Internal and External Transport of Redox Species across the Porous

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Internal and External Transport of Redox Species Across the Porous Thin-film Electrode/Electrolyte Interface Pradipkumar Leuaa, Divya Priyadarshani, Anand Kumar Tripathi, and Manoj Neergat J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02795 • Publication Date (Web): 09 Aug 2019 Downloaded from pubs.acs.org on August 9, 2019

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The Journal of Physical Chemistry

Internal and External Transport of Redox Species Across the Porous Thinfilm Electrode/Electrolyte Interface Pradipkumar Leuaa1, Divya Priyadarshani2, Anand Kumar Tripathi1 and Manoj Neergat*,1 1Department

of Energy Science and Engineering, Indian Institute of Technology Bombay

(IITB), Powai, Mumbai 400076, India 2Centre

for Research in Nanotechnology & Science, Indian Institute of Technology Bombay

(IITB), Powai, Mumbai 400076, India Abstract Transport of redox species (VO2+/VO2+, V2+/V3+, Ti3+/Ti4+ and Fe2+/Fe3+) across the electrode/electrolyte interface is investigated in a thin-film rotating disk electrode (TF-RDE) configuration using electrochemical impedance spectroscopy (EIS). The transport features depend on the constituents of the thin-film catalyst layer and on the rate constant of the redox reaction. On Nafion-free porous electrodes, finite and semi-infinite linear transport features are observed under hydrodynamic and static conditions of the electrode, respectively. Depending on the rate constant of the electrochemical reaction, equivalent circuit consisting of either resistance (R) and constant phase element (Q) or Warburg short (Ws) element is proposed to explain the finite transport features. Addition of Nafion (binder) in the electrode offers extra resistance to the transport of redox species, which helps resolve EIS features of the transport of redox species through the porous thin-film electrode and that through the bulk of the electrolyte. The features of the transport of redox species through the porous electrode media are independent of the hydrodynamic conditions.

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1. INTRODUCTION Transport of redox species from the bulk of the electrolyte to electrode/electrolyte interface is an important process that decides the performance of electrochemical systems (batteries, fuel cells, electrolyzers and supercapacitors).1, 2 Electrochemical impedance spectroscopy (EIS) is a sensitive tool, which allows simultaneous resolution of various physical processes (electron-transfer and transport of redox species) of different relaxation frequencies and it is used for the investigation of electrode/electrolyte interface.3−7 It is well-understood that electrodes, as components, play a crucial role in determining the performance of electrochemical devices. Porous electrodes are widely used due to their enhanced surface area which can offer more connecting sites between electrode and electrolyte to easily facilitate the transport of electrons and redox species. The porous electrode materials are usually coated on a conducting supporting electrode (i.e., glassy carbon, carbon paper, graphite felts etc.) and it contains, binders to keep the active porous material bound to the electrode surface. However, the transport of redox species through porous thin-film electrodes is not understood properly, and therefore, interpretation of EIS features is difficult as it is often carried out by fitting the data by complex non-linear least square (CNLS) method. The redox active species in the electrolyte usually undergoes semi-infinite linear transport under the static electrode conditions and finite transport under the hydrodynamic conditions.8−10 The semi-infinite linear transport features a 45° straight line in the impedance spectra, known as Warburg impedance.8 On the other hand, the finite transport features a semi-circle in the impedance spectra, which is usually fitted with the R and C elements, where, R and C represent resistance to transport of redox species and diffusion capacitance, respectively.11−20 However, sometimes a Warburg short element is also used to fit the finite transport features.21−22 Moreover, these EIS features are assigned to the transport of redox species from the bulk of the electrolyte to the electrode surface. But, transport of the active 2 ACS Paragon Plus Environment

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species across the porous electrode may present a different resistance than that of the transport through the bulk of the electrolyte solution. Thus, the transport loss may have contributions from both the processes. To our knowledge, this distinction is not reported in the literature. Therefore, in this manuscript, evolution of EIS features due to transport of redox species on a typical carbon material (Vulcan XC-72, in an RDE configuration) is illustrated, and for this purpose, various redox couples (VO2+/VO2+, V2+/V3+, Fe2+/Fe3+ and Ti3+/Ti4+) are used. The transport of redox species through porous electrode and from the bulk of the electrolyte to the electrode surface are resolved by varying the electrode composition using Nafion ionomer (binder). It is shown that the resolution of transport features depends on the rate constant of the redox reaction. The origin of the constant phase element (CPE) in the EIS features due to transport of the redox species is explored by varying the electrolyte concentrations. 2. EXPERIMENTAL DETAILS 2.1 Materials Vanadium (V) oxide (V2O5, 99.6% purity), potassium ferricyanide (K3[Fe(CN)6], 99% purity), potassium ferrocyanide (K4[Fe(CN)6], 99% purity), Titanium(IV) oxysulfate (TiOSO4, 29%), Nafion suspension (5 wt% solution in lower aliphatic alcohols/H2O) from Sigma Aldrich; isopropanol (C3H7OH, 99.5% purity) and sulfuric acid (H2SO4, 98% GR) from Merck were used as-received without any further purification. High purity (18.2 MΩ) de-ionized (DI) water was obtained from Direct Q Millipore. 2.2 Electrolyte preparation In this work, electrolytes with an equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4, equimolar (0.2 M) solution of V2+ and V3+ in 3 M H2SO4, equimolar (20 mM) solution of Fe2+ and Fe3+ in 1 M H2SO4, equimolar (0.5 M) solution of Ti3+ and Ti4+ in 3 M H2SO4 solution were used for the electrochemical measurements. The VO2+ electrolyte was 3 ACS Paragon Plus Environment


prepared by dissolving V2O5 in 3 M H2SO4 solution. The VO2+, V2+ and V3+ electrolytes were prepared by electrochemical reduction of VO2+ electrolyte. Similarly, Ti4+ electrolyte was prepared by dissolving TiOSO4 in 3 M H2SO4 solution and Ti3+ electrolyte by electrochemical reduction of Ti4+ electrolyte. The Fe2+ and Fe3+ electrolytes were prepared by dissolving K4[Fe(CN)6] and K3[Fe(CN)6] in 1 M H2SO4 solution, respectively. 2.3 Electrode preparation The thin-film electrode was prepared by the method reported in the literature.23 Carbon-black (5 mg) was dispersed in 5 mL DI water. Subsequently, 10 mL of iso-propanol and the required amount of Nafion (10, 20, or 40 μL) solution was added to the mixture and it was ultrasonicated for 30 min to get a free-flowing smooth ink. A measured volume of the ink was drop-cast using a micro-pipette on a polished glassy-carbon disk electrode (GCE, disk area = 0.196 cm2) to get a carbon-black loading of 128 μg cm−2. The surface of the working electrode was then air-dried for 2 h prior to the electrochemical measurements. 2.4 Physical Characterization Scanning Electron Microscopy (SEM) of the sample was recorded with a JSM-7600F instrument. Atomic force microscopy (AFM) imaging of the sample was carried out using Asylum Research Oxford Instruments Model MFP-3D from USA. Surface imaging of the samples were performed using Zita 3D Microscope Model Zeta 20 from USA. 2.5 Electrochemical Characterization The impedance spectra were recorded in a conventional three-electrode rotating disk electrode (RDE) configuration using a SP-300 potentiostat [from BioLogic Science Instruments (Seyssinet-Pariset, France)]. The prepared thin-film electrode was the working electrode, Ag/AgCl (saturated KCl) was the reference electrode and a platinum coil (area = 5 cm2) was the counter electrode. All the experiments were conducted with an AC amplitude of 4 ACS Paragon Plus Environment

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10 mV rms by sweeping the frequency from 20 kHz to 50 mHz at 10 points per decade. The impedance spectra were fitted using complex non-linear least square (CNLS) method with “ZSimpWin” software from Solartron. 3 RESULTS AND DISCUSSION 3.1 CV and EIS of VO2+/VO2+ redox couple on Nafion-free carbon-modified GCE

Figure 1. CV of an equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte on a carbon-modified GCE under static electrode condition recorded at 20 mV s−1 scan rate. Figure 1 presents the voltammograms of an equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte on a carbon-modified GCE (Nafion-free) at 20 mV s−1 scan rate. The VO2+ to VO2+ oxidation peak (𝐸𝑎𝑝𝑒𝑎𝑘) is observed at ~0.89 V and the corresponding reduction peak (𝐸𝑐𝑝𝑒𝑎𝑘) is at ~0.77 V; the peak potential separation is ~0.12 V. The separation of peak potentials and peak current ratio indicate the reversibility of a redox reaction.1,

24

For a

reversible redox reaction, the separation of peak potential should be less than 58/n mV and peak current ratio should be 1 at all scan rates, where n is the number of electrons involved in 5 ACS Paragon Plus Environment


the redox reaction.1,

24

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Therefore, results suggest that VO2+/VO2+ redox couple exhibits a

quasi-reversible reaction on carbon-modified GCE. The quasi-reversible reaction indicates that the electron-transfer rate across the electrode/electrolyte interface is slow and higher overpotentials are required to drive the electron-transfer.24−27 In this work, the EIS is recorded at the equilibrium potential (EP), which is the mid-point potential between the oxidation and the reduction peak potentials.28, 29 𝐸𝑃 =

𝐸𝑎𝑝𝑒𝑎𝑘 + 𝐸𝑐𝑝𝑒𝑎𝑘 2

[1]

Here, the EP is found to be 0.83 V. At the EP, oxidation and reduction currents are equal, and hence, the net current is zero. The CV suggests that the EP is a potential corresponding to a current in the mixed diffusion-controlled region of the oxidation and reduction waves. Thus, recording EIS at EP should give features corresponding to the electron-transfer and transport of redox species. Figure 2 shows the EIS patterns recorded on Nafion-free carbon-modified GCE under static (without rotation of the electrode) and hydrodynamic (1600 rpm) conditions. The EIS pattern recorded under static electrode condition shows one high frequency (HF) semi-circle and a low frequency (LF) ~45° line corresponding to the electron-transfer process and the semiinfinite linear transport of the vanadium ions, respectively. The corresponding bode phase plot (Figure 2(b)) confirms that the LF line is at 45°. Under the hydrodynamic electrode condition (1600 rpm), the recorded EIS pattern features two semi-circles (Figure 2). The HF semi-circles in the spectra recorded under the static as well as hydrodynamic conditions of the electrode overlap and it confirms that the HF semi-circle corresponds to the electrontransfer process.8, 11, 28, 29 On the other hand, the LF 45° line converges to a semi-circle on recording the EIS under hydrodynamic condition. Therefore, the semi-infinite linear transport


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feature (45° line) in the EIS recorded under static condition of the electrode converges to a finite transport feature of vanadium ions under the hydrodynamic condition (1600 rpm).8−10

Figure 2. EIS patterns recorded on carbon-modified GCE at EP with equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte along with the equivalent circuits (inset). The symbols and solid lines show the experimental and the fitted data, respectively. The corresponding Bode phase plots are shown in Figure 2(b). The EIS patterns are fitted with the equivalent circuits (ECs) using complex non-linear least square (CNLS) method. A series combination of Rs and ((R1W), Q1) element is used to fit the EIS pattern recorded under static condition of the electrode. Here, Rs is solution resistance, R1 is electron-transfer resistance, Q1 is constant phase element and W is Warburg (W) element in series with R1 (see inset to Figure 2(a)). The HF (R1, Q1) element is associated with the electron-transfer process through the electrode-electrolyte interface. Whereas, a series combination of Rs, HF (R1, Q1) and LF (R2, Q2) element is used to fit the EIS pattern recorded under hydrodynamic conditions of the electrode. The LF (R2, Q2) element is associated with the transport of redox species, where, R2 and Q2 represent the resistance to the transport of redox species and constant phase element associated with the diffusion capacitance, respectively. The quality of the fit is poor with a pure capacitor, and therefore, a constant phase element (CPE) is used to fit the experimental data (see Figure S1). The 7 ACS Paragon Plus Environment


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physical reason for replacing capacitor with CPE is due to the frequency dependence of the measured electrode-electrolyte interfacial capacitance.30−33 The CPE behavior is attributed to surface inhomogeneity, reactivity and current and potential distributions associated with the electrode geometry.30−33 The SEM, AFM and Zita 3D images show the porous electrode structure and surface inhomogeneity (see Figure S2, S3 and S4 in the SI). Recently, Martin et al. attributed the CPE behaviour to the presence of trace amounts of impurities in the solution.34 In the literature, sometimes a Warburg short (Ws) element is also used to fit the EIS feature due to finite transport of redox species observed under hydrodynamic conditions of the electrode.21−22 Therefore, the EIS pattern is fitted with the series combination of Rs and ((R1Ws), Q1) element (see Figure S5(a)). The quality of the fit with the Ws element is poor compared to that of the (R2, Q2) element and it is justified with the Fisher-Snedecor test (Ftest) (see Figure S5 and relevant text in SI).8 The reason for better fitting of the finite masstransport feature with the (R2, Q2) element compared to the Ws element is discussed in detail in the later sections (Section 3.3 and 3.4). From the value of CPE, the double layer capacitance (Cdl) and diffuse layer capacitance (Cd) are estimated using the following formula (equation 1) for the normal distribution (hierarchical structure of elements that form the electrode) of the time constants of electrode elements: 𝐶𝜙 =

𝑄 (𝑅𝑝

―1 1 ― 𝜙

)

(1)

The origin of the CPE for the HF semi-circle corresponding to the electron-transfer process is extensively discussed in the literature.30−34 However, the origin of the CPE for the LF semicircle corresponding to the finite transport of redox species is not discussed in detail. The


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concentration of the electrolyte and the electrode composition affects the transport features of the redox species. The origin of the constant phase element (Q2) in explaining the transport process is discussed in the following by varying the concentrations of the redox species in the electrolyte.

Figure 3. EIS recorded under hydrodynamic condition of the electrode (1600 rpm) at EP with the equimolar solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte. The symbols and solid lines show the experimental and the fitted data, respectively. Figure 3 shows the EIS patterns recorded at the EP with equimolar solutions of VO2+ and VO2+ in 3 M H2SO4. Two well-resolved semi-circles appear at high concentration (0.2 M) of the vanadium ions (VO2+/VO2+) and they merge at lower concentrations. The semi-circles (EIS features) corresponding to the electron-transfer and transport of redox species get merged when the time constants for both the reactions are of the same order.8, 12, 35 The ratio of the time constants (Ʈ2/Ʈ1) is ~6 for the lower concentration (0.025 M) and ~30 for the higher concentration (0.2 M), which is the reason for better resolution of semi-circles, with 9 ACS Paragon Plus Environment


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higher concentrations. It is observed that the diameter of HF semi-circle and that of LF semicircle increases with the decrease in vanadium ions concentration, and it indicates rise in resistance to the electron-transfer process and to the transport of redox species. From the EC fittings, the obtained values of electron-transfer resistance (Rct), transport resistance of the redox species (Rd), double layer capacitance (Cdl) and capacitance of diffuse layer (Cd), are shown in Table 1. Table1. Electron-transfer resistance (Rct), transport resistance to the redox species (Rd), double layer capacitance (Cdl) and diffuse layer capacitance (Cd) evaluated from the EIS recorded from electrolytes with equimolar mixture of VO2+ and VO2+ in 3 M H2SO4. Concentration of VO2+ and VO2+ (M) 0.025

Rct (Ω)

Cdl (μF)

Rd (Ω)

Cd (μF)

Ʈ1 (ms)

Ʈ2 (ms)

92.7 ± 5.2

516 ± 36

340 ± 13.2

910 ± 53

48 ± 6

310 ± 30

0.05

56.9 ± 2.3

425 ± 28

131 ± 5.6

1745 ± 86

24.2 ± 2.6

229 ± 21

0.1

25.3 ± 1.8

360 ± 21

53.3 ± 2.2

3417 ± 109

9.1 ± 1.2

182 ± 13

0.2

8.2 ± 0.3

318 ± 13

10.3 ± 0.6

7644 ± 160

2.6 ± 0.2

79 ± 6

The double layer capacitance is observed to be nearly the same for all the concentrations, whereas, the capacitance from the diffuse layer increases with the vanadium ion concentrations. The model of two capacitances (double layer capacitance and diffuse layer capacitance) across the electrode/electrolyte interface is well-established in the literature and the schematic of the same is reported by Bard et al.1 and Memming.36 The double layer capacitor is of two layers. One layer is of the solid electrode surface, which is in contact with the electrolyte. The other layer is of solvated ions with opposite polarity that have moved towards the polarized electrode. These two layers are separated by a monolayer of solvent molecules. The molecular monolayer forms the inner Helmholtz plane (IHP). It adheres to the


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electrode by physisorption on the surface and separates the oppositely polarized layers from each other, forming a molecular dielectric. The amount of charge in the electrode is matched by the magnitude of counter-charges in the outer Helmholtz plane (OHP).1, 36 This is the area in which the polarized electrolyte ions are collected and it is close to the IHP. The concentration in the OHP does not get affected by the concentration of the electrolyte. Hence the double layer capacitance remains nearly the same with the vanadium ion concentration. On the other hand, at higher concentrations, the ions get accumulated near the outer Helmholtz layer making the diffusion layer compact and thin, and at lower concentrations, the ions are distributed over a much thicker diffuse layer. Therefore, the capacitance from the diffuse layer increases with the vanadium ion concentration. The diffusion layer is not compact and uniform as the concentration of the solvated ions decreases gradually from OHP towards the bulk of the electrolyte, causing a distribution of relaxation times. Therefore, CPE is used to fit the LF semi-circle and it represents the charge storage capacity of the diffusion layer, with dispersion in time constants due to the gradient of vanadium ions. The above results are with Nafion-free carbon-modified GCE electrode. However, binder is often required to hold the catalyst on the electrode surface. In the literature, Nafion is the extensively used binder for the electrode preparation, especially in the RDE configuration.27, 37-40

The addition of Nafion in the electrode adds extra ionomer resistance to the transport of

redox species

11, 39, 40

and it results in additional EIS features, which are discussed in the

following section. 3.2 EIS of VO2+/VO2+ redox couple on carbon-modified GCE prepared with various contents of Nafion



Figure 4. EIS recorded at EP with equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte under the static electrode condition on Nafion-free electrode (a) and electrodes prepared with 10 μL (b), 20 μL (c) and 40 μL (d) Nafion containing ink. The corresponding Bode phase plots are shown in Figure 4(e), (f), (g) and (h), respectively. The symbols and solid lines show the experimental and the fitted data, respectively.


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The EIS patterns recorded at EP with the electrolyte containing equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 on carbon-modified GCE prepared with different contents of Nafion are shown in Figure 4. For the Nafion-free electrode, as already discussed in Section 3.1 (see Figure 2), the EIS pattern shows one high frequency (HF) semi-circle and a low frequency (LF) ~45° line (Figure 4(a)) under static conditions of the electrode. On introducing Nafion in the carbon layer (electrode prepared with the ink containing 10 µL Nafion; see the experimental section on the preparation of electrode), the features of the EIS pattern changes. Here, a new feature (arc) start to appear in the mid-frequency (MF) region and it shifts the LF 45º line to further lower frequencies (Figure 4(b)); the HF semi-circle is attributed to the electron-transfer process. Perhaps, the introduction of Nafion helps resolve the transport of redox species to a MF arc and 45° line due to the transport of redox species (vanadium ions) through the thin-film porous electrode and that through the bulk of the electrolyte to the electrode surface, respectively. From here on, the former is referred to internal transport and the latter to external transport of redox species. To investigate the origin of this additional feature due to the presence of Nafion in the electrode, EIS is recorded on electrodes prepared with higher content of Nafion (electrodes prepared with 20 and 40 µL Nafion containing ink). On increasing the Nafion content, a distorted larger HF semi-circle, larger MF semi-circle and a shift in the 45º line to further LF region are observed in the EIS patterns (Figure 4 (c) and (d)). Here, the MF arc appears for the electrode prepared from the 10 μL Nafion containing ink (Figure 4(b)) and it converges to semi-circle with higher content of Nafion (Figure 4(c) and (d)). The larger HF semi-circle is due to the addition of Nafion in the electrode; it blocks a few of the electrochemically active sites on the electrode surface, which in turn causes a slight increase in electron-transfer resistance. Also, the internal transport feature becomes more prominent with the addition of extra Nafion. These features are more apparent from the Bode phase plots. The HF peak is 13 ACS Paragon Plus Environment


observed with both Nafion-free and Nafion containing electrodes, whereas, the MF peak is observed only with the latter (see Figure 4 (e), (f), (g) and (h)). With the increase in the Nafion content, the 45° line shifts towards lower frequencies. 3.3 Effect of rotation rate (rpm) on the EIS pattern The effect of rotation (rpm) of the electrode on the EIS features at EP on carbon-modified GCE prepared with different contents of Nafion is shown in Figure 5. With the Nafion-free electrode, the diameter of the HF semi-circle does not change with the rpm, whereas, the diameter of the LF semi-circle decreases with the increase in rpm (Figure 5(a)). Therefore, the HF semi-circle is attributed to the electron-transfer process and the LF semi-circle to the transport of redox species. The effect of rotation rate on the resistance to the electron-transfer process (Rct) and the transport of redox species (Rd) is shown in the inset to Figure 5. The Rct remains constant, whereas, the Rd decreases with increase in rpm. The strong dependence of LF semi-circle diameter on rpm suggests that it is due to the transport limitation of vanadium ions. Similar features are observed with the electrode prepared from the catalyst ink containing 10 µL Nafion (Figure 5(b)). However, the EIS patterns recorded under static conditions of the electrode shows internal and external transport features of the vanadium ions (see Figure 4(b)). Under hydrodynamic conditions, a distorted (unresolved) semi-circle is observed due to the finite transport of vanadium ions.8, 12, 35 The strong dependence of the diameter of the LF semi-circle on rpm suggests that the external transport limitation of vanadium ions dominates, and therefore, the internal transfer feature is not observed with the rotation. Also, for the electrode prepared from the catalyst ink containing 20 µL Nafion, dependence of the diameter of the LF semi-circle on rpm is observed (Figure 5(c)), but, it is not as noticeable as compared to that of the 10 µL Nafion electrode.


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Figure 5. EIS recorded at EP in the equimolar (0.2 M) solution of VO2+ and VO2+ in 3 M H2SO4 electrolyte on electrodes prepared without Nafion (a), with 10 μL (b), 20 μL (c) and 40 μL (d) Nafion at 800, 1200, 1600, and 2000 rpm. Insets to Figure 5(a), (b), (c) and (d) show the plot of Rct and Rd as a function of rpm. The symbols and solid lines show the experimental and the fitted data, respectively. However, on increasing the Nafion content to 40 μL in the catalyst ink, the diameter of LF semi-circle does not change with the rotation rate (Figure 5(d)), as vanadium ion transport through the porous medium of the electrode (internal transport) becomes prominent due to higher transport resistance with the addition of extra ionomer. The external transport feature is shifted to the further lower frequency (below 50 mHz, see Figure 4(d) and 4(h)) and thus, the LF semi-circle is independent of the external transport limitation of the vanadium ions. Similarly, well-resolved internal and external transport features of the redox species are observed for the EIS recorded with V2+/V3+ and Ti3+/Ti4+ redox couples (see Figure S6 and 15 ACS Paragon Plus Environment


S7 in SI). In the literature, most of the reported rate constants for the V2+/V3+ and VO2+/VO2+ redox reactions are in the range of ~10-5 cm s-1.28, 41, 42 Such a low rate offers enough time for the reaction of the ions present in the pores of the electrode. Therefore, the transport of the redox species through the porous thin-film electrode is taking place at the MF region and the transport through the bulk of the electrolyte takes place at lower frequencies. On the other hand, the rate constant of Ti3+/Ti4+ redox couple is even lower and is in the order of ~10-6 cm s-1.43 Such a low rate constant leaves enough residual Ti3+/Ti4+ ions in the pores of the electrode than that of the VO2+/VO2+ and V3+/V4+ ions. Therefore, more prominent feature of internal transport process is observed for the Ti3+/Ti4+ redox couple (see Figure S7 in supplementary information). Even for the electrode prepared with 20 μL Nafion containing ink, the external transport feature is shifted to frequencies lower than 50 mHz (Figure S7(g)). To investigate the EIS spectra of redox couple with faster reaction kinetics, the Fe2+/Fe3+ redox couple is used and the features are discussed in the following section. 3.4 EIS of Fe2+/Fe3+ redox couple on carbon-modified GCE

Figure 6. EIS recorded on carbon-modified GCE at EP with equimolar (20 mM) solution of Fe2+ and Fe3+ in 1 M H2SO4 electrolyte. The corresponding Bode phase plots are shown in Figure 6(b). The symbols and solid lines show the experimental and the fitted data, respectively. 16 ACS Paragon Plus Environment

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The EIS patterns recorded at EP in equimolar (20 mM) solution of Fe2+ and Fe3+ in 1 M H2SO4 electrolyte on carbon-modified GCE (prepared with 10 μL Nafion containing ink) is shown in Figure 6(a). The Fe2+/Fe3+ is a fast redox reaction, such that the electron-transfer resistance is very low. Therefore, only a straight line at 45° corresponding to the semi-infinite linear transport of iron ions is observed in the whole frequency range of the EIS pattern recorded under static conditions. The overall reaction is limited by transport of iron ions. Under hydrodynamic conditions of the electrode, semi-infinite linear transport converges to finite transport of the iron ions. Here, the finite transport feature follows the 45° line from HF to MF region and then converges to the semi-circle at LF. The EIS pattern is fitted by the Rs (solution resistance) in series with the Ws (Warburg short) element - unlike the (R, Q) elements used for the VO2+/VO2+ redox couple (see Figure 2). Warburg short describes impedance of a finite-length transport with transmissive boundary. This element has two parameters: Wsr and Wsc. Impedance of Ws element is given by the formula:

𝑍𝑊𝑠(𝜔) =

𝑊𝑠𝑟 (1 ― 𝑗)tanh [ 𝑊𝑠𝑐 𝑗𝜔] 𝜔

Where, Wsr is Warburg coefficient, Wsc = d/D0.5, where, d is the Nernst diffusion layer thickness and D is diffusion coefficient. The reported rate constant for the Fe2+/Fe3+ and VO2+/VO2+ are in the order of 10-3 and 10-5 cm s-1, respectively.28, 41, 42, 44, Since the rate constant of Fe2+/Fe3+ is ~100 times higher than that of VO2+/VO2+ redox reaction, the time required for the transport of Fe2+/Fe3+ ions through the thin-film porous electrode is very less compared to that of VO2+/VO2+ redox reaction. Moreover, the faster reaction rate of Fe2+/Fe3+ creates very high concentration gradient at the electrode/electrolyte interface such that the transport of Fe2+/Fe3+ redox species through the bulk of the electrolyte dominates. Therefore, the internal transport features are not observed for the Fe2+/Fe3+ reaction (even when the electrode prepared with ink containing higher 17 ACS Paragon Plus Environment


content of Nafion, see Figure S8). The faster rate of the reaction makes it limited by transport of redox species even in the hydrodynamic condition such that the finite transport feature follows the semi-infinite linear transport line before converging to a semi-circle.

Figure 7. EIS recorded at EP with equimolar (20 mM) solution of Fe2+ and Fe3+ in 1 M H2SO4 electrolyte on carbon-modified GCE at 1600, 2400, 3600, and 4800 rpm. The corresponding Bode phase plots are shown in Figure 7(b). The symbols and solid lines show the experimental and the fitted data, respectively. Figure 7 Shows the EIS spectra recorded under hydrodynamic conditions. It is observed that increasing the rotation rate decreases the diameter of semi-circle. Similar features are observed for the VO2+/VO2+ redox couple; however, for the VO2+/VO2+ redox reaction at higher rpm (above 2400), the diameter of LF semi-circle remains nearly same (see Figure S9). On the other hand, the diameter of LF semi-circle decreases for the Fe2+/Fe3+ redox reaction, confirming that the reaction is limited by transport of redox species even at an rpm higher than 3600. CONCLUSIONS Transport of redox species (VO2+/VO2+, V2+/V3+, Ti3+/Ti4+ and Fe2+/Fe3+) across the porous thin-film electrode/electrolyte interface is investigated in an RDE configuration using EIS.


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Under static conditions of Nafion-free electrode, a LF semi-infinite linear transport feature (Warburg feature) is observed, along with a HF electron-transfer semi-circle. On introducing Nafion (binder) in the electrode, an additional MF feature appears with VO2+/VO2+, V2+/V3+ and Ti3+/Ti4+ redox couples. It seems, the addition of Nafion offers extra resistance to the transport of ions through the porous electrode medium, which in turn helps resolve the transport of ions through the porous electrode medium and that through the bulk of the electrolyte. The former is termed internal transport and the latter external transport of the redox species. Under hydrodynamic conditions, with redox couples of relatively larger rate constant (Fe2+/Fe3+), the semi-infinite linear transport feature (observed under the static electrode conditions) converges to a Warburg short (Ws) feature of finite length transport; the redox species depletes through the porous electrode medium. On the other hand, for the redox couples with relatively lower rate constant (VO2+/VO2+, V2+/V3+ and Ti3+/Ti4+), the reminiscence of the redox species in the porous electrode medium contributes to the diffusion capacitance, and it couples with the transport resistance to yield features of a semi-circle (R, Q) under the hydrodynamic condition. ASSOCIATED CONTENT Supporting information Role of constant phase element (Figure S1); SEM, AFM and Zita 3D images of the carbonmodified GCE (Figure S2, S3 and S4); F-test for the EC of EIS patterns recorded under hydrodynamic conditions of the electrode (Figure S5, Table S1 and Table S2); EIS patterns of V2+/V3+, Ti3+/Ti4+ and Fe2+/Fe3+ redox couples on carbon-modified GCE prepared with various contents of Nafion (Figure S6, S7 and S8); Effect of rotation rate (rpm) on the EIS patterns of VO2+/VO2+ redox couple (Figure S9) AUTHOR INFORMATION *Corresponding author: 19 ACS Paragon Plus Environment


Tel.: +91 22 2576 7893; Fax: +91 22 2576 4890 E-mail address: [email protected] (M. Neergat). ACKNOWLEDGMENTS Ministry of new and renewable energy (MNRE), India, is acknowledged for the financial support of the project through the national centre for photovoltaic research and education (NCPRE, P16MNRE002) at IIT Bombay. REFERENCES 1. Bard, A.; Faulkner, L. Electrochemical Methods: Fundamentals and Applications; Harris, D.; Swain, E.; Robey, C.; Aiello, E.; Eds. John Wiley and Sons: New York, 2001. 2. Gileadi, E.; Electrode Kinetics for Chemists, Chemical Engineers and Material Scientists, VCH Publishers, New York, 1993. 3. Eikerling, M.; Kornyshev, A. A. Electrochemical Impedance of the Cathode Catalyst Layer in Polymer Electrolyte Fuel Cells. J. Electroanal. Chem. 1999, 475, 107−123. 4. Kulikovsky, A. A.; Eikerling, M. Analytical Solutions for Impedance of the Cathode Catalyst Layer in PEM Fuel Cell: Layer Parameters from Impedance Spectrum Without Fitting. J. Electroanal. Chem. 2013, 691, 13−17. 5. Bockris, J. O’M.; Conway, B. E. Modern Aspects of Electrochemistry, Vol. 5; Plenum: New York, 1969. 6. Morita, H.; Komoda, M.; Mugikura, Y.; Izaki, Y.; Watanabe, T.; Masuda, Y.; Matsuyama, T. Performance Analysis of Molten Carbonate Fuel Cell Using a Li/Na Electrolyte. J. Power Sources 2002, 112, 509–518. 7. Macdonald, J. R. Impedance Spectroscopy: Emphasizing Solid Materials and Systems, Wiley, New York, 1987.


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Internal and External Transport of Redox Species across the Porous

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