Activated Carbons from Apricot Kernel Shells for Wastewater Treatment: Adsorption of Pb²⁺ and Rhodamine B with Equilibrium, Kinetics, Thermodynamics, and DFT Analysis

Abstract

Apricot kernel shells were evaluated as a sustainable activated carbon precursor for wastewater treatment using experimental and theoretical methods. Two adsorbents were synthesized: physically activated with CO₂ (AKS-CO₂) and chemically activated with H₃PO₄ (AKS-H₃PO₄). Comprehensive materials characterization and adsorption tests using Pb²⁺ ions and Rhodamine B dye (RhB) as model pollutants revealed that AKS-H₃PO₄ significantly outperformed its physically activated counterpart. With an exceptionally high specific surface area (1159.4 m²/g) enriched with phosphorus-containing functional groups, the chemically activated carbon demonstrated outstanding removal efficiencies of 85.1% for Pb²⁺ and 80.3% for RhB. Kinetic studies showed Pb²⁺ adsorption followed pseudo-second-order kinetics, indicating chemisorption, while RhB adsorption fitted pseudo-first-order kinetics, suggesting intra-particle diffusion control. The thermodynamic analysis confirmed the spontaneity of both processes: Pb²⁺ adsorption was exothermic under standard conditions with positive isosteric heat at higher concentrations, reinforcing its chemisorption nature, whereas RhB adsorption was endothermic, consistent with physisorption. Density Functional Theory (DFT) calculations further elucidated the mechanisms, revealing that Pb²⁺ preferentially binds to oxygen-containing functional groups, while RhB interacts through hydrogen bonding and π–π stacking. These findings establish chemically activated apricot kernel shell carbon as a high-performance adsorbent, exhibiting exceptional removal capacity for both ionic and molecular contaminants through distinct adsorption mechanisms.

1. Introduction

Due to increasing industrialization and urbanization, widespread contamination of water resources with toxic pollutants has created an urgent need for sustainable and cost-effective solutions to mitigate risks to human health and the environment. The dual challenges of increasing industrial production and the depletion of finite energy resources have driven the development of innovative technologies that leverage renewable, easily accessible waste materials. These technologies aim to address two critical environmental issues: reducing pollution caused by industrial activities and harnessing energy from sustainable sources. Among the various types of waste materials, lignocellulosic (LC) biomass has garnered significant attention due to its abundance, low cost, and versatile physicochemical properties. LC biomass, generated in large quantities across industries such as agriculture, forestry, and food processing, represents a valuable resource that can be revalorized for multiple purposes. One promising application is the use of LC waste as a precursor for bio-adsorbents, with biochar emerging as a sustainable and versatile material for environmental applications [1].

Biochar is a carbonaceous material produced through the thermochemical conversion of biomass under oxygen-limited conditions, typically at temperatures ranging from 300 °C to 1000 °C [2]. Defined as a carbon-neutral or even carbon-negative product (International Biochar Initiative, 2012) [3], biochar has demonstrated high efficiency in removing various contaminants from wastewater, making it a cost-effective and environmentally friendly adsorbent [4,5,6]. Biochar production by pyrolysis or carbonization offers significant environmental advantages, primarily by enabling the long-term sequestration of carbon in a stable form. This process effectively mitigates CO₂ emissions that would otherwise be released during the decomposition of natural biomass [7].

Apricot (Prunus armeniaca L.), a member of the Rosaceae family, is widely cultivated in regions such as North Africa, Asia, and Europe [8]. The fruit is renowned for its nutritional value, containing natural acids, vitamins, carbohydrates, phenolic compounds, and minerals. However, the apricot kernel, a by-product of fruit processing, is equally valuable, being a rich source of proteins, vitamins, and carbohydrates [9]. Apricot kernel shells (AKS), as LC waste, consist primarily of acid and neutral detergent fibers, including hemicellulose, cellulose, and lignin [10]. Despite their limited sorption capacity in their raw form [11], through thermochemical conversion [12] and subsequent activation, the AKS can be transformed into effective activated carbons (ACs), suitable for removing inorganic and organic contaminants from water [13]. AKS is a common waste in food production and processing. There are many pores on the surface and interior of apricot shells, which have a wood structure, and they are an excellent porous biomass material. AKS are often discarded or incinerated as garbage. At present, most research focuses on the preparation technology and the pore structure of the walnut shell AC [14], while research on the micro-morphology, phases, and pore structure of AKS-activated carbon is rarely reported. It should be noted that the United Nations (UNs) projects that by 2050, provide that there will be 9.7 billion people on the planet, up from 7.7 billion in 2019 [15]. This possibility presents a number of concerns regarding the expected two-fold increase in the consumption of fuels, fossil metals, biomass, and minerals, as well as the projected 70% increase in annual waste production if the current trends continue for the next 40 years [16]. These ideas contradict the trend toward a circular economy and more sustainable development. The circular economy is a production and consumption model that promotes the life span of the products by advocating for practices such as recycling, leasing, repairing, sharing, re-furbishing, and re-using existing materials and products. A crucial element of the proposed circular bio-based economy involves the conversion of biomass wastes and residues into valuable commodities. It means cutting waste to a minimum. Upon reaching the end of its functional lifespan, every effort is made to retain the materials of a product within the economic system, and these have the potential to be productively utilized repeatedly, adding more value to the waste [17]. In alignment with the objective of the circular economy and enhanced resource efficiency, the transition involves the incorporation of new inputs and resources, coupled with the conversion of waste into valuable resources. Keeping all this in mind, AKS presents the ideal ‘based’ biomass waste candidate for the production and consumption of “green” adsorbents in their application in wastewater treatment industries.

The transformation of biochar into activated carbons through physical or chemical activation has been widely studied, with each method imparting distinct properties to the resulting adsorbents [18,19]. Physical activation, typically involving CO₂ or steam, creates a highly porous structure by gasifying the carbon matrix at high temperatures. This process often results in activated carbons with a well-developed microporous structure, ideal for adsorbing small molecules such as heavy metal ions [20]. In contrast, chemical activation, using agents such as H₃PO₄, KOH, or ZnCl₂, not only enhances porosity but also introduces functional groups on the carbon surface, which can improve adsorption capacity for both organic and inorganic contaminants [21,22]. Chemical activation is particularly effective in enhancing the yield of activated carbons during the carbonization process, as it dehydrates the feedstock and inhibits the formation of tar and volatile compounds [23].

A comparison of physically and chemically activated carbons derived from AKS reveals distinct advantages and limitations [24]. Physically activated carbons, such as those produced using CO₂, often exhibit higher thermal stability and a more uniform pore size distribution, making them suitable for applications requiring precise control over adsorption kinetics [25]. However, chemically activated carbons, particularly those activated with H₃PO₄, tend to have higher surface areas and superior adsorption capacities for dyes and heavy metals compared to their physically activated counterparts [26,27], owing to the synergistic effects of increased porosity and surface chemistry [28,29].

The study also investigated the adsorption performance of the produced ACs for two highly toxic pollutants: lead (in the form of Pb²⁺ ions) and Rhodamine B dye (RhB). Lead, ranked as the second most toxic element by the Agency for Toxic Substances and Disease Registry [30], poses significant risks to human health and the environment. RhB, a widely used dye in the textile industry, is known for its toxic effects on aquatic life and potential carcinogenic and neurotoxic effects on humans [31]. Contaminant removal efficiency was evaluated using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) for Pb²⁺ and Ultraviolet-Visible (UV-Vis) spectroscopy for RhB. The adsorption mechanisms, kinetics, and thermodynamics of these contaminants onto the AKS-H₃PO₄ were explored, supported by Density Functional Theory (DFT) computations to model interaction scenarios and adsorption energies.

By combining experimental and theoretical approaches, this study provides a comprehensive understanding of the adsorption process. The detailed kinetic and thermodynamic analysis, supported by DFT calculations, provides a deeper understanding of the interaction mechanisms between the adsorbents and contaminants. This dual approach not only enhances the scientific understanding of the adsorption process but also offers practical insights for optimizing the design and application of carbon-based adsorbents in wastewater treatment. By leveraging the unique properties of AKS-derived ACs and employing a combination of experimental and theoretical methods, this study contributes to the development of sustainable and efficient solutions for water decontamination.

2. Materials and Methods

2.1. Preparation of Activated Carbons

In this study, AKS was used as a precursor for the production of biochar through carbonization at 800 °C for 1 h, followed by physical activation using CO₂ (Messer Tehnogas, Belgrade, Serbia), and chemical activation using H₃PO₄ (Sigma-Aldrich, St. Louis, MO, USA). The raw apricot kernel shells (AKS) were initially washed with water, dried (naturally for two days, followed by oven drying at 105 °C for two hours), and then crushed using a heavy-duty electrical grinder (Pulverisette 15, Laval Lab, Laval, QC, Canada). The crushed material was sieved (304 Stainless Steel Mesh Lab Sieve 60 Mesh, Xinxiang Dahan Vibrating Machinery Co., Ltd., Xinxiang, China) to obtain AKS precursor particles with a diameter of 0.3 mm for subsequent activation. For physical activation, the AKS precursor was carbonized in a CO₂ stream (gas flow rate of 200 cm³/min) at 800 °C for 1 h, with a heating rate of 3 °C/min, using a horizontal tube electric furnace (PZF Series, Protherm, Ankara, Turkey). The resulting activated carbon was labeled as AKS-CO₂. For chemical activation, the AKS precursor was impregnated in a 30% H₃PO₄ solution (25 mL per 10 g of AKS, corresponding to a biomass-to-acid ratio of ≈1:3) for 2 h, soaked in water for 24 h, and dried at 100 °C for 1 h. The dried material was then carbonized under the same conditions as physical activation, but in an N₂ (nitrogen) atmosphere to ensure an oxygen-free environment. The chemically activated carbon, labeled AKS-H₃PO₄, was washed twice with hot distilled water and dried at 105 ± 5 °C in an oven (ELP-32, ELEKTRON, Banja Koviljača, Serbia).

2.2. Structural Analysis of Activated Carbons

The synthesized ACs (AKS-CO₂ and AKS-H₃PO₄) were characterized using advanced analytical techniques: Fourier Transform Infrared (FTIR) spectroscopy, X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Brunauer–Emmett–Teller (BET) analysis for nitrogen adsorption–desorption isotherms. Detailed descriptions of the instruments and measurement conditions are provided in Text S1 (Supplementary Materials). The precursor material (non-activated carbonized AKS) has been comprehensively characterized in our previous work [12], with full physicochemical properties reported therein.

2.3. Adsorption Experiments

2.3.1. Preparation of Stock Solutions of Inorganic and Organic Contaminants

Stock solutions of the desired concentrations for adsorption studies were prepared by dissolving an appropriate mass of each contaminant in distilled water. For the inorganic contaminant, lead(II) chloride (PbCl₂) (Sigma Aldrich, St. Louis, MO, USA; purity ≥ 98%, molar mass = 278.11 g/mol) was used as the starting compound to prepare solutions of Pb²⁺ ions. For the organic contaminant, Rhodamine B (RhB) dye (molecular formula: C₂₈H₃₁ClN₂O₃, the molar mass = 479.02 g/mol, purity ≥ 97.0%) was obtained from Sigma Aldrich (St. Louis, MO, USA).

2.3.2. Adsorption Optimizations in the Experimental Procedure

Adsorption experiments were carried out in 25 mL flasks with agitators to ensure thorough mixing. A fixed mass of 0.01 g of ACs (AKS-CO₂ or AKS-H₃PO₄) was added to 10 mL of adsorbate solutions containing Pb²⁺ ions or RhB dye at known initial concentrations (c₀). The experiments were conducted at the natural pH conditions resulting from contaminant dissolution and adsorbent addition, which typically ranged between pH ≈ 5–6 for both Pb²⁺ and RhB systems. Adsorption equilibrium was studied by exposing adsorbents to solutions with initial concentrations of 50, 75, 100, 125, and 150 mg/L for 24 h at 25 °C, 35 °C, and 45 °C. For adsorption kinetics, solutions with an initial concentration of 100 mg/L were stirred for varying durations (0.083, 0.25, 0.5, 1, 2, 3, 6, and 24 h). Based on preliminary adsorption isotherm results, kinetic experiments for Pb²⁺ were conducted at 25 °C (room temperature), while RhB kinetics was examined at 35 °C. After adsorption, mixtures were filtered, and equilibrium concentrations (c_e) were measured. Pb²⁺ concentrations were determined using Inductively Coupled Plasma Optical Emission Spectrometry—ICP-OES (Thermo Scientific iCAP 7000 Series, Waltham, MA, USA), while RhB concentrations were quantified using a UV-Vis spectrophotometer (Lambda 35, PerkinElmer, Waltham, MA, USA) on a wavelength of 554 nm. All aliquots were diluted 20-fold to comply with the Lambert-Beer law. The adsorption capacity (amount of adsorbate adsorbed) and removal efficiency were calculated using Equations (S2)–(S4) provided in Text S2 of the Supplementary Materials.

2.4. Adsorption Kinetics and the Equilibrium Models

To describe the equilibrium during the adsorption process, various isotherm models have been developed, including two- and three-parameter models [32]. In this study, Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich (D–R) models were used to interpret the experimental data. To explore the adsorption mechanism and identify rate-controlling steps, eight kinetic models were evaluated, categorized into: (1) adsorption-reaction models (pseudo-first-order (PFO), pseudo-second-order (PSO), Avrami, and Elovich) and (2) adsorption-diffusion models (Boyd, intra-particle diffusion (IP), diffusion-chemisorption (DC), and Bangham). Theoretical details of these models, along with the procedure for estimating their parameters, are provided in Text S3 (Supplementary Materials). Model selection was performed through comprehensive statistical analysis, including Pearson correlation coefficient, sample correlation coefficient, coefficient of determination (R²), adjusted coefficient of determination, root mean square error, residual sum of squares (RSS), norm of residuals, and Fisher’s F-test (F-value), with additional validation via comparison between model predictions and experimental data.

2.5. Thermodynamic Analysis

Thermodynamic considerations of the adsorption process are necessary to determine the nature of the process itself, consider the influence of physical operating parameters, and define optimal conditions for practical implementation. The complete thermodynamic theory with the equations used in determining important thermodynamic quantities related to the observed adsorption processes, is presented in Text S4 (Supplementary Materials).

2.6. DFT Computations—Methodology

DFT calculations were performed using the pwscf code within the Quantum ESPRESSO package version 7.2 [33], an open-source software package for first-principles calculations based on plane-wave basis sets and pseudopotentials. Calculation details, including the assumptions of the models, geometry, and parameters, are provided in Text S5 (Supplementary Materials).

The visualization of structures was carried out using the XcrySDen software, version 1.6.2 [34]. Adsorption energies (ΔE_ads) were calculated as the difference between the total energy of the optimized slab–adsorbate system (E_slab+ads) and the sum of the total energies of the isolated adsorbate (E_tot,isol) and the bare surface slab (E_tot,slab):

$$∆E_{ads}=E_{slab+ads}-E_{tot,slab}-E_{tot,isol}$$

(1)

Defined like this, a more negative ΔE_ads value indicates a stronger surface-adsorbate interaction, with negative values signifying favorable adsorption (either physisorption or chemisorption).

3. Results

3.1. FTIR Analysis of Functional Groups in Prepared Activated Carbons

The FTIR spectra of AKS-CO₂ and AKS-H₃PO₄ samples are presented in Figure S1 (Supplementary Materials). As summarized in

Table 1. Characteristic FTIR vibration frequencies, allocations, and origins for AKS-CO₂ and AKS-H₃PO₄ activated carbons.

AKS-CO2			AKS-H3PO4
Frequency (cm−1)	Allocation of Bands	Components	Frequency (cm−1)	Allocation of Bands	Components
3551	The stretching vibration of O−H bonds in hydroxyl groups	Alcohols	3551	The stretching vibration of O–H bonds in hydroxyl groups	Alcohols
3480	Dimeric OH stretch	The water dimer	3478	Dimeric OH stretch	The water dimer
3415	O–H tensile vibration	The presence of phenols, alcohols, or carboxylic acid	3413	O–H tensile vibration	The presence of phenols, alcohols, or carboxylic acid
3234	Vibrational (stretching) of O–H bond with hydrogen bonding	Present in physically activated biochar	3234	Vibrational (stretching) of O–H bond with hydrogen bonding	Present in chemically activated biochar
3120	Aromatic C–H stretching band in polynuclear system	Aromatics present in physically activated biochar	2348	P–H stretching of ester compound	P-molecule-specific functional group in chemically activated biochar
2027	C–H (alkane) stretching vibrations in aromatic compound	Aromatics present in physically activated biochar	1797	Carbonyl (C = O) vibration of ester	Esters present in chemically activated biochar
1636	C = O group stretching vibration	Presence of aldehyde, esters, carboxylic acid, and ketone, in physically activated biochar	1636	C = O group stretching vibration	Presence of aldehyde, esters, carboxylic acid, and ketone, in physically activated biochar
1618	Aromatic skeletal vibration, C = C stretching	Aromatic structures present in physically activated biochar	1618	Aromatic skeletal vibration, C = C stretching	Aromatic structures present in chemically activated biochar
1370	Phenolic OH in-plain deformation	From lignin	1383	C = O symmetric stretching vibration of COO− groups	Oxygen-containing groups in chemically activated biochar
618	C–H bond in aromatic and hetero-atomic compounds	Aromatics present in physically activated biochar	754	Aromatic hydrocarbons (δCH); aromatic C–H stretching vibration	Aromatics structures present in chemically activated biochar
480	Bending motions of the Si–O–Si bonds	Silica (SiO2)	618	C–H bond in aromatic and hetero-atomic compounds	Aromatics present in chemically activated biochar
			480	Bending motions of the Si–O–Si bonds	Silica (SiO2)

, both samples exhibit several common spectral features: a three-finger band at 3551 cm⁻¹, ≈3479 cm⁻¹, and ≈3414 cm⁻¹ [35]; a band at 3234 cm⁻¹ [36]; a doublet at 1636 cm⁻¹ and 1618 cm⁻¹ [37,38,39]; phenolic OH deformation at 1370 cm⁻¹ [40]; and bands at 618 cm⁻¹ and 480 cm⁻¹ [41]. However, their spectral profiles diverge significantly, revealing distinct functional groups.

AKS-CO₂ spectrum is characterized by a band at 3120 cm⁻¹, indicative of the aromatic C–H stretching in polynuclear systems, and a band at 2027 cm⁻¹, assigned to C–H stretching in aromatic compounds [42]. In contrast, the AKS-H₃PO₄ spectrum displays a distinct peak at 2348 cm⁻¹, attributed to P–H stretching in esters [43], and a smaller peak at 1797 cm⁻¹, corresponding to carbonyl (C = O) vibrations in esters [44], highlighting the influence of chemical activation. A strong peak at 1383 cm⁻¹, assigned to C = O symmetric stretching in deprotonated COO⁻ groups, further underscores the prevalence of oxygen-containing functionalities [45] in AKS-H₃PO₄. Additionally, a band at 754 cm⁻¹, attributed to aromatic C–H stretching, confirms the presence of aromatic structures [46,47].

These differences in the spectral features arise from the distinct chemical environments and functional groups introduced by CO₂ and H₃PO₄ activation. Notably, AKS-H₃PO₄ exhibits phosphorus-specific functionalities and a higher abundance of oxygen-containing groups, highlighting the advantages of chemical activation over physical activation.

3.2. Results of the XRD Analysis

The XRD patterns of the synthesized ACs, AKS-CO₂ and AKS-H₃PO₄, are shown in Figure S2 (Supplementary Materials). Both samples exhibit two broad diffraction peaks at 2θ ≈ 26° and 2θ ≈ 45°, corresponding to (002) and (100) planes, respectively. These peaks indicate the presence of graphite crystallites and amorphous regions, though their broad and overlapping nature makes them difficult to resolve. The AKS-H₃PO₄ shows broader peaks, suggesting reduced graphite crystallite size and increased structural disorder, which likely enhances its specific surface area. In contrast, the sharper and more intense peak at 2θ ≈ 26.7° for AKS-CO₂ indicates higher crystallinity. This is confirmed by the crystallinity index (CrI) calculated using Equation (S1) (Supplementary Materials): 44.37% for AKS-CO₂ and 16.73% for AKS-H₃PO₄, demonstrating that AKS-CO₂ is approximately 2.5 times more crystalline than AKS-H₃PO₄. These differences arise from the distinct activation agents used, which significantly influence the structural properties of the ACs. The peak at 2θ ≈ 45.6° in AKS-H₃PO₄, associated with the (100) plane, reflects the role of H₃PO₄ in promoting pore formation through carbon breakdown along graphitic structures. This suggests an optimized activation process, yielding a well-organized aromatic carbon structure with a highly developed pore system [48,49]. Additionally, the peak at 2θ ≈ 12.9° in AKS-H₃PO₄ indicates increased interlayer spacing (up to ~0.72–0.73 nm; [50]), consistent with the formation of a graphene oxide structure due to the introduction of oxygen functionalities. This is attributed to the oxidizing properties of H₃PO₄ at high temperatures (800 °C), which facilitate the formation of C = O, C–H, COOH, and C–O–C bonds within the graphite layers, as supported by FTIR results. In contrast, AKS-CO₂ lacks such features, aligning with its lower oxygen content. Both samples exhibit peaks at 2θ ≈ 22.2° (AKS-H₃PO₄) and 2θ ≈ 23.5° (AKS-CO₂), attributed to amorphous silica within the 2θ range of 22–27° [51,52,53]. The AKS-H₃PO₄ also shows a sharp peak at 2θ ≈ 31.8°, indicative of crystalline quartz [54]. These findings underscore the influence of activation temperature on graphitic structure size and silica crystallization.

3.3. Morphological Comparison of Activated Carbons (SEM Analysis)

Morphological features of activated carbons derived from AKS—physically activated AKS-CO₂ and chemically activated AKS-H₃PO₄—were compared by analyzing representative SEM images of the two samples (Figure 1). These images highlight distinct morphological differences resulting from their respective activation methods.

AKS-CO₂ exhibits a layered structure (Figure 1a), indicative of the increased graphitization and crystallinity, as supported by earlier XRD findings. This sample features a relatively smooth surface with narrow pores, small pores distributed across flat regions, and random depressions surrounded by additional small pores. In contrast, the AKS-H₃PO₄ displays a spongy-like morphology (Figure 1b), with well-defined, uniformly distributed pores arranged in hollow spherical or elliptical shapes. The pore walls in AKS-H₃PO₄ are smoother and exhibit sharper edges, suggesting structural reorganization during chemical activation. White spots observed on the AKS-H₃PO₄ surface are likely due to the incorporation of phosphorus into the carbon matrix, which is consistent with previous studies [55,56]. Additionally, AKS-CO₂ contains miscellaneous inorganic particles on its surface, while AKS-H₃PO₄ shows minimal inorganic content, primarily silica. These morphological differences—including pore volume, shape, size, and arrangement—are a result of the activation methods used and are expected to affect the material’s performance in removing contaminants from aqueous solutions by adsorption.

3.4. Textural Properties of Activated Carbons (BET Analysis)

Textural properties of AKS-CO₂ and AKS-H₃PO₄ samples were evaluated through nitrogen (N₂) adsorption–desorption isotherms at 77 K (Figure 2). Both isotherms exhibit plateaus, with key differences observed at low relative pressures (up to ≈P/p₀ = 0.04). AKS-CO₂ isotherm (Figure 2a) corresponds to a Type I (a) isotherm (IUPAC classification), indicative of narrow microporous materials with pore widths <~1 nm. This isotherm shows a rapid increase in adsorption at low pressures, followed by a horizontal plateau, suggesting a predominantly microporous structure with limited mesoporosity [57,58,59]. In contrast, AKS-H₃PO₄ isotherm (Figure 2b) aligns with a Type I (b) isotherm, characterized by continuous adsorption uptake until saturation. This behavior reflects a broader pore size distribution, including wider micropores and narrow mesopores (<~2.5 nm). A sharp rise in adsorption near p/p₀ = 1 for AKS-CO₂, indicates condensation in inter-particle voids [60].

Table 2. Textural properties of synthesized activated carbons (AKS-CO₂ and AKS-H₃PO₄): BET surface area (S_BET), micropore volume (V_micro), mesopore surface area (S_meso), and pore size distributions—median and maximum pore radius and the cumulative pore volume (r_m, r_max and V_p) calculated using Horvath–Kawazoe (H-K), Brunauer–Joyner–Halenda (BJH), Cranston–Inkley (C-I), and Dollimore–Heal (D-H) methods.

Sample	SBET (m2/g)	Smeso (m2/g)	Vp(H-K) (cm3/g)	rm(H-K) (nm)	rmax(H-K) (nm)	Vmicro (cm3/g)	Vp(B.J.H.) (cm3/g)	rm(B.J.H.) (nm)	rmax(B.J.H.) (nm)	Vp(C-I) (cm3/g)	rm(C-I) (nm)	rmax(C-I) (nm)	Vp(D-H) (cm3/g)	rm(D-H) (nm)	rmax(D-H) (nm)
AKS-CO2	378.08	59.089	0.2148	0.2635	1.4330	0.1839	0.0051	1.7776	1.3414	0.0051	1.7793	1.7796	0.0050	1.7795	1.7792
AKS-H3PO4	1159.4	547.55	0.5902	0.3512	0.2887	0.2966	0.0694	1.7883	1.3283	0.0694	1.7884	1.3283	0.0688	1.7905	1.3283

summarizes the textural parameters of considered samples. The AKS-H₃PO₄ sample exhibits a significantly higher specific surface area (1159.4 m²/g) compared to AKS-CO₂ (378.08 m²/g), along with a larger mesopore surface area and micropore volume. Furthermore, AKS-H₃PO₄ demonstrates a broader pore size distribution, with slightly wider micropores, and the presence of narrow mesopores, as confirmed by the morphological analysis (Figure 1).

In summary, the AKS-H₃PO₄ exhibits superior textural properties, including an exceptionally very high specific surface area (>1000 m²/g), a combination of micropores (<1 nm) and narrow mesopores (1–2 nm), and a well-defined pore structure. In contrast, AKS-CO₂ shows limited mesoporosity, and a less uniform pore network, with surface irregularities rather than geometrically consistent pores (Figure 1). These differences suggest that the AKS-H₃PO₄, as an engineering-manufactured activated carbon, is better suited for adsorption applications compared to AKS-CO₂.

3.5. Removal Efficiency, Equilibrium and Kinetics of Adsorption Process

3.5.1. Removal Efficiency of Pb²⁺ and RhB Using AKS-CO₂ and AKS-H₃PO₄ Adsorbents

The adsorption performance of AKS-CO₂ and AKS-H₃PO₄ was evaluated for the removal of Pb²⁺ and RhB from aqueous solutions (initial concentration, c₀ = 100 mg/L, adsorbent dose of 1 g/L). Under applied experimental conditions, determined removal efficiencies are numerically equivalent to the adsorption capacity in mg/g. As shown in Figure 3, the removal efficiency of both contaminants was significantly higher for chemically activated carbon (AKS-H₃PO₄) compared to physically activated carbon (AKS-CO₂). After 24 h, AKS-H₃PO₄ achieved 80.5% removal for Pb²⁺ at 25 °C (Figure 3a), with the highest removal efficiency (85.1%) observed at 45 °C. In contrast, AKS-CO₂ reached only 34% Pb²⁺ removal. For RhB, AKS-H₃PO₄ achieved a maximum removal efficiency of 80.3% at 35 °C, while AKS-CO₂ reached approximately 20% (Figure 3b).

The superior performance of AKS-H₃PO₄ is attributed to its enriched surface functional groups, particularly oxygen-containing groups, and its well-developed porous structure, as evidenced by SEM images (Figure 1). Due to the low efficiency of AKS-CO₂, further analyses focused exclusively on AKS-H₃PO₄ for adsorption equilibrium and kinetics.

3.5.2. Adsorption Isotherms for Pb²⁺ and RhB onto AKS-H₃PO₄

Adsorption isotherms were analyzed using linearized models (Equations (S6), (S9), (S11) and (S14), Supplementary Materials), with results illustrated in Figures S3 and S4 for Pb²⁺ and RhB, respectively. A comparison between the experimental data and model predictions is presented in Figures S5 and S6 (Supplementary Materials), for Pb²⁺ and RhB, respectively. For both contaminants, the Langmuir model provided the best fit across all temperatures, indicating monolayer adsorption onto energetically equivalent sites (fit statistics summarized in

Table 3. Langmuir model fit statistics (coefficient of determination, R²; residual sum of squares, RSS; Fisher’s F-test, F-value) and derived adsorption parameters (separation factor, R_L; average adsorption energy, E (kJ/mol); removal efficiency, R (%)) for Pb²⁺ and RhB.

	Pb2+			RhB
	25 °C	35 °C	45 °C	25 °C	35 °C	45 °C
R2	0.999	0.997	0.995	0.977	0.992	0.916
RSS	2.60 × 10−4	1.12 × 10−4	4.53 × 10−5	0.08113	8.7453 × 10−4	0.11949
F-value	2552.7	969.7	623.1	129.11968	420.90161	32.9
RL	0.027–0.077	0.033–0.092	0.046–0.127	0.12–0.28	0.06–0.17	0.11–0.27
E, kJ/mol	15.9	13.6	12.8	15.9	13.4	13.4
R, %	80.5	82.7	85.1	30.1	80.3	44.9

; complete data in Tables S1 and S2 for Pb²⁺ and RhB, respectively, in Supplementary Materials).

The separation factor (R_L), calculated via Equation (S7) (Supplementary Materials), consistently yielded values below 1, confirming thermodynamically favorable adsorption (R_L < 1). Average adsorption energy (E, kJ/mol) values derived from Equation (S15) (Supplementary Materials) suggest physisorption with moderately strong interactions or weak chemisorption (potentially via ion-exchange mechanisms) [61,62,63]. Notably, Pb²⁺ removal efficiency (R, %) exceeded 80% at 25 °C, justifying subsequent kinetic studies at this temperature. For RhB, optimal adsorption occurred at 35 °C, which guided our investigation of its adsorption dynamics under these conditions.

3.5.3. Adsorption-Reaction Kinetics of Pb²⁺ and RhB onto AKS-H₃PO₄

Model parameters for the adsorption-reaction models were estimated using their non-linear forms (Equations (S17), (S22), (S24), and (S28), as provided in the Supplementary Materials). Estimated parameters and goodness-of-fit measures are summarized in Tables S3 and S4, while experimental data and model predictions are compared in Figures S7 and S8 (Supplementary Materials) for Pb²⁺ and RhB, respectively.

For Pb²⁺, the PSO model provided the best fit (R² > 0.985) at 25 °C, consistent with a second-order ion exchange mechanism dependent on temperature and initial contaminant concentration (Table S3). Adsorption was rapid within the first six hours, followed by a decline in rate and a saturation plateau (Figure S7). This behavior is attributed to the initial availability of adsorption sites and a high concentration gradient, followed by site occupation as Pb²⁺ accumulated on the adsorbent surface. The Langmuir isotherm and PSO kinetics provide a robust framework for describing the adsorption of Pb²⁺ onto AKS-H₃PO₄.

For RhB, the Avrami model provided the best fit (R² > 0.970) at 35 °C, though PFO and PSO models were also predictive (Table S4). The Avrami model’s fractal-like behavior, characterized by a time-dependent adsorption rate coefficient [64], suggests potential for future studies on multi-step adsorption processes. As shown in Figure S8, the RhB adsorption was slower than Pb²⁺ adsorption, likely due to RhB’s larger molecular volume, which hinders diffusion into the adsorbent’s pores.

3.5.4. Adsorption-Diffusion Kinetics of Pb²⁺ and RhB onto AKS-H₃PO₄

The experimental data were fitted linearly using adsorption-diffusion models (Equations (S34), (S35), (S36) and (S40)), as respectively illustrated in Figures S9 and S10 (Supplementary Materials) for Pb²⁺ and RhB, with models’ predictions compared to experimental results in Figure S11 and S12 (Supplementary Materials).

Multi-linear segments in Figure S9a and the parameters C for the IP model suggest that both film diffusion and surface-controlled reactions influence Pb²⁺ adsorption. The adsorption is not solely limited by intra-particle diffusion but is also controlled by a combination of diffusion and chemisorption, a common mechanism for heavy metal adsorption on heterogeneous surfaces [65]. It should be noted that, from a closer look at the results shown in Figure S9a, we can see that the arrangement of experimental points forms three well-defined diffusion zones. The first zone (Zone I) consists of the first three points from the coordinate origin, the second zone (Zone II) consists of a pair of points in the range approximately between t^0.5 = 0.5 and t^0.5 = 1.75, while the last, third zone (Zone III) is made up of the last three points. In accordance with Módenes et al. [66], Zone I is attributed to the adsorption, which takes place on the surface layer of the adsorbent, Zone II is attributed to the adsorption in macropores of the adsorbent, while Zone III can be attributed to the adsorption on micropores of the adsorbent. A longer period of time is attributed to Zone III compared to the other stages (see Figure S9a), thus indicating the limiting step of the considered process, where the metal ion adsorption primarily takes place in the micropores of the adsorbent. For Pb²⁺, the Boyd diffusion plot (Figure S9c) did not intersect the origin, also indicating multiple adsorption mechanisms. The diffusion-chemisorption (DC) model provided the best fit, with a high coefficient of determination (R² > 0.997; Table S5, Supplementary Materials). The high diffusion-chemisorption constant (K_DC, Table S5) reflects a strong concentration gradient between the adsorbent’s inner and outer regions, consistent with the high sorption capacity of AKS-H₃PO₄. This capacity is attributed to its large specific surface area, pore volume, and the prevalence of micropores (<2 nm) (Table 2), which facilitates Pb²⁺ adsorption due to the ion’s small ionic radius (0.119 nm–0.24 nm diameter).

For RhB, the adsorption data were most effectively fitted using the IP and Boyd diffusion models (Figure S10), both of which exhibited high accuracy (R² > 0.970; Table S6, Supplementary Materials). The fitted lines suggest multiple adsorption mechanisms, though the minimal deviations and high linearity indicate that intra-particle diffusion is the dominant rate-limiting step. Unlike Pb²⁺ adsorption, RhB adsorption showed two linear sections in Figure S10a and a small boundary layer thickness (parameter C, Table S6), implying negligible film diffusion. Instead, intra-particle diffusion dominates, facilitated by the larger micropore diameter of AKS-H₃PO₄, which allows RhB molecules to penetrate and diffuse through the pores. Considering the positions of the experimental points in Figure S10a (Supplementary Materials), it can be concluded that dye adsorption occurs both on the surface of the adsorbent and in its pores of a larger radius [66]. This behavior is different from that shown in Figure S9a. Therefore, the adsorption occurs after dye molecules are transported to active sites, driven by the concentration gradient across the adsorbent surface. The IP model accounts for RhB adsorption across pores of varying sizes, linking it to adsorption at internal sites within AKS-H₃PO₄. A comparison of experimental data and model predictions (Figure S12) revealed that the IP model fits the data better than the Boyd model. Although the DC model showed a low residual sum of squares (indicating good agreement with experimental data), its poor linear fit statistics (adjusted R² and F-value, Table S6) indicate a weak fit. The K_DC value for RhB adsorption was over twelve times smaller than that for Pb²⁺ (Tables S5 and S6), confirming distinct adsorption mechanisms for the two contaminants. These differences highlight the role of AKS-H₃PO₄’s pore structure and the molecular characteristics of adsorbates in governing adsorption kinetics.

3.6. Thermodynamic Study of Pb²⁺ and RhB Adsorption onto AKS-H₃PO₄

Adsorption equilibrium of Pb²⁺ and RhB onto AKS-H₃PO₄ was best described by the Langmuir model, as evidenced by isotherm analysis (Tables S1 and S2, Supplementary Materials). Although, the Langmuir model assumes temperature independence of maximum adsorption capacity (q_m) [67,68], attempts to fit the isotherms nonlinearly under the condition q_m = const. were unsuccessful. However, the best nonlinear fits (Figure 4) yielded parameters consistent with those obtained from linear fitting (Tables S1, S2, and S7, Supplementary Materials).

Given this inconsistency, the use of the Langmuir model to derive $∆G^{\circ }$ was reconsidered (Text S4, Supplementary Materials). Instead, the partitioning model was employed to estimate thermodynamic parameters (Equation (S42), Supplementary Materials). Values of $K^{°}$ as $q_e⟶0$ were determined from the intercept of ln($K^{\circ }$) versus $q_e$ plots (Figure S13, Supplementary Materials). Subsequently, $K^{\circ }$ values were derived by fitting the data to the nonlinear Van’t Hoff equation (Equation (S46), Supplementary Materials) using plots of $K^{\circ }$ $(q_e⟶0)$ versus 1/T.

3.6.1. Standard Thermodynamic Parameters

For Pb²⁺ (Figure S13a), surface coverage significantly influenced $K^{\circ }$, with the relationship becoming nonlinear at higher $q_e$. To determine $K^{\circ }$ at $q_e⟶0$, only data points corresponding to low concentrations, where linearity was observed, were used for fitting. For RhB (Figure S13b), a linear dependence of ln($K^{\circ }$) on $q_e$ was only evident at 35 °C. Despite this, the data were processed to gain insights into the adsorption phenomenology of RhB onto AKS-H₃PO₄. Linear fit statistics are provided in Table S8 (Supplementary Materials).

Van’t Hoff plots (Figure S14, Supplementary Materials) were used to determine the standard thermodynamic parameters for Pb²⁺ and RhB adsorption. The appropriate fit statistics are presented in Tables S9 and S10 (Supplementary Materials).

For Pb²⁺, $\Delta H^{\circ }$ = –10.54 kJ/mol, and $∆S^{\circ }$ = –2.95 J/(mol·K) were calculated, indicating an exothermic process ($\Delta H^{\circ }$< 0) with a decrease in randomness at the solid/solution interface ($∆S^{\circ }$< 0). The small absolute value of $∆S^{\circ }$ suggests the process is primarily “enthalpy-driven”, with minimal structural changes in the adsorbate or adsorbent [69]. Consequently, $∆G^{\circ }$ was nearly temperature-independent, with values of –9.66 kJ/mol, –9.63 kJ/mol, and –9.60 kJ/mol at 25 °C, 35 °C, and 45 °C, respectively.

For RhB, it was found $\Delta H^{\circ }$ = 17.47 kJ/mol and $∆S^{\circ }$ = 78.86 J/(mol·K), indicating an endothermic process ($\Delta H^{\circ }$> 0) with increased disorder at the solid/solution interface ($∆S^{\circ }$> 0). This suggests potential structural changes in both the adsorbate and adsorbent during RhB adsorption. The process was more temperature-sensitive compared to Pb²⁺ adsorption, with $∆G^{\circ }$ values of –6.04 kJ/mol, –6.82 kJ/mol, and –7.61 kJ/mol at 25 °C, 35 °C, and 45 °C, respectively. The negative $∆G^{\circ }$ values for both Pb²⁺ and RhB confirm the spontaneity and feasibility of the adsorption process.

3.6.2. Isosteric Heat of Adsorption

The isosteric heat of adsorption (${\Delta }_{ist}H$) was calculated by estimating $c_e$, for specific $q_e$ values using the nonlinear Langmuir model (Figure 4 and Table S7), which provided excellent agreement with experimental data. Figure S15 (Supplementary Materials) shows the estimated $c_e$ values for selected $q_e$, fitted exponentially according to Equation (S48) (Supplementary Materials). Fit statistics are provided in Tables S11 and S12 (Supplementary Materials). As expected, higher adsorbent loading resulted in more nonlinear $c_e$ versus temperature dependencies, raising uncertainties about the Langmuir model’s applicability. Figure 5 shows distinct ${\Delta }_{ist}H$ versus $q_e$ relationships for Pb²⁺ and RhB, respectively. Linear fit statistics are provided in Tables S13 and S14 (Supplementary Materials). Although ${\Delta }_{ist}H$ versus $q_e$ dependencies are complex, they were assumed linear within the studied temperature and concentration ranges.

For Pb²⁺ (Figure 5a), two possibilities emerge: (a) the adsorbent surface may be energetically heterogeneous, or (b) adsorbate molecules may interact, with interactions strengthening at higher concentrations. Extrapolating ${\Delta }_{ist}H$ to $q_e=0$ yielded a value of –10.37 kJ/mol, consistent with $\Delta H^{\circ }$ within experimental error, suggesting physical interactions dominate Pb²⁺ adsorption. However, within the operational concentration range, ${\Delta }_{ist}H$ ranged from 5.7 kJ/mol to 43.5 kJ/mol, indicating the presence of hydrogen bonding (≈2 kJ/mol – 40 kJ/mol), dentate interactions (≈40 kJ/mol), or dipole–dipole forces (≈2 kJ/mol – 29 kJ/mol) [70,71]. While Pb²⁺ adsorption is inherently exothermic under standard conditions, it becomes more favorable with increasing temperature (${\Delta }_{ist}H>0$) within operational ranges of concentrations, likely due to enhanced interaction frequencies and Pb²⁺ complex formation, highlighting the chemical nature of the process. In other words, energy input is necessary to facilitate bond formation, as the process involves overcoming repulsive forces between ions at short distances. Due to the proximity of the ions during bonding, an external energy source, such as heat, is required to drive the endothermic reaction and enable the adsorbent to effectively bind the ions.

As for Pb²⁺, for RhB (Figure 5b), ${\Delta }_{ist}H$ exhibited a strong dependence on q_e, suggesting an energetically heterogeneous AKS-H₃PO₄ surface, but unlike Pb²⁺, RhB molecules do not interact during adsorption. Extrapolating ${\Delta }_{ist}H$ to $q_e=0$ yielded a value of 9.91 kJ/mol, deviating from $\Delta H^{\circ }$, but confirming the endothermic nature of the process. Within the studied concentration range, ${\Delta }_{ist}H$ ranged from 21.9 kJ/mol to 52.6 kJ/mol, comparable to Pb²⁺ but at tenfold lower q_e values. This variation may also be attributed to lateral interactions between adsorbed Pb²⁺ ions.

3.7. Summary Regarding Thermodynamics and Mechanisms of Adsorption Processes onto AKS-H₃PO₄

The adsorption processes of Pb²⁺ and RhB onto AKS-H₃PO₄ exhibit distinct energetic behaviors, as reflected by the opposite signs of their standard enthalpy changes ($\Delta H^{°}$). This difference arises from the adsorption mechanism, which involves the displacement of pre-adsorbed water molecules by the adsorbate species. In endothermic processes, such as RhB adsorption, the adsorbate species replaces multiple water molecules, resulting in energy-requiring adsorption. Conversely, in exothermic processes like Pb²⁺ adsorption, the energy released during bond formation between the adsorbate and adsorbent exceeds the energy required for bond breaking, leading to heat release [69].

The size disparity between RhB and Pb²⁺ further influences their adsorption behavior. RhB, with an effective diameter of ~1.3 nm, is approximately five times larger than Pb²⁺ (~0.24 nm). This size difference also explains the lower saturation capacity of AKS-H₃PO₄ for RhB, despite similar enthalpy changes (${\mathit{\Delta }}_{ist}H$) for both adsorbates. The comparable ${\mathit{\Delta }}_{ist}H$ values suggest that similar bonding forces govern the adsorption of both species, indicating a physicochemical nature of the processes within the observed concentration range. The standard entropy change ($∆S^{°}$) also differs significantly between the two adsorbates, reflecting their structural and size differences. Pb²⁺ adsorption is associated with $∆S^{°}$ < 0, indicating minimal structural changes in the adsorbent and adsorbate. In contrast, RhB adsorption exhibits $∆S^{°}$ > 0, suggesting significant structural rearrangements, likely due to RhB’s ability to exist in multiple forms (cationic or zwitterionic) depending on the pH [72,73,74]. This structural variability may explain why the RhB removal is most efficient at 35 °C.

The activation agent for biomass precursor, particularly at high temperatures (>550 °C), significantly influences on adsorption capacity of ACs by increasing mesopore width and creating new micropores. This structural adaptation is crucial for efficient contaminant removal, as evidenced by the superior performance of chemically activated carbon — AKS-H₃PO₄, compared to physically activated carbon-AKS-CO₂, which experiences reduced pore volume and surface area, under similar carbonization conditions. It should be noted that a higher gas flow rate of the CO₂ activating agent may result in activated carbon with a smaller specific surface area [75]. At lower temperatures (e.g., 25 °C), Pb²⁺ adsorption is primarily driven by oxygen-containing functional groups and smaller micropores. However, at elevated temperatures (e.g., 45 °C), AKS-H₃PO₄ demonstrates enhanced Pb²⁺ adsorption capacity. In contrast, RhB adsorption is more temperature-sensitive, with optimal removal achieved at 35 °C, likely due to the restructuring of the solid/solution interface and the occupation of diverse adsorption sites. Figure 6 provides a schematic representation of the proposed adsorption mechanisms for Pb²⁺ and RhB onto AKS-H₃PO₄, highlighting the distinct processes involved.

Table 4. Comparison of agricultural waste/by-product-based adsorbents for Pb²⁺ and RhB removal: maximum adsorption capacity (q_m, mg/g), maximum removal efficiency (R, %), pH, dose (D, g/L), concentration (C, mg/L), and temperature (T, °C).

Pb2+
Adsorbent	qm (mg/g)	R (%)	pH	D (g/L)	C (mg/L)	T (°C)	Reference
Rice husks	−	99.0	6.5	5.0–40.0	25.0	25.0	[76]
Rice husk biochar	−	96.4	5.5	1.0–4.0	1950.0	25.0	[77]
Polythiophene-coated rice husk ash nanocomposite	34.5	98.1	4.0	5.0–20.0	50.0–400.0	25.0–65.0	[78]
Lentil husk	81.4	98.0	5.0	2.0	20.0–250.0	20.0–35.0	[79]
Walnut shell	9.9	92.3	4.0	1.0–50.0	100.0	25.0	[80]
Peanut hull-g-methyl methacrylate	370.4	99.3	5.7	2.0–12.0	5.0–100.0	20.0–50.0	[81]
Modified peanut shells	130.5	−	4.6–5.0	−	4144.0	25.0	[82]
Chitosan/rice husk ash/nano-γ alumina	181.8	91.0	5.0	−	250.0–550.0	10.0–40.0	[83]
Peanut hulls	69.8	−	5.0	0.1–10.0	15.0–200.0	25.0	[84]
Hazelnut husks	13.1	97.2	5.7	2.0–20.0	5.0–200.0	18.0	[85]
Palm kernel husk	−	88.0	5.0	20.0–100.0	5.0–15.0	25.0	[86]
Groundnut shell	−	98.0	3.0	2.4–8.8	5.0–105.0	25.0	[87]
Rice husk nanocomposite	1665.0	96.8	5.2	0.1–2.0	15.0–150.0	25.0	[88]
Apricot stone	−	89.6	6.0–10.0	−	30.0	25.0	[89]
Functionalized graphene from rice husk	748.5	99.8	7.0	10.0–50.0	20.7	18.0–80.0	[90]
Treated rice husk	93.5	95.0	7.0	5.0	100.0–800.0	20.0–50.0	[91]
Mustard husk	30.5	100.0	6.0	6.0–12.0	1.0–5.0	20.0–60.0	[92]
Magnetic coconut husk-activated carbon	43.4	−	2.0–6.0	−	50.0–500.0	25.0	[93]
Cocoa shells	33.4	95.0	2.0	15.0	100.0	22.0	[94]
Apricot stone	1.3	95.3	7.0	10.0–40.0	5.0–500.0	25.0	[95]
Peach stone	2.3	97.6	7.0	10.0–40.0	5.0–500.0	25.0	[95]
Coconut shell-activated carbon	26.5	92.5	4.5	0.2–2.0	10.0–50.0	35.0–45.0	[96]
Shells of groundnut	22.0	82.8	4.9	20.0	116.0–651.4	30.0	[97]
Magnetic rice husk biochar	148.0	95.0	2.5–5.8	2.5	10.0–500.0	25.0	[98]
Rice husk	5.7	−	5.0	2.0–20.0	10.0–200.0	30.0–60.0	[99]
Peach stone modified by the citric acid	118.8	93.4	2.0–7.0	−	6.0–120.0	30.0	[100]
AKS-H3PO4	127.6	85.1	5.0 a	1.0	50.0–150.0	45.0	This study
RhB
Adsorbent	qm (mg/g)	R (%)	pH	D (g/L)	C (mg/L)	T (°C)	Reference
Sulfuric acid-activated coconut husk	16.7	99.2	7.0	−	200.0–1000.0	30.0–50.0	[101]
Palm shell-based activated carbon	−	95.0	3.0	−	41.8–208.8 b	50.0	[102]
Surfactant-modified coconut coir pith	14.9	90.0	10.0	20.0	10.0	−	[103]
Modified pine nut shell biochar	110.7	≈ 100.0	3.0	0.5	10.0	25.0	[104]
Rice husk ash (RHA)	6.0	84.0	7.0	0.05–0.5	10.0	27.0	[105]
Acid-functionalized coconut husk	1666.7	−	3.0–11.0	0.1	200.0–1000.0	30.0–50.0	[101]
Pine nut shell impregnated with CaCl2	34.0	84.0	2.0–10.0	2.0–8.0	65.0–140.0	25.0–45.0	[106]
Pine nut shell impregnated with H3PO4	33.1	82.5	2.0–10.0	2.0–8.0	65.0–140.0	25.0–45.0	[106]
Acid modified locust bean pod (H3PO4)	1111.1	95.0	3.0–11.0	0.1	200.0–1000.0	30.0–50.0	[107]
Rich husk with chitosan composited activated with H3PO4	1.2	94.0	2.0–8.0	0.1–1.2	4.0–20.0	30.0–70.0	[108]
Olive stones biochar	2.5	97.8	2.0−12.0	4.0	1.0–100.0	20.0–50.0	[109]
Coir pith biochar	2.6	50.0	2.1–11.1	7.0	10.0–40.0	32.0	[110]
Treated rice husk-activated carbon (KOH)	290.0	95.3	1.3–10.2	10.0	300.0	19.8	[111]
Bagasse pith activated carbon (H3PO4)	198.6	−	5.7	1.0	100.0–600.0	20.0	[112]
AKS-H3PO4	94.7	81.3	5.0 a	1.0	50.0–150.0	35.0	This study

^a In the experimental procedures implemented in this work, the natural pH was applied. ^b In [μ·mol/L].

compares the performance of AKS-H₃PO₄ with other agricultural waste-derived adsorbents in removing Pb²⁺ and RhB. It underscores the effectiveness of agricultural waste (husks, hulls, and stones/shells) as a precursor for adsorbent preparation, with performance influenced by solution conditions, such as pH, temperature, and adsorbate concentration.

The results presented in Table 4 demonstrate that agricultural waste and by-products serve as excellent carbon precursors for synthesizing effective adsorbents capable of removing both inorganic and organic contaminants, such as heavy metal ions (e.g., Pb²⁺) and dyes (e.g., RhB). The performance of adsorbents is influenced not only by the experimental conditions but also by the chemical nature of the biomass precursor, which collectively determine the optimal adsorption efficiency. Transport phenomena also play a critical role in adsorption processes. Factors such as mixing intensity, adsorbate concentration (dilute or non-dilute), particle size, and the affinity of the adsorbate for the adsorbent determine whether external transport or intra-particle diffusion limits the process. The degree of pore development in the adsorbent is particularly important in regulating the adsorption mechanism [113], especially for achieving maximum RhB removal, as shown in Table 4. In the context of activated carbons–liquid phase interactions, the maximum sorption capacity is influenced by: (a) the physical properties of the adsorbent, such as pore structure, inorganic content, and functional groups; (b) the properties of the adsorbate, including functional groups, polarity, molecular weight, and size; and (c) solution conditions, such as temperature, pH, adsorbate concentration, ionic strength, and adsorbent dose. The pH of the solution, in particular, profoundly affects RhB adsorption. At pH < 4, RhB exists in a cationic, monomeric form, facilitating its entry into the adsorbent pores. However, at pH > 4, RhB adopts a zwitterionic form, leading to molecular aggregation and reduced pore accessibility due to strong electrostatic interactions [114,115,116]. The maximum adsorption capacity of AKS-H₃PO₄ for RhB (Table 4), far exceeds that of many other agricultural waste-derived adsorbents, such as banana bark carbon, nano-porous Jack fruit peel carbon, palm kernel shell adsorbent, sugarcane fiber, microwave-activated rice husk ash, animal bone meal, oil palm empty fruit bunch AC, and ZnCl₂-activated wood apple carbon [117]. This superior performance of AKS-H₃PO₄, coupled with its physicochemical properties that facilitate easy regeneration [118,119], highlights its potential for further optimization and application in water treatment processes.

3.8. Results of DFT Computations

3.8.1. The Estimation of AKS-H₃PO₄ Surface Coverage

To estimate the equilibrium surface coverage from adsorption experiments, the adsorption sites were modeled as boxes with dimensions approximating the size of the adsorbate species: 11 × 17 Ų for RhB and 3 × 3 Ų for Pb²⁺ ions. The total number of adsorption sites was calculated by dividing the total surface area obtained from BET experiments (Table 2) by the area of a single adsorption site. The AKS-H₃PO₄ surface coverage, expressed as a percentage of occupied sites, was determined by dividing the equilibrium amount of adsorbed moles of adsorbate by the total number of moles of adsorption sites in an experimental setup. The dependence of equilibrium adsorbate coverage on the initial concentrations of Pb²⁺ and RhB is illustrated in Figure 7.

For Pb²⁺, equilibrium coverage did not exceed 2% of total adsorption sites across all temperatures. At 25 °C, the saturation coverage of 1.45% was achieved at 120 ppm. At the higher temperatures (at 35 °C and 45 °C), saturation was not reached within the tested concentration range, indicating that Pb²⁺ adsorption becomes “more efficient” with increasing temperature, and the adsorbent seems able to collect more Pb²⁺ ions at higher temperatures (Figure 7a). These results suggest that Pb²⁺ adsorption is dominated by chemisorption at sites activated by functional groups on the adsorbent surface. On the other hand, the equilibrium coverage of RhB ranged from 5% to 20%, depending on temperature (Figure 7b). This indicates that RhB adsorption, at least within the studied concentration range, is less chemically sensitive compared to Pb²⁺ adsorption, and occupies a wider variety of adsorption sites. These findings align well with the assumptions and conclusions drawn earlier in this study.

3.8.2. Model Surfaces for Adsorption of Pb²⁺ and RhB

The surface models were created to match the experimental data from the surface characterization as much as possible. AKS-H₃PO₄ surface was considered to include bare graphene, graphene edges (modeled as an H-saturated mono-vacancy), oxygen (modeled as a mono-vacancy-MV with a bound OH-group, and phosphorus (modeled as a mono-vacancy with a bound PH₂ group) (see Figure S16, Supplementary Materials). Model surfaces are created for the most functionalized graphene-oxide adsorbent material, in the case of conventional wastewater treatments [120,121].

3.8.3. Adsorption of Pb²⁺ Ions

Adsorption of Pb²⁺ ions (represented as PbCl₂ in a gas phase) was calculated on the appropriate model surfaces. The results are presented in

Table 5. Surface models, optimized geometry of adsorbed PbCl₂ and the corresponding adsorption energies. “n.s.” stands for “not stable”. Color code: carbon—black, oxygen—dark red, phosphorus—dark yellow, hydrogen—light blue, Pb—grey, chlorine—green.

Surface Model	Optimized Geometry	ΔEads
Bare graphene		−1.42 eV
H-saturated MV		n.s.
H-saturated MV with OH group		−1.81 eV
H-saturated MV with COOH group		−0.25 eV
Simple MV with PH2 group		−2.67 eV

.

Oxygen-rich defects represent the sites of strong PbCl₂ binding, being in good agreement with the proposition that Pb²⁺ binds chemically on the adsorbent surface, occupying exactly the particular oxygen-rich active sites. Interestingly, PbCl₂ is thermodynamically stable even on bare graphene, suggesting that “perfect” carbon sites could also be occupied by Pb²⁺. Moreover, a site with the PH₂ group also exhibits affinity to bind PbCl₂. On the other hand, PbCl₂ is not stable on the H-saturated MV surfaces, suggesting that edges probably do not have any significant share in the adsorption of Pb²⁺. These results align with published DFT studies demonstrating that carboxyl and hydroxyl groups significantly enhance Pb²⁺ adsorption through strong electrostatic interactions and complexation, facilitated by coordination bond formation [122].

3.8.4. Adsorption of RhB Dye

Adsorption of the RhB molecule is more complex, due to the size of the considered molecule. The optimized adsorption geometries and the calculated adsorption energies of the RhB molecule are represented in

Table 6. Adsorption of RhB on the selected model surfaces—the optimized geometries and adsorption energies. Color code: carbon—black, oxygen—dark red, phosphorus—dark yellow, hydrogen—light blue, nitrogen—purple.

Surface Model	Optimized Geometry	ΔEads
Bare graphene		−0.63 eV
H-saturated MV		−0.771 eV
Simple MV with PH2 group		−3.92 eV
Simple MV with OH group		−3.41 eV

.

Different from PbCl₂, the obtained adsorption geometries for bare graphene and surface groups do not suggest any formation of a real chemical bond between the adsorbate and the substrate. However, the RhB is in all cases stabilized about 3 Å (~0.3 nm) above the surface, similar to the distance between layers in graphite, suggesting the probable existence of π–π interactions between the graphene and RhB [123]. In the previous work [124], the contribution of Van-der-Waals interactions to the adsorption of RhB on the bare graphene was discussed. When a defect is introduced to provoke the formation of a real chemical bond between surface and adsorbate (H-saturated MV, simple MV with OH and PH₂ groups), a transfer of the proton occurs from the surface group (PH₂ or OH) to the negatively charged carboxyl group of RhB. In this case, the interaction energy between the surface and the adsorbate increases, due to the redistribution of the bonds in the gas phase. However, the high interaction energies still do not originate from the formation of a chemical surface–adsorbate bond. In the case of simple MV with PH₂ group, the distance between carboxyl oxygen and the surface hydrogen of PH₂ is 2.5 Å (~0.25 nm), implying that the formation of hydrogen bonds is also possible between the adsorbate and the surface functional group. Overall, the obtained results in this contribution pointed out that the physisorption based on hydrogen bonds with functional groups, and π–π interactions with bare carbon surface dominate, while covalent binding hardly contributes to the adsorption of RhB on the investigated surfaces. The consistencies between these results, the mechanistic insights from Section 3.7, and the established literature [125,126] strongly support the validity of our conclusions.

4. Discussion

Activated carbons derived from lignocellulosic biomass, such as AKS, exhibit excellent physicochemical properties, making them highly effective for the removal of contaminants from water [127,128,129,130,131,132,133]. In this study, novel types of activated carbon were synthesized from AKS, an agricultural waste material, using both physical and chemical activation methods. Physical activation was achieved using CO₂ gas, while chemical activation employed phosphoric acid (H₃PO₄), resulting in the production of AKS-CO₂ and AKS-H₃PO₄ activated carbons, respectively. The physicochemical properties of the synthesized materials were characterized using advanced analytical techniques, including FTIR, XRD, SEM, and BET analysis.

The characterization of AKS-CO₂ and AKS-H₃PO₄ revealed significant differences in their structural and functional properties. The chemically activated AKS-H₃PO₄ demonstrated an exceptionally large specific surface area (S_BET = 1159.4 m²/g), placing it within the range of commercial engineering adsorbents. Its N₂ adsorption–desorption isotherm, classified as Type I(b), indicated a broad pore size distribution, including wider micropores and potential narrow mesopores, which significantly enhanced its adsorption capabilities. AKS-H₃PO₄ exhibited phosphorus-specific functionalities and a higher abundance of oxygen-containing groups, underscoring the advantages of chemical activation over physical activation. In contrast, AKS-CO₂ adsorbent had a much lower specific surface area and a narrower pore size distribution, which limited its adsorption capacity, compared to AKS-H₃PO₄ adsorbent.

To evaluate the application potential of these carbon materials in wastewater treatment, adsorption experiments were conducted using aqueous solutions contaminated with Pb²⁺ ions and RhB dye. The results demonstrated that the ACs derived from chemically activated AKS exhibited high adsorption capacities for both contaminants. Moreover, AKS-H₃PO₄ proved to be a far superior adsorbent compared to AKS-CO₂. Consequently, further detailed analyses were performed exclusively on AKS-H₃PO₄. A detailed kinetic and thermodynamic analysis of the adsorption process was performed, revealing that RhB adsorption is more temperature-dependent yet less chemically sensitive than the Pb²⁺ adsorption, while also providing insights into the most probable adsorption mechanisms and the spontaneity of the process.

Removal efficiencies for Pb²⁺ ions and RhB dye were 85.1% and 80.3%, respectively, with maximum adsorption observed at 45 °C for Pb²⁺ and 35 °C for RhB. The adsorption equilibrium for both contaminants was well-described by the Langmuir isotherm, suggesting monolayer adsorption on a homogeneous surface. However, further analysis revealed structural changes and interactions within adsorbent–adsorbate system, raising questions about the applicability of the Langmuir model for evaluating thermodynamic parameters. Kinetic analyses revealed that the adsorption of Pb²⁺ was most closely aligned with the pseudo-second-order model, suggesting film diffusion and surface chemisorption as the dominant mechanisms. In contrast, RhB adsorption was best described by the pseudo-first-order model, with intra-particle diffusion playing a primary role. Thermodynamic analysis confirmed the spontaneous nature of both adsorption processes. However, enthalpy changes revealed distinct differences between the two contaminants: Pb²⁺ adsorption was exothermic under standard conditions ($\Delta H^{°}<0$) yet exhibited positive values of the isosteric heat of adsorption (${\Delta }_{ist}H$) within the studied concentration and temperature ranges, consistent with chemisorption. In contrast, for RhB dye, both $\Delta H^{°}$ and ${\Delta }_{ist}H$ values were positive, but for lower adsorption loadings (q_e) associated with ${\Delta }_{ist}H$, emphasizing the predominance of physisorption mechanisms. Furthermore, DFT computations provided atomic-level insights into adsorption mechanisms. For Pb²⁺ ions, chemisorption dominated, occurring primarily at functional group-activated sites, with minimal contribution from bare graphene edges. In contrast, RhB adsorption was governed by physisorption, driven by hydrogen bonding with functional groups and π–π interactions with the carbon surface, while covalent binding played a negligible role. These DFT findings fully supported the proposed adsorption mechanisms for both contaminants onto AKS-H₃PO₄ surface.

5. Conclusions

In summary, this study highlights the potential of AKS-derived activated carbons, particularly AKS-H₃PO₄, as highly efficient and sustainable adsorbents for the removal of inorganic and organic contaminants from wastewater. The prepared activated carbons were characterized using advanced analytical techniques that offered comprehensive insights into the structural, chemical, and surface properties of the adsorbents. The analysis revealed critical information about the microstructure and functional groups of the produced ACs, confirming their formation and the underlying reaction mechanisms. Such insights are essential for classifying the materials and determining their suitability for practical applications. The combination of experimental characterization, detailed kinetic and thermodynamic analyses, and DFT modeling provides a comprehensive understanding of the adsorption processes, supporting the rational design and optimization of biochar-based adsorbents for environmental applications.