Kinetics Study on CO₂ Adsorption of Li₄SiO₄ Sorbents Prepared from Spent Lithium-Ion Batteries

Abstract

With the advancement of global carbon reduction efforts and the rapid development of battery industries, the scale of spent lithium-ion batteries (LIBs) has increased dramatically. Extracting lithium from spent LIBs to synthesize Li₄SiO₄ sorbents not only addresses the challenge of battery recycling but also reduces the production cost of CO₂ sorbents, making it a research hotspot. However, the CO₂ adsorption behavior of these sorbents under the effect of impurities may differ from the traditional Li₄SiO₄, and there is a lack of systematic research on the adsorption kinetics. To address this issue, two Li₄SiO₄ sorbents are prepared from spent ternary LIBs, and their adsorption kinetics are comprehensively investigated using classical kinetic models. Results show that the reaction order of LSO and Na-LSO is 0.41 and 1.63, respectively, with activation energies of 72.93 kJ/mol and 99.23 kJ/mol in the initial kinetic-controlled stage, and 323.15 kJ/mol and 176.79 kJ/mol in the following diffusion-controlled stage. In the cyclic processes, loss-in-capacity is observed on LSO due to the simultaneous decrease in rate constants in both the kinetic and diffusion-controlled stages, while Na-LSO could almost maintain its capacity by having a much bigger rate constant during the kinetic-controlled stage. This study reveals the adsorption kinetics of Li₄SiO₄ prepared from spent LIBs and could provide theoretical support for the targeted design of efficient and low-cost CO₂ sorbents.

1. Introduction

The extensive use of various fossil fuels has released a large amount of CO₂, intensifying the greenhouse effect [1,2,3]. To alleviate the pressure of carbon reduction, various renewable energy sources are accelerating their large-scale applications [4]. Batteries, as key energy storage carriers, have witnessed an explosive growth in production and consumption [5], leading to a simultaneous surge in the scale of spent LIBs. It is expected that, by 2035, the potential output of spent LIBs in China will reach 11.77 million tons [6]. If spent LIBs are not properly processed, it will not only cause the waste of various metallic resources within batteries, but also result in severe environmental pollution due to the leakage of heavy metals and evaporation of electrolytes [7].

Currently, the recycling of spent LIBs mainly involves pyrometallurgical [8] or hydrometallurgical [9] processes to recover precious metals such as Li and Ni for the preparation of battery raw materials or direct repair and regeneration of battery materials [10]. However, traditional methods have certain limitations. The former requires an extremely high purity of these metals [11], while the latter demands highly precise and complex recycling processes [12]. Therefore, it is necessary to explore a more suitable recycling path for spent LIBs. On the other hand, Li₄SiO₄, as an efficient high-temperature CO₂ sorbent, Equation (1), has drawn significant attention owing to its high adsorption capacity (theoretical CO₂ capacity of 0.367 g/g), relatively mild regeneration conditions, and good cycling performance [13]. However, its large-scale industrial application is limited by the expensive lithium source [14]. Under this circumstance, the lithium element rich in spent LIBs may provide a cheap lithium source for the synthesis of Li₄SiO₄. Our group pioneeringly proposed to extract lithium from spent LIBs to prepare Li₄SiO₄ sorbents through a pyrometallurgical recycling process. The obtained sorbent reached a stable CO₂ adsorption capacity of 0.19 g/g at a cost of only 1/20 to 1/3 of the conventional method [14]. Since then, the preparation of Li₄SiO₄ sorbents using spent LIBs has attracted a growing attention [14,15,16,17,18,19,20,21]. For example, Liao et al. [18] synthesized Li₄SiO₄ from spent LIBs and iron tailings, and it showed an excellent CO₂ capacity and cycling stability (0.25 g/g, 100 cycles), with a preparation cost of only 1/7 of the traditional method. The transformation path from batteries to sorbents not only overcomes the limitations of traditional LIBs recycling methods, endowing spent LIBs with a higher value, but also further reduces the cost of Li₄SiO₄ sorbents, achieving a win-win situation for the environment and resources.

$$\mathrm{L}{\mathrm{i}}_4\mathrm{S}\mathrm{i}{\mathrm{O}}_4+\mathrm{C}{\mathrm{O}}_2\underset{\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}{\overset{\mathrm{a}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}{\rightleftarrows }}\mathrm{L}{\mathrm{i}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_3+\mathrm{L}{\mathrm{i}}_2\mathrm{C}{\mathrm{O}}_3$$

(1)

However, research on Li₄SiO₄ sorbents prepared from spent LIBs is still in its infancy, especially regarding the lack of systematic and in-depth analysis of their adsorption kinetics. It is known that adsorption kinetics are crucial for revealing the essence of adsorption and optimizing the performance of sorbents. Our previous work [22] revealed that during the preparation of CO₂ separation materials from spent LIBs, key impurity elements underwent migration, and the contents of these impurities were clarified. Due to the interference of such impurity elements, reaction kinetics of Li₄SiO₄ derived from spent LIBs often differ from those of traditional Li₄SiO₄. Therefore, it is urgent to further investigate the adsorption kinetic behaviors of Li₄SiO₄ sorbents derived from spent LIBs. For the CO₂ adsorption process of Li₄SiO₄ sorbents, it usually involves complex physical and chemical steps. To describe the kinetics of such gas–solid reactions, various classical theoretical models have been developed. The grain model [23] is used to describe the kinetics of gas–solid reactions in porous materials composed of spherical grains, making it suitable for high-porosity sorbents. The shrinking core model [24,25,26] is often adopted to describe adsorption processes with a distinct reaction interface advancement, distinguishing between surface chemical reaction control and product layer diffusion control. The Jander model [27,28,29] is more suitable for describing reaction kinetics processes controlled by product layer diffusion, particularly focusing on diffusion activation energy. The Avrami–Erofeev [30,31,32] model is commonly used to describe the nucleation and growth mechanism of product crystals in Li₄SiO₄ adsorption. These models are crucial for revealing the rate-controlling steps of adsorption, calculating key kinetic parameters such as reaction orders and activation energies.

Overall, the Li₄SiO₄ sorbent prepared from low-cost spent LIBs is a highly promising material for CO₂ adsorption, and a systematic analysis of its adsorption kinetics is a prerequisite for performance optimization. In this work, two Li₄SiO₄ sorbents with/without additional Na doping are prepared using spent ternary LIBs as the lithium source and fumed silica as the silicon source. Through kinetic analysis, adsorption behavior between the above two sorbents is compared, revealing the reaction order, activation energy, and the variation in kinetic parameters with different particle sizes and cyclic reactions. This work is expected to lay a theoretical foundation at the kinetic level for further regulation of the performance and doping modification design of Li₄SiO₄ sorbents.

2. Materials and Methods

2.1. Raw Materials and Sorbents Preparation

Spent 18650 cylindrical batteries were adopted as lithium raw materials in the work. The experiment also employed sodium hydroxide (AR, Chengdu Kelong Chemical Co., Ltd., Chengdu, China), sodium chloride (AR, Aladdin Reagent (Shanghai) Co., Ltd., Shanghai, China), and 20 vol.% CO/Ar for extracting lithium carbonate from spent LIBs. Fumed silica (AR, Aladdin Reagent (Shanghai) Co., Ltd., Shanghai, China) was selected as the silicon source to synthesize Li₄SiO₄. Sodium carbonate (AR, Shandong Keyuan Biochemical Co., Ltd., Shandong, China) was used for doping and modifying Li₄SiO₄.

To obtain lithium carbonate from the spent LIBs, they were placed in a 10 wt.% NaCl solution to be fully discharged. Then, cathode materials adhering to the aluminum foil were manually stripped. Subsequently, they were immersed in a 2 mol/L NaOH solution for 2 h and then filtered to obtain the cathode material powder with Al removed. Next, the cathode material was pyrolyzed at 550 °C for 1 h in 20 vol.% CO/Ar. The pyrolysis products were dispersed in deionized water, stirred at room temperature for 2 h, and then filtered. The filtrate was dried at 120 °C for 12 h to obtain Li₂CO₃. To synthesize Li₄SiO₄ sorbents, the obtained Li₂CO₃ and fumed silica were mixed in a molar ratio of 2.05:1 and calcined at 750 °C for 6 h in a muffle furnace, and the sorbent was named LSO. Moreover, the obtained Li₂CO₃ from spent LIBs, SiO₂, and Na₂CO₃ were mixed in a molar ratio of 2.05:1:0.1 and calcined under the same conditions to obtain the Na-doped sorbent, which was named Na-LSO. Finally, sorbents of different sizes were obtained through sieving.

2.2. CO₂ Adsorption Test Using TGA

CO₂ adsorption kinetics of Li₄SiO₄ sorbents were tested using a thermogravimetric analyzer (NETZSCH TG209F3). To eliminate the influence of internal and external diffusion effects, the sorbents with different particle sizes and loading masses were first heated to 625 °C at a heating rate of 10 °C/min and then adsorbed for 30 min under 15 vol.% CO₂/N₂. To evaluate the kinetic behavior under different conditions, the following experimental designs were included: (1) effect of CO₂ concentration: 5 mg sorbent (0.054–0.075 mm) at 600 °C with 15–50 vol.% CO₂ balanced by N₂; (2) effect of adsorption temperature: 5 mg sorbent (0.054–0.075 mm) under 15 vol.% CO₂/N₂ at 550 °C, 575 °C, and 600 °C; (3) effect of particle size: 5 mg sorbent with four discrete size fractions (0.054–0.075 mm, 0.1–0.2 mm, 0.5–0.6 mm, and 0.9–1.0 mm) at 625 °C under 15 vol.% CO₂/N₂; and (4) effect of cycle number: 5 mg sorbent (0.054–0.075 mm) for 20 cycles of adsorption at 625 °C in 15 vol.% CO₂/N₂ for 30 min and desorption at 700 °C in pure N₂ for 10 min.

In this work, the adsorption conversion x is defined as follows:

$$x={\displaystyle \frac{m_t-m_0}{m_{\max }-m_0}}\times 100\%$$

(2)

where $m_0$, $m_t$ and $m_{\max }$ represent the initial mass, real-time mass, and theoretical maximum mass in adsorption, respectively.

2.3. Characterization Methods

The phase composition of the prepared Li₄SiO₄ sorbent was characterized by X-ray diffraction (Bruker D8 Advance, Bruker AXS GmbH, Karlsruhe, Germany). The microstructure and surface morphology were observed by environmental scanning electron microscopy (Hitachi Regulus 8100, Hitachi High-Technologies Corporation, Tokyo, Japan), and the distribution of various elements on the surface was obtained by energy dispersive spectroscopy mapping. The pore structure was characterized by an automatic physical adsorption instrument (ASAP 2460, Micromeritics Instrument Corporation, Norcross, GA, USA). Following degassing (200 °C, 8 h), the specific surface area, pore volume, and pore size distribution were determined based on the N₂ adsorption/desorption isotherms.

3. Results and Discussion

3.1. Physicochemical Characteristics of Sorbents

The phase composition of the two sorbents prepared was analyzed by XRD. As depicted in Figure 1a, the major diffraction peaks are all associated with Li₄SiO₄. Additionally, a certain amount of NaLi₃SiO₄ is observed in both sorbents, indicating that the Na element tends to form new crystals with Li₄SiO₄. It should be noted that the presence of NaLi₃SiO₄ in the sorbent of LSO is due to the inflow of Na from spent LIBs during recycling. Figure 1b,c shows that the specific surface area and pore volume of LSO are both small at 0.1764 m²/g and 0.00099 cm³/g, respectively, implying a relatively dense surface. In contrast, the specific surface area and pore volume of Na-LSO increase to 1.5187 m²/g and 0.00688 cm³/g, respectively. This might be due to the lattice distortion induced by Na doping, which inhibits particle agglomeration and increases the specific surface area and porosity [33,34]. The pore size distribution in Figure 1c shows there are almost no pores in LSO, indicating an underdeveloped pore structure. Comparatively, there are obvious peaks at 2–3 nm and 10–50 nm for Na-LSO, representing the presence of meso-pores, which is consistent with the specific surface area of the sample. Furthermore, the surface morphologies of two sorbents seem to be very smooth in Figure 1d,e, though there are more gaps among the particles of Na-LSO. Turning to the energy spectrum, both O and Si are observed to be well dispersed, indicating a good quality of Li₄SiO₄ sorbents prepared from spent LIBs. The uniform distribution of Na in Na-LSO also proves the good doping of Na₂CO₃ in the sorbent.

3.2. Effect of CO₂ Concentration and Temperature

3.2.1. Intrinsic Kinetics in the Kinetic-Controlled Stage

To eliminate the influence of internal and external diffusion of CO₂ during adsorption, sorbents with different particle sizes and loading masses were tested firstly, as shown in Figure 2a–d. It is seen that the adsorption curves of sorbents with a particle size below 0.1 mm and mass less than 10 mg are almost the same, implying the absence of internal and external diffusion. It is also seen that the adsorption process consists of two stages: a kinetic-controlled fast reaction stage within the first few minutes and a diffusion-controlled slow reaction stage, where the former is close to the intrinsic chemical reaction situation.

When the effects of external and internal diffusion resistance are eliminated, the adsorption behavior of CO₂ sorbents can reflect its intrinsic reaction kinetics. Then, the relationship between the adsorption conversion and intrinsic reaction rate can be derived as follows based on the mechanism of surface reaction for gas–solid reactions and the assumption of uniform advancement of the reaction interface:

$$1-{(1-x)}^{{\displaystyle \frac{1}{3}}}={\displaystyle \frac{k}{3}}t$$

(3)

$$k={\displaystyle \frac{3M}{\rho R_0}}{k}_i$$

(4)

where k denotes the apparent reaction rate constant (s⁻¹), while k_i represents the intrinsic reaction rate (mol·m⁻²·s⁻¹). M, ρ, and R₀ are the molar mass, density, and initial radius of Li₄SiO₄, respectively.

By further combining the reaction rate equation and the Arrhenius equation, the intrinsic kinetic equations are established as follows [25,30]:

$$k_i=k_0\exp (-{\displaystyle \frac{E_a}{RT}})C_{C{O}_2}^n$$

(5)

$$k={\displaystyle \frac{3M}{\rho R_0}}{k}_0\exp (-{\displaystyle \frac{E_a}{RT}})C_{C{O}_2}^n$$

(6)

where k₀ represents the pre-exponential factor (m³ⁿ⁻²·mol¹⁻ⁿ·s⁻¹), $C_{C{O}_2}$ denotes the CO₂ concentration (mol/m³), and R is the gas constant, which is 8.314 J·mol⁻¹·K⁻¹. T is the reaction temperature (K), E_a is the activation energy (J·mol⁻¹), and n is the reaction order.

To obtain the reaction order in the kinetic-controlled stage, adsorption curves at different CO₂ concentrations were tested, as shown in Figure 3a,d. The reaction order in the kinetic-controlled stage can be calculated according to the following formula:

$$\ln k=\ln \left[{\displaystyle \frac{3M}{\rho R_0}}{k}_0\exp (-{\displaystyle \frac{E_a}{RT}})\right]+n\ln C_{C{O}_2}$$

(7)

The apparent reaction rate constants (k) of LSO and Na-LSO at different CO₂ concentrations are obtained from Figure 3b,e, with the relationships between lnk and $\ln C_{C{O}_2}$ plotted in Figure 3c,f. Slopes of the fitted lines are determined as the reaction orders, which are 0.41 and 1.63 for LSO and Na-LSO, respectively. It indicates that the two sorbents have different degrees of dependence on the CO₂ concentration, and the adsorption by the Na-LSO sorbent is more susceptible to CO₂ concentration.

To obtain the intrinsic activation energies of two sorbents during CO₂ adsorption, tests were conducted at different temperatures of 550 °C, 575 °C, and 600 °C. Activation energy in the kinetic-controlled stage is described by the following formula:

$$\ln k=\ln ({\displaystyle \frac{3M}{\rho R_0}}{k}_0{C}_{C{O}_2}^n)-{\displaystyle \frac{E_a}{RT}}$$

(8)

Figure 4a,d demonstrates that the reaction rate and the final conversion increase significantly at higher temperatures under the conditions studied. The apparent reaction rate constants (k) of LSO and Na-LSO at different temperatures are obtained from Figure 4b,e, and the relationships between lnk and 1/T are shown in Figure 4c,f. Then, slopes are obtained through linear fitting, and activation energies can be calculated. Activation energies of LSO and Na-LSO during the kinetic-controlled stage are 72.93 kJ/mol and 99.23 kJ/mol, respectively, indicating that Na-LSO exhibits a stronger temperature dependence. It is reported in some of the literature that metal-doped Li₄SiO₄ has a higher reactivity and smaller activation energy than undoped Li₄SiO₄ [35,36]. Here, the larger activation energy of the Na-doped sorbent is mainly due to the fact that Na-doped sorbent has a “self-activation” property [35,37,38], and its reaction rate is inhibited in the first cycle. The activation energy for LSO during the kinetic-controlled stage is similar to the values of 94.14 kJ/mol and 102.93 kJ/mol reported by Lopez-Ortiz et al. [25] and Peltzer et al. [30]. The small deviation is possibly caused by the different methods in synthesizing Li₄SiO₄ and the impurity contents [26].

3.2.2. Reaction Kinetics in the Diffusion-Controlled Stage

The Jander model is specifically tailored to reaction processes controlled by product layer diffusion and is suitable for describing the stage in the middle and late phases of a reaction where diffusion resistance becomes dominant due to the increasing thickness of the product layer. In this work, after the adsorption reaction proceeds to a certain extent, the product layer formed on the surface of Li₄SiO₄ gradually thickens, and diffusion becomes the rate-limiting step. Therefore, the Jander model is adopted to conduct a kinetic analysis on the diffusion-controlled stage of adsorption at different temperatures, as detailed below:

$${\left[1-{(1-x)}^{{\displaystyle \frac{1}{3}}}\right]}^2=k_{b}t$$

(9)

where x represents the conversion of the sorbent, t stands for time, and k_b refers to the diffusion-controlled reaction rate constant (s⁻¹).

The model fitting results are shown in Figure 5a,c, and the k_b at each temperature is obtained. The specific parameters obtained through fitting are listed in

Table 1. Reaction fitting of the sorbents at different temperatures in the diffusion-controlled stage.

Sorbent	Temperature (°C)	Diffusion-Controlled Stage
		kb (s−1)	R2	Ea (kJ/mol)
LSO	600	1.59 × 10−4	0.9893	323.15
	575	5.94 × 10−5	0.9984
	550	1.07 × 10−5	0.9952
Na-LSO	600	1.64 × 10−5	0.9627	176.79
	575	1.08 × 10−5	0.9307
	550	3.76 × 10−6	0.9727

. By substituting k_b into the Arrhenius equation, Equation (10), the activation energy in the diffusion-controlled stage can be obtained.

$$\ln k_b=\ln k_0-{\displaystyle \frac{E_a}{RT}}$$

(10)

The activation energy of CO₂ adsorption by LSO in the diffusion-controlled stage is 323.15 kJ/mol, while that of Na-LSO is 176.79 kJ/mol. It is seen that the activation energy of Na-LSO in this stage is significantly lower than that of LSO, which may be due to the structural changes introduced by Na doping that inhibit particle agglomeration and reduce the diffusion resistance in the product layer [33,39,40]. It is worth noting that the activation energy obtained here for the diffusion-controlled stage is higher than the reported values in the literature. For instance, Kaniwa et al. [28] obtained an activation energy of 201 kJ/mol using the Jander model, and Zhang et al. [41] reported a value of 272 kJ/mol using the Avrami–Erofeev model. The differences in activation energy among different studies, apart from the different models used, are attributed to the varying specific surface area and impurity content of the synthesized Li₄SiO₄. In this work, the LSO sorbent is prepared from the recycled lithium carbonate from spent LIBs, which has a relatively low specific surface area and contains more impurities [14,15]. These factors would affect the apparent reaction rate of the overall adsorption, leading to a higher activation energy in the diffusion stage.

3.3. Reaction Kinetics with Different Particle Sizes

CO₂ adsorption curves with different particle sizes (0.054–0.075 mm, 0.1–0.2 mm, 0.5–0.6 mm, and 0.9–1 mm) are shown in Figure 6a,d. It can be observed that the conversion of LSO gradually increases with the decreasing particle size, from the final 43% at 0.9–1 mm to 74% at 0.054–0.075 mm after a reaction time of 30 min. For Na-LSO, the increase in conversion with the decreasing particle size is more significant, from 12% at 0.9–1 mm to 49% at 0.054–0.075 mm at the end of adsorption. Based on the methods described in prior studies [42] and considering the kinetic characteristics of CO₂ adsorption in this work, the grain model Equation (11) is employed to describe gas–solid reaction kinetics during the kinetic-controlled fast reaction stage. This stage is characterized by a rapid CO₂ reaction on Li₄SiO₄ surfaces and product layer formation. For the diffusion-controlled slow reaction stage, the Jander model is used to analyze the diffusion resistance-dominated process caused by product layer thickening:

$$1-{(1-x)}^{{\displaystyle \frac{1}{3}}}=k_{a}t$$

(11)

where x represents the conversion of the sorbent, t stands for time, and k_a is kinetic-controlled reaction rate constant (s⁻¹).

The results of grain model fitting for the kinetic-controlled stage of LSO and Na-LSO are shown in Figure 6b,e, and the fitting results using the Jander model are presented in Figure 6c,f. The high fitting degrees indicate the rationality of the model selection. The specific parameters obtained from the fitting are summarized in

Table 2. Reaction fitting of the sorbents at different particle sizes.

Sorbent	Particle Size (mm)	Kinetic-Controlled Stage		Diffusion-Controlled Stage
		ka (s−1)	R2	kb (s−1)	R2
LSO	0.054–0.075	1.88 × 10−2	0.9488	6.96 × 10−5	0.9825
	0.1–0.2	3.30 × 10−3	0.9853	5.18 × 10−5	0.9605
	0.5–0.6	8.61 × 10−4	0.9623	2.92 × 10−5	0.9711
	0.9–1	6.13 × 10−4	0.9724	1.65 × 10−5	0.9782
Na−LSO	0.054–0.075	1.34 × 10−3	0.9946	1.88 × 10−5	0.9950
	0.1–0.2	8.82 × 10−4	0.9918	1.23 × 10−5	0.9915
	0.5–0.6	5.66 × 10−4	0.9730	2.24 × 10−6	0.9963
	0.9–1	5.10 × 10−4	0.9675	5.43 × 10−7	0.9494

. It is seen that the kinetic change patterns of LSO and Na-LSO are similar. k_a is about two orders of magnitude larger than k_b. As the particle size decreases, both reaction rates in the kinetic and diffusion-controlled stages increase gradually. This is because a reduction in particle size increases the contact area between the sorbent and CO₂, which means that more active sites on the surface of Li₄SiO₄ come into contact with CO₂ molecules [43], thereby enhancing the reaction probability. On the other hand, a smaller particle size shortens the diffusion distance of CO₂ in the product layer, which can also increase the reaction rate [28].

3.4. Reaction Kinetics at Different Reaction Cycles

To understand the variation in reaction kinetics during the cyclic reaction process, 20 cycles of adsorption and desorption were tested. Figure 7a shows that the sorbent of LSO achieves a conversion of 74% in the first adsorption cycle, which is at a relatively high level. However, the conversion decreases to 52% at the 10th cycle, and only 41% conversion remains after 20 adsorption cycles. To explore kinetic change during the cycling process, conversion curves at the 1st, 10th, and 20th adsorption cycle are plotted in Figure 7b, and a kinetic analysis is conducted on the kinetic and diffusion-controlled stages. The fitting results are shown in Figure 7c,d, and the detailed fitting parameters are listed in

Table 3. Reaction fitting of the sorbents in different cyclic processes.

Sorbent	Cycles Number	Kinetic-Controlled Stage		Diffusion-Controlled Stage
		ka (s−1)	R2	kb (s−1)	R2
LSO	1	2.07 × 10−2	0.9834	6.95 × 10−5	0.9858
	10	2.54 × 10−3	0.9923	1.58 × 10−5	0.9596
	20	2.12 × 10−3	0.9899	8.94 × 10−6	0.9585
Na-LSO	1	8.91 × 10−4	0.9843	1.86 × 10−5	0.9960
	10	2.47 × 10−3	0.9981	3.72 × 10−5	0.9871
	20	4.24 × 10−3	0.9977	2.12 × 10−5	0.9456

. Overall, as the cycle progresses, reaction rate constants in both the kinetic and diffusion-controlled stages decrease, indicating that the decline in CO₂ capacity is due to the loss of surface active sites and the increase in diffusion resistance within the product layer [44].

The varying conversion of Na-LSO in 20 cycles of CO₂ adsorption and desorption is depicted in Figure 8a. An initial increase in conversion is followed by a very slight decrease. The conversion is 49% in the 1st adsorption cycle, which becomes 65% in the 10th cycle, and a value of 62% is still maintained at the end of 20th cycle, indicating that Na doping significantly improves the cyclic stability of the sorbent [45]. The adsorption curves in the 1st, 10th, and 20th cycle are plotted in Figure 8b, and the model fitting results for the kinetic and diffusion-controlled stages are demonstrated in Figure 8c,d. Moreover, Table 3 summarizes the detailed model fitting parameters. It is seen that the k_a of Na-LSO in the kinetic-controlled stage increases continuously during the cyclic reaction, while k_b in the diffusion-controlled stage remains basically unchanged. Thus, the stable CO₂ capacity maintained during the cycle is mainly attributed to the kinetic-controlled stage. The increase in surface activity during the cycle may be due to the structural reconstruction caused by Na doping, which reduces the degree of dense surface formation caused by sintering [39].

4. Conclusions

This work conducts an adsorption kinetic analysis on two Li₄SiO₄ sorbents prepared from spent LIBs. After eliminating the influence of internal and external diffusion, adsorption tests are carried out at different CO₂ concentrations and reaction temperatures. The reaction order of LSO is determined to be 0.41, with an initial activation energy of 72.93 kJ/mol, while that of Na-LSO is 1.63, with an initial activation energy of 99.23 kJ/mol. Then, the Jander model is used to fit the adsorption processes at different temperatures, and the activation energies for LSO and Na-LSO in the diffusion-controlled stage are calculated to be 323.15 kJ/mol and 176.79 kJ/mol, respectively. Tests on sorbents of different particle sizes reveal that particle size significantly affects the reaction rate and final conversion. Reducing particle size can effectively increase the reaction rate, thereby achieving a higher conversion. In 20 cycles of adsorption and desorption tests, it is found that the CO₂ capacity of LSO decreases significantly with the increasing number of cycles, which is attributed to the reduction in rate constants of k_a and k_b in the kinetic and diffusion-controlled stages, respectively. In contrast, Na-LSO maintains better cycle stability as a result of the higher reaction rate constant k_a in the kinetic-controlled stage.