The Effect of pH on the Electrodeposition of Pd Clusters onto Highly Ordered Pyrolytic Graphite—A Kinetic and Morphological Study

Abstract

In this study, we carried out an electrochemical investigation of the palladium electrodeposition process at pH 5 and 8, evaluating the kinetic parameters related to its nucleation and growth processes on a Highly Oriented Pyrolytic Graphite (HOPG) electrode from a plating bath containing 1 mM of Pd and 1 M NH₄Cl. The voltammetric study allowed us to identify the potential values at which palladium can be electrodeposited, along with the adsorption and desorption processes of hydrogen absorbed on the deposited Pd. Analysis of the peak currents of the deposited Pd indicated diffusional control at both pH values. The evaluation of kinetic parameters, such as the number of active nucleation sites (N₀), the nucleation rate (A), and the rate constant of the proton reduction process (k_PR), was determined via potentiostatic studies, revealing their dependence on the applied potential to the electrode. The number of active nucleation sites predicted by the nucleation model correlated well with the number of nuclei observed via Scanning Electron Microscopy (SEM). SEM images revealed that at pH 5, the Pd clusters had an average diameter of 27 nm and a height of 39 nm, while at pH 8, the clusters had an average diameter of 12.8 nm and a height of 16.6 nm. At pH 5, homogeneous and dispersed Pd clusters were obtained, while at pH 8, agglomeration of Pd clusters was observed.

1. Introduction

Palladium-based materials have been extensively utilized in various applications, such as sensor development, fuel cell anode electrode fabrication, hydrogen storage, and catalysis [1]. Additionally, owing to the presence of localized magnetic moments on their surfaces, these materials exhibit magnetic properties at room temperature [2], making them advantageous for the creation of information-storage devices [3]. The synthesis of these materials has been accomplished using various techniques, including chemical reduction [4], ion exchange [5], vapor deposition [6,7,8], thermal evaporation in ultra-high vacuum [9,10], and electrochemical deposition, among others. Palladium (Pd) has been electrodeposited in a wide range of electrolytes [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25], with processes broadly categorized based on pH [26]. Ammonia stands out as the optimal complexing agent for palladium electrodeposition due to its ability to generate trans square planar palladium (II) complexes in these solutions, such as Pd(NH₃)₂X₂ (where X is Cl, Br, or NO₂), with intermediate stability levels [27]. Based on equilibrium constants reported by Smith and Martell [28], the primary chemical species of Pd(II) vary with pH. Thus, for electrolytic baths with a pH range of 2–6, the predominant species is [Pd(NH₃)₂Cl₂], whereas at pH values above 6, [Pd(NH₃)₄]²⁺ becomes predominant, and at pH values below 2, PdCl₄²⁻ predominates [28]. Here, it is important to mention that in a plating solution containing PdCl₂, NH₃, and NaOH, the predominant chemical species of Pd(II) are expected to include PdCl₄²⁻, [Pd(NH₃)₂Cl₂], and [Pd(NH₃)₄]²⁺, depending on the solution’s pH. Additionally, it is noteworthy that within solutions having pH values between 8 and 11, NH₃ rapidly displaces X in Pd(NH₃)₂X₂, facilitating the formation of [Pd(NH₃)₄]²⁺ [24].

Pd has been electrodeposited at liquid/liquid interfaces [29], and onto various substrates such as Au [4,30,31,32,33,34], Indium Tin Oxide [34,35], stainless steel [17,32,36], Pt [32], alumina [37], aluminum [38], nickel [39], and carbon surfaces [12,22,23,40]. However, carbon substrates are recommended for palladium electrodeposition due to their ability to provide large reactive surfaces at a reasonable cost. Here, it is important to consider that the type of carbon substrate and the composition of the plating solution significantly influence the kinetics of Pd electrodeposition. Pd electrodeposition onto glassy carbon electrodes (GCE), Highly Oriented Pyrolytic Graphite (HOPG), and pencil graphite substrates occurs under diffusion control [41], while the nucleation process of Pd from chloride solutions onto GCE can transition from instantaneous to progressive tridimensional nucleation (3D) [42]. Moreover, the mechanism of Pd electrodeposition on graphite substrates can be adequately elucidated via a kinetic model considering a mixed control of charge transfer and diffusion [43]. Pd nucleation on carbon paste substrates proceeds progressively and follows a three-dimensional growth pattern [44], whereas on graphene, Pd electrodeposition is significantly influenced by the proton reduction process [25]. Based on the aforementioned discussion, it is evident that the kinetics of Pd electrodeposition are significantly influenced by both the composition of the plating bath and the type of carbon substrate utilized. In this sense, the type of carbon matrix significantly affects the kinetic parameters of electrodeposition and the resulting particle morphology. For example, Pd electrodeposited on carbon nanotubes tends to form nanoparticles with relatively uniform sizes and necklace-like arrangements [45,46], while on glassy carbon electrodes, the surface is covered by flower-like Pd structures [12]. During Pd electrodeposition onto HOPG, atoms preferentially adsorb at the edges of steps and defects, forming nearly uniform structures [15]. As deposition time progresses, Pd particles align along the step edges of HOPG, creating nanowires. With further deposition, the Pd nuclei begin to coalesce into nanostructures, and with extended deposition times, the atomic clusters become more compact. This behavior follows the 3D island formation model, underscoring the critical role of step-edge energy barriers in determining growth patterns during metal electrodeposition [15]. Hence, detailed comprehension of the kinetics governing Pd electrodeposition on diverse substrates is crucial for effectively controlling the deposition of Pd nanoparticles on them. However, there is limited information available regarding the kinetic parameters involved in Pd electrodeposition on HOPG electrodes from ammoniacal solutions, particularly considering the pH value of the plating bath. In this sense, it is important to consider that HOPG is a highly oriented material with a well-defined crystal structure, which makes it an ideal substrate for studying electrodeposition processes with high resolution and reproducibility. Moreover, its flat and uniform surface and chemical and thermal stability facilitate the formation of homogeneous deposits, which is essential for the construction of electrochemical devices. Therefore, the goal of the present study is to conduct an electrochemical investigation of the Pd electrodeposition process onto HOPG substrates at two pH values of the plating bath. This aims to gain deeper insights into the system to synthesize Pd nanoparticles via an adequate understanding of the kinetic parameters associated with the Pd electrodeposition process on HOPG.

2. Materials and Methods

Pd was electrodeposited onto HOPG electrodes from a plating bath comprising 0.001 M PdCl₂ + 1 M NH₄Cl at pH values of 5 and 8, maintained at a temperature of 298 K. The solution’s initial pH was 6.0, and it was adjusted to pH 5.0 using 1 M HCl and to pH 8.0 using 1 M NaOH. All plating baths utilized in this study were prepared using analytical grade reagents and ultra-pure water (Millipore-Q system, St. Louis, MO, USA) and deoxygenated by N₂ bubbling for 15 min before each experiment. Freshly cleaved HOPG surfaces were employed for each experiment, with a graphite bar serving as the counter electrode and an Ag/AgCl electrode (in saturated KCl) utilized as the reference electrode. All experiments were conducted under room conditions in unstirred solutions. The electrochemical experiments were performed using an EPSILON potentiostat with the BASi-Epsilon EC software Ver. 2.00.71_USB (West Lafayette, IN, USA). Cyclic voltammetry was carried out within the potential range of 0.600 V to −1.100 V. The nucleation kinetics of Pd deposits were investigated by analyzing the experimental current density transients obtained via the single potential step technique. The characterization of Pd nanoparticles was conducted using a Scanning Electron Microscope JEOL JSPM 4210, JEOL LTD, Tokio, Japan.

3. Results and Discussion

3.1. Thermodynamic Study

The pH of the electrolyte solution significantly influences the solution chemistry, especially in relation to the formation of palladium complexes. Under our experimental conditions, there are several Pd²⁺ complexes that exhibit distinct metal-ligand interactions as a function of pH. Consequently, the complexation of Pd²⁺ with ligands can be described by the following reaction:

$${\mathrm{P}\mathrm{d}}^{2+}+\mathrm{x}\mathrm{L}\leftrightarrow {\mathrm{P}\mathrm{d}\mathrm{L}}_{\mathrm{x}}^{2+}$$

(1)

which is characterized by the equilibrium constant (β):

$$\mathsf{\beta }=\frac{\left[{\mathrm{P}\mathrm{d}\mathrm{L}}_{\mathrm{x}}^{2+}\right]}{\left[{\mathrm{P}\mathrm{d}}^{2+}\right]{\left[\mathrm{L}\right]}^x}$$

(2)

According to the equilibrium constants reported in the literature, the predominant chemical species of Pd(II) in the function of the pH in an aqueous ammoniacal plating bath are [PdCl₄]², [Pd(NH₃)₂Cl₂], and [Pd(NH₃)₄]²⁺ [26,28,47]. Here, it is important to mention that in the tramscomplexes Pd(NH₃)₂X₂, the substitution of X by NH₃ takes place rapidly, by which the predominant chemical species is [Pd(NH₃)₄]²⁺ [24]. Under these premises, we plotted the corresponding Pourbaix’s diagram considering a solution with a composition plating bath of 1 mM of PdCl₂, 1 M of NH₄Cl, and NaOH, employing the predominance diagram algorithm as implemented in Hydra-Medusa software [48], and the results are depicted in Figure 1.

From Pourbaix’s diagram depicted in Figure 1, note that for electrolytic baths with a pH value below 4, PdCl₄²⁻ is the predominant chemical species. At a pH value between 4 and 11.5, the predominant chemical species corresponds to the soluble chemical species Pd(NH₃)₄²⁺. These results agree with those reported in the literature when ultraviolet-visible spectra were recorded to detect Pd chemical species in an ammoniacal medium [20]. Also, it is important to mention that the tetrammine palladium complexes, such as Pd(NH₃)₄²⁺, are stable in aqueous solutions, which ensures that the complex does not decompose or react prematurely, allowing for controlled deposition of palladium on the electrode. Moreover, Pd tetrammine complexes are the basis of the commercially available chemistries [49,50], and the electrodeposition process from this complex is given by [24]

$$\mathrm{P}\mathrm{d}{\left({\mathrm{N}\mathrm{H}}_3\right)}_4^{2+}+2\mathrm{e}\to \mathrm{P}\mathrm{d}+4\mathrm{N}{\mathrm{H}}_3$$

(3)

Thus, in this work, we analyzed the Pd electrodeposition process by maintaining plating baths at pH values of 5 and 8. This was carried out to ensure that Pd(NH₃)₄²⁺ remained the predominant chemical species in the electrolytic bath.

3.2. Voltamperometric Study

Figure 2 depicts typical cyclic voltammograms obtained from a plating bath containing 0.001 M PdCl₂ and 1 M NH₄Cl at pH 5 (solid line), with the inset showing the voltammogram obtained at pH 8. In both cases, a direct comparison is made with the respective supporting electrolyte (1 M NH₄Cl at pH 5 or 8), highlighting the emergence of peaks associated with the Pd²⁺-containing plating bath. For the voltammogram recorded at pH 5, during the direct scan, a decrease in current was detected at 0.110 V (peak A), at −0.121 V (peak B), and a peak C at −0.724 V. During the reverse scan, peaks I, II, and D were observed at −0.305 V, 0.013 V, and 0.479 V, respectively. Cathodic peaks A and B are attributed to the electrodeposition of palladium onto the HOPG substrate, while peak C is associated with hydrogen adsorption on the metallic Pd electrodeposited previously. The anodic peaks I and II correspond to hydrogen desorption, and the broad peak D corresponds to the oxidation of previously electrodeposited Pd. In the voltammogram obtained at pH 8, current density peaks A′ and B′ are located at −0.563 V and −0.698 V, respectively. In the anodic region, peak II′ was recorded at 0.271 V, preceded by a shoulder (I′), and peak D′ appeared at 0.515 V. Peaks A′ and D′ are associated with the reduction and oxidation of Pd on HOPG, respectively, while peaks I′ and II′ to hydrogen desorption. When comparing both voltammograms, it is evident that peaks A and B appear to have a greater positive potential than peaks A′ and B′, suggesting a higher energy requirement for electrodepositing Pd at pH 8. Additionally, the current density recorded from the electrolytic bath at pH 5 is higher than that recorded at pH 8, indicating a higher electroreduction rate in the acidic bath.

It is well accepted that plotting the logarithm of peak current versus the logarithm of scan rate provides detailed information about electrochemical mechanisms [51]. Thus, we plotted log j_p vs. log ν for each cathodic peak. The equations for peaks A and B are log j_pA = 0.4559log ν − 0.7079 and log j_pB = 0.5096log ν − 0.5182, respectively. For peak A′, the equation is log j_pA′ = 0.505log ν − 0.6022, and for peak B′, it is log j_pB′ = 0.4648log ν − 0.4845. The slopes of the graphs for cathodic peaks A, B, A′, and B′ are close to 0.5, indicating diffusion-controlled electrochemical behavior. However, the plot of log j_pC vs. log ν for peak C gives log j_pC = 0.6424log ν − 0.2956, suggesting the influence of an adsorption process [51]. Also, the current density value associated with (j_p) was plotted as a function of ν^1/2 according to the Berzins–Delahay equation (Equation (4)) [52]:

$$j_{\mathrm{p}}=\frac{i_{\mathrm{p}}}{S}=367n^{3/2}{C}_0{D}^{1/2}{v}^{1/2}$$

(4)

In this equation, j_p is the peak current value in amperes, n is the number of electrons transferred, S is the area in cm², C₀ is the molar concentration in bulk in mol cm⁻³, D is the diffusional coefficient in cm² s⁻¹, and ν is the potential scan rate in V s⁻¹. Figure 3 shows the plot of the j_p vs. ν^1/2 at pH 5 and 8. Note the linear relationship, which suggests a diffusion-controlled process during Pd electrodeposition, confirming the results obtained from the log j_p vs. log v plots. From the slope values of the linear trend shown in Figure 3a,b for peak A, the Pd diffusion coefficient was calculated to be 3.77 × 10⁻⁷ cm² s⁻¹ at pH 5, and for peak A′, it was 2.21 × 10⁻⁷ cm² s⁻¹ at pH 8.

Also, a plot of the cathodic peak potential of peaks A and A’ vs. log v was performed, and it was found that E_p increased linearly with log ν. The equation obtained at pH = 5 is $E_p=0.1496\log v-0.2238$, while at pH = 8, the equation is $E_p=0.1376\log v-0.7043$. Here, it is important to remember that an irreversible diffusion-controlled process can be described by Equation (5) [53,54]

$$E_p=\frac{2.3\mathrm{R}T}{2\mathrm{n}\alpha F}\mathrm{l}\mathrm{o}\mathrm{g}v+\mathrm{c}$$

(5)

where R is the gas constant, T is the absolute temperature (K), F is the Faraday constant, α is the transfer charge coefficient, and c is a constant. Based on Equation (5), the α value for Pd reduction at pH 5 is 0.19, while at pH 8, it is 0.21, which compares favorably with values reported in the literature during the Pd electrodeposition onto Pt from nitric acid media [55].

3.3. Chronoamperometric Study

It is well known that current density transients can provide valuable information about the kinetics of the electrodeposition process. Thus, in this work, we perform a kinetic study employing the chronoamperometric technique to evaluate the kinetic parameters associated with the nucleation and growth of palladium on HOPG. Figure 4 and Figure 5 show a set of current density transients recorded at different pH values by using a step potential technique. These transients were obtained by applying an initial potential of 0.600 V to the HOPG surface electrode. At this potential value, the Pd deposition still had not begun. After the application of this initial potential, a negative potential step was applied to the electrode surface. In the case of the solution with a pH 5, the potential range used was [−0.050 to −0.300] V, while at pH 8, the potential range was [0.000 to −0.500] V. Note that in all transients depicted in Figure 4 and Figure 5, the j vs. t plot passes through a maximum and then approaches the limiting diffusion current to a planar electrode. This behavior has been related to multiple 3D nucleation and growth processes controlled by a mass transfer reaction [56,57,58]. The last results and those obtained from the voltammetric study suggest a diffusion-controlled process of Pd electrodeposition onto HOPG.

From the transients reported in Figure 4 and Figure 5, it is possible to classify the nucleation as instantaneous or progressive following the Sharifker equations [59]. Thus, the experimental transients of non-dimensional $j^2/j^2\mathrm{m}$ vs. $t/t_{\mathrm{m}}$ forms are compared with those theoretically generated from the instantaneous and progressive equations, Equations (6) and (7), respectively, see Figure 6. In the case of instantaneous nucleation, it occurs rapidly and simultaneously on the electrode surface, leading to a homogeneous morphology with uniformly growing nuclei, which is beneficial for applications requiring uniform coverage. On the other hand, progressive nucleation involves the continuous formation of new nuclei throughout the process, resulting in a heterogeneous morphology with a wider particle size distribution and increased surface roughness.

$$\frac{j^2}{j_{\mathrm{m}}^2}=1.9542{\left(\frac{t}{t_{\mathrm{m}}}\right)}^{-1}{\left\{1-exp\left[-1.2564\left(\frac{t}{t_{\mathrm{m}}}\right)\right]\right\}}^2$$

(6)

$$\frac{j^2}{j_{\mathrm{m}}^2}=1.2254{\left(\frac{t}{t_{\mathrm{m}}}\right)}^{-1}{\left\{1-exp\left[-2.3367{\left(\frac{t}{t_{\mathrm{m}}}\right)}^2\right]\right\}}^2$$

(7)

Note that in both cases (Figure 6a,b), the current density transients fall within the validity range of the model proposed by Sharifker. Also, note that after the maxima, the transients closely follow instantaneous nucleation, which may lead to the formation of homogeneous Pd particles on the HOPG surface. However, it is important to consider that the nucleus of Pd electrodeposited may serve as a catalytic center for the proton reduction process [25]. Therefore, the current density transients depicted in Figure 5 and Figure 6 should be explained by the following equation [60].

$$\begin{array}{l}{j}_{3\mathrm{D}-\mathrm{PR}}(t)=\left\{P_1+P_4{t}^{-1/2}\right\}\\ \times \left\{1-\exp \left[-P_2\left[t-\frac{1-\exp (-P_{3}t)}{P_3}\right]\right]\right\}\end{array}$$

(8)

where $j_{3\mathrm{D}-\mathrm{PR}}\left(t\right)$ represents the current density associated with the palladium nucleation and growth process, which occurs concurrently with the proton reduction reaction on the electrode surface. In Equation (8)

$$P_1=z_{\mathrm{PR}}F{k}_{\mathrm{PR}}{\left(\frac{2cM}{\pi \rho }\right)}^{1/2}$$

(9)

$$P_2=N_0\pi {\left(\frac{8\pi c}{\rho }\right)}^{1/2}D$$

(10)

$$P_3=A$$

(11)

$$P_4=\frac{2F{D}^{1/2}c}{{\pi }^{1/2}}$$

(12)

z_PR is the number of electrons transferred during the proton reduction reaction, and k_PR is the rate constant of the proton reduction process. The nucleation rate and the number of active nucleation sites are represented as A and N₀, respectively. All the other parameters used in Equations (9) to (12) have their electrochemical conventional meanings.

The evaluation of the kinetic parameters associated with the transients depicted in Figure 4 and Figure 5 was carried out via a non-linear fitting of the experimental data to Equation (8). Figure 7 shows a comparison of an experimental current density transient obtained at −0.300 V at pH 5 and pH 8 with the theoretical current density transients generated by Equation (8). It is noteworthy that the proposed model adequately describes the experimental current density transient behavior. However, it is important to mention that fitting the curve with a single equation (Equation (8)), which involves multiple variables, may lead to several possible mathematical solutions, some of which may lack physical meaning. To avoid this issue, a common strategy is to restrict the initial values of the parameters within a broad range while ensuring they retain physical significance. Another strategy is to allow the parameters to vary freely but verify the physical validity of the final values by using another experimental or theoretical technique. In our case, we chose the latter approach. We allowed the parameters to vary freely and validated the values by comparing them with those obtained from the voltammetric study. If one compares the diffusion coefficient values obtained from the voltammetric and potentiostatic studies, it is clear that these values are in the same range. Moreover, the values of N₀ and k_PR determined in this work fell within the limits found in the literature. The kinetic parameters derived in this study are detailed in

Table 1. Potential dependence for the nucleation parameters during Pd electrodeposition onto a HOPG electrode from an aqueous solution containing 10⁻³ M of PdCl₂ and 1 M of NH₄Cl at pH 5. These values were derived from the best-fit parameters obtained via the fitting process of experimental j-t plots using Equation (8).

E /V	A /s−1	N0 × 10−9 /cm2	D × 10−7 /cm2s−1	kPR × 109 /cm2s−1
−0.050	7.48	0.085	6.84	1.56
−0.075	8.80	0.206	7.62	2.14
−0.100	8.88	0.420	8.70	2.14
−0.150	14.09	1.131	8.70	3.18
−0.175	16.18	2.050	8.70	3.22
−0.200	19.44	3.421	8.44	3.98
−0.250	31.00	7.512	8.21	5.53
−0.275	41.19	10.641	8.33	5.78
−0.300	43.88	13.056	8.71	6.49

and

Table 2. Potential dependence for the nucleation parameters during Pd electrodeposition onto a HOPG electrode from an aqueous solution containing 10⁻³ M of PdCl₂ and 1 M of NH₄Cl adjusted with NaOH at pH 8. These values were derived from the best-fit parameters obtained via the fitting process of experimental j-t plots using Equation (8).

E /V	A /s−1	N0 × 10−9 /cm2	D × 10−7 /cm2s−1	kPR × 109 /cm2s−1
−0.235	2.50	0.12	0.34	1.13
−0.250	3.50	23.83	0.62	1.15
−0.300	12.50	49.11	0.95	1.17
−0.350	32.00	65.00	1.79	1.20
−0.375	47.00	95.34	2.03	1.21
−0.400	62.50	104.83	2.11	1.23
−0.450	175.00	122.78	2.84	1.26

.

The average diffusion coefficient values are 8.2 × 10⁻⁷ cm² s⁻¹ and 1.5 × 10⁻⁷ cm² s⁻¹ at pH 5 and 8, respectively. Here, it is important to mention that the diffusion coefficients of Pd(II) ions in different plating baths range between 10⁻⁵ and 10⁻⁸. For example, in baths based on ClO₄ [61], Cl [15], or SO₄ [41], the diffusion coefficient is on the order of 10⁻⁵, while in ammoniacal media, it ranges between 10⁻⁵ [25] and 10⁻⁶ [23]. On the other hand, in eutectic liquids, the value ranges between 10⁻⁷ and 10⁻⁸ [62,63]. It is interesting to mention that the highest diffusion coefficient values have been obtained when the predominant chemical species in the bath corresponds to PdCl₄²⁻, while intermediate values correspond to cases where the predominant chemical species is Pd(NH₃)₄²⁺. In our case, the value of the diffusion coefficient at pH 5 is close to 10⁻⁶, while at pH 8, it is close to 10⁻⁷. This is probably due to the change in concentration of the predominant chemical species as the pH value is changing. It is also interesting to mention that in cases where nucleation proceeds from PdCl₄²⁻, the number of active sites ranges between 10⁶ [23] and 10⁸ [11,61,62], while in cases where the aminocomplex is employed, the values rise to eutectics ranging between 10⁸ and 10⁹ [62]. This suggests that the composition of the medium and its interaction with the surface may cause these kinetic parameters to be appreciably modified. On the other hand, the high values of the nucleation rate reported in Table 1 and Table 2 suggest an instantaneous nucleation process and the formation of homogeneous nuclei on the HOPG surface. Also, note that from Table 1 and Table 2, note that the k_PR, A and N₀ values increase as the applied potential becomes more negative. An increment in k_PR values at lower applied potentials indicates that the reduction proton process is favored at greater overpotentials. The last result suggests a competition by H⁺ ions with the Pd²⁺ ions by the active sites on the electrode surface.

Analysis of the Kinetic Parameters

Using the physical constants provided in Table 1 and Table 2, we were able to calculate the saturation nuclear number (N_s) using Equation (13):

$$N_S={\left(\frac{A{N}_0}{2k^{\prime }D}\right)}^{1/2}$$

(13)

where

$$k^{\prime }=\frac{4}{3}{\left(\frac{8\pi {\mathrm{c}}_{\mathrm{o}}M}{\rho }\right)}^{1/2}$$

(14)

Table 3. N_s values calculated from physical constants reported in Table 1 and Table 2 according to Equation (13).

pH 5		pH 8
E /V	NS × 10−9 /cm2	E /V	NS × 10−9 /cm2
−0.050	0.15	−0.235	0.46
−0.100	0.33	−0.250	5.84
−0.150	0.68	−0.300	12.75
−0.200	1.41	−0.350	17.11
−0.250	2.67	−0.375	23.57
−0.275	3.64	−0.400	27.94
−0.300	4.07	−0.450	43.61

reports the N_S values obtained in the present work. Note that these values increase with applied potential. Additionally, it can be observed that the values of N_S are lower at pH 5 compared to pH 8, likely due to the occupation of active sites on the HOPG electrode surface by NH₄⁺ and H⁺ ions in the acid solution [64].

In the context of the atomistic theory of electrolytic nucleation, one can estimate the critical size of the Pd nucleus (n_c) based on the potential dependence of A using the following equation [65].

$$n_c=\left(\frac{K_{B}T}{{ze}_0}\right)\left(\frac{dlnA}{d\eta }\right)-\alpha$$

(15)

where α is the transfer coefficient for Pd reduction. The plots ln A vs. η, Figure 8, exhibited a linear trend, and the critical cluster’s size calculated employing Equation (15) was n_c = 0 at pH 5, indicating that each active site serves as a critical nucleus. At pH 8, n_c = 1, suggesting that the critical nuclei require a Pd atom. The rate constant k_PR can also be represented by a Butler–Volmer type relationship, as described in Equation (16) [66], and by examining the slope of the ln k_PR versus E plot, Figure 9, one can estimate the value of α_PR. In this study, we found that c_PR = 0.07 at pH 5 and α_PR = 0.006 at pH 8. These values fall within the range reported for the proton reduction process on various substrates [67].

$$k_{\mathrm{P}\mathrm{R}}=k_{\mathrm{P}\mathrm{R}}^{0}exp\left[\frac{-{\propto }_{\mathrm{P}\mathrm{R}}zFE}{\mathrm{R}T}\right]$$

(16)

3.4. Morphological Study

The morphology of the electrodeposits was investigated using Scanning Electron Microscopy (SEM). SEM images were acquired for electrodeposits formed potentiostatically at −0.300 V under both pH 5 (Figure 10a,b) and pH 8 (Figure 10c,d) conditions. If one directly counts the number of nuclei in Figure 10b,d, there are approximately 318 nuclei and 210 nuclei, respectively, in the area shown. From this number, one can calculate the number of nuclei per cm². For pH = 5, the value is 39.8 × 10⁹ nuclei per cm², while for pH = 8, the value is 28.7 × 10⁹ nuclei per cm². Note that these values are in the same order as the number of active nucleation sites reported in Table 1 and Table 2. However, there is a higher number of nuclei at pH 5 in comparison to pH 8. This is probably due to the overlapping of nuclei observed at pH 8, which is less pronounced at pH 5. These results suggest that this phenomenon must be considered to predict more accurate values when the nuclei overlapping is significant. However, from the results, it is clear that the number of nuclei predicted by the nucleation model employed in this work compares favorably with those obtained via SEM studies. Thus, as shown in Figure 10, these SEM images clearly depict the formation of dispersed and small Pd clusters on the HOPG surface. Based on the SEM images acquired for electrodeposits formed at different pH conditions, it is evident that there are significant differences in the sizes of Pd clusters obtained. At pH 5, larger Pd clusters with an average diameter of 27 nm and a height of 39 nm were observed, while at pH 8, Pd agglomerates with Pd clusters with an average diameter of 12.8 nm and a height of 16.6 nm were obtained. The Pd clusters obtained in this study resemble those achieved on HOPG when KCl is used as the supporting electrolyte [15], but they appear smaller when HCl is utilized [62]. Thus, these variations in cluster size suggest a competition for the available nucleation active sites between the proton reduction and the Pd electrodeposition processes. This competition between the proton and palladium processes ultimately influences the size and morphology of the Pd clusters formed on the HOPG surface. Thus, at pH 5, where the proton reduction process is more dominant, dispersed larger Pd clusters tend to form. Conversely, at pH 8, where conditions favor Pd electrodeposition, smaller Pd clusters are favored in agglomerates of different sizes.

4. Conclusions

In this study, we investigated the electrochemical deposition of palladium from ammoniacal solutions, specifically focusing on pH values of 5 and 8, where the predominant chemical species in the plating bath is Pd(NH₃)₄²⁺. Voltammetric studies revealed a higher energy requirement for Pd electrodeposition at pH 8 compared to pH 5. Additionally, voltamperometric studies indicated a diffusional control mechanism. Via potentiostatic studies, we evaluated and analyzed kinetic parameters such as the diffusion coefficient (D), the number of active nucleation sites (N₀), the nucleation rate (A), and the rate constant of the proton reduction process (k_PR). These parameters are dependent on the applied potential and are influenced by the concurrent proton reduction process. Scanning Electron Microscopy provided insights into the structure of Pd clusters deposited on the HOPG electrode. Interestingly, at pH 5, the clusters exhibited larger dimensions, with an average diameter of 27 nm and a height of 39 nm. In contrast, at pH 8, smaller clusters were observed, characterized by an average diameter of 12.8 nm and a height of 16.6 nm, forming agglomerates of various sizes. These observations underscore the competition for nucleation sites between the proton reduction and Pd electrodeposition processes.