Reduction of Cd(II) Ions in the Presence of Tetraethylammonium Cations. Adsorption Effect on the Electrode Process

1. Introduction

The reduction of Cd(II) ions at the dropping mercury electrode (DME) has been widely used to test models for electrode reactions. Nowadays, some characteristics of the process seem well established, as the CEE mechanism (C: chemical reaction, E: electron transfer) [1,2,3,4], but other questions remain unsolved when adsorption or complexation is present [5,6,7,8,9]. The catalytic effect or inhibition by organic substances could introduce changes in the mechanism or only influence values of the parameters and velocity constants. Particularly, the catalytic effect of thiourea has been studied [5,6], and it was concluded that thiourea adsorption changes the mechanism of Cd(II) reduction; however, the inhibition effect of sucrose [8] only influence the values of the velocity constants but the CEE mechanism remains. It seems interesting to study the effect of other adsorbing substances. Tetraethylammonium (TEA) ions have been selected because of their double character of ionic and organic, and because their adsorption has been studied previously [10,11]. TEA was selected formerly due to it be an organic cation but with an organic character in between that of TMA and TBA. TMA exhibits a behavior somewhat similar to an inorganic cation with a weak specific adsorption [12,13,14,15]. On the other hand, TBA presents a high organic character with a high specific adsorption, which induces a high adsorption of the salt anion [16]. In a previous polarographic study of the Eu(III)/Eu(II) reduction in the presence of TEA [11,17], both surface blocking and electrostatic interaction effects between the adsorbate and the electroactive ions were observed.

In this paper, the reduction of Cd(II) in the presence of TEA in a perchloric acid medium is presented, using dc and ac measurements. The activity of the perchloric acid was maintained constant [10,18,19] in order to apply a correct thermodynamic treatment. The adsorption results, obtained previously, are related to the electrode kinetic values obtained in the present study. This study is a recognition to the notable contribution of Profs J.H. Sluyters and M. Sluyters-Rehbach and their group of the Van’t Hoff Laboratory—University of Utrecht, and also a posthumous tribute to Prof F. Sanz, my PhD thesis supervisor, who introduced me to the electrochemical research field.

2. Theory

2.1. Polarograms

The equations that apply for the current intensity versus potential, i − E, in polarography are [20] the Ilkovic equation for the limit diffusion current (Equation (1)) with sphericity correction (Equation (2)), where i_d is the limit current intensity, D is the diffusion coefficient, m is the drop mass and t is the drop time.

$${\mathrm{i}}_{\mathrm{d}}=708{\mathrm{ncD}}^{1/2}{\mathrm{m}}^{2/3}{\mathrm{t}}^{1/6}$$

(1)

$${\mathrm{i}}_{\mathrm{d}}=708{\mathrm{ncD}}^{\frac{1}{2}}{\mathrm{m}}^{\frac{2}{3}}{\mathrm{t}}^{\frac{1}{6}}(1+39.7{\mathrm{D}}^{\frac{1}{2}}{\mathrm{t}}^{\frac{1}{6}}/{\mathrm{m}}^{1/3})$$

(2)

Equations (1) and (2) enable the calculation D once the other parameters are known.

The slope of log(i/(i_d − i)) vs. E (see Equation (3)) enables testing of the reversibility of the process and to obtain the half wave potential, E_1/2.

$$\mathrm{E}={\mathrm{E}}_{1/2}+\frac{\mathrm{RT}}{\mathrm{nF}}\ln \frac{{\mathrm{i}}_{\mathrm{d}}-\mathrm{i}}{\mathrm{i}} \mathrm{Reversible}\mathrm{process}$$

(3)

2.2. Impedance

2.2.1. General Equations

The Randles circuit (Scheme 1) has been used for the treatment of impedance data [20], where the Warburg element, Z_w, and Warburg coefficient, σ, are:

$${\mathrm{Z}}_{\mathrm{W}}={\mathsf{\sigma }\mathsf{\omega }}^{-1/2}-{\mathrm{j}\mathsf{\sigma }\mathsf{\omega }}^{-\frac{1}{2}}$$

(4)

$$\mathsf{\sigma }=\frac{\mathrm{RT}}{{\mathrm{n}}^2{\mathrm{F}}^2\mathrm{A}\sqrt{2}}\left(\frac{1}{{\mathrm{D}}_{\mathrm{O}}{}^{1/2}{\mathrm{C}}_{\mathrm{O}}^{*}}+\frac{1}{{\mathrm{D}}_{\mathrm{R}}^{1/2}{\mathrm{C}}_{\mathrm{R}}^{*}}\right)$$

(5)

The impedance data were analyzed by fitting them to the expressions valid in the case of Randles behavior [21,22], giving the values of the Warburg coefficient, σ, the charge transfer resistance, R_ct, the irreversibility quotient, p′ = R_ct/σ, and the capacitance of the double layer, C_dl.

2.2.2. Other Treatments

Additionally, other equations can be used to obtain parameter values. When a Nernstian behavior (reversibility) is considered, Equation (6) can be applied.

$${\mathrm{p}}^{\prime }=\frac{\sqrt{2{\mathrm{D}}_{\mathrm{O}}}}{\mathrm{K}{\left[1+\exp \in \right]}^{}}$$

(6)

$$\mathrm{where}\in =\frac{\mathrm{nF}}{\mathrm{RT}}\left(\mathrm{E}-{\mathrm{E}}_{\frac{1}{2}}^{\mathrm{r}}\right)$$

(7)

This equation enables calculation of the velocity constant, K (which, in fact, is the apparent velocity constant, K_ap), if E_1/2^r and D_O are known.

The plot of p′ vs. E present a maximum at

$${\mathrm{E}}_{\max }={\mathrm{E}}_{1/2}^{\mathrm{r}}+\frac{\mathrm{RT}}{\mathrm{nF}}\ln \left(\frac{\mathsf{\alpha }}{1-\mathsf{\alpha }}\right)$$

(8)

$${\mathrm{p}}_{\max }^{\prime }=\sqrt{2{\mathrm{D}}_{\mathrm{O}}}\frac{1-\mathsf{\alpha }}{\mathrm{K}}$$

(9)

These equations enable calculation of the transfer coefficient, α, and K. If E_max < E_1/2^r, then α < 0.5.

For the Warburg coefficient, in the minimum in the plot σ vs. E, we obtain

$${\mathrm{E}}_{\mathrm{m}}={\mathrm{E}}^{\mathrm{f}}+\frac{\mathrm{RT}}{\mathrm{nF}}\ln \sqrt{\frac{{\mathrm{D}}_{\mathrm{R}}}{{\mathrm{D}}_{\mathrm{O}}}}={\mathrm{E}}_{1/2}^{\mathrm{r}}$$

(10)

$${\mathsf{\sigma }}_{\mathrm{m}}=\frac{4\mathrm{RT}}{{\mathrm{n}}^2{\mathrm{F}}^2({\mathrm{C}}_{\mathrm{O}}^{*}\sqrt{2{\mathrm{D}}_{\mathrm{O}}}+{\mathrm{C}}_{\mathrm{R}}^{*}\sqrt{2{\mathrm{D}}_{\mathrm{R}}})}$$

(11)

where C_O* and C_R* are the concentrations of the species O and R in the bulk and E^f is the formal potential. Equation (10) simplifies when C_R* = 0. These equations enable the determination of E_1/2^r and D_O.

The plot of R_ct presents a minimum at

$${\mathrm{E}}_{\mathrm{m}}={\mathrm{E}}_{1/2}^{\mathrm{r}}+\frac{\mathrm{RT}}{\mathrm{nF}}\ln \left(\frac{1-\mathsf{\alpha }}{\mathsf{\alpha }}\right)$$

(12)

$${\mathrm{Rct}}_{\mathrm{m}}=\frac{{\mathrm{RTD}}_{\mathrm{O}}^{1/2}}{{\mathrm{n}}^2{\mathrm{F}}^2({\mathrm{C}}_{\mathrm{O}}^{*}\sqrt{{\mathrm{D}}_{\mathrm{O}}}+{\mathrm{C}}_{\mathrm{R}}^{*}\sqrt{{\mathrm{D}}_{\mathrm{R}}})\mathrm{K}\left(1-\mathsf{\alpha }\right)}$$

(13)

If E_m > E_1/2^r, then α < 0.5.

2.3. Kinetic Parameters

To obtain the velocity constant K = K_ap, which is the apparent velocity constant (K indicates, in our case, the forward velocity constant for the reduction process Cd²⁺ + 2e⁻ = Cd), the following equations can be applied:

$${\mathrm{p}}^{\prime }=\frac{\sqrt{2\mathrm{Do}}}{{\mathrm{K}}_{}}{\left(1+{\mathrm{e}}^{\in }\right)}^{-1}$$

(14)

$${\mathrm{R}}_{\mathrm{ct}}=\frac{\mathrm{RT}}{{\mathrm{n}}^2{\mathrm{F}}^2}\frac{1+{\mathrm{e}}^{-\in }}{{\mathrm{C}}_{\mathrm{o}}^{*}{\mathrm{K}}_{}}$$

(15)

$${\mathrm{K}}_{}={\mathrm{K}}_{\mathrm{s}}\exp \left(-\mathsf{\alpha }\frac{\mathrm{nF}}{\mathrm{RT}}\left(\mathrm{E}-{\mathrm{E}}^{\mathrm{f}}\right)\right)$$

(16)

2.3.1. The Influence of the Double Layer (Adsorption)

It is possible to study the influence of the adsorption and the double-layer effects on the kinetic process of Cd(II) reduction. The values of Φ₂, potential at the diffuse layer, and the values of adsorption of TEA and electrode coverage obtained in a previous study [10,11] can be applied here with the corresponding equations.

The following equation represents the Frumkin correction

$$\ln {\mathrm{K}}_{\mathrm{t}}=\ln {\mathrm{K}}_{\mathrm{ap}}+\frac{2\mathrm{F}}{\mathrm{RT}}{\varnothing }_{\mathrm{r}}$$

(17)

$${\mathrm{K}}_{\mathrm{t}}={\mathrm{K}}_{\mathrm{s}}\exp \left(-\mathsf{\alpha }\frac{\mathrm{nF}}{\mathrm{RT}}\left(\mathrm{E}-{\mathrm{E}}^{\mathrm{f}}-{\varnothing }_{\mathrm{r}}\right)\right)$$

(18)

where K_ap is the apparent velocity constant at which values can be obtained through the impedance analysis (through p′ parameter), K_t is the corrected velocity constant, or true velocity constant, and Φ_r can be calculated as Φ₂. Once K_t is obtained, we can plot ln K_t vs. E − Φ_r and test the model.

2.3.2. Coverage

When adsorbed species are present that influence the electron transfer, some expressions relate the rate constant with the surface coverage [11,17]:

$$\mathrm{K}={}_0{}^{}\mathrm{K}\left(1-\mathsf{\theta }\right)+{}_1{}^{}\mathrm{K}\mathsf{\theta }$$

(19)

$$\mathrm{K}={}_0{}^{}\mathrm{K}\left(1-\mathsf{\theta }\right)\exp \left(\mathrm{A}\mathsf{\theta }\right)$$

(20)

$$\mathrm{K}={}_0{}^{}\mathrm{K}{\left(1-\mathsf{\theta }\right)}^{\mathrm{a}}$$

(21)

$$\mathrm{K}={}_0{}^{}\mathrm{K}\exp \left(\mathrm{B}\mathsf{\theta }\right)$$

(22)

where ${}_0{}^{}\mathrm{K}$ is the rate constant at null surface coverage (θ = 0) and ${}_1{}^{}\mathrm{K}$ is the rate constant at full surface coverage (θ = 1). These expressions are usually applied in the logarithmic form in order to create linear dependences. In these equations, K is the apparent rate constant, K_ap, or the true rate constant, K_v or K_t, according to previous equations.

3. Material and Methods

Measurements were performed in a three-electrode cell. The working electrode (WE) was a DME (see ref. [20] for general details); the counter electrode (CE) was a pool of mercury; and the reference electrode (RE) was a sodium-saturated calomel electrode (SSCE or NaSCE) connected to the cell via a salt bridge filled with the supporting electrolyte. The temperature was 25 ± 0.1 °C. Solutions were prepared from twice-distilled water and analytical-grade chemicals. The supporting electrolyte was perchloric acid maintained at constant activity a_± = 0.418 (c ≈ 0.55 m), according to previous thermodynamic studies on the activity coefficients of perchloric acid and TEA perchlorate mixtures [10,18,19]. The concentrations of TEA perchlorate were 0, 0.75, 2, 5, 10 and 20 mM, but the results for the 20 mM concentration are only taken as a qualitative indication due to their significant dispersion.

Before measurements, oxygen was removed by bubbling argon through the cell. The dc and ac measurements were performed at 1.5 mM Cd(II) concentration (as CdSO₄) and at 4 s after the mercury drop birth. A new drop was used for each measurement. The Hg mass drop is indicated in

Table 1. Ilkovic equation (Equations (1) and (2)) with n = 2, c = 1.5 mM, t = 4 s.

c(TEA) (mM)	0	0.75	2	5
m (mg)	4.258	4.324	4.196	4.179
id (μA)	7.1	7.1	6.7	6.7
D × 106 (cm2/s)	12.6	12.6	11.4	11.4
Corr sphericity D × 106 (cm2/s)	9.1	9.1	8.3	8.3

. For these measurements, the network analyzer system described earlier [23,24] was used. The cell impedance was analyzed in the frequency range of 80–10,000 Hz at 5 mV intervals of the dc potential within the Faradaic region. The dc polarograms were also obtained at 5 mV intervals.

4. Results and Discussion

4.1. DC Measurements

The polarographic curve for the solution without TEA (Figure 1) shows a reversible reduction of the Cd(II) ions. The half-wave potential is E_1/2^r = −575 mV (vs. SSCE), with a value only slightly more negative than that of E_1/2^r reported for other perchlorate media: the value of E_1/2^r = −570 mV (vs. SSCE) in 0.8 M NaClO4 was reported by [8,9], and the value of E_1/2^r = −567 mV or −569 mV (vs. SSCE) in 0.5 M NaClO₄ + 0.5 M HClO₄ medium is reported in the bibliography. Figure 2 plots log(i/(i_d − i)) vs. E. The slope of log(i/(i_d − i)) vs. E is 0.033 mV⁻¹ =33 V⁻¹, practically the value of the reversible case (nF/(2.3RT), see Equation (3)). The diffusion coefficients for Cd(II) obtained from the Ilkovic equation (Equation (1)) and considering the correction of sphericity (Equation (2)) are 12.6 and 9.1 × 10⁻⁶ cm²·s⁻¹, respectively (see Table 1). These coefficients were also obtained from ac measurements.

The values of D_O obtained with the Ilkovic equation are higher than those reported in the bibliography (even the experimental conditions of the concentration and electrolyte are different), but the latter are more similar to the value of D_O obtained with the equation that considers the sphericity correction. As we will see later, the value of D_O obtained with the equation that considers the sphericity correction also agrees better with the value obtained from impedance analysis. The values of D_O reported in the bibliography are 8.0 × 10⁻⁶ cm²·s⁻¹ in 0.8–1 M NaClO₄ medium [8,9], and 7.0 (or 8.0) × 10⁻⁶ cm²·s⁻¹ in 0.5 M NaClO₄ + 0.5 M HClO₄ medium.

The solution containing the lowest TEA concentration showed the same polarographic results as the solution without TEA. When the TEA concentration increased, the half-wave potential remained practically the same, although a small decrease was observed in the limit current. For the highest TEA concentrations, the polarographic wave resolved in two sections (Figure 1), showing a maximum and a minimum in the transition from the first wave to the second. The second wave extended to more negative potentials. The current after the first wave when TEA concentration was 20 mM was half of the limit current of the overall process, which seemed to indicate a process involving two electrons, and that the second discharge was inhibited or delayed by TEA. The existence of a “maximum” could be explained because the TEA cations adsorb strongly at negative charges of the electrode [9], and at high TEA concentrations and negative charges of the electrode, TEA cations tend to form an adsorbed monolayer.

The observed influence of the TEA adsorption on the one-step process Eu(III) → Eu(II) [11,17] was to shift the polarographic waves to more negative potentials. This reduction is considered to present a mechanism of “outer sphere”. The reduction of Cd(II) occurs in a multiple-step process, and the adsorption could influence each step in different ways. For Cd(II) reduction in the presence of sucrose, a strong influence in the chemical step and in the first electron transfer was observed at low sucrose concentrations.

4.2. AC Measurements

The impedance or admittance data were analyzed by fitting to the expressions valid in the case of Randles behavior [21,22] giving the values of the Warburg coefficient, σ, resistance to the charge transfer, R_ct, the irreversibility quotient, p′, and double-layer capacitance, C_dl, at different dc potentials. These values are plotted in Figure 3 and Figure 4 and Figures S1 and S2 (in the Supplementary Information).

From the minimum in the plot of the Warburg coefficient values vs. E (Figure 3) and from Equations (9) and (10) [22], we can obtain E_1/2^r and D_O. The results for the different solutions are in

Table 2. Different parameter values from σ − E plots, and in the minimum (m).

CTEA/mM	0	0.75	2	5	10
−Em = −E1/2r/mV	573.0	572.9	573.4	572.4	570.5
σm/Ω·s−1/2	39.9	39.0	41.6	41.4	46.8
DO × 106/cm2·s−1	9.9	10.4	9.1	9.2	7.2
−Ef/mV	573	573	574	573	573

. For all solutions except those with high TEA concentration, we see that E_1/2^r = −573 mV, and this value is close to that obtained from polarography (−575 mV). The value obtained for Do was 9–10 × 10⁻⁶ cm²·s⁻¹. If we take the value in the minimum of σ_m = 40 Ω·s⁻¹, with n = 2 and c = 1.5 × 10⁻⁶ mol·cm⁻³, we thus obtain Do = 9.8 × 10⁻⁶ cm²·s⁻¹.

From the value of D_R = 10.7 × 10⁻⁶ cm²·s⁻¹ in a mercury amalgam [25], the formal potential could be calculated (see Equation (9)); the value E^f = −573 mV is in good agreement with the bibliographic values for perchlorate media (the values of E^f = −572 mV (vs. SSCE) in 0.8 M NaClO₄ [9], and that of −570 mV vs. SSCE in 1 M NaClO₄ was also reported [8]). The decrease in the D_O for TEA concentrations of 2 and 5 mM could be an effect of the TEA cation, because this phenomenon has also been observed for the reduction of Eu(III) [17], but the value for the TEA concentrations of 10 mM is not realistic and corresponds to the effect of the adsorption on the electrode discharge, already seen in the polarographic waves.

From the expression of p′ (Equation (6)), we can see that the plot of p′ vs. E (Figure 4) presents a maximum, predicted by Equations (7) and (8).

Table 3. Different parameter values from the plots p′ − E, and in the maximum (max).

CTEA/mM	0	0.75	2	5	10
−Emax/mV	598.1	600.4	604.5	598.4	593.0
p′max × 103/s1/2	7.0	9.9	21.5	88.7	317.0
Kf/cm·s−1	0.57	0.40	0.19	0.045	0.013

presents the values of p′ at the maximum. The maximum of p′ is shifted to more negative potentials, which means, according to Equation (7), that α < 0.5. From Equation (7) and E_1/2^r, we obtain α_ap = 0.11, and from Equation (6), values of K can be obtained. In Table 3, the values of K at the formal potential are shown (K^f). Values of α between 0.1 and 0.25 in perchlorate medium have been reported, but in some cases, values of α = 0 or 0.68 have also been reported.

K^f is calculated from p′_max (Equation (8)), taking Do = 10 × 10⁻⁶ cm²·s⁻¹ and α = 0.11. The value of α is obtained from Equation (7) with E_max = −600.0 mV and taking E_1/2^r = −573.0 mV. K^f is an apparent constant.

The plot of R_ct vs. E (Figure S1) does not show a clear minimum, and for that was not used. This indicates that α will present a low value, in agreement with the value found previously. Figure S2 plots the values of C_dl versus E. There is some influence of the frequency of the determination of the differential capacity (C_dl), which has not been discussed here

The shape of the σ − E and p′ − E plots agrees with the quasi-reversible character of the process, indicated by previously observing the polarographic curves. This reversible character points to large enough values for the velocity constant, K. From the analysis of the values of the Randles circuit parameters, electrode kinetic parameters, as the velocity constant K, can be obtained at different potentials (see Equations (13) and (14)).

From the slope in the plot of lnK vs. E (see Equation (15) and Figure 5), we can also obtain the values of α_ap. A linear relationship only holds for the low TEA concentrations within a range of potentials. The obtained value agrees with that indicated before. When the TEA concentration increases, the value of α becomes more potential-dependent. The slopes are higher at the more negative potentials, indicating an increase in the α value. A plot of lnK vs. E will be curved in the case of a linear mechanism with more than one rate-determining step.

When the effects of the double layer are considered through${\Phi }_2$, the values of K_t can be obtained, according to Equation (16). Thus, the values of K_t can be related to the surface coverage, according to Equations (18)–(21). Figure 6 plots lnK_t vs. E − Φ₂. The value of α obtained from this plot is 0.15, very close to that of 0.11 obtained above. The value of α in a multi-step mechanism, if n = 2 and CEE mechanism for example, can be 0, 0.25 or 0.75, depending on the rate controlling step, or taking values in between if there is more than one rate-determining step.

4.3. Kinetics and Coverage

The effect of TEA electrode coverage on the velocity constants of the reduction of Cd(II) has been analyzed using several isotherms (Equations (18)–(21)). The adsorption and coverage results were obtained previously [10,11]. The analysis has been performed at several values of E − Φ₂ in order to consider effects of the double layer (Figure S3, in the Supplementary Information, plots the values of coverage at several values of E − Φ₂). The best fit for the whole coverage range was obtained using Equation (20), with a value of the parameter a close to 3 (see Figure 7). This indicates an effect of the TEA coverage; a value a > 1 indicates not only a blocking by the physical space occupied by TEA molecules but an electrostatic repulsion between positive ions.

It is also of interest to show other fits. A fit with Equation (21) presented two zones, as did the fit of Equation (19) (see Figure 8). Equation (19) separated the blocking effect by space (1 − θ) from the repulsive interaction by the exponential term on θ (exp(Aθ)). This could indicate a greater effect of the repulsive interactions at higher coverages, whereas at low coverages, the repulsive interaction would be compensated by the adsorption of perchlorate anions, of opposite charge. This suggest that perhaps a better analysis should include the total adsorption, which is that of a TEA cation plus that of a perchlorate anion (see ref. [10]).

5. Conclusions

The existence of two waves in polarograms when the TEA concentration is high, with the second wave shifted to more negative potentials, indicates that a strong TEA adsorption inhibits the second electron transfer. A big change on the surface coverage, θ, at low TEA concentrations provokes little change in the current intensity. A slight change in the adsorption at high TEA concentrations provokes a strong change in the current intensity. Thus, it seems that adsorption especially effects the second electron transfer.

Values of E_1/2 and D_O obtained from both dc and ac measurements agree. The velocity constants showed a decrease as TEA concentration increased, with values ranging from 0.6 to 0.01 cm·s⁻¹. The change in the value of α (α_ap is potential-dependent) could indicate that the adsorption of TEA changes the mechanism or perhaps influences the electron transfer energy.

Testing the relationship between electrode coverage and velocity constant using several isotherm equations shows that the best fit is obtained with the equation K = ₀K(1 − θ)^a, with an a value close to three, indicating a blocking effect and electrostatic repulsion due to the TEA cation.