DIELECTRIC PROPERTIES OF ION - CONDUCTING MATERIALS F. Kremer Coauthors: J. Rume, A. Serghei,

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

The spectral range of Broadband Dielectric Spectroscopy (BDS) and its information content for studying dielectric relaxations and charge transport.

(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

Dielectric spectroscopy Debye relaxation complex dielectric function electric field E polarization P

Analysis of the dielectric spectra

(sample amount required < 5 mg) The spectral range (10 -3 Hz to Hz) of Broadband Dielectric Spectroscopy (BDS)

Brief summary concerning Broadband Dielectric Spectroscopy (BDS) 1. The spectral range of BDS ranges from Hz to 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

Phenomenology of the conductivity of charge – conducting materials

Frequency and temperature dependence of the conductivity of a mixed alkali-glass 50LiF-30KF-20Al(PO 3 ) 3

Frequency and temperature dependence of the conductivity of a zwitterionic polymer

Frequency and temperature dependence of the electronic conductivity of poly(methyl-thiophene)

Frequency and concentration dependence of the electronic conductivity of composites of carbonblack and poly(ethylene terephthalate)

Mixed alkali-glass: Scaling with temperature is possible

poly(methyl-thiophene): Scaling with temperature is possible

composites of carbonblack and poly(ethylene terephthalate): Scaling with concentration is possible

The Barton-Nakajima-Namikawa (BNN) – relationship holds for all materials examined:

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

The dielectric properties of zwitterionic poly- methacrylate: poly{3-[N-[  -oxyalkyl)-N,N- dimethylammonio]propanesulfonate}

Dielectric data as displayed for the complex dielectric function    T)

Dielectric data as displayed for the complex conductivity    T)

Dielectric data as displayed for the complex electrical modulus M *  T) =1/    T)

Dyre‘s random free energy barrier model Hopping Conduction in a spatially randomly varying energy barrier :

Fits using the Dyre theory „work well“

The rates  c,  M and 1/  e nearly coincide and have - over 5 decades - a similar temperature dependence

The BNN-relationship holds for varying the charge carrier concentration

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

The dielectric properties of „Ionic Liquids“ BMIM BF4 BMIM SCN 1-n-butyl-3-methylimidazolium thiocyanate 1-butyl-3-methylimidazolium tetrafluoroborate

Temperature dependence Imaginary and real part of the complex dielectric function are strongly temperature dependent

Temperature dependence The complex conductivity of the ionic liquid BMIM BF4 is also strongly temperature dependent

Broadband dielectric measurements displayed for the complex dielectric function    T)

Broadband dielectric measurements displayed for the complex conductivity    T)

Scaling with temperature possible

Scaling with temperature as displayed in terms of the complex conductivity    T) All data collapse into a single characteristic curve

Scaling with concentration for NaCl solutions as displayed for the complex dielectric function Scaling possible but deviations on the low frequency side

Scaling with concentration for NaCl solutions as displayed for the complex conductivity  s is the angular frequency of the minimum in  ´´

Fits using the Dyre-model of conduction The Dyre –model describes the observed frequency- and temperature dependence; additionally electrode polarization effects show up

Fits using the Dyre-model Electrode polarization effects show up already at 100 kHz

The BNN Relation is fulfilled for  0 and  e as obtained from Dyre-fits

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

Activation plots Both  0 and 1/  e show a VFT - dependence

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

A. Serghei Thanks to Joshua Rume and and financial support through the DFG