Enhancing Adsorption and Desorption of Arsenic on Carbon Xerogel Nanocomposites in Aqueous Solution: Process Optimization

Abstract

Arsenic, a widespread contaminant, has become a major public health concern, threatening millions globally. This study aims to develop magnetic adsorbents for easy recovery from aqueous media to remove arsenic, mitigating its environmental and health impacts. Response surface methodology (RSM) is proposed to optimize the adsorption-desorption process of As(III) and As(V) on carbon xerogel nanocomposites from aqueous solutions. A second-order polynomial model under a central composite design with a central face was employed to optimize arsenic desorption. The model parameters were estimated using least squares. Additionally, a novel linear model approach was employed to develop a second-degree polynomial model for optimizing arsenic adsorption-desorption by analyzing the effects of various factor combinations. RSM’s ability to analyze the response variable over a wide range of independent variable values allows it to identify the region where the response variable reaches its optimum value.

1. Introduction

1.1 Arsenic contamination and its health limitations

Trivalent arsenic (As(III), arsenites) and pentavalent arsenic (As(V), arsenates), are well-established carcinogens and significant environmental and public health hazards. Notably, arsenic has emerged as a leading global chemical contaminant due to its natural presence at elevated levels in groundwater, particularly in arid northern and central Mexico, where weathering of silica volcanic rock results in its migration into the water [1]. The presence of arsenic in the environment has significantly emerged as a major public health problem in surpassing the World Health Organization’s maximum permissible limit of 10.0 μg/L, it poses a potential risk of adverse health effects, including cancer, peripheral neuropathy, arsenicosis, and cardiovascular diseases. This threat is further amplified by the element’s high solubility in water [2, 3]. In Mexico, the maximum permissible limit for arsenic in drinking water is also set at 10.0 μg/L, as outlined in NOM-127-SSA1-2021.

1.2 Addressing arsenic with adsorption

Adsorption using porous materials is a widely employed technique for treating drinking water and wastewater [4]. This method allows for the selective removal of specific contaminants by choosing an appropriate adsorbent. To enhance the economic and environmental sustainability of this process, studying the desorption and reuse of adsorbents is crucial [5, 6]. In this case, composite gels with magnetite nanoparticles were prepared to have electrostatic attraction of nanoparticles of iron oxide, high surface area, easy to recover from the aqueous medium, and reusable of magnetic polymers [7, 8]. One of the most important factors in designing an adsorption process is the quantity and types of pollutants (adsorbents) present in the water source. These pollutants can interact competitively with each other, or simply reduce the adsorbent’s functionality through early saturation or synergies within the aquatic system. This decreased functionality further complicates the availability of clean drinking water, especially when dealing with contaminants like inorganic arsenic compounds present in water bodies.

1.3 Application of response surface methodology

Knowledge and understanding of adsorption process design and optimization are essential. Several factors must be considered for effective adsorption, such as pH, synthesis method, initial concentration, particle size, competing ions, and contact medium [9, 10]. Experimental design is a valuable tool for optimizing and predicting the interactive effects of adsorption processes [10, 11]. Response surface methodology (RSM) is a mathematical and statistical method widely used to evaluate multiple factors and their interactions with various response variables [12]. RSM has been effectively applied in various studies to optimize the adsorption process. RSM has been used to examine the interactive effects and predict the model building and optimization of arsenic adsorption by activated carbon derived from food industry waste [9], biodegradable biopolymer chitosan [13], and natural zeolite with magnesium oxide [14]. RSM was used to optimize the adsorption of heavy metals, nickel, and cadmium, respectively [15, 16], from aqueous solutions. RSM was also utilized to optimize the ultrasound-assisted adsorption of anionic and cationic dyes, demonstrating the versatility of RSM in different adsorption processes [17]. These studies collectively highlight the effectiveness of RSM in optimizing the adsorption process for various contaminants.

1.4 Experimental design with RSM

In this study, the adsorption and desorption of arsenic on carbon xerogel nanocomposites propose establishing and carrying out RSM. RSM employs a series of mathematical and statistical techniques to model and analyze problems where the goal is to obtain the best-fitting mathematical model that relates a dependent response variable (often denoted as “y”) to various independent variables (“x_i”).

1.5 Advantages of RSM over ordinary factorial designs

Unlike traditional factorial designs (e.g., 2^k), RSM allows us to identify the optimal operating conditions for a process. This refers to the specific combination of “x_i” values that maximize or minimize the response variable. This achievement is possible through the utilization of more advanced mathematical techniques. While a factorial design can identify a “winning” combination or treatment within the tested values, it cannot necessarily be extrapolated to untested values.

RSM offers several advantages over ordinary factorial designs. It minimizes the number of experiments required for a specific number of factors and levels, making it more efficient [18]. Additionally, RSM can be used to construct cost-efficient response surface designs for experiments with both qualitative and quantitative factors [19]. These advantages collectively make RSM a powerful tool for experimental design and optimization.

1.6 Strength of RSM

The key strength of RSM lies in its ability to interpolate between different values of the independent variables. This means we can not only identify the optimal combination from the tested data but also predict the optimal values for untested combinations. This prediction is done by constructing 3D surface graphics or 2D contour plots of the response variable.

2. The experiment design for As(III) and As(V) adsorption on carbon xerogel nanocomposites

This study aims to develop magnetic adsorbents that remove both As(III) and As(V) efficiently from groundwater. Carbon xerogel nanocomposites were synthesized via sol-gel polymerization of a resorcinol-formaldehyde composite incorporating magnetite nanoparticles [7]. The process utilized sonication-assisted direct methods, followed by carbonization and H₂O₂-induced surface modification. This study evaluated the effects of dosage, solution pH, and initial concentration of arsenic on the removal process using an experimental design. RSM was used to optimize the adsorption process of arsenic on magnetic carbon xerogel nanocomposites from aqueous solutions using a central composite design (CCD) 2³ with a central face.

2.1 Experimental design and optimization method

The magnetic carbon xerogel nanocomposite was selected for study using a CCD and evaluated for arsenic removal using RSM. RSM allows the interpolation of various independent variable values and identifies optimal combinations for the response variable by constructing 3D surface graphs and projecting their contours onto a 2D surface.

The RSM application is proposed through a second-order polynomial model under a CCD scheme with a central face. The least squares method estimates parameters in this model. For each independent variable combination (“x_i”), 3D graphs and 2D contour plots will be obtained, along with various statistical parameters evaluating their fitting and reliability, such as: R-squared (R²), adjusted R², F test statistic, lack of fit test, and locating the stationary point (maximum response point).

This method can be implemented using statistical software R v4.2. Table 1 summarizes the evaluation method, which consists of one response variable (As removal efficiency) and three independent variables (adsorbent dose, initial As concentration, and solution pH) at three levels (low, medium, and high).

Factors	Coding factors	Low (−1)	Center (0)	High (1)	Units
Solution pH	x1	3.0	5.0	7.0	pH value
Adsorbent dose	x2	0.5	2.5	4.5	g/L
As concentration	x3	0.05	0.15	0.25	mg/L

Table 1.

Coded factors and levels for As(V) and As(III) adsorption experiment.

2.2 Arsenic batch adsorption experiment

For the batch adsorption experiment, sodium arsenite (NaAsO₂, Sigma-Aldrich) and sodium arsenate dibasic heptahydrate (HAsNa₂O₄·7H₂O, Sigma-Aldrich) were used to prepare As(III) and As(V) stock solutions at various desired concentrations. These solutions were prepared by diluting with ultrapure (type 1) water. The pH of the solution was adjusted using 0.1 M HCl and 0.1 M NaOH solutions and then measured with a pH meter (Orion Star A211, Thermo Scientific, USA).

Following the conditions outlined in Table 1, all experiments were conducted in 50 mL centrifuge tubes at 150 rpm with a room temperature range of 25°C to 28°C. All the results obtained from the experiment were evaluated for removal efficiency and adsorption capacity.

Equations:

The removal efficiency was evaluated using the following equation (Eq. (1)):

$$\%\text{removal}=\left({\mathrm{C}}_0–{\mathrm{C}}_{\mathrm{e}}\right)/{\mathrm{C}}_0\times 100$$E1

where:

• C₀: initial concentration of arsenic (mg/L)

• C_e: final concentration of arsenic (mg/L)

The adsorption capacity (q_e) was calculated using formula (Eq. (2)):

$${\mathrm{q}}_{\mathrm{e}}=\left({\mathrm{C}}_0–{\mathrm{C}}_{\mathrm{e}}\right)/\mathrm{m}\times \mathrm{V}$$E2

where:

• m: Mass of adsorbent (g)

• V: Solution volume (L)

2.3 Determination of As(V) and As(III) concentrations in water samples

After the adsorption experiment, each solution was filtered using a vacuum pump and 0.45 μm cellulose nitrate membrane filters (Whatman) to separate the solid from the supernatant. The concentrations of As(V) and As(III) were determined using a fast sequential flame atomic absorption spectrometer (SpectrAA-220, Varian, Australia) at a wavelength of 193.7 nm [20].

2.4 Models fitted and their corresponding optimal parameters

The evaluation of the removal of arsenic using magnetic carbon xerogel nanocomposite was carried out by executing an RSM. The response variable was arsenic removal efficiency, and the independent variables were adsorbent dose, initial arsenic concentration, and solution pH. Each variable had three levels: Low, medium, and high. The experimental method and data analysis were implemented using statistical software R v4.2

Eqs. (3) and (4) present the most significant parameters identified using RSM for As(V) and As(III) removal efficiency, respectively. Categorical variables were coded according to Table 1.

$$\mathrm{As}\left(\mathrm{V}\right)\text{removal}\left[\%\right]=28.6177‒23.4317{\mathit{x}}_1+10.8115{\mathit{x}}_2‒11.9858{\mathit{x}}_1{\mathit{x}}_2+26.0798{\mathit{x}}_1{}^2–9.5217{\mathit{x}}_3{}^2$$E3

$$\mathrm{As}\left(\mathrm{III}\right)\text{removal}\left[\%\right]=51.96523–7.42122{\mathit{x}}_1+13.36756{\mathit{x}}_2{\mathit{x}}_3–18.22614{\mathit{x}}_1{}^2+15.53519{\mathit{x}}_3{}^2$$E4

Figures 1 and 2 show the contour plots of the removal efficiency of As(V) and As(III) with two different factors, respectively. The x and y axes show the two variable input parameters (pH, dose, or initial concentration) that maximize arsenic removal. The most efficient As(V) removal was achieved for the significant quantitative factors pH and adsorbent dose (Figure 1). Figure 2 shows the contour plot of the As(III) removal efficiency. The highest As(III) removal efficiency was obtained for the significant quantitative factors of adsorbent dose and initial concentration.

Figure 1.

The 2D representation visualizes the optimized results obtained by applying the RSM to optimize pH, initial concentration, and dose for the removal efficiency of As(V).

Figure 2.

The 2D representation visualizes the optimized results obtained by applying the RSM to optimize pH, initial concentration, and dose for the removal efficiency of As(III).

Figure 3 presents the adjusted model based on significant parameters, resulting from the RSM. It visualizes the removal efficiency of As(V) as a function of pH vs dose. Figure 4 presents the adjusted model resulting from the RSM, visualizing the removal efficiency of As(V) as a function of pH and initial concentration. The maximum As(V) removal efficiency was obtained at a low pH and a high adsorbent dose. Studies on the adsorption of various compounds by carbon xerogel have found similar results, suggesting that both pH and the dose of the xerogel play a significant role [21, 22].

Figure 3.

The 3D surface estimation plots of As(V) removal efficiency as a function of pH vs. dose.

Figure 4.

The 3D surface estimation plots of As(V) removal efficiency as a pH and initial concentration.

The optimal values were determined by calculating the estimated marginal means for factor combinations in a linear model using the “emmeans” package in R [23]. The optimum values for pH, adsorbent dose, and initial concentration for the removal of As(V) were 3.0, 4.5 g/L, and 0.15 mg/L, respectively, with a removal efficiency of 95.03 ± 5.98%, which was achieved within 3 h in aqueous solutions. The optimum values for pH, adsorbent dose, and initial concentration for the removal of As(III) were 4.0, 4.5 g/L, and 0.18 mg/L, respectively, with a removal efficiency of 65.04 ±10.32% (Table 1).

3. The experiment design for arsenic desorption on carbon xerogel nanocomposites

In this study, the desorption capacity, and the possibility of regeneration of the carbon xerogel nanocomposites were evaluated in the arsenate adsorption process from an aqueous solution. The optimal condition for the arsenate desorption process was studied using a RSM, varying the concentration of desorbing agents, adsorbent doses, and the agitation at which the magnetic gels were prepared.

The use of RSM is proposed by using a 16-run CCD with a central point and fitting a second-order polynomial model. The parameters of the model are estimated using the least squares method.

The 3D graphs and 2D contour plots are obtained for combinations of the independent variables “x_i”. Statistical parameters like R-squared, adjusted R-squared, F-statistic, lack of fit test, and the location of the stationary point (the point on the response surface where the percentage removal of arsenic is maximized) are used to evaluate the fit and reliability of the model.

This method can be implemented using the statistical software R (version 4.2). The setup is consisted of:

One response variable: Percentage removal of arsenic.

Three independent variables at three levels (low, medium, and high values): The concentration of desorbing agents, adsorbent doses, and the agitation.

A central face: Treatment with mean values of the three independent variables.

The experimental data are composed of 14 different combinations of the independent variables plus two additional “central face” treatments in two replicates for a total of 32 measurements.

3.1 The optimal condition for the arsenic desorption process using RSM

The optimization study of the desorption of arsenic was carried out by using a RSM. The experimental method and data analysis were implemented using the software R. The experimental design of CCD with three factors and two center points was applied in this study with the varying concentration of desorbing agent (M), spent adsorbent dose (g/L), and orbital shaker speed (rpm) as shown in Table 2.

Factors of arsenic desorption	Coding factors	Low (−1)	Center (0)	High (1)
Concentration of KOH solution (M)	$x_1$	0.5	1	1.5
Orbital shaker speed (rpm)	$x_2$	80	120	160
Spent adsorbent dose (g/L)	$x_3$	0.4	1.2	2

Table 2.

Configuration of variables for implementation of the RSM method to optimize arsenic desorption on carbon xerogel nanocomposites.

3.2 Analysis of results implementing the RSM for arsenic desorption

For the experimental design of the RSM configuration for optimizing arsenic desorption using KOH on carbon xerogel nanocomposites [24], results of a second-degree polynomial model are shown in Tables 3 and 4. The variables encoded were x₁ (KOH concentration), x₂ (Agitation speed), and x₃ (Adsorbent dose).

Variable	Estimate	Std. error	t value	Pr(>|t|)
(Intercept)	49.0661	5.4488	9.0050	0.0001049***
x1	2.3998	3.6395	0.6594	0.5341302
x2	3.7816	3.6395	1.0391	0.3388262
x3	29.3671	3.6395	8.0690	0.0001940***
x1:x2	−2.5448	4.0691	−0.6254	0.5547302
x1:x3	3.8370	4.0691	0.9430	0.3820983
x2:x3	4.9842	4.0691	1.2249	0.2665189
x1^2	−8.8971	7.0882	−1.2552	0.2560800
x2^2	11.0396	7.0882	1.5574	0.1703725
x3^2	−3.1746	7.0882	−0.4479	0.6699693

Table 3.

Statistical analysis of the second-degree polynomial model generated using the RSM method.

Significant Codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Df	Sum	Sq mean	Sq F value	Pr(>F)
rsm:FO (x1, x2, x3)	3	8824.9	2941.62	22.2077	0.001195
TWI (x1, x2, x3)	3	368.3	122.78	0.9269	0.483106
PQ (x1, x2, x3)	3	424.1	141.36	1.0672	0.430404
Residuals	6	794.8	132.46
Lack of fit	5	677.0	135.39	1.1495	0.606208

Table 4.

RSM analysis of the second-degree polynomial model’s statistics.

The variable x₃ (dose) has a significantly stronger effect (indicated by more asterisks) on the response variable As desorption.

The resulting second-degree model is:

$$\begin{array}{lll}\mathrm{As}\text{desorption}& =& 49.07+2.4x_1+3.78x_2+29.37x_3–2.54x_1{x}_2+3.84x_1{x}_3\\ & & +4.98x_2{x}_3–8.9x_1^2+11.04x_2^2–3.17x_3^2\end{array}$$E5

With the coded variables x₁(Conc), x₂(Speed), and x₃(Dose).

R-squared: 0.9237, Adjusted R-squared: 0.8092

F-statistic: 8.067, 9 DF, 6 DF, p-value: 0.009712

The p-value of the model is significant (p-value < 0.05).

The coefficient of lack of fit is not significant (Lack of fit > 0.05), which means the fitting level for the model is acceptable.

Figure 5 demonstrates the behavior of arsenic desorption with respect to the variables considered, using the stationary points in their original units, namely, concentration (conc) of 1.64, speed of 77.6, and dose of 4.85. It can be observed that the agitation speed and the concentration of the desorbing agent increase, and the arsenic desorption of the material improves.

Figure 5.

The 2D representation (contour lines) of As desorption behavior as a function of concentration, speed, and dose, using the stationary points: Concentration = 1.64, speed = 77.6, and dose = 4.85, found by the RSM method.

Figure 6 depicts a 3D surface plot of arsenic desorption percentage as a function of both desorbing agent concentration (KOH) and adsorbent dose. The plot is generated using the RSM method and utilizes an agitation speed of 77.6 rpm, determined as the stationary point through analysis. As visually indicated by the increased number of asterisks, the adsorbent dose (variable x₃) exerts a significant influence on the response variable, arsenic desorption. Furthermore, the model demonstrates statistical significance with a p-value less than 0.05.

Figure 6.

The 3D representation of As desorption behavior as a function of concentration (conc) versus dose, with speed = 77.6 fixed as the stationary point estimated by the RSM method.

Table 5 presents combinations of values that maximize the As desorption parameters within specified ranges: KOH solution concentration (conc) = 0.5–3.0 M, orbital shaker speed (speed) = 120–180 rpm, and dose of spent adsorbent (dose) = 0.4–5.0 g/L. The highest As desorption values are based on the best parameter combinations.

conc	speed	dose	As_des_avg	SE	df	lower.CL	upper.CL
1.05	160	2	95.3442	9.7559	6	71.4725	119.216
1.25	160	2	94.6857	9.4133	6	71.6521	117.7193
0.85	160	2	93.1557	9.6096	6	69.6417	116.6696
1.05	160	1.9	91.7464	8.9601	6	69.8219	113.6709
1.05	150	2.1	91.7295	9.8582	6	67.6073	115.8516
1.25	150	2.1	91.5173	9.5527	6	68.1427	114.8918
1.45	160	2	91.1801	9.7877	6	67.2306	115.1297
1.25	160	1.9	90.896	8.6362	6	69.7641	112.028
0.85	160	1.9	89.7497	8.817	6	68.1752	111.3242
0.85	150	2.1	89.0946	9.7244	6	65.2998	112.8893
1.05	150	2	88.3866	8.4758	6	67.647	109.1262
0.65	160	2	88.12	9.3719	6	65.1878	111.0522
1.05	160	1.8	88.0494	8.4758	6	67.3098	108.7889
1.25	150	2	87.9826	8.1787	6	67.9699	107.9952
1.45	160	1.9	87.1986	9.1539	6	64.7997	109.5974
1.25	160	1.8	87.0072	8.1787	6	66.9945	107.0198
0.85	160	1.8	86.2445	8.3395	6	65.8385	106.6505
1.25	140	2.1	86.0383	9.4231	6	62.9808	109.0959
1.05	140	2.1	85.996	9.6731	6	62.3267	109.6653
0.85	150	2	85.9435	8.3395	6	65.5376	106.3495

Table 5.

Combinations of values maximizing the As desorption parameters subject to the restriction that the variables range between concentration, speed, and dose.

Conc = Concentration of initial; speed = Speed of agitation; dose = Dose of adsorbent; As_des_avg = Average of arsenic desorption; SE = Standard error; df = degrees of freedom; lower.CL = lower confidence level; upper.CL = upper confidence level.

Desorption of arsenic from spent carbon xerogel nanocomposites predicted by the second-degree model estimated with RSM, visualized as a 3D plot as shown in Figure 7. Dose and concentration are the model variables, while speed is fixed at 160 rpm (as specified in Table 2) and was used to maximize As desorption. Similar findings show that the removal efficiency of arsenic increased with higher adsorbent dosages, indicating a potential for strong adsorption [25, 26].

Figure 7.

Implementation of the second-degree model estimated using the RSM method based on the dose vs conc variables, with a constant value of speed = 160 rpm.

Limitations of the implemented methodology are related to the probable need to perform different modeling when using the RSM method to find the best combinations of predictor variables that optimize the response variable. Otherwise, the model and the obtained response will only be valid for the range of values considered in the modeling with the risk of obtaining a local maximum instead of a global maximum value that considers a wider range of values of the predictor variables.

Future research could focus on comparing the results of the RSM method with models created from machine learning techniques. These techniques generally require a larger amount of data for their construction but could have better adaptation to nonlinear behaviors and compensate for those situations in which the RSM method shows difficulty in fitting.

4. Conclusions

This study presents a significant advancement in arsenic removal technology. Carbon xerogel nanocomposites loaded with magnetite nanoparticles were synthesized using a streamlined process involving direct sonication during sol-gel polycondensation. Subsequent carbonization and hydrogen peroxide surface modification further enhanced the material’s adsorption capacity.

Employing RSM proved to be a powerful tool. It revealed not only the critical factors influencing arsenic adsorption (solution pH and nanocomposite dose for both As(III) and As(V)) but also established a predictive model for optimizing arsenic capture under various conditions. This paves the way for efficient and targeted arsenic removal strategies.

The impact of RSM extended beyond adsorption. It facilitated the optimization of the desorption process, identifying the adsorbent dose as the key factor governing arsenic release. Moreover, a novel RSM-based model was developed to predict the effects of combined factors on desorption. This innovative approach offers valuable insights for future research and practical applications.

The next phase of this research will prioritize evaluating the efficacy of these nanocomposites under environmentally relevant conditions to assess their arsenic removal efficiency in a more complex matrix. The reusability of the As-loaded nanocomposite will be investigated through multiple adsorption-desorption cycles. Potential changes in performance will be analyzed, and regeneration methods explored to maintain long-term efficiency. This comprehensive investigation will ensure the technology’s effectiveness and sustainability for practical arsenic remediation.

Acknowledgments

Khamkure S. acknowledges the ‘Investigadoras e Investigadores por México CONACYT’ program (Project No. CIR/0069/2022). This work was partially supported by Universidad Autónoma Agraria Antonio Narro (Grant No. 38111-425401001-2320). The authors would also like to thank Manuel Sanchez-Zarza, Socorro García-Guillermo, and José Martín Baas-López for their contributions with technical equipment and analysis.

Conflict of interest

The authors declare no conflict of interest.

Thanks

The authors thank María-Fernanda Cabello-Lugo and Arael Torrecilla-Valle for their helping and supporting in the laboratory.