The frequency dependence of nonlinear conductivity in non-homogeneous systems: An analytically solvable model

Mattner, Clara; Roling, Bernhard; Heuer, Andreas

doi:10.1016/j.ssi.2014.03.020

Cited by 9 publications

(7 citation statements)

References 31 publications

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“…Our results bear strong analogies to the third-order conductivity spectra σ 3 3 obtained in the framework of a singleparticle hopping model, 21 but there are also discrepancies. In the hopping model, a dc plateau regime and a conductivity minimum in σ 3 3 were found, in agreement with our results.…”

Section: Discussionsupporting

confidence: 79%

“…[15][16][17][18] This kind of frequency dependence was also found in a single-particle hopping model. 21 In this model, the dispersive third-order conductivity decreases with increasing frequency, goes through a minimum, and then increases with increasing frequency. The frequency of the minimum is thermally activated, with the activation energy being determined by local barriers in an asymmetric double-well potential.…”

Section: Introductionmentioning

confidence: 89%

“…However, a minimum of the third-order conductivity as predicted by the single-particle hopping model could not be observed, since the nonlinearity at higher frequencies became too weak. 21 By constructing a new sample cell for nonlinear conductivity spectroscopy, we are now able to carry out measurements on thinner IL layers and thereby at higher electric field amplitudes. In this paper, we show the results of nonlinear conductivity measurements on the ionic liquid [C 6 mim][NTf 2 ] with applied field amplitudes up to 200 kV/cm.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

Patro

Burghaus

Roling

2015

The Journal of Chemical Physics

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We have carried out nonlinear ion conductivity measurements on the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide[C6mim][NTf2] by applying ac electric fields with amplitudes up to about 200 kV/cm. At these field amplitudes, 3ω and 5ω harmonic components in the current response were detected, and the higher-order conductivity coefficients σ3 (1),σ3 (3),σ5 (3), and σ5 (5) were determined. The frequency and temperature dependence of these conductivity coefficients was analyzed in detail. The most important findings were the following: (i) The third-order spectra σ3 (1) and σ3 (3) exhibit very similar values in the dc plateau regime but differ considerably in the dispersive regime. The same was observed for the fifth order spectra σ5 (3) and σ5 (5). (ii) In the dispersive regime, the third-order spectra display a minimum, while the fifth-order spectra display a maximum. (iii) The frequencies of these minima and maxima are thermally activated with the same activation energy as the low-field dc conductivity σ1,dc, whereas the dc values of the higher-order conductivity coefficients, σ3,dc and σ5,dc, are characterized by lower activation energies.

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Section: Discussionsupporting

confidence: 79%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

Patro

Burghaus

Roling

2015

The Journal of Chemical Physics

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“…Jonsher [34], the frequency dependence of a linear electric response attracts much attention and is considered until now as fundamental [35][36][37][38][39][40][41]. A new field of investigations appeared.…”

Section: Jonsher's "Universal" Dynamic Response In Nanoionicsmentioning

confidence: 99%

Maxwell displacement current and nature of Jonsher’s “universal” dynamic response in nanoionics

Despotuli

Андреева

2014

Ionics

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New notion -Maxwell displacement current on potential barrier -is introduced in the structuredynamic approach of nanoionics for description of collective phenomenon: coupled ion-transport and dielectric-polarization processes occurring during ionic space charge formation and relaxation in non-uniform potential relief. We simulate the processes: (i) in an electronic conductor/advanced superionic conductor (AdSIC) ideally polarizable coherent heterojunction, (ii) in a few strained monolayers of solid electrolyte (SE) located between two AdSICs forming coherent interfaces with SE. We prove the sum of ionic current over any barrier and Maxwell displacement current through the same barrier is equal to the current of current generator.-Universal‖ dynamic response, Re*()   n (n < 1), was found for frequency-dependent conductivity *() for case (ii) with an exponential distribution of potential barrier heights in SE. The nature of phenomenon is revealed. The amplitudes of non-equilibrium ion concentrations (and induced voltages) in space charge region of SE change approximately as   -1 . Amplitudes yield a main linear contribution to Re*(). The deviation from linearity is provided by the cosine of phase shift  between current and voltage in SE-space charge but cos depends relatively slightly on  (near constant loss effect) for coupled ion-transport and dielectric-polarization processes.The canonical physical-mathematical formalism for the description of ion transport in solids [1] is based on the concept of a regular crystalline potential relief, i.e. the heights  of potential barriers are const. As a consequence, ion-transport characteristics (mean-square displacement, diffusion coefficient, mobility, activation energy) have a clear physical meaning only at averaging in the scale much exceeding the length of an elementary ion jump. However, the variation of  with a space coordinate x can be considerable in objects of solid state ionics. For example, local regions with  variation about 1 eV/nm exist in disordered solid electrolytes (SE) [2][3][4] and in crystals of superionic conductors (SIC) [5]. Various degrees of ordering occur near surfaces and in the region of interphase and intercrystalline boundaries [6] where specific ion dynamics can arise on the nanoscale [7] due to a non-uniform potential relief. The interface structure exhibits itself in, e.g., frequency-capacitance characteristics of EC/SIC heterojunctions [8][9][10]. The classification of solid ionic conductors [8-10] distinguishes a class of advanced superionic conductors (AdSIC) among SE and SIC because AdSIC-crystal structure is close to optimal for fast ion transport (FIT). This crystal structure determines the record high level of iontransport characteristics. The FIT structure represents a rigid sub-lattice of immobile ions in which there are the crystallographic positions interconnected with each other by low potential barriers (conduction tunnels) for hopping mobile ions. The number of such positions is several times larger ...

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“…to determine mobile ion concentration and mobility of single ion conductors [5]. Nonlinear conductive spectra have found interest recently [6] and the influence of hopping dynamics on nonlinear conduction spectra has been investigated [7,8]. In this work the time-dependent distribution of ions reacting to an external electric field has been simulated numerically.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of frequency-dependent nonlinear interfacial polarization in electrolytes with blocking electrodes

Hahne

Ploss

2015

IEEE Trans. Dielect. Electr. Insul.

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The frequency dependence of nonlinear conductivity in non-homogeneous systems: An analytically solvable model

Cited by 9 publications

References 31 publications

Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

Maxwell displacement current and nature of Jonsher’s “universal” dynamic response in nanoionics

Numerical simulation of frequency-dependent nonlinear interfacial polarization in electrolytes with blocking electrodes

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