Understanding the Cu2+ adsorption mechanism on activated carbon using advanced statistical physics modelling

Adsorption modeling via statistical physics theory allows to understand the adsorption mechanism of heavy metal ions. Therefore, this paper reports the analysis of the mechanism of copper ion (Cu2+) adsorption on four activated carbons using statistical physics models. These models contain parameters that were utilized to provide new insights into the possible adsorption mechanism at the molecular scale. In particular, a monolayer adsorption model was the best alternative to correlate the Cu2+ adsorption data at 25–55 °C and pH 5.5. Furthermore, the application of this model for copper adsorption data analysis showed that the removal of this heavy metal ion was a multi-cationic process. This theoretical finding indicated that Cu2+ ions interacted via one functional group of activated carbon surface during adsorption. In this direction, the adsorption energy was calculated thus showing that Cu2+ removal was endothermic and associated with physical interaction forces. Furthermore, these activated carbons showed saturation adsorption capacities from 54.6 to 87.0 mg/g for Cu2+ removal, and their performances outperformed other adsorbents available in the literature. Overall, these results provide new insights of the adsorption mechanism of this water pollutant using activated carbons.


Introduction
Copper is a transition metal, electrically and thermally conductive, but it is also considered as an environmental pollutant (Kayalvizhi et al. 2022). Natural disasters (e.g., volcanic phenomena) and anthropogenic activities (e.g., metal industries, tanning factories, and automobile industries) contribute to the pollution caused by copper. This metal is toxic even at relatively low concentrations, and, consequently, the highest permissible concentration level of copper ions (Cu 2+ ) in marine water has been established as 4.8 μg/L. In comparison, the maximum Cu 2+ concentration for drinking water is 1300 μg/L, as reported by the WHO and EPA (Katiyar et al. 2021;Kayalvizhi et al. 2022). Chronic exposure to this metal can affect vital organs such as the intestines, stomach, and liver. It can also generate diverse symptoms such as liver disease, gallbladder, and metabolic disturbances (Dou et al. 2019;Sun et al. 2022).
Consequently, the drinking water resources and effluents polluted with Cu 2+ must be treated to reduce their concentration thus avoiding environmental impacts and to protect human health. Various procedures have been reported to remove Cu 2+ ions from liquid phase. They include ion exchange, precipitation, electrolysis, reverse osmosis, flocculation, biochemical methods, and membrane-based filtration (Godiya et al. 2019;Nyström et al. 2020;Anbazhagan et al. 2021;Lemes and Tarley 2021). However, these removal methods have disadvantages such as unfavorable cost-effectiveness tradeoffs or the generation of toxic sediments and wastes (e.g., sludge) (Rukayat et al. 2021). In contrast, the adsorption process is a competitive technique compared to other methods due to its ease of handling, low cost, and removal efficacy even at low concentrations of heavy metal ions (Vocciante et al. 2014;Pan et al. 2019;Khan et al. 2021).Activated carbon is the most employed adsorbent in this process because it effectively removes inorganic and organic pollutants from wastewaters and industrial effluents. This adsorbent outperforms other materials reported for water treatment in terms of its production cost and the availability of a wide spectrum of preparation routes that is already exploited and commercialized at large industrial scale. The adsorption performance of activated carbon is governed by its pore structure and surface chemistry. The modification of activated carbon is aimed to optimize these properties (Bell et al. 2011), and this adsorbent can be obtained from different feedstock and preparation conditions, thus affecting its adsorption properties. Surface functionalization of activated carbons can be performed with several chemicals to tailor their performance for the removal of target pollutants. Under this context, citric wastes can be an option to produce activated carbons since they are generated in large amounts by industries of juices and jams. During the production process of juices and jams, around 50-60% of the entire citric fruit is discarded. These wastes cannot be released into the environment since they generate CH 4 . On the other hand, they are rich in lignin, cellulose, hemicellulose, and pectin, thus being an attractive feedstock for pyrolysis and their conversion into activated carbon (Lam et al. 2016(Lam et al. , 2018. The modeling of adsorption data of heavy metals and other water pollutants is important for water treatment design. Therefore, it is possible to apply classical models (e.g., Langmuir) to theoretically study the adsorption data. Unfortunately, this and other traditional models are not useful to understand the adsorption mechanism due to the limitations in their hypotheses. For instance, Langmuir model considers that each functional group can accept one ion for all adsorption systems. This assumption is an obstacle to provide proper interpretations of more complex adsorption mechanisms. The application of reliable models to analyze and explain the adsorption of heavy metal ions on activated carbon surfaces is paramount to develop effective and lowcost water treatment methods.
In this research, two homogeneous and heterogeneous models based on statistical physics theory were implemented to explain the adsorption mechanism of Cu 2+ on a set of activated carbons obtained from different citric wastes, namely orange (OP), tangerine (MP), lemon (RLP), and lime (SLP). These models allowed to analyze the adsorption mechanism at the microscopic scale. New insights on steric and energetic parameters that governed the removal of this relevant water pollutant were developed for all tested activated carbons.

Preparation of AC and quantification of Cu 2+ adsorption isotherms
Cu 2+ adsorption isotherms were quantified with four activated carbons prepared from citrus waste (Dotto et al. 2011;Perondi et al. 2017). For the adsorbent preparation, 100 g of each citrus waste were located in a stainless reactor of 127 × 8.5 cm. The reactor was heated at 5 ºC/min until 900 °C and remained at this temperature for 15 min. Then, the system was cooled until ambient temperature. All these steps were performed with N 2 flow of 0.2 L/min. Subsequently, the N 2 flow was replaced by CO 2 flow (2 kg/h for 15 min). Finally, the adsorbent samples were removed from the reactor, washed, and used in adsorption experiments. These adsorbents were labelled as AC CO 2 -orange-OP, AC CO 2 -tangerine-OP, AC CO 2 -lemon-RLP, and AC CO 2 -lime-SLP.
Typical batch equilibrium experiments were performed to obtain the Cu 2+ adsorption isotherms. Aqueous solutions (50 mL) with different initial Cu 2+ concentrations up to 150 mg/L were prepared from copper sulfate and the solution pH was adjusted to 5.5. Next, these solutions were placed in Erlenmeyer flasks located in a thermostated shaker. Adsorption isotherms were quantified at 25, 35, 45, and55 °C using an activated carbon dosage of 0.5 g/L under constant stirring of 200 rpm for 5 h. The solid-liquid separation was performed by centrifugation and Cu 2+ concentration in the liquid was quantified by flame atomic absorption spectroscopy. Then, the equilibrium adsorption capacities were calculated via a mass balance for a stirred tank using the initial and final Cu 2+ concentrations used in the experiments and the corresponding adsorbent dosage. Figure 1 shows the 54883 experimental isotherms of Cu 2+ adsorption on the four activated carbons analyzed in this paper.
Solution temperature positively affected all adsorbed quantities of Cu 2+ ions on these activated carbons, thus suggesting an endothermic removal process. All experimental isotherms followed the monotonic trend of adsorbed Cu 2+ quantities as a function of equilibrium concentration until the saturation region was reached. This adsorbent saturation was caused by forming a layer of Cu 2+ ions adsorbed on the surfaces of tested activated carbons. In this regard, homogeneous and heterogeneous monolayer models developed from statistical physics theory were implemented to analyze Cu 2+ adsorption isotherms at the microscopic scale. The next two scenarios were tested in this modeling study: Scenario 1 A homogeneous monolayer model (HMM) was considered where only one type of functional group participated in the adsorption of Cu 2+ ions on tested adsorbents. It was assumed that only one adsorption energy was involved in the metal ion removal, which represented the interaction of Cu 2+ ion-activated carbon surface. The adsorbed quantity calculated with this model is given by Sellaoui et al. (2018) and Dhaouadi et al. (2020a, b, c): Scenario 2 A heterogeneous monolayer model (IMM) was also applied. Two functional groups participated in the adsorption of Cu 2+ ions with two different adsorption energies: Cu 2+ ion-adsorption site 1 and Cu 2+ ion-adsorption site 2. In this model, the adsorbed quantity as a function of (2) Q e = n 1 S m1 For these models, n and n i (i = 1, 2) are the numbers of Cu 2+ ions adsorbed per functional group(s), S m and S mi are the densities of these surface functionalities, and C 1/2 and C i ( i = 1, 2) are the concentrations at half-saturation, respectively.
Characterization results showed that these activated carbons contained different functional groups that can contribute to the adsorption of Cu 2+ ions. Therefore, these adsorption models were consistent with the surface chemistry of these activated carbons. Note that these models were developed by applying a grand canonical ensemble of statistical physics with the aim of obtaining a better analysis of the adsorption mechanism of this pollutant. Overall, these models assumed that the adsorption of Cu 2+ ions was a monolayer process, but with the contribution of one (homogeneous monolayer model) and two (heterogeneous monolayer model) functional groups in the removal of this cation (Dhaouadi et al. 2020b(Dhaouadi et al. , 2021. In summary, these models can describe the role of these functional groups on the adsorption of this metallic ion and can also characterize the nature of their interactions (i.e., multi-interaction or multi-ionic process).
These models were employed to fit all Cu 2+ ion adsorption isotherms, and their parameters were determined via a multivariable nonlinear regression with the Levenberg-Marquardt method. Determination coefficients (R 2 ) and the trends of steric and energetic parameters indicated that the HMM model was the most suitable for analyzing the Cu 2+ removal at the microscopic scale. Table 1 provides the results of Cu 2+ adsorption data fitting for the

Evaluation of the number of Cu 2+ ions adsorbed per functional group and their adsorption site densities
The impact of temperature on the number of adsorbed Cu 2+ ions per functional group and their corresponding adsorption site densities for these activated carbons is represented in Fig. 2. All parameters n were higher than unity except for AC CO 2 -lemon-RLP adsorbent at 25 °C. This result indicated that the adsorption of this heavy metal was multi-cationic for these activated carbons, where the functional groups could adsorb several cations simultaneously (Dhaouadi et al. 2020a, b). Indeed, the exceptional case (i.e., n = 0.63) showed that Cu 2+ ions could be adsorbed on the surface of AC CO 2 -lemon-RLP via a combined interaction where one and two functional groups can participate in the removal with two different proportions (Dhaouadi et al. 2021). Thermally speaking, the temperature increased the number of Cu 2+ ions adsorbed per functional group from 1.13 to 1.82, 1.07 to 4.20, 0.63 to 4.59, and 1.15 to 3.16 for the adsorbents AC CO 2 -orange-OP, AC CO 2 -tangerine-MP, AC CO 2 -lemon-RLP, and AC CO 2 -lime-SLP, respectively. Overall, these results indicated that the temperature played a relevant role to adsorb the Cu 2+ ions. Figure 2 indicated that the density of functional groups of these activated carbons reduced as a function of temperature. Moreover, this tendency was inversely proportional to the  number of Cu 2+ ions adsorbed per functional group. Thus, the increment of the parameter n as a function of temperature suggested a reduction of the occupied functional groups and, consequently, a decrement of the adsorption density and vice versa.

Performance evaluation of different activated carbons for Cu 2+ adsorption
The performance of tested adsorbents was complemented via the calculation of adsorption capacities at saturation using the next expression: The impact of thermal agitation on the adsorbed quantity at saturation Q s for the different adsorbents is given in Fig. 3. Figure 3 indicated that the adsorbed quantity at saturation for the four activated carbons increased with the solution temperature. This result confirmed that the solution temperature enhanced the mass transfer phenomena and the diffusion of Cu 2+ ions inside the porous structure of these adsorbents. Thus, the increment of this quantity was associated with the number of adsorbed ions per functional group and the adsorption energy. Comparatively, the AC CO 2 -lemon-RLP adsorbent showed the highest Cu 2+ removal and was the most effective for this purpose. Furthermore, characterization results reported in Dotto et al. (2011) indicated that the acidic functionalities of these activated carbons were responsible for Cu 2+ removal. In particular, FTIR analysis of activated carbon samples before and after Cu 2+ adsorption indicated that the main acidic functional groups were OH and COOH. The absorption bands relative to these groups presented significant shifts after Cu 2+ adsorption thus suggesting that OH and COOH were involved in the interactions with Cu 2+ ions, and confirming the statistical physics calculations.
For illustration, Table 2 shows the Cu 2+ adsorption capacities for different activated carbons reported in the literature. It was clear that these activated carbons can be an alternative to remove the Cu 2+ ions from wastewaters and to contribute to the reduction of solid waste generation. They can also outperform other adsorbents reported in the literature. For instance, the Cu 2+ adsorption capacities of 1-iron-modified flaxseed waste, sodium dodecyl sulfate-modified iron pillared montmorillonite, and activated carbons functionalized with magnetic iron oxide nanoparticles were 7.64, 20.6, and (3) Q s = nS m 41.6 mg/g (Li and Wu 2010;Gu et al. 2019;Cerrahoğlu Kaçakgil and Çetintaş 2021).

Cu 2+ adsorption energy
Adsorption energy for the interaction Cu 2+ ion-activated carbon surface was determined from the concentration values at half-saturation and the following equation (Dhaouadi et al. 2021): where R = 8.314 J/mol·K is the ideal gas constant, and C s is the copper solubility. The adsorption energy for the interaction of acidic functional groups of these activated carbons and Cu 2+ ions is depicted in Fig. 4.
All interaction energy values were lower than 40 kJ/mol, thus suggesting that this adsorption process was associated with physical forces. As stated, the acidic functional groups (e.g., OH and COOH) of these activated carbons were involved in the Cu 2+ adsorption. Furthermore, this adsorption energy increased with solution temperature for all activated carbons.

Conclusions
A reliable modeling of adsorption data and the corresponding analysis of adsorption mechanism are paramount for the design of water treatment processes effective to remove heavy metals with activated carbons. Therefore, this study reports the statistical physics-based interpretation of Cu 2+ adsorption using four activated carbons obtained from citrus wastes, which are low-cost feedstock to prepare new adsorbents. Steric and energetic parameters were calculated for the adsorption of this heavy metal using a monolayer adsorption model. Results showed that the Cu 2+ adsorption was multi-cationic via one functional group (i.e., acidic surface functionalities). In addition, Cu 2+ adsorption was endothermic and associated with physical interaction forces. At saturation, Cu 2+ adsorption capacities ranged from 54.6 to 87.9 mg/g for these activated carbons. Finally, this advanced modeling provided interesting interpretations of the adsorption mechanism of this relevant water pollutant with lowcost activated carbons. Data availability Note applicable.