Diffusion to an assembly of slowly growing particles on a substrate

Bobbert, PA Peter; Wind, M.M.; Vlieger, J.

doi:10.1016/0378-4371(87)90223-8

Cited by 51 publications

(35 citation statements)

References 10 publications

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“…This approach gives a overestimated current density that Heerman et al [17] deemed resulted from inaccurate detailed mass balance at individual diffusion zones when these are born at different times; thus they defined a single planar diffusion zone for the overall ensemble of growing nuclei instead of manifold zones associated to each of the growing centers. This introduces a uniform diffusion layer, related to the mean concentration field brought in by Bobbert et al [18].…”

Section: Overlap Of Planar Diffusion Zonesmentioning

confidence: 98%

“…The hierarchical overlap introduced in the present work avoids mean field approximations [17,18] or reducing all disks to a uniform width, notwithstanding their different ages due to progressive nucleation. We followed two approaches to compare transients obtained from simulations of hierarchical overlap with theoretical models considering the KJMA non-hierarchical overlap.…”

Section: Comparison Of Transients Arising From Hierarchical and Nonhimentioning

confidence: 98%

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Three-dimensional nucleation with diffusion-controlled growth: Simulation of hierarchical diffusion zones overlap

Mazaira

Borrás

Mostany

et al. 2009

Journal of Electroanalytical Chemistry

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Section: Overlap Of Planar Diffusion Zonesmentioning

confidence: 98%

Section: Comparison Of Transients Arising From Hierarchical and Nonhimentioning

confidence: 98%

Three-dimensional nucleation with diffusion-controlled growth: Simulation of hierarchical diffusion zones overlap

Mazaira

Borrás

Mostany

et al. 2009

Journal of Electroanalytical Chemistry

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“…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 Fig. 2, where the curves for the temporal evolution of the nuclear radius are shown, it can be seen that the simulation curve obtained with the correction parameter fits properly the theoretical curve that describes the growing of an isolated nucleus with an initial radius R 0 [5][6][7][8][9].…”

Section: The Reaction Distance Parametermentioning

confidence: 50%

“…Each one has its own advantages and limitations. Analytical models exist only for very simple cases and under limiting conditions [1][2][3][4], and they become approximate when the electrode has no simple geometry (flat or hemispherical) or when the process involves single or multinuclear growth [5][6][7][8][9][10][11][12]. The use of numerical methods [13,14] allows the description of processes with a rigid or time-dependent moving boundary.…”

Section: Introductionmentioning

confidence: 99%

Brownian dynamics simulation of nucleation and growth processes at electrode surfaces: instantaneous nucleation

Trias

Vilaseca

2004

Journal of Electroanalytical Chemistry

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Diffusion to an assembly of slowly growing particles on a substrate

Cited by 51 publications

References 10 publications

Three-dimensional nucleation with diffusion-controlled growth: Simulation of hierarchical diffusion zones overlap

Three-dimensional nucleation with diffusion-controlled growth: Simulation of hierarchical diffusion zones overlap

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

Brownian dynamics simulation of nucleation and growth processes at electrode surfaces: instantaneous nucleation

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