Resistance, capacitance, and electrode kinetic effects in Fourier-transformed large-amplitude sinusoidal voltammetry: emergence of powerful and intuitively obvious tools for recognition of patterns of behavior.
Large-amplitude sinusoidal ac voltammetric techniques, when analyzed in the frequency domain using the Fourier transform-inverse Fourier transform sequence, produce the expected dc and fundamental harmonic ac responses in addition to very substantial second, third, and higher ac harmonics that arise from the presence of significant nonlinearity. A full numerical simulation of the process, Red right arrow over left arrow Ox + e(-), incorporates terms for the uncompensated resistance (R(u)), capacitance of the double layer (C(dl)), and slow electron transfer kinetics (in particular, the reversible potential (E degrees ), rate constant (k(0)), and charge transfer coefficient (alpha) from the Butler-Volmer model). Identification of intuitively obvious patterns of behavior (with characteristically different sensitivity regimes) in dc, fundamental, and higher harmonic terms enables simple protocols to be developed to estimate R(u), C(dl), E degrees , k(0), and alpha. Thus, if large-amplitude sinusoidal cyclic voltammograms are obtained for two concentrations of the reduced species, data obtained from analysis of the recovered signals provide initial estimates of parameters as follows: (a) the dc cyclic component provides an estimate of E degrees (because the R(u) and k(0) effects are minimized); (b) the fundamental harmonic provides an estimate of C(dl) (because it has a high capacitance-to-faradaic current ratio); and (c) the second harmonic provides an estimate of R(u), k(0), and alpha (because the C(dl) effect is minimized). Methods of refining the initial estimates are then implemented. As a check on the fidelity of the parameters (estimated on the basis of an essentially heuristic approach that solely utilizes the dc, fundamental, and second harmonic voltammograms), comparison of the predicted simulated and experimental third (or higher) harmonic voltammograms can be made to verify that agreement between theory and experiment has been achieved at a predetermined level. The use of the heuristic pattern recognition approach to evaluate the oxidation of ferrocene at a platinum electrode (a reversible process) in the very high resistance solvent dichloromethane (0.1 M Bu(4)NPF(6)) and the reduction of [Fe(CN(6))](3)(-) at a glassy carbon electrode (a quasi-reversible process) in much lower resistance but higher capacitance conditions found in aqueous (0.5 M KCl) media is described and verifies the inherent advantages of employing large-amplitude sinusoidal techniques in quantitative studies of electrode processes.
Sher
Anna A
AA
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom.
Bond
Alan M
AM
Gavaghan
David J
DJ
Harriman
Kathryn
K
Feldberg
Stephen W
SW
Duffy
Noel W
NW
Guo
Si-Xuan
SX
Zhang
Jie
J