pubs.acs.org/Langmuir © 2009 American Chemical Society
Impedance Analysis for Hydrogen Adsorption Pseudocapacitance and Electrochemically Active Surface Area of Pt Electrode Hyun D. Yoo,† Jong Hyun Jang,‡ Bok H. Ka,† Choong Kyun Rhee,*,§ and Seung M. Oh*,† †
Department of Chemical and Biological Engineering and Research Center for Energy Conversion & Storage, Seoul National University, 599 Gwanangno, Gwanak-gu, Seoul, 151-744, Korea, ‡Center for Fuel Cell Research, Korea Institute of Science and Technology, Seoul 136-791, Korea, and §Department of Chemistry, Chungnam National University, Daejeon 305-764, Korea
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Received January 23, 2009. Revised Manuscript Received July 20, 2009 Electrochemically active surface area (ECA) of a polycrystalline Pt electrode is measured from the pseudocapacitance (Cp) values that are associated with hydrogen underpotential deposition. The potential-dependent Cp values are extracted from the raw impedance data by removing the interferences coming from the double-layer charging and hydrogen evolution. Three different approaches have been made: (i) by using the proportionality between the capacitance and area of the capacitive peak on imaginary capacitance plots, (ii) by complex nonlinear least-squares (CNLS) fitting on both the imaginary and real part of complex capacitance with appropriate equivalent circuits, and (iii) by using the modified Kramers-Kronig (K-K) relation. The first approach is the simplest one for the Cp measurement but cannot be used in the hydrogen evolution region ( fmax. The Cp(E) profiles obtained by the two algorithms are very close to each other. Moreover, they are well-matched with that obtained by the CNLS fitting within the experimental or fitting errors. Figure 8b shows the accumulated charge (Qads) obtained by integrating the Cp vs E profiles; the results obtained from two algorithms are very close to that derived from the CNLS fitting. The accumulated charge is also comparable for all three measurements (Table 4). The Qads vs E data obtained from the area of capacitive peak (C00 integration) was fitted with three superimposed Frumkin isotherms and the fitting curve is presented in Figure 8b along with the duplicated Frumkin isotherm (from Figure 6a). The saturation charge (Q0) shows a marginal difference (312 and 304 μC cm-2) between the two fitted isotherms (Table 3 and 5). As compared to the second approach (CNLS fitting), which needs impedance data down to 1 Hz for the fitting, this method can shorten the acquisition time. A simple calculation illustrates that 46 measurements in the potential range of 0.02-0.42 V for the frequency range of 2 105 to 1 Hz takes 70 min, but this can be shortened to 15 min by raising the lower frequency limit to 100 Hz. In summary, the modified K-K relation can be used to obtain Cp(E) values with a greatly reduced acquisition time. Two DOI: 10.1021/la900290b
11953
Article
Yoo et al.
Table 5. Fitting results on the Qads (from C00 integration) vs E profile by Frumkin isotherma Q0/μC cm-2
K
g
strong adsorption at ∼ 0.25 V
90
5.0 10
weak adsorption at ∼ 0.1 V
58
0.22
3
-1.5 -11
the 3rd adsorption at ∼ 0.0 V 156 85 2.0 a The fitting was performed with three superimposed isotherms; strong adsorption (near 0.25 V), weak adsorption (near 0.1 V), and the 3rd adsorption (near 0.0 V).
limitations have been identified. One is the difficulty in the location of fmax in the H2 evolution region. The other is that this scheme is only valid when the capacitive peak is perfectly symmetric. Hence, this method is not applicable in a very general way, but only for systems for which the behavior is known a priori; for instance, the routine analysis of electrocatalysts of identical or at least similar compositions. The algorithms can be implemented in an instrument using a circuitry,42 such that this method is more likely to be applied for a rapid and automatic measurement of capacitance, especially for slowly relaxing systems with a large solution resistance or porous structure.
Conclusions In this work, three analysis schemes were devised to estimate the electrochemically active surface area of a polycrystalline Pt electrode by using the potential-dependent hydrogen adsorption pseudocapacitance (Cp vs E profiles). The following points of value are summarized. (i) It is demonstrated that impedance analysis can separate hydrogen adsorption from H2 evolution by their frequency-dependence. It was found that hydrogen adsorption reaction is faster than H2 evolution; the capacitive peak associated with the former appears in the higher frequency region than that of the resistive tail that is relevant to H2 evolution reaction. (ii) Total capacitance (Cdl þ Cp) can be assessed simply from the area of the capacitive peak on imaginary capacitance plots or from the real part of the complex capacitance at the low frequency limit. This method cannot, however, be employed in the potential range where H2 evolution is severe. (iii) The CNLS fitting on both the imaginary and real capacitance plots with the appropriate equivalent circuits provides a more quantitative measurement on the pseudocapacitance. The generalized finitelength Warburg element was the most appropriate one for the description of H2 evolution, with which the Cp measurement can be extended down to -0.01 V. (iv) A faster data acquisition is possible by using the modified K-K relation, in which the impedance data at >100 Hz is ample enough for the analysis. One limitation is the difficulty in the location of fmax on the imaginary capacitance plots when H2 evolution is severe. Another limitation is that this scheme is only valid when the capacitive peak is perfectly symmetric. (42) Hladky, K.; Callow, L. M.; Dawson, J. L. Corros. J. 1980, 15, 20.
11954 DOI: 10.1021/la900290b
(v)
Estimation of the roughness factor and electrochemically active surface area can be made by using the accumulated charge derived from the double-layer region (∼0.42 V) to the lower potential limits (-0.01 V for CNLS fitting and 0.02 V for the modified K-K relation) since the accumulated charge amounts to 90-95% of the saturation value. For a more quantitative measurement, the saturation charge can be obtained by fitting the potentialdependent charge (Qads vs E) profiles with three Frumkin isotherms.
Acknowledgment. This work was supported by the WCU program through KOSEF, funded by the Ministry of Education, Science and Technology (400-2008-0230). The authors would also like to acknowledge the Research Center for Energy Conversion and Storage for financial support.
Appendix: Derivation of Eq 2 for the Complex Capacitance Analysis For an electrochemical system that satisfies causality, linearity, stability, and convergence, the real and imaginary parts of a complex function F(ω) = F0 (ω) þ jF00 (ω), F0 (ω) and F00 (ω), are correlated according to Kramers-Kronig relation:43 F 0 ðWÞ -F 0 ð¥Þ ¼ -
Z ¥ 2 ½XF 00 ðXÞ -WF 00 ðWÞ dX π 0 X 2 -W 2
ð17Þ
Here, W ωτ0, X x/x0, and the values of τ0 = 1/(2πf0) and x0 are arbitrary. The real and imaginary parts of complex capacitance are further correlated as follows: Z ¥ 2 ½XC 00 ðXÞ dX C ð0Þ -C ð¥Þ ¼ π 0 X2 Z ¥ 2 ¼ C 00 ðXÞ d½ln X π -¥ 0
0
ð18Þ
Let x = f Hz and x0 = 1 Hz, then Z ¥ 2 C 00 ðf Þ d½ln f C ð0Þ ¼ C ð¥Þ π -¥ 0
0
Z ¥ 2 C 00 ðf Þ d½log f ¼ C ð¥Þ -2:303 π -¥ 0
ð19Þ
Since C0 (0) = Ctot and C0 (¥) = C00 (¥) = 0 for a finite value of Z(¥) = Resr, total capacitance is expressed as Z Ctot ¼ -1:466
¥ -¥
C 00 ðf Þ d½log f
ð20Þ
That is, the area of capacitive peak on the imaginary capacitance plots (vs log f ) has a linear relationship with the total capacitance of the systems. (43) Macdonald, J. R. Electrochim. Acta 1993, 38, 1883.
Langmuir 2009, 25(19), 11947–11954
