１３
Figure 1.14. OER volcano plot for metals. The volcano relationship is plotted with experimentally measured overpotentials at 1 mA cm-2 against ΔGO−ΔGOH from density functional theory (DFT).
Reprinted with permission from ref 35. Copyright © 2017 American Association for the Advancement of Science.
１４
(10 and 100 mA cm-2) are generally compared to catalytic activities for HER and OER. Meanwhile, there is inevitable resistance originating from the electrochemical system such as wires, equipment that causes ohmic potential drop.43 Thus, the potential drop by the series/solution resistance (Rs) is usually required to correct for fair comparison of intrinsic catalytic performance. The Rs value is determined by electrochemical impedance spectroscopy (EIS) and iRs compensated overpotentials for HER and OER can be described as ηHER = ERHE – 0 V – iRs and ηOER = ERHE – 1.23 V – iRs, respectively.44-45
1.4.2 Tafel Analysis
The Tafel analysis is utilized to investigate the intrinsic property of a catalyst which is related to the kinetics of the electrocatalytic reaction. By plotting the overpotential (η) as a function of logarithmic values of the current density (log |j|) which is derived from Butler-Volmer equation (Eqn 1.1).
𝑗 = 𝑗0[exp (𝛼𝑎𝑛𝐹𝐸
𝑅𝑇 ) + exp (𝛼𝑐𝑛𝐹𝐸
𝑅𝑇 )] (1.1)
Under high anodic or cathodic overpotential range, the overall current is mainly attributed to the anodic or cathodic current, respectively. Therefore, the Butler-Volmer equation for cathodic and anodic conditions can be depicted as Eqn 1.2 and 1.3.
𝑗𝐶 = 𝑗0[exp (𝛼𝑐𝑛𝐹𝐸
𝑅𝑇 )] (1.2) 𝑗𝐴= 𝑗0[exp (𝛼𝑎𝑛𝐹𝐸
𝑅𝑇 )] (1.3)
By translating the equation to logarithm function form, the Tafel equation can be described as η = b log (j/j0) = a + b log j, where j and j0 are the current density and exchange current density, and b = 2.303𝑅𝑇
𝛼𝐹
which is known as Tafel slope, respectively. The b can be obtained from the slope of the linear part in the Tafel plot.44 The Tafel slope can be also determined by plotting the linear relationship between log Rct vs η, where Rct is the charge transfer resistance measured from the EIS.46-47 The smaller b means less η is required for the same current density, which implies faster reaction kinetics. In HER, the reaction mechanism can be estimated from the Tafel slope. If the Tafel slope is in between 30 to 40 mV dec-1, the HER would follow the Volmer-Tafel mechanism, and if it is more than 40 mV dec-1, the Volmer-Heyrovsky pathway would be preferred. The exchange current density (j0) is another important kinetic parameter. The j0 is obtained at zero overpotential. Thus, a highly performed electrocatalyst should have a large j0 value and a small b value.
1.4.3 Electrocatalytic Stability
The electrocatalytic stability for any reaction is a crucial parameter for the commercialization of the
１５
water electrolysis system. There are several methods to evaluate the durability: 1) Accelerated degradation test (ADT), 2) Chronoamperometry (CA, I-t curve), or 3) Chronopotentiometry (CP, E-t curve). The ADT is compared the changes in onset potential and overpotential before and after the repetitive cyclic voltammetry (CV) more than 5000 cycles. The potentiostatic and galvanostatic methods (CA and CP) are to monitor the current density or the potential variation at a constant overpotential or current density. A current density of 10 mA cm-2 is frequently used to estimate the electrocatalytic stability for more than 10 h.48
1.4.4 Electrochemical Impedance Spectroscopy (EIS)
The electrochemical impedance spectroscopy (EIS) is used to measure several resistances at electrode or electrode-electrolyte interface in water splitting system. As shown in Figure 1.15a, the EIS Nyquist plot is employed to evaluate the series resistance (Rs) that is used for iRs compensation, the charge transfer resistance (Rct) at the interface, and the diffusion or Warburg resistance. In the case of HER and OER, the electrochemical reaction is usually conducted in 0.5 M H2SO4 and 1.0 KOH solutions. Since the reactions are totally controlled by kinetics at the extreme pH conditions, there is generally no contribution from Warburg impedance. Thus, the simple Randle’s circuit (Figure 1.15b) is considered as a basic model for EIS analysis.49 The Rct can be estimated from the diameter of the semicircles in the high-frequency zone. The smaller Rct value indicates the faster charge transfer leading to a faster reaction rate. Before the EIS measurement, the open-circuit voltage should be stabilized. After being stable in the open-circuit voltage, impedance measurement should be carried out under hydrogen/oxygen evolution potential, which corresponds to the potential at 10 mA cm–2. EIS measurements are generally conducted from the frequency range of 105 – 0.01 Hz.49
Figure 1.15. (a) A Nyquist plot for electrochemical cell accompanying regions of mass transfer controlled (diffusion, Warburg) and kinetic controlled regions (from kinetics of the electrochemical reaction, charge-transfer resistance). (b) The corresponding equivalent circuit of Randle’s circuit.
１６ Reprinted from ref 49.
1.4.5 Electrochemical Active Surface Area (ECSA)
The actual electrochemical surface area at the electrode-electrolyte interface is generally estimated from the double layer capacitance (Cdl). The Cdl is obtained by employing CV at various scan rates (10–
200 mV s–1) in the non-Faradaic region. The 5–10 points of the differences in current density variation ((∆J = Ja – Jc) at an overpotential (usually intermediate value of the applied potential range) are selected and plotted against scan rates.47 The plot is fitted to estimate the Cdl from the linear slope. The specific capacitance for a flat surface is typically in the range of 20–60 μF cm-2 and the ECSA for a flat electrode is calculated by assuming the specific capacitance as 40 μF cm-2 (Eqn 1.4).50-51
𝐸𝐶𝑆𝐴𝐹𝑙𝑎𝑡= 𝐶𝑑𝑙
40 𝜇𝐹 𝑐𝑚−2 (1.4) 1.4.6 Turnover Frequency
The turnover frequency (TOF) is another crucial kinetic parameter to evaluate how rapidly the desired electrochemical reaction is conducted. The TOF is determined by the total number of molecules transformed from the reactant molecules per catalytic active site in unit time. Thus, high TOF indicates efficient catalytic activity. First, the number of active sites should be obtained to estimate TOF values.
The number of active sites can be calculated by CV from -0.2 V to +0.6 V vs RHE in 1.0 M phosphate buffer solution (PBS, pH = 7). The cathodic or anodic charges are used to obtain the number of active sites (m) assuming a one-electron process for both reduction and oxidation (Eqn 1.5).47, 52-53
𝑚 = 𝑄
𝑛𝐹 (1.5)
Here, Q is the charge (C) that was calculated by half-integration of cyclic voltammetry (CV) curve for the whole potential range, and n stands for the number of electrons consumed to produce a molecule of gas (in the case of H2: 2 for HER and in the case of O2: 4 for OER). Then TOF is estimated by normalizing the HER or OER current with the number of active sites (Eqn 1.6).
𝑇𝑂𝐹 = 𝐽×𝐴
𝑛𝐹𝑚 (1.6)
Where J is the current density (C∙s-1∙cm-2), A is the surface area of the electrode (cm2), F is Faraday constant (96485 C/mol), m is the number of surface-active sites (moles) and the factor 1/n is 1/2 or 1/4 related to the number of electrons required to produce one molecule of H2 or O2, respectively.54-55 For HER, other methods to obtain the number of active sites are developed such as CO-stripping, hydrogen underpotential deposition (H-UPD), metals-UPD (e.g. Ag, Cu), or peroxide oxidation, and so on.32
１７
However, all these methods are only applicable to noble metal-based electrocatalysts or have their own limitations due to the assumptions. Thus, it is very difficult to precisely approach the TOF for most solid-state catalysts or heterogeneous catalysts because all of the surface atoms cannot be catalytically active or equally accessible.56-57 For OER, the 3d transition metals (e.g. Fe, Co, Ni, etc) undergo redox reactions. Therefore, it is the most appropriate and meaningful method to determine the surface-active concentration of metal sites is integrating the area below the redox peak of oxide/hydroxide/oxyhydroxide formation.56, 58 Although the calculated TOF is relatively inaccurate, it still provides a useful way to compare the catalytic activities of various catalysts, especially within a similar system.
1.4.7 Faradaic Efficiency
The faradaic efficiency reflects the selectivity of the catalyst for a particular electrochemical reaction.
It describes how efficiently a catalytic system utilizes the supplied electrical energy selectively for the desired electrochemical reaction. The faradaic efficiency is defined as the ratio between the utilized charge by reactants and the amount of total charge of the external circuits. The total charge by the external circuits can be calculated from the galvanostatic or potentiostatic measurement. The utilized charge is an experimentally detected quantity of H2 or O2 gas evolved by the water-gas displacement method or gas chromatography method.32, 48
1.4.8 Theoretical Descriptor
Density functional theory (DFT) calculations have demonstrated the theoretical descriptor such as Gibbs free energy of hydrogen bonding (ΔGH) for HER and oxygen/hydroxide bonding (ΔGO−ΔGOH) for OER. The more positive ΔG indicates the reactant strongly adsorbed on the surface of the electrode material while the more negative ΔG makes too weak adsorption of reactant. Thus, the catalyst having zero close ΔG value which located near the summit of the volcano plot (Figure 1.13 and 1.14) gives the best HER and OER performance as the reaction intermediates bound neither too strongly nor too weakly which emerges Sabatier principle.30, 35