Chronoammetry and Chronopotentiometry on Electrodes with a Microrough Surface: Theoretical Consideration

Abstract

The problem of transient two-dimensional diffusion to a microrough electrode under galvano-and potentiostatic polarization conditions is solved. The effect of the scale and morphology of roughness, as well as the diffusivity on the time dependences of I current and η overpotential is analyzed. Both of them are found to be practically independent of the type of the roughness, while its degree (the microroughness factor f r ) decisively affects the shape of the current-and overpotential-decay curves. At a relatively short polarization when the diffusion front profile repeats the electrode surface relief, the parameters of transient electrochemical methods (the I current in the potentiostatic measurements and the τ 1/2 rooted transient time in the galvanostatic ones) linearly depend on the microroughness factor. Upon a relatively long polarization when the diffusion front is noticeably distant from the surface and almost planar, the current and overpotential values fit in with classical equations of chronoammetry and chronopotentiometry, being independent of f r . At a thickness of the diffusion layer comparable to the height of surface irregularities, the current (as well as the rooted transient time) ratio of the microrough to perfectly smooth electrode surface looses its linear dependence on the surface parameters. The time location of this range is chiefly determined by the diffusivity and the mean distance between the microscopic surface irregularities.

Solid-Phase Diffusion at a Galvanostatic Anodic Dissolution of Zn-Ag and Cu-Au Alloy

“…(16) are smaller than those estimated from Eq. (13) by a factor of ; such a difference noticeably exceeds typical experimental errors.…”

“…The role of the roughness factor in chronopotentiometry was analyzed in [15,16] for planar electrodes with diverse types of repeated microscopic surface irregularities, the parameters of which were either determinate or statistically normally distributed, and the roughness factor f r = S / S g (where S is the true electrode surface area) did not exceed three. As was found, irrespective of the surface geometrical profile (sinusoidal, smoothened saw-tooth and trapezoidal, or a system of separate kinks), the transient times and the P ( t , τ A ) functions for the electrodes with the rough and perfectly smooth ( f subscript) surfaces are related as follows:…”

Solid-Phase Diffusion at a Potentiostatic Dissolution of Silver Alloyed with Gold

“…To answer a question on whether the electrode roughness causes the distortion of the i Ag -t -1/2 dependence, one needs at least an approximate estimate of the mean distance λ between the microscopic surface irregularities [26]. This parameter can be evaluated from the roughness factor, which is related to λ and the mean height of the irregularities via relation [32]: (19) Here, ς(x) is a function of the surface profile, which depends only on the lateral coordinate x, and x 0 is the length of the rectangular electrode.…”

“…In an intermediate range t 1 < t < t 2 , the ϕ' function noticeably changes with time; the M' values are given in [26]. Physical meaning of the relation (6) is quite clear: in the initial period of recording a chronoammogram (t ≤ t 1 ), the diffusion front completely repeats the surface profile.…”

“…The effect produced by roughness in chronoammetry was analyzed in [25,26] for the case of planar electrodes with diverse types of periodic microscopic irregularities, the parameters of which can be either determinate or statistically normally distributed, while the roughness factor was f r ≤ 3. It turned out that irrespective of the geometrical profile of the surface (sinusoidal, smoothened saw-tooth or trapezoidal, or a system of singular kinks), the currents on electrodes with rough and perfectly smooth ("f" subscript) surfaces are related as follows:…”