**1. Introduction**

Given its increasing volume and high content of both hazardous and valuable materials contained within, electronic and electric equipment (e-waste) represents an emerging environmental challenge as well as a business opportunity [1]. It is globally recognized that e-waste can be considered as a secondary metallic source to compensate for the excessive demand for mining, enabling a more circular economy for these materials [2].

Printed circuit boards, the key components of electronic devices, are, in their simplest form, a mixture of woven glass reinforced resin and multiple types of metal, and are currently recycled by pyrometallurgy, along with other e-waste products. Table 1 shows the content of selected WPCBs. Waste printed circuit boards can contain up to 60 elements that are classified into two categories: metallic and non-metallic materials [3]. Generally, a printed circuit board is composed of approximately 30–40% metals (such as: copper, iron, nickel, lead, tin, silver, gold, and palladium), 30% organic resin and 30% refractory oxides (mainly glass fibers). The composition of printed circuit boards varies depending on their designs, ages, and applications.


**Table 1.** Selected material composition of Waste Printed Circuit Boards (WPCBs).

As of November, 2017, current payout rates of sorted boards, such as low-grade boards, mid-grade boards, metal multi socket server motherboards, laptop motherboards, hard drive boards, and cell phone boards, ranged from \$0.3 to \$20 per kilogram [10], depending on the various designs, ages, and chemical compositions of the boards. In addition, an estimation of the market value of the metals present in PCBs was conducted to verify if the recovery of metals from the PCBs is cost-effective. For this calculation, an averaged concentration of metals in the printed circuit boards based on data from Table 1 and prices of metals (Cu, Au, Ag, Pd, Sn, Ni, and Zn) on December 1st, 2017 from InvestmentMine [11–18] were used and shown in Table 2. The price of iron was taken from Scrap Metal Pricer on March 21st, 2020 [19].

**Table 2.** Market value of printed circuit boards.


This data yields a market value of approximately \$ 15,231/ tonne of WPCBs. More than 80% of the overall market value is from precious metals (Au, Ag and Pd), even though the concentration of base metals (Cu, Zn, Ni and Sn) is much greater than the concentration of precious metals present in printed circuit boards.

As our previous review article summarized [20], oxidative acids are extensively used to recover base metals from waste printed circuit boards. Table 3 summarizes the advantages and disadvantages of four selected reagents for base metal extractions. Precious metals are noble in the normal environment and require high oxidation potential during leaching. The most common leaching reagents for precious metal leaching include cyanide, thiourea and thiosulfate because they form stable metal complexes [2]. Table 4 demonstrates a comparison between several common leaching reagents for gold extraction.


**Table 3.** Comparison of potential leaching reagents for base metal extraction from waste printed circuit boards [2,20–23].

**Table 4.** Comparison of potential leaching reagents for gold [2,20,24,25].


Using a halide system provides the possibility of direct leaching and recovery of precious metals. Chlorination was extensively introduced to the gold extraction industry in the 1800 s, prior to cyanide leaching, for the treatment of gold sulfide minerals and refractory gold ores. Two other important halide leaching reagents are bromine and iodine. Generally, the major advantage of halide reagents in the gold leaching is their powerful oxidizing ability, leading to a high dissolution rate compared to alkaline cyanide leaching.

Iodine/iodide has been reported as an alternative to cyanidation with air as the oxidant. The stable gold-diiodo and tetraiodo complexes are stable up to pH 14 [26]. Xu et al. reported that the gold extraction reached approximately 95% under the optimum conditions: an iodide concentration of 1.0–1.2%, H2O2 concentration of 1–2%, leaching time of 4 h, solid/liquid ratio of 1/10, pH 7 and 25 ◦C [27]. Batnasan et al. [28] demonstrated an iodine–iodide leaching process to recover valuable metals from waste printed circuit boards. The results indicated that more than 99% of gold was dissolved, while less

than 1% of silver and palladium were dissolved at the conditions: iodine/iodide mass ratio of 1/6, pulp density of 10%, agitation speed of 500 rpm, 24 h and 40 ◦C [28].

Bromine, one of the halide elements, is used in the production of clear brines for the oil drilling industry, bromine-based biocides for water treatment, and brominated flammable retardants [29]. Bromine is the key element in the production of brominated flammable retardants, and manufacturers commonly produce PCBs with flammable retardants to help meet fire safety standards. Thus, it is necessary to monitor and remove bromine/bromide during e-waste recycling processes. It will be beneficial to investigate the bromine chemistry in the extraction of precious metals from e-waste. Unfortunately, studies on bromine leaching of waste printed circuit boards are limited.

This study first characterizes the printed circuit board material to provide a qualitative and quantitative guidance of a methodology to efficiently separate desirable metals from waste printed circuit boards. Based on the material characterization, the investigation of leaching behavior of waste printed circuit boards using bromine to recover valuable metal was conducted, as bromine can provide a high oxidation–reduction potential.

#### **2. Material and Methods**

#### *2.1. Material*

Waste printed circuit board samples used in this study were provided from Aurubis. Their applications are unknown. All the motherboards were shredded into approximately 2 cm2 by a pilot scale shredder, and then split into approximately 60 kg by a Jones splitter. A Wiley-Mill shredder (Fellner & Ziegler GmbH, Frankfurt, Germany) shredder with a 1 cm round-hole screen was employed to further grind the material. All of the aluminum heat sinks and lithium ion batteries were removed from the motherboards to prevent being stuck in the Wiley Mill. After mixing and splitting, the 27.8 kg of −1 cm material was then ground again by the Wiley-Mill shredder to −5 mm. The 27.8 kg of −5 mm material was then split to 7 kg samples which were used for subsequent experiments. The size distribution is shown in Figure 1.

**Figure 1.** Size distribution of shredded printed circuit boards.

#### *2.2. Chemical Analysis Methods*

The elemental analysis of the shredded waste printed circuit boards was conducted by a two-step digestion (Aqua Regia and HF-HCl-HNO3-H3BO3) for Atomic Absorption spectroscopy (AA) (PerkinElmer AAnalyst 400, PerkinElmer, Inc., Waltham, MA, USA) and Inductively Coupled Plasma Mass Spectrometry (ICP-MS) (Thermo Fisher Scientific, MA, USA) analysis.

#### *2.3. Mineral Liberation Analysis*

Mineral liberation analysis of the WPCBs was conducted by the Center for Advanced Mineral and Metallurgical Processing (CAMP), at Montana Tech of the University of Montana. The analysis was performed by water/methanol separation to remove the fine low-density particles and hydrophobic material, which mostly consisted of fibrous paper and resin. The residue that has heavier density was treated by a heavy liquid separation using di-iodomethane (d = 3.3 g/mL) to further remove circuit board resins and fibers floated in the heavy liquid. The denser particles remained in the bottom of the separation vessel were then mounted in epoxy blocks for examination using Scanning Electron Microscopy-Mineral Liberation Analysis (SEM-MLA).

#### *2.4. Leaching Tests*

A series of bromide leaching experiments were conducted in 250 mL beakers sealed by Parafilm sealing films for a given time period. A schematic diagram of the leaching set-up is given in Figure 2. Since the gold dissolution is known to be exothermic, the 250 mL beaker was placed in a 1 L beaker filled with 300 mL tap water to maintain the desired temperature. A leaching solution of 200 mL with the desired quantity of reagents was used for each experiment. All experiments were carried out using solutions prepared from analytical-grade reagents and distilled water. Unless specified, the solutions contained 10 g of shredded printed circuit boards (particle size-5 mm) and were mixed by a magnetic stir bar at 400 RPM. The oxidation–reduction potential (ORP) and pH were measured by Fisher ScientificTM accumetTM XL 600 m (Fisher Scientific International, Inc., Hampton, USA). Samples of the solution were taken at fixed intervals of time during the leaching experiment and filtered on filter papers (Whatman Grade 42). The filtrate was diluted by 2% HNO3 (TraceSELECTTM nitric acid, Honeywell International Inc., Charlotte, NC, USA), and then analyzed immediately by atomic absorption spectroscopy in order to determine contents of gold and silver. The residue after leaching was then filtered and rinsed with distilled water. The filtered residue was dried, weighed and treated by a 4-acid digestion (HCl-HNO3-HF-H3BO3). The gold and silver contents were then again determined by AA. ICP-MS was utilized to analyze the rest of elements. The concentrations of bromine and sodium bromide, temperature, and inorganic acids were the variables, which were investigated by parametric study.

**Figure 2.** Schematic diagram of leaching set-up.

#### **3. Result and Discussions**

#### *3.1. Sample Characterization*

Table 5 gives a summary of the elemental analysis, where copper is the most abundant metal, followed by iron (6.3%), tin (3.8%) and zinc (3.3%). The most abundant precious metal is silver at 513 ppm. Gold and palladium are also found in the printed circuit boards at 145 and 20 ppm, respectively.


**Table 5.** Elemental composition of shredded printed circuit boards.

The MLA analysis (Table 6) also confirmed that copper was the most abundant metallic element and silver was the primary precious metal found in the printed circuit board. The MLA analysis (Figure 3) also shows that copper is either present as a free copper particle, or associated with other metals, such as silver and gold. Gold is usually found liberated or as gold–nickel alloys (Figures 3 and 4). Moreover, silver either occurs alone or is associated with tin, lead and nickel, as shown in Figures 3 and 5.

**Table 6.** Selected phase concentrations of the concentrated shredded printed circuit boards.


**Figure 3.** Image of gold and silver associations in shredded printed circuit boards (**A**: isolated gold particles; **B**: gold-nickel alloy coatings; **C**: Au coatings; **D**: Ag with FeNi; **E**: Ag with aluminum oxide).

**Figure 4.** Electron Dispersive Spectroscopy (EDS) spectra corresponding to Figure 3 (The label of spectra is corresponding to the label of compounds in Figure 3A–C).

**Figure 5.** EDS spectra corresponding to Figure 3 (The label of each spectra is corresponding to the same label in Figure 3D,E).

#### *3.2. Bromine Leaching Tests*

Methods such as heavy liquid separation, shaking table, flotation, and electrostatic separation proved difficult to extract the metals of interest from shredded waste printed circuit boards with a satisfactory recovery. However, bromine is capable of dissolving gold, silver, palladium and copper. Thus, a direct bromide leaching was utilized to leach the desired metals from printed circuit boards.

Gold dissolves in an aqueous bromine–bromide solution to form both the Au(I) and Au(III) bromide complexes, as follows:

$$\text{Au} + 2\text{Br}^- = \text{AuBr}\_2^- + \text{e} \tag{1}$$

$$\mathbf{A}\mathbf{u} + 4\mathbf{B}\mathbf{r}^- = \mathbf{A}\mathbf{u}\mathbf{B}\mathbf{r}\_4^- + 3\mathbf{e} \tag{2}$$

Figure 6 shows the stability of an Au-Br-H2O system at room temperature. It is evident that gold is readily formed as AuBr4 - ions, except for a narrow potential range (approximately 0.7–0.8 V vs. Ag/AgCl) in which the AuBr2 − ions are dominant. Compared to chlorine (pH 0–7), bromine seems to offer a wider pH range for gold leaching. Eh-pH diagrams for the systems of Ag-Br-H2O, Pd-Br-H2O and Cu-Br-H2O were also constructed for [Br] = 0.775 M and varying concentrations of silver, palladium and copper (Supplementary Materials SM-A1, A2, and A3). These indicate that AgBr3 <sup>2</sup><sup>−</sup> can be found

across the entire pH range when the Eh value is below approximately 0.5 V (vs. Ag/AgCl). In the acidic solution, AgBr3 <sup>2</sup><sup>−</sup> exists if the Eh value is less than 1.1 V (vs. Ag/AgCl). Copper can be dissolved as Cu2<sup>+</sup> and CuBr<sup>+</sup> in the region in which the Eh value is above 0.3 V (vs. Ag/AgCl) and the pH is less than approximately 6. Moreover, there are four major palladium species that are dissolvable (Pd2<sup>+</sup>, PdBr6 <sup>2</sup>−, PdBr4 <sup>2</sup><sup>−</sup> and PdBr3−). The general Eh-pH region in which palladium is present as soluble species is Eh > 0.3 V (vs. Ag/AgCl) and pH < 12.

**Figure 6.** Eh-pH diagram of Br-Au-H2O system at 25 ◦C ([Au] = 10–5 M, [Br] = 0.775 M).

#### 3.2.1. Effect of Liquid Bromine

A series of leaching trials were conducted to investigate the effect of initial liquid bromine concentrations on leaching gold and silver from shredded waste printed circuit boards, given that bromine is not only the source of bromide ions, but also acts as an oxidant, offering a high potential (approximately 1.1 V vs. Ag/AgCl).

Figure 7 shows that the dissolution of gold and silver was significantly influenced by bromine concentration. The bromine concentration increase also leads to an increasing gold dissolution after the 10-h leaching. Other than providing a sufficient amount of bromide ions and bromine, the high concentration of bromine also assures the high potential of the solution throughout the leaching trial, further resulting in a high gold extraction.

**Figure 7.** Dissolution of gold and silver at various concentrations of liquid bromine (23.5 ◦C and natural pH).

In terms of silver, the increasing bromine concentration accelerates the initial silver dissolution rate, until a certain concentration limit (0.97 M Br2) is reached, beyond which bromine has no further effect. It is because the limiting factor for the initial reaction rate is bromine concentration, when the bromine concentration is lower than 0.97 M; beyond 0.97 M, the reaction rate is likely to be limited by active particle surfaces.

In addition, it is interesting to note that at 0.78 M bromine the dissolved silver content increases quickly in the first two hours of leaching, and then a plateau is observed in the next two hours. Subsequently, the dissolved silver continues to increase, as the leaching proceeds. The plateau could be explained by the coating of silver bromide precipitates. Specifically, silver is thought to be initially dissolved by bromine to become silver–bromide complexes and silver–bromide precipitates in the first two hours. As the leaching proceeds in the next two hours, the AgBr(s) and soluble silver complexes are likely to reach equilibrium. However, after the 4-hour leaching, the free bromide/bromine ions react with AgBr(s) precipitates to become soluble silver–bromide complexes, leading to the further increase of dissolved silver in the solution. At the highest concentration of bromine, bromine is excessive; therefore, silver is always soluble in the solution as silver–bromide complexes, leading to an increasing trend of silver extraction [30].

Regarding other metals, such as copper, zinc, and nickel, more than 90% of copper, zinc and nickel can be dissolved over 10 h (Figure 8), when the concentration of bromine is more than 0.78 M.

**Figure 8.** Dissolution of base metals (Cu, Ni and Zn) at various concentrations of bromine (23.5 ◦C and natural pH).

#### 3.2.2. Effect of Sodium Bromide

As stated in previous studies [26,31,32], both bromine and sodium bromide are responsible for gold dissolution. It is, therefore, of interest to investigate the effect of sodium bromide in the presence of bromine, given that sodium bromide itself cannot provide an ORP that is higher than 0.87 V (vs. SHE).

Taking 0.78 M as the bromine concentration, a series of leaching trials was performed to investigate the effect of sodium bromide at room temperature and natural pH. Figure 9 presents leaching performances at various concentrations of sodium bromide, 1.17 M, 1.75 M and 2.33 M. It is evident that the addition of sodium bromide has a positive effect on the dissolution of precious metals (Au and Ag). The addition of sodium bromide raises the gold dissolution from approximately 83% (no NaBr) to more than 96% (1.75 M NaBr) in 10 h. However, beyond a concentration of 1.75 M, the increase of NaBr has no appreciable effect on gold dissolution for the 10-h leaching.

**Figure 9.** Dissolution of gold and silver at various concentrations of sodium bromide (0.78 M Br2, 23.5 ◦C and natural pH).

As shown in Figure 9, it is observed that the initial Ag dissolution rate increases with the NaBr concentration. Meanwhile, a dissolution plateau was also observed when the NaBr concentration is between 0 and 2.33 M. The plateau can be also explained by the formation of AgBr precipitates. Additionally, the initial Au dissolution rate increases significantly as the NaBr concentration increases from 0 to 2.33 M.

Figure 10 indicates that the addition of sodium bromide only has a slightly positive effect on dissolving base metals and palladium, given that the base metals have approached high dissolutions (> 90%). Generally, in order to achieve high extractions for the metals of interest, high consumption of liquid bromine and sodium bromide are likely to be required, which reduces the practical feasibility of this process due to the resulting process economics. Therefore, more efforts should be made to study the effect of other chemical reagents that can either replace or reduce the consumption of bromine and sodium bromide.

**Figure 10.** Dissolution of base metals (Cu and Zn) and palladium at various concentrations of sodium bromide (0.78 M Br2, 23.5 ◦C and natural pH).

#### 3.2.3. Effect of Selected Acids

Despite the technical feasibility of using bromine and sodium bromide to dissolve valuable metals from shredded waste printed circuit boards, their relatively high prices and the high consumption of sodium bromide during the process limits its industrial feasibility. Therefore, it is important to investigate alternative approaches to either replace sodium bromide or reduce its usage.

In the leaching system, the dissolution of gold and silver requires the presence of bromine, because bromine serves not only as the bromide source, but also offers a high oxidation–reduction potential, which is essential for the reaction to proceed. Meanwhile, sodium bromide provides sufficient bromide ions, along with bromine, for forming soluble gold–bromide/silver–bromide complex ions. With regard to copper, bromine plays a role in maintaining a high potential for copper oxidation. At the same time, as shown in Equation (3), bromine reacts with water to reversibly produce HBr and HBrO. Hydrobromic acid serves as a strong acid to dissolve copper at a high oxidation–reduction potential.

$$\rm HBr\_2 + H\_2O = HBr + HBrO \tag{3}$$

Other base metals are likely to react with hydrobromic acid to form metal ions, and sodium bromide does not appear play a role in their leaching. Therefore, in order to lower the sodium bromide usage, several relatively inexpensive mineral acids (HCl, HNO3 and H2SO4) were investigated to leach shredded waste printed circuit boards.

Given that sulfur is abundantly available [33] and sulfuric acid is relatively cheap, sulfuric acid is widely used for the leaching of a wide variety of metal resources, including oxides, sulfides, silicates, phosphates, and a number of others [34]. Pesic and Sergent (1993) studied the effect of sulfuric acid on gold dissolution and found that the presence of sulfuric acid did not affect the dissolution of pure gold in a bromine–bromide leaching system [32]. Therefore, a study was performed in the presence of two concentrations (0.9 M and 2.7 M) of sulfuric acid under the condition of 0.77 M Br2, 1.17 M NaBr and 23.5 ◦C, as well as 400 RPM. Table 7 shows a summary of the experimental data. Notably, the increase of H2SO4 concentration significantly decreases the gold dissolution, which could be explained by gold surface passivation. Based on the literature [35], a passive oxide layer may be formed on the surface of gold particles in the presence of sulfuric acid, and the passivation behavior is more pronounced at the high concentration of sulfuric acid.


**Table 7.** Summary of leaching experiment in the presence of inorganic acids.

To investigate the effect of various mineral acids, a series of 10-h leaching trials was conducted under the condition of 0.77 M Br2, 1.17 M NaBr and 23.5 ◦C, as well as 400 RPM. Hydrochloric acid, nitric acid and sulfuric acid were chosen and diluted to a concentration of 5 v/v% (2.0 M HCl, 1.2 M HNO3, and 0.9 M H2SO4).

The experimental results indicated that the presence of the three acids significantly increased the silver extraction, compared to the leaching performance in the absence of mineral acids (shown in Table 7). Sulfuric acid, nitric acid and hydrochloric acid are capable of dissolving more than 95% of base metals, including nickel, zinc, tin and copper. However, sulfuric acid can only dissolve 91% of gold, which is lower than nitric acid and hydrochloric acid. Nitric acid and hydrochloric acid give similar leaching performances; hydrochloric acid, nonetheless, is likely to be superior compared to nitric acid, due to the following reasons:


In order to validate the leaching reproducibility under optimal conditions, more leaching experiments were conducted, and the data is shown in Table 8. The optimal condition is 50 g/L solid/liquid ratio, 1.17 M NaBr, 0.77 M Br2, 2 M HCl, 400 RPM agitation speed and 23.5 ◦C for 10 h.


**Table 8.** Triplicate leaching results under optimal conditions.

To characterize the leaching residue from the triplicate experiments, a SEM-EDS analysis was conducted. Prior to the SEM analysis, the leaching residue was first ground and then rinsed by deionized water and acetone to eliminate the bromine effect and liberate the leaching residue of the waste printed circuit boards. As shown in Figures 11 and 12, it is obvious that there is a gold particle with a particle size of 50 μm. The reason that the gold was not dissolved during the leaching process is that it was not well liberated. Since the residue was further ground before the SEM analysis, the gold was exposed, as shown in Figure 11.

**Figure 11.** Backscattered Electron (BSE) image of leaching residues.

**Figure 12.** EDS spectra for Point B and C (BSE image).

#### *3.3. Leaching Kinetics*

To understand the kinetics of bromide leaching of gold from waste printed circuit boards, it is of interest to first determine a rate expression of the bromine–gold system, which can subsequently be utilized to create a leaching model. To do so, the first step is to determine the variables in the leaching system. In this study, the concentrations of bromine, sodium bromide and copper, and agitation speed, as well as temperature, were the parameters investigated.

In this study, the gold present in waste printed circuit boards is dissolved in a bromine–sodium bromide system to form a gold–bromine complex. The metallic copper in the waste printed circuit boards precipitates the metallic gold from the gold–bromine complex, as shown in Equation (4).

$$\text{Cu} + 2\text{AuBr}\_4^- = \text{Cu}^{2+} + 2\text{Au} + 8\text{Br}^- \tag{4}$$

Therefore, the reaction rate of the gold dissolution can be written in an explicit form shown as Equation (5), and the overall order of the reaction is simply the sum of a, b and c. In this study, given that the concentrations of the reagents are low, it is reasonable to assume that the activity coefficient is equal to 1.

$$\mathbf{r} = \mathbf{k} \cdot \mathbb{C}\_{\text{Br2}} \mathbf{a}^{\text{a}} \cdot \mathbb{C}\_{\text{NaBr}} \mathbf{b}^{\text{b}} \cdot \mathbb{C}\_{\text{Cu}} \mathbf{c}^{\text{c}} \tag{5}$$

An isolation method was utilized to determine the reaction order for each reactant by isolating each reactant in turn and keeping all other reactants in large excess.

Table 9 illustrates the initial reaction rates of gold dissolution with respect to various concentrations of bromine, copper and sodium bromine at 23.5 ◦C and 400 RPM. The reaction orders regarding bromine concentration, sodium bromide concentration and copper concentration, respectively, were estimated to be 0.55, 0.16 and −0.41, respectively. The experimental data is displayed in Supplementary Materials (SM-B1, B2, B3 and B4). Therefore, the rate expression can be written as Equation (6).

$$\mathbf{k} \cdot \mathbf{r} = \mathbf{k} \cdot \mathbf{C}\_{\text{Br2}} ^{0.55} \cdot \mathbf{C}\_{\text{NaBr}} ^{0.16} \cdot \mathbf{C}\_{\text{Cu}} ^{-0.41} \tag{6}$$


**Table 9.** Gold dissolution rates at various concentrations of Br2, NaBr and Cu at 23.5 ◦C and 400 RPM.

The boiling point of liquid bromine is around 58.8 ◦C, so the selected temperatures are 23.5, 34 and 42 ◦C. The Arrhenius Plot (Supplementary Materials SM-B6) showed that the activation energy was 26.37 KJ/mole (6.3 Kcal/moles). Therefore, by taking 26,365 J/mole for the activity energy, the Equation (6) can be rewritten as follows:

$$\text{Tr} = 0.196 \cdot \text{EXP} \text{(-26365/RT)} \cdot \text{C}\_{\text{Br2}} \,^{0.55} \cdot \text{C}\_{\text{NaBr}} \,^{0.16} \cdot \text{C}\_{\text{Cu}} \,^{-0.41} \tag{7}$$

The geometry of the shredded printed circuit boards is classified into two categories, spherical particles and flat plates, due to chemical compositions and structures of printed circuit boards. Based on the average thickness of printed circuit boards, minus 149 μm particles were likely to have spherical geometries; whereas the particles larger than 149 μm were considered as being flat. As shown in Figure 1, approximately 15% of the shredded waste printed circuit boards are smaller than 149 μm; while approximately 85% of the boards are larger than 149 μm.

In this study, assuming bromide ions are excessive, silver is completely dissolved as soluble silver bromide complexes. Thus, there is no solid product and the solid A always shrinks, the heterogeneous irreversible reaction can be expressed as follows:

$$\text{aA}\_{\text{(solid)}} + \text{bB}\_{\text{(augeous)}} = \text{cC}\_{\text{(augeous)}} \tag{8}$$

There are two assumptions as follows, (1): the concentration of reactant B at the interface of solid A is zero in a diffusion-controlling process; (2): the concentration of reactant B at the interface of solid A is equal to the bulk concentration of B in a chemical-controlling process.

In a quasi-steady state with a constant atmospheric pressure, the kinetic derivation was displayed in Supplementary Materials (SM-C). The fluid film diffusion control and chemical reaction control can be expressed as follows:

Diffusion control for spherical particles

$$\mathbf{t}/\mathbf{t}\_{\mathbb{C}} = 1 - \left\langle 0.15(1 - \chi\_{\text{Au}}) \right\rangle^{2/3} \tag{9}$$

Chemical reaction control for spherical particles

$$\text{tf}\mathfrak{t}\_{\text{c}} = 1 - \left[ 0.15(1 - \chi\_{\text{Au}}) \right]^{1/3} \tag{10}$$

Diffusion control for flat particles

$$\mathbf{t}\dagger\mathbf{t}\_{\mathbf{c}} = 0.85\mathbf{\hat{X}}\_{\mathbf{A}\mathbf{u}} \tag{11}$$

Chemical reaction control for flat particles

$$\mathbf{t}/\mathbf{t}\_{\mathrm{c}} = 0.85 \mathbf{\hat{X}}\_{\mathrm{Au}} \tag{12}$$

The calculated gold extraction from a selected kinetic test was substituted into Equations (9–12) for each of the possible controlling mechanisms, and the values of t/tc were plotted as a function of time, as shown in Figure 13.

**Figure 13.** Kinetic calculation for a leaching trial in the presence of 0.776 M Br2 and 0.166 M NaBr at 23.5 ◦C and 400 RPM.

R-squared values (Figure 13) for chemical control are relatively higher than fluid control for spherical particles. Moreover, the calculated data shows that the fluid film diffusion controlling is still responsible for the bromide leaching of gold. The mechanism is complex with both a chemical controlling and fluid film diffusion controlling. This could be explained as follows:

	- (1) Adsorption of bromine and bromide on the gold surface to form AuBr2 [32],
	- (2) Oxidation of AuBr2 <sup>−</sup> to produce a stable species, AuBr4 −,
	- (3) Copper cementation to reduce AuBr4 <sup>−</sup> to Au0.

Generally, in the current study, gold dissolving in a bromide system is complex, especially in extremely heterogeneous printed circuit boards. By calculating the activation energy (26.37 KJ/mole), the combination of diffusion and chemical controlling are responsible for the gold dissolution. By assuming that the acceptable R-squared value is 90%, the spherical and flat models demonstrate that the reaction is controlled by chemical reaction and fluid film diffusion. However, additional studies should be performed to eliminate the impurity effect by using a gold disc technique and correlate the existing kinetic model with other factors, such as gold distribution and adsorption.
