A numerical study of the equilibrium and nonequilibrium diffuse double layer in electrochemical cells

Murphy, W. D.; Manzanares, José A.; Mafé, Salvador; Reiss, Howard

doi:10.1021/j100203a074

Cited by 65 publications

(69 citation statements)

References 11 publications

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“…[6,11,43,44], (10) where the first term represent the conduction current and the second term the Maxwell current. At the elec trodes the conduction term equals the Faradaic cur rent, and we obtain [11,43] (11) for the potential gradient at the reaction plane. The contribution of the Faradaic current in 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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“…Related work has focused on super-limiting currents and hydrodynamic instability at large voltages [31] [32], but for this class of problems much simpler Dirichlet boundary conditions of constant ion concentrations and constant electrostatic potential are commonly used to describe the membrane-electrolyte interface. In the present context of Faradaic charge transfer reactions, some authors modeling diffuse charge in electrolytic cells [28] [29] have simplified the problem by taking the Gouy-Chapman limit of a zero Stern layer thickness, but this removes any local field strengthdependence from the charge-transfer reaction rate and thus predicts a reaction-limited current, which cannot be exceeded without negative ion concentrations in the model. With a Stern layer included, it can be shown that ion concentrations are always positive [13] [15].…”

Section: Introductionmentioning

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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“…Accurate analysis of this interaction requires solving the one-dimensional nonlinear Poisson-Boltzmann equation (PBE) to determine the potential profile w(x) within the electrical double layer (EDL) as a function of distance x from the interacting surfaces. Though explicit relations have been developed for the potential profile w(x) in the vicinity of a single plate [1,2], obtaining analytical solutions for two interacting plates is only possible for the linearized versions of the PBE for weakly charged systems [3][4][5][6], and analysis of highly charged asymmetrical surfaces is only possible by the use of unwieldy complex elliptic integrals or numerical methods [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of Poisson?Boltzmann equation for interacting plates of arbitrary potentials and same sign

Polat

2010

Journal of Colloid and Interface Science

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a b s t r a c tEfficient calculation of electrostatic interactions in colloidal systems is becoming more important with the advent of such probing techniques as atomic force microscopy. Such practice requires solving the nonlinear Poisson-Boltzmann equation (PBE). Unfortunately, explicit analytical solutions are available only for the weakly charged surfaces. Analysis of arbitrarily charged surfaces is possible only through cumbersome numerical computations. A compact analytical solution of the one-dimensional PBE is presented for two plates interacting in symmetrical electrolytes. The plates can have arbitrary surface potentials at infinite separation as long they have the same sign. Such a condition covers a majority of the colloidal systems encountered. The solution leads to a simple relationship which permits determination of surface potentials, surface charge densities, and electrostatic pressures as a function of plate separation H for different charging scenarios. An analytical expression is also presented for the potential profile between the plates for a given separation. Comparison of these potential profiles with those obtained by numerical analysis shows the validity of the proposed solution.

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A numerical study of the equilibrium and nonequilibrium diffuse double layer in electrochemical cells

Cited by 65 publications

References 11 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

Analytical solution of Poisson?Boltzmann equation for interacting plates of arbitrary potentials and same sign

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