Diffusion to a slowly growing truncated sphere on a substrate

Evaluation of the intrinsic kinetic activity of nanoparticle ensembles under steady-state conditions

“…h = 0), a limiting current due to diffusion to the spherical nanoparticles (i L,NP ) [104][105][106] that are separated by a distance 2R 0 and assuming that each NP acts individually, and a kinetic current (i K ) [49]. The resulting expression is similar to that used in describing the steady-state current at modified electrodes assuming a pin-hole model [49,59,60,62,107],…”

“…Additionally there is a steady-state diffusion length, d ss , that must be established around an individual supported NP for it to display steady-state behavior; this distance follows from the spherical form of Fick's First Law and, assuming a linear concentration profile, is found to be [104][105][106]108] …”

Simple Analytical Equations for the Current–Potential Curves at Microelectrodes: A Universal Approach

“…The above process will be analyzed by assuming that the diffusion coefficients of species O and R are equal and that a large excess of supporting electrolyte is present in the solution in such a way that migration can be neglected. When the boundary values of the concentrations of electroactive species at the electrode surface and in the bulk are constant, the solution for the diffusion equation at any electrode geometry can be written as 6,7 …”

Nucleation and growth of clusters through multi-step electrochemical reactions

“…(13)-(15) transform into the theoretical expressions describing the nucleation and growth kinetics under complete diffusion limitations (see, e.g. [6][7][8][9][10][11][12][13][14]19] and the references cited therein). As expected, in this latter case the fact that the charge transfer reaction takes place in two-steps does not influence the growth process and is of no importance.…”

“…The growth kinetics of individual clusters was theoretically considered by many authors and explicit formulae were derived for the time dependence of the clusters' linear size and growth current accounting for different limitation factors [1][2][3][4][5][6][7][8][9][10][11][12][13][14] (see also [15][16][17][18][19] and the references cited therein). In most cases, however, the authors assume that the ions' discharge takes place as one-step reaction, which is not always the case of electrochemical metal deposition.…”