Anal. Chem. 2001, 73, 4059
Correspondence
Comments on the Article “An Electrochemical Impedance Measurement Technique Employing Fourier Transform” by J.-S. Yoo and S.-M. Park SIR: In the recent article, Yoo and Park1 presented a new technique of impedance measurements using discrete time Fourier transform, DTFT, of the derivative of current, di/dt, after application of a small potential step. The authors measured the transient current up to (n0 + 1)∆t, where n0 + 1 is the number of points sampled and ∆t is the sampling time. They assumed that for longer times, the current and its derivative are equal to zero. Then, they reconstructed the whole frequency spectrum, even for very low frequencies (assuming that i ) 0 for t > (n0 + 1)∆t). The problem with this method is that in the measured current i(t) there is no information about lower frequencies, as i(t > (n0 + 1)∆t) ) 0. The authors simply extrapolate the information obtained at short times (or high frequencies) to low frequencies. The statement that “our method would allow possible measurements of impedance data between the half of the highest frequency down to almost dc” by carrying out the experiments in a very short time period (n0 + 1)∆t is not true. Let us look at the circuit in Figure 1 of that paper.1 In a real case presented in the paper, that is, oxidation of Fe(CN)64-, the faradaic impedance must be present. The faradaic impedance is expressed as Rp + ZW, where ZW is the Warburg (semiinfinite diffusion) impedance described as ZW ) σ/xjω. At very short times, which correspond to very high frequencies, ZW , Rp, and the information about ZW is absent in the observed current, especially because the authors work with a relatively high concentration, 50mM, of the electroactive species. Reconstruction of the Fourier spectrum based on this *
[email protected]. (1) Yoo, J.-S.; Park; S.-M. Anal. Chem. 2000, 72, 2035.
10.1021/ac0014055 CCC: $20.00 Published on Web 07/12/2001
© 2001 American Chemical Society
information reveals only one semicircle on the complex plane plots and the total absence of the Warburg impedance. The statement that “since it takes a long time to make impedance measurements for a frequency range between 50 kHz and submilihertz, the system itself changes as a result of electrolysis during the measurements or by the time the measurements are over....our technique solves this problem better than any other conceivable methods would have” is only partially true. This technique simply extrapolates the shorttime information to low frequencies without creation of any new information, which is absent in the original transient. It is very well-known, that the most interesting information in studying corrosion or intercalation processes may be obtained at low frequencies (long times). Such information is absent in the spectra obtained at short times. Nevertheless, such information may be obtained if the current sensitivity is increased at longer times. This effect is used in the differential pulse voltammetry.2 By carrying out the measurements up to longer times, the Warburg impedance and other low-frequency phenomena may be recovered. Reassuming, the presented method extrapolates the highfrequency information to low frequencies; however, about the low-frequency, the phenomena are absent. This technique is quite advantageous in extracting high-frequency information from the experiment. It cannot, however, present any information about the low-frequency phenomena. Another weak point of this method is the necessity of differentiation of the noisy data (see Figure 5, ref 1). It is wellknown that such a procedure demands a smoothing procedure that may change the real shape of the experimental curve.3 The combination of this problem with the limited response time of the potentiostat produces distortions of the high-frequency phase-angle plot, observed in Figure 7.1
Andrzej Lasia*
De´ partement de chimie, Universite´ de Sherbrooke, Sherbrooke, Que´ bec, J1K 2R1 Canada AC0014055 (2) Bard, A. J.; Faulkner, L. F. Electrochemical Methods, Fundamentals and Applications; J. Wiley and Sons: New York, 1980; p 190. (3) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes, The Art of Scientific Computing, 2nd ed.; Cambridge University Press: Cambridge, 1992, Chapter 14.
Analytical Chemistry, Vol. 73, No. 16, August 15, 2001 4059
