Diclofenac sodium removal by powdered activated carbon of coconut endocarp: process optimization, kinetics, and isotherms

Pharmaceuticals are chemical compounds used in the treatment of diseases, promoting the well-being of living organisms. With the increase in life expectancy and changes in demographic structures (Tannoury & Attieh 2017), coupled with the growing number of pets (Kaczala & Blum 2016), there has been an increase in the use of medications. Both the production and consumption of these drugs are responsible for these agents.

Many pharmaceutical compounds persist in the environment (Rogowska et al. 2020), and can bioaccumulate, and their subsequent metabolic products also have the potential to generate adverse effects (Xue et al. 2021). Additionally, in both animals and humans, the ability to absorb these substances is generally limited (Bamfo et al. 2021). For example, about 80% of the administered dose of ibuprofen is absorbed by humans, while in animals, absorption ranges from 60 to 86% (AHFS 2021). In contrast, the absorption of diclofenac in humans is 60%, and in animals, it ranges from 30 to 60% (Stierlin et al. 1979), with the remainder being excreted. As a result, these compounds can reach aquatic and terrestrial ecosystems, affecting non-target organisms and potentially leading to ecological imbalances. Proper management and treatment of pharmaceutical waste are crucial to mitigate their environmental impact and protect public health.

The presence of pharmaceuticals in the environment was initially identified in the 1970s and persists in ecosystems to this day, raising significant concerns, especially regarding the quality of public water supplies (Montagner et al. 2017).

Non-steroidal anti-inflammatory drugs (NSAIDs), antiepileptics, lipid regulators, and antibiotics are commonly detected pharmaceutical substances in aquatic environments. Among these, NSAIDs, analgesics, and antibiotics are particularly prevalent in domestic effluents (Ortúzar et al. 2022). A review study by Beek et al. (2016) compiled data from 1,166 academic publications, revealing the presence of 631 different drugs in environmental matrices across 71 countries. Diclofenac sodium (DS) was the most frequently detected substance, found in 50 countries with concentrations exceeding 0.1 μg·L⁻¹, a level deemed to have potential ecotoxicological risk according to European legislation recommendations (Beek et al. 2016).

This particular compound exhibits the highest acute toxicity among NSAIDs. Furthermore, chronic exposure to this drug has been associated with hemodynamic alterations and the development of thyroid tumors in humans (Álvarez et al. 2015; Bhadra et al. 2016). Given the threat posed by this substance, measures are being adopted globally. Recently, in 2022, DS was added to the list of priority substances under the Water Framework Directive by the European Environment Agency (EEA) due to its significant impacts on biodiversity, necessitating the reduction of its presence in the environment (European Commission 2022).

In the context of the issue addressed, it is important to note that water treatment plants (WTPs) and wastewater treatment plants (WWTPs) worldwide were not originally designed for pharmaceutical removal. Therefore, the exploration of additional technologies that can effectively eliminate these substances is pertinent.

Various technologies are being studied to remove such contaminants, including catalytic ozonation, photocatalytic oxidation, ultrafiltration, nanofiltration, adsorption, among others (Westerhoff et al. 2005; Yoon et al. 2006; Sotelo et al. 2014; Rakić et al. 2015; Martínez-Huitle et al. 2018; Derco et al. 2021). Among them, adsorption emerges as a notable technology due to its simplicity in both project conception and operation, its low cost, the absence of risk byproduct generation, and the adsorbent's regeneration viability (Quesada et al. 2019). In addition to its applicability in WTP and WWTP, adsorption can be applied for in situ remediation, such as point source pollution from pharmaceuticals.

Among several materials of vegetal and mineral origin that can be employed in adsorption, coconut endocarp is considered an agricultural waste and constitutes about 15% of the fruit produced by Cocos nucifera L. (Li et al. 2021). Moreover, global coconut production in 2019 reached 62.9 million tons across 11.8 million hectares of cultivation, with 74.1% of production concentrated in Indonesia, the Philippines, and India (Brainer 2021). Therefore, the abundant availability of this biomass for use as a precursor material makes activated carbon from coconut endocarp a low-cost and viable alternative for large-scale use in removal of EC by adsorption (Alves et al. 2021).

However, before that, it is necessary to understand their maximum adsorptive capacity, achieved only under saturation conditions (with high EC concentrations in the range of mg/L), as well as the adsorption mechanisms involved in the process and their limitations. This knowledge can be applied in mathematical modeling of the adsorption process, predicting the lifetime of treatment cells, verifying efficiency repeatability, and understanding limitations related to other compounds with similar properties.

In this context, this study aimed to analyze the adsorption process of sodium diclofenac from an aqueous medium, using powdered activated carbon (PAC) of coconut endocarp as the adsorbent material. For this purpose, batch adsorption tests were conducted, and the optimization, kinetics, and adsorption isotherms were evaluated.

The experiments were conducted following a methodological approach based on the central composite design (CCD). This empirical method employs an interactive model that seeks to evaluate the isolated effects of each variable, aiming to optimize processes.

For the present situation, the effects of four factors (initial adsorbate concentration, adsorbent mass, contact time, and pH) on adsorption capacity were evaluated. The intervals for each of these factors and the randomized runs obtained from this statistical design are presented in Table 1.

The significance of the developed model and each term was evaluated by analysis of variance (ANOVA) based on the probability value (p-value) and the Fisher test value (F-value) at a confidence level of p < 0.05. The accuracy and predictability of the model were also measured using the lack-of-fit criterion, coefficient of correlation (R²), adjusted R², predicted R², adequate precision, and residual normalization.

The range of DS and PAC concentrations from coconut endocarp used was chosen to reach the saturation of PAC pores and surface by the pharmaceuticals and to determine the maximum adsorption capacity, as well as to understand the influence of their variation under different conditions. The pH ranges selected are those most commonly found in surface water, groundwater, and wastewater in the pharmaceutical industry (CONAMA 2011; Kumari & Tripathi 2019). The contact time was defined based on the equilibrium time (Poorsharbaf Ghavi et al. 2020).

The PAC of coconut endocarp (CAS 7440-44-0) was obtained from Labsynth, Brazil, with a particle size smaller than 150 μm.

The morphological and microstructural properties of the PAC from the coconut endocarp (Labsynth, Brazil) were obtained by scanning electron microscopy with field emission gun (SEM-FEG), energy-dispersive spectrometer (EDS), and high-resolution transmission electron microscopy (HRTEM) on a FEI TECNAI G2 F20 microscope operating at 200 kV. The functional groups present in the PAC were analyzed using Fourier-transform infrared spectroscopy on an IRTracer-100 Shimadzu in the region of 400 to 4,000 cm⁻¹ operating in transmittance mode with an attenuated total reflectance (ATR) detector. X-ray diffraction (XRD) profiles were obtained under CuKα radiation (λ = 0.15418 nm) at 40 kV and 30 mA in the range of 5° ≤ 2θ ≤ 80 with a step size of 0.02° and a speed of 1 °C · min⁻¹. The combustion profile of the material was obtained by thermogravimetric analysis (TGA/DTG) in a nitrogen atmosphere from room temperature to 1,000 °C with a heating rate of 10 °C min⁻¹ and a flow rate of 150 mL · min⁻¹ on a Shimadzu TGA-51/51H. The material's transitions under heat influence were analyzed by differential scanning calorimetry (DSC) with heating from 25 to 400 °C, cooling from 400 to 30 °C, and then heating from 30 to 400 °C at a rate of 10 °C min⁻¹ in a nitrogen atmosphere with a flow rate of 20 mL · min⁻¹ on a PerkinElmer. The point of zero charge (PZC) was obtained by potentiometry at 11 points with an adsorbent-solution ratio of 1 mg:1 mL, where fractions of the adsorbent were placed in flasks containing an aqueous solution at room temperature under different pH conditions (1–6, 8–12) and a contact time of 24 h. The surface area was evaluated by the Brunauer–Emmett–Teller (BET).

The adsorption tests were carried out in batch and developed following the protocol below: (a) preparation of a 500 mg · L⁻¹ stock solution of DS (Farmafórmula, Brazil) by dissolving 0.500 g of the substance in 1 L of deionized water; (b) dilution of the DS stock solution to obtain different solution concentrations (50, 150, 250, 350, and 450 mg · L⁻¹); (c) adjustment of the pH of the solutions by dropwise addition of hydrochloric acid (HCl 37%, Labsynth, Brazil) or sodium hydroxide (NaOH P.A., ISOFAR, Brazil) in a solution with deionized water at 0.025 N; (d) adsorption tests in Erlenmeyer flasks containing 20 mL of solution under specific conditions of adsorbate concentration, adsorbent mass, pH, and contact time (see Table 1); (e) performance of the tests at room temperature on a shaker table at 200 rpm; (f) filtration of the samples after the end of each test using a qualitative filter with a white band of 45 μm (Qualy, Brazil); (g) measurement of the residual DS concentration by UV spectrophotometry at a wavelength of 274 nm, with readings performed in triplicate.

The data obtained from the experiments were adjusted to adsorption kinetics and isotherm models using a non-linear regression method.

To describe the temporal behavior of the adsorption process, three kinetic models were employed, namely: pseudo-first-order (PFO), pseudo-second-order (PSO), and intraparticle diffusion (IPD) models.

To estimate the maximum adsorption capacity, the Langmuir and Freundlich models were applied.

The models obtained will be evaluated using the coefficient of determination (R²) and Chi-squared test (χ²).

The PAC exhibited peaks at 2θ = 25.82° corresponding to carbon (C), 31.98° to silica (Si), and 39.78° to potassium (K) (Raju & Rao 2017; Sujiono et al. 2022). The Si and K can come from the soil and from macronutrients in the coconut endocarp (Sujiono et al. 2022). In addition to the crystalline peaks, the baseline contains broad bands with diffuse scattering across most of the range, indicating the presence of an amorphous phase. This is the characteristic of activated carbons, which gain surface area and porosity due to the activation/carbonization process, features associated with a higher adsorption potential.

The spectrum absorbed by PAC shows bands between 3,550 and 3,200 cm⁻¹, corresponding to the hydroxyl functional group, two wavenumbers in the range of 3,000 and 2,840 cm⁻¹ related to the sp³ hybridization of the C–H bond. It was also observed that PAC has a hydroxyl group (O–H) at the wavenumber of 1,414 cm⁻¹, epoxy groups (C–O) at 1,018 cm⁻¹, and aromatic rings at 2,013, 1,616, and 1,454 cm⁻¹ (Bakti et al. 2018).

Elementally, the microscopy primarily shows the presence of plates (overlapping), flakes (see Figure 3(a)), and laminated fragments (Andrés et al. 2023). These characteristics resemble the organic form of coconut endocarp (basically a shell), as observed by Naswir & Lestari (2014) and Khuluk et al. (2019) who used this material as a precursor.

The coconut endocarp used as a precursor for activated carbon is mainly composed of cellulose, hemicellulose, and lignin, which are considered basic constituents of plants (Andrés et al. 2023). The chemical elements detected by EDS are listed in Table 2.

These materials are rich in silicon, oxygen, and carbon, which explain the high prevalence of these elements in the analysis. Additionally, the activation process by pyrolysis oxidizes the structure, incorporating more oxygen. Potassium, calcium, and magnesium minerals are commonly found in analyses of fruit constituent elements, mainly originating from the soil (a nutrient source) where they are cultivated (Andrés et al. 2023).

The PAC exhibited water loss due to evaporation up to 100 °C, corresponding to 10.96% of its total weight. Additionally, there was a subtle loss of functional groups up to around 400 °C. Subsequently, there was a gradual mass loss until reaching 1,000 °C, attributed to the degradation of the graphitic structure. The residual mass of PAC was 93.70%.

These thermal events are confirmed by DTG, which showed a peak in water removal between 0 and 100 °C and in the combustion of functional groups near 400 °C.

In the first heating cycle, the DSC curve exhibits an exothermic trend with a peak between 25 and 100 °C, followed by degradation after 250 °C, characterizing the CAP as an amorphous material. In the second heating cycle, a characteristic vitrification movement is observed at a temperature of 350 °C, possibly attributed to the expansion/formation of silicon dioxide (SiO₂) (Feyzi et al. 2015).

The CAP remained ionized for pH > 5 and <7.34, with a positively charged surface for pH > 7.34 and <9. It is noteworthy that DS remained ionized throughout the experiment, as its pKa is 4.15 and the pH range tested was from 5 to 9 (Drugbank 2024). In theory, there was an electrostatic attraction between the adsorbent and the adsorbate in solution for pH > 5 and <7.34, and repulsion for pH > 7.34 and <9.

The BET method allowed estimating the surface area of PAC at 642.348 m² · g⁻¹ (Figure 7) with a correlation coefficient of 0.9976. The PAC derived from coconut endocarp, obtained by Freitas et al. (2019), exhibited a surface area of 560 m²/g for carbon with a particle size smaller than 300 μm. This suggests that the larger surface area can be attributed to the smaller particle size of the carbon used in this study. Additionally, the adsorption–desorption isotherm was compared with IUPAC (1984) standards and classified as Type IV, with hysteresis (overlap of adsorption–desorption curves) of type H4. The Type IV isotherm is related to mesoporous materials, indicating the complete formation of a monolayer at approximately 200 cm³ · g⁻¹ of adsorbed N₂ and 0.15 P/P₀ (Figure 7). After this point, a multilayer adsorption begins, characterized by a constant slope. Hysteresis of type H4 is associated with the presence of narrow pores.

The experimentally obtained data (q_real), the responses predicted by the model (q_predicted), and their respective residuals are shown in Table 3.

The adequacy of the model to the actual data was verified using the lack-of-fit test, resulting in a Fisher's test value (F-value) of 33.17 and a significance of p-value = 0.0002, indicating the presence of outliers and unbalanced non-linearity in the real values (Figure 8; Table 4). The difference between the real and predicted values for the response q mainly occurred in runs 8 and 11, respectively, with lower (0.2 g · L⁻¹) and higher (5.0 g · L⁻¹) adsorbent mass administration, especially in run 8, where an aggressive q response was observed when administering a mass of 0.2 g · L⁻¹ (run 8), resulting in a higher residual module (14.55) (Table 3).

Table 4

ANOVA for the model of adsorption capacity response of DS on PAC

Parameters .	GL .	SQ .	MQ .	F-value .	p-value .
Model	14	21.11	1.51	10.65	<0.0001
CDS	1	6.58	6.58	46.51	<0.0001
CPAC	1	6.67	6.67	47.16	<0.0001
Ct	1	2.52	2.52	17.83	0.0007
pH	1	0.2153	0.2153	1.52	0.2363
CDS·CPAC	1	0.0945	0.0945	0.6675	0.4267
CDS·Ct	1	0.0014	0.0014	0.0098	0.9223
CDS·pH	1	0.0786	0.0786	0.5557	0.4675
CPAC·Ct	1	0.0001	0.0001	0.0004	0.9847
CPAC·pH	1	0.0942	0.0942	0.6660	0.4272
Ct·pH	1	0.0377	0.0377	0.2662	0.6134
	1	2.53	2.53	17.90	0.0007
	1	1.26	1.26	8.92	0.0092
	1	0.4709	0.4709	3.33	0.0881
pH²	1	0.0361	0.0361	0.2554	0.6206
Residual	15	2.12	0.1415
Lack of fit	10	2.10	0.2102	50.11	0.0002
Pure error	5	0.0210	0.0042
Cor total	29	23.23
Fit statistics				R²	0.9086
		SD	0.3762	Adjusted R²	0.8234
		Mean	6.47	Predicted R²	0.4776
		CV %	5.81	AP	15.6981

Parameters .	GL .	SQ .	MQ .	F-value .	p-value .
Model	14	21.11	1.51	10.65	<0.0001
CDS	1	6.58	6.58	46.51	<0.0001
CPAC	1	6.67	6.67	47.16	<0.0001
Ct	1	2.52	2.52	17.83	0.0007
pH	1	0.2153	0.2153	1.52	0.2363
CDS·CPAC	1	0.0945	0.0945	0.6675	0.4267
CDS·Ct	1	0.0014	0.0014	0.0098	0.9223
CDS·pH	1	0.0786	0.0786	0.5557	0.4675
CPAC·Ct	1	0.0001	0.0001	0.0004	0.9847
CPAC·pH	1	0.0942	0.0942	0.6660	0.4272
Ct·pH	1	0.0377	0.0377	0.2662	0.6134
	1	2.53	2.53	17.90	0.0007
	1	1.26	1.26	8.92	0.0092
	1	0.4709	0.4709	3.33	0.0881
pH²	1	0.0361	0.0361	0.2554	0.6206
Residual	15	2.12	0.1415
Lack of fit	10	2.10	0.2102	50.11	0.0002
Pure error	5	0.0210	0.0042
Cor total	29	23.23
Fit statistics				R²	0.9086
		SD	0.3762	Adjusted R²	0.8234
		Mean	6.47	Predicted R²	0.4776
		CV %	5.81	AP	15.6981

GL, degrees of freedom; SQ, sum of squares; MQ, mean squares; SD, standard deviation; F-value, Fisher's value; p-value, significance; C_DS, diclofenac sodium concentration; C_PAC, adsorbent concentration; C_t, contact time; pH, hydrogen potential; CV % – coefficient of variation; R², coefficient of determination; AP, adequate precision.

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By applying multiple linear regression, the coefficient of determination (R²) for the model was obtained as 0.9086, a satisfactory value for model validation. The adjusted R² was 0.7149, with a difference of >20% from the predicted R² of 0.1601. This result indicates that the model can be mathematically reduced to obtain a better result. However, when considering the selection criteria of factors with a p-value <0.1, a lower correlation was obtained and therefore was not adopted (Sheikhmohammadi et al. 2017).

The model developed for the q response was subjected to ANOVA, and the results can be seen in Table 5. In general, a p-value < 0.05 indicates statistical significance at a confidence level of 95%. Evaluating the data based on this reference, the model is statistically significant, with a p-value < 0.0001. The individual analysis of the factors suggests the significance of C_DS, C_PAC, C_t, ⁠, and ⁠.

Based on the maximum coefficient of variation (CV) of 10% as a relative measure for validating the repeatability of the model, it can be inferred that the model for q was adequate, with a CV of 5.81% (Torgut et al. 2017). As for precision, values greater than 4 are considered adequate (Torgut et al. 2017), indicating a better response in the signal-to-noise ratio. The precision of the model was 15.70, considered satisfactory. The F-value of 10.65 corroborates the validation of the model, with a significance p-value < 0.0001.

In agreement with the ANOVA test, the factors of adsorbate concentration, adsorbent mass, and contact time exerted influence on the response, showing pronounced curvatures in the perturbation study, indicating high sensitivity of q to these factors. On the other hand, pH does not significantly alter the efficiency of the process, but sensitivity to it is observed. The factors C_DS and C_t are considered synergistic, while C_PAC and pH are antagonistic.

The decrease in adsorbent dosage resulted in an increase in adsorptive capacity (antagonistic effect), with greater effectiveness in the region below 1.4 g · L⁻¹, converging to 0.2 g · L⁻¹ (Figure 10(a)). The probable cause of this phenomenon is that powdered adsorbents, when administered at low concentrations, disperse more homogeneously in the liquid column. Additionally, SEM-FEG and BET showed that CAP is abundant in surface area; however, its plate-like morphology with varying sizes may allow for overlap, and if administered at high concentrations, it may make areas unavailable for adsorption, consequently decreasing process efficiency (Afkhami et al. 2010).

The increase in contact time correlated with an increase in adsorptive capacity (synergistic effect), with the optimal contact time observed at approximately 40 min (Figure 10(b), 10(d), and 10(f)). This can be explained by the porous nature of the PAC, where adsorption depends on internal diffusion within the pores, a mass transfer process known to be slower and more limited. Therefore, extending the contact time optimizes this process.

An increase in adsorptive capacity was also observed at a pH close to 5 (Figure 9(c), 9(e), and 9(f)). It is noteworthy that DS has a pKa of 4.15, and an acidic environment can lead to the adsorbate's precipitation onto the adsorbent and force mass transfer. Additionally, it was found that PAC exhibited a positively charged surface when dispersed in a solution with pH > 5 and <7.34 (PZC_PAC), while DS was in an anionic state at a solution pH > 4.15 (pKa_DS), favoring the mechanism of electrostatic attraction, which may have influenced the increase in adsorptive capacity (Drugbank 2024).

Reversals of pH influence were also observed in some cases (Figure 10(c) and 10(e)). In the situation of higher mass concentration (C_PAC > 3.8 g · L⁻¹), the basic pH close to 9 > 7.34 (PZC_PAC) may have promoted electrostatic repulsion (greater interaction in the liquid), reducing the formation of aggregates (Figure 10). Similarly, the basic pH 9 > 4.15 pKa_DS, increased the capacity for C_DS close to 50 mg · L⁻¹, while conversely, the acidic pH 5 showed better efficiency in the response at concentrations close to 450 mg · L⁻¹, also demonstrating greater curvature, which can be explained by the high concentration of the drug in solution, making it saturated and more prone to the dissolution and precipitation of DS. These results suggest that the ionization state of DS may have a greater influence on the adsorption mechanisms in less saturated solutions with diclofenac and/or lower adsorbent concentrations. The same phenomenon was observed in the adsorption of diclofenac and 4-octylphenol on graphene oxide, respectively, by Medeiros et al. (2022) and Araújo et al. (2024), both using CCD as an optimization tool. Thus, these results indicate a possible relationship between the influence of pH as a function of the ratio between adsorbent mass and adsorbate concentration, necessitating specific studies for a better understanding.

Analyzing the data with the aim of achieving the maximum adsorption capacity of PAC, Derringer's desirability function (di) was set up to find the best combination of factors that would maximize the response q. Based on the response surface, the following search criteria were used: maximum C_DS, minimum C_PAC, minimum pH, and contact time varying within the tested limits. The results of the maximum adsorptive capacity and the experimental confirmation runs can be seen in Table 5.

The maximum adsorption capacity obtained by the model was 89.89 mg · g⁻¹, corresponding to di = 1.00. In order to reproduce this result, the combination of factors was experimentally tested in duplicate, resulting in an average capacity of 169.39 mg · g⁻¹, which is 88.45% higher than the average value predicted by the model.

It is worth noting that experimentally, in run 8 (C_DS – 250 mg · L⁻¹, C_PAC – 0.2 g · L⁻¹, C_t – 25 min, pH – 7), the obtained capacity was 88.54 mg · g⁻¹, a value very close to the maximum predicted capacity. Combining this information with the fact that the adsorption capacity model had an R² of 0.9086, it can be observed that there is a discrepancy in the region of the maximum adsorption capacity predicted by the model, as it explains 90.89% of the results. Therefore, the average capacity obtained in the confirmation runs is closer to the upper limits predicted by the model, especially the one based on the p-value < 0.05, corresponding to 99% of the population, a value of 159.19 mg · g⁻¹.

The variation can be explained by the disturbance of adsorption observed for concentrations higher than 350 mg · L⁻¹, which caused a decrease in the average adsorptive capacity, thus influencing the model to predict lower values in that region.

The IPD model reveals that there is more than one mechanism (intraparticle and film diffusion) controlling the adsorption process, as the line does not intersect the origin in the plot of q_t versus t^1/2 (Figure 12; Webber & Morris 1963). Observing the values of the parameter C_d (Table 7), it was found that the increase in DS concentration from 25 to 350 mg · L⁻¹ increased the efficiency of initial film formation by 340.58%, forcing the mass transfer process. Nevertheless, the model reaffirms that the adsorption of DS by PAC is a time-limited process, as the initial film formation on the adsorbent varied from 31.44 to 50.49% for the tested concentrations, with adsorbate still remaining in solution to be transferred by the intraparticle mechanism, considered slow.

The isotherm shape was categorized using the classification system proposed by Giles et al. (1960), and it was considered to be of type ‘L2’ or normal, indicative of surface adsorption, in accordance with the previous discussions. The data for PAC fit satisfactorily to both models (with very close determination coefficients), but the Freundlich model best describes the adsorption with R² = 0.97273 and lower X². The model is based on surface heterogeneity and does not predict a finite number of active sites, consistent with the BET assay that identified multilayer adsorption due to the morphological nature of PAC, which is mainly composed of plates. It is also evident that there is a resistance curve to the adsorption of DS on PAC, and the decrease in efficiency at high adsorbate concentrations can be explained by the increase in adsorbate–adsorbate interactions at the expense of adsorbate–adsorbent interactions. As shown in Table 8, the 1/n factor of the Freundlich isotherm is far from 1, and the R_L factor decreases from 0.6310 to 0.0867 for concentrations from 25 to 450 mg · L⁻¹, both results confirming that concentration is a limiting factor of the process.

The maximum adsorption capacity obtained for PAC in this study and that of different materials found in the literature are listed in Table 9.

The PAC is among the materials with the highest adsorptive capacity along with shorter contact times and a low adsorbent–adsorbate dosage ratio, as seen in Table 9. Its adsorbent–adsorbate dosage ratio (g · mg⁻¹) was 0.0006, ranking among the three lowest, near to reduced graphene oxide (OGR) at 0.0003, graphene oxide (0.0004), and porous graphitic biochar (PGB) at 0.0005. These results suggest that these materials may have better distribution in the liquid column, resulting in greater availability of surface area compared with other materials. Regarding contact time, it is noticeable that OGR and PGB, reached their maximum capacity at prolonged contact times (200–1,440 min) compared with other materials. OGR has a plate-like structure, and despite its low dosage, its basic composition reduces its efficiency by not providing functional groups involved in the adsorption mechanisms with DS than the graphene oxide nanosheets (GONs). Therefore, its maximum capacity is reduced, and its contact time is prolonged compared with PAC and other materials. As for PGB, its porous structure may be the main reason for the increased contact time required to reach saturation, as intraparticle adsorption is a secondary process to intra-film adsorption. Regarding pH, OGR is the only one indicating a basic environment (pH 10) as optimal. This could be explained by the electrostatic attraction of its positively charged surface attracted to the ionized DS. PAC, GON, and CPN are the materials with the three highest q_max values on this list. However, although CPN has a shorter contact time, it requires a dosage six times higher to achieve approximately double the capacity of PAC. GON, on the other hand, has an efficiency about four times greater than PAC, which can be explained by its surface being rich in oxygenated groups that facilitate chemical adsorption. It is worth noting that GON and CPN are synthetic adsorbent materials, which typically involve higher production costs and chemical waste.

The PAC has physical, chemical, and morphological characteristics suitable for the adsorption of DS dissolved in aqueous solution. However, when considering its implementation in water treatment cells, the contact time and adsorbate concentration are limiting factors. Additionally, the cost-effectiveness of natural or agricultural waste-based adsorbent materials compared with synthetic adsorbents that require various chemicals in their synthesis process should be analyzed, as the former are readily available and low-cost materials.

The kinetic and isotherm models complemented the discussion of limiting factors and mechanisms involved in the adsorptive process. The PSO model best explains the adsorption of DS on PAC. The adsorption equilibrium is best described by the Freundlich model. Furthermore, adsorption is governed by a combination of intraparticle and intra-film mechanisms, with a greater prevalence of intraparticle adsorption (requiring longer contact times) for concentrations below 350 mg · L⁻¹.

The CCD is a suitable optimization tool for use in adsorption processes. However, some factors used in this study need to be adjusted, such as the C_PAC concentration and pH. The C_PAC range was wide (0.2–5 g L⁻¹), leading to a damping of the adsorption capacity response and influencing the average of the predicted values downwards. Thus, values closer to 0.2 g L⁻¹ could generate results for verifying the maximum adsorptive capacity. Regarding pH, it was observed that the model is sensitive to this parameter; however, it does not have a significant influence. Therefore, sensitivity to pH can be further refined by adjusting the C_PAC, with greater pH influence at low adsorbent concentrations, or by expanding the range, which was limited to values from 5 to 9.

This work was partially funded by CNPq (Conselho Nacional de Pesquisa – National Council for Scientific and Technological Development) through process 403130/2023-9.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.