled),
but the slope of the line connecting the onset frequencies in a plot of log (σ
0 T) versus
log(ν) differs from one, in most cases exceeding one. As explained in [41, 71], the
latter effect can be explained by a number density of mobile ions that increases
with temperature. Analagous deductions can also be made on the basis of the
Ion Conduction in Solid Polyelectrolyte Complex Materials
133