Apple Pruning-Derived Activated Biochar and Hydrochar for Efficient Dye Adsorption: Response Surface Methodology-Guided Optimization, Kinetic Analysis, and Mechanistic Modelling

Abstract

This study explores the valorisation of apple pruning (AP) residues into sustainable carbonaceous adsorbents for dye-contaminated wastewater. Activated biochars (ABCs) were produced via single-step (ABC-1S) and two-step (ABC-2S) KOH activation, while activated hydrochar (AHTC) was obtained through hydrothermal carbonization followed by H₃PO₄ activation. The materials were comprehensively characterized using proximate analysis, FTIR spectroscopy, SEM imaging, and N₂ adsorption–desorption to evaluate surface chemistry, morphology, and textural properties. Batch adsorption experiments using MB (5–100 mg/L) demonstrated the superior performance of ABCs compared to AHTC. At low dye concentrations, adsorption on ABCs was partially influenced by external mass transfer, while kinetic data were best described by the Avrami model, indicating complex adsorption mechanisms. Isotherm analysis showed that ABC-2S exhibited heterogeneous adsorption behaviour, whereas AHTC poorly conformed to conventional isotherm models. The Langmuir model indicated higher monolayer capacities for ABCs (up to 22.9 mg/g) relative to AHTC (9.7 mg/g), reflecting a greater density of accessible adsorption sites induced by alkaline activation. Notably, nearly complete methylene blue (MB) removal was maintained over three regeneration cycles, confirming the stability, reusability, and practical potential of AP-derived ABCs and AHTC for sustainable wastewater treatment.

1. Introduction

Water pollution is increasingly recognized as a major global environmental threat, largely driven by industrial expansion and rising population, which together intensify wastewater generation [1]. Among the sectors contributing most to this problem, the textile industry stands out for releasing large volumes of dye-containing effluents that accumulate persistently in aquatic systems [2]. Textile dye effluents present considerable ecological and human health hazards due to the persistence and degradation resistance of synthetic dyes in natural environments, frequently resulting in prolonged contamination of aquatic systems [3]. Approximately 10–15% of dyes utilized in textile manufacturing do not adhere to fabrics and are released into wastewater, resulting in significant contamination and pronounced coloration of aquatic habitats [4]. This pronounced pigmentation diminishes light penetration and hinders photosynthesis in aquatic vegetation, resulting in decreased dissolved oxygen levels and disrupting aquatic food webs [5]. Numerous dye compounds and their breakdown products demonstrate hazardous, mutagenic, and carcinogenic properties, potentially affecting fish, invertebrates, and human health via direct exposure or bioaccumulation [6]. In humans, contact with dye-contaminated water has been associated with dermal irritation, respiratory complications, organ damage, and an elevated risk of cancer, especially with prolonged exposure [7] Overall, recent comprehensive assessments underscore that dye pollution is a significant environmental concern linked to industrial wastewater and stress the urgent necessity for effective and sustainable remediation strategies [8]. These dyes often coexist with additional hazardous pollutants such as heavy metals and phenolic compounds, reinforcing the need for efficient and sustainable treatment methods [9].

Although several advanced technologies have been proposed for wastewater purification, adsorption has emerged as one of the most effective and economically viable options due to its simplicity, adaptability, and high removal efficiency [10]. Conventional activated carbon is known for its excellent adsorptive performance, but its elevated production cost drives the search for renewable and low-cost alternatives [11]. Biomass-derived carbonaceous materials, particularly biochar (BC) and hydrochar (HTC), are gaining interest because they are abundant, structurally tunable, and environmentally sustainable [12].

BC is produced by pyrolysis under oxygen-limited conditions, yielding amaterial with high surface area and reactive functional groups that can vary depending on the feedstock and process temperature [13]. HTC, by contrast, is obtained through hydrothermal carbonization, which converts biomass into a carbon-rich solid under moderate temperatures and self-generated pressure in a water-based reaction environment [14]. HTCs typically contain abundant oxygenated functional groups, making them suitable materials for pollutant adsorption [15]. However, agro-residue-based BCs and HTCs often show limited surface area and structural stability, which can restrict their performance [10]. However, agro-residue -based BCs and HTCs often show limited surface area and structural stability, which can restrict their performance [16]. To mitigate these limitations, chemical activation has proven an effective strategy to create porosity, increase surface area, and promote stronger interactions between adsorbent and pollutant molecules [17]. These enhancements are particularly advantageous for chemical adsorption processes, where the formation of stable covalent or ionic bonds plays a central role [18].

Agricultural residues from apple production represent an attractive biomass source for adsorbent preparation. In northern Spain, and specifically in the Gipuzkoa region, apple cultivation generates substantial residual annual biomass (apple pruning, AP), offering both a waste management solution and an opportunity to create value-added carbon materials [19].

In this study, activated biochars (ABCs) and hydrochar (AHTC) were synthesized from AP to assess their performance in removing methylene blue (MB) from aqueous solutions. ABCs were produced by two different schemes: a one-step (1S) route based on a simultaneous thermochemical and activation process, and a two-step (2S) one, with sequential thermochemical and activation stages. In both schemes, the thermochemical process was conducted at 900 °C, above conventional pyrolysis temperatures to enhance carbon structural consolidation and explore the resulting impact on material stability [20]. Hydrothermal treatment was performed at 200 °C for 24 h, followed by chemical activation with H₃PO₄, conditions associated with structural dehydration and the development of porosity through phosphate decomposition [21].

The strength of this work lies in its comprehensive mechanistic assessment. The materials were characterized using ATR-FTIR to analyse surface chemistry [15], SEM to investigate morphology [14], and NLDFT to determine surface area and pore structure [16]. Adsorption kinetics were examined through multiple non-linear models to identify rate-controlling steps and diffusion mechanisms, while adsorption isotherms were evaluated using a diverse set of equilibrium models to provide deeper insight into adsorption capacity and surface heterogeneity [22].

Finally, the reusability of adsorbents was assessed over three adsorption–desorption cycles using acetone as the desorbing agent. MB removal remained consistently high across all cycles, demonstrating excellent structural stability and regeneration efficiency, and highlighting the potential of these materials for real wastewater treatment applications [20].

2. Results and Discussion

2.1. Characterization of Adsorbents

2.1.1. Proximate and Ultimate Analysis

The results obtained from the proximate and ultimate analyses of the biomass precursor and the ABCs and AHTC samples are shown in

Table 1. Proximate and ultimate analysis (dry basis, wt.%) of AP and adsorbents (ABC-1S, ABC-2S and AHTC).

Analysis	Parameter	AP	ABC-1S	ABC-2S	AHTC
Proximate analysis (wt.%)	Fixed carbon (%)	14.86	-	-	-
	Volatile matter (%)	79.69	-	-	-
	Inorganic matter (%)	5.45	-	-	-
	Moisture (%)	8.68	-	-	-
Ultimate analysis (wt.%, ash free)	C (%)	45.04	85.05	74.87	76.67
	H (%)	5.71	-	-	0.38
	N (%)	0.73	0.40	-	0.56
	S (%)	0.72	0.11	0.48	2.60
	O (%)	42.35	14.44	24.65	19.79
	O/C	0.94	0.17	0.33	0.26
	H/C	0.13	-	-	0.005

. The activated material shows significant carbon enrichment compared to AP (45% C), the activation process indicates more condensed aromatic/graphitic structure (C–C/C=C) [9] that improves π–π interactions with organic pollutants (dyes, phenols, pharmaceuticals) [18]. The extremely low H/C ratio in HTC (0.005) and the low O/C ratio refer to hydrophobicity and high long-term stability [23]. These factors impact the performance to absorb polar and non-polar contaminants and lipophilic organic compounds, like MB, during repeated adsorption cycles [24]. ABC-1S and AHTC still contain some nitrogen (0.40 and 0.56 dry basis, wt.%) while ABC-2S does not. Activation at higher temperatures (900 °C) promotes decomposition and volatilisation of heteroatom species (e.g., N-functional groups), resulting in a carbon matrix with negligible (ABC-2S) or low (ABC-1S) nitrogen content compared to AHTC, which was treated at lower temperatures (450 °C) [24]. In addition, sulfur was effectively incorporated, with its content reaching up to 2.6% for AHTC. This increases the surface basicity, attracting cationic MB and enhancing charge transfer [25]. Meanwhile, the sulphur groups provide polarizable sites and promote MB adsorption through soft-acid soft-base interactions [26].

2.1.2. Pore Structure of the Adsorbents

The N₂ adsorption/desorption isotherms shown in Figure 1a for ABC-1S and ABC-2S demonstrate a swift rise in adsorbed volume at low relative pressures, subsequently followed by a hysteresis loop at higher relative pressures. This observation signifies the coexistence of micropores and mesopores, a common feature of ABCs. The presence of such Type IV profiles with hysteresis has been documented in the literature as a hallmark of hierarchical pore structures in mesoporous carbon materials and ABCs, which exhibit an integration of high surface area with capillary condensation effects in mesopores [27].

The pore size distribution data, Figure 1b,c reveal the presence of dominant micropore peaks (<2 nm) in addition to features in the 2–10 nm range, thus confirming a mixed pore structure. This finding is in accordance with recent research, which demonstrates that effective activation strategies result in ABCs with concentrated microporosity and a high surface area, in conjunction with secondary mesopores that facilitate faster diffusion and capillary condensation [27]. ABC-1S sample’s mesoporous structure begins with pores at the lower end of the mesoporous range (around 2 nm), followed by a broad distribution with pronounced features between 12 and 40 nm, with the main maximum centred at 12 nm. In contrast, the ABC-2S sample showed its most intense pore size contributions in the 10–14 nm region, accompanied by a residual porosity extending up to 50 nm.

The N₂ adsorption/desorption of AHTC, Figure 2a, displays a characteristic Type I behaviour, exhibiting a pronounced nitrogen uptake at low relative pressures (p/p₀ < 0.1). This observation signifies a micropore-dominated structure and constrained mesoporosity, which is a hallmark of carbons subjected to chemical activation with H₃PO₄ [28]. The plateau observed at higher relative pressures provides further confirmation that adsorption is primarily governed by micropore filling rather than mesopore capillary condensation.

The pore size distribution, Figure 2b, provides support for this observation, indicating that most of the pore volume is concentrated in the micropore region (<2 nm). This finding is consistent with the literature on phosphoric acid-AHTCs, where narrow pore formation is commonly reported to be promoted by dehydration and cross-linking reactions during activation [29]. It has been demonstrated that a microporous structure is associated with enhanced adsorption performance towards small molecules, such as MB. This enhanced performance is understood to result from a combination of factors, including π–π interactions, electrostatic attraction, and hydrogen bonding [30].

A summary of the porosity and surface properties is presented in

Table 2. Porosity and textural properties.

Sample	SBET (m2/g)	Stot (m2/g)	Smicro (m2/g)	Smeso (m2/g)	Vtot (cm3/g)	Vmicro (cm3/g)	Vmeso (cm3/g)	Average Pore Width (nm)
ABC-1S	1297.2	1480.1	1425.5	54.61	0.5523	0.5066	0.0457	1.753
ABC-2S	1176.2	1401.5	1305.6	95.93	0.4960	0.4640	0.0320	1.709
AHTC	1342.8	1528.6	1453.6	75.00	0.5771	0.5166	0.0605	1.761

Where S_BET: BET specific surface area; S_tot/V_tot: total pore surface/ volume obtained using 2D-NLDFT models; S_micro/V_micro: Surface and volume of micropores using Dubinin-Radushkevich models; S_meso/V_meso: The mesopore surface/volume was determined by subtracting S_micro and V_micro from S_tot and V_tot, respectively.

, where a strong influence of the activating agent on pore development and adsorption behaviour can be observed. ABC-1S and ABC-2S exhibit a highly developed microporous structure with average pore widths of 1.753 and 1.709 nm, respectively, as well as extremely high microporous surface areas of 1425.5 and 1305.6 m²/g. This strongly suggests that micropore formation is the dominant effect of KOH activation. This extensive microporosity is the key parameter responsible for their high adsorption potential, as adsorption in such materials is primarily governed by micropore filling.

Nitrogen adsorption in microporous materials proceeds predominantly through pore-filling mechanisms rather than multilayer adsorption, which leads the BET model to systematically underestimate surface area in highly microporous systems. In contrast, Dubinin–Radushkevich (DR) analysis more accurately accounts for micropore filling phenomena, thereby providing a more reliable estimation of microporous contributions. These discrepancies between BET-derived and DR-derived surface areas have been extensively discussed in the literature for a wide range of microporous and mesoporous adsorbents, underscoring the importance of using complementary characterization methods [31].

To obtain a more comprehensive textural assessment, the total surface area (Stot) and total pore volume were derived from nitrogen adsorption isotherms using 2D-NLDFT models, which offer enhanced resolution of micro- and mesopore structures compared with traditional BET analysis. The 2D-NLDFT framework incorporates pore geometry, adsorbate–adsorbent interactions, and surface heterogeneity, enabling more robust and physically realistic characterization of porous carbons [32].

ABC-1S has a higher microporous surface area and pore volume than ABC-2S, suggesting a greater density of accessible adsorption sites. In contrast, AHTC exhibits the highest overall S_BET (1342.8 m²/g) and total pore volume (0.5771 cm³/g), as well as the largest mesoporous contribution (V_meso = 0.0605 cm³/g). This reflects the ability of phosphoric acid activation to generate a hierarchical micro-mesoporous structure.

While AHTC remains microporous (S_micro = 1453.6 m²/g; pore width = 1.781 nm), Mesopores improve mass transfer and micropore access, enhancing adsorption kinetics. Key structural parameters for adsorption capacity include microporous surface area, micropore volume, narrow pore width, and activating agent influence.

2.1.3. ATR-FTIR Analysis

The FTIR spectra in Figure 3 reveal several shared functional groups characterized by specific wavenumbers. Both AHTC and ABC-2S show strong aliphatic bond at 2981 cm⁻¹ and 2896 cm⁻¹ [16], corresponding to asymmetric and symmetric [33] sp³ C–H [34] stretching vibrations of alkyl group [35] such as methyl and methylene groups [36], along with overlapping O–H stretching from carboxylic acids [34]. The aliphatic groups mostly contribute to hydrophobic and van der Waals interactions, enhancing surface heterogeneity and promoting pore diffusion and molecular access, in accordance with findings in modified materials utilized for MB adsorption [37].

The peak at 2343 cm⁻¹ observed in ABC-1S and ABC-2S is attributed to C=O stretching from atmospheric CO₂ [38] and amide groups [39]. At 1756 cm⁻¹, ABC-2S exhibits C=O stretching linked to carboxyl, lactone [34], ester, ketone, and aldehyde groups [35] which offer active sites for electrostatic attraction, hydrogen bonding and surface complexation with cationic MB [21].

Aromatic skeletal vibrations (C=C stretch) [16] and C=N bonds [40] are noted at 1588 cm⁻¹ in AHTC and 1542 cm⁻¹ in ABC-1S, indicating aromatic ring structures [41]. Those groups are crucial for π–π stacking and π–π electron-donor–acceptor (EDA) interactions with the aromatic rings of MB, thereby enhancing affinity and chemisorption strength [42].

Additionally, bending vibrations such as C–H sp³ bending [9] and O–H bending for methyl symmetric deformation [41] occur around 1395 cm⁻¹ in ABC-2S. C–O stretching vibrations, related to lignin, cellulose, acyl, phenol, and alcohol groups [41], appear prominently at 1320 cm⁻¹ of methyl symmetric deformation of CH₃ Group [40], 1229 cm⁻¹, and 1048 cm⁻¹ across the samples are promoting hydrogen bonding and increase surface polarity which enable N–π interactions by having lone-pair electrons interact with the aromatic system of MB [43]. Lastly, AHTC shows a distinct C–OH out-of-plane bending at 720 cm⁻¹ [41]. Overall, functional groups enhance surface heterogeneity, promoting strong chemisorption (electrostatic attraction, hydrogen bonding, surface complexation) and weaker physisorption (π–π interactions, van der Waals forces, pore filling) in adsorbents for MB removal [44].

2.1.4. Scanning Electron Microscopy (SEM)

The SEM micrographs of the three materials (Figure 4) reveal clear morphological distinctions that reflect their different synthesis routes and directly influence their adsorption behaviour.

Both ABC-1S and ABC-2S display the characteristic features of high-temperature pyrolyzed biochars, including a rigid and fractured carbon matrix with irregular cavities and open mesoporous structures generated by extensive devolatilization and carbon restructuring at 900 °C. ABC-1S’ images, Figure 4a,b, manifest a polished and compact surface with minimal visible pores, which is consistent with the concurrent pyrolysis/KOH activation process [45], in which rapid devolatilisation and vigorous KOH-carbon reactions can result in the fusion of surface layers or the collapse of pore channels [45,46],. Recent mechanistic studies have indicated that the activation of KOH results in the generation of porosity through redox and gasification pathways (KOH → K₂O/K → K₂CO₃ + CO/CO₂). Moreover, it has been observed that the application of excessive activation conditions leads to an increase in structural damage [47]. In contrast, the ABC-2S sample Figure 4c,d exhibits a rough, irregular surface with numerous small pores, while also preserving fragments of the original biomass cellular structure. This morphology has been previously reported for 2-S KOH activation, where controlled chemical etching leads to the development of micro/mesopores without fully collapsing the precursor framework [46]. AHTC sample Figure 4e,f, produced via hydrothermal carbonization followed by H₃PO₄ activation, retains the smoother, rounded morphology typical of hydrochar-derived materials. Its surface appears more compact, composed of aggregated spherical or bead-like structures, and although activation introduces porosity, the resulting texture is more uniform and less fractured than that of the ABC samples. These morphological differences imply that the ABC materials provide greater external pore accessibility and more efficient diffusion pathways due to their open fissures and broader mesoporous structures, while AHTC’s more compact and chemically etched surface likely favours interactions driven by surface functionalities rather than extensive external porosity. Together, the SEM observations show that ABC-type adsorbents possess a more open and accessible morphology conducive to rapid mass transfer, whereas AHTC offers a chemically functional but less externally porous architecture, explaining the performance differences observed between the materials.

2.2. Adsorption Studies

2.2.1. 3D Response Surface for MB Removal

The coefficients of the quadratic models for ABC-1S, ABC-2S, and AHTC generated through RSM are listed in

Table 3. Regression coefficients of the quadratic RSM models for ABC-1S, ABC-2S and AHTC.

Coefficient	ABC-1S	ABC-2S	AHTC
${\beta }_0$	62.38	50.12	25.39
${\beta }_1$	0.19	−0.60	0.04
${\beta }_2$	0.07	0.1	0.0563
${\beta }_{12}$	0.0004	0.0004	0.0001
${\beta }_{11}$	−0.0046	0.0019	−0.0011
${\beta }_{22}$	−4.24 × 10−5	−5.077 × 10−5	−1.607 × 10−5

, where ABC-1S and ABC-2S have higher intercept (β₀) values than AHTC, showing their better MB removal capability. This is due to their greater microporosity and higher surface area created by KOH activation [48]. ABC-1S shows improved adsorption with higher activation severity, while ABC-2S’s negative linear coefficient suggests KOH activation leading to pore widening or collapse, as seen with alkali-ABCs. Small interaction terms and negative quadratic coefficients show limited synergistic effects, confirming an optimum adsorption region consistent with RSM studies on KOH-ABCs.

As demonstrated in

Table 4. Fit Statistics of the Quadratic Models for MB Removal.

Sample	${\mathit{R}}^2$	$\mathbf{Adjusted} {\mathit{R}}^2$	AIC	BIC
ABC-1S	0.5611	0.5568	3928.83	3954
ABC-2S	0.8677	0.8664	3524.29	3550
AHTC	0.4987	0.4937	4254.68	4279

, the key model fit statistics, including R², adjusted R², AIC, and BIC, are presented. The high R² and adjusted R² values for ABC-2S demonstrate excellent agreement between experimental and predicted MB removal, reflecting the homogeneous pore structure and strong dependence on operating variables, which are typical of KOH-ABCs optimised by RSM. In contrast, the lower R² values for ABC-1S and AHTC indicate greater heterogeneity and weaker model predictability.

Where AIC and BIC are respectively Akaike Information Criterion and Bayesian Information Criterion [49], those two statistical model-selection tools evaluate model adequacy by balancing goodness of fit with model complexity [50].

The removal efficiency curves for MB Figure 5 for ABC-1S (a), ABC-2S (c) and AHTC (e), demonstrate a rapid increase in percentage removal at early contact times, followed by a slower approach to equilibrium. This pattern is commonly observed in MB adsorption due to the abundance of available active sites initially, and their progressive occupation with time. This has been reported in many MB adsorption studies. Efficiency increases quickly at the start because surface sites are available, and then gradually plateaus as sites become occupied and mass transfer limitations take over [51]. Higher concentrations typically result in lower removal rates at a fixed time due to competition for adsorption sites and take longer to reach high removal levels, as shown in graphs [15].

The RSM 3D surface plots indicate that MB removal escalates with both contact duration and initial dye concentration, paralleling results from other RSM investigations where prolonged contact time and optimized parameters markedly improved MB adsorption [52]. Figure 5 ABC-1S (b), and particularly ABC-2S (d), exhibit more pronounced surfaces and enhanced removal efficiencies, indicating more robust interactions and superior adsorption kinetics, similar to the significant removal and strong quadratic model fits documented for carboxymethyl cellulose–based hydrogel beads optimized through RSM-BBD for MB removal [51]. In comparison, the AHTC surface displays Figure 5f a more gradual increase in removal with time and Ci, corresponding with prior AHTC RSM investigations where ideal conditions still required careful management of factors to attain high efficiencies [53]. These comparisons highlight the significance of contact time and initial concentration as critical parameters in RSM models for dye adsorption.

2.2.2. Kinetic Study

The results of the kinetic fitting reveal different ways in which MB is adsorbed depending on the type of material and how it is activated. For ABC-1S and ABC-2S Figure 6 and Figure 7, adsorption at low concentrations is partly determined by external mass transfer, as shown by the high liquid film diffusion fits for ABC-1S at 5 mg/L (R² = 0.949), Figure 6f and ABC-2S at 10–25 mg/L (R² ≈ 0.96–0.98), Figure 7f, which is commonly reported for highly porous ABCs at low driving forces [54]. At intermediate concentrations (10–50 mg/L), both ABC-1S and ABC-2S are best described by the Avrami model, Figure 6e and Figure 7e, (R² = 0.996–1.000), in conjunction with strong Elovich, Figure 6c and Figure 7c, and Bangham fits, Figure 6g and Figure 7g. This finding indicates heterogeneous chemisorption and pore-controlled uptake, a conclusion that is consistent with recent Avrami-based analyses of MB adsorption on ABCs with non-uniform energy sites [55]. In contrast, AHTC (Figure 8) demonstrates consistently high Elovich, Figure 8c, Bangham, Figure 8g, and Weber–Morris, Figure 8h, fits across most concentrations (e.g., R² = 0.993–0.996 at 5–35 mg/L), suggesting that adsorption is dominated by surface heterogeneity and intra-particle diffusion rather than strong chemisorption. This behaviour has been widely observed for AHTCs with lower graphitisation and higher oxygen functionality [56].

In short, KOH activation promotes the uptake of MB by chemisorption, while phosphoric-acid-AHTC exhibits diffusion-dominated heterogeneous adsorption. This agrees with recent ABC–AHTCs dye adsorption studies.

The adsorption kinetics of MB onto both ABC-1S

Table 5. Kinetic parameters for the adsorption of MB onto ABC-1S.

Model	Parameter	Initial MB Concentration (mg/L)
		5	10	20	25	35	50	100
PFO	$q_e$	0.7418	1.3738	3.2584	3.8280	5.6923	8.244	16.3257
	$k_1$	0.1022	0.0877	0.0066	0.0104	0.0986	0.1089	0.0040
	$R^2$	0.222	0.951	0.990	0.924	0.975	0.974	0.957
PSO	$q_e$	0.7503	1.3928	3.6139	4.0953	5.7506	8.3218	19.7912
	$k_2$	0.3178	0.1358	0.0027	0.0045	0.0448	0.0346	0.0002
	$R^2$	0.322	0.985	0.989	0.980	0.995	0.993	0.923
Elovich	$\beta$	45.72	20.5665	1.6382	1.8890	6.9530	4.9641	0.2096
	$\alpha$	1.99 × 1010	1.513 × 108	0.1372	0.8932	3.68 × 1013	2.01 × 1014	0.1341
	$R^2$	0.365	0.998	0.940	0.969	0.997	0.999	0.870
Avrami	$q_{av}$	0.7906	1.4904	3.3159	4.0516	5.8368	8.5919	15.5990
	$K_{av}$	2.8930	1.2111	0.0067	0.0111	1.4595	4.7658	0.0043
	$n_{av}$	0.1390	0.1437	0.7875	0.5038	0.1988	0.1489	1.9390
	$R^2$	0.369	0.999	0.997	0.996	0.999	1.000	0.985
Boyd	$B_t$	0.0029	0.0031	0.0051	0.0049	0.0032	0.0035	0.0048
	$q_e$	0.7574	1.4126	3.2898	3.9394	5.7851	8.3797	16.0797
	intercept	1.8100	1.3277	−0.2440	−0.1061	1.8689	1.7097	−0.6479
	$R^2$	0.911	0.835	0.986	0.962	0.851	0.862	0.962
LFD	$K_{lfd}$	0.0028	0.0029	0.0049	0.0047	0.0030	0.0034	0.0046
	$q_e$	0.7574	1.4126	3.2898	3.9394	5.7851	8.3797	16.0797
	$R^2$	0.949	0.332	0.988	0.924	0.269	0.284	0.963
Bangham	$k_B$	1.1594	1.0279	0.0195	0.1037	5.7851	8.3797	16.0797
	$n_B$	0.1392	0.1437	0.7875	0.5038	0.5000	0.5000	0.5000
	$R^2$	0.369	0.999	0.997	0.996	0.960	0.964	0.119
W-M	$k_{wb}$	0.0022	0.0098	0.0624	0.0592	0.0350	0.0500	0.4290
	C	0.6841	1.1050	1.3385	2.0783	4.7211	6.8448	2.4890
	$R^2$	0.845	0.297	0.754	0.717	0.229	0.228	0.756

and

Table 6. Kinetic parameters for the adsorption of MB onto ABC-2S.

Model	Parameter	Initial MB Concentration (mg/L)
		5	10	20	25	35	50	100
PFO	$q_e$	0.7198	1.4795	3.0210	3.6558	5.3603	7.1606	16.2642
	$k_1$	0.0493	0.0052	0.0082	0.0037	0.0043	0.0038	0.0024
	$R^2$	0.919	0.927	0.852	0.975	0.941	0.963	0.978
PSO	$q_e$	0.7375	1.6628	3.2723	4.3240	6.1742	8.4646	11.7082
	$k_2$	0.1247	0.0047	0.0043	0.0010	0.0009	0.0005	−76,039.33
	$R^2$	0.986	0.964	0.932	0.984	0.962	0.982	0.084
Elovich	$\beta$	24.6600	3.3659	2.1347	1.0789	0.8370	0.5513	0.1543
	$\alpha$	3264.027	0.0430	0.3420	0.0418	0.0970	0.0832	0.0559
	$R^2$	0.989	0.989	0.988	0.986	0.981	0.989	0.940
Avrami	$q_{av}$	0.7532	1.8654	4.0930	4.2362	7.6073	8.9098	14.9615
	$K_{av}$	0.1033	0.0027	0.0028	0.0026	0.0014	0.0021	0.0028
	$n_{av}$	0.2845	0.4529	0.3242	0.6168	0.4442	0.5593	1.5560
	$R^2$	1.000	0.993	0.991	0.993	0.988	0.992	0.993
Boyd	$B_t$	0.0026	0.0039	0.0042	0.0037	0.0038	0.0031	0.0038
	$q_e$	0.7467	1.5444	3.1842	3.7578	5.5725	7.5693	15.4630
	intercept	1.2615	−0.5570	−0.3725	−0.6849	−0.6824	−0.5975	−0.9023
	$R^2$	0.798	0.892	0.918	0.868	0.873	0.796	0.886
LFD	$K_{lfd}$	0.0023	0.0037	0.0039	0.0034	0.0035	0.0028	0.0035
	$q_e$	0.7467	1.5444	3.1842	3.7578	5.5725	7.5693	15.463
	$R^2$	0.424	0.960	0.918	0.983	0.962	0.979	0.977
Bangham	$k_B$	0.5243	0.0694	0.1502	0.0259	5.5725	7.5692	15.463
	$n_B$	0.2845	0.4529	0.3242	0.6168	0.5000	0.5000	0.5000
	$R^2$	1.000	0.993	0.991	0.993	0.223	0.185	0.084
W-M	$k_{wb}$	0.0063	0.0300	0.0530	0.0868	0.1189	0.1706	0.4819
	C	0.5465	0.5122	0.0530	0.8152	1.5365	1.6052	−0.5945
	$R^2$	0.402	0.906	0.841	0.938	0.937	0.946	0.892

and ABC-2S demonstrate a process dominated by chemisorption and surface interactions modulated by diffusion phenomena. The equilibrium capacities (qₑ) from the PSO model exhibited an increase with initial MB concentration, with PSO qₑ ranging from ~0.75 to ~19.79 mg/g for ABC-1S and ~0.74 to ~11.71 mg/g for ABC-2S. This is consistent with enhanced site occupancy at higher dye loads and with similar trends reported for rice straw and other ABCs [54], where PSO best describes MB uptake. This indicates chemisorptive control via electron sharing and surface bonding [57]. The observed decrease in PSO rate constants (k₂) with increasing MB concentration is indicative of the saturation of high-energy active sites and competitive adsorption. This phenomenon has also been observed in MB adsorption into various ABCs, where Elovich parameters indicate heterogeneous surfaces and varying energetic sites [57,58].

The Avrami exponents $n_{av}$ are typically below unity for most concentrations, indicating a multi-step uptake process involving both rapid surface binding and slower pore penetration. This finding is corroborated by diffusion analyses (Boyd, Weber–Morris, Bangham) that demonstrate intraparticle diffusion contributes to the uptake but is not the sole rate-limiting factor. This observation aligns with the prevailing phenomenon of film and pore diffusion in activated biochar systems, suggesting a multifaceted uptake mechanism [54]. These insights support a mechanism where MB adsorption proceeds through fast external surface interaction, followed by progressive diffusion.

The kinetics of MB adsorption onto AHTC (

Table 7. Kinetic parameters for the adsorption of MB onto AHTC.

Model	Parameter	Initial MB Concentration (mg L−1)
		5	10	20	25	35	50	100
PFO	$q_e$	0.5920	1.8047	2.5866	5.1410	5.1801	3.9640	15.9514
	$k_1$	0.0054	0.0008	0.0022	0.0004	0.0102	0.0875	0.0012
	$R^2$	0.893	0.961	0.948	0.907	0.830	0.860	0.986
PSO	$q_e$	0.6678	2.7665	3.2797	7.9558	5.5682	4.0299	8.7255
	$k_2$	0.0118	0.0002	0.0007	0.00004	0.0031	0.0397	−90,723.56
	$R^2$	0.955	0.960	0.961	0.903	0.933	0.902	0.071
Elovich	$\beta$	8.1943	1.0136	1.1777	0.3541	1.3454	4.9797	0.1175
	$\alpha$	0.0161	0.0018	0.0115	0.0028	0.9773	128,334	0.0237
	$R^2$	0.993	0.959	0.977	0.897	0.996	0.968	0.983
Avrami	$q_{av}$	0.7946	1.5415	3.2520	3.2978	6.6887	5.2039	15.310
	$K_{av}$	0.0021	0.0010	0.0013	0.0008	0.0044	0.0477	0.0013
	$n_{av}$	0.4305	0.9521	0.6513	0.9012	0.3170	0.1087	1.0456
	$R^2$	0.990	0.942	0.978	0.854	0.997	0.965	0.987
Boyd	$B_t$	0.0026	0.0027	0.0027	0.0022	0.0032	0.0024	0.0023
	$q_e$	0.6622	1.2846	2.7100	2.7481	5.5739	4.3366	14.0123
	intercept	−0.3542	−1.0256	−0.8317	−0.9445	−0.0862	0.5245	−0.7994
	$R^2$	0.690	0.647	0.648	0.510	0.845	0.550	0.612
LFD	$K_{lfd}$	0.0022	0.0023	0.0024	−0.9445	0.003	0.0021	0.0019
	$q_e$	0.6622	1.2846	2.7100	2.7481	5.5739	4.3366	14.0123
	$R^2$	0.927	0.839	0.943	0.763	0.876	0.388	0.974
Bangham	$k_B$	0.0739	0.0010	0.0010	0.0010	5.5739	0.0001	14.0123
	$n_B$	0.3763	0.6573	0.4331	0.6884	0.5000	0.0538	0.5000
	$R^2$	0.991	0.971	0.996	0.904	0.422	0.971	0.071
W-M	$k_{wb}$	0.0127	0.0349	0.0656	0.0652	0.0861	0.0359	0.4082
	C	0.1978	−0.1016	0.1913	−0.1393	2.6613	2.9926	−1.6810
	$R^2$	0.923	0.949	0.995	0.864	0.821	0.436	0.975

) reflect a mix of surface-controlled mechanisms and mass transfer limits. PSO equilibrium capacities (qₑ) have been observed to increase with initial MB concentration (e.g., from ~0.668 to ~8.73 mg/g), while decreasing rate constants ($k_2$) have been shown to suggest saturation of high-energy active sites. This is consistent with the findings of studies in which MB kinetics on phosphoric-acid-activated hydrochars fit PSO models indicative of strong surface interactions, including electrostatic attraction and π-π/staking interactions between dye molecules and functional groups introduced during activation [30]. Elovich and Avrami parameters show surface heterogeneity and multi-step adsorption. Diffusion analyses indicate that although intra-particle diffusion contributes, it is not the sole rate-limiting step. Initial uptake is followed by slower pore diffusion into the internal structure [30].

2.2.3. Isotherms Studies

The adsorption data show different mechanisms for MB across the three materials. For ABC-2S (Figure 9), the highest fits (R² ≈ 0.977, lowest RMSE ≈ 0.41) with Freundlich, Figure 9b, Redlich–Peterson, Figure 9c, and Koble–Corrigan, Figure 9f, models are indicative of adsorption on a heterogeneous surface with multilayer and variable energy sites. This finding aligns with recent research that complex isotherm models provide a more accurate description of MB uptake on highly porous and functionally heterogeneous activated carbons (e.g., mesopore-dominant ABCs with superior MB binding) [59]. Conversely, ABC-1S (Figure 10) demonstrates only moderate fits across all models (R² ≈ 0.75), indicating a diminished overall equilibrium affinity and less significant surface heterogeneity, aligning with research indicating that reduced activation development results in inferior adherence to classical isotherms for MB adsorption (e.g., lower R² and RMSE patterns in base-modified chars) [54].

For AHTC (Figure 11), consistently low R² (≤0.32) and elevated RMSE (>3.4) across models indicate that MB adsorption deviates from conventional Langmuir, Figure 11a, or Freundlich (Figure 11b), models, likely influenced by irregular site interactions and diffusion processes rather than standard monolayer or multilayer equilibrium. This phenomenon is similarly observed in AHTC systems, where surface functionality and pore structure exhibit significant variability, such as AHTC derived from coffee husk, demonstrating mixed kinetics and isotherm behaviour [56]. Collectively, data suggest that KOH-activated materials demonstrate enhanced, heterogeneous MB adsorption, while phosphoric-acid-AHTC exhibits poorly characterized equilibrium behaviour under the examined conditions.

The equilibrium adsorption was investigated using various isotherm models (

Table 8. Isotherm Model Fitting Results for MB Adsorption by Adsorbents.

Model	Parameter	ABC 1-S	ABC-2S	AHTC
Langmuir	$q_L$	22.915	17.789	9.6704
	$k_L$	0.1532	0.0256	0.1944
	$R^2$	0.752	0.969	0.318
	RMSE	2.192	0.481	3.461
Freundlich	$k_F$	3.295	0.7709	2.2113
	n	1.6236	1.499	2.3974
	$R^2$	0.756	0.977	0.281
	RMSE	2.175	0.412	3.555
Redlich Peterson	$k_R$	12.177	50	1.8797
	$a_R$	2.7281	64.07	0.1944
	g	0.4637	0.335	1
	$R^2$	0.757	0.977	0.318
	RMSE	2.174	0.412	3.461
Sips	$q_{max}$	50	50	8.6869
	$K_S$	0.0691	0.0139	0.1755
	n	0.7365	0.7471	1.2493
	$R^2$	0.756	0.976	0.321
	RMSE	2.176	0.419	3.453
Temkin	$A_T$	2.1657	0.9722	1.8360
	$b_T$	591.004	1255.98	1156.35
	$R^2$	0.716	0.803	0.310
	RMSE	2.347	1.205	3.482
Toth	$q_{max}$	50	50	9.6703
	$k_T$	0.1061	0.0142	0.1944
	t	0.5239	0.4897	1
	$R^2$	0.755	0.974	0.318
	RMSE	2.180	0.442	3.461
Koble Corrigan	A	3.3253	0.7709	1.5250
	B	0.0119	0.001	0.1755
	n	0.634	0.6671	1.2492
	$R^2$	0.756	0.977	0.321
	RMSE	2.175	0.412	3.453
MacMillan-Teller	Qs	7.426	4.9591	7.7361
	k	0.3066	0.3695	0.3629
	Cs	11.460	44.15	37.8935
	$R^2$	0.731	0.850	0.165
	RMSE	2.283	1.054	3.830

). The Langmuir model revealed that ABC-1S exhibited the highest monolayer adsorption capacity (qₗ = 22.915 mg/g), followed by ABC-2S (17.789 mg/g) and AHTC (9.6704 mg/g). This indicates that KOH-ABCs possess a greater density of accessible adsorption sites than phosphoric-acid- AHTC. This enhancement is commonly ascribed to improved pore development and surface functionality resulting from alkaline activation, as has been reported for ABCs used in dye adsorption applications [21].

Despite exhibiting a lower adsorption capacity, AHTC demonstrated the highest Langmuir affinity constant (kₗ = 0.1944 L/mg), indicating stronger adsorbate–adsorbent interactions. This behaviour is indicative of H₃PO₄ AHTCs, which characteristically contain a lower number of adsorption sites, albeit those with higher energetic favourability, a consequence of the presence of acidic oxygen-containing functional groups. A similar trend in adsorption has been observed for AHTC derived from biomass waste [56].

Favourable adsorption was confirmed for all materials by the isotherm parameters. Surface properties were indicated as heterogeneous by the range of n values (1.499–2.397). ABC-1S had a higher $k_F$ value (3.295), showing superior performance. Freundlich behaviour is often observed in ABCs and AHTCs made from waste [60].

Three-parameter models like Redlich–Peterson and Sips are applicable when dealing with complex adsorption behaviour involving both homogeneous and heterogeneous mechanisms. The Redlich–Peterson exponent (g < 1) for ABC-1S and ABC-2S indicates deviation from ideal monolayer adsorption, whereas the Henry constant (g ≈ 1) exhibited Langmuir-type behaviour. The present findings are consistent with those of recent studies, in which hybrid models were required to accurately describe the process of dye adsorption onto chemically ABCs and AHTCs [61,62].

2.2.4. Influence of Wastewater Matrix Complexity

In real wastewater systems, the adsorption behaviour of methylene blue (MB) is strongly influenced by the intrinsic complexity of the aqueous matrix. Industrial effluents rarely contain a single pollutant; instead, they incorporate a diverse combination of organic and inorganic compounds whose relative abundance depends on both the characteristics of the local water supply—such as pH, ionic strength, hardness, salinity, and calcareous origin—and the specific industrial processes involved. These coexisting substances can compete with MB for adsorption sites, interfere with electrostatic interactions, alter pore accessibility, or form surface coatings that reduce the availability of active sites on biochar and hydrochar. Consequently, the removal efficiency observed under ideal single-solute laboratory conditions is often reduced in real matrices. This phenomenon has been widely documented: for example, Li et al. reported that the coexistence of multiple organic and inorganic substances in solution leads to a noticeable decline in dye removal due to competition for adsorption sites and interference from the surrounding medium [63], and similar inhibiting effects have been observed for MB adsorption onto carbon-based adsorbents exposed to complex water compositions [64]. These findings highlight that actual wastewater composition—starting from the baseline characteristics of the water itself and extending to the full suite of process-derived contaminants—has a substantial impact on adsorption performance. Therefore, although the present study elucidates the intrinsic adsorption mechanisms and capacities of the prepared adsorbents under controlled conditions, their behaviour in real industrial effluents may differ. Future work should evaluate these materials in multicomponent or real wastewater systems to quantitatively assess matrix effects and confirm their practical robustness.

2.3. Potential for Recovery or Recycling of Adsorbents

Maintaining an adsorbent’s suitability for prolonged application depends largely on its capacity to be regenerated once saturation is reached. Reusing the material across several adsorption–desorption cycles not only reduces the amount of solid waste produced but also allows for the retrieval of the previously retained dye. For the regeneration trials, (

Table 9. Performance of adsorbents in three adsorption-desorption cycles (after 24 h).

	Fresh ABC			1st Cycle			2nd Cycle			3rd Cycle
	1S	2S	AHTC	1S	2S	AHTC	1S	2S	AHTC	1S	2S	AHTC
MBremoval (%)	99.8 ± 0.1	99.3 ± 0.2	99.8 ± 0.1	99.8 ± 0.1	99.3 ± 0.1	99.6 ± 0.1	99.7 ± 0.1	99.2 ± 0.2	99.7 ± 0.2	99.7 ± 0.3	99.3 ± 0.1	99.6 ± 0.2
Qe	5.81 ± 0.03	5.78 ± 0.02	5.80 ± 0.01	5.81 ± 0.03	5.78 ± 0.02	5.76 ± 0.01	5.80 ± 0.02	5.77 ± 0.03	5.74 ± 0.01	5.80 ± 0.02	5.78 ± 0.03	5.74 ± 0.01

), the MB solution was prepared at a concentration of 35 mg/L, consistent with the value previously identified as representative of typical industrial wastewater. Acetone was chosen as the desorption solvent, and the spent adsorbents were first isolated by filtration and dried at 60 °C for 24 h prior to the recovery procedure [17]. Afterwards, the materials were transferred to a flask containing acetone, continuously stirred for 4 h, filtered again, rinsed with distilled water, and dried once more at 60 °C for 24 h.

MB removal remained almost 100% consistent across all regeneration cycles, clearly demonstrating the strong reusability of the adsorbents and their capacity to withstand repeated adsorption–desorption steps without structural degradation or loss of performance. The desorbed MB was efficiently recovered through a combined distillation and evaporation process, while both the recovered acetone and the dye exhibited high purity, supporting their potential for recycling and consequently reducing chemical consumption and waste generation. Although the reusability assessment was limited to three cycles, this number is widely adopted in laboratory-scale studies as a practical benchmark for evaluating preliminary adsorbent stability due to the operational and economic costs associated with each regeneration step, including solvent usage, energy demand for drying, and additional processing time. Beyond a certain number of cycles, the marginal scientific benefit of additional testing diminishes relative to these costs, especially at the proof-of-concept stage. Moreover, previous works have shown that three consecutive cycles are sufficient to confirm the short-term robustness of carbonaceous sorbents. For example, porous biochar obtained via KOH activation from bamboo biochar maintained effective MB removal over three cycles, thereby supporting the conclusion that a three-cycle assessment provides a reliable indication of material stability under controlled laboratory conditions [21].

3. Materials and Methods

3.1. Synthesis and Surface Activation of Carbonaceous Adsorbents

In this study, AP was processed as follows: biomass was washed, dried, and homogenized to 1–2 mm. For the 1-S route, AP was impregnated with KOH with a KOH-to-biomass ratio of 1:3 (w/w) and heated in a tube furnace at 20 K/min to 900 °C for 2 h, with a 40 mL/min nitrogen flow. For the 2-S activation, pyrolysis occurred in a tube furnace at 10 °C/min to 900 °C for 1 h under a 40 mL/min nitrogen flow. Afterwards, for the activation step, the biochar sample was impregnated with KOH at a 1:1 (w/w) ratio. Post-activation, all samples were washed using the same procedure as described elsewhere [17].

In parallel, H₃PO₄-assisted hydro-thermal carbonization was performed by mixing biomass with a 25% H₃PO₄ solution in a Teflon-lined hydrothermal reactor. Hydrothermal carbonization was performed at 200 °C for 24 h in an oven. The resulting mixture (HTC and resulting liquid phase) was thermally treated, for activation, in a tube furnace at 5 °C/min to 450 °C for 2 h under 40 mL/min nitrogen flow.

Due to the high temperature thermochemical conversion applied during their production, both biochar and hydrochar exhibit intrinsically high chemical stability and negligible leaching potential, as volatile and labile compounds are removed during carbonization, yielding structurally inert carbonaceous solids.

In all activation procedures, the quantities of chemical activating agents were selected based on optimized ratios to ensure effective pore development while minimizing excess reagent use. For the KOH-activated materials, the post-activation treatment incorporated a controlled neutralisation step using nitric acid, which fully converted residual alkaline species into potassium nitrate (KNO₃). This compound is non-toxic and widely used as a fertiliser, offering the potential for recovery and valorisation rather than disposal. Following neutralisation, the materials underwent an optimized three-step washing process until the filtrate reached neutral pH, ensuring the complete removal of any remaining activating agent. Similarly, in the case of H₃PO₄ activation, the acid was employed in carefully controlled quantities, and the resulting hydrochar was repeatedly washed with deionized water until neutrality was achieved, effectively eliminating free phosphoric acid from the final product. Through these protocols, the presence of environmentally harmful residues was mitigated, and the activation process was aligned with principles of safety and sustainability, demonstrating that the preparation of the adsorbents does not introduce residual chemical risks and, in the case of KOH, even enables the potential recovery of valuable by-products [65].

3.2. Characterization of Biochar and Hydrochar

Proximate and ultimate analyses of the raw biomass (AP) and the generated substrates (ABC-1S, ABC-2S, HTC) were conducted using an automated elemental analyser (TruSpec Micro, LECO (Saint Joseph, MI, USA)). This technique facilitates the precise determination of carbon (C), hydrogen (H), nitrogen (N), sulfur (S), and oxygen (O) contents in solid or liquid micro-samples, typically requiring approximately 2 mg of sample. Surface functional groups were characterized by ATR-FTIR (Perkin Elmer (Waltham, MA, USA) Spectrum Two, 4000–600 cm⁻¹, 4 cm⁻¹ resolution, 20 scans) using a diamond ATR accessory. The morphology and microstructure of the samples were examined by SEM (JEOL (Tokyo, Japan) JSM-7000F) [66]. Textural properties, including specific surface area, micropore volume, and average pore width, were determined from nitrogen adsorption/desorption isotherms at −196 °C (Micromeritics ASAP 2010, Norcross, GA, USA). The NLDFT method was applied for pore size distribution calculations. Additionally, porosity and surface characteristics were analysed using the Dubinin–Radushkevich (D–R) method to evaluate micropore volume, adsorption potential, and characteristic adsorption energy, providing insights into the adsorbent performance.

3.3. Batch Adsorption Experiments

Batch adsorption experiments of MB were performed in a quartz vessel with a 10.0 mm optical path at the natural pH of the dye solution (pH = 6.3).

An adsorbent dosage of 6 g/L was added to MB solutions with initial concentrations ranging from 5 to 100 mg MB/L. The suspensions were stirred for 10 s at the beginning of each experiment to guarantee adequate adsorbent-solution interaction. All tests were performed at room temperature, conditions that allowed the sorbent particles to maintain a low settling velocity, remaining predominantly suspended in the solution throughout the 24-h adsorption experiments due to their diminutive and slender particle morphology. The adsorption process was monitored continuously for 24 h using a UV–Vis spectrophotometer (JASCOV (Tokyo, Japan) JASCOV-730) by recording the absorbance at 665 nm. The concentration of MB remaining in solution at each time point was calculated from the measured absorbance using the Beer–Lambert law [67].

The adsorption capacity at a specific time and the removal efficiency were calculated using the following equations [68]. Meanwhile, the quantity of MB adsorbed at equilibrium Qe was extracted after the adsorption experiment reached the equilibrium, and time $t_e$ where there is no change in the concentration C_t:

$$Q_t={\displaystyle \frac{\left(C_0-C_t\right)V}{m}}$$

(1)

$$R_t=100\ast {\displaystyle \frac{\left(C_0-C_t\right)}{C_0}}$$

(2)

where $R_t$ was the removal rate (%), and $C_0$, $C_t$ was the initial and t-time concentration of MB (mg MB/L). V was the volume of the MB solution (mL), and m was the mass of the adsorbents (g).

3.4. Adsorption Modelling

3.4.1. Response Surface Methodology (RSM) Framework

Response surface methodology (RSM) integrates mathematical and statistical tools to optimize processes by analysing interactions among factors [69]. It investigates experimental input parameters’ influence on response parameters and evaluates issues where multiple factors affect the solution’s outcome [70].

In this research, a quadratic Central Composite Design (CCD) was employed using Python code (version 3.13) to investigate the interactions between contributing variables on MB adsorption, considering two independent variables: initial MB concentration C₀, varied across seven levels, and contact time t. The CCD included factorial runs at the extreme coded levels $\left(-1,+1\right)$, center runs replicated at the mid-levels $\left(\mathrm{0,0}\right)$to estimate pure error, and axial (star) runs positioned at $\left(-\alpha ,+\alpha \right)$ to ensure model rotatability and capture curvature within the design space [71].

The mathematical modelling process entails identifying a function such that:

Y = f (x₁, x₂, x₃, …, xₙ)

(3)

where: Y represents the response variable, and x₁, x₂, x₃, …, xₙ denote the factors [72].

The response variable (adsorption rate) was modelled as a function of the independent factors using a second-order polynomial. The resulting quadratic model, identified as the optimal predictor by the experimental design, was employed to correlate the variables with the MB removal efficiency Y, given by Equation (4) [73].

$$Y={\beta }_0+\sum _{i=1}^2{\beta }_i{X}_i+\sum _2^2{\beta }_{ii}{X_i}^2+\sum _{i<j}^2{\beta }_{ij}{X}_i{X}_j$$

(4)

where $X_i$ is initial concentration C₀, $X_j$ is contact time t and the coefficients ${\beta }_0$, ${\beta }_i,{ \beta }_{ii}$, and ${\beta }_{ij}$correspond respectively to the intercept, linear terms, quadratic terms, and interaction terms, It is important to note that these coefficients are not initially known and are instead determined from experimental results. Accordingly, the explicit form of the quadratic model for the two factors, $C_0$ and $t$, is given by:

$$Y={\beta }_0+{\beta }_1{C}_0+{\beta }_{2}t+{\beta }_{12}{C}_{0}t{+\beta }_{11}{C}_0^2+{\beta }_{22}{t}_0^2$$

(5)

3.4.2. Adsorption Kinetics

The adsorption system’s kinetics were examined by applying non-linear fitting of several alternative kinetic models in

Table 10. Nonlinear Kinetic Models and their Equations for MB adsorption.

Model	Equation	Parameter	Mechanism	Reference for the Equation
Pseudo first order	$q_t=q_e\left(1-e^{-K_{1}t}\right)$	$q_t$: adsorption capacity at time t (mg/g) $q_e$: adsorption capacity at equilibrium (mg/g) $k_1$: pseudo–first–order rate constant (min−1) $t$ = contact time (min)	Adsorption is known to occur through a physisorption mechanism, whereby the rate of occupation of adsorption sites is directly proportional to the number of unoccupied sites [74].	[75]
Pseudo Second Order	$q_t={\displaystyle \frac{q_e^2{k}_{2}t}{1+q_e{k}_{2}t}}$	$q_t$: adsorption capacity at time t (mg/g) $q_e$: adsorption capacity at equilibrium (mg/g) $k_2$: pseudo second order rate constant (min−1)	Each adsorption event occupies one site, consistent with monolayer formation on a finite set of homogeneous sites. Chemisorption is the rate-determining step [21].	[75]
Elovich	$q_t={\displaystyle \frac{1}{\beta }}\ln \left(1+\alpha \beta t\right)$	$\beta$: the quantity of sites available for absorption $\alpha :$ initial adsorption rate (mg/g min)	Adsorption occurs on a highly heterogeneous surface, where the activation energy decreases exponentially with increasing surface coverage [76].	[53]
Avrami	$q_t=q_{av}\left(1-e^{{\left(K_{av}t\right)}^{n_{av}}}\right)$	$q_{av}:$Avrami theoretical value of the amount of the adsorption (mg/g) $K_{av}$: Avrami constant rate $n_{av}:$ Avrami order model	The reaction is located on the surface sites of the solid that are active [77].	[77]
Boyd	$B_t=-0.4977-\mathrm{l}\mathrm{n}(1-{\displaystyle \frac{q_t}{q_e}})$	$B_t:$Boyd constant $q_t$: adsorption capacity at time t (mg/g)	Provides insight into how adsorbates stick. The model can be used to identify the slow step in the process, which is known as the rate-determining step in the adsorbent [78].	[78]
Bangham	$q_t=q_B(1-e^{-k_B{t}^{n_B}}$)	$k_B:$Rate constant of adsorption process $n_B$: Constant	Investigates the phase of slow diffusion in the pores of the adsorption process [77].	[79]
Liquid film diffusion	$L_n\left(1-{\displaystyle \frac{q_t}{q_e}}\right)=-K_{Lfd}$t	$q_t$: adsorption capacity at time t (mg/g) $K_{Lfd}:$Liquid film Diffusion constant	Adsorption involves the movement of dye ions from the bulk solution to the liquid film surface, influenced by diffusion impediments and determined by external and internal diffusion factors [78].	[78]
Weber-Morris	$q_t=k_{wb}{t}^{0.5}+C$	$k_{wb}$: the intra-particle diffusion rate constant (mg/g min−1/2) C: intercept	Intraparticle diffusion is the internal pore-diffusion phase that frequently dictates adsorption kinetics [34].	[40]

using Python. The models applied to the experimental data were evaluated using the coefficient of determination (R²).

3.4.3. MB Adsorption Isotherms

Adsorption isotherms quantify the equilibrium distribution of adsorbate molecules between the solid surface and the solution [74], offering critical insight into adsorption capacity, surface characteristics, and interaction mechanisms. Although linearized isotherm equations remain common in the literature, their use can introduce substantial errors due to linearization and subjective data selection, leading to inaccurate estimates of adsorption constants and capacities. These limitations are exacerbated for heterogeneous sorbents exhibiting multiple adsorption mechanisms [80]. Consequently, in the present work, nonlinear regression for several isotherm models, which offer a more reliable approach for determining adsorption capacities and affinities, was employed, as summarized in the accompanying table (

Table 11. Nonlinear Isotherm Models and their Equations for MB adsorption.

Model	Equation	Parameter	Mechanism	Reference for the Equation
Langmuir	$q_e={\displaystyle \frac{q_L{K}_L{C}_e}{1+K_L{C}_e}}$	$q_e$: adsorption capacity at equilibrium (mg/g) $q_L$: Maximum monolayer coverage capacities (mg/g) $k_L$: Langmuir isotherm constant (L/mg) $C_e:$ Equilibrium concentration (mg/L)	There is a fixed number of energetically identical adsorption sites, reversible monolayer adsorption with no further uptake once a site is filled, and no interactions between adsorbed species [80].	[80]
Freundlich	$q_e=K_F{\left(C_e\right)}^{{\displaystyle \frac{1}{n}}}$	$q_e$: adsorption capacity at equilibrium (mg/g) $K_F$: Freundlich isotherm constant (mg/g) (L/g) n: Adsorption intensity	Site density decreases exponentially with increasing adsorption heat due to adsorption occurring on sites with varying energy but uniform entropy [77].	[77]
Redlich Peterson	$q_e={\displaystyle \frac{K_R{C}_e}{1+a_R({C_e)}^g}}$	$a_R:$Redlich–Peterson isotherm constant (L/mg) $C_e:$ Equilibrium concentration (mg/L) g: Redlich–Peterson isotherm exponent $K_R:$ Redlich–Peterson isotherm constant	describes adsorption equilibrium across a wide concentration range in both homogeneous and heterogeneous systems [77].	[77]
Sips	$q_e={\displaystyle \frac{q_{max}{K}_s{\left(C_e\right)}^n}{1+K_s{\left(C_e\right)}^n}}$	$q_{max}:$maximum adsorption capacity (mg/g) $C_e:$ Equilibrium concentration (mg/L) $K_S$: Sips isotherm model constant (L/g) n: Sips isotherm model exponent	A hybrid of Langmuir and Freundlich isotherms, describes adsorption on heterogeneous surfaces, reducing limitations at high concentrations [77].	[81]
Temkin	$q_e={\displaystyle \frac{RT}{b_T}}\mathrm{l}\mathrm{n}\left(A_T{C}_e\right)$	$A_T:$ Temkin isotherm equilibrium binding constant $b_T:$Temkin isotherm constant $C_e:$ Equilibrium concentration (mg/L) R: universal gas constant (8.314 J mol−1 K−1) T: temperature (K)	As the coverage of the adsorbent surface increases, with adsorption characterized by a uniform distribution of binding energies, the heat of adsorption for all molecules drops linearly to the highest bond energy [77].	[77]
Toth	$q_e={\displaystyle \frac{q_{max}{K}_T{C}_e}{{{(1+{(K}_T{C}_e)}^t)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$t$}\right.}}}$	$q_{max}$: Toth maximum adsorption capacity (mg/g) $C_e:$ Equilibrium concentration (mg/L) $K_T$: Toth isotherm constant (mg/g) t: Toth model exponent	Derived from the Langmuir framework, better fits experimental data by accounting for lateral interactions, surface heterogeneity, and other non-ideal behaviours [77].	[81,82]
Koble Corrigan	$q_e={\displaystyle \frac{A{\left(C_e\right)}^n}{1+B{\left(C_e\right)}^n}}$	A: Koble–Corrigan isotherm constant (Lnmg1-n g−1) B: Koble–Corrigan isotherm constant (L/mg) $n:$ Adsorption intensity $C_e:$ Equilibrium concentration (mg/L)	A three-parameter model integrating Langmuir and Freundlich isotherms is applied to heterogeneous adsorption surfaces [77].	[77]
MacMillan-Teller	$q_e=q_s{\left({\displaystyle \frac{k}{\mathrm{l}\mathrm{n}\left(\frac{C_s}{C_e}\right)}}\right)}^{{\displaystyle \frac{1}{3}}}$	K: MacMillan–Teller isotherm constant $q_s$: theoretical isotherm saturation capacity (mg/g) $C_e:$ Equilibrium concentration (mg/L) $C_s:$Adsorbate monolayer saturation concentration (mg/L)	The isothermal model has been enhanced by incorporating the effects of surface tension into the Brunauer-Emmett-Teller isotherm [77].	[77]

), and their corresponding parameters were rigorously evaluated using Python, consistent with the methodology applied in the kinetic analyses.

4. Conclusions

This study demonstrates the successful conversion of AP into high-performance ABCs through three activation routes: 1-S and 2-S KOH activation at high temperature, and a low-temperature H₃PO₄-AHTC. Beyond the sustainable valorisation of agricultural waste, this work introduces a novel computational approach, employing Python-based nonlinear fitting to evaluate kinetic and isotherm models. This method avoids the distortions inherent to linearised equations and enables more accurate interpretation of complex adsorption behaviour; an approach rarely applied in similar studies.

All prepared materials exhibited strong adsorption performance, removing more than 70% of (MB) within the first 8 h at 35 mg/L, using a sorbent dose of 6 g/L, consistent with that applied in the kinetics and equilibrium studies. Across the full concentration range, the KOH-ABCs (ABC-1S and ABC-2S) consistently outperformed the H₃PO₄-AHTC, confirming that the activation process effectively enhances pore development and increases the capacity to adsorb higher MB concentrations.

The nonlinear modelling approach revealed that all three adsorbents successfully fitted multiple kinetic and isotherm models, demonstrating their versatile adsorption behaviour. ABC-1S and ABC-2S showed excellent agreement with Avrami and pseudo-second-order kinetics (R² = 0.996–1.000), indicating chemisorption-dominated, multi-step uptake. AHTC, in contrast, aligned strongly with Elovich and diffusion-controlled models (R² ≈ 0.993–0.996), reflecting heterogeneous surface interactions. Equilibrium analysis further confirmed these trends, with ABC-1S achieving the highest Langmuir monolayer capacity (qₗ = 22.9 mg/g), while AHTC exhibited the strongest Langmuir affinity constant (kₗ = 0.194 L/mg), indicating fewer but more energetically favourable sites. A key practical outcome of this work is the excellent regeneration performance of all adsorbents, which retained nearly 100% removal efficiency over multiple cycles when regenerated with a 35 mg/L MB solution. This confirms their robustness and suitability for real-world wastewater treatment applications.