We experimentally validate theoretical
relation between the roughness
power spectrum (PS) and electrochemical current transient for a reversible
charge transfer system under a single potential step. Roughness features
at the electrochemically roughened electrode are characterized using
standard measurements such as scanning electron microscopy (SEM),
atomic force microscopy (AFM) and cyclic voltammetry (CV). The PS
obtained from AFM shows composite finite fractal and nonfractal nature
in roughness, whereas the PS from SEM shows only a finite fractal
nature. AFM or SEM measurements provide knowledge of fractal dimension
(D
H) and two fractal cutoff lengths (
scriptl
.25em
and
.25em
L
).
Topothesy length (
scriptl
τ
) or the related proportionality
factor
(
μ
≡
scriptl
τ
2
D
normalH
−
3
) from
PS data of AFM requires extrapolation
of data for unit wavenumber, but this method usually provides unphysical
values of μ. We provide a novel method to determine the topothesy
of electrodes from CV measurements of electroactive area in conjunction
with SEM or AFM measurements. Chronoamperometric measurements were
made on morphologically characterized Pt-electrodes for a solution
of K4[Fe(CN)6] and K3[Fe(CN)6] in 3 M NaNO3. The transient response observed
experimentally is validated using the measured PS in the theoretical
equation for the current. The transient response does not show contributions
from Gaussian PS in the low wavenumber region; this is due to the
fact that the effective lower cutoff wavenumber is usually limited
up to the inverse of the width of roughness (or topothesy length).
Fractal dimensions obtained through chronoamperometric measurement
on electrodes using Pajkossy’s approach do not correspond to
the one obtained from AFM and SEM measurements. Finally, the anomalous
response in the Cottrell measurements can be understood through PS-based
theory.
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