Impedance spectra of mixed conductors: a 2D study of ceria

Ciucci, Francesco; Hao, Yong; Goodwin, David G.

doi:10.1039/b907740e

Cited by 29 publications

(34 citation statements)

References 36 publications

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“…40 The mesh was adaptively refined up to seven times at each solution step according to the method illustrated in previous work. 12 The h-adaptation ensures high regularity of the H 1 estimator, locally below 0.01%, and it guarantees that the mesh is finer where the sharpest gradients occur. Accordingly, the mesh adaptivity results in coarseness everywhere except in the vicinity of the interfaces (Fig.…”

Section: Methodsmentioning

confidence: 99%

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Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Ciucci

Chueh

Goodwin

et al. 2011

Phys. Chem. Chem. Phys.

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A two-dimensional, small-bias model has been developed for describing transport through a mixed ionic and electronic conductor (MIEC) with electrochemically-active surfaces, a system of particular relevance to solid oxide fuel cells. Utilizing the h-adaptive finite-element method, we solve the electrochemical potential and flux for both ionic and electronic species in the MIEC, taking the transport properties of Sm 0.15 Ce 0.85 O 1.925Àd (SDC15). In addition to the ionic flux that flows between the two sides of the cell, there are two types of electronic fluxes: (1) cross-plane current that flows in the same general direction as the ionic current, and (2) in-plane current that flows between the catalytically-active MIEC surface and the metal current collectors. From an evaluation of these fluxes, the macroscopic interfacial resistance is decomposed into an electrochemical reaction resistance and an electron diffusion-drift resistance, the latter associated with the in-plane electronic current. Analysis of the experimental data for the interfacial resistance for hydrogen electro-oxidation on SDC15 having either Pt or Au current collectors (W. Lai and S. M. Haile, J. Am. Ceram. Soc., 2005, 88, 2979-2997; W. C. Chueh, W. Lai and S. M. Haile, Solid State Ionics, 2008Ionics, , 179, 1036Ionics, -1041 indicates that surface reaction rather than electron migration is the overall rate-limiting step, and suggests furthermore that the surface reaction rate, which has not been directly measured in the literature, scales with p À1=4 O 2 . The penetration depth for the in-plane electronic current is estimated at 0.6 mm for the experimental conditions of interest to SDC15, and is found to attain a value as high as 4 mm within the broader range of computational conditions.

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Section: Methodsmentioning

confidence: 99%

“…1 has been presented in brief elsewhere. 12 The model, described in full here, adopts the following sequence of steps. First, the carrier concentrations are solved analytically under equilibrium conditions (section 3.1).…”

Section: Modelmentioning

confidence: 99%

Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Ciucci

Chueh

Goodwin

et al. 2011

Phys. Chem. Chem. Phys.

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“…But the new expression will make the model easier to understand and be consistent with other models developed for mixed conducting electrolytes. 20,22,23,[25][26][27][28] In the following, we are going to show the detailed derivation procedure of the thermodynamic factor and mass conservation equations in the appendix of Adler et al's work, A3a. From Adler et al's Eqs.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Wachsman and Duncan 24 utilized Nernst-Planck equation to develop an analytical relation between voltage and current for SOFC with mixed conducting electrolyte. Haile and Goodwin [25][26][27][28] developed an impedance model for mixed conducting electrolytes such as Sm-and Gd-doped CeO 2 , based on Nernst-Planck equation. 29 The governing Nernst-Planck equation contains electrochemical potential without the thermodynamic factor, which is different from the modified Fick's first law.…”

Section: Journal Of the Electrochemical Society 163 (13) A2702-a2719mentioning

confidence: 99%

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Simulating Charge Transport in Solid Oxide Mixed Ionic and Electronic Conductors: Nernst-Planck Theory vs Modified Fick's Law

Jin

White

Huang

2016

J. Electrochem. Soc.

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With the assumption that the Fermi level (electrochemical potential of electrons) is uniform across the thickness of a mixed ionic and electronic conducting (MIEC) electrode, the charge-transport model in the electrode domain can be reduced to the modified Fick's first law, which includes a thermodynamic factor A. A transient numerical solution of the Nernst-Planck theory was obtained for a symmetric cell with MIEC electrodes to illustrate the validity of the assumption of a uniform Fermi level. Subsequently, an impedance numerical solution based on the modified Fick's first law is compared with that from the Nernst-Planck theory. The results show that Nernst-Planck charge-transport model is essentially the same as the modified Fick's first law model as long as the MIEC electrodes have a predominant electronic conductivity. However, because of the invalidity of the uniform Fermi level assumption for a MIEC electrolyte with a predominant ionic conductivity, Nernst-Planck theory is needed to describe the charge transport behaviors. The methods of Electrochemical Impedance Spectroscopy (EIS) 1,2 and Electrical Conduction Relaxation (ECR) [3][4][5] have been utilized widely in characterizing the bulk transport properties and the electrochemical/chemical reactions at the surface of the mixed ionic and electronic conducting (MIEC) electrodes and electrolytes. Both of these methods rely upon transient responses of the system subject to external perturbations (electrical stimulus or partial pressure of oxygen change). To interpret the experimental data obtained from these two techniques, two theoretical approaches have been commonly applied to describe the flux of species in the MIEC: modified Fick's first law and Nernst-Planck theory.Fick's first law with inclusion of the thermodynamic factor A is referred to as the modified Fick's first law throughout this paper. It describes the transport of species j as a simple diffusion process driven by a concentration gradient of species j under the assumption that the electrochemical potential of the electron hole/electron is uniform in the MIEC electrodes. For this modified Fick's first law, the flux of species is written as,where D j is the diffusion coefficient of species j (component diffusion coefficient);D j = AD j is the chemical diffusion coefficient of species j. Eq. 1 was originally proposed by Carl Wagner, 6,7 and then adopted by Weppner and Huggins 8 in 1977 to describe the transport of neutral species in the ionization equilibrium for mixed-conducting Li 3 Sb system. In their original paper, the following expression was used for the flux of species j:where,D j is the chemical diffusion coefficient for species j; D j is the self-diffusion coefficient; W is an enhancement factor introduced by Weppner and Huggins and defined as follows for a system with only one ionic species and one electronic species with the activity coefficient as constant: [3] where, t e is the transference number of electronic species; z j is the charge number of species j; c j and a j are th...

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Probing Bias‐Dependent Electrochemical Gas–Solid Reactions in (La_xSr_1–x)CoO_3–_δ Cathode Materials

Kumar

Ciucci

Leonard

et al. 2013

Adv Funct Materials

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Spatial variability of bias-dependent electrochemical processes on a (La 0.5 Sr 0.5 ) 2 CoO 4 ± δ modifi ed (La x Sr 1-x )CoO 3-δ surface is studied using fi rstorder reversal curve method in electrochemical strain microscopy (ESM). The oxygen reduction/evolution reaction (ORR/OER) is activated at voltages as low as 3-4 V with respect to bottom electrode. The degree of bias-induced transformation as quantifi ed by ESM hysteresis loop area increases with applied bias. The variability of electrochemical activity is explored using correlation analysis and the ORR/OER is shown to be activated in grains at relatively low biases, but the fi nal reaction rate is relatively small. At the same time, at grain boundaries, the onset of reaction process corresponds to larger voltages, but limiting reactivity is much higher. The reaction mechanism in ESM of mixed electronic-ionic conductor is further analyzed. These studies both establish the framework for probing bias-dependent electrochemical processes in solids and demonstrate rich spectrum of electrochemical transformations underpinning catalytic activity in cobaltites.

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Impedance spectra of mixed conductors: a 2D study of ceria

Abstract: 1In this paper we develop an analytical framework for the study of

Cited by 29 publications

References 36 publications

Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Simulating Charge Transport in Solid Oxide Mixed Ionic and Electronic Conductors: Nernst-Planck Theory vs Modified Fick's Law

Probing Bias‐Dependent Electrochemical Gas–Solid Reactions in (La_xSr_1–x)CoO_3–_δ Cathode Materials

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Impedance spectra of mixed conductors: a 2D study of ceria

Abstract: 1In this paper we develop an analytical framework for the study of

Cited by 29 publications

References 36 publications

Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Surface reaction and transport in mixed conductors with electrochemically-active surfaces: a 2-D numerical study of ceria

Simulating Charge Transport in Solid Oxide Mixed Ionic and Electronic Conductors: Nernst-Planck Theory vs Modified Fick's Law

Probing Bias‐Dependent Electrochemical Gas–Solid Reactions in (LaxSr1–x)CoO3–δ Cathode Materials

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Probing Bias‐Dependent Electrochemical Gas–Solid Reactions in (La_xSr_1–x)CoO_3–_δ Cathode Materials