The concept of planar diffusion zones. Theory of the potentiostatic transient for multiple nucleation on active sites with diffusion-controlled growth

Heerman, L.; Matthijs, Edward; Langerock, Steven

doi:10.1016/s0013-4686(01)00792-7

Cited by 35 publications

(29 citation statements)

References 17 publications

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“…In coordinates vs. logt, potentiostatic curves were characterized each by two linear portions: 0.5-0.6, then 0.03-0.10. Initial portions of current transients were approximated by a linear dependence of I c on t 1/2 , which is characteristic of instantaneous diffusion-controlled nucleation [13][14][15] or diffusion-controlled growth of nuclei on microelectrodes [16,17]: I(t) = zFDck(πDt) 1/2 , where c is the bulk concentration of electrochemically active species, D is the diffusion coefficient, F is Faraday's constant, z is the number of electrons that take part in an analysis of redox process, and k is a dimensionless constant that depends on the experimental conditions.…”

Section: Resultsmentioning

confidence: 99%

Effect of the Electrode Material on the Reduction of La3+ and Ce3+ in Fluoride-Conducting Solid Electrolytes

et al. 2005

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The reduction of immobile cations La 3+ and Ce 3+ in fluoride-conducting solid electrolytes (FSE) LaF 3 ( Eu 2+ 0.8 mol %), LaF 3 ( Sr 2+ 5 mol %), and CeF 3 ( Sr 2+ 5 mol %) in contact with Ag, Bi, Si, La, Ce, and Sm working electrodes is studied by chronoamperometry and voltammetry with linear potential scan. Discovered is linear dependence of initial segments of potentiostatic transients of cathodic current on t 1/2 at FSE interfaces with Ag, Bi, La, Ce, and Sm. The dependence is due to diffusion-controlled instantaneous nucleation of Ln and Ce. The La 3+ and Ce 3+ reduction at the FSE/Ag interface is reversible in a narrow region. The reduction and oxidation of La 3+ and Ce 3+ (cations of the FSE rigid lattice) at the FSE/Me (Me = La, Ce and Sm, Bi, Si) interface is irreversible and involves a chemical reaction.

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Section: Resultsmentioning

confidence: 99%

Effect of the Electrode Material on the Reduction of La3+ and Ce3+ in Fluoride-Conducting Solid Electrolytes

et al. 2005

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“…The problem of interference of the diffusion fields of the nuclei then can be described by the overlap of the associated diffusion zones, which forms the basis of the ''standard model'' of Scharifker and Mostany [3]. The concept of planar diffusion zones has been amply discussed in the literature and more details can be found in the original papers [2,3,8,12].…”

Section: The Concept Of Planar Diffusion Zonesmentioning

confidence: 99%

“…Several models have been proposed for the theoretical description of the potentiostatic transient for 3D nucleation on active sites with diffusion-controlled growth [1][2][3][4][5][6][7][8][9][10][11][12]. All these models describe the rate law for the formation of nuclei on a finite number of active sites, which are distributed randomly over the electrode surface, by the equation…”

Section: Introductionmentioning

confidence: 99%

The potentiostatic transient for 3D nucleation with diffusion-controlled growth: theory and experiment for progressive nucleation

Matthijs

Langerock

Michailova

et al. 2004

Journal of Electroanalytical Chemistry

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The theory of the potentiostatic transient for 3D nucleation with diffusion-controlled growth is discussed. It is shown that the theoretical model of Mirkin and Nilov [J. Electroanal. Chem., 283 (1990) 35] and Heerman and Tarallo [J. Electroanal. Chem., 470 (1999) 70] predicts too high values of the current, which becomes very apparent for high values of the site density and low values of the nucleation rate constant (progressive nucleation). For example, the model then predicts that the current in the limit of long times will be higher than the Cottrell limit by a factor of 4/3 which is physically unacceptable. Therefore, a modification to this model is proposed which is based on a careful analysis of the Kolmogorov-Avrami theorem. The ''extended area'' in the KolmogorovAvrami theorem includes contributions from ''phantom nuclei'' that are born inside already existing zones but do not exist physically. This is necessary to preserve the randomness of the system and allows the correct calculation of the appearance rate of the nuclei and the nucleus saturation density. The ''extended current'', defined in analogy with the ''extended area'', then also attributes current to the phantom nuclei. It follows that the ratio j ex ðtÞ=h ex ðtÞ which appears in the model of Mirkin and Nilov and Heerman and Tarallo does not correspond to the actual number of nuclei formed on the electrode. Therefore, the ''extended quantities'' in this ratio must be replaced with quantities that relate directly to the real number of clusters (this implies what is fairly obvious, that the appearance rate of the clusters must be calculated first). This makes it is possible to derive an equation that predicts correctly the current in the limits of both short and long times which is directly linked to the N a ðtÞ vs. time relation (where N a ðtÞ is the actual number of nuclei on the electrode). Experiments for the nucleation of silver on glassy carbon electrodes, with the simultaneous recording of both jðtÞ vs. time and N a ðtÞ vs. time relations, are described. The experimental results obtained from the transients and the direct visual counting of nuclei are compared with the theoretical predictions.

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“…In this regard, they identify two main approaches to classify the models that describe the current transients. On the one hand there are the models that use the Avrami theorem [2,3] and/or adopt the concept of diffusion zones [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. On the other are those models that avoid the Avrami theorem and the extended area concept [18][19][20][21][22][23] to describe the currents.…”

Section: Introductionmentioning

confidence: 99%

“…They all aim to describe the general behavior of the current transients and they all exhibit current transient expressions that show no connection with potential, temperature or concentration, with the exception of time. In fact these models [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] are applied to situations where these parameters are set to constants; however a realistic description of the transients requires an explicit relation, involving the real parameters and the theoretical ones employed by the models.…”

Section: Introductionmentioning

confidence: 99%

Current–time and current–potential profiles in electrochemical film production. (I) Current–time curves

D'Ajello

2004

Journal of Electroanalytical Chemistry

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The concept of planar diffusion zones. Theory of the potentiostatic transient for multiple nucleation on active sites with diffusion-controlled growth

Cited by 35 publications

References 17 publications

Effect of the Electrode Material on the Reduction of La3+ and Ce3+ in Fluoride-Conducting Solid Electrolytes

Effect of the Electrode Material on the Reduction of La3+ and Ce3+ in Fluoride-Conducting Solid Electrolytes

The potentiostatic transient for 3D nucleation with diffusion-controlled growth: theory and experiment for progressive nucleation

Current–time and current–potential profiles in electrochemical film production. (I) Current–time curves

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