Project: Non-linear Dielectrics |
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In this project, we exploit that high electric fields (up to 450 kV/cm) facilitate dielectric relaxation experiments beyond the linear response regime. High electric fields lead to the sample absorbing energy from the field, analogous to heating by microwave radiation. Only modes that overlap with the power spectrum of the external signal will be affected, and the result of the energy uptake will thus differ from the effect of an increase in the (phonon) temperature. The relaxation behavior during or after the influx of energy serves as a sensitive indicator of the configurational temperatures Tcfg in this non-equilibrium situation. Here, Tcfg is defined as the temperature that would lead to the same relaxation time in equilibrium. As shown in the figure below, we observe significant increases in the higher frequency dielectric loss at high fields compared with the low field limit which can develop or fade over considerable lengths of time. |
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Experimental results (symbols) for the frequency resolved dielectric loss, ε'',
and its relative field induced change, Δlnε'',
of propylene carbonate at T = 166 K. (a): The loss curves at high (E0 = 177 kV/cm)
and low (E0 = 14 kV/cm) fields. (b): The relative change of the dielectric loss,
Δlnε'', for a field of E0 = 177 kV/cm.
The dashed lines reflect the calculation following the equations given below, using
ΔCp= 0.47 J K-1 cm-3.
The relative signal increase reaches 20 % at E0= 177 kV/cm. The right panel shows
the low-to-high field transition with period-by-period time resolution, demontrating that it can
take 50 periods to fully develop the change in configurational temperature. [157, 162, 168]
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The interpretation of these non-linear dielectric effects rests upon dynamic heterogeneity regarding both the dielectric and the thermal relaxation times, analogous to models of dielectric hole-burning. The loss ε''(ω) determines the amount of energy q transferred per period and volume from a field E(t) = E0sin (ωt), q = πε0 ε''(ω)E02. This results in a increase ΔT of the configurational temperature, the amount of which depends on the configurational heat capacity ΔCp of that mode. The effect on the relaxation time τ is quantified by the activation parameter TA. The final loss spectrum is calculated from the superposition of Debye peaks with relaxation times τ*, see equations below. The model provides a quantitative rationale of the the observed field effects, and allows us to extract the configurational contributions to excess heat capacities. |
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Schematic representation of five independent slow modes with different relaxation times
(τi) and how they contribute to heat capacity Cp
(top) and to the dielectric loss spectrum ε''(ω)
(bottom). The shaded arrows indicate the difference in where energy enters via conventional heating
('heat') and via absorption from an external field ('ext. field'). Each mode contributes with a Debye
peak to the entire loss spectrum, shown as overall solid line in the ε''
versus logω graph. The arrows at the individual loss peaks indicate the
shift in relaxation time that originates from the increased configurational temperatures after applying
a large electric field at frequency ω0. The net effect of these
shifts is an increase of the loss at ω0, represented by the dot.
The dashed line represents ε'' at large fields across the entire spectrum.
[162, 168, 185] |
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Reference numbers refer to the list of publications |
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Experimental techniques:
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Selected projects:
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