Fe-containing polyimide-based high-performance ORR catalysts in acidic medium: a kinetic approach to study the durability of catalysts

Abstract

The ORR activity and durability of Fe-containing non-precious N-doped carbon catalysts in acidic medium were studied using a rotating ring-disk electrode voltammetry and XPS technique. The catalysts (Fe/PI) were synthesised from the pyrolysis of the Fe(acac)₃ and polyimide nanoparticle (PI) mixture. The catalytic activity and durability of Fe/PI are superior to that of the conventional phthalocyanine-based catalyst. The onset potential of ORR was 0.915 V vs. RHE in 0.5 M H₂SO₄ which is very close to that of a commercially available Pt/C catalyst. The Fe/PI catalyst sustains its activity and stability even after 11 110 repeating potential steps between 0.6 and 1.0 V vs. RHE in O₂-saturated 0.5 M H₂SO₄ and 1110 potential cycles between 1.0 and 1.5 V vs. RHE in argon-saturated 0.5 M H₂SO₄, respectively. The kinetic and mechanistic analyses of the ORR on this catalyst indicate that the ORR, as a whole, follows a 4-electron (parallel) pathway. The N 1s XPS spectra before and after the durability test indicate that pyridinic and graphite-like nitrogens take part in improving the ORR activity, whereas nitrogen oxides have a negative role in the ORR. The loss of ORR activity was observed after the acid washing of the catalysts, which suggests the role of Fe in the overall 4-electron reduction of O₂.

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1. Introduction

Recently, many researchers have focused on developing non-precious metal catalysts for oxygen reduction reaction (ORR) in polymer electrolyte membrane fuel cells in order to overcome the cost and scarcity of platinum and its alloy catalysts. Non-precious metal nitrogen-doped carbon catalysts have been proposed as promising catalysts for this purpose.^1–18 The ORR activity of these catalysts is sometimes found to be better than that of platinum-based catalysts in alkaline media but is inferior to that of platinum-based catalysts in acidic media. Moreover, their metal-free catalysts are active only in alkaline media.^17,19–24 Early studies were focused on heat-treated transition metal macrocyclic complexes,^25–28 and later, nitrogen-containing organic polymers, especially polyaniline (PANI), have been used as precursors^29–32 for preparing the effective ORR catalysts. Recently, many researchers have confined their attention to the heat treatment of small nitrogen-containing organic molecules^33–41 and also to N-doped carbon nanotubes (NCNT)^4,10,42–46 and N-doped graphene (NGr)^11,46–61 for obtaining better ORR activity in acidic as well as in alkaline media. In addition, our research group has recently reported a very active non-precious metal catalyst prepared from polyimide nanoparticles,⁶² which is one of the catalysts exhibiting the best fuel cell performance in the world and can be prepared from ordinary chemicals, such as pyromellitic acid dianhydride (PMDA) and 4,4′-oxydianiline (ODA), which are the most common polyimide precursors.

Studying the kinetics of such highly active catalysts is very useful in understanding the mechanism of ORR and further improving the catalytic performance. Rotating ring-disc electrode voltammetry is often used to study the kinetics of the ORR. In general, the mechanism of ORR is considered to follow one of the two different reduction pathways or both of them during the reduction of O₂ to water as proposed by Damjanovic et al.⁶³ (Scheme 1). The two pathways of ORR are the direct reduction involving 4-electron transfer (direct pathway) and the stepwise reduction via a H₂O₂ intermediate involving 2-electron transfer in each step (sequential pathway). This model was proposed with three assumptions: (a) no catalytic decomposition of H₂O₂, (b) adsorption–desorption of H₂O₂ is fast and in equilibrium and (c) re-oxidation of H₂O₂ is negligible.

Scheme 1 Proposed model for the electrochemical reduction of O₂ by Damjanovic et al.⁶³ Indices b and * designate the bulk species and the species in the vicinity of the disk electrode, respectively.

In this work, using rotating ring-disk electrode voltammetry, we have studied the ORR activity of the Fe/PI and acid-washed Fe/PI (hereafter referred to as Fe/PI-aw) catalysts. Fig. 1 shows the precursors for the Fe/PI catalyst: polyimide and Fe(acac)₃ as carbon–nitrogen and Fe sources, respectively. The effect of acid washing of the Fe/PI catalyst on its durability and activity in ORR is examined. The durability of the catalysts is studied in two different modes of potential application with reference to those used in the durability test of Pt/C catalysts.^64,65 Based on the individual rate constants of ORR (k₁, k₂ and k₃) estimated according to the Damjanovic model⁶³ before and after the durability test, the ORR performance and durability of Fe/PI and Fe/PI-aw catalysts are discussed. In addition, the possibility of the disproportionation reaction of H₂O₂ catalysed by the porous Fe/PI and Fe/PI-aw catalysts is also discussed.

Fig. 1 The chemical structures of the Fe and N sources for Fe/PI and Fe/PI-aw.

2. Experimental

2.1 Preparation of Fe-containing polyimide catalyst (Fe/PI)

Fe/PI was prepared according to the recently reported procedure.⁶² A solution of pyromellitic acid dianhydride (PMDA) in acetone was added to a solution of 4,4′-oxydianiline (ODA) and tris(acetylacetonato) iron(III) (Fe(acac)₃, >98.0%, Dojindo) in acetone (>99.0%, Wako). The amount of Fe species was 2 wt% relative to the resulting polyimide. The mixture was stirred at 0 °C for 30 min and the solvent was removed with a rotary evaporator to collect poly(amic acid). The curing reaction was conducted by heating the poly(amic acid) at 200 °C under vacuum to obtain fine particles of polyimide. The thus-obtained composite was converted into Fe/PI by multistep pyrolysis.⁶⁶ The precursor was heated at 600 °C under nitrogen atmosphere for 5 h and washed with concentrated HCl. Then, the product was again heated at 800 °C under ammonia atmosphere for 1 hour and washed with concentrated HCl. Finally, it was further heated at 1000 °C under ammonia atmosphere for 1 hour to obtain Fe/PI. Fe/PI-aw was prepared by washing Fe/PI with concentrated HCl.

2.2 Preparation of Fe/PI-modified GC electrodes

The composition and coating of the Fe/PI ink play an important role in preparing a uniform thin layer of Fe/PI on the GC electrode surface. 5 mg of each Fe/PI was placed into a 1 ml bottle followed by the addition of 150 μl of ethanol, 150 μl of Milli-Q water (18.2 MΩ) and 50 μl of 5 wt% Nafion. This mixture was sonicated in an ice-cold water bath for 1 hour. 4 μl of the uniformly dispersed ink was taken using a micropipette and transferred onto a clean, polished GC disk electrode, and the whole surface of the GC disk electrode was covered with the ink in uniform thickness. (Care must be taken that the ink should cover the GC disk of the rotating ring-disk electrode completely and it should not flow into the Teflon gap between the ring and disk electrodes.) The electrode was then dried under low flow of argon environment until it dried completely. The thus-prepared Fe/PI-modified GC electrodes contained 0.2 mg of Fe/PI per cm² with 0.1 mg of the Nafion binder per cm².

2.3 Electrochemical measurements

All the measurements were carried out in 0.5 M H₂SO₄ using a CHI bi-potentiostat (model 700D) in a custom-built electrochemical cell. A rotating ring-disk electrode (RRDE) with a GC disk (6 mm in diameter, 0.283 cm²) and a Pt ring (0.252 cm²), a carbon plate (~7 cm²) and Ag/AgCl (sat. KCl) were used as a working electrode, a counter electrode and a reference electrode, respectively. The working electrode was polished with 1 μm and 0.06 μm alumina powder to mirror finish and sonicated to remove the alumina particles before each experiment. After the disk electrode was modified with each Fe/PI, its surface was completely wetted with 0.5 M H₂SO₄ without any air droplets on the surface. The pretreatment of the Fe/PI-modified GC disk electrode was carried out by repeating potential scan at 0.05 V s⁻¹ between 1.1 and 0.05 V in argon-saturated 0.5 M H₂SO₄ until stable voltammograms were obtained. Similarly, the Pt ring electrode was also treated by potential scanning at 0.05 V s⁻¹ between the onset potential of hydrogen evolution (ca. 0 V) and 1.2 V until a voltammogram characteristic of a clean Pt electrode was obtained. The thus-pretreated electrodes were used to study the ORR by scanning the disk electrode potential from 1.1 to 0.05 V in O₂-saturated 0.5 M H₂SO₄ at a scan rate of 5 mV s⁻¹ at various electrode rotation speeds of 400 to 3600 rpm. At the same time, the Pt ring electrode was polarized at a constant potential of 1.2 V to measure the amount of H₂O₂ formed during the ORR at the disk electrode (the collection efficiency is 0.37). The blank response was also measured in argon-saturated 0.5 M H₂SO₄ under the same experimental conditions used above. Electrode potential was finally corrected to a reversible hydrogen electrode (RHE) by adding 0.227 V, estimated from the pH of the 0.5 M H₂SO₄, to the electrode potential measured against Ag/AgCl (sat. KCl). Unless otherwise mentioned, the potentials in this article are referred to as a RHE.

The durability or stability test of Fe/PI was carried out in two different modes of potential application: the stability of the “carbon support” in Fe/PI was tested using the protocol based on the potential cycling between (typically using 10 110 and 1110 cycles) 1.0 and 1.5 V at a scan rate of 0.5 V s⁻¹ in argon-saturated 0.5 M H₂SO₄. On the other hand, the stability in the Fe/PI′s ORR activity was tested by repeating the potential step between the ORR-off region (1.0 V for 3 s) and the ORR-on region (0.6 V for 3 s) for 11 110 times (max). Hereafter, the former and latter durability tests will be called start–stop durability (SSD) test and loading durability (LD) test, respectively.^64,65

2.4 XPS measurements

For XPS measurements, the Fe/PI samples, which were prepared by a coating procedure similar to that used in the preparation of Fe/PI-modified GC disk electrodes for their electrochemical measurements, were placed under ultra-high vacuum conditions (10⁻⁶ Pa) where an ESCA3400 electron spectrometer (SHIMADZU) with an unmonochromatized X-ray source [Mg Kα (hν = 1253.6 eV) anode, emission current of 20 mA and acceleration voltage of 10 kV] was employed, operating at 200 W. The photoelectron take-off angle was set to 75°, the analyzer pass energy was set to 75 eV, and the XPS spectra were corrected to the internal reference spectra of C 1s at 284.5 eV, being the binding energy of the C=C bond of the Fe/PI in order to compensate for the electrostatic charging. Then, the core level spectra were carefully deconvoluted to investigate the different nitrogen species, i.e., pyridinic nitrogen, pyrrolic nitrogen, graphite-like nitrogen and nitrogen oxide on the Fe/PI and Fe/PI-aw surfaces. The XPS spectra of the N core levels were fitted with partial Gaussian functions (usually around 50–80% and the rest being Lorentzian).

3. Results and discussion

3.1 XPS analysis

Fig. 2 shows the N 1s XPS spectra of Fe/PI and Fe/PI-aw before and after the LD test (11 110 potential steps). The N 1s spectra were carefully deconvoluted to investigate the chemical state of nitrogen in these catalysts. The four common nitrogen groups observed in nitrogen-containing carbonaceous materials are pyridinic nitrogen (Py-N), pyrrolic nitrogen (Pr-N), graphite-like nitrogen (Q-N) and nitrogen oxide (N-O), the peaks of which were observed in the regions of 398.2–398.7, 400.1–400.3, 401.5–401.2 and 402.2–403.1 eV, respectively.⁶⁷ The percentage of each type of nitrogen can be calculated from the corresponding peak area before and after the LD test (Table 1). Previous studies suggest that Py-N and Q-N improve the ORR activity,^68–70 whereas N-O shows a negative effect on the ORR. In this study, we have found that the amount of Py-N and Q-N is 22% and 27%, respectively, for the Fe/PI catalyst, whereas in the Fe/PI-aw catalyst, the quantity of Py-N and Q-N decreases to 0% and 21%, respectively. This observation indicates that the acid-washed catalyst did not render high ORR activity compared with the non-washed one. Moreover, the amount of N-O is abnormally high in the Fe/PI-aw catalyst (48%), also supporting a poor activity of the acid-washed catalyst towards the ORR. However, the situation changes after the durability test of the Fe/PI-aw catalyst, that is, after the 11 110 durability cycles the relative amount of Py-N and Q-N increases, while the N-O amount decreases considerably, being in agreement with the increasing activity of the Fe/PI-aw catalyst towards the ORR after the durability test (see the inset in Fig. 5B). Each quantity of the nitrogen species before and after the durability test of 11 110 potential steps remains almost unchanged for the Fe/PI catalyst, reflecting a high stability towards the ORR. The relative quantity of Pr-N in both catalysts decreases by ca. 2% after the durability test. The XPS peak found at 711 eV for Fe/PI corresponds to Fe-2p_3/2, but this peak was not observed for Fe/PI-aw. This confirmed the removal of iron from the catalyst by acid washing.

Fig. 2 Core level N-1s XPS spectra obtained for (A) Fe/PI and (B) Fe/PI-aw. The deconvoluted peaks correspond to pyridinic nitrogen (dark yellow), pyrrolic nitrogen (magenta), graphite-like nitrogen (cyan) and nitrogen oxide (blue), and the overall fitting in each spectrum is shown by a red line. C and D correspond to the XPS spectra of Fe/PI and Fe/PI-aw after 11 110 cycles of the LD test.

Table 1 Percentages of each kind of nitrogen surface groups in Fe/PI and Fe/PI-aw before and after the LD test (11 110 potential steps)

Types of nitrogen groups	Fe/PI		Fe/PI-aw
	Before	After	Before	After
Pyridinic	22	23	0	9
Pyrrolic	33	30	31	28
Graphite-like	27	26	21	31
Nitrogen oxide	18	21	48	32

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Table 2 Tafel slopes and exchange current densities for the ORR at Fe/PI, Fe/PI-aw and Pt/C

Catalysts	Tafel slope (mV dec^−1)	Exchange current density (A cm^−2)
a Lower current density region. b Higher current density region.
Fe/PI	−66	1.1 × 10^−10
Fe/PI-aw	−65	4.6 × 10^−11
Pt/C	−77^a, 167^b	3.9 × 10^−8,^a, 3.9 × 10^−5,^b

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3.2 Rotating ring-disk electrode voltammetry

The RRDE voltammograms obtained for Fe/PI and Fe/PI-aw catalysts (before the durability test) at 1600 rpm in O₂-saturated 0.5 M H₂SO₄ are shown in Fig. 3A. The onset potential (E_onset) of the ORR was measured as a potential at which the disk current reaches 10 μA cm⁻². The Fe/PI catalyst exhibits a fairly positive E_onset (0.915 V) which is ~100 mV more negative than that of the commercially available Pt/C catalyst (TEC 10E50E (46 wt% Pt, purchased from Tanaka Kikinzoku Kogyo (TKK) Corp., Japan)) with a loading density of 55.8 μg_Pt cm⁻², and Fe/PI-aw shows a slight negative shift in E_onset (0.902 V). The half-wave potential (E_1/2) obtained at Fe/PI-aw (0.724 V) was found to be more negative than that at Fe/PI (0.751). The limiting current density (i_DL) obtained at Fe/PI is close to that obtained at the Pt/C. A slight decrease in the i_DL was observed for the acid-washed catalyst.

Fig. 3 (A) Steady-state voltammograms for the ORR obtained at the Fe/PI and Fe/PI-aw catalyst-modified GC disk–Pt ring electrode in O₂-saturated 0.5 M H₂SO₄ solution. The lower panel shows the disk currents, and the corresponding Pt ring currents are shown in the upper panel corresponding to the oxidation of H₂O₂ produced at the relevant disk electrode. Potential scan rate: 5 mV s⁻¹. Electrode rotation speed: 1600 rpm. The Pt ring electrode was potentiostated at 1.2 V. The voltammograms indicated by green lines were obtained at the Pt/C-modified GC disk–Pt ring electrode (Pt loading of Pt/C: 55.8 μg cm⁻²) under the same conditions as mentioned above. (B) Variation of the number of electrons (n) and χ_H2O2 with the disk electrode potential during the ORR at the Fe/PI, Fe/PI-aw and Pt/C catalysts.

3.3 Number of electrons and percentage of hydrogen peroxide

The background-subtracted RRDE voltammograms were used for the estimation of potential-dependent parameters of ORR such as the number of electrons (n), the percentage of hydrogen peroxide produced (χ_H2O2) and the rate constants. The estimation of n in the kinetically controlled region helps us to identify the reaction pathway for the reduction of oxygen to water as described in Scheme 1. The value of n can be estimated using the ring and disc currents as follows:^71–74where I_D and I_R represent the disk and ring currents, respectively. N is the collection efficiency (in this case, 0.37). Similarly, χ_H2O2 is also estimated using the following equation:^71–74

Potential-dependent variation in n and χ_H2O2 is shown in Fig. 3B. n increases as the electrode potential becomes more negative, and at the limiting current region, its values are 3.8 to 3.95 (depending on the catalysts), which are very close to that expected for 4-electron reduction of oxygen to water. The percentage of H₂O₂ increases as the potential becomes more positive and the value is ~20% in the ORR onset region, whereas at the limiting current region, it is less than 5%, indicating that the ORR actually follows both a direct pathway of the 4-electron reduction of O₂ to H₂O and a sequential pathway, where O₂ is first reduced to H₂O₂ followed by the reduction of H₂O₂ to H₂O, rather than only either of both, i.e., a parallel pathway (Scheme 1).

3.4 Stability tests

3.4.1 Stability of the carbon support. The stability test of Fe/PI as “carbon support” was carried out at the potential region where carbon corrosion may occur using the protocol (i.e., SSD test) described in the experimental section. E_1/2 and I_DL are the two important parameters reflecting the stability of Fe/PI. E_1/2 is shifted to the negative direction of the potential after the stability test (the degree in E_1/2 shift is noted by the difference in E_1/2 (ΔE_1/2) before and after the stability test), and the ΔE_1/2 values for the Fe/PI and Fe/PI-aw catalysts are 40 and 60 mV, respectively. The decreased I_DL after the SSD test is attributed to the leaching of the ORR active sites from the electrode surface, probably resulting from the carbon corrosion of Fe/PI. The difference in i_DL before and after the stability test was found to be within 5%.

3.4.2 Stability of the Fe/PI catalyst in its ORR activity. The stability in the Fe/PI′ ORR activity was also examined by applying the potential-step protocol (i.e., LD test) as mentioned in the experimental section. In this study, the potential step was repeated 11 110 times (max.) and the ORR performance of the individual catalysts was checked at the 10th, 110th, 1110th and 11 110th steps using the RRDE voltammetry and the results are shown in Fig. 4. The negative shift of E_1/2 was observed after the LD test as in the case of the SSD test. This shift increased with increasing number of potential steps and was 36 mV after 11 110 potential steps. No appreciable changes were observed in E_onset and I_DL. However, n and χ_H2O2 decreased and increased, respectively, with increasing number of potential steps. The values of n and χ_H2O2 (%) before the LD test were found to be, for example, approximately 3.9 and 6% (at 0 V), respectively, whereas they did not change so much after 11 110 LD potential steps. In the case of Fe/PI-aw, the values of n and χ_H2O2 (%) before and after the LD test are found to be approximately 3.8 and 11%, respectively, at 0 V.

Fig. 4 Comparison of RRDE voltammograms obtained for the ORR at the Fe/PI/GC electrode after each stage of the LD test: before LD test (black) and after 10 (red), 110 (green), 1110 (blue) and 11 110 (cyan) potential steps. The inset shows the variation of E_1/2 with the number of the potential steps.

3.5 Kinetics and mechanism of ORR

To study the kinetics and mechanism of the ORR, the analytical procedure based on a RRDE voltammetry on the ORR (Scheme 1), which was originally given by Damjanovic et al.⁶³ and later developed by Hsueh et al.,⁷⁵ was used in this study. The individual rate constants (k₁, k₂ and k₃) were estimated from the slopes and intercepts of the I_D/I_Rvs. ω^−1/2 and I_DL/(I_DL − I_D) vs. ω^−1/2 plots, where I_DL and ω are the limiting disk current and rotational speed, respectively. The plots of I_DL/(I_DL − I_D) vs. ω^−1/2 at various potentials indicated a linear behaviour with an intercept equal to unity, suggesting that the decomposition (i.e., disproportionation) of the intermediate H₂O₂ formed during the ORR is negligible. The catalytic decomposition of H₂O₂ on the surface of the catalysts has also been studied separately as shown later. Following the procedure of Hsueh et al., the individual rate constants are calculated using the following equations:⁷⁵where S₁ and I₁ are the slope and the intercept of the I_D/I_Rvs. ω^−1/2 plot, respectively, and S₂ indicates the slope of the I_DL/(I_DL − I_D) vs. ω^−1/2 plot. and with the values of D_O2 = 1.4 × 10⁻⁵ cm² s⁻¹, D_H2O2 = 6.8 × 10⁻⁶ cm² s⁻¹ and ν = 0.01 cm² s⁻¹.⁷⁶ The estimated rate constants in the potential range from 0.75 to 0.4 V are shown typically in Fig. 5A and B for the Fe/PI and Fe/PI-aw catalysts, respectively. The rate constants k₁ and k₂ are both potential dependent, while k₃ is almost potential independent. The ratios of k₁/k₂ are much larger than unity in the examined range of potential for the Fe/PI catalyst (0.4–0.7 V), i.e., 5.5–8.3 and 4–7.5 before and after the LD test, respectively (the inset in Fig. 5A), indicating that O₂ is mainly reduced to H₂O via the 4-electron reduction path and only trace amounts of O₂ are reduced via the sequential path which involves H₂O₂ as an intermediate. Similarly, Fe/PI-aw shows that the ratios of k₁/k₂ are larger than unity, but after the durability test the ratios are increased from ca. 2–3 to ca. 4–7.5, i.e., the 4-electron reduction is facilitated (cf. the inset in Fig. 5B). The k₁/k₂ ratios are almost linearly dependent on potential and the values are smaller at more positive potential. The rate constant k₃ is smaller than k₂. This indicates that the intermediate H₂O₂ formed in the sequential path is reduced to H₂O at a relatively slow rate. A similar behaviour has also been reported for the Mo–Ru–Se-based electrocatalyst for ORR.⁷⁶

Fig. 5 Comparison of individual rate constants (k₁, k₂ and k₃) of the ORR at (A) Fe/PI/GC and (B) Fe/PI-aw/GC electrodes before (solid lines) and after (dashed lines) the LD test. The insets indicate the potential-dependent k₁/k₂ values before and after the durability.

As discussed in section 3.4.2, a negative shift of E_1/2, a decrease in n and an increase in H₂O₂ generation were observed after the durability test. These preliminary observations indicate that the electrode kinetics of the ORR becomes more sluggish after the durability test. An appreciable decrease in k₁ was observed for Fe/PI, typically 42%. A similar trend was observed for k₂ and k₃, but the extent of decrease was not as high as that of k₁. On the other hand, interestingly, the rate constants were found to increase after the durability test for Fe/PI-aw, although this remains to be clarified. Furthermore, Fe/PI-aw showed less stability compared with Fe/PI.

3.6 Disproportionation of H₂O₂

It is important in clarifying the overall ORR mechanism to know the catalytic decomposition of the H₂O₂ intermediate formed during the ORR. In the above-mentioned kinetic analysis, based on the fact that I_DL/(I_DL − I_D) vs. ω^−1/2 plots are linear with an intercept of unity, we have considered that the disproportionation of H₂O₂ on the catalyst surface is negligible. This was actually confirmed by estimating the disproportionation rate constants in the presence of Fe/PI or Fe/PI-aw according to the procedure proposed by Jaouen and Dodelet.⁷⁷ A known amount (2 mg) of each of the catalysts was added to the known volume (50 mL) of O₂-saturated 0.1 M HClO₄ and the solution was stirred with a uniform distribution of the catalyst. 51.1 μL of 30% H₂O₂ was added to the solution, resulting in an initial H₂O₂ concentration of 10 mM. Immediately after addition of H₂O₂, the RRDE voltammetric diffusion-limited current (I_DL,t) was measured at constant intervals with the Pt/C electrode (the loading density of the Pt/C electrode is 37.2 μg_Pt cm⁻²) at 1600 rpm rotational speed. The RRDE voltammogram was also measured before the addition of H₂O₂ in the O₂-saturated solution and the obtained time-independent current limited by O₂ diffusion is given as I_DL,O2. Finally, the time-dependent H₂O₂ diffusion-limited current (I_DL,H2O2) was calculated as follows:

I_DL,H2O2 = I_DL,t − I_DL,O2 (4)

The rate constants (k₄) of the homogeneous disproportionation reaction of H₂O₂ can be calculated from log(I_DL,H2O2) vs. time plots as shown in Fig. 6. The slopes for both catalysts gave the values of k₄.

Fig. 6 Variation of the H₂O₂ diffusion-limited current at 0.2 V vs. Ag/AgCl (sat. KCl) with time elapsed since 10 mM H₂O₂ was introduced in O₂-saturated 0.1 M HClO₄ solution containing 2 mg of each catalyst.

To compare the thus-estimated disproportionation rate constants with the ORR rate constants, the unit (cm s⁻¹) of k₁, k₂ and k₃ needs to be converted to the same unit of the homogenous rate constant (k₄) by taking into account the thickness (l) of the catalyst coated on the electrode. The ORR rate constants divided by the thickness of the film leads to the unit of s⁻¹ as shown in Appendix A. The thickness of the film coated on the GC surface was estimated to be 23 ± 3 μm using a 3D laser scanning microscope (Keyence Co., Japan). Finally, k₁/l, k₂/l and k₃/l are calculated as 104.3, 12.0 and 1.2 s⁻¹, respectively, for the Fe/PI catalyst and 26.1, 9.4 and 1.4 s⁻¹, respectively, for the Fe/PI-aw catalyst. k₄ is normalized to the amount of the catalyst coated on the electrode for comparison and the estimated values are 10.4 × 10⁻⁵ and 5.0 × 10⁻⁵ s⁻¹ for the Fe/PI and Fe/PI-aw catalysts, respectively. These values are very low compared with k₁/l, k₂/l and k₃/l, and hence, the disproportionation of H₂O₂ is negligible. From the mechanistic point of view, it is expected that k₄ might have an influence on k₃ but not on k₁ and k₂.⁷⁵ As mentioned above, k₄ is too small compared to k₃. Hence, the catalytic disproportionation reaction of H₂O₂ on these catalysts is considered to be very slow and negligible.

3.7 Tafel analysis

Tafel plots are very useful in examining the mechanism of ORR on a particular catalyst. For estimating the kinetic current to obtain the mass transfer-corrected Tafel plot, the modified Koutecky–Levich equation was used as shown below:where i_k and i_DL are the kinetic and limiting current densities, respectively. The estimated i_k values are plotted against potential in Fig. 7. For both Fe/PI and Fe/PI-aw catalysts, the good linear plots were obtained, and thus, the Tafel slopes were estimated to be −66 and −65 mV dec⁻¹ for Fe/PI and Fe/PI-aw catalysts, respectively (Table 2). It is well recognized for Pt/C catalysts^73,78–80 that the slope of −60 mV dec⁻¹ is expected for the ORR at a low current density (lcd) region, and it is attributed to the adsorbed oxygen species with the fast initial electron transfer step followed by the rate-determining chemical step or adsorption under the Temkin adsorption conditions and larger values of Tafel slopes (from ca. −120 to −160 mV dec⁻¹) are usually obtained at a high current density (hcd) region in agreement with the expectation that the initial electron transfer is the rate-determining step under the Langmuir adsorption conditions. The exchange current density (I_ex) can be estimated from the intercept of a linear Tafel plot and it is a key parameter to judge the catalytic efficiency. For Pt/C, these values were estimated to be 3.9 × 10⁻⁸ and 3.9 × 10⁻⁵ A cm⁻² for lcd and hcd regions, respectively. The I_ex values obtained for Fe/PI and Fe/PI-aw are 1.1 × 10⁻¹⁰ and 4.6 × 10⁻¹¹ A cm⁻², respectively, which are by two to three orders of magnitude smaller than that at lcd for the Pt/C. The Fe/PI catalyst gives a larger I_ex compared with Fe/PI-aw.

Fig. 7 Mass transfer-corrected Tafel plots for the ORR at Fe/PI, Fe/PI-aw and Pt/C catalysts.

4. Conclusions

In conclusion, we have successfully demonstrated the high performance of Fe-containing N-doped carbon catalyst (Fe/PI) for the ORR in acidic medium. Fe/PI was prepared from the high-temperature pyrolysis of the polyimide precursor with the Fe(acac)₃. The durability of Fe/PI, which was estimated based on the SSD and LD tests, is relatively good in acidic medium compared with other catalysts reported in the literature.^16,81–83 The XPS and RRDE results suggested that the catalyst enriched with Py-N and Q-N shows a high activity towards the ORR, while that enriched with N-O shows less activity. The ORR rate constants (k₁, k₂ and k₃) were estimated by a RRD voltammetry, indicating that the 4-electron reduction of oxygen is relatively predominant compared to the 2-electron reduction. The rate constant of the disproportionation reaction of H₂O₂ was estimated; it is by about 4 to 6 orders of magnitude smaller than the ORR rate constants, and hence, in the present case, the disproportionation reaction is actually negligible. The role of iron was also studied by comparing the activity and durability in ORR of the Fe/PI and Fe/PI-aw catalysts. Its role in the catalytic performance is not known exactly, but it seems true that Fe plays a vital role in the overall 4-electron reduction of O₂.

Appendix A

According to the definition of the Damjanovic model, the current corresponding to the reduction of H₂O₂ to water (I₃) can be represented as

I₃ = 2S_DFk₃C^*₂ (A1)

where S_D, F and C^*₂ represent the surface area of the disk electrode, the Faraday constant and the concentration of H₂O₂, respectively. The rate of the reduction of H₂O₂ is also defined as

Substituting eqn (A1) with eqn (A2),

where l is the thickness of the electrode evolved from the ratio of the surface area to the volume of the electrode. The rate of the disproportionation reaction of H₂O₂ (r₄) can be written aswhere k₄ is the homogeneous disproportionation rate constant (s⁻¹), and w_cat and m are the weight of the catalyst on the electrode surface in the ORR study and the weight of the catalyst used for the disproportionation study (2 mg), respectively. By taking can be compared with k₃/l. Similarly, k₁/l and k₂/l are also compared with k^*₄.

Acknowledgements

This work was financially supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan. The authors thank Dr. T. Fuchigami and Dr. D. Zhang for helpful discussions.

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