pH Overpotential for Unveiling the pH Gradient Effect of H ⁺ /OH ⁻ Transport in Electrode Reaction Kinetics

Abstract

Open AccessCCS ChemistryRESEARCH ARTICLE10 Apr 2021pH Overpotential for Unveiling the pH Gradient Effect of H+/OH− Transport in Electrode Reaction Kinetics Fengjun Yin, Ling Fang and Hong Liu Fengjun Yin Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714 Key Laboratory of Reservoir Aquatic Environment, Chinese Academy of Sciences, Chongqing 400714 University of Chinese Academy of Sciences, Beijing 100049 Google Scholar More articles by this author , Ling Fang Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714 Key Laboratory of Reservoir Aquatic Environment, Chinese Academy of Sciences, Chongqing 400714 Google Scholar More articles by this author and Hong Liu *Corresponding author: E-mail Address: [email protected] Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714 Key Laboratory of Reservoir Aquatic Environment, Chinese Academy of Sciences, Chongqing 400714 Google Scholar More articles by this author https://doi.org/10.31635/ccschem.021.202000604 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesTrack Citations ShareFacebookTwitterLinked InEmail The pH gradient caused by H+/OH− transport on an electrode surface is the key factor determining reaction performance, but its detailed impact on the electrode reaction kinetics has yet to be clarified. Here, the pH gradient effect was determined by developing electrode reaction equations, considering the overpotential assigned to the pH gradient called pH overpotential. The pH gradient effect was revealed to involve two aspects: (1) the Nernst pH overpotential, accounting for the common Nernst relationship with pH, and (2) the pH-dependent function of the electron-transfer coefficient (αpH). Both parts were verified experimentally using oxygen reduction reaction and hydrogen evolution reaction, obviously, with different αpH functions. Detailed αpH function effect was clarified based on numerical calculations of the electrode reaction equations. We found that the effect could be assessed suitably by an apparent constant (αapp) and a nonlinear fitting method proposed for αapp value estimation. The results of this study provide the kinetic fundamentals of electrode reactions involving H+/OH− and contribute to the understanding and assessment of their performance with the H+/OH− transport effect. Download figure Download PowerPoint Introduction Protons (H+) and hydroxide ions (OH−) are required by many electrode half-cell reactions to maintain charge and substance balance. During these electrode reactions, the transport of H+/OH− between the electrode surface and the bulk solution usually causes a pH gradient near the electrode surface,1,2 proven to lower the electrode reaction performance significantly, as reported for the oxygen reduction reaction (ORR), the hydrogen evolution reaction (HER), and microbial electrochemical systems encompassing electrolytes with low acidity and alkalinity.3–5 The addition of buffer ions has been applied widely to alleviate the pH gradient;6–8 however, the influence of the pH gradient on the electrode reaction performance relative to the kinetics remains to be elucidated. The electrode reaction overpotential usually serves as a kinetic measurement of the process effect on reaction rate. Overpotentials resulting from the pH gradient have been frequently reported to reach values as high as 300 mV at near-neutral pH sometimes.9,10 In previous reports,10–13 this pH-associated overpotential was ascribed to the concentration overpotential, assigned to the concentration gradient of reagents and products.14 However, the pH-associated overpotential is, in fact, different from the concentration overpotential in mathematical terms; the former is thought to follow the Nernst equation,15 whereas the latter is derived from the Butler–Volmer equation.16 To distinguish between the two, the pH-associated overpotential is called pH overpotential in this study, which is the third type of process overpotential acting on the electrode kinetics, in addition to the concentration overpotential and the activation overpotential assigned to the electron transfer process. To understand how the pH gradient influences the electrode reaction performance in kinetics, viz, the pH gradient effect, it is necessary to disclose the quantified relationships between the pH overpotential and the pH gradient. Currently, the pH overpotential is mainly addressed by the Nernst equation, which only indicates the equilibrium potential shift caused by the pH gradient.12,15 However, it has also been reported that the interfacial pH state is closely related to the interfacial solvation and the double-layer structure near the active center.17,18 How the pH gradient determines the reaction rate and the detailed kinetics involved have not yet been clarified. It is believed that the electrode reaction equations involving pH overpotential are the cornerstone to the illustration of the pH gradient effect of H+/OH− transport. The major challenges regarding the equation establishment lie in the fact that the conventional Butler–Volmer-based equations are not applicable, because two forms of the equation will be derived with respect to the acidic and alkaline types of an electrode reaction. Two forms of the equation can be derived with respect to the acidic and alkaline types of electrode reactions. For example, ORR could be expressed as either O2 + 4H+ + 4e → 2H2O or O2 + 2H2O + 4e → 4OH−,19 and their equations are developed from a Butler–Volmer analogous method aiming at multielectron and multistep irreversible reactions,20 given as follows (detailed derivation is presented in Supporting Information): Acidic type : j = j 0 c O 2 * c O 2 b c H + * c H + b exp ( − α f η ) − j 0 ( c H + b c H + * ) 3 exp ( ( 4 − α ) f η ) Alkaline type : j = j 0 c O 2 * c O 2 b exp ( − α f η ) − j 0 ( c O H − * c O H − b ) 4 exp ( ( 4 − α ) f η ) where the superscripts * and b denote the species on the electrode surface and the bulk solution, respectively, α is the electron-transfer coefficient, j0 is the exchange current density (A/m2), and η is the overall overpotential. f = F/RT, where R is the ideal gas constant (J/mol·K), F is the Faraday constant (C/mol), and T is the temperature in Kelvin (K). As shown in the two equations above, the concentration term of H+/OH− relies on the stoichiometric relationship; thus, they are different, making it impossible to define a uniform pH overpotential. Once the terms of H+/OH− are neglected, the two equations become the same. This is also true for HER, which is typically described by equations of an electrode reaction that neglect the concentration terms of H+/OH−.21 This indicates that the role of H+/OH− is different from that of other normal reactants, and thus, a new strategy needs to be explored that would involve the pH gradient effect in electrode reaction equations. In this context, it is necessary to investigate the experimental relation between the pH gradient and pH overpotential. Previous studies on the pH gradient effect were mainly conducted in buffered solutions in which the intricate relationships between the transport factors and pH overpotential were difficult to quantify.22–24 In this study, unbuffered solutions were applied, in which only direct transport of H+ and OH− ions occurred. Under these conditions, a pH gradient higher than that of the buffered solutions25 could be quantified easily by the transport equations of H+/OH− ions,26 benefiting the pH overpotential extraction from the experimental polarization curves. The electrode reaction equations were developed by incorporating the dependence of the reaction equilibrium state and kinetic properties of the interfacial pH. The detailed relationships between the pH gradient and pH overpotential were verified from both experimental results and numerical calculations from the established equations. Finally, insight into the role of H+/OH− in the rate kinetics is discussed for electrode reactions involving H+/OH−. Methods and Experiments Experimental investigation of pH overpotential Extraction methods for pH overpotential The overall overpotential is the sum of the pH overpotential (ηpH), activation overpotential (ηact), and concentration overpotential (ηcon). Thus, the j–ηpH response of a polarization curve could be obtained by subtracting ηact and ηcon from the overall overpotential. ηact and ηcon are calculated using the following equations 27: η act = − 1 α f ln j j 0 (1) η con = 1 α f ln ( 1 − K Ox j ) (2)where KOx is the mass transfer-limited coefficient of a reactant (m2/A), which is the reciprocal of the limiting current. The polarization curve measured in a control experiment with an adequately high buffering capacity was used to estimate the α and j0 values. The estimation was performed by a nonlinear fitting method that fit the entire polarization curve using eq 3.27 j = j 0 exp ( − α f η ) − j 0 exp ( ( n − α ) f η ) 1 + j 0 K Ox exp ( − α f η ) (3) In addition, for some simpler reactions with a negligible ηcon value, such as HER, ηpH can be estimated directly from the potential gap between the polarization curves measured in the target experiment and control experiment. To calculate the potential gap, the two polarization curves require interpolation treatment to acquire the same j coordinate, performed in Origin version 8 software ( https://originpro.informer.com/8.5/) for graphing and data analysis by selecting mathematics/interpolate Y from the X/cubic spline method. Electrochemical experiments Both ORR and HER were applied for the experimental investigation of the pH overpotential, with Pt/C (HiSPEC 3000) as the catalyst. The rotating electrode experiments were the same as in our previous work.26 A linear sweep voltammetry (LSV) was applied to measure polarization curves with a scan rate of 5 mV/s at 1200 rpm and an equilibrium time of 30 s before scanning initiation. For the ORR, we used 0.4 M NaClO4 aqueous solution under O2-saturated conditions as the unbuffered solution, adjusting the pH with 4 M HClO4 or 4 M NaOH solution. Six pH levels (pH 2.9, 3.1, 3.5, 4.5, 7.0, and 9.2) were investigated using both an unbuffered (target experiments) and buffered (control experiments) solutions. For the HER, 0.4 M NaCl under N2-saturated conditions was used as the unbuffered solution, which was adjusted with 4 M HCl or 4 M NaOH, and six pH levels (pH 2.4, 3.0, 3.5, 4.5, 7.0, and 9.2) were investigated. The buffered solutions of the control experiments were prepared according to the ingredients summarized in Table 1. Note that the specific ion adsorption was taken into consideration in the buffer selections. Table 1 | Buffer Ingredients of ORR and HER for Each pH Level ORR HER pH Buffer Ingredient pH Buffer Ingredient 2.9 0.2 M NaH2PO4a + 0.3 M NaClO4 2.4 0.2 M NaH2PO4a + 0.3 M NaCl 3.1 0.2 M NaH2PO4a + 0.3 M NaClO4 3.0 0.2 M citric acid + 0.3 M NaCl 3.5 0.2 M sodium acetate + 0.3 M NaClO4 3.5 0.1 M citric acid + 0.2 M sodium acetate + 0.3 M NaCl 4.5 0.2 M sodium acetate + 0.3 M NaClO4 4.5 0.2 M sodium acetate + 0.3 M NaCl 7.0 0.2 M NaH2PO4b + 0.3 M NaClO4 7.0 0.2 M NaH2PO4b + 0.3 M NaCl 9.2 0.2 M H3BO3 + 0.3 M NaClO4 9.2 0.2 M H3BO3 + 0.3 M NaCl aPrimary dissociation of H3PO4, pKa = 2.12. bSecondary dissociation of H3PO4, pKa = 7.20. Calculation of the Nernst pH overpotential The shift in equilibrium potential caused by the interfacial pH variation follows the Nernst relationship and is called the Nernst pH overpotential (ηpH,Ner), which is proportional to the pH variation, as shown in the equation below (detailed derivation is in Supporting Information): η pH , Ner = 0.059 | pH b − pH * | (4) Thus, the j–ηpH,Ner response of a polarization curve can be calculated from the j–ΔpH curve. Calculation of the j–ΔpH curve The j–ΔpH curve of an electrode reaction in an unbuffered solution could be quantified using the direct transport equations of H+/OH− ions, as previously reported.26 The transport equations of the cathodic and anodic reactions are given separately, as follows: Cathodic reactions (pH* ≥ pHb): j = j H , l ( 1 − 10 pH b − pH * ) + j O H , l ( 10 pH * − pH b − 1 ) (5) Anodic reactions (pH* ≤ pHb): j = j O H , l ( 1 − 10 pH * − pH b ) + j H , l ( 10 pH b − pH * − 1 ) (6)where pH* is the electrode interfacial pH and pHb is the bulk solution pH; jH,l and jOH,l are the transport-limiting currents of H+ and OH−, respectively, expressed as follows: j H , l = 1000 Fm H 10 − pH b (7) j O H , l = 1000 F m O H 10 pH b − p K w (8)where m H = D H / δ N (m/s), m O H = D O H / δ N (m/s), DH, and DOH are the diffusion coefficients of H+ and OH− (m2/s), respectively, δN is the diffusion layer thickness (m), and pKw is the logarithm of the ionization constant of water, which equals 14 at 25 °C. To calculate the j–ΔpH curve using eq 5 or 6, jH,l and jOH,l should be determined first. Herein, the j–ΔpH curve calculations of a cathodic reaction are introduced as an example: (1) Under the condition in which the measured polarization curve has a prominent H+ transport-limiting stage, typically at pHb < 5, jH,l could be determined as the average value of this stage. Then jOH,l is estimated using eq 9, derived from eqs 7 and 8, as shown below: j H , l j O H , l = m H m O H 10 − 2 pH b + p K w (9)Herein, mH/mOH = DH/DOH, where the values of DH and DOH were applied for the calculation, according to the literature,28 viz, DH = 7.3 × 10−9 m2/s (estimated in 1.0 M KCl) and DOH = 4.9 × 10−9 m2/s (estimated in 0.1 M Na2SO4); thus, DH/DOH = 1.49. (2) Under the condition where the value of jH,l could not be determined, jH,l and jOH,l are calculated from eqs 7 and 8, given mH and mOH values. The mH value is first estimated from the linear fittings of lgjH,l versus pHb (eq 7) using HER as a standard reaction because of its high accuracy in determining jH,l. Then mOH is estimated according to mH/mOH = DH/DOH. Notably, for cathodic reactions, the OH− transport related to jOH,l, or mOH in eq 5 is far less important than the H+ transport related to jH,l, or mH and vice versa for anodic reactions. Thus, rough estimations of jOH,l, or mOH from jH,l, or mH are acceptable. The HER performed in the unbuffered solution for mH value estimation is shown in Figure 1. The mH value estimated from the intercept of the linear fitting in the inserted figure is 2.93 × 10−4 m/s, and thus, mOH = 1.97 × 10−4 m/s. These parameter values were applied for the j–ηpH,Ner curve calculations in this study. Figure 1 | Polarization curves of HER performed in 0.4 M NaCl for mH value estimation; the pHb condition is listed near the lines; inset: the extracted jH,l plotted vs pHb and the fitting result. The curves were measured at a scan rate of 5 mV/s, a rotating speed of 1200 rpm, and an equilibrium time of 30 s. Download figure Download PowerPoint Results and Discussion Electrode reaction kinetics considering pH overpotential According to a general equation describing a multielectron and multistep reaction process with one rate-limiting step,20 an original electrode reaction equation at any transient interfacial pH state (pH*) in an irreversible case is given as follows: j = n F k 0 c Ox * exp ( − α pH f ( E − E std * ) ) (10)where n is the electron-transfer number, k0 is the standard rate constant, c Ox * is the reagent concentration on the electrode surface, E std * is the standard potential at pH*, and αpH is a pH-dependent function of the electron-transfer coefficient. At the initial equilibrium state, the net current equals zero; thus, pH* equals the bulk solution pH (pHb) and c Ox * equals the bulk solution concentration ( c Ox b ). In this state, eq 10 could be rewritten as the exchange current density (j0, A/m2), as follows: j 0 = n F k 0 c Ox b exp ( − α eq f ( E eq b − E std b ) ) (11)where E eq b is the equilibrium potential at pHb, E std b is the standard potential at pHb, and αeq is the electron-transfer coefficient corresponding to the equilibrium state at pHb. Dividing eq 10 by eq 11 yields the following equation: j = j 0 c Ox * c Ox b exp ( − α pH f ( E − E std * ) + α eq f ( E eq b − E std b ) ) (12) Based on eq 12, two types of electrode reaction equations are derived: the equations expressed by αeq or pH-dependent αpH. Electrode reaction equations expressed by αeq Equation 12 could be transformed into the following form in terms of αeq: j = j 0 c Ox * c Ox b exp ( − α eq f ( η − η pH , Ner − ( 1 − α pH α eq ) ( E − E std * ) ) ) (13)where η is overall overpotential calculated using E − E eq b , and ηpH,Ner is the Nernst pH overpotential calculated using E std * − E std b . Furthermore, eq 13 can be transformed into an overpotential form: η = − 1 α eq f ln j j 0 + 1 α eq f ln c O 2 * c O 2 b + η pH , Ner + ( 1 − α pH α eq ) ( E − E std * ) (14) On the right side of eq 14, the first term designates ηact, the second term designates ηcon, and both are related to αeq. According to the Nernst relationship E std * = E std θ − 0 . 059 pH * , where E std θ is the standard potential under standard acid conditions. Thus, the pH overpotential has the following form: η pH = η pH , Ner + ( 1 − α pH α eq ) ( E − E std θ + 0 . 059 pH * ) (15) It can be seen that αpH adds a modified term to pH overpotential in addition to ηpH,Ner. In a simple case where αpH = αeq, the modified term equals zero and eq 13 becomes j = j 0 c Ox * c Ox b exp ( − α eq f ( η − η pH , Ner ) ) (16) Equation 16 describes a special case in which the αpH function effect is negligible. Electrode reaction equations expressed by αpH Equation 12 can be transformed into the following form in terms of αpH: j = j 0 c Ox * c Ox b exp ( − α pH f ( η − η pH , Ner − ( α eq α pH − 1 ) ( E eq b − E std b ) ) ) (17) The overpotential form of eq 17 is shown as η = − 1 α pH f ln j j 0 + 1 α pH f ln c O 2 * c O 2 b + η pH , Ner + ( α eq α pH − 1 ) ( E eq b − E std b ) (18) The right side of the equation also contains ηact (the first and ηcon (the second to eq 14, and both are related to αpH. A modified term to ηpH also a cathodic reaction as an example, the Nernst relationship at pHb E eq b = E std b + ln ( c Ox / c θ ) / n f , where c θ is the standard this equation to eq η pH = η pH , Ner + ( α eq α pH − 1 ) 1 n f ln c Ox c θ In the modified term is for a value or only to of the ln ( c Ox / c θ ) / n f in the Thus, the modified term is and eq 17 can be to a form to eq αeq is by as follows: j = j 0 c Ox * c Ox b exp ( − α pH f ( η − η pH , Ner ) ) Once αpH = αeq, eq becomes eq Finally, two types of electrode reaction equations expressed by αeq or αpH are This that the pH gradient effect two the Nernst pH overpotential, which for the equilibrium potential shift with pH, and the pH-dependent variation effect of α (αpH). In the equations expressed by αeq, the αpH function effect is assigned to the pH overpotential as a modified In the equations expressed by the αpH function effect is assigned to ηact and ηcon, and ηpH to ηpH,Ner. The two types of equations are summarized in Table Table 2 | The Electrode Reaction of Cathodic the pH Gradient Effect by αeq by αpH equation j = j 0 c Ox * c Ox b exp ( − α eq f ( η − η pH ) ) j = j 0 c Ox * c Ox b exp ( − α pH f ( η − η pH ) ) Overpotential form η = − 1 α eq f ln j j 0 + 1 α eq f ln c O 2 * c O 2 b + η pH η = − 1 α pH f ln j j 0 + 1 α pH f ln c O 2 * c O 2 b + η pH pH overpotential η pH = η pH , Ner + m ( α pH ) m ( α pH ) = ( 1 − α pH / α eq ) ( E − E std θ + 0 . 059 pH * ) η pH η pH , Ner of the relationships derived from the pH overpotential The pH for ORR and HER The pH obtained from ORR and HER were applied for the following The polarization curves of ORR measured in buffered and unbuffered solutions at six pHb levels are shown in and the results are shown in Supporting Figure The buffered solutions were as control where the pH overpotential was negligible. The HER results are shown in and Supporting Figure In potential were between the polarization curves in the buffered and unbuffered an overpotential caused by the pH gradient. H+ transport-limiting current viz, the stage, was for both ORR and HER in the unbuffered results at pHb < This limiting current was also in buffered In to HER, ORR from the oxygen transport and thus, two limiting current as shown in Figure 2 | Polarization curves of ORR measured in unbuffered and buffered solutions at six pHb the the nonlinear fittings based on eq The curves were measured at a scan rate of 5 mV/s, a rotating speed of 1200 rpm, and an equilibrium time of 30 s. Download figure Download PowerPoint The pH overpotential of an unbuffered case was obtained by subtracting ηact and ηcon from the overall overpotential estimated from the buffered solutions. fittings in of the polarization curves in buffered solutions were performed for the and KOx the estimated results are listed in Supporting Table Then ηact and ηcon were calculated using eqs 1 and 2 to the j–ηpH curves of ηact and For HER, ηpH was obtained directly from the potential between the polarization curves in buffered and unbuffered as shown in The results of ORR and HER are shown in Supporting and respectively, that the j–ηpH curves are into two parts by the jH,l stage. the jH,l stage, the pH overpotential is by H+ whereas the jH,l stage, it is by OH− transport. The pH overpotential in both parts was at the jH,l stage, where the overpotential was on the interfacial pH variation to the H+ transport Figure 3 | Polarization curves of HER measured in unbuffered and buffered solutions at six pHb The curves were measured at a scan rate of 5 mV/s, rotating speed of 1200 rpm, and equilibrium time of s. Download figure Download PowerPoint Figure 4 | pH overpotential of ORR between the experimental results determined from Figure 2 and the calculated results pH from eq Download figure Download PowerPoint The Nernst pH overpotential of an unbuffered case was calculated from j–ΔpH curves for The j–ΔpH curves were calculated from eq 5 by either using the jH,l value determined from the unbuffered polarization curves or using the estimated mH value presented in Figure 1. As shown in the values of ηpH,Ner of ORR are higher than the experimental ηpH the jH,l stage. However, the ηpH,Ner curves of HER in are in with the experimental ηpH curves. These of ORR and HER that the Nernst pH overpotential could not for the entire pH overpotential. Figure 5 | pH overpotential of HER between the experimental results from Figure 3 and the calculated results pH from eq Download figure Download PowerPoint αpH of the ORR and HER the pH overpotential Note that the experimental pH shown in 4 and 5 were determined based on eq 14, using constant αeq to calculate ηact and the between the experimental ηpH and ηpH,Ner curves is ascribed to the modified term related to αpH (eq To the α values of ORR and HER under different pH conditions were as shown in Figure 6, where the α values of ORR been estimated from Figure 2 and Supporting Figure Supporting Table and of HER were estimated from fittings ( Supporting Figure using the buffered polarization curves in Figure The α values of ORR presented a linear relationship with pHb in the pHb and from to with a variation of In the α values of HER an between and with a variation of the α of ORR a pH-dependent relationship than that of For ORR, the αpH function caused a modified term according to eq thus, it the in Figure it is that the ηpH,Ner curves of HER are different from the ηpH as revealed in Figure Figure | The α values of ORR estimated from the nonlinear fittings in Figure 2 and Supporting Figure and of HER estimated from the fittings in Supporting Figure The linear fitting results are in the Download figure Download PowerPoint we the αpH function effect of ORR by the ηpH,Ner curves in Figure 4 using eq to fit the experimental ηpH curves. The αpH function the linear fitting equation shown in Figure The E std θ values were determined from the fitting and are plotted in Supporting Figure Then the ηpH,Ner were with the experimental ηpH curves in which fitting that the between the experimental ηpH and ηpH,Ner curves were caused by the αpH function of the electrode reaction. Figure 7 | The Nernst pH overpotential curves in Figure 4 using eq with the experimental pH overpotential at the six pHb Download figure Download PowerPoint calculations to investigate the αpH function effect To the effect of αpH on the electrode reaction performance, a and αpH αpH = was for the numerical calculations using the electrode reaction equations. The calculations were performed under ORR at pHb 7 and as shown in Figure 2 (the are in the Supporting

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