DIELECTRIC PROPERTIES OF ION -CONDUCTING MATERIALS

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DIELECTRIC PROPERTIES OF ION -CONDUCTING
MATERIALS

• F. Kremer
• Coauthors J. Rume, A. Serghei,

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The relationship between the complex dielectric
function e and the complex conductivity
s Phenomenology of the conductivity of charge
conducting materials The dielectric properties
of zwitterionic polymethacrylate The dielectric
properties of Ionic Liquids Theoretical
descriptions of the observed frequency and
temperature dependemce of the complex
conductivity
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The spectral range of Broadband Dielectric
Spectroscopy (BDS) and its information content
for studying dielectric relaxations and charge
transport.
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The linear interaction of electromagnetic
fields with matter is described by Maxwells
equations
(Ohms law)
Current-density and the time derivative of D are
equivalent
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Dielectric spectroscopy
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Analysis of the dielectric spectra
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The spectral range (10-3 Hz to 1011 Hz) of
Broadband Dielectric Spectroscopy (BDS)
(sample amount required lt 5 mg)
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Brief summary concerning Broadband Dielectric
Spectroscopy (BDS)
1. The spectral range of BDS ranges from 10-3 Hz
to 1011 Hz. 2. Orientational polarisation of
polar moieties and charge transport are
equivalent and observed both. 3. The main
information content of dielectric spectra
comprises for fluctuations of polar moieties the
relaxation- rate, the type of its thermal
activation, the relaxational strength and the
relaxation-time distribution function.
For charge transport the mean attempt rate to
overcome the largest barrier determining
the d.c.conductivity and its type of thermal
activation can be deduced
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Phenomenology of the conductivity of charge
conducting materials
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Frequency and temperature dependence of the
conductivity of a mixed alkali-glass
50LiF-30KF-20Al(PO3)3
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Frequency and temperature dependence of the
conductivity of a zwitterionic polymer
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Frequency and temperature dependence of the
electronic conductivity of poly(methyl-thiophene
)
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Frequency and concentration dependence of the
electronic conductivity of composites of
carbonblack and poly(ethylene terephthalate)
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Mixed alkali-glass Scaling with temperature is
possible
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poly(methyl-thiophene) Scaling with temperature
is possible
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composites of carbonblack and poly(ethylene
terephthalate) Scaling with concentration is
possible
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The Barton-Nakajima-Namikawa (BNN)
relationship holds for all materials examined
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Experimental findings In
all examined materials the conductivity shows a
similar frequency and temperature (resp.
concentration) dependence There is no principle
difference between electron and ion
conducting materials The conductivity scales
with the number of effective charge-carriers as
determined by temperature or concentration A
characteristic frequency exists where the
frequency dependence of the conductivity sets in
With increasing number of effective
charge-carriers the conductivity increases. The
BNN-relationship is fulfilled
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The dielectric properties of zwitterionic
poly-methacrylate poly3-N-?-oxyalkyl)-N,N-dim
ethylammoniopropanesulfonate
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Dielectric data as displayed for the complex
dielectric function e(w,T)
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Dielectric data as displayed for the complex
conductivity s(w,T)
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Dielectric data as displayed for the
complex electrical modulus M(w,T) 1/ e(w,T)
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Dyres random free energy barrier model

• Hopping Conduction in a spatially randomly
  varying energy barrier

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Fits using the Dyre theory work well
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The rates wc, wM and 1/te nearly coincide and
have - over 5 decades - a similar temperature
dependence
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The BNN-relationship holds for varying the
charge carrier concentration
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Summary The
dielectric properties of the zwitterionic
poly-methacrylate poly3-N-?-oxyalkyl)-N,N-dime
thylammoniopropane sulfonate are characterized
by a pronounced frequency - and temperature
dependence. It should be analysed in terms of
the complex dielectric function e(w,T), the
complex conductivity s(w,T) and the complex
electrical modulus M(w,T) 1/ e(w,T) The
data can be well described by Dyres random
free energy barrier model The BNN-relation is
fulfilled At low frequencies electrode
polarisation effects show up
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The dielectric properties of Ionic Liquids

• BMIM BF4 BMIM SCN

1-butyl-3-methylimidazolium tetrafluoroborate
1-n-butyl-3-methylimidazolium thiocyanate
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Temperature dependence
Imaginary and real part of the complex
dielectric function are strongly temperature
dependent
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Temperature dependence
The complex conductivity of the ionic liquid
BMIM BF4 is also strongly temperature dependent
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Broadband dielectric measurements displayedfor
the complex dielectric function e(w,T)
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Broadband dielectric measurements displayedfor
the complex conductivity s(w,T)
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Scaling with temperature possible
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Scaling with temperature as displayed in terms
of the complex conductivity s(w,T)
All data collapse into a single characteristic
curve
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Scaling with concentration for NaCl solutions
as displayed for the complex dielectric function
Scaling possible but deviations on the low
frequency side
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Scaling with concentration for NaCl solutions
as displayed for the complex conductivity
ws is the angular frequency of the minimum in s
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(No Transcript)
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Fits using the Dyre-model of conduction
The Dyre model describes the observed
frequency- and temperature dependence
additionally electrode polarization effects show
up
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Fits using the Dyre-model
Electrode polarization effects show up already
at 100 kHz
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The BNN Relation is fulfilled for s0 and te as
obtained from Dyre-fits
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Alternative approach Superposition of a
thermally activated d.c. conductivity and nearly
constant loss contribution.
Near constant loss contribution
The BNN relation is a trivial consequence
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Activation plots
Both s0 and 1/te show a VFT - dependence
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Final Summary The
dielectric properties of Ionic Liquids are
similar to other ion - conducting
systems They should be analysed in terms of the
complex dielectric function e(w,T), the complex
conductivity s(w,T) and the complex electrical
modulus M(w,T) 1/ e(w,T) The data can be
well described by Dyres random free energy
barrier model but as well a superposition a
thermally activated d.c.conductivity,a power law
and a nearly constant loss contribution The
BNN-relation is fulfilled At low frequencies
electrode polarisation effects show up
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Thanks to Joshua Rume and
A.
A.
Serghei
and financial support through the DFG