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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 and the complex conductivity 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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(Ohm‘s law) The linear interaction of electromagnetic fields with matter is described by Maxwell‘s equations Current-density and the time derivative of D are equivalent
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Dielectric spectroscopy Debye relaxation complex dielectric function electric field E polarization P
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Analysis of the dielectric spectra
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(sample amount required < 5 mg) The spectral range (10 -3 Hz to 10 11 Hz) of Broadband Dielectric Spectroscopy (BDS)
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Brief summary concerning Broadband Dielectric Spectroscopy (BDS) 1. The spectral range of BDS ranges from 10 -3 Hz to 10 11 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(PO 3 ) 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: poly{3-[N-[ -oxyalkyl)-N,N- dimethylammonio]propanesulfonate}
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Dielectric data as displayed for the complex dielectric function T)
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Dielectric data as displayed for the complex conductivity T)
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Dielectric data as displayed for the complex electrical modulus M * T) =1/ T)
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Dyre‘s 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 c, M and 1/ e 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: poly{3-[N-[ -oxyalkyl)-N,N-dimethylammonio]propane sulfonate} are characterized by a pronounced frequency - and temperature dependence. It should be analysed in terms of the complex dielectric function T), the complex conductivity T) and the complex electrical modulus M* T) =1/ T) The data can be well described by Dyre‘s 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-n-butyl-3-methylimidazolium thiocyanate 1-butyl-3-methylimidazolium tetrafluoroborate
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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 displayed for the complex dielectric function T)
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Broadband dielectric measurements displayed for the complex conductivity T)
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Scaling with temperature possible
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Scaling with temperature as displayed in terms of the complex conductivity 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 s is the angular frequency of the minimum in ´´
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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 0 and e 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 0 and 1/ e 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 T), the complex conductivity T) and the complex electrical modulus M* T) =1/ T) The data can be well described by Dyre‘s 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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A. Serghei Thanks to Joshua Rume and and financial support through the DFG
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