Kinetics of Hydrogen Evolution on Copper Electrode Involving Organic Acids as Proton Donors

Abstract

Linear potential sweep (LPS) voltammetry was applied to study the kinetics of hydrogen evolution in solutions containing glycolic, malic, tartaric, and gluconic acids. The CE mechanism of hydrogen evolution was analyzed invoking the 2nd Fick's law equations supplemented by terms that account for chemical interactions between diffusing particles. Acids are considered as components that are capable of releasing hydrated protons taking part in the charge-transfer step. Current peaks observed on LPS voltammograms are in linear dependence on √𝜈 (𝜈 is the potential sweep rate). They obey well-known relationships obtained for simple redox processes, provided that the concentration of oxidant is treated as total concentration of proton donors. Determination of surface concentrations as current density functions makes it possible to transform LPS voltammograms into linear Tafel plots normalized with respect to the surface concentration of hydronium ions. Similar kinetic parameters (𝛼≈0.6 and 𝑖₀≈ 10 μA cm⁻²) obtained at pH 3 for all OA solutions indicate that the nature of OA has no noticeable influence on the charge-transfer process.

1. Introduction

Organic acids containing OH groups are often used as ligands capable of forming quite stable coordination compounds with different metals including copper. Due to their environmental compatibility, most of them have found use in various industrial applications. Tartaric and citric acids are used in plating baths as additives producing compact, fine-grained copper coatings. Besides, electroless plating of dielectrics involving Cu(II)-tartrate complexes is also worthy of mention.

Hydrogen evolution often attends the electrodeposition of metals. This side reaction should be taken into account when the main process is studied. Often the reduction of hydronium ions can be complicated and involves some chemical steps. In the case of CE mechanism (chemical + electrochemical step), electroactive particles are formed in a chemical reaction that precedes the electron transfer step. Components that produce hydronium ions are often referred to as proton donors. Aforementioned organic acids, which are commonly added to improve the coatings, can also play such a role.

Fundamentals of CE processes, that have been substantially elaborated for present (see, e.g., [1–3]), can serve as a basis for studies of hydrogen evolution. However, some difficulties emerge, when a wide range of proton donors is considered; then, certain extensions and generalizations are desirable. The literature data on this problem show that the knowledge in this area is not sound. Therefore, the investigations of kinetics and mechanism of hydrogen evolution in such systems still remain an actual problem. In this connection, we referred to some concepts [4] that have been applied by us for reduction of metal complexes. This paper presents the main characteristics of the processes occurring on the copper electrode in solutions containing some organic acids that act as proton donors.

2. Experimental Details

Solutions under investigation contained 0.04 M analytical grade glycolic, malic, or tartaric acid (Reakhim, Russia), 0.02 or 0.05 M sodium gluconate (Sigma-Aldrich, 99% purity). 0.3 M Na₂SO₄ or K₂SO₄ (Reakhim, Russia, high purity) and 0.5 M Na₂SO₄ (Lach-Ner, Czech Republic, 99% purity) served as supporting electrolytes. Some experiments were carried out with addition of 0.01 M CuSO₄ ( Mallinckrodt, USA). Specified values of pH were adjusted by addition of H₂SO₄ or KOH. Twice-distilled water was used to prepare solutions. A pure argon stream was passed through solutions for 0.5 h prior to measurements. All experiments were carried out at 20°C.

To prepare a working electrode, a platinum disc was coated with a 5–7 μm thick copper layer in the solution containing (g dm⁻³): CuSO₄⋅5H₂O–200, H₂SO₄ –50 at 10 mA cm⁻². Electrode potentials were measured with respect to the Ag|AgCl|KCl(sat) reference electrode and were converted to the standard hydrogen scale.

Voltammograms were recorded under linear potential sweep (LPS) conditions using a potentiostat PI-50-1 (Belorussia). Potential sweep rates 𝜈 ranged from 10 to 200 mV s⁻¹. Some supporting experiments were carried out using a conventional RDE technique.

3. A Quantitative Model

Let us assume that an aqueous solution of weak acid LH₂ is prepared and an excess of indifferent (supporting) electrolyte is added. The main reversible processes occurring in such a system can be depicted as follows: LH₂⇄LH⁻+H⁺,LH⁻⇄L²⁻+H⁺H₂,O⇄H⁺+OH⁻. (1)(2)(3) (in the case of dibasic acid LH₂, the stability of intermediate anion LH⁻ is also characterized by the relationship similar to (12)).

Table 1 

Selected stability constants of organic acids.

Due to a sufficiently high difference between the standard potentials of Cu∣Cu²⁺ and H₂∣H⁺ electrodes, partial processes of Cu(II) reduction and hydrogen evolution are well-separated, unless very stable Cu(II) complexes are formed. This can be seen from a typical example shown in Figure 1. Experimental voltammograms contain two well-defined maxima that are indicative of two different cathodic processes. The first current peak (𝑖_p1) observed at a relatively low cathodic polarization (𝐸_p1≈−0.1V) results from Cu(II) reduction. A further increase in cathodic polarization gives rise to the second process with a distinctive current peak (𝑖_p2) observed at 𝐸_p2≈−0.9V. This maximum may be conditioned by different reasons, such as Cu₂O reduction or hydrogen evolution [12]. EQCM investigations of Cu(II)-glycolic acid solutions have shown [12] that no extra changes in copper electrode mass are observed in this region. Moreover, similar current peaks are also observed in Cu(II)-free solutions. The voltammograms obtained in the latter case and brought to the level of partial Cu(II) reduction current (dotted lines in Figure 1) coincide sufficiently well with the data recorded in the presence of Cu(II). This effect, as well as large difference between E_p1 and E_p2, gives grounds to suppose that the two partial processes may be analyzed independently. The limiting current of Cu(II) reduction, specified by the relationship𝑖_lim=𝑛𝐹𝐷𝛿𝑐_Cu(II), (14) could serve as the base line for hydrogen evolution. In this connection, it should be said, that the thickness, 𝛿, of the Nernst-type diffusion layer (that develops under the natural convection conditions) depends on the potential sweep rate 𝜈. Voltammetric investigations of Fe(CN)₆⁴⁻/Fe(CN)₆³⁻ redox system have shown [13] that the empirical condition 𝛿√𝜈≈ const is obeyed in this case. According to the results of our further investigations, this relation is also valid for Cu(II) systems containing OA. The procedures used for estimation of δ values are described elsewhere [13].

Figure 1 

Comparison of voltammetric data obtained at different potential sweep rates 𝜈 for Cu(II)-containing (solid lines) and Cu(II)-free (symbols) solutions. The latter data are superimposed on the limiting currents of Cu(II) reduction (dotted lines).

Solution pH should be mentioned in the first place as a factor which determines the rate of hydrogen evolution. This can be clearly seen from the typical data shown in Figure 2. Naturally, current density significantly falls with increase in solution pH, that is, when the concentration of hydronium ions decreases. However, when pH is kept constant, the rate of the process under discussion increases with the total concentration of acid (𝑐_ac). This effect will be analyzed below in more detail. Finally, the supporting electrolyte plays a part in these processes: the height of the second current peak decreases gradually when sulphate is replaced by perchlorate (Figure 3). Revealed experimental phenomena imply that not only LH⁻ or LH₂ but also HSO⁻₄ should be treated as a proton donor and should be included into (8).

(a)

(b)

(c)

Figure 2 

Voltammograms obtained for 0.02 M gluconic acid solutions containing 0.5 M Na2SO4 at different pH. Potential sweep rates are indicated at the respective curves.

Figure 3 

Comparison of voltammetric data obtained at 𝜈=0.2Vs−1 for 0.02 M gluconic acid solutions containing different supporting electrolytes as indicated.

The composition of solutions was calculated using modified material balance equations (7) and (8): 𝑐_ac=L²⁻1+𝛽₁H⁺+𝛽₂H⁺²𝑐_H,=H⁺1+𝛽₁L²⁻+2𝛽₂L²⁻H⁺+𝐾_slfSO²⁻₄-[OH⁻], (15)(16) and the expression written for total sulphate concentration: 𝑐_slf=SO²⁻₄1+𝐾_slfH⁺. (17) Stability constants  𝛽₁ and 𝛽₂ are listed in Table 1; a similar characteristic of hydrosulfate, 𝐾_slf= 30, was taken from a handbook [8, 9] as best-matched to the ionic strength of the solutions under discussion. To obtain the concentration of hydronium ions from pH measurements, the activity coefficient 𝛾_H=0.7 was used. It was obtained by empirical equations given in [14, 15]. The concentration of OH⁻ ions was obtained from the ion product of water. An example of the results obtained is given in Table 2. It can be seen that the amount of hydronium ions is not great in the solutions containing a large excess of sulphate. Thus, LH molecules and hydrosulphate anions are the species that should be related to predominating proton donors.

Table 2 

Distribution of different species in the solutions containing 0.02 M of gluconic acid and 0.5 M of Na₂SO₄ as a supporting electrolyte.

Most of the experimental data obtained are typical of every OA under investigation. Therefore, to minimize the size of this paper, we present below freely selected results obtained for either system. According to them, current peaks (that further are simply symbolized as 𝑖_p) increase with the potential sweep rate 𝜈, and linear dependences between 𝑖_p and √𝜈 are observed (Figures 4 and 5). The slopes of these lines, 𝑆, increase when the acidity of solutions grows (pH falls) and the acid concentration is increased. The observed phenomena are consistent with the aforestated assumptions concerning the mechanism of electrode reactions. Since the position of current peaks depends on 𝜈 (Figures 1 and 2 and the data given below), the cathodic process should be treated as irreversible. Then, the simplified kinetic equation is valid for sufficiently high overvoltages:log𝑖_norm=log𝑖₀−𝛼𝑛𝐹2.303𝑅𝑇𝜂, (18) where 𝑖₀ is an exchange current density, 𝛼 is a cathodic charge-transfer coefficient, overvoltage 𝜂=𝐸−𝐸_eq, and 𝐸_eq is equilibrium potential. Normalized current density is defined by the relationship:𝑖_norm=|𝑖|H⁺_s/H⁺_b, (19) where subscripts 𝑠 and 𝑏 denote the surface and bulk concentrations of hydronium ions. Once the latter two quantities are determined, linear normalized Tafel plots (NTP) can be obtained.

(a)

(b)

Figure 4 

Peak current densities versus √𝜈 obtained at different pH for 0.04 M malic and tartaric acid solutions.

Figure 5 

Peak current densities versus √𝜈 obtained at different pH for 0.02 M (dashed lines) and 0.05 M (solid lines) gluconic acid solutions.

Procedures of data treatment might be as follows. Firstly, special integration of experimental voltammograms, transformed into 𝑖−𝑡 functions, is performed (see (10)) and Δ𝑐_H quantities, as 𝐸 functions, are obtained (Figure 6). The latter operation needs a certain diffusion coefficient to be used. Traditionally, it can be obtained from RDE data and tested for the condition according to which the limiting Δ𝑐_H value (see plateau in Figure 6) cannot exceed the bulk concentration of proton donors.

Figure 6 

Changes in the surface concentration of proton donors calculated by (10) from voltammetric data obtained for 0.04 M glycolic acid solution at different potential sweep rates.

The second step consists, in determination, of distribution of proton donors at the electrode surface under cathodic polarization conditions. For this purpose, (15)–(17) are used. The surface value of total concentration of proton donors, 𝑐_Hs, is decreased from the bulk value 𝑐_H (initial state) to zero (limiting current region) keeping 𝑐_ac and 𝑐_slf constant. It should be emphasized that the surface concentration of the electrically active substance (hydronium ions) does not fall to zero in contrast to common redox processes (see (8) or (16)). In the absence of proton donors, a neutral medium is created at the electrode surface ([H⁺]_s=[OH⁻]_s), otherwise alkalization occurs. An example of the data obtained is shown in Figure 7.

Figure 7 

Distribution of proton donors at the electrode surface during the electrolysis of 0.04 M glycolic acid solution. Cathodic current density increases from left to right.

Notice that the same data can be presented as 𝐸 functions, since the interrelation between 𝑐_Hs and 𝐸 is easily obtained from Figure 6. This makes it possible to assign the value of [H⁺]_𝑠 at any potential of voltammograms and to transform them into normalized Tafel plots. Some results of the procedures performed are shown in Figure 8. The data obtained at different 𝜈 are very close and can be approximated by one average NTP. The kinetic parameters of charge-transfer process obtained by (18) are shown in Figure 8 and listed in Table 3. Though the equilibrium potential of H⁺∣H₂ electrode is uncertain in H₂-free solutions, the exchange of current density, named as “effective”, was determined by extrapolation of NTP to the theoretical quantity defined by the relationship: 𝐸_eq=−2.303𝑅𝑇𝐹pH. (20) Low 𝑖^eff₀ values are responsible for a high overvoltage of hydrogen evolution: current densities are low over a wide initial range of potentials. The rise of voltammograms is observed at rather negative potentials ranging up to ∼−0.6V.

Table 3 

Equilibrium characteristics of OA solutions and the kinetic parameters of hydrogen evolution.

(a)

(b)

Figure 8 

Normalized Tafel plots obtained at different potential sweep rates for 0.04 M glycolic (a) and tartaric (b) acid solutions. Indicated kinetic parameters are calculated from general regression lines.

LPS voltammograms possess characteristic maxima, the coordinates of which are convenient to use in the kinetic analysis. At present, relationships for 𝑖_p and 𝐸_p are available for different mechanisms, including the case of simple redox processes that are controlled by the charge transfer and diffusive mass transport [1–3]. The latter case is somewhat similar to that presented here, but one peculiarity needs to be considered. When a simple redox process occurs, both current density and electrode potential depend on the concentration of the same electroactive species. However, the case under consideration offers the following distinctive feature: the electrode potential is determined by [H⁺], whereas the current density is determined by the total flux of all proton donors and is dependent on 𝑐_H. Keeping this in mind, we reasoned that the certain modification of common relationships, with 𝑐_H in place of c, is permissible. Then, the current peak expression takes the following form: 𝑖_p=0.282𝑛𝐹𝜋𝐹𝑅𝑇𝛼𝜈𝐷𝑐_H. (21)

To check the correctness of this equation, the slopes 𝑆≡𝜕𝑖_p/𝜕√𝜈 of linear “𝑖_p−√𝜈” plots were analyzed with the values of 𝛼,𝐷, and 𝑐_H taken from the foregoing analysis. According to the results obtained, experimentally determined slopes are in a good agreement with the quantities that follow from (21) (Table 3).

It can be also seen from these data that the kinetic parameters of the charge-transfer step, obtained for different OA, are quite similar. Then, according to (21), the linear interrelation between 𝑆 and 𝑐_H should be governed only by the equilibrium and mass transport parameters. In this regard, all experimental data, obtained for different OA solutions at various 𝑐_ac and pH, were generalized and collected in Figure 9. It can be seen that a satisfactory approximation can be performed by single general regression line. The results obtained show that the processes of hydrogen evolution, proceeding in the systems under consideration, possess very similar features, and the same theoretical model is acceptable for their description.

Figure 9 

Experimental slopes 𝑆≡𝜕𝑖p2/𝜕√𝜈 versus total concentration of proton donors. Summation of the data obtained for different solutions at 2.5 < pH < 4.0.

It is of interest to view the data concerning the position of current maxima in the scale of potentials. The model presented above supposes a linear dependence between 𝐸_p and log𝜈, the slope of which is determined by the relationship: 𝜕𝐸_p𝜕log𝜈=−2.303𝑅𝑇2𝛼𝐹. (22) This regularity is consistent with the most experimental data obtained for moderately acidic Cu(II)-free solutions. For instance, the average slope of lines, presented in the lower part of Figure 10, is ca 50 mV/decade; then, the value 𝛼≈0.6 that follows from (22) is in agreement with the experimental data listed in Table 3. However, 𝐸_p ceases to depend on 𝜈 in more acidic (pH 2.0) 0.02 M gluconic acid solutions, this is indicative of the reversible character of the charge-transfer process. When pH of such solutions was increased, a tendency for a certain increase in 𝜕𝐸_p/𝜕log𝜈 magnitudes was observed, but this was not the case for more concentrated (0.05 M) solutions.

(a)

(b)

Figure 10 

Dependencies of peak potentials on potential sweep rate presented in semilogarithmic coordinates. The data are obtained for 0.02 M gluconic acid solutions containing Cu(II) (a) and for Cu(II)-free solutions (b), the composition of which is given in the Table 3.

Nonlinear 𝐸_p dependences on log v are observed in the case of Cu(II)-containing solutions (Figure 10(a)). It is necessary to point out that the situation at the electrode surface is not exactly the same as that in identical Cu(II)-free solutions containing the same 𝑐_ac and pH. As what was stated above, hydrogen evolution starts in the region of limiting current, where the surface concentration of Cu(II) approaches zero but 𝑐_acand𝑐_H remain unchanged. However, a certain amount of OA anions is released from the reduced Cu(II)-OA complexes. This results in the shift of chemical equilibria and in the relevant increase in surface pH. Again, simultaneous deposition of copper can also modify the properties of original coatings that were prepared as working electrodes (see Section 2).

The kinetic parameters listed in Table 3 have been determined using not only experimental, but also the literature data. It is common knowledge that stability constants expressed in concentration terms depend on the ionic strength of solutions and on the nature of supporting electrolyte. Unfortunately, data given in different handbooks concern, as a rule, perchlorate or nitrate media and the certain problems arise when fitting such data for sulphate media. Therefore, the reliability of the parameters established here also depends on the reliability of the data selected from the literature. Nevertheless, it can be stated that the kinetic parameters of hydrogen evolution, occurring on the same copper substrate, are very similar in the case of all the systems under investigation. Organic acids seem to be of minor importance for the charge-transfer process and act in general as sufficiently labile proton donors.

5. Conclusions

The CE mechanism of hydrogen evolution occurring in organic acids (OAs) solutions was analyzed invoking the 2nd Fick’s law equations supplemented by terms that account for chemical interactions between diffusing particles. OA are considered as components that are capable of releasing hydrated protons (hydronium anions) taking part in the charge-transfer step. Simple equations containing no kinetic terms were obtained for total concentration of proton donors and acceptors, 𝑐_H. When the dissociation of OA is sufficiently fast, the surface concentrations of species can be obtained from the material balance equations involving the stability constants of proton donors.

Linear potential sweep (LPS) voltammetry was applied to study the kinetics of hydrogen evolution in the solutions containing glycolic, malic, tartaric, and gluconic acids. Current peaks observed on LPS voltammograms are in a linear dependence on √𝜈 (𝜈 is the potential sweep rate). They obey well-known relationships obtained for simple redox processes, provided that the concentration of oxidant is treated as 𝑐_H.

Determination of surface concentrations as current density functions makes it possible to transform LPS voltammograms into linear Tafel plots normalized with respect to the surface concentration of hydronium ions. Similar kinetic parameters (𝛼≈0.62 and 𝑖₀≈10 μA cm⁻²)) obtained at pH 3 for all OA solutions indicate that the nature of OA has no noticeable influence on the charge-transfer process.