1 Introduction

The global population growth has led to a significant increase in the demand for freshwater, straining traditional sources like rivers, lakes, and groundwater. Industrial development has further exacerbated the issue by polluting these sources with heavy metals like lead, copper, chromium, and arsenic, posing environmental and health risks [1,2,3]. Therefore, it is essential to treat industrial and municipal wastewater to protect our conventional water sources. The severity of clean water scarcity especially in the deserts and rural areas of some developing countries cannot be overemphasized.

Arsenic (As) is a naturally occurring heavy metal found in the environment, ranking 20th in natural abundance [4]. Arsenic is considered one of the most harmful trace elements in the environment and it exists in both inorganic (iAs) and organic (oAs) forms, with its chemical form and concentration affecting its solubility, mobility, reactivity, bioavailability, and toxicity [5]. Increase in As levels in the soil over time are primarily caused by human activities such as uncontrolled industrial processes, using As in the production of tools, cosmetics, ornaments, pigments, coal-fired furnaces, glass, tanneries, mirror manufacturing, and its use in pesticides during the twentieth century [6]. In water, As presence is associated with natural processes including soil erosion, leaching from rocks, chemical reactions, biological activity, volcanic emissions, and industrial activities [7, 8].

Arsenic (As) contamination in water is a widespread issue globally. Groundwater and drinking water in many countries [9, 10], including India, Bangladesh, Malaysia, Mexico, Hungary, New Zealand, the USA, Spain, Japan, Canada, Taiwan, and Mainland China, have been impacted by As pollution. Long-term exposure to As in drinking water can increase the incidence of cancer of the skin, lung, liver, bladder, arsenicosis, dermal lesions, peripheral neuropathy, kidney, and prostate [11, 12]. Given the global extent of As contamination, it is essential to research and develop methods to understand As chemistry and remove it from water. Common methods for removing As include coagulation, flocculation, adsorption, ion exchange, membrane filtration, bioremediation, solar oxidation, and electrochemical treatments. Adsorption is particularly effective and cost-efficient due to its simplicity [13,14,15,16,17,18,19]. Several adsorbents, such as clay, polymers, biological materials, metal oxides, and composite materials, have shown potential for removing arsenic. Despite these advancements, there are still limitations to their use. As a result, there is a pressing need to create new and effective adsorbents that can efficiently remove As from water.

The literature surveys have revealed that numerous researchers consistently strive to develop effective and efficient materials for eliminating heavy metals [15,16,17], including As pollutants, from wastewater often discharged by industrial production processes. Some of these works explored the use of metal–organic frameworks [20, 21], biochar [17, 22, 23], molybdenum-iron nanosheets [24], and other carbon-based materials [15, 16, 25,26,27,28]. Among the works is Mojiri et al. [29] that used mineral or clay-based adsorbents like bentonites and zeolites to eliminate As from polluted water, which was similar to the work of Egbosiuba et al. [30], which used kaolin clay to eliminate As from wastewater with an adsorption capability of 337.22 mg/g. Another is Hua [31] that confirms the effectiveness of modified bentonite using manganese oxide and poly-dimethyl diallyl ammonium-chloride for eliminating As from wastewater. A biobased adsorbent was also synthesized by Guisela et al. [13] from eucalyptus bark (a readily available material) using an acid treatment, which shows an adsorption capacity of 0.944 mg/g in their studies. The bulk of the works in the literature have consistently focused more on the deployment of experimental approaches in their studies for As elimination from wastewater. Only a few of the works [32,33,34] deployed either computational or hybrid approaches in their investigation. Some of these theoretical studies explored metallic oxides like calcium oxides, iron oxides, and other related sorbents. Wijaj et al. [35] studied the interaction trends of doping elements on the periodic table with graphene sheets. However, a detailed report for the adsorption mechanism is not reported in the report. Among the few computational studies that explored As adsorption, there are insignificant reports accounting for the molecular-scale details of As adsorption on graphene-based surfaces or membranes.

This study advance upon existing computational methods for designing efficient adsorbents and provide deeper insights into the adsorption mechanisms on graphene-based materials, integrating computational and theoretical approaches to optimize the adsorption of As at the molecular level. Specifically, we employ Density Functional Theory (DFT) and the Parametric Method 3 (PM3) calculations to evaluate the interaction between arsenic and graphene, considering adsorption in both vacuum and aqueous environments. By analyzing key properties such as adsorption energy, adsorption geometry, this work contributes to the development of advanced adsorbents and focus on offering computational insights that can complement experimental efforts, addressing critical challenges in environmental remediation strategies with greater precision and efficiency.

2 Computational methodology and details

This section presents the overall approach to the research objective which includes the study strategy, adsorption energy analysis, and other computational details employed in our study.

2.1 Study strategy

Here, we explored the various adsorption mechanisms taking advantage of all possible adsorption sites, which include the top edge and center (TE/TC) sites, the bridge edge and center (BE/BC) sites, and the hollow edge and center (HE/HC) sites. Schematic diagrams illustrating the molecular structure of each mechanism of adsorption before geometry (or structural) optimization are presented in Fig. 1.

Fig. 1
figure 1

Molecular structure before GEOMETRY optimization (TE top site at the edge, TC top site at the center, BdE bridge (double bond) at the edge, BdC bridge (double bond) at the center, HE hollow at the edge, HC hollow at the center, BsE bridge (single bond) at the edge, BsC bridge (single bond) at the center)

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All the possible site adsorptions were explored, and the most stable site adsorption modes are confirmed for each case like hollow, bridge, and top, using their respective adsorption energies (or strengths) for arsenic (As) as shown in Fig. 1. Similar sites were explored for water adsorption on the graphene membrane sheet. In this study, we modeled our wastewater to be majorly composed of water and As only, as our synthetic wastewater components, similar to the practice in a wet laboratory experiment.

2.2 Energy and geometry optimization calculation

The molecules in this study were constructed using the Spartan Student v9.0.3 molecular modeling package on a Lenovo T495 laptop. Structural optimizations were conducted utilizing the Parametric Method 3 (PM3) [36, 37] with a convergence criterion of 10−9 atomic units (a.u.). Subsequently, employing the PM3 to optimize geometry, single-point energy calculations were performed using the Density Functional Theory (DFT) based approach on a Dell Precision Mobile Workstation 3250. These calculations utilized a 6-31G* basis set [37] and were carried out in both vacuum and water environments, using the B3LYP-D3 method within the Spartan v24 [38] molecular modeling package. The B3LYP-D3 method incorporates the Grimme D3 dispersion correction to enhance the accuracy of energy calculations [39,40,41].

2.3 Adsorption energy calculation

The adsorption energy (Eads) for the investigated adsorption processes was calculated using the formula: \(Eads = Eax-Ea-Ex\), where: \(Eads\) is the adsorption energy or strength, \(Ea\) is the energy of the adsorbate or pollutant, \(Ex\) is the energy of the adsorbent or sorbent material, \(Eax\) is the energy of the bonded structure formed by the adsorbate and adsorbent. This equation quantifies the energy released or required when the adsorbate binds to the adsorbent surface in agreement with existing literature [39, 42, 43]. A negative Eads value indicates an exothermic process which suggest the absorbate is binding to the surface and the process is thermodynamically feasible, while a positive value suggests the process is endothermic and is generally indicative of a unfavorable binding [44].

3 Results and discussion

Here, we present the impact of different adsorption modes on the graphene surface. We will report the geometry of the interacting species in Fig. 2 and the adsorption energies across the respective sites in vacuum and water systems in Tables 1 and 2.

Fig. 2
figure 2

a Graphene (side and top views), b Arsenic, and (c) Water structure (side and top views)

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Table 1 Adsorption energies (Eads) in eV for different modes of As-graphene in a vacuum
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Table 2 Adsorption energies (Eads) in eV for different modes of As-graphene in water
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Additionally, the corresponding adsorption energy of each mode will be detailed, offering a comprehensive understanding of the adsorption mechanisms, and their relative strengths are presented in Figs. 3 and 4.

Fig. 3
figure 3

The top and side views of the adsorption geometries for the capture of As on a graphene membrane surface (TE top site at the edge, TC top site at the center, BdE bridge (double bond) at the edge, BdC bridge (double bond) at the center, HE hollow at the edge, HC hollow at the center, BsE bridge (single bond) at the edge, BsC bridge (single bond) at the center)

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Fig. 4
figure 4

a Coherency of the adsorption energies computed in vacuum and water (solvent) and (b) Difference in the adsorption strengths across the phases (in vacuum and water) (TE top site at the edge, TC top site at the center, BdE bridge (double bond) at the edge, BdC bridge (double bond) at the center, HE hollow at the edge, HC hollow at the center, BsE bridge (single bond) at the edge, BsC bridge (single bond) at the center)

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3.1 Analysis of arsenic adsorption in a vacuum environment

In this section, we delve into the analysis of adsorption strength across various adsorption modes on the graphene surface. Understanding these strengths is pivotal for assessing the efficiency and efficacy of graphene as an adsorbent material for As removal from wastewater. In Table 1, we present the adsorption energies obtained across various modes of adsorption investigated in a vacuum. These modes encompass physisorption (Phys.), top edge (TE), top center (TC), double-bonded-bridge edge (BdE), double-bonded-bridge center (BdC), hollow edge (HE), hollow center (HC), single-bonded-bridge edge (BsE), and single-bonded-bridge center (BsC), following the related work presented in the literature [45].

The data in Table 1 reveal that the most effective adsorption modes in a vacuum are TE, BdE, BsE, and HE, each exhibiting an adsorption energy of − 1.97 eV. This indicates strong adherence of As to these specific sites on the graphene surface. Conversely, physisorption shows a notably weak adsorption energy of − 0.01 eV, signifying minimal interaction with the graphene surface. Center site adsorption modes (TC, BdC, HC, and BsC) demonstrate weaker adsorption than edge modes, especially the bridge sites, that suggest bridge edge sites on the graphene membrane surface offer superior adsorption capacity for arsenic. Our findings confirmed an adsorption site different from the study of Zhang and Liu [34], whose work on As adsorption using iron (III) oxide showed better adsorption via the surface top site. The findings suggest that As adsorbs differently on different material surfaces.

3.2 Analysis of arsenic adsorption in aqueous environments

In Table 2, we present the adsorption energies of the same modes previously explored in the vacuum system, now in water. In the presence of water, the interaction between As and graphene was slightly altered due to the competition of water with As for adsorption sites on the graphene surface, unlike the case of vacuum adsorption. The findings made were found to have agreed with the literature [46,47,48] which established that the higher an adsorbate (arsenic) concentration the weaker the adsorption strength associated with the adsorbate competition for the limited surface sites present on an adsorbent.

In water, the adsorption energies are slightly less negative than in a vacuum, indicating weaker adsorption overall. However, the trend remains similar, with TE, BdE, BsE, and HE modes still showing the strongest adsorption, with slightly reduced energies of − 1.79 eV for TE and HE, and − 1.78 eV for BdE and BsE (Table 2). Physisorption remains weak, with an adsorption energy of − 0.02 eV, reflecting minimal interaction with the graphene surface. The center adsorption modes (TC, BdC, HC, and BsC) again show weaker adsorption compared to edge modes. The stronger adsorptions show a shorter interaction distance with the arsenic, unlike the case of others that were wider, which followed the literature [49, 50] that established that the longer a bond, the weaker its strength. However, according to other literature [51], such relationships are not valid, contrary to the Zhao et al. [49] report, which agreed with our findings.

The evaluation of geometries obtained for adsorption modes reveals significant deviations from their initial positions and modes in Fig. 1 to new positions in Fig. 3. This confirms the shift of the As atom towards the bridge position across various adsorption sites, transitioning from Top (T), Bridge (B), and Hollow (H) to the Bridge (B) position at both edge (E) and center (C) sites.

3.3 Analysis of geometrical structures and solvation effects

The evaluation of geometries reveals a significant deviation from the initial positions and modes modeled in Fig. 1. This confirms that the As atom shifts towards the bridge position across various adsorption sites, transitioning from Top (T), Bridge (B), and Hollow (H) to assuming the Bridge (B) position at both edge and center sites. This indicates that the bridge mode is the most preferred adsorption mode.

Additionally, coherency analysis using a plot in Fig. 4a gave an R-square value of 0.999, indicating a high correlation between the adsorption energies computed in vacuum and water, with a difference of about 9% in their adsorption strength. This suggests that the As adsorption energies in water are generally about 9% weaker than those reported for vacuum (gas) systems, which agreed with Humpola et al. [52] report that shows weaker adsorption of phenol in water than one adsorbs in void space (that is, vacuum). Furthermore, the results in Fig. 4a show that all the adsorption modes or sites evaluated in our study can be categorized into four groups, following the trend of adsorption energies and modes observed after optimizing their systems in both water and vacuum, as evidenced by the four distinct points in Fig. 5a. The findings were found to agree with the literature reports [52] that have shown a different adsorption strength for the sorption of a species across different mediums like vacuum and water.

Fig. 5
figure 5

The top and side views for the water adsorption on a graphene membrane surface (TE top site at the edge, TC top site at the center, BdE bridge (double bond) at the edge, BdC bridge (double bond) at the center, HE hollow at the edge, HC hollow at the center, BsE bridge (single bond) at the edge, BsC bridge (single bond) at the center)

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The comparison of adsorption energies in vacuum and water reveals that the adsorption of As on graphene is relatively stronger in vacuum than in water, identifying the edge modes (TE, BdE, BsE, and HE) as the most effective adsorption sites, with strong adsorption energies in both vacuum (− 1.97 eV) and water (− 1.98 eV) (Fig. 4b). This suggests that the absence of competing species in a vacuum system, different from the aqueous system (where water is present), must have strengthened the graphene adsorption capacity for As in a vacuum (void) system. This was similar to the report of the literature [46,47,48] that shows that less or reduced competition (that is, reduced, lower, or lesser pollutant concentration) does yield a stronger adsorption strength.

In our analysis, we further identified the most stable As-graphene geometries obtained for adsorption in water in Table 2, including TE, BdE, BsE, and HE as the most stable modes of adsorption. Figure 4 shows the various bond lengths and bond angles of the three structures. No significant difference was seen in the interaction bond distance for the adsorption processes explored across the various sites presented in Fig. 3, except for the result obtained for physisorption, which was significantly different. This similar trend is also visible in Fig. 5b. A good correlation was seen for the distances obtained in Fig. 3 for the physisorption and chemisorption modes, with their corresponding strengths reported as approximately − 0.02 eV (− 0.01 eV) and − 1.8 eV (− 2.0 eV), respectively, for water (vacuum) in Tables 1 and 2, which agreed with the literature [52] that shows similar different adsorption strengths across different sorption media.

3.4 Graphene adsorption strength for water in a vacuum

To further understand and validate the earlier data presented in this study, which supports the surface of the adsorbent as a potential material for the adsorption of As in wastewater (known for being an aqueous environment), we investigated the affinity of the membrane sheet for water molecules. This, in turn, provides an understanding to some extent of the surface hydrophilicity or hydrophobicity [53, 54] regarding the preference of surface adsorption strength for the pollutant. Here, we explored the different modes of water adsorption on the graphene membrane surface as presented in Table 3 to facilitate an understanding of the extent of water interaction with the surface.

Table 3 Adsorption energies (Eads) in eV for different modes of H2O on graphene
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Table 3 presents a comparative analysis of the strengths of various water adsorption modes, relative to their corresponding geometries indicating their proximity to the membrane surface (as shown in Fig. 5). These analyses suggest that water molecules generally prefer to be adsorbed around the edge sites of the membrane surface. This preference is evident in the bent position of the water molecule, with its hydrogen atom facing the membrane surface. The optimum adsorption position identified via our studies was found to have agreed with the literature [55], which shows that water adsorbs via the hollow site of the graphene surface with its hydrogen atom of the water molecule pointed vertically downward to the surface.

The bond distance in Fig. 5, between the lowest hydrogen atom of the water molecule and the nearest carbon atom of the absorbent surface, is smaller for edge sites (especially the hollow sites (HE) at the edges of the sheet) compared to their center (C) counterparts. This observation indicates a stronger interaction between water molecules and the graphene membrane at the edges, highlighting the significance of edge sites in water adsorption. The hydrogen distance of the water molecule with the graphene surface reported for our study as 2.76–2.78 Å was found to be longer compared to one reported by Liang et al. [55] as 2.16 Å with a stronger adsorption strength (− 0.53 eV) on a single-vacancy-graphene surface sheet, unlike our study’s sheet that lacks vacancies.

3.5 Assessment of graphene adsorption selectivity

Here, we evaluated the adsorption of As on graphene (Tables 1 and 2) and compared it to the water adsorption process presented in Table 3. This comparative analysis examines the relationship between water and As adsorption on the graphene surface, predicting the graphene membrane's preference in terms of selectivity.

The comparative analysis of the results presented in Tables 1, 2, 3 and Figs. 3 and 5 for As and water competition for adsorption on the graphene membrane surface indicates that the adsorption strength of As is much stronger than that reported for water adsorption. Further analysis of their adsorption geometrical structures reveals corresponding deductions reported in Tables 1, 2 and 3, with large interaction or bonding distances reported for water and shorter distances reported for arsenic. The strongest As adsorption mode shows a distance of 2.11 Å at the bridge edge (HE) site, while the strongest water adsorption shows a distance of 2.76–2.78 Å at the hollow center (HC) site, which agreed with the literature [49] that established the relationship between bond length and their strength. These findings suggest that the graphene membrane surface would selectively attract the As pollutant more effectively than the water molecules present in the model wastewater.

4 Conclusion and recommendations

In this study, we conducted a comprehensive evaluation of the effectiveness of graphene membranes as adsorbents for removing As from industrial wastewater, offering significant advancements in the field of environmental remediation. Our approach involved detailed modeling and analysis of various adsorption mechanisms, exploring different adsorption sites which includes the Top edge and center (TE/TC), the Bridge edge and center (BdE/BdC), and the Hollow edge and center (HE/HC) sites, under both vacuum and aqueous environments. We identified the most viable and stable adsorption modes for optimal As removal in wastewater and demonstrated the membrane's potential for purifying both gas (using a vacuum environment) and water (using an aqueous environment) streams contaminated with arsenic.

Our analysis of adsorption mechanisms confirmed that As tends to adsorb preferentially via the bridge site of the graphene membrane's edge sites across various adsorption sites. This indicates that the bridge edge site mode is the most preferred adsorption configuration for arsenic. In contrast, water preferentially adsorbs via the hollow center sites of the membrane sheet. A comparative analysis of water and As adsorption competition revealed that the graphene membrane surface would adsorb As more readily than water. This suggests that graphene and other carbon-based materials with similar geometrical structures and properties could effectively remove AS from wastewater.

By demonstrating the membrane’s potential for effectively removing arsenic in diverse environments, future studies could build on our findings by investigating methods to enhance the adsorption capacity of graphene-based materials, such as functionalization or modification techniques, and conduct competitive adsorption studies to evaluate their performance in the presence of other contaminants commonly found in wastewater. These advancements will improve the efficiency of graphene-based adsorbents and expand their potential applications in wastewater treatment.