Dynamic Diffuse Double-Layer Model for the Electrochemistry of Nanometer-Sized Electrodes

He, Rui; Chen, Shengli; Yang, Fan; Wu, Bin

doi:10.1021/jp060084j

Cited by 117 publications

(184 citation statements)

References 27 publications

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“…From Eq. (13) we obtain a replacement for Poisson's equation according to (15) which, by neglecting any redistribution of species and after the Maxwell current died out, follows Ohm's law where the electrical current is given by I = κ∂ X V, with the electrolyte conductivity, κ = fFc ∞ (D c + D a ). Though Eq.…”

Section: Generalized Frumkin-butler-volmer Equationmentioning

confidence: 99%

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Frumkin-Butler-Volmer theory and mass transfer in electrochemical cells

Soestbergen

2012

Russ J Electrochem

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Abstract-An accurate mathematical description of the charge transfer rate at electrodes due to an electro chemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin Butler-Volmer (gFBV) equation to describe electrochemical reactions, an equa tion which, contrary to the classical Butler-Volmer approach, includes the effect of the double layer compo sition on the charge transfer rate. The gFBV theory is transparently coupled to the Poisson-Nernst-Planck ion transport theory to describe mass transfer in an electrochemical cell that consists of two parallel plate electrodes which sandwich a monovalent electrolyte. Based on this theoretical approach we present analytical relations that describe the complete transient response of the cell potential to a current step, from the first initial capacitive charging of the bulk electrolyte and the double layers all the way up to the steady state of the system. We show that the transient response is characterized by three distinct time scales, namely; the capac itive charging of the bulk electrolyte at the fastest Debye time scale, and the formation of the double layers and the subsequent redistribution of ions in the bulk electrolyte at the longer harmonic and diffusion time scales, respectively.

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Section: Generalized Frumkin-butler-volmer Equationmentioning

confidence: 99%

“…In addition, applications of the Frumkin approach were reported on e.g. corrosion, [11,12] fuel cells, [13,14] nano electrodes, [15] and batteries [16,17].…”

Section: Introductionmentioning

confidence: 99%

Frumkin-Butler-Volmer theory and mass transfer in electrochemical cells

Soestbergen

2012

Russ J Electrochem

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“…Bazant et al [14], Chu and Bazant [15] and Prieve [30] extend these calculations. He et al [39] use the gFBV-formulation in the represention of Eq. (4), for a steady-state calculation for a spherical nanoelectrode, with the counterelectrode as a infinitely large shell, infinitely far away.…”

Section: History Of Modeling Electrochemical Charge Transfer Includinmentioning

confidence: 99%

“…Polarization layer effects in electrochemical cells have been included in a limited amount of previous work [13]- [17], [28]- [30], [39], [40] but except for refs. [16][17] these papers consider electrolytic operation where the open-circuit voltage (OCV) is zero and no current is generated spontaneously upon closing the electrical circuit.…”

Section: Introductionmentioning

confidence: 99%

Imposed currents in galvanic cells

Biesheuvel

Soestbergen

Bazant

2009

Electrochimica Acta

123

162

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We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open circuit voltage, and (ii) the "super-galvanic" discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-)charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models.Notably, we consider effects of diffuse charge on electrochemical charge transfer rates by combining a generalized Frumkin-Butler-Volmer model for reaction kinetics across the compact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio δ of the effective thicknesses of the compact and diffuse layers: (i) the "Helmholtz limit" ( δ → ∞ ) where the compact layer carries the double-layer voltage as in standardButler-Volmer models, and (ii) the opposite "Gouy-Chapman limit" ( 0 δ → ) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact-layer, diffuse-layer and membrane thicknesses.2

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“…The goal of this work is thus to construct and solve a general model for voltammetry for charged electrolytes. We consider the simplest Poisson-Nernst-Planck (PNP) equations for ion transport for dilute liquid and solid electrolytes and leaky membranes, coupled with "generalized" Frumkin-Butler-Volmer (FBV) kinetics for Faradaic reactions at the electrodes [12,[33][34][35][36][37], as reviewed by Biesheuvel, Soestbergen, and Bazant [14] and extended in subsequent work [10,11,15]. Unlike most prior analyses, however, we make no assumptions about the electrical double layer (EDL) thickness, Stern layer thickness, sweep rate, or reaction rates in numerical solutions of the full PNP-FBV model.…”

Section: Introductionmentioning

confidence: 99%

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Yan

Bazant

Biesheuvel³

et al. 2017

Phys. Rev. E

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Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent PoissonNernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

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Dynamic Diffuse Double-Layer Model for the Electrochemistry of Nanometer-Sized Electrodes

Cited by 117 publications

References 27 publications

Frumkin-Butler-Volmer theory and mass transfer in electrochemical cells

Frumkin-Butler-Volmer theory and mass transfer in electrochemical cells

Imposed currents in galvanic cells

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

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