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Different charge storage mechanisms at some carbon electrodes in redox active electrolyte revealed by electrochemical impedance spectroscopy
Electrochimica Acta 195 (2016) 77–84
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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Different charge storage mechanisms at some carbon electrodes in redox active electrolyte revealed by electrochemical impedance spectroscopy K. Magdi c Koši9 cek1, K. Kvastek1, V. Horvat-Radoševi c1,* Rudjer Boškovic Institute, Bijeni9 cka c. 54, 10000 Zagreb, Croatia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 14 January 2016 Received in revised form 17 February 2016 Accepted 21 February 2016 Available online 24 February 2016
Different charge storage mechanisms at some carbon electrodes in redox active electrolyte are distinguished by electrochemical impedance spectroscopy technique. Significance of monitoring capacitive impedance contribution(s) in distinguishing battery-like and pseudocapacitive charge storage mechanisms is predicted by impedance modelling and verified experimentally. Experimental verification is made by comparison of capacitive impedance contributions in impedance spectra of graphite vs. glassy carbon electrodes. Impedance measurements are made at the same potential values in the supporting H2SO4 electrolyte and H2SO4/K4Fe(CN)6 redox active electrolyte, respectively. ã 2016 Elsevier Ltd. All rights reserved.
Keywords: Charge storage mechanism ferri/ferrocyanide redox couple graphite glassy carbon electrochemical impedance spectroscopy
1. Introduction Presence of a redox couple in a supporting electrolyte has already been found valuable in the field of electrochemical capacitor, EC, and supercapacitor, SC devices [1–4]. Within this context of research, fast redox reaction coupled with high electrode capacitance(s) accomplished mostly by high surfaceporous carbon electrodes, has been found advantageous for devices with improved charge storage capacities. Different redox systems have already been tested for such a purpose. Among them, Fe(CN)63/4, I/I2, or quinone/hydroquinone, Q/HQ, are found useful, mostly due to proper formal redox potentials, high redox reaction rates, good solubilities and moderate stabilities of compounds [4–6]. It has already been pointed out that utility of an EC/SC electrode in redox active electrolyte is related to the type of involved charge storage mechanism [1,3,7]. Two types of charge storage mechanisms with different electrochemistry lying behind have generally been defined [7,8]. For the battery-like mechanism, the quantity of charge generated by redox reaction is stored by the amount of reactants in the bulk of electrolyte solution. In this case, the EC/SC electrode stores charges through a combined effect of high surface electrode capacitance and faradaic redox reaction. For
* Corresponding author. Tel.: +385 1 4561 152. E-mail addresses: [email protected] (K. M. Koši9 cek), [email protected] (K. Kvastek), [email protected] (V. Horvat-Radoševi c). 1 ISE member http://dx.doi.org/10.1016/j.electacta.2016.02.140 0013-4686/ ã 2016 Elsevier Ltd. All rights reserved.
the pseudocapacitive charge storage mechanism, however, the amount of charge generated by faradaic redox reaction is manifested as additional enhancement of electrode capacitance [3,7,8]. This phenomenon has already been explained in terms of either surface adsorption of redox species [3] or their retention at the electrode surface region by thin-layer electrochemistry, TLE, usually accomplished with highly porous electrodes [9,10]. Fast redox reaction at surface confined species with restricted mass transport makes the pseudocapacitive charge storage more beneficial for high power applications than the battery-like mechanism [1,3,10]. For evaluation of a charge storage mechanism, electrochemical techniques such as cyclic voltammetry and galvanostatic charging/discharging have usually been applied [3,7,11]. Electrochemical impedance spectroscopy technique [12], however, has been applied more sporadically, providing data focused mainly to the changes of electron transfer resistance values [5,6,13], what is generally insufficient for evaluation of any charge storage mechanism. Herein the results of measurements, modelling and comparison of impedance spectra of different charge storage mechanisms at graphite and glassy-carbon electrodes in the supporting electrolyte containing potassium ferrocyanide will be presented. K4Fe(CN)6 is the water soluble compound where negatively charged Fe(CN)64 complex ions generate one electron transfer oxidation/reduction reaction of the Fe(CN)63/4 redox couple [14]: FeII(CN)64 $ FeIII(CN)63 + e
(R-1)
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R-1 reaction is considered either like typical outer-sphere electron transfer reaction, inherently associated with fast electron transfer controlled by mass transport of redox active species toward/from the electrode surface [15–17], or slower reaction with suppressed electron transfer [18–20]. In both cases, the overall kinetics of R-1 can relatively easily be handled to derive the electrical impedance analogue, describing at the same time the battery-like charge storage in impedance terms. Electrical impedance analogue has to be modified for more complex R-1 that involves surface confined redox species corresponding to either TLE [9,10], adsorption of Fe(CN)63/4 complex ions [3,11], or even some forms of adsorbed complexes such as ferri-ferrocyanide (Prussian Blue) generated by oxidation-reduction potential cycles [21,22]. In this case, the electrical impedance analogue must take into account the amount of surface confined redox species defining a pseudocapacitance. Thus modified impedance analogue has already been applied for some other systems with surface confined redox active species [23,24], but never in the context of pseudocapacitive charge storage mechanism at carbon electrodes in a redox active electrolyte. 2. Experimental All experiments were performed in the conventional threeelectrode cell (diameter of 6 cm and volume of 250 cm3). Glassy carbon, GC, standard electrode (EG&G, USA) and graphite, G, rod (Goodfellow, UK) embedded into glass tube (diameter of 0.6 cm) working electrodes were put vertically into the cell, exposing 0.03 cm2 and 0.07 cm2 of respective geometrical surfaces to electrolyte. High surface area (20 cm2) platinum spiral in separate compartment and saturated calomel electrode, SCE, (Radiometer, Denmark) equipped with Haber-Luggin capillary and
a Pt wire pseudo-reference electrode [25] were used as the counter and reference electrode, respectively. All potentials, E, are reported with respect to the SCE. Electrochemical experiments were carried in 0.5 mol dm3 H2SO4 (Sigma-Aldrich Inc.) (pH = 0.55) as the supporting electrolyte. Balanced quantities of K4Fe(CN)6 3H2O (Sigma-Aldrich Inc.) were added directly into supporting electrolyte to give the final concentration of 5 103 mol dm3. Always freshly prepared redox active electrolyte solutions of low K4Fe(CN)6/H2SO4 ratio were used in an order to suppress formation of Fe3III[FeIII(CN)6]3 and/or free Fe3+ ions, necessary for generation of Prussian Blue, Fe4III[FeII(CN)6]3, and similar hexacyanoferrate complexes [21,22]. High-purity water with resistivity of 18 106 V cm was used for all solution preparations. Working electrode surfaces were hand-polished, sonicated in ultrapure water and slightly electrochemically pre-conditioned in 0.5 mol dm3 H2SO4. Ten potential cycles between 0.30 and 1.60 V were applied at the scan rate of 10 mV s1, finishing always by the reduction step at 0.20 V [26,27]. All experiments were performed in non-stirred electrolyte solutions, at ambient temperature of (25 2) C and oxygen free atmosphere maintained by blowing nitrogen through electrolyte solution for 30 min prior measurements. Impedance spectroscopy, EIS, data were recorded at different fixed bias potentials using 1255B FRA and 1287 ECI (Solartron Analytical, UK) under the Zplot software (Scribner Associates Inc.) control. Sine wave ac signal of 10 mV amplitude, frequency, f, ranged between 105 and 0.02 Hz and 10 frequency points measured per decade were applied. For impedance data fittings, the complex non-linear least squares, CNLS, program of Zview software (Scribner Associates Inc.) in the impedance modulus weighting mode and appropriate electrical equivalent circuits were used. Contributions
Fig. 1. EECs for an electrode showing A) battery-like; B) pseudocapacitive in combination with battery-like; C) pseudocapacitive charge storage mechanisms. Definitions of elements are given in the text.
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of experimental artefacts were corrected as before [27]. Statistical criteria for a reasonable fit were settled as low standard deviation of the overal fit, x2 < 1 103, and low value, <15%, of relative standard deviation for each impedance parameter value [27]. 3. Results and Discussion 3.1. Modelling of electrode impedance for different charge storage mechanisms in redox electrolyte For the battery-like charge storage mechanism, the amount of charge generated by a redox reaction like R-1 is stored in the bulk of electrolyte solution [1,7,8], defining the faradaic current as a function of E. The electrical analogue for electrode impedance, Zel, is in the form of electrical equivalent circuit, EEC, [12] drawn in Fig. 1A. The EEC in Fig. 1A comprises the uncompensated electrolyte resistance with possible contributions of contact and/or electrode material resistances, RV, capacitive impedance related usually to double-layer electrode impedance, Zdl, and faradaic impedance of redox reaction defined as the sum of electron transfer resistance, Ret, and diffusion impedance, Zdiff. Potential dependent pseudocapacitance contributing to Zdl/ps in Fig. 1A has been found specific for carbon electrodes and generated by fast oxidation/reduction of oxygen containing surface groups, OSGs, formed inherently at carbon surfaces in aqueous solutions [26–30]. Frequency dependences of Zdl/ps considered in the terms of constant phase element, CPE, based on the concept of capacitance distribution [31] and Zdiff describing semi-infinite linear diffusion of reacting species toward/from the electrode surface are defined as: 1 a ðivÞ ð1Þ Z dl=ps ðivÞ ¼ Q dl=ps
Z dif f ðivÞ ¼ 20:5 s ðivÞ0:5
ð2Þ
In Eqs. (1) and (2) i is imaginary unit, v = 2pf is radial frequency, while Qdl/ps, a and (20.5s )1 are fitting impedance parameters. s is the Warburg diffusion impedance parameter related to concentrations and diffusion coefficients of redox species [12,16]. Qdl/ps represents essentially double-layer capacitance/pseudocapacitance, while a describes a divergence from pure capacitive impedance response (Q = C for a = 1). Effective double-layer capacitance/pseudocapacitance, C0, is related to Q via Brug’s equations [31] for either polarisable electrode (Eq. (3a)) or electrode with kinetically controlled faradaic charge transfer (Eq. (3b)): ð1aÞ=a
C 0 ¼ Q 1=a RV
ð3aÞ
h ið1aÞ=a C 0 ¼ Q 1=a RV Ret ðRV þ Ret Þ1
ð3bÞ
When pseudocapacitive charge storage mechanism is involved, certain amount of generated charge is stored at surface-confined reacting species [3,9–11]. Irrespectively to the origin of confinement [3,10], faradaic current becomes additionally affected by the amount of surface-confined species through the E dependent state variable, G /mol cm2, leading to the modified EEC presented in Fig. 1B. The EEC in Fig. 1B describes contributions of two different charge storage mechanisms, where storage of electroactive species as surface confined species are described by G related capacitive impedance, Zscs. Electron transfer resistance is defined as Ret = Ret1 + Ret2, while semi-infinite linear diffusion of reacting species toward/from the electrode surface is described by Zdiff [23]. Frequency dependences of Zscs and Zdiff are the same as already
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defined by Eqs. (1)–(2). For fast formation of surface confined species, the EEC in Fig. 1B is reduced to the form analogous to the EEC in Fig. 1A but with diminished capacitive impedance, Zdl/ps/scs, based on the enhanced capacitance (Cdl/ps + Cscs). This case is fully equivalent to the case of a faradaic reaction with specific adsorption of reactants [12]. Pseudocapacitive charge storage mechanism would merely be operative for the reaction like R-1 proceeding as fast surface process with negligible electrolyte solution related faradaic activity. This case is described by capacitive impedance Zdl/ps/scs and the EEC in Fig. 1C [1,23,24]. According to differences between EECs in Fig. 1, distinction between two different charge storage mechanisms generated by a redox reaction like R-1 should be made by comparison of capacitive impedance contributions in impedance spectra measured in presence and absence of a redox couple in electrolyte solution. Whereas for the battery-like charge storage there would be no changes in electrode capacitive impedances, for the pseudocapacitive charge storage mechanism involved, an additional capacitive impedance would be detected for the impedance spectrum measured in the electrolyte containing redox couple. Therefore, the experiments performed in the pure supporting electrolyte should inevitably be presented for comparison purposes. Besides, due to potential dependence of Zdl/ps of most of carbon electrodes [26,27,32], impedance measurements must be performed at the same potential value(s), chosen close to the formal potential of a redox couple, E . It must be stressed that any reaction or charge storage mechanism would be impossible for evaluation not only when baseline impedance spectrum is missing [13,33,34], but also when potential of measurement is not denoted at all [5,13,33]. 3.2. Modelling of electrode impedance of carbon electrode in pure supporting electrolyte In this context, it is worth saying that electrode impedance/ frequency responses of carbon electrodes measured in absence of redox reaction are usually more complex than is expected by Eq. (1) [26–30,35–38]. Thus in impedance data analysis of some different or differently treated carbon electrodes in pure supporting electrolytes, Eq. (4) has been found more appropriate to account Zdl/ps (iv) than Eq. (1) [27,35]: !1 1 1 1 þ R þ Z ð i v Þ ð4Þ Z dl=ps ðivÞ ¼ p 1 Q 1 ðivÞa1 Eq. (4) defines the interfacial electrode impedance/frequency response in terms of two different impedance branches describing impedances of outer and inner carbon surface regions. Capacitive impedance of the outer region is described by usual CPE impedance/frequency response defined by Eq. (1), while capacitive impedance of the inner region, Zp, takes into account surface porosity. R1 is usually related to the uncompensated part of electrolyte solution due to developed surface morphology. For highly developed porous surfaces, insignificant contributions from outer parts will reduce Eq. (4) to Zp(iv). Impedance of a porous electrode/electrolyte interface can be modelled by a transmission line consisting of unlimited number of R//C components [37]. According to the De Levie's theory of cylindrical pores [39],Zp shows the following frequency dependence: Z p ðivÞ ¼ Rp ðivt Þ0:5 cothðivt Þ0:5
ð5Þ
Impedance parameters Rp and Cp = t /Rp in Eq. (5) denote electrolyte resistance within pores and double-layer capacitance at pore walls, respectively. Fitting impedance parameters Rp and time constant t are dependent on pore length, resistance per unit pore length and capacitance per unit pore length. Two last ones are dependent on specific conductivity of electrolyte, number and
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radius of pores [26,39]. It has already been shown [38] that for high values of t , Eq. (5) is reduced to the ordinary semi-infinite diffusion impedance, indicating transport limitation for electrolyte ions within pores. For low values of t , however, there is no transport limitation and double-layer capacitance at pore walls is realised fast. These two limited cases of Eq. (5) change the Eq. (4) to the forms that have already been applied in impedance analysis of different types of carbon electrodes in pure supporting electrolyte (s) [27,29,30,36]. The marked problem with application of either Eq. (4) or its reduced form(s) in evaluation of charge storage mechanisms at EC/SC electrodes in a redox active electrolyte is related to their close similarity with frequency responses of the EECs in Fig. 1, predicted for the electrode impedance in presence of redox reaction. Such similarity has already been demonstrated by common presentation of graphene paper electrode impedances measured in absence and presence of the Fe(CN)63/4 redox couple in Na2SO4 electrolyte [5] and activated carbon/H2SO4 slurry electrode impedances measured in absence and presence of H2Q/Q redox pair [6]. Although application of the correct model in these circumstances is of outmost importance, impedance data were analysed mostly by use of the EEC in Fig. 1A, providing thus faradaic impedance parameters even for measurements without redox pair in the electrolyte solution [6]. Just this complication could also be the reason why impedance analysis for the GC/carbon nanotube film electrode in the KCl/K4Fe(CN)6 electrolyte has been announced but not performed at all [36]. To avoid the problem, impedance measurements must be carried out at potentials near
E , where faradaic impedance is usually dominating at low to medium frequencies of impedance spectra. 3.3. Experimental verification of different charge storage mechanisms in the redox active electrolyte using EIS Experimental impedance spectra of GC and G electrodes in 0.5 mol dm3 H2SO4 containing 5 103 mol dm3 K4Fe(CN)6 are presented in Figs. 2 and 3 together with impedance spectra measured in pure 0.5 mol dm3 H2SO4 electrolyte. Impedance spectra are presented in forms of Bode (log ǀZelǀ and f vs. log v) (Fig. 2) and Nyquist (Zel0 vs. Zel00 ) (Fig. 3) plots, where ǀZelǀ is modulus, f is phase angle, Zel0 is real part and Zel00 is imaginary part of the measured electrode impedance, Zel. Impedance measurements were performed at E = 0.40 V, i.e. close to E of the Fe(CN)63/4 redox couple in acid sulphate solution [14]. As is shown in Fig. 2A–B, Bode plots of two different carbon electrodes measured in absence of the Fe(CN)63/4 redox couple are quite similar. At high to medium frequencies, both impedance spectra show resistive to capacitive responses what is generally expected for Zel exhibiting RV and Zdl/ps according to Eq. (1). Single difference in the type of frequency response can be noticed at low frequencies, where nearly constant log ǀZelǀ and apparent decrease of f values in the impedance spectrum of G electrode deviate from the frequency dependence defined by Eq. (1). This part can be better seen in the Nyquist plots in Fig. 3 that for capacitive
Fig. 2. Experimental and fitted Bode plots of A) GC and B) G electrodes measured at E = 0.40 VSCE in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe (CN)6.
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Fig. 3. Experimental and fitted Nyquist plots of A) GC and B) G electrodes measured at E = 0.40 VSCE in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe (CN)6.
impedances generally show only low frequency parts of impedance spectra. For GC electrode, Fig. 3A shows not ideal capacitive impedance response that is in general agreement with Eq. (2). For G electrode, a bending of impedance curve in Fig. 3B suggests an impact of some resistive contribution, probably due to more developed surface morphology with impedance/frequency response described better by Eq. (4) than Eq. (2). This can be approved by the results of CNLS fittings of Eqs. (2) or (4) to impedance spectra of GC or G electrodes shown by solid lines in Figs. 2 and 3. Fitting impedance parameter values, their standard errors and qualities of the overall fits, x2, are listed in Table 1. When K4Fe(CN)6 is present in the electrolyte solution, low to medium frequency parts of Bode plots in Fig. 2 and impedance spectra in Fig. 3 are changed according to Eq. (2), i.e. to the shapes typical for a fast, semi-infinite linear diffusion controlled faradaic reaction [12,16]. In Bode plots of both electrodes in Fig. 2, this is indicated by log ǀZelǀ with slopes of about 0.5 and f of about 45 , while in Nyquist plots, it is indicated by straight lines with slopes of about 45 (insets in Fig. 3). Similarly shaped impedance spectra have already been obtained for more or less flat carbon surfaces [16,34,40] and also for nano-structured porous electrodes in electrolyte solutions containing Fe(CN)63/4 redox couple [17,33,34]. The resemblance between faradaic impedance responses at rather different electrode surface morphologies, proved here by similar Nyquist plots in Fig. 3A and B, suggests that redox reaction of large, Fe(CN)63/4, ions is occurring mostly at the outer parts of a porous surface [17]. Bode plots in Fig. 2A and B show, however, remarkable difference between impedance spectra of two electrodes, what must obviously be related to capacitive
impedance contributions. For the GC electrode, capacitive impedance lines are almost identical when measured in either absence or presence of the Fe(CN)63/4 redox couple in electrolyte solution (denoted by arrows in Fig. 2A). Similar phenomenon indicating the battery-like charge storage mechanism, can also be noticed in Bode plots of the graphene paper electrode measured in pure Na2SO4 and Na2SO4/Fe(CN)63/4 electrolyte solutions but the electrode was inaccurately stated as pseudocapacitive [5]. For the impedance spectrum of G electrode measured in presence of redox couple, however, there is significant shift of capacitive impedance line toward one order of magnitude lower values (denoted by shaded area in Fig. 2B), indicating appearance of pseudocapacitance. CNLS fittings to experimental impedance spectra of GC and G electrodes measured in presence of the Fe(CN)63/4 redox couple were done using the EECs in Fig. 1A and B (reduced form). The results are shown by solid lines in Figs. 2 and 3 and impedance parameter values listed in Table 2. The most remarkable result of Table 2 concerns the capacitance related value Q, that is for G electrode more than order of magnitude higher in comparison to Qdl/ps value for the same electrode in pure electrolyte (cf. Table 1). According to the EEC in Fig. 1B this has to be ascribed to the pseudocapacitance related Qdl/ ps/scs value of G electrode generated in presence of the redox couple. Similarly increased electrode capacitance can also be discerned from the list of superfluous number of fitting parameter values for the activated carbon/H2SO4 slurry electrode measured at the open circuit potential in absence and presence of the HQ/Q redox pair [6]. Although just increase of electrode capacitance should be essential for denomination of electrode as pseudocapacitive, it has not been even mentioned in the given discussion
Table 1 Impedance parameter values and qualities of the overall fits, x2, calculated by CNLS fittings (105–0.02 Hz) of denoted equations to impedance spectra of GC and G electrodes in 0.5 mol dm3 H2SO4 presented in Figs. 2 and 3. Electrode GC G
RV + Eq. (2) RV + Eq. (4)
RV/V cm2
103 Qdl/ps/V1 sa cm2
a
R1/kV cm2
Rd/kV cm2
t /s
104 x2
0.388 0.003 0.724 0.002
2.78 0.03 0.661 0.005
0.935 0.001 0.951 0.001
– 2.70 0.07
– 3.6 0.4
– 30 7
8.5 8.4
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Table 2 Impedance parameter values and qualities of the overall fits, x2, calculated by CNLS fittings (105–0.02 Hz) of denoted EECs to impedance spectra of GC/Fe(CN)63/4 and G/Fe (CN)63/4 electrodes in 0.5 mol dm3 H2SO4 presented in Figs. 2 and 3. Electrode
EEC
RV/V cm2
103 Qdl/ps/V1 sa cm2
a
Ret/ kV cm2
103 (20.5s )1/V1 s0.5 cm2
104 x2
GC/Fe(CN)63/4
Fig. 1A
0.379 0.001
0.834 0.003
0.019 0.001
10.97 0.09
3.1
G/Fe(CN)63/4
Fig. 1B
0.740 0.002
5.47 0.01 103 Qdl/ps/scs/ V1 sa cm2 18.0 0.2
0.86 0.02
0.14 0.02
14.6 0.6
7.5
Fig. 4. E dependence of kinetic impedance parameter values (20.5s )1 and Ret obtained by CNLS fittings of the EECs in Fig. 1A and B to impedance spectra of A) GC and B) G electrodes in 0.5 mol dm3 H2SO4 in presence of 5 103 mol dm3 K4Fe(CN)6.
dealing completely with small and irrelevant changes of diffusion and various resistance values [6]. Higher significance of electrode capacitance vs. kinetic terms in evaluation of the charge storage mechanism can also be seen after comparison of Figs. 4 and 5, where potential dependences of kinetic impedance parameter values, Ret and (20.5s )1, are confronted to potential dependences of C0 values for two carbon electrodes. The range of potentials explored was E = (0.40 0.20) V, what is somewhat higher than E 0.10 V stated as effective voltage range for a redox reaction based pseudocapacitance [1].
Kinetic impedance parameter values shown in Fig. 4 were calculated by the CNLS fittings of the EECs in Figs. 1A and 1B to experimental impedance spectra of GC and G electrodes, measured in presence of the Fe(CN)63/4 redox couple at given potentials. Qualities of fits were similar to that given in Table 2, while standard errors for these two fitted values are denoted by bars in Fig. 4. It is shown in Fig. 4 that faradaic impedance parameters Ret and s of both carbon electrodes show minimums at E and infinite values far from E , what is characteristic for reversible/quasy-reversible redox reactions [12]. Values of s at E are similar for both
Fig. 5. C0 vs. E of A) GC and B) G electrodes in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe(CN)6. C0 values are calculated by Eqs. (3a) or (3b) and data from Tables 1 or 2, respectively.
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electrodes (64 and 48 V s0.5 cm2), while at the same time, Ret value at E is seven times higher for G (140 V cm2) than for GC (19 V cm2) electrode. Although these data suggest some decrease of the electrolyte solution related faradic activity for G vs. GC electrode, they do not point towards any particular type of the charge storage mechanism. The most important results for evaluation of the charge storage mechanisms are shown in Fig. 5. Fig. 5 shows potential dependences of C0 values of two carbon electrodes measured in absence and presence of the Fe(CN)63/4 redox couple in electrolyte solution. C0 values were calculated using either Eq. (3a) or Eq. (3b) and the corresponding CNLS fitted impedance parameter values. Due to complex relations between fitting parameters in Eq. (3a) and Eq. (3b), only calculated values of C0 without errors are presented in Fig. 5. In spite of probably more developed morphology of G electrode, Fig. 5 shows higher C0 values for the GC electrode, suggesting higher contribution of the OSGs related pseudocapacitance at GC vs. G electrode. This is also supported by formation of “slight maximums” at 0.30 V [26,27] observed in Fig. 5A in either presence or absence of redox couple in the electrolyte solution. The key result of Fig. 5, however, is related to comparison of C0 values of each electrode obtained in presence and absence of the Fe(CN)63/4 redox couple in electrolyte solution. For the GC electrode, Fig. 5A shows similar C0 values at all examined potentials, what has already been expected for the battery-like charge storage mechanism. For the G electrode, however, Fig. 5B shows a prominent difference in C0 values at E = (0.40 0.10) V. Compared to C0 obtained in the pure supporting electrolyte, C0 obtained in presence of the Fe(CN)63/4 redox couple traced the peak shaped curve with generally higher values and about order of magnitude higher C0 value at the peak potential E E . Significantly increased C0 values appearing in the voltage range E 0.10 V are indicative for the redox reaction based pseudocapacitance [1], what in turn indicates contribution of the pseudocapacitive charge storage mechanism for G electrode in the Fe(CN)63/4 redox active electrolyte. 4. Conclusions Electrochemical impedance spectroscopy technique can be used for distinguishing battery-like and pseudocapacitive charge storage mechanisms at carbon electrode(s) in redox active electrolyte. As is predicted by impedance modelling and shown experimentally for GC and G electrodes in H2SO4/K4Fe(CN)6 redox active electrolyte, distinguishing between charge storage mechanisms has to be performed by monitoring capacitive electrode impedance contributions in experimental impedance spectra. Comparison must be made between impedance spectra measured both in absence and presence of redox couple in the supporting electrolyte solution and at the same potential values near E . Almost no changes of capacitive impedance are expected for the battery-like charge storage mechanism, while significant decrease of capacitive impedance is expected when the pseudocapacitive charge storage mechanisms is involved. Conflict of interest None Acknowledgement Financial support of the Croatian Science Foundation under the project ESUPCAP (8825–2014) is acknowledged.
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Liobuashevsky, I. Willner, Electromechanics of a redox-active rotaxane in a monolayer assembly on an electrodes, J. Am. Chem. Soc 126 (2004) 15520. [25] Horvat-Radoševi c K. Kvastek, Role of a Pt-probe pseudo-reference electrode in impedance measurements of Pt and polyaniline (PANI) modified electrodes, J. Electroanal. Chem. 591 (2006) 217. [26] M.G. Sullivan, R. Kötz, O. Haas, Thick active layers of electrochemically modified glassy carbon; electrochemical impedance study, J. Electrochem. Soc 147 (2000) 308. [27] K. Magdi c, K. Kvastek, V. Horvat-Radoševi c, Concept of spatial surface heterogeneity in impedance modelling of electrochemically activated glasslike carbon electrode, Electrochim. Acta 117 (2014) 310. [28] C.-H. Kim, S.-I. Pyun, H.-C. Shin, Kinetics of double-layer charging/discharging of activated carbon electrodes. Role of surface acidic functional groups, J. Electrochem. Soc 149 (2002) A93. [29] Y.-R. Nian, H. 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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Different charge storage mechanisms at some carbon electrodes in redox active electrolyte revealed by electrochemical impedance spectroscopy K. Magdi c Koši9 cek1, K. Kvastek1, V. Horvat-Radoševi c1,* Rudjer Boškovic Institute, Bijeni9 cka c. 54, 10000 Zagreb, Croatia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 14 January 2016 Received in revised form 17 February 2016 Accepted 21 February 2016 Available online 24 February 2016
Different charge storage mechanisms at some carbon electrodes in redox active electrolyte are distinguished by electrochemical impedance spectroscopy technique. Significance of monitoring capacitive impedance contribution(s) in distinguishing battery-like and pseudocapacitive charge storage mechanisms is predicted by impedance modelling and verified experimentally. Experimental verification is made by comparison of capacitive impedance contributions in impedance spectra of graphite vs. glassy carbon electrodes. Impedance measurements are made at the same potential values in the supporting H2SO4 electrolyte and H2SO4/K4Fe(CN)6 redox active electrolyte, respectively. ã 2016 Elsevier Ltd. All rights reserved.
Keywords: Charge storage mechanism ferri/ferrocyanide redox couple graphite glassy carbon electrochemical impedance spectroscopy
1. Introduction Presence of a redox couple in a supporting electrolyte has already been found valuable in the field of electrochemical capacitor, EC, and supercapacitor, SC devices [1–4]. Within this context of research, fast redox reaction coupled with high electrode capacitance(s) accomplished mostly by high surfaceporous carbon electrodes, has been found advantageous for devices with improved charge storage capacities. Different redox systems have already been tested for such a purpose. Among them, Fe(CN)63/4, I/I2, or quinone/hydroquinone, Q/HQ, are found useful, mostly due to proper formal redox potentials, high redox reaction rates, good solubilities and moderate stabilities of compounds [4–6]. It has already been pointed out that utility of an EC/SC electrode in redox active electrolyte is related to the type of involved charge storage mechanism [1,3,7]. Two types of charge storage mechanisms with different electrochemistry lying behind have generally been defined [7,8]. For the battery-like mechanism, the quantity of charge generated by redox reaction is stored by the amount of reactants in the bulk of electrolyte solution. In this case, the EC/SC electrode stores charges through a combined effect of high surface electrode capacitance and faradaic redox reaction. For
* Corresponding author. Tel.: +385 1 4561 152. E-mail addresses: [email protected] (K. M. Koši9 cek), [email protected] (K. Kvastek), [email protected] (V. Horvat-Radoševi c). 1 ISE member http://dx.doi.org/10.1016/j.electacta.2016.02.140 0013-4686/ ã 2016 Elsevier Ltd. All rights reserved.
the pseudocapacitive charge storage mechanism, however, the amount of charge generated by faradaic redox reaction is manifested as additional enhancement of electrode capacitance [3,7,8]. This phenomenon has already been explained in terms of either surface adsorption of redox species [3] or their retention at the electrode surface region by thin-layer electrochemistry, TLE, usually accomplished with highly porous electrodes [9,10]. Fast redox reaction at surface confined species with restricted mass transport makes the pseudocapacitive charge storage more beneficial for high power applications than the battery-like mechanism [1,3,10]. For evaluation of a charge storage mechanism, electrochemical techniques such as cyclic voltammetry and galvanostatic charging/discharging have usually been applied [3,7,11]. Electrochemical impedance spectroscopy technique [12], however, has been applied more sporadically, providing data focused mainly to the changes of electron transfer resistance values [5,6,13], what is generally insufficient for evaluation of any charge storage mechanism. Herein the results of measurements, modelling and comparison of impedance spectra of different charge storage mechanisms at graphite and glassy-carbon electrodes in the supporting electrolyte containing potassium ferrocyanide will be presented. K4Fe(CN)6 is the water soluble compound where negatively charged Fe(CN)64 complex ions generate one electron transfer oxidation/reduction reaction of the Fe(CN)63/4 redox couple [14]: FeII(CN)64 $ FeIII(CN)63 + e
(R-1)
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R-1 reaction is considered either like typical outer-sphere electron transfer reaction, inherently associated with fast electron transfer controlled by mass transport of redox active species toward/from the electrode surface [15–17], or slower reaction with suppressed electron transfer [18–20]. In both cases, the overall kinetics of R-1 can relatively easily be handled to derive the electrical impedance analogue, describing at the same time the battery-like charge storage in impedance terms. Electrical impedance analogue has to be modified for more complex R-1 that involves surface confined redox species corresponding to either TLE [9,10], adsorption of Fe(CN)63/4 complex ions [3,11], or even some forms of adsorbed complexes such as ferri-ferrocyanide (Prussian Blue) generated by oxidation-reduction potential cycles [21,22]. In this case, the electrical impedance analogue must take into account the amount of surface confined redox species defining a pseudocapacitance. Thus modified impedance analogue has already been applied for some other systems with surface confined redox active species [23,24], but never in the context of pseudocapacitive charge storage mechanism at carbon electrodes in a redox active electrolyte. 2. Experimental All experiments were performed in the conventional threeelectrode cell (diameter of 6 cm and volume of 250 cm3). Glassy carbon, GC, standard electrode (EG&G, USA) and graphite, G, rod (Goodfellow, UK) embedded into glass tube (diameter of 0.6 cm) working electrodes were put vertically into the cell, exposing 0.03 cm2 and 0.07 cm2 of respective geometrical surfaces to electrolyte. High surface area (20 cm2) platinum spiral in separate compartment and saturated calomel electrode, SCE, (Radiometer, Denmark) equipped with Haber-Luggin capillary and
a Pt wire pseudo-reference electrode [25] were used as the counter and reference electrode, respectively. All potentials, E, are reported with respect to the SCE. Electrochemical experiments were carried in 0.5 mol dm3 H2SO4 (Sigma-Aldrich Inc.) (pH = 0.55) as the supporting electrolyte. Balanced quantities of K4Fe(CN)6 3H2O (Sigma-Aldrich Inc.) were added directly into supporting electrolyte to give the final concentration of 5 103 mol dm3. Always freshly prepared redox active electrolyte solutions of low K4Fe(CN)6/H2SO4 ratio were used in an order to suppress formation of Fe3III[FeIII(CN)6]3 and/or free Fe3+ ions, necessary for generation of Prussian Blue, Fe4III[FeII(CN)6]3, and similar hexacyanoferrate complexes [21,22]. High-purity water with resistivity of 18 106 V cm was used for all solution preparations. Working electrode surfaces were hand-polished, sonicated in ultrapure water and slightly electrochemically pre-conditioned in 0.5 mol dm3 H2SO4. Ten potential cycles between 0.30 and 1.60 V were applied at the scan rate of 10 mV s1, finishing always by the reduction step at 0.20 V [26,27]. All experiments were performed in non-stirred electrolyte solutions, at ambient temperature of (25 2) C and oxygen free atmosphere maintained by blowing nitrogen through electrolyte solution for 30 min prior measurements. Impedance spectroscopy, EIS, data were recorded at different fixed bias potentials using 1255B FRA and 1287 ECI (Solartron Analytical, UK) under the Zplot software (Scribner Associates Inc.) control. Sine wave ac signal of 10 mV amplitude, frequency, f, ranged between 105 and 0.02 Hz and 10 frequency points measured per decade were applied. For impedance data fittings, the complex non-linear least squares, CNLS, program of Zview software (Scribner Associates Inc.) in the impedance modulus weighting mode and appropriate electrical equivalent circuits were used. Contributions
Fig. 1. EECs for an electrode showing A) battery-like; B) pseudocapacitive in combination with battery-like; C) pseudocapacitive charge storage mechanisms. Definitions of elements are given in the text.
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of experimental artefacts were corrected as before [27]. Statistical criteria for a reasonable fit were settled as low standard deviation of the overal fit, x2 < 1 103, and low value, <15%, of relative standard deviation for each impedance parameter value [27]. 3. Results and Discussion 3.1. Modelling of electrode impedance for different charge storage mechanisms in redox electrolyte For the battery-like charge storage mechanism, the amount of charge generated by a redox reaction like R-1 is stored in the bulk of electrolyte solution [1,7,8], defining the faradaic current as a function of E. The electrical analogue for electrode impedance, Zel, is in the form of electrical equivalent circuit, EEC, [12] drawn in Fig. 1A. The EEC in Fig. 1A comprises the uncompensated electrolyte resistance with possible contributions of contact and/or electrode material resistances, RV, capacitive impedance related usually to double-layer electrode impedance, Zdl, and faradaic impedance of redox reaction defined as the sum of electron transfer resistance, Ret, and diffusion impedance, Zdiff. Potential dependent pseudocapacitance contributing to Zdl/ps in Fig. 1A has been found specific for carbon electrodes and generated by fast oxidation/reduction of oxygen containing surface groups, OSGs, formed inherently at carbon surfaces in aqueous solutions [26–30]. Frequency dependences of Zdl/ps considered in the terms of constant phase element, CPE, based on the concept of capacitance distribution [31] and Zdiff describing semi-infinite linear diffusion of reacting species toward/from the electrode surface are defined as: 1 a ðivÞ ð1Þ Z dl=ps ðivÞ ¼ Q dl=ps
Z dif f ðivÞ ¼ 20:5 s ðivÞ0:5
ð2Þ
In Eqs. (1) and (2) i is imaginary unit, v = 2pf is radial frequency, while Qdl/ps, a and (20.5s )1 are fitting impedance parameters. s is the Warburg diffusion impedance parameter related to concentrations and diffusion coefficients of redox species [12,16]. Qdl/ps represents essentially double-layer capacitance/pseudocapacitance, while a describes a divergence from pure capacitive impedance response (Q = C for a = 1). Effective double-layer capacitance/pseudocapacitance, C0, is related to Q via Brug’s equations [31] for either polarisable electrode (Eq. (3a)) or electrode with kinetically controlled faradaic charge transfer (Eq. (3b)): ð1aÞ=a
C 0 ¼ Q 1=a RV
ð3aÞ
h ið1aÞ=a C 0 ¼ Q 1=a RV Ret ðRV þ Ret Þ1
ð3bÞ
When pseudocapacitive charge storage mechanism is involved, certain amount of generated charge is stored at surface-confined reacting species [3,9–11]. Irrespectively to the origin of confinement [3,10], faradaic current becomes additionally affected by the amount of surface-confined species through the E dependent state variable, G /mol cm2, leading to the modified EEC presented in Fig. 1B. The EEC in Fig. 1B describes contributions of two different charge storage mechanisms, where storage of electroactive species as surface confined species are described by G related capacitive impedance, Zscs. Electron transfer resistance is defined as Ret = Ret1 + Ret2, while semi-infinite linear diffusion of reacting species toward/from the electrode surface is described by Zdiff [23]. Frequency dependences of Zscs and Zdiff are the same as already
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defined by Eqs. (1)–(2). For fast formation of surface confined species, the EEC in Fig. 1B is reduced to the form analogous to the EEC in Fig. 1A but with diminished capacitive impedance, Zdl/ps/scs, based on the enhanced capacitance (Cdl/ps + Cscs). This case is fully equivalent to the case of a faradaic reaction with specific adsorption of reactants [12]. Pseudocapacitive charge storage mechanism would merely be operative for the reaction like R-1 proceeding as fast surface process with negligible electrolyte solution related faradaic activity. This case is described by capacitive impedance Zdl/ps/scs and the EEC in Fig. 1C [1,23,24]. According to differences between EECs in Fig. 1, distinction between two different charge storage mechanisms generated by a redox reaction like R-1 should be made by comparison of capacitive impedance contributions in impedance spectra measured in presence and absence of a redox couple in electrolyte solution. Whereas for the battery-like charge storage there would be no changes in electrode capacitive impedances, for the pseudocapacitive charge storage mechanism involved, an additional capacitive impedance would be detected for the impedance spectrum measured in the electrolyte containing redox couple. Therefore, the experiments performed in the pure supporting electrolyte should inevitably be presented for comparison purposes. Besides, due to potential dependence of Zdl/ps of most of carbon electrodes [26,27,32], impedance measurements must be performed at the same potential value(s), chosen close to the formal potential of a redox couple, E . It must be stressed that any reaction or charge storage mechanism would be impossible for evaluation not only when baseline impedance spectrum is missing [13,33,34], but also when potential of measurement is not denoted at all [5,13,33]. 3.2. Modelling of electrode impedance of carbon electrode in pure supporting electrolyte In this context, it is worth saying that electrode impedance/ frequency responses of carbon electrodes measured in absence of redox reaction are usually more complex than is expected by Eq. (1) [26–30,35–38]. Thus in impedance data analysis of some different or differently treated carbon electrodes in pure supporting electrolytes, Eq. (4) has been found more appropriate to account Zdl/ps (iv) than Eq. (1) [27,35]: !1 1 1 1 þ R þ Z ð i v Þ ð4Þ Z dl=ps ðivÞ ¼ p 1 Q 1 ðivÞa1 Eq. (4) defines the interfacial electrode impedance/frequency response in terms of two different impedance branches describing impedances of outer and inner carbon surface regions. Capacitive impedance of the outer region is described by usual CPE impedance/frequency response defined by Eq. (1), while capacitive impedance of the inner region, Zp, takes into account surface porosity. R1 is usually related to the uncompensated part of electrolyte solution due to developed surface morphology. For highly developed porous surfaces, insignificant contributions from outer parts will reduce Eq. (4) to Zp(iv). Impedance of a porous electrode/electrolyte interface can be modelled by a transmission line consisting of unlimited number of R//C components [37]. According to the De Levie's theory of cylindrical pores [39],Zp shows the following frequency dependence: Z p ðivÞ ¼ Rp ðivt Þ0:5 cothðivt Þ0:5
ð5Þ
Impedance parameters Rp and Cp = t /Rp in Eq. (5) denote electrolyte resistance within pores and double-layer capacitance at pore walls, respectively. Fitting impedance parameters Rp and time constant t are dependent on pore length, resistance per unit pore length and capacitance per unit pore length. Two last ones are dependent on specific conductivity of electrolyte, number and
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radius of pores [26,39]. It has already been shown [38] that for high values of t , Eq. (5) is reduced to the ordinary semi-infinite diffusion impedance, indicating transport limitation for electrolyte ions within pores. For low values of t , however, there is no transport limitation and double-layer capacitance at pore walls is realised fast. These two limited cases of Eq. (5) change the Eq. (4) to the forms that have already been applied in impedance analysis of different types of carbon electrodes in pure supporting electrolyte (s) [27,29,30,36]. The marked problem with application of either Eq. (4) or its reduced form(s) in evaluation of charge storage mechanisms at EC/SC electrodes in a redox active electrolyte is related to their close similarity with frequency responses of the EECs in Fig. 1, predicted for the electrode impedance in presence of redox reaction. Such similarity has already been demonstrated by common presentation of graphene paper electrode impedances measured in absence and presence of the Fe(CN)63/4 redox couple in Na2SO4 electrolyte [5] and activated carbon/H2SO4 slurry electrode impedances measured in absence and presence of H2Q/Q redox pair [6]. Although application of the correct model in these circumstances is of outmost importance, impedance data were analysed mostly by use of the EEC in Fig. 1A, providing thus faradaic impedance parameters even for measurements without redox pair in the electrolyte solution [6]. Just this complication could also be the reason why impedance analysis for the GC/carbon nanotube film electrode in the KCl/K4Fe(CN)6 electrolyte has been announced but not performed at all [36]. To avoid the problem, impedance measurements must be carried out at potentials near
E , where faradaic impedance is usually dominating at low to medium frequencies of impedance spectra. 3.3. Experimental verification of different charge storage mechanisms in the redox active electrolyte using EIS Experimental impedance spectra of GC and G electrodes in 0.5 mol dm3 H2SO4 containing 5 103 mol dm3 K4Fe(CN)6 are presented in Figs. 2 and 3 together with impedance spectra measured in pure 0.5 mol dm3 H2SO4 electrolyte. Impedance spectra are presented in forms of Bode (log ǀZelǀ and f vs. log v) (Fig. 2) and Nyquist (Zel0 vs. Zel00 ) (Fig. 3) plots, where ǀZelǀ is modulus, f is phase angle, Zel0 is real part and Zel00 is imaginary part of the measured electrode impedance, Zel. Impedance measurements were performed at E = 0.40 V, i.e. close to E of the Fe(CN)63/4 redox couple in acid sulphate solution [14]. As is shown in Fig. 2A–B, Bode plots of two different carbon electrodes measured in absence of the Fe(CN)63/4 redox couple are quite similar. At high to medium frequencies, both impedance spectra show resistive to capacitive responses what is generally expected for Zel exhibiting RV and Zdl/ps according to Eq. (1). Single difference in the type of frequency response can be noticed at low frequencies, where nearly constant log ǀZelǀ and apparent decrease of f values in the impedance spectrum of G electrode deviate from the frequency dependence defined by Eq. (1). This part can be better seen in the Nyquist plots in Fig. 3 that for capacitive
Fig. 2. Experimental and fitted Bode plots of A) GC and B) G electrodes measured at E = 0.40 VSCE in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe (CN)6.
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Fig. 3. Experimental and fitted Nyquist plots of A) GC and B) G electrodes measured at E = 0.40 VSCE in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe (CN)6.
impedances generally show only low frequency parts of impedance spectra. For GC electrode, Fig. 3A shows not ideal capacitive impedance response that is in general agreement with Eq. (2). For G electrode, a bending of impedance curve in Fig. 3B suggests an impact of some resistive contribution, probably due to more developed surface morphology with impedance/frequency response described better by Eq. (4) than Eq. (2). This can be approved by the results of CNLS fittings of Eqs. (2) or (4) to impedance spectra of GC or G electrodes shown by solid lines in Figs. 2 and 3. Fitting impedance parameter values, their standard errors and qualities of the overall fits, x2, are listed in Table 1. When K4Fe(CN)6 is present in the electrolyte solution, low to medium frequency parts of Bode plots in Fig. 2 and impedance spectra in Fig. 3 are changed according to Eq. (2), i.e. to the shapes typical for a fast, semi-infinite linear diffusion controlled faradaic reaction [12,16]. In Bode plots of both electrodes in Fig. 2, this is indicated by log ǀZelǀ with slopes of about 0.5 and f of about 45 , while in Nyquist plots, it is indicated by straight lines with slopes of about 45 (insets in Fig. 3). Similarly shaped impedance spectra have already been obtained for more or less flat carbon surfaces [16,34,40] and also for nano-structured porous electrodes in electrolyte solutions containing Fe(CN)63/4 redox couple [17,33,34]. The resemblance between faradaic impedance responses at rather different electrode surface morphologies, proved here by similar Nyquist plots in Fig. 3A and B, suggests that redox reaction of large, Fe(CN)63/4, ions is occurring mostly at the outer parts of a porous surface [17]. Bode plots in Fig. 2A and B show, however, remarkable difference between impedance spectra of two electrodes, what must obviously be related to capacitive
impedance contributions. For the GC electrode, capacitive impedance lines are almost identical when measured in either absence or presence of the Fe(CN)63/4 redox couple in electrolyte solution (denoted by arrows in Fig. 2A). Similar phenomenon indicating the battery-like charge storage mechanism, can also be noticed in Bode plots of the graphene paper electrode measured in pure Na2SO4 and Na2SO4/Fe(CN)63/4 electrolyte solutions but the electrode was inaccurately stated as pseudocapacitive [5]. For the impedance spectrum of G electrode measured in presence of redox couple, however, there is significant shift of capacitive impedance line toward one order of magnitude lower values (denoted by shaded area in Fig. 2B), indicating appearance of pseudocapacitance. CNLS fittings to experimental impedance spectra of GC and G electrodes measured in presence of the Fe(CN)63/4 redox couple were done using the EECs in Fig. 1A and B (reduced form). The results are shown by solid lines in Figs. 2 and 3 and impedance parameter values listed in Table 2. The most remarkable result of Table 2 concerns the capacitance related value Q, that is for G electrode more than order of magnitude higher in comparison to Qdl/ps value for the same electrode in pure electrolyte (cf. Table 1). According to the EEC in Fig. 1B this has to be ascribed to the pseudocapacitance related Qdl/ ps/scs value of G electrode generated in presence of the redox couple. Similarly increased electrode capacitance can also be discerned from the list of superfluous number of fitting parameter values for the activated carbon/H2SO4 slurry electrode measured at the open circuit potential in absence and presence of the HQ/Q redox pair [6]. Although just increase of electrode capacitance should be essential for denomination of electrode as pseudocapacitive, it has not been even mentioned in the given discussion
Table 1 Impedance parameter values and qualities of the overall fits, x2, calculated by CNLS fittings (105–0.02 Hz) of denoted equations to impedance spectra of GC and G electrodes in 0.5 mol dm3 H2SO4 presented in Figs. 2 and 3. Electrode GC G
RV + Eq. (2) RV + Eq. (4)
RV/V cm2
103 Qdl/ps/V1 sa cm2
a
R1/kV cm2
Rd/kV cm2
t /s
104 x2
0.388 0.003 0.724 0.002
2.78 0.03 0.661 0.005
0.935 0.001 0.951 0.001
– 2.70 0.07
– 3.6 0.4
– 30 7
8.5 8.4
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Table 2 Impedance parameter values and qualities of the overall fits, x2, calculated by CNLS fittings (105–0.02 Hz) of denoted EECs to impedance spectra of GC/Fe(CN)63/4 and G/Fe (CN)63/4 electrodes in 0.5 mol dm3 H2SO4 presented in Figs. 2 and 3. Electrode
EEC
RV/V cm2
103 Qdl/ps/V1 sa cm2
a
Ret/ kV cm2
103 (20.5s )1/V1 s0.5 cm2
104 x2
GC/Fe(CN)63/4
Fig. 1A
0.379 0.001
0.834 0.003
0.019 0.001
10.97 0.09
3.1
G/Fe(CN)63/4
Fig. 1B
0.740 0.002
5.47 0.01 103 Qdl/ps/scs/ V1 sa cm2 18.0 0.2
0.86 0.02
0.14 0.02
14.6 0.6
7.5
Fig. 4. E dependence of kinetic impedance parameter values (20.5s )1 and Ret obtained by CNLS fittings of the EECs in Fig. 1A and B to impedance spectra of A) GC and B) G electrodes in 0.5 mol dm3 H2SO4 in presence of 5 103 mol dm3 K4Fe(CN)6.
dealing completely with small and irrelevant changes of diffusion and various resistance values [6]. Higher significance of electrode capacitance vs. kinetic terms in evaluation of the charge storage mechanism can also be seen after comparison of Figs. 4 and 5, where potential dependences of kinetic impedance parameter values, Ret and (20.5s )1, are confronted to potential dependences of C0 values for two carbon electrodes. The range of potentials explored was E = (0.40 0.20) V, what is somewhat higher than E 0.10 V stated as effective voltage range for a redox reaction based pseudocapacitance [1].
Kinetic impedance parameter values shown in Fig. 4 were calculated by the CNLS fittings of the EECs in Figs. 1A and 1B to experimental impedance spectra of GC and G electrodes, measured in presence of the Fe(CN)63/4 redox couple at given potentials. Qualities of fits were similar to that given in Table 2, while standard errors for these two fitted values are denoted by bars in Fig. 4. It is shown in Fig. 4 that faradaic impedance parameters Ret and s of both carbon electrodes show minimums at E and infinite values far from E , what is characteristic for reversible/quasy-reversible redox reactions [12]. Values of s at E are similar for both
Fig. 5. C0 vs. E of A) GC and B) G electrodes in 0.5 mol dm3 H2SO4 in absence and presence of 5 103 mol dm3 K4Fe(CN)6. C0 values are calculated by Eqs. (3a) or (3b) and data from Tables 1 or 2, respectively.
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electrodes (64 and 48 V s0.5 cm2), while at the same time, Ret value at E is seven times higher for G (140 V cm2) than for GC (19 V cm2) electrode. Although these data suggest some decrease of the electrolyte solution related faradic activity for G vs. GC electrode, they do not point towards any particular type of the charge storage mechanism. The most important results for evaluation of the charge storage mechanisms are shown in Fig. 5. Fig. 5 shows potential dependences of C0 values of two carbon electrodes measured in absence and presence of the Fe(CN)63/4 redox couple in electrolyte solution. C0 values were calculated using either Eq. (3a) or Eq. (3b) and the corresponding CNLS fitted impedance parameter values. Due to complex relations between fitting parameters in Eq. (3a) and Eq. (3b), only calculated values of C0 without errors are presented in Fig. 5. In spite of probably more developed morphology of G electrode, Fig. 5 shows higher C0 values for the GC electrode, suggesting higher contribution of the OSGs related pseudocapacitance at GC vs. G electrode. This is also supported by formation of “slight maximums” at 0.30 V [26,27] observed in Fig. 5A in either presence or absence of redox couple in the electrolyte solution. The key result of Fig. 5, however, is related to comparison of C0 values of each electrode obtained in presence and absence of the Fe(CN)63/4 redox couple in electrolyte solution. For the GC electrode, Fig. 5A shows similar C0 values at all examined potentials, what has already been expected for the battery-like charge storage mechanism. For the G electrode, however, Fig. 5B shows a prominent difference in C0 values at E = (0.40 0.10) V. Compared to C0 obtained in the pure supporting electrolyte, C0 obtained in presence of the Fe(CN)63/4 redox couple traced the peak shaped curve with generally higher values and about order of magnitude higher C0 value at the peak potential E E . Significantly increased C0 values appearing in the voltage range E 0.10 V are indicative for the redox reaction based pseudocapacitance [1], what in turn indicates contribution of the pseudocapacitive charge storage mechanism for G electrode in the Fe(CN)63/4 redox active electrolyte. 4. Conclusions Electrochemical impedance spectroscopy technique can be used for distinguishing battery-like and pseudocapacitive charge storage mechanisms at carbon electrode(s) in redox active electrolyte. As is predicted by impedance modelling and shown experimentally for GC and G electrodes in H2SO4/K4Fe(CN)6 redox active electrolyte, distinguishing between charge storage mechanisms has to be performed by monitoring capacitive electrode impedance contributions in experimental impedance spectra. Comparison must be made between impedance spectra measured both in absence and presence of redox couple in the supporting electrolyte solution and at the same potential values near E . Almost no changes of capacitive impedance are expected for the battery-like charge storage mechanism, while significant decrease of capacitive impedance is expected when the pseudocapacitive charge storage mechanisms is involved. Conflict of interest None Acknowledgement Financial support of the Croatian Science Foundation under the project ESUPCAP (8825–2014) is acknowledged.
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