1 Introduction

In recent years, the rising pollution and contamination of surface and groundwater, coupled with the depletion of this vital resource, have raised significant concerns among researchers. Depending on the nature of the contaminant, various techniques can be employed for decontamination. Among these techniques, adsorption has gained prominence due to its simplicity, speed, cost-effectiveness, and low energy requirements, making it the preferred choice for eliminating diverse pollutants [1,2,3].

Porous materials exhibit appropriate adsorption characteristics due to their large surface area, substantial pore volume, and adjustable pore size. Among the diverse range of porous materials, functionalized silica stands out as an appealing option due to its ease of synthesis and functionalization, along with its desirable mechanical properties [4,5,6,7]. Numerous studies have emphasized the effectiveness of mesoporous functionalized silica in removing heavy metals [8,9,10,11,12,13,14,15,16,17], dyes [18, 19], ions [20], and bisphenol A [21,22,23].

Heavy metals have received significant attention among pollutants due to their environmental and health impacts. Remediation efforts for heavy metal pollution have primarily focused on adsorption techniques. Major materials employed in these procedures include natural adsorbents derived from biomass [24,25,26] and mesoporous functionalized silica.

Chromium, extensively used in various industrial activities, is recognized as one of the most hazardous pollutants. It can be found in a variety of oxidation states, predominantly as Cr(III) and Cr(VI) ions. While Cr(III) ions have lower solubility and can precipitate as Cr(OH)3, Cr(VI) ions exhibit high solubility in water. Due to its extreme toxicity, the hexavalent form poses a serious risk to human health when present in water [27]. Therefore, the elimination of these species is of great importance for water treatment [28,29,30,31]. Extensive research has been dedicated to the removal of hexavalent ions using various materials, including natural adsorbents [32,33,34] and mesoporous functionalized silica [35,36,37,38,39,40]. Our solid is synthesized using an environmentally responsible process: the sol-gel method, which offers the advantage of preparation at ambient temperature. This sustainable eco-friendly process results in a significantly lower carbon footprint compared to alternative materials that require high-temperature treatments.

In the literature, while removing Cr(VI) ions by adsorption the most commonly reported interactions are of three types: electrostatic, hydrogen bonding, π–π interactions, and hydrophobic effects. When Cr(VI) ions are adsorbed, the dominant forces involved are primarily electrostatic interactions between HCrO4− anions and the positively charged surface of the functionalized silica, particularly in pH conditions below its point of zero charge (PZC) [41].

The modeling of chromium adsorption involves comparing the obtained experimental data with various mathematical models. Recently, the nonlinear method has been increasingly preferred over the linear approach due to its ability to provide more reliable results for the best model fit with its parameters [42]. Although the iterative nature of this method makes it more complex compared to the linear approach, computational operations have made it feasible and easier to perform. Mathematical software such as MATLAB, Python, SPSS, Origin, R, Solver add-in for Microsoft Excel, and Polymath are commonly utilized for these calculations [43, 44]. The investigation of the kinetic model is of utmost relevance, as it enables a deeper understanding of the process. It is postulated that three consecutive adsorption stages occur as follows: firstly, adsorbate ions undergo film diffusion toward the external surface of the adsorbent. Then, particle diffusion takes place, where adsorbate ions migrate through the pores of the adsorbent, excluding some adsorption on the external surface. Finally, the adsorbate ions are adsorbed onto the inner surface of the adsorbent.

In this study, we report the eco-friendly and facile synthesis of quaternary ammonium functionalized silica. The adsorption and the kinetic modeling were easily achieved by the help of the libraries PUPAIM and PUPAK of the R software.

2 Experimental

2.1 Materials

All reagents were handled under the hood, while wearing PPE, including a lab coat, gloves, and eye protection. Tetraethoxysilane (TEOS) (98%), Cetyltrimethylammonium bromide (CTAB) (98%), 1-propanol (99.5%), acetic acid (99%), hydrogen chloride (37%) were used as received.

2.2 Synthesis

The synthesized material was named S-CTAB, it was obtained by the sol gel method which was conducted at 35 °C. First, we add 1.48 g of CTAB and acetic acid to a mixture of 38 mL of water and 2 mL of propanol. The solution was stirred for 30 min, followed by the addition of TEOS. The solution was kept under stirring until gelification. The molar composition was 1 TEOS, 26.33 H2O, 0.05 CTAB, 0.345 propanol, 1 acetic acid.

The obtained gel was kept in the reaction medium for additional 24 h. Next, it was aged in a Teflon-lined autoclave at 120 °C for 24 h. Finally, it was oven dried at 120 °C for 24 h.

2.3 Chromium uptake experiments

A series of batch adsorption studies have been conducted to evaluate the material’s adsorption properties. A Cr(IV) solution with a concentration of 1 g/L was prepared using K2Cr2O7. Subsequent solutions for the experiments were derived from this stock solution through appropriate dilutions.

In the adsorption experimental process, 10 mL of the Cr(IV) solution were mixed with 20 mg of S-CTAB. The mixture was shaken for a specified duration. Following that, the samples were filtered through 0.45 m membranes while keeping the solid phase, called S-CTAB-Cr. The remaining concentration of Cr(VI) ions in the filtrate was measured using a UV–Visible spectrometer with a maximum absorbance peak at 540 nm, employing the 1,5-diphenylcarbazide method as detailed in ISO 11083:1994. The efficiency removal of Cr(VI) was evaluated by the percentage removal noted as RE%, it was calculated via Eq. (1):

$${{\rm{RE}}} \% =\frac{{C}_{0}-{C}_{{{\rm{eq}}}}}{{C}_{0}}$$
(1)

C0 and Ceq are, respectively, the initial and equilibrium concentrations (mg/L) of Cr(VI) ions.

The uptake capacity of each solid in removing Cr(VI) ions at any time t (qt) were determined using Eq. (2):

$$\,{q}_{t}=\frac{\left({C}_{0}-C(t)\right)V}{m}$$
(2)

where qt (mg/g) represents time dependent Cr(VI) removal capacity. C0 and C(t) are the liquid phase concentration of Cr(IV) at the initial concentration and at any time t(s), respectively. m(g) is the adsorbent dose and V (L) is the volume of Cr(IV) solution.

All samples with concentrations below the WHO limit have been evacuated into the sanitation circuit [45]. Filtrates with concentrations greater than 50 μg/L have undergone an additional adsorption step with the same material to the required concentration.

pH studies were conducted at various values (1.0, 2.0, 5.1, and 8.2) by mixing 0.02 g of S-CTAB adsorbent with 10 mL of an aqueous solution containing 100 mg/L of Cr(VI) ions. These solutions were shaken for 60 min at 298.15 K.

To investigate the impact of adsorbent amounts, different quantities of S-CTAB (0.01, 0.02, and 0.03 g) were tested to establish the relationship between the adsorbent dosage and the quantity of Cr(VI) ions adsorbed.

For the temperature effect study, 0.02 g of S-CTAB adsorbent was mixed with 10 mL of a 100 mg/L Cr(VI) ion solution at a pH of 2.0. All suspensions were stirred for 60 min at temperatures of (15 ± 0.01), (25 ± 0.01), and (35 ± 0.01) °C, respectively.

2.4 Isotherm models and data evaluation

Adsorption isotherms served as a pivotal tool in investigating experimental data concerning Cr(VI) ions and their interaction with the adsorbent surface. These isotherms facilitate understanding the interplay between the quantity of adsorbed material on the solid surface and the ion concentration in the solution at phase equilibrium. Various isotherm models, differing in parameter counts, were employed to ascertain the most fitting model for the experimental data. This in-depth analysis covered two-parameter models such as Langmuir, Freundlich, Dubinin–Radushkevich, Temkin, Jovanovic, and Harkin–Jura, three-parameter models: Langmuir–Freundlich, Khan, Redlich–Peterson, Hill, Toth, and Sips, as well as four-parameter models: Fritz–Schlunder and Weber–Van Vliet. This rigorous approach was adopted to determine the optimal alignment of these models with the experimental data. The equation for each model is described in detail below. Within all these models, qeq symbolizes the adsorbate amount at equilibrium, while Ceq signifies the chromium solution concentration at equilibrium.

We used the PUPAIM library [46] built within the R software to evaluate each model’s validity in relation to the experimental data. The values for each model parameter were computed. Diverse statistical metrics were determined, including the adjusted coefficient of determination (adjusted R2), residual-root-mean-square (RMSE), F-statistic, p value, and AIC (Akaike’s information criterion). The adjusted R2 is related to the accordance between the experimentally observed adsorbed amount at equilibrium (qeq,exp) and the corresponding calculated value from the model (qeq,cal). The RMSE measures the agreement between the model’s calculated value (qeq,cal) and the experimental amount (qeq,exp).

Evaluating adjusted R2, RMSE, F-statistic, and p value values aids in determining the most accurate model that aptly describes the adsorption of chromium ions on the quaternary ammonium functionalized silica surface. The best fitting model is characterized by a higher adjusted R2 value (approaching 1) [47]. In this study, we opted to set the risk threshold at 1%, thereby requiring a p value below 0.01. To enhance our statistical analysis, we also conducted comparisons using AIC and AICcorrected for selected models. We employed Akaike’s Information Criterion (AIC) to gauge the effectiveness of the models independently of the model’s parameter count, where a smaller value indicates a better fit to the data. AIC serves as a valuable tool for model selection by weighing both model fit and complexity, allowing for a fair assessment of model performance regardless of the number of parameter variations. This statistical metric was derived from the software. When the dataset comprises fewer than 40 data points, the utilization of AICcorrected is recommended. This criterion is defined as follows: \({{{\rm{AIC}}}}_{{{\rm{corrected}}}}={{\rm{AIC}}}+\frac{2K(K+1)}{N-K-1}\) with K the number of parameters, and N the number of data points. Despite its significance and accuracy, this statistical parameter is not as commonly employed as it should be [44]. The PUPAK and PUPAIM libraries provide easy access to this parameter, without the need for additional steps unlike many other softwares. The theory of the different adsorption models are detailed in the supporting material.

2.5 Kinetic study

The kinetic investigations were conducted within a temperature-controlled thermostatic water bath shaker. Initially, 10 mL of a chromium ion solution was mixed with 20 mg of S-CTAB and agitated for durations ranging from 5 to 360 min. At specific time intervals, the adsorbent was separated from the solution via filtration. The concentration of chromium ions was quantified using a UV-Visible spectrometer employing the 1,5-diphenylcarbazide method.

It was generally assumed that the adsorption process follows three primary stages. The first involves the external mass transfer of the adsorbate from the solution to the external surface of the adsorbent. The second stage comprises the internal diffusion of the adsorbate to the sorption sites, and the final stage involves their adherence to these sites [48]. Utilizing various models for fitting, we aimed to elucidate the most probable adsorption mechanism by determining the rate of the limiting step, which could be either the adsorption or the diffusion step. Herein, different kinetic and diffusion models are detailed in the supporting material.

2.6 Antibacterial experiment

The comparative antibacterial activities of S-CTAB before and after chromium loading, noted S-CTAB-Cr were screened against four bacterial strains obtained from American Type Culture Collection (ATCC) and the local culture collection of the Centre of Biotechnology of Sfax. They included: a Gram-positive bacteria: Bacillus subtilis ATCC 6633 and two Gram-negative bacteria: Salmonella enteritidis (food isolate) and Escherichia coli ATCC 25922. LB medium (Luria Bertani Broth), was used for the preparation of the pre-inoculum [49] at 37 °C for 12–14 h. For the antibacterial test, the turbidity of the overnight broth was adjusted by Densimat spectrophotometer (BioMérieux, Italy) and diluted in LB broth to a final inoculum concentration of 107 CFU/mL. Antimicrobial test was performed by agar well diffusion method as described by Tagg and McGiven using sterile LB medium. A total of 100 μL of a fresh cell suspension (107 CFU/mL) were inoculated into the surface of agar plates [50]. Then, wells with 6 mm of diameter were perforated in the inoculated agar medium using sterile Pasteur pipettes and the extracts were added to each well. Negative control consisted of a mixture of 50% DMSO and 50% distilled water was used to dissolve S-CTAB and S-CTAB-Cr with a final concentration of 35 mg/mL. Gentamicin (30 μg/well) was taken as the standard antibiotic. The plate was allowed to stand for 2 h at 4 °C to permit the diffusion of the extracts followed by incubation at 37 °C for 24 h in a bacteriological incubator. The antibacterial activity was evaluated by measuring manually the zones of inhibition (clear zone around the well) against the tested micro-organisms. All tests were done in triplicate.

2.7 Characterization

The N2 adsorption isotherm was conducted using a Micromeritics 2100 automatic apparatus at 77 K. Prior to the measurement of the isotherm, the adsorbent underwent a degassing process at a temperature of 120 °C for a duration of 12 h. FTIR–ATR spectra of the materials were recorded with a Thermo Scientific Nicolet 6700/Smart iTR spectrophotometer in the range of 500 to 4000 cm−1. Microstructure and morphology of the solid was carried out using Thermo Scientific™ Q250 Analytical SEM operating at 15 kV combined with a powerful EDS detector. The elemental analysis is provided by the UltraDry EDS Detector and Pathfinder Software. UV–Visible spectrophotometer is used for the quantifying the concentration of chromium at equilibrium. We used a HANON i3 spectrophotometer.

The determination of the Point of zero charge (PZC) corresponding to our synthesized silica was carried out as follows: 100 mL of 0.01 M NaCl solution was placed in a closed Erlenmeyer flask. Solutions with different pH ranged between 2 and 12 were prepared by adding HCl (0.1 M) or NaOH (0.1 M) solutions. Then 50 mg of silica sample was added to each solution. After 48 h under agitation at room temperature, the final pH was measured.

3 Results and discussion

3.1 Physisorption of N2

Figure 1 presents the N2 adsorption isotherms and pore size distribution of the developed adsorbent. According to the data, the specific surface area measures 222 m2/g, with a pore volume of 0.267 cm3/g. Notably, the isotherm displays a characteristic IUPAC type IV pattern, indicative of a mesoporous solid. Additionally, the adsorbent exhibits a type H2 hysteresis, typical of structures with narrow access pores and wide pore bodies known as bottlenecks. The BJH pore size distribution shows the presence of two different sizes of porosity: mesopores with a diameter of 51 Å and micropores. It is plausible to assume that the produced adsorbent is mesoporous.

Fig. 1
figure 1

a N2 adsorption-desorption isotherm and b pore size distribution of the adsorbent S-CTAB

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3.2 FTIR spectroscopy

FTIR spectroscopy is a valuable tool for characterizing functionalized silica. Figure 2a presents the spectrum of the S-CTAB material. Figure 2b depicts the FTIR spectra of the adsorbent loaded with chromium in the range from 400 to 1500 cm−1, after the uptake of Cr(VI) ions. As can be seen in Fig. 2a, the broad band centered at 3240 cm−1 is assigned to the hydrogen bonded silanol groups. The shoulder noted at 3630 cm−1 is relative to isolated silanols. The band at 956 cm−1 is due to Si-OH stretching. At 1059 cm−1 a broad peak with a large shoulder at 1223 cm−1 are noted, which correspond to the siloxan units vibrations (SiO)n− [51, 52]. The bands at 797 cm−1 and 442 cm−1 are respectively attributed to Si-O-Si stretching and Si-O-Si bending [53]. The existence of these bands demonstrates the presence of silica framework with silanol groups [54].

Fig. 2
figure 2

FTIR spectra of (a) the adsorbent S-CTAB and (b) the material S-CTAB-Cr

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The spectrum also shows a week band at 720 cm−1 which is attributed to the rocking vibration of (CH2)n with n > 2 [55]. Moreover, Fig. 2a reveals the presence of bands at 2852 and 2922 cm−1 which are respectively assigned to the symmetric and asymmetric stretching of C-H groups of CTAB alkyl tail. The week peak observed at 2956 cm−1 is associated to asymmetrical stretching of C-CH3 groups and symmetrical stretching of N–CH3. This figure also reveals weak peaks centered at 1468 cm−1 attributed to C-H bending in CH3 group and the asymmetric deformation mode of CH3–N+ of the CTAB head group [56]. The existence of CTAB in the silica framework is confirmed by the occurrence of all these peaks.

After chromium ions loading, the spectrum shown in Fig. 2b reveals the presence of the same bands listed before and the emergence of a new band situated in 895 indicative of the Cr-O group [39]. These results confirm the adsorption of Cr(VI) ions on silica functionalized with CTAB.

3.3 Point of zero charge

The dependence of surface charge with pH can be obtained from the graphical representation of the variation of pH versus the initial pH of NaCl solutions, which is presented in Fig. 3.

Fig. 3
figure 3

Determination of point of zero charge of the silica material S-CTAB

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Figure 3 indicates that the point of zero charge is found to be 2.4. At pH values below 2.4, the silica surface is positively charged, while at pH values higher than 2.4, the surface is negatively charged.

The point of zero charge of pure silica material has been reported to be around 2 and does not surpass 3.5, depending on crystallinity and purity [57, 58]. In this work, it seems that PZC is not significantly affected by the presence of CTAB molecules. The main portion of surfactant molecules is likely gathered into micelles and incorporated into the silica framework. Likewise, a small portion of CTAB might only be kept on the surface. Therefore, the silica surface’s acid-base properties are not significantly influenced by the quaternary ammonium head repartition.

3.4 SEM images

The SEM micrographs of the silica materials are represented in Fig. 4.

Fig. 4
figure 4

SEM images of the synthesized material S-CTAB: (a) low magnification, (b) medium magnification and (c) high magnification.

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The surface morphology of S-CTAB was examined using scanning electron microscopic (SEM) analysis and energy dispersive x-ray analysis (EDX). Initially, it’s evident that the surface of all silica particles appears remarkably smooth (Fig. 4a, b). In addition, all structures share the presence of clearly defined stripe patterns, regardless of their size or shape. This observation might indicate the existence of extensive internal channels within the structures [38]. At higher magnification (Fig. 4c), the overlapping of planes along the same direction becomes notably evident. In the upper left portion of the image, the distance between these planes was estimated using ImageJ. Proceeding from left to right, the distances between the planes measure 11.35, 10.59, and 8.74 µm, respectively.

Additionally, the adsorbent exhibits an irregular morphology characterized by small-sized particles ranging from 2 to 53.4 μm, as well as larger-sized particles featuring craters and cavities that offer efficient active sites and a substantial contact area. Furthermore, a variety of morphologies were seen, including wafers, elongated, thin rods, and voids of different sizes, all of which pointed to the substance’s porous nature.

EDX spectra were used to determine the adsorbent’s composition, and the findings are shown in Fig. 5. The theoretical concentration of CTAB is 0.635 mmol/g, while the determined concentration based on the results of the EDX study is 0.697 mmol/g.

Fig. 5
figure 5

Elemental analysis of silica material S-CTAB

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3.5 Chromium uptake experiments

The pH of the system affects the removal percentage by influencing the charge density of the adsorbent and the ionic forms of chromium ions in the solution. The results, shown in Fig. 6, indicate that the initial pH of the Cr(VI) solution significantly impacts the removal percentage, with maximum adsorption occurring at a pH of 2.0. This finding aligns with the point of zero charge of the adsorbent, which is 2.4. At pH values below 2.4, the silica surface is positively charged, whereas at pH values above 2.4, the surface is negatively charged.

Fig. 6
figure 6

Effect of pH on Cr(VI) removal. Experiment conditions: initial Cr(VI) concentration = 100 mg/L, adsorbent dosage 2 g/L, temperature = 25 °C and contact time 60 min

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When the pH is below 2.4, the adsorbent surface becomes more positively charged, increasing electrostatic attraction between the surface and the predominant HCrO4− species. However, the removal percentage decreases at pH values below 2. Under these conditions, the electrostatic attraction between the adsorbent surface and Cr(VI) was much lower, as Cr(VI) mainly existed in the form of HCrO4− and H2CrO4 [59, 60]. Conversely, at pH values above 2, the surface becomes less positively charged, leading to reduced metal uptake. Therefore, a pH of 2.0 was selected as the optimum value for further studies.

The effect of adsorbent dosage on adsorption was assessed within the range of 1–3 g/L by measuring the adsorption percentage. The adsorbent was dispersed in a Cr(VI) solution (100 mg/L) at 25 °C for 60 min. The results depicting the relationship between adsorption percentage and adsorbent dosage are illustrated in Fig. 7.

Fig. 7
figure 7

Effect of adsorbent dosage on Cr(VI) removal. Experimental conditions: initial concentration 100 mg/L, T = 25 °C and contact time = 60 min

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The results demonstrated that increasing the adsorbent dosage from 1 to 3 g/L significantly enhanced the adsorption percentage, rising from 68.8 to 81.3%. This improvement in removal efficiency is attributed to the increased availability of binding sites, which facilitated the removal of 81.3% of chromium ions within just 1 h from an initially high concentration solution of 100 mg/L.

The influence of the temperature on the removal percentage was explored in the range 15–35 ± 0.01 °C. The obtained results are shown in Fig. 8. As can be seen, the percentage removal increases while the temperature rises from 15 to 35 °C. These findings are consistent with the literature [35]. It is noticeable that the removal percentages at 25 and 35 °C, which are 72.4% and 74.6%, respectively, are rather close. Throughout this experiment, we maintain the following values: a pH of 2, an adsorbent dosage of 2 g/L, and a temperature of 25 °C.

Fig. 8
figure 8

Effect of the temperature on the percentage of Cr(VI) adsorption with C0 = 100 mg/L, adsorbent dose = 2 g/L, contact time = 1 h

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During the investigation of the adsorption model, certain parameters were maintained at constant levels: the ratio (m/V) was set to 2 g/L, the contact time remained fixed at 60 min, and the pH of the chromium solution was maintained at pH 2. The chromium solutions employed covered an initial concentration range spanning from 20 mg/L to 600 mg/L. As per the subsequent equations, it is notable that at a pH value of 2, the predominant form of Cr(VI) species is the HCrO4− ion [61]:

$${{\rm{H}}}_{2}{{{\rm{CrO}}}}_{4}\rightleftarrows {{{\rm{HCrO}}}}_{4}^{-}+{{\rm{H}}}^{+}\,\,\,{{{K}}}_{1}=1.58\times{10}^{-1}$$
$${{{\rm{HCrO}}}}_{4}^{-}\rightleftarrows {{{\rm{CrO}}}}_{4}^{2-}+{{\rm{H}}}^{+}\,\,\,{{{K}}}_{2}=3.16\times{10}^{-7}$$
$${2{{\rm{HCrO}}}}_{4}^{-}\rightleftarrows {{{{\rm{Cr}}}}_{2}{\rm{O}}}_{7}^{2-}+{{\rm{H}}}_{2}{\rm{O}}\,\,\,{{{K}}}_{3}=3.31\times10$$
$${{{{\rm{HCr}}}}_{2}{\rm{O}}}_{7}^{-}\rightleftarrows {{{{\rm{Cr}}}}_{2}{\rm{O}}}_{7}^{2-}+{H}^{+}\,\,\,{K}_{4}=1.17$$

Figure 9 presents the evolution of the adsorbed amount of chromium (a) and the adsorption percentage (b) with the initial concentration.

Fig. 9
figure 9

Evolution of (a) adsorbed amount and (b) the percentage removal with initial concentration solution of Cr(VI)

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A significant increase in the amount adsorbed is seen at lower concentrations (below 150 mg/L), highlighting quick adsorption kinetics within this concentration range. Additionally, Fig. 6b illustrates that a remarkable removal of 99% of Cr(VI) ions from starting solutions takes place when initial concentrations range from 20 mg/L to 50 mg/L.

Whereas, the adsorbed quantity increases gradually and reaches an equilibrium at 57 mg/g as concentrations rise beyond 300 mg/L. Notably, at an initial solution concentration of 600 mg/L, only 19% of Cr(VI) ions are removed. This decline in adsorption percentage could be attributed to the saturation of the adsorbent surface by HCrO4− ions.

The adsorption mechanism supporting the interaction between chromium ions and quaternary ammonium functionalized silica is fundamentally based on electrostatic forces. This interaction occurs between the positively charged sites at the surface and the negatively charged Cr(VI) ions [41, 62]. At a pH of 2, the surface exhibits a composition characterized by two distinct categories of positively charged adsorption sites: Si-OH2+ and N(CH3)3+. During the initial period, these positively charged sites are quickly saturated as they become occupied by the negatively charged chromium ions. A schematic illustration of this process is presented in Schema 1.

Schema 1
scheme 1

Schematic illustration of Cr(VI) adsorption on quaternary ammonium functionalized silica at pH= 2

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A comparison of the outcomes from previous studies and those obtained in this current research is consolidated in Table 1.

Table 1 Comparison of adsorption capacity and conditions between previous studies and this work
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In comparison to prior investigations focused on chromium removal with silica based materials, it becomes evident that quaternary functionalized silica facilitates significant adsorption after just 60 min from a solution reaching a concentration of 600 mg/L of Cr(VI) ions. The interest of this material lies in its quick adsorption when removing chromium from highly charged solutions.

Table 2 exhibits the results of modeling for two-parameter models: Langmuir, Freundlich, Temkin, Dubinin–Radushkevich, Harkin–Jura and Jovanovic. Here, qeq (mg/g) represents the equilibrium adsorption capacity for Cr(VI) and Ceq (mg/L) is the concentration of the remaining Cr(VI) at equilibrium.

Table 2 Adsorption isotherm constants for two parameters models with adjusted R2, RMSE, F-statistic, p value, AIC and AICcorrected
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Table 2 reveals the Dubinin–Radushkevich model with the lowest adjusted R2 value (0.7886). Moreover, the F-statistic for this model is notably lower in comparison to values obtained for other models, while the RMSE is relatively high. These outcomes collectively suggest the inadequacy of the Dubinin–Radushkevich model in effectively depicting the adsorption mechanism of chromium ions. Consequently, this model was excluded from the subsequent model comparison, and it will not be taken into consideration in the following sections.

Among the residual models, a p value lower than 0.01 was observed. Furthermore, the order of correlation capability among the different models, as indicated by adjusted R2, RMSE, and F-statistic, follows a descending pattern: Temkin, Freundlich, Harkin–Jura, Jovanovic, and Langmuir. Notably, the Temkin model emerges with the highest adjusted R2 and F-statistic, along with the lowest RMSE. Consequently, Temkin model stands out among the two-parameter models as being able to accurately describe the alignment with the experimental data.

The comparison between the values found for AIC and AICcorrected leads in the increasing order to: Temkin, Freundlich, Jovanovic, Harkin–Jura, and Langmuir. This order is the same as the one found before for the comparison of adjusted R2 and F-statistic. Thus, it is very clear that Temkin isotherm model has the lowest AICcorrected value, which is closely followed by Freundlich model. This confirms that this model is better suited to describe the adsorption mechanism of chromium ions than the other isotherm models with two-parameters considered in this study.

Temkin isotherm model assumes the existence of relation between the adsorbate-adsorbent interactions, as it takes into account the effects of indirect adsorbate/adsorbate interactions on the relative operation. In the equation model, the constant AT represents the Temkin isotherm equilibrium binding constant, while the constant \(\frac{R\bullet T}{{b}_{T}}\) represents the adsorption heat (J/mol), which can be calculated from the value of \({b}_{T}\). At 298 K, the adsorption heat is equal to 2.257 J/mol. This heat is less than 8 kJ/mol, which indicates that adsorption occurs via physical interactions [63].

Freundlich model could also represents well the adsorption system since the adjusted R2 and F-statistic are very close to those found for Temkin isotherm model. This feature assumes that adsorption process occurs via multilayer on heterogeneous sites, each of which is homogeneous. From Table 2, nF is equal to 8.066, which is higher than 1, this demonstrates once again that adsorption process occurs via physical interactions. \(\frac{1}{{nF}}\) value is related to the adsorption intensity, it is equal to 0.124. As seen, it is ranged between 0 and 1, which indicates a favorable adsorption. Besides, \(\frac{1}{{nF}}\) value is near 0, this shows the high heterogeneity of the adsorption sites [44, 64].

In the next step, we applied the experimental data for three-parameter models: Langmuir–Freundlich, Khan, Redlich–Peterson, Hill, Toth, and Sips. The constants of each model with the adjusted R2 RMSE, F-statistic and the p value are resumed in Table 3.

Table 3 Adsorption isotherm constants for three-parameters models with adjusted R2, RMSE, F-statistic, p value, AIC and AICcorrected
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From Table 3, it can be seen that for all tested models the adjusted R2 are higher than 0.8, F-statistic is high and ranged between 37.87 and 95.42, and the p value are too small and less than 0.01. The most accurate model is the one that presents the highest adjusted R2 value and F-statistic and the lowest RMSE. Considering this condition, the order of accuracy is the following: Khan, Redlich–Peterson, Sips, Hill, Toth and Langmuir–Freundlich.

The comparison between the AICcorrected values also allows to classify the tested models in the decreasing order of accuracy as follows: Redlich–Peterson, Khan, Sips, Hill, Toth and Langmuir–Freundlich. As seen, this order of fitting to the experimental data isn’t the same as found in the comparison based on adjusted R2 and F-statistic. The models Redlich–Peterson and Khan are inverted. We can deduce that, considering three parameters models, Khan and Redlich–Peterson models could predict the adsorption mechanism significantly well. Table 4 presents the modeling results for four-parameter models: Fritz–Schlunder and Weber–Van Vliet.

Table 4 Adsorption isotherm constants for four parameters models with adjusted R2, RMSE, F-statistic, p value, AIC and AICcorrected
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From Table 4, it can be seen for both models, the adjusted R2 are higher than 0.9255, the F-statistic is elevated and the p value are too small and less than 0.01. The obtained values of adjusted R2 and F-statistic demonstrate that Fritz–Schlunder could better describe the adsorption mechanism than Weber–Van Vliet model. The comparison between the values of AIC and AICcorrected reveals that the lowest values are found for Fritz–Schlunder isotherm.

We can deduce that, considering the studied four parameters models, Fritz–Schlunder isotherm model can provide a better description than Weber–Van Vliet model for chromium adsorption.

Table 5 resumes the best models fittings considering the number of parameters.

Table 5 Comparison between the best fitting models with different parameters number
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The comparison between the adjusted R2 values, RMSE and F-statistic showed that the models are classified in descending order: Khan, Redlich–Peterson, Fritz–Schlunder, Temkin and Freundlich. We can conclude that Khan model provides the best fit to the experimental data. Additionally, it’s worth noting that the statistical parameters for Khan and Redlich–Peterson models are close.

3.6 Adsorption kinetic

The adsorption capacity of Cr(VI) ions and the percentage removal with quaternary functionalized silica versus the contact time are presented in Fig. 10. As shown, both the adsorbed amount and the adsorption percentage increased quickly during the first hour. The slope of each graph is steep; they reached respectively, 35 mg/g and 72%.

Fig. 10
figure 10

Effect of contact time on the adsorption capacity of Cr(VI) ions (qt) and the percentage removal with functionalized silica

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Moreover, the chromium ions loading can be highlighted visually. In the first 5 min, the solid’s color changes from white to yellow. Later after an hour, the color becomes more intense. These findings point out the high affinity between chromium ions and the adsorption sites. Next, as the adsorption on the solid continues as a function of contact time, the solid’s color becomes more intense changing, to a light brown, as seen in Fig. 10. After 6 h of contact, 97% of chromium ions were adsorbed and the capacity reached 47.73 mg/g.

In order to investigate the kinetic of the adsorption mechanism, the experimental data were modeled using theoretical models. Among them, we used pseudo-first order, pseudo-second order, Elovich, Weber–Morris Diffusion model and Boyd external diffusion model. In this work, the linear modeling was achieved using software R with the PUPAK library. The obtained parameters for each model and the statistical results are gathered in Table 6. The corresponding plot for each model is represented in Fig. 11.

Table 6 Kinetic models parameters and their corresponding statistical results
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Fig. 11
figure 11

Kinetic models for the adsorption of chromium ions on quaternary ammonium functionalized silica, a pseudo-first order, b pseudo-second order, c Elovich model, d Weber–Morris model, e Boyd external diffusion

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The pseudo-second order kinetic model has a high adjusted R2 (0.9949), a low RMSE, and a low AIC, according to an analysis of the statistical results of the pseudo-first, pseudo-second order, and Elovich models in Table 6. These findings demonstrate that this model, followed by the pseudo-first order and Elovich, best fits the experimental data. The mass transfer into the interior of the particle was evaluated using Weber–Morris Model. In Fig. 11d, two distinct linear segments are evident. The initial linear portion signifies the swift and immediate adsorption phase, specifically adsorption occurring on the external surface. The subsequent segment depicts gradual adsorption, indicating the intraparticle diffusion process occurring across the boundary layer. This phase could potentially act as the limiting stage within the adsorption mechanism. The effectiveness of the Boyd external diffusion model in explaining the adsorption process was limited, as evidenced by the relatively low linear regression coefficient R2 value of approximately 0.8258. Furthermore, various researchers have proposed that external diffusion is an unlikely route for adsorption. It’s important to note that the influence of transport is eliminated due to the constant agitation of the solution.

Based on these results, it is conceivable that initially, chromium ions are swiftly and readily adsorbed onto the available cationic sites on the outer surface. The rapid adsorption rate can be partly attributed to the presence of mesopores in the adsorbent, which are accessible to the adsorbate. The textural properties of S-CTAB confirm its mesoporous character, with a pore diameter of 51 Å. Consequently, a rapid pseudo-second-order surface reaction occurs, suggesting that sorption mechanism involves a chemisorption acting as the rate-limiting step. The adsorption capacity predominantly relies on the active surface sites of the adsorbent.

As contact time increases, the outer surface reaches its saturation point, and the particle becomes enveloped by a boundary layer of adsorbed ions, slowing the adsorption rate due to the decreasing number of active sites on the surface. This marks the initiation of a gradual diffusion process toward the less accessible sites within the particle. Based on the pore size distribution shown in Fig. 1b, the adsorbent also exhibits micropores, which likely represent the less accessible active sites. Over time, HCrO4− ions are electrostatically attracted to the cationic sites within these micropores. In correlation with the Weber–Morris model, the two linear regions identified in Fig. 11d could correspond respectively, to the boundary layer diffusion of the adsorbate on the external surface and the adsorption due to intraparticle diffusion. These findings indicate that intraparticle diffusion is not the sole rate-limiting mechanism in the Cr(VI) adsorption process. The values of the intraparticle diffusion model parameters are summarized in Table 6. The highest intraparticle diffusion rate constant corresponds to the first stage (kw1), indicating that film diffusion of Cr(VI) is relatively fast. The rate constant kw2 observed in the second stage is lower, suggesting that intraparticle diffusion occurs at a slower rate, making it the plausible limiting stage of adsorption. As observed in Fig. 11d, this phase starts after a contact duration of 225 min.

Therefore, the adsorption process of chromium ions onto quaternary ammonium-functionalized silica evolves over time and becomes governed by the availability of active accessible sites. Initially, there is a rapid adsorption stage characterized by a pseudo-second-order reaction, indicating the chemisorption of Cr(VI) ions on the easily accessible active sites, primarily on the surface and within the mesopores. After 225 min, the adsorption mechanism shifts to a diffusion phase, consistent with the Weber-Morris model. During this phase, adsorption predominantly occurs at the less accessible active sites located within the micropores.

3.7 Recycling studies

Han et al. [39] studied the influence of the concentration of NaOH solution used for regeneration, on silica sorbent containing NH groups loaded with Cr(VI) ions, in a domain ranged between 1 M and 0.001 M. It was found that the optimal concentration for regeneration is equal to 0.005 M. This concentration was adopted in this work with an adsorbent dose of 1 g/L, and the results found are represented in Fig. 12.

Fig. 12
figure 12

Evolution of the adsorption percentage upon four cycles. Experimental conditions: pH = 2, adsorbent dose = 2 g/L, Cr(VI) solution concentration = 100 mg/L, contact time = 60 min

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After each recycling cycle, there is a slight decline in the adsorption percentage. Following the initial cycle, only a minor decrease is observed, stabilizing at 70.3%. By the fourth cycle, the adsorbent shows a removal percentage of approximately 50% for Cr(VI) ions. These results indicate an effective regeneration cycle of the ammonium functionalized silica.

3.8 Antibacterial activity

Previously, CTAB has demonstrated its efficacy as a powerful agent against a spectrum of microorganisms, including bacteria, fungi and viruses, across a versatile range of concentrations [65, 66]. Furthermore, it has recently been demonstrated that CTAB could also be utilized as a grazer pesticide in microalgal cultures, even at low concentrations of 3 µM [67]. The incorporation of CTAB molecules into silica framework, which are well-known for their interesting antibacterial properties, adds an innovative dimension to our work. A question can be asked: What happens when this material is put in contact with bacteria? The answer to this question stands to guide us in the choice of other potential applications of this material. Furthermore, another path opens up, encouraging us to explore the anti-bacterial properties of chromium-charged silica, a new material resulting from the interaction with HCrO4− ions.

The antibacterial activities of the hybrid silica materials before and after chromium ions loading (S-CTAB and S-CTAB-Cr) were investigated for three pathogenic bacteria (one Gram-positive and two Gram-negative). The results are shown in Table 7 and Fig. 13.

Table 7 Inhibition zone (in mm) of the antibacterial activity of S-CTAB and S-CTAB-Cr compared with standard antibiotic
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Fig. 13
figure 13

Antimicrobial activity (zone of inhibition) of S-CTAB and S-CTAB-Cr against Bacillus Subtilis (a), Escherichia Coli (b) and Salmonella (c)

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In the current study, the obtained results for the antibacterial activity of S-CTAB and S-CTAB-Cr were compared with the standard antibiotic gentamycin (Table 7).

Table 7 and Fig. 13 show that both S-CTAB and S-CTAB-Cr are active against the three tested bacteria. Besides, it can be seen that inhibition zones are close to the results found with the standard antibiotic with gram-negative and gram-positive bacteria.

The quaternary ammonium agent has demonstrated antibacterial activity against the studied microorganisms even after immobilization in the siliceous framework. After chromium uptake, the obtained material conserves its antibacterial activity against the considered microorganisms. The interaction of the quaternary ammonium compounds with cell membranes is the fundamental cause of their toxicity toward living cells. This interaction happens as the positively-charged quaternary ammonium head of CTAB entwines with the negatively-charged phospholipids of the plasma membrane. After that, the hydrophobic tail of the active agent gets into the lipid bilayer through hydrophobic exclusion. These series of events set up a significant change in the integrity of the membrane, which culminates in the expulsion of intracellular components and, unavoidably, directs the path toward cellular death [67].

Hence, both materials hold great promise for applications with a high risk of bacterial cross-contamination. They could be utilized for surfaces coatings that are bacterially exposed.

3.9 Economic cost

The operational cost of any effluent treatment method is a crucial factor in determining its feasibility for industrial-scale application. To evaluate the economic viability of the prepared adsorbent, we can compare its cost per gram of adsorbate removed with that of other well-established adsorbents [68]. This comparison allows us to evaluate the cost-effectiveness of the adsorption process. The cost per gram of adsorbate removed provides a practical measure for determining the overall expense of the adsorption operation, as illustrated in Eq. (3):

$${{\rm{Adsorption}}\; {\rm{cost}}}=\frac{{{\rm{Chemical}}\; {\rm{purchase}}\; {\rm{cost}}}+{{\rm{Energy}}\; {\rm{cost}}}}{{{\rm{Adsorption}}\; {\rm{capacity}}}\times {10}^{-3}}$$
(3)

Where the adsorption cost, chemical purchase cost, energy cost are respectively expressed in US$/gadsorbate, US$/g, US$/g, while, the adsorption capacity is expressed in mg/g. The estimation of the cost of our adsorbent is summarized in Table 8.

Table 8 Adsorption cost estimate of S-CTAB adsorbent
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According to the literature, hierarchical ZnS-Ga2S3 and chitosan/cellulose composites have been employed as adsorbents for Cr(VI) removal, with economic costs of 0.0895 US$/g and 0.62 US$/g, respectively [68].

The comparison reveals that the adsorption process for these adsorbents is cheaper than the calculated cost of the adsorbent S-CTAB. However, S-CTAB adsorbent loaded with Cr(VI) offers a distinct advantage: it can be utilized as an antibacterial agent, thereby preventing the creation of additional pollution.

4 Conclusion

The research examined the effectiveness of quaternary ammonium functionalized silica in removing Cr(VI). Additionally, isotherm and kinetic modeling were conducted using R software. The “PUPAIM” and “PUPAK” libraries proved to be valuable resources, enabling a comprehensive analysis of the modeling process. Moreover, in our pursuit of environmental responsibility, we deliberately selected a synthesis approach that aligns with this commitment by employing a one-step sol-gel synthesis method. This choice adheres to eco-friendly values, thereby yielding a solid material with a notably reduced carbon footprint. In order to eliminate solid waste after adsorption, the chromium charged adsorbent has been investigated for its potential as an antibacterial agent, aligning with the principles of a circular economy.

From this work, the following conclusions could be drawn:

  • The presence of CTAB molecules in the adsorbent was confirmed by FTIR. N2 physisorption indicated that S-CTAB exhibits a developed surface area and features two types of porosity: micropores and mesopores with a diameter of 51 Å. The point of zero charge was determined to be 2.4, indicating that the silica surface is positively charged at pH values below 2.4 and negatively charged at higher pH values. SEM images revealed irregular morphology with small particles ranging from 2 to 53.4 μm. Additionally, the material displayed a variety of structures, including wafers, elongated, thin rods, and voids of different sizes, all highlighting its porous nature.

  • The investigation of the effect of pH on chromium removal revealed that optimal adsorption pH is equal to 2. While exploring the effect of adsorbent dose and temperature on chromium removal, it was demonstrated that increasing the adsorbent dosage from 1 to 3 g/L significantly enhanced the removal efficiency. This is attributed to the increase in the available binding sites. While raising the temperature from 15 to 35 °C the percentage removal increases.

  • The newly developed adsorbent, S-CTAB, has demonstrated a remarkable capability for efficiently removing chromium from aqueous solutions. It achieved 99% elimination of this pollutant in solutions with concentrations below 50 mg/L, exhibiting a notable adsorption capacity of 57 mg/g. Furthermore, S-CTAB demonstrated effective regeneration through four cycles of reuse.

  • Utilizing the “PUPAIM” library within the R software, model fitting was extensively conducted using two, three, and four-parameter models. Upon comparing statistical parameters, Khan and Redlich–Peterson models emerged as the most suitable models for representing the experimental data, as evidenced by an adjusted-R2 value superior to 0.94 and a p value of 0.0006.

  • Kinetic modeling analysis using “PUPAK” library revealed that the pseudo-second order kinetic model offers the most favorable fit to the experimental data. It is plausible to assume that the initial adsorption of chromium ions promptly transpires at exposed cationic sites on the outer surface and into the mesopores, initiating a rapid pseudo-second-order surface reaction. As the contact time progresses, the saturation of the outer surface and the mesopores prompts the formation of an adsorbed ion boundary layer around the particle, initiating a gradual diffusion process toward less accessible sites within the particle, which are the micropores. Consequently, both the rapid pseudo-second-order adsorption and the subsequent diffusion process contribute to the overall mechanism of chromium ion adsorption onto quaternary ammonium functionalized silica.

  • Both materials, S-CTAB and S-CTAB-Cr, have exhibited antibacterial activity against the diverse tested bacteria, encompassing both positive and negative gram classifications. Considering these findings, these materials hold significant potential for applications where bacterial contaminations pose a substantial risk. As a potential application, these materials could be effectively employed for coating surfaces, offering a promising avenue for enhancing bacterial control and preventing contamination.