A Kinetic Study of Silver Extraction from End-of-Life Photovoltaic Panels through Gold-REC1 Process

Abstract

Recycling materials from end-of-life devices and products is becoming increasingly a fundamental activity for the sustainable development of nations. With the return from the market of immense quantities of photovoltaic panels at the end of their life, it is essential to foresee processes for recovering and valorizing all the raw materials present in them to avoid wasting important flows of raw materials. This research introduces a novel process aimed at the recovery of silver and silicon from end-of-life photovoltaic panels. The leaching efficiency and kinetics of ground cake powder in sulfuric acid, ferric sulfate, and thiourea were investigated in the leaching system. In particular, the influences of significant parameters, including particle size, leaching temperature, and stirring rate, on the extraction kinetics were analyzed using the shrinking core model. The results showed silver dissolving mechanisms, in which more than 90% of silver recovery at 60 min of reaction time and 99% at 120 min was achieved (120 rpm, 53–125 µm, and 40 °C). The significant effect of the leaching temperature suggests that the process is under the control of the chemical reaction. Moreover, these results were confirmed by the regression analysis of the experimental data with the shrinking core model. It can be concluded that this newly proposed process, called Gold-REC1, allows the recovery of Ag and Si (solid residue from the process) with extremely high yields and rapid kinetics. The obtained results can provide fundamental data for developing end-of-life photovoltaic recycling on an industrial scale.

1. Introduction

Over the past decade, photovoltaic (PV) panels have been recognized as a new technology for electricity generation worldwide. PV modules convert solar energy into electricity without emitting pollutants, creating waste, or producing greenhouse gases. In addition, this operation uses minimal material resources and is a completely environmentally friendly option [1,2]. The expansion of photovoltaic power plants, low efficiency of module production processes resulting in waste generation during production, as well as the increase in waste from panels reaching the end of their life cycle (the average lifespan of these modules is about 25 to 30 years), have caused the production of a considerable amount of waste [3,4]. This surge in waste production poses a pressing need for safe disposal solutions to manage the substantial volume of waste created [5].

Since 2012, PV modules have been included in the scope of waste electrical and electronic equipment (WEEE) regulations in the European Union. In response, the European Union has published specific policies and guidelines addressing end-of-life PV module management [6,7]. These regulations mandate manufacturers and importers to undertake these operations’ collection, transportation, recycling, and financing. According to the WEEE directive, EU member states are required to achieve a collection rate of 85% and a recycling rate of 80% for materials used in PV modules. Although the global average recycling rate for PV modules was 14% in 2019, it is predicted that under an optimistic recycling scenario, this rate could increase to 35% by 2030 and reach 70% by 2050 [8].

Disposal of end-of-life photovoltaic panels is a dual challenge. These panels contain dangerous elements such as lead, tin, and cadmium, which cause environmental pollution and human health. On the other hand, these end-of-life (EOL) panels also contain valuable and basic elements such as silver, tin, aluminum, copper, and silicon [9,10,11]. Therefore, recycling these materials not only reduces environmental and health risks but is also significant from an economical and sustainable development point of view and ensures the long-term stability of the supply chain [12]. It is necessary to implement effective recycling methods for valuable and dangerous elements to exploit the economic power of these resources while preserving the environment and human health [13,14]. The rapid expansion of greenhouse technology underscores the increasing need for efficient recovery methods for end-of-life PV panels within this industry [15]. While the advanced technology discussed shows promise, a thorough cost–benefit analysis is essential to assess the feasibility of recycling PV panels from greenhouse applications. It is important to note that greenhouses are among the primary users of PV panels.

PV panels are classified into three generations based on manufacturing technology [16,17]: (1) Silicon crystalline (Si-C) panels, which use silicon as the main material for both mono and polycrystalline form [18]. (2) Thin layer panels (also known as CIGS panels) which contain essential metals such as tellurium, germanium, indium, and gallium; the composition of thin film panels make them very suitable for recycling and promises many benefits in terms of sustainability and resource recovery [19]. (3) Concentrated photovoltaics (CPVs) and emerging technologies where advanced technology has been used to produce these panels, and are mainly in the research step and not widely commercialized [20,21]. Currently, Si-C panels make up most of the PV market, accounting for about 95% of total production in 2020. The primary structure of these panels (whether monocrystalline or polycrystalline) typically comprises an aluminum frame, glass cover sheets, a back sheet, and multi-layer crystalline silicon wafers laminated between two ethyl vinyl acetate (EVA) sheets [22]. These panels are mainly made of silicon and silver strips [23]. As a result, at the end of the life cycle of PV panels, most of them can be considered Si-C panels.

Although various methods to recycle solar panels have been explored, they typically include three main stages: delamination, separation of materials (including metallic and non-metallic compounds), and extraction and purification [2,14]. The delamination process can be performed through various methods, including mechanical, chemical, thermal, and solvent processes where aluminum, glass, and silicon are removed [24]. The extraction stage is carried out to attain the necessary purity level of the metals in the production process [16]. This process often utilizes hydrometallurgical methods, including leaching, precipitation, liquid–liquid extraction, electrowinning, and ion exchange, to extract and purify metals efficiently [25,26].

Extracting valuable metals from waste materials is a fundamental aspect of recycling, especially in sustainability and resource conservation. Among these metals, silver extraction from photovoltaic panels is pivotal in the panel recovery process.

In 2012, Kuczyńska-Łażewska et al. investigated the dissolving of silver from PV modules using nitric acid as a leaching agent, and silver was precipitated using sodium chloride. The recovery of silver in this method reached 94%. In another experiment, they recovered silver through a pyrolysis process preceding leaching; this approach’s efficiency was reported to be 92% [27].

In 2023, Kastanaki et al. studied the hydrothermal leaching of silver and aluminum from crystalline silicon panels. Before the leaching process, pre-treatment was conducted to remove and thermally destroy the polymers. This research was carried out using response surface methodology to design experiments and optimize the parameters. The results showed that the leaching time parameter had the most significant effect on the dissolution efficiency of silver in nitric acid, while the effect of leaching temperature was insignificant. Based on the results, the optimal parameters for the hydrothermal process for nitric acid concentration, solid-to-liquid ratio, reaction time, and leaching temperature were 2 M, 10%wt./vol., 120 min, and 140 °C, respectively. At these levels, Ag and Al were efficiently extracted. Considering the temperature as an insignificant parameter, other experiments were conducted at a lower temperature and a longer time, which showed that silver dissolving efficiency decreased from 100 to ~80% and aluminum dissolving reduced to ~60% [28].

In 2022, Theocharis et al. employed a thermal treatment process followed by a hydrometallurgical approach to extract silver and silicon. This process involved crushing PV modules, recovery of aluminum frames, junction boxes, copper cables, and silicon cell delamination. Silver and aluminum were leached by nitric acid at an ambient temperature, and in the following experiment, sulfuric acid was applied to extract aluminum, and silver was leached by nitric acid at room temperature. The dissolved silver was precipitated as AgCl and separated from the nitrate solution by electrowinning. Subsequently, aluminum was separated by the neutralization method [29].

In another study, PV panels (Si-C) were subjected to a two-step leaching process consisting of nitric acid at 80 °C for 4 h, followed by leaching using 3 M sodium hydroxide at 70 °C for 3 h. This method achieved a high leaching efficiency, which reached 99.7% for silver and 99.9% for aluminum. Subsequently, the mixture of Cyanex 272 and kerosene was used to separate aluminum from silver, from which a remarkable extraction efficiency of 96% was obtained. Furthermore, the dissolved silver was precipitated as silver chloride. Notably, the silicon obtained from this process had a purity of 99.5% [1].

Thiourea is another important leaching agent for silver recovery. In 2012, Jing-ying et al. studied the influence of particle size, thiourea and Fe³⁺ concentrations, and temperature on the leaching of gold and silver from waste mobile phones. They found that 50% of silver was dissolved by the reaction of 2 h by 24 g/L thiourea and 0.6% of Fe³⁺ leaching solution [30].

In 2018, Lee et al. studied the recovery of gold and silver from electronic waste through thiourea leaching. The thiourea leaching was carried out under different leaching conditions, obtaining very high leaching efficiencies for gold and silver (90% and 100%, respectively) using one-step thiourea leaching [31].

This research investigates the dissolution mechanism of silver from PV panels utilizing the GOLD-REC1 process [32]. The patent was developed to recover precious metals from printed circuit boards, particularly gold (as the name suggests). Numerous studies have demonstrated that thiourea effectively recovers precious metals as a cyanide substitute. Ferric sulfate is an excellent oxidant, with sulfuric acid acting as a catalyst. With increasingly large quantities of end-of-life panels, evaluating the technical and economic feasibility of treating this type of waste with the GOLD-REC1 process is important.

This process allows selectively separating silver and silicon from mechanical pre-treatment of end-of-life panels. The first step of the process consists of leaching the silicon and silver powder using an acid solution of sulfuric acid/thiourea/ferric sulfate. The leaching solution of this step, loaded with silver, is transferred to a silver recovery step where the different reagents are partially regenerated. The residual solid can be further refined to be sold as high-purity silicon. The process is highly advantageous compared to others in the literature, given the high extraction yields, the purities of the products that can be achieved, and the very low CAPEX and OPEX (elementary and consolidated operations at the industrial level). In fact, for a flow rate of 1000 tons/year of powder (about 4000 tons/year of panels), a payback period (PBP) of about three years was calculated.

Although some previously published articles studied the leaching kinetics of silver from PV panels, the dissolution of valuable metals from the EoL PV Panels using sulfuric acid/thiourea/ferric sulfate was not evaluated. This research, in addition to evaluating the kinetics of silver leaching from PV panels, focuses on studying the influence of operational parameters, such as particle size, reaction temperature, and mixing rate, on the dissolution efficiency of Ag. Moreover, this research tries to optimize these parameters to increase the overall process efficiency. By providing a thorough analysis of metal behavior during the leaching process using the GOLD-REC1 approach, this study contributes valuable insights for scaling up this process to industrial applications.

2. Materials and Methods

The sample used as raw material in the leaching process was provided by an Italian company after a mechanical pre-treatment of end-of-life photovoltaic panels; the powdered sample is shown in Figure 1.

This pre-treatment was performed through the SOLAR 4.0 system [33]. This method allowed the recovery of the aluminum frame as well as the valuable metals. The process of glass delamination occurred through a series of special steel tools that gradually removed the glass without contaminating it with other items within the photovoltaic panel. After the glass was removed, the panel was shredded, and the materials were mechanically divided into three parts: copper, plastic, and silicon powder. Figure 2 shows the simplified scheme of the SOLAR 4.0 system.

The silicon powder contained traces of various metals, of which silver was the most important from economic and strategic points of view, initially present as a conductive material to create electrical contacts on solar panels. This silicon powder was the sample used as the feed in the leaching process.

2.1. Sample Characterization

The particle size distribution of the received powder was studied. In this regard, the sieve method (40, 53, 125, 212, 425, 850, and 1180 mm) was applied to determine the size distribution of raw materials.

In addition, the concentration of the metals present in the three fractions of smaller than 53 µm, 53 µm to 125 µm, and larger than 125 µm was measured using inductively coupled plasma optical emission spectroscopy (ICP-OES), which the composition of the solid sample was calculated through an element balance. It should be noted that aqua regia (HCl:HNO₃ of 3:1) was used to dissolve the solid samples. This procedure was carried out with three replications for each fraction to establish the average concentration and standard deviation.

2.2. Experimental Procedures

Several leaching experiments were conducted to investigate the mechanisms of dissolving silver by the GOLD-REC1 process and determine the kinetics of leaching silver from EoL photovoltaic panels according to operational parameters. For this reason, the effects of particle size of raw material, reaction temperature, and stirring rate on the dissolving of silver were studied, and the mechanisms of dissolving were evaluated by the kinetic coefficients and dissolving efficiency.

The experimental tests were carried out following a precise operational scheme, with an overall duration of 225 min. First, the water with the thiourea was placed in a beaker and left for 10 min to allow the thiourea to dissolve fully. In the second step, the ferric sulfate and sulfuric acid were added (after 15 min). In the next step, the solid sample was added (after 20 min). After 3 h (reaction time between the leaching reagents and the silver), the solution was filtered with a vacuum filtration system, obtaining a permeate rich in Ag⁺ ions. This liquid solution was then analyzed via ICP-OES (Agilent, model 5100) to determine the concentration of the ions of interest.

Throughout the leaching reaction, solution samples were taken at pre-established times (5, 10, 15, 30, 60, 120, and 180 min) to study the progress of the reaction over time. In order to keep the concentration of the reagent almost constant during the experiment, the solid-to-liquid ratio (S/L) was set at 2% wt./vol. Thus, 2 g of powder was added to 100 mL of leach solution in a glass flask. The concentration of the reagents is shown in

Table 1. Reagents concentration for all different tests according to the GOLD-REC1 process.

Reagent	Concentration
Thiourea	20 g/L
Ferric sulfate	22 g/L
Sulfuric acid	0.1 mol/L

.

2.3. Kinetics Model

Silver leaching through the GOLD-REC1 process occurs by the following reactions:

Ag + Fe³⁺ + 3 SC(NH₂)₂ → (Ag(SC(NH₂)₂)₃)⁺ + Fe²⁺

(1)

2 SC(NH₂)₂ + 2 Fe³⁺ → C₂H₆N₄S₂ + 2 Fe²⁺ + 2 H⁺

(2)

2 C₂H₆N₄S₂ → SC(NH₂)₂ + CN₂H₂ + S

(3)

The reactions mentioned above are heterogeneous as they involve the solid phase containing silver and the liquid phase with the other ions coming from the reagents. To understand the mechanisms underlying silver leaching with this process, the shrinking core model [34] was used. To describe the progress of silver dissolution over time, the conversion $X$ was defined as the following:

$$X(t)={\displaystyle \frac{C_{Ag}^L\left(t\right)·V^L}{{\omega }_{A_g}^S{·m}^S}}$$

(4)

where $C_{Ag}^L\left(t\right)$, is the concentration of silver in the leaching solution (mg/L), $V^L$ is the volume of the leaching solution (L), ${\omega }_{A_g}^S$ is the mass fraction of silver in the initial solid (%wt.), and $m^S$ is the mass of the initial solid used in the test (mg).

Under the assumptions of constant reagent concentration throughout the test, it is possible to use the equations of the shrinking core model in integral form. It should be noted that three phenomena mainly influence the overall silver dissolution reaction: diffusion through the boundary layer external to the solid particles, chemical reaction, and diffusion internal to the solid particle. The equations describing these phenomena are reported in

Table 2. Equations of the shrinking core model.

Phenomenon	Model
Diffusion of chemicals outside the solid particles	$X=k_{F}t$
Chemical reaction	$1-{\left(1-X\right)}^{1/3}=k_{R}t$
Diffusion of products into the solid particle	$1-3{\left(1-X\right)}^{2/3}+2\left(1-X\right)=k_{P}t$

.

All three equations were obtained by assuming the reactant concentration in the solution was constant. This ideal condition approximates the cases where the solid–liquid ratio is meager. A suitable kinetic model was selected based on the results of the analysis of variance. Thus, a factorial plan 2³ was set up with agitation, particle size, and temperature as factors; agitation mainly influences diffusion through the liquid layer. A similar discussion applies to the particle size linked to internal diffusion and the temperature associated with the reaction rate.

The mixing conditions mainly influence the thickness of the liquid film surrounding the particles and the presence of chemical species on the surface of the unreacted nucleus. The size of the particles is a parameter that affects the extraction rate. A greater surface area is available for smaller particles to interact with the liquid, and the boundary layer is thinner, leading to a faster extraction [34]. Temperature can influence extraction kinetics in several ways. It can accelerate the diffusion rate, promote the rate of chemical reactions, influence the solubility of compounds (reactants and products), and change the direction of reversible reactions. The activation energy of a chemical reaction is generally greater than diffusion, which is a physical phenomenon. Consequently, the chemical reaction is more sensitive to temperature than diffusion [35]. In general, the effect of temperature on the extraction rate can be represented by the Arrhenius equation:

$$k\left(T\right)=k_0{e}^{-\left({\displaystyle \frac{E_a}{RT}}\right)}$$

(5)

Each model described was considered and compared with the others while interpreting the experimental data. For the calculation of the $E_a$ and the pre-exponential parameter, the model with the greatest fit compared to the experimental data and which best explains the results obtained on a theoretical level will be chosen each time.

3. Results and Discussions

3.1. Characterization

Figure 3 shows the cumulative and non-cumulative plots of particle size distribution (PSD) and the results of XRD (X’Pert PRO powder and film diffractometer) for the granulometric fraction having a diameter < 125 μm. Common PSD functions were analyzed to find the best data fit [36]. The Log-normal is the PSD function that describes the experimental data with the highest accuracy.

Based on the results obtained from the particle size distribution and the available material, three different particle size fractions, such as −53 µm, 53–125 µm, and +125 µm, were selected to study the effect of this factor on the silver dissolution yield.

Table 3. Metal composition of the three particle size fractions.

	Particle Size Fraction
	<53 μm	53 μm–125 μm	>125 μm
Ag	0.19 ± 0.06%	0.25 ± 0.07%	0.20 ± 0.02%
Al	7.00 ± 0.13%	0.44 ± 0.02%	0.97 ± 0.78%
Cu	0.22 ± 0.03%	0.14 ± 0.02%	1.70 ± 0.64%
Fe	0.68 ± 0.05%	0.15 ± 0.02%	0.18 ± 0.06%
Sn	0.58 ± 0.08%	0.33 ± 0.11%	0.59 ± 0.07%
Si *	31.89 ± 0.02%
Plastics **	24.20 ± 0.12%
Other	40.23 ± 0.60%

* Si concentration is estimated by XRF analysis on the initial sample. ** Plastics are estimated by weight loss at 600 °C on the initial sample.

shows the average value and uncertainty relating to the composition of the different metals in these size fractions.

Si, plastics, and others were determined not for all fractions but for the original sample. The unidentified fraction contains oxygen in SiO₂ and traces of several metals (such as Zn, Ni, and Pb) principally. The presence of these metals in the panels could be due to traces of other fractions from the SOLAR4.0 mechanical pre-treatment (for example, Zn comes from the aluminum alloy frame material, where it is present with a percentage of about 0.1%wt. [37]). Plastic refers to the material used for encapsulation of photovoltaic panels. The most widely used polymeric material is EVA, whose primary function is to protect and insulate solar cells [38].

Figure 4 shows the SEM and elemental mapping results of silicon powder.

3.2. ANOVA Results

The three different particle size fractions selected are used as three levels of the factorial plan.

Table 4. Results of the factorial plan.

Run	Run Code	A	B	C	Silver Recovery Yield
		Stirring Rate (rpm)	Particle Size (μm)	Temperature (°C)	60 min	120 min	180 min
1	(1)	60	<53	25	55.1%	65.9%	69.0%
2	A	180	<53	25	54.2%	63.5%	70.9%
3	B	60	>125	25	16.0%	24.7%	23.1%
4	Ab	180	>125	25	21.9%	24.5%	27.6%
5	C	60	<53	55	66.3%	93.8%	100.0%
6	Ac	180	<53	55	76.0%	87.9%	100.0%
7	Bc	60	>125	55	41.5%	51.4%	54.2%
8	Abc	180	>125	55	65.2%	71.7%	72.4%
9	R1	120	53–125	40	95.7%	100.0%	100.0%
10	R2	120	53–125	40	94.4%	100.0%	100.0%
11	R3	120	53–125	40	91.7%	100.0%	100.0%

shows the results obtained for each test of the factorial plan.

The results obtained were analyzed via ANOVA to establish the effect and significance of each factor and the related interactions on the recovery yields of the various elements. In particular, F-test was performed to determine the significance of the effects of factors and interactions throughout the reaction time. The results obtained from this analysis, in terms of significance and effects plots [39], are reported below (Figure 5 and Figure 6).

First of all, it is possible to see how the significance of the effects is very similar at different times. From the ANOVA, the most significant effects are those linked to temperature and particle size. The strong dependence on temperature and particle size suggests that the process may be controlled by chemical reactions or internal diffusion. In particular, an increase in the temperature and a decrease in the particle size positively affects the extraction yield. As temperature rises, the kinetic energy of Fe³⁺ and SC(NH₂)₂ in the system increases. This higher kinetic energy enhances the movement and collisions of these molecules with the solid particles, promoting faster and more efficient mass transfer. This results in improved extraction rates.

Decreasing the particle size of the solid matrix increases its surface area. A larger surface area provides more sites for contact between the solid and the chemicals, facilitating a more efficient extraction process. Indeed, smaller particles generally have shorter diffusion path lengths. This means that the chemicals have to travel a shorter distance to reach the interior of the solid particles, leading to faster extraction kinetics.

3.3. Kinetics Results

Through sampling at pre-established times, the trend of silver extraction over time was analyzed for each test of the factorial plan. Furthermore, three tests were added to obtain the graphs shown in Figure 7, Figure 8 and Figure 9. The three new experimental points were added to the existing factorial plan with a well-defined scheme in order to have three new trends comparable with the tests:

• Run α. Stirring rate: 120 rpm, Particle size: <53 μm; Temperature: 25 °C.
• Run β. Stirring rate: 60 rpm, Particle size: 53–125 μm; Temperature: 25 °C.
• Run γ. Stirring rate: 60 rpm, Particle size: <53 μm; Temperature: 40 °C.

Observing the effect of the particle size variation over the time on the silver recovery yield, it is once again confirmed that particle size is one of the most influential parameters in the leaching process. The curves move farther apart from each other as time passes. For a fine particle size, the silver recovery yield increases rapidly in the first 30 min until it reaches a value of approximately 50%. Subsequently, the extraction rate decreases and reaches approximately 70% after 120 min from the start of the test.

Even for the intermediate particle size, a rapid increase in the recovery yield is observed until it reaches a value of approximately 80% after only 60 min from the start of the test. After this interval, the increase continues until it exceeds 90% after approximately 120 min.

The recovery yield for the coarser particles increases very slowly compared to the other two particle sizes, reaching only 20% after approximately 120 min.

Regarding the effect of temperature, it can be seen from Figure 8 that it is less significant than that of particle size. The silver recovery yield for low temperatures (25 °C) increases gradually, reaching about 60% after 120 min of reaction. With a temperature of 40 °C, the silver recovery yield rises rapidly in the first 40 min, reaching even 50% recovery yield; subsequently, the increase is more gradual and reaches about 70% yield after 120 min from the start of the test. Finally, for a temperature of 55 °C, the silver recovery yield increases rapidly in the first 40 min, reaching about 65%. This increase continues steadily until reaching about 90% yield after 120 min.

As for the effect of stirring rate, it is seen that it is more significant than temperature and less significant than particle size. The silver recovery yield increases gradually in the 60 rpm test, reaching about 60% after 120 min. The silver recovery yield for the 120 rpm test rises rapidly in the first 30 min, reaching about 50%. Subsequently, the increase continues until the yield reaches 90% after 120 min. In the case of the 180 rpm test, there is a very rapid increase in the silver recovery yield in the first 20 min until reaching the value of 40%. Subsequently, the growth is more gradual, reaching about 60% after 120 min, similar to the trend at 60 rpm.

Through regression of the experimental data with the different SCM equations, the results reported in

Table 5. Silver kinetic constants (min⁻¹) and determination coefficients at different runs.

Run	$\mathit{X}={\mathit{k}}_{\mathit{F}}\mathit{t}$		$1-{\left(1-\mathit{X}\right)}^{1/3}={\mathit{k}}_{\mathit{R}}\mathit{t}$		$1-3{\left(1-\mathit{X}\right)}^{2/3}+2\left(1-\mathit{X}\right)={\mathit{k}}_{\mathit{P}}\mathit{t}$
	${\mathit{k}}_{\mathit{F}}$ (min−1)	R2	${\mathit{k}}_{\mathit{R}}$ (min−1)	R2	${\mathit{k}}_{\mathit{P}}$ (min−1)	R2
1	7.36 × 10−3 ± 1.96 × 10−3	0.701	3.25 × 10−3 ± 7.82 × 10−4	0.743	2.16 × 10−3 ± 3.94 × 10−4	0.834
a	6.91 × 10−3 ± 1.63 × 10−3	0.749	2.99 × 10−3 ± 6.07 × 10−4	0.802	1.87 × 10−3 ± 1.93 × 10−4	0.940
b	2.36 × 10−3 ± 3.06 × 10−4	0.908	8.50 × 10−4 ± 1.02 × 10−4	0.921	1.85 × 10−4 ± 7.08 × 10−6	0.991
ab	2.67 × 10−3 ± 6.22 × 10−4	0.754	9.65 × 10−4 ± 2.16 × 10−4	0.769	2.21 × 10−4 ± 2.76 × 10−5	0.914
c	8.92 × 10−3 ± 9.35 × 10−4	0.938	5.10 × 10−3 ± 1.43 × 10−4	0.995	4.92 × 10−3 ± 4.07 × 10−4	0.961
ab	9.66 × 10−3 ± 2.51 × 10−3	0.711	5.12 × 10−3 ± 9.81 × 10−4	0.820	4.68 × 10−3 ± 4.58 × 10−4	0.946
bc	5.27 × 10−3 ± 8.29 × 10−4	0.871	2.13 × 10−3 ± 2.88 × 10−4	0.901	1.04 × 10−3 ± 5.51 × 10−5	0.984
abc	7.96 × 10−3 ± 1.94 × 10−3	0.737	3.68 × 10−3 ± 7.95 × 10−4	0.781	2.70 × 10−3 ± 4.41 × 10−4	0.862
α	1.04 × 10−2 ± 2.24 × 10−3	0.781	6.62 × 10−3 ± 6.90 × 10−4	0.939	6.78 × 10−3 ± 1.50 × 10−4	0.997
β	9.86 × 10−3 ± 1.45 × 10−3	0.885	5.96 × 10−3 ± 4.80 × 10−4	0.963	6.06 × 10−3 ± 3.70 × 10−4	0.979
γ	7.79 × 10−3 ± 2.03 × 10−3	0.710	3.52 × 10−3 ± 8.02 × 10−4	0.763	2.48 × 10−3 ± 3.77 × 10−4	0.879

were obtained.

The results reported in Table 5 show that the model best describes the phenomenon considered: internal diffusion to the solid particle. This model has the highest coefficient of determination compared to the other two. The particle size level is sufficiently high to cause diffusion problems of the reactants and counter diffusion of the products through the reacted layer. The mean value and the standard deviation of the Log-normal PSD were calculated. These values allowed us to determine the coefficient of variation (CV), which equals about 0.1. This value is lower than the critical value of 0.3. The shrinking core model (SCM) can be used without considering the PSD for systems with CV less than the critical value [40].

This result made it possible to first optimize the GOLD-REC1 process to treat this waste. In particular, it was seen that for certain conditions, a residence time of the solid in the leaching reactor of about 1–2 h is sufficient. This aspect is fundamental for reducing CAPEX associated with the reactor volume. Furthermore, since the particle size is the most critical parameter, it is necessary to improve the grinding phase.

Figure 10 shows the comparison between this model and the experimental data.

For the other two models, the temperature control model certainly comes much closer to reality than the external diffusion control model. For further confirmation that the leaching process is under the control of internal diffusion, the activation energy was estimated by linearization of the Arrhenius equation. The order of magnitude of this parameter is an index of the RDS.

From a physical point of view, the comparison between the particle size > 125 μm and the other two is very immediate. The smaller particles (<53 μm and 53–125 μm) have a larger specific surface area than the larger ones, allowing a larger contact area with the reagents and accelerating the process. On the other hand, reducing the particle size (grinding) is the most energy-intensive stage in the recycling process, leading to an increase in operational expenses (OPEX) [41]. Therefore, finding the optimal particle size for PV panels is crucial, both technically and economically. Regarding the comparison between test (1) and β, the intersection of the two curves suggests the presence of some more complex physical and chemical phenomena. The smaller particles are initially more reactive than the intermediate ones, but the latter becomes more efficient in extracting silver as time passes. This result is the combination of the effects of the specific surface area of the particles, diffusion, and initial problems of aggregation and accessibility of the reagents. The smaller particles (<53 μm) tend to aggregate at the beginning of the reaction, reducing the available surface area below that of the intermediate particles. The dissolution kinetics for larger particles (53–125 µm) slows after the rapid increase. In contrast, the results showed that smaller particles (<53 μm) reacted consistently once the initial aggregation issues were resolved.

At higher temperatures, the reagent molecules possess greater kinetic energy, increasing the frequency and power of collisions between molecules. This phenomenon leads to an increase in effective collisions and the overall rate of the dissolution reaction. Furthermore, temperature usually increases the solubility of the reagents and the ability to diffuse through the reaction medium to interact with the solid particles. As in Figure 7, the intersection between trends is also present in Figure 8. First, it should be noted that for all three tests at different temperatures, the particle size is kept constant at the low level (<53 μm), which is the level for which a more significant effect due to aggregation was seen. It is possible that the temperature of 55 °C favors the process from the point of view of collisions between molecules and diffusivity and favors the initial aggregation of the particles, temporarily influencing the silver recovery yield. In fact, at higher temperatures, the particles tend to move faster. This greater mobility increases the probability of collision and aggregation. Over time, continuous agitation and the action of the reagents break up the aggregates, exposing a greater specific surface area to the reaction. This result explains why, after about 50 min, the recovery yield of the test at 55 °C exceeds those of the tests at 25 °C and 40 °C.

A stirring rate of 120 rpm is high enough to keep the particles well dispersed in the reaction environment and promote reasonable contact between reagents and silver. These effects allow faster dissolution in the first minutes and a higher final yield. A decrease in the stirring rate to 60 rpm results in a slower reaction rate and a lower final yield. This stirring rate may not be sufficient to keep all the particles optimally dispersed, reducing the contact surface between the reagents and the silver. However, a stirring rate of 180 rpm presents its own set of challenges. It can lead to solid particle aggregation and the formation of vortices, which, in turn, diminish the effectiveness of the contact between the reagents and the silver particles.

Figure 11 shows the graph for estimating the Arrhenius parameters, constructed using the kinetic constants.

The activation energy is approximately 22.04 ± 9.13 kJ/mol. The uncertainty of the result found is slightly high due to the low concentrations of Ag in the solution and an experimental error that is very difficult to handle. However, Chang et al. found an activation energy of 22.60 kJ/mol in a similar leaching system [35]. Compared with other research, this value confirms that the internal diffusion phenomenon is the mechanism underlying the leaching kinetics. $E_a$ values lower than 20 kJ/mol suggest that the RDS is diffusion, while for values higher than 40 kJ/mol, the RDS is the chemical reaction. Different mechanisms alternate over time when $E_a$ takes intermediate values to control the process.

Finally, the correlation between the silver extraction and those of silicon was evaluated. Silicon represents another critical raw material, and the recovery of this material would lead to significant advantages from an economic point of view. The correlation between the silver leaching extraction and that of silicon was evaluated using the Pearson correlation index:

$${\rho }_{Ag,Si}={\displaystyle \frac{Cov(Ag,Si)}{{\sigma }_{Ag}{\sigma }_{Si}}}$$

(6)

where $Cov(Ag,Si)$ is the covariance of silver and silicon concentrations in the leaching solution, ${\sigma }_{Ag}$ and ${\sigma }_{Si}$ are the standard deviation of silver and silicon concentrations, respectively. A Pearson correlation index of 0.321 was achieved based on the results. This low correlation between the two elements of greatest interest is also visible in Figure 12.

The differences in leaching behaviors arise from the different chemical affinities of silver and silicon with the leaching agents used. Silver forms complexes with thiourea, while silicon reacts with sulfuric acid to form complexes with ferric ions. Reagent concentrations optimized for silver extraction do not allow the dissolution of silicon (or totally inert behavior).

The correlation between the two elements is very low. Furthermore, as shown in Figure 12, silicon concentration in the leaching solution is very low. The silicon has a completely inert behavior to the reagents used. This result confirms that the diffusive phenomenon controlling the process is the one through the inert layer of silicon. SEM confirms this aspect: silicon represents the solid matrix, while silver is present on the surface and in some internal regions. This result is particularly interesting as it highlights the possibility of selective recovery of both elements: the silver is leached and subsequently recovered from the solution, and the silicon remains as a solid residue of the leaching process for further refinement. In this way, the proposed method allows for not only obtaining profits through the selective recovery of high-purity silver, but also having a new silicon powder to be sent for further refining processes to perhaps reach 7–9 N (99.99999–99.9999999%) purity for the fabrication of new high-efficiency silicon solar cells.

4. Conclusions

This work studied the extraction process of silver from end-of-life photovoltaic panels powder through leaching by sulfuric acid, ferric sulfate, and thiourea solution. In particular, the effects of some parameters on silver extraction kinetics were evaluated.

ANOVA observed that temperature and particle size are the most significant factors in recovery yield. It was observed that increasing the temperature from 25 °C to 55 °C led to an increase in silver extraction yield of about 30% after 60 min. Contrary to temperature, the recovery yield decreases by increasing the particle size. From a size < 53 mm to a size > 125 mm, the recovery yield decreases by approximately 25% after 60 min.

The dissolving kinetics of the silver was investigated using the shrinking core model. This analysis shows that the rate-determining step is internal diffusion to the solid particle. This model has the highest coefficient of determination compared to the other two: the coefficient of determination averaged over all tests is 0.92. The activation energies and pre-exponential factors of the Arrhenius equation were estimated. This analysis made it possible to confirm the predominance of internal diffusion in the chemical reaction. The activation energy is determined to be approximately 22 kJ/mol.

The recovery yield of silicon during leaching has been found to be practically zero, a significant finding. This result underscores the feasibility of selectively recovering the two elements under consideration: silver through leaching and subsequent recovery, and silicon as a solid residue of the process for further refinement. These findings not only contribute to the optimization of the studied process but also inspire the potential for a successful scale-up on a pilot and industrial scale.