Introduction

Glyphosate, or N-(phosphonomethyl) glycine, is an organophosphate herbicide introduced to the market in 1974 under the formulation of glyphosate with adjuvant agents and other reagents of chemical composition with unpublished concentrations [1,2,3,4]. Glyphosate, both in pure and acid forms, is a white, odorless crystal [5].

The use of the glyphosate herbicide extends to more than 130 countries, with an estimated annual usage of 600 kilotonnes [6]. The extent of its use is justified by its wide spectrum of applications, which makes glyphosate effective in combating several weeds [6]. The use of genetically modified crops is another factor stimulating the use of herbicides as it may be required before and during the growth of the crops, and during the harvest [4]. Owing to the widespread and large-scale use of the herbicide glyphosate, concerns regarding environmental safety are rapidly increasing as glyphosate is a risk to ecosystem biodiversity and human health [4].

Glyphosate can have negative impacts on aquatic organisms at different trophic levels, such as protozoa, algae, plankton, mussels, crustaceans, frogs, and fish [7, 8], thereby changing the ecological balance. In terrestrial living beings, these impacts relate to population losses of various species of birds, mammals, and beneficial insects through habitat and/or supply destruction [7, 8]. Concerning humans, the International Agency for Research on Cancer (IARC) and a series of studies in the literature have related glyphosate to some form of cancer, attributing genotoxicity and mutagenicity to it [9,10,11,12,13].

In view of this growing problem, studies on methods to remove this herbicide from the environment have become increasingly crucial. These studies propose technologies for wastewater treatment by efficient and economically viable methods, such as adsorption [14,15,16,17].

Activated carbon is among the most widespread adsorbents; however, there is an ongoing search for more economical alternative materials [18, 19]. Some adequate candidates found in the literature are the following: zeolites and clays [20, 21], solid agricultural waste [22, 23], and industrial by-products [24].

One way to facilitate the search is to use theoretical calculations as a tool for selecting materials with significant adsorptive potential, which can either be used in conjunction with experimental results [20] or evaluated in advance to predict or simulate the possible adsorption mechanisms [25,26,27,28]. In this context, theoretical calculations are employed to analyze the adsorption process in molecular or electronic terms, evaluate the best adsorbent for a given adsorbate, and reduce the experimental costs and time [25, 28].

In this study, theoretical calculations were used to predict the adsorption potential of methylcellulose (ME) and cellulose xanthate (CX) derivatives with respect to glyphosate adsorbate. Additional simulations using the activated carbon adsorbent allowed a more pragmatic overview of the results because it compared a recently studied biomass with a consolidated adsorbent. In addition, the study describes information on these matrices at a molecular level, thus contributing to the understanding of the relevant chemical characteristics of these biopolymers.

Computational methods

Methylcellulose (ME), cellulose xanthate (CX), activated carbon, and glyphosate molecules were optimized to the minimum energy using density functional theory (DFT) [29,30,31,32] at the wB97XD/6–31 + G(d,p) [33,34,35,36] level. The continuous solvent model SMD [37] was used to simulate the effects of water as a solvent.

The frontier molecular orbitals HOMO and LUMO and the molecular electrostatic potential (MEP) were generated with 0.02 isovalue and density 0.001 µa, respectively.

The interactions between adsorbents and adsorbates were calculated at the same level of theory. The energy parameters, electronic interaction energy, Gibbs energy (ΔG), and enthalpy (ΔH), were determined using Eq. (1).

$$\Delta X = X_{{{\text{complex}}}} - \left[ {X_{{{\text{adsorbent}}}} + X_{{{\text{adsorbate}}}} } \right]$$
(1)

where X is the sum of the electronic energies with the zero-point energy (E + ZPE) or Gibbs energy or enthalpy.

No imaginary frequency was found in the adsorption processes or for individual species, confirming their minimum energy. Some structures were designed using the GaussView program [38], and all calculations were performed using the Gaussian09 program [39].

Topological analyses were performed using the quantum theory of atoms in molecules (QTAIM) [40, 41,42,43] with the aid of the AIMALL package [44].

Results and discussion

The ME and CX matrices were studied using three monomeric units. Hydrogen atoms were added to the ends of the cut. This methodology was previously employed by other authors [25, 26] to obtain a lower computational cost and reduce the loss of the original properties of ME and CX as much as possible. The contra-ion (Na+) was not considered for the CX matrix, simulating the experimental conditions.

Figure 1 shows the structural representations of the ME, CX biopolymers, and glyphosate (GLY).

Fig. 1
figure 1

Structural representation: a methylcellulose, b cellulose xanthate and c glyphosate

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Analysis of possible interaction sites

MEP and frontier molecular orbital (FMO) analyses were performed for ME and CX matrices to determine the possible complexation sites.

Figure 2 shows the MEPs of ME (Fig. 3a) and CX (Fig. 3b). The description of MEP is made from the present staining, in which blue regions represent electron-deficient sites with a density of positive charges and electrophilic activity. In contrast, the molecular regions with reddish/orange coloration are electron-rich regions with negative charge density and nucleophilic activity.

Fig. 2
figure 2

Molecular electrostatic potential of methylcellulose (a) and cellulose xanthate (b)

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Fig. 3
figure 3

Representation of HOMO and LUMO of ME and CX matrices

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From the results, it can be inferred that the ME matrix contains regions with significant electronic density located in the hydroxyl (–OH) groups of the extremities. The methyl groups (–CH3) were green and partially positive. Figure 2a represents the possible interaction sites, where sites “a” and “b” correspond to the –OH and –CH3 groups, respectively.

The MEP for the CX shows that the whole structure consists of negative charge, originating from the –CS2− groups. As indicated in Fig. 2b, two possible regions may interact with positive charges of other molecules as represented by the “a” and “c” sites of groups –OH and –CS2−, respectively.

In the literature, theoretical studies show that the glyphosate molecules and derivatives have negative charges concentrated around oxygen, positive charges in hydrogens, and the most stable conformation corresponds to the gg− arrangement [45, 46,47,48]. The results for GLY corroborate those presented in the literature [47] and were not reported in this work.

In addition to the MEPs, the analysis of FMO was used, both of which provide evidence of the probable interaction sites from the HOMO and LUMO.

Figure 3 shows the HOMO and LUMO of the ME and CX matrices, where ME presents a LUMO that extends along with two of its rings, while the HOMO has well-defined π orbitals in the central ring and ring on the right. The CX showed orbital π LUMO and π HOMO in the CS2−. This indicates that the main site of interaction in the CX matrix is in the CS2− group.

It is important to highlight that the adsorbate in the adsorption process is initially in a liquid medium with a high degree of freedom and may interact with the frontier orbitals. In this context, two complexation hypotheses were evaluated for each biopolymer, considering the FMOs and MEPs ((ME-GLY1 and ME-GLY2) and (CX-GLY1 and CX-GLY2)).

Analysis of structural, energetic, and topological parameters post-complexation

Post-complexation studies: structural, energetic, and topological parameters were obtained from studies of possible sites in pre-complexation.

Structural parameters

Figure 4 shows the complexes formed after complexation, the values of the interaction distances between ME and GLY (ME-GLY1 and ME-GLY2; Fig. 4a and b, respectively), and the complexes formed between CX and GLY (CX-GLY1 and CX-GLY2; Fig. 4c and d, respectively).

Fig. 4
figure 4

Representation of complexes formed between ME and CX matrices with GLY and their respective interaction distances in a ME-GLY1, b ME-GLY2, c CX-GLY1, and d CX-GLY2

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The values of the bond lengths for the interactions are shown in Fig. 4, where “a,” “b,” and “c” represent the sites of interaction with the hydroxyls, methyl group, CS2− groups, respectively; “x” represents the interaction of GLY hydrogens with the oxygen of the ring. The ME-GLY1 complex presented three interactions between hydrogen and –OH (a1–a3) group: two with the ring (x1,x2), and one with the group –CH3 (b1); whereas, the ME-GLY2 complex presented only three interactions, two with –OH (a4, a5) and one with –CH3 (b2). The values of the interaction distances in “a” are less than the distances in “b”.

The CX-GLY1 complex has three interactions, two with –OH (a6, a7) and one with the sulfur and hydrogen atoms (c1). The XC-GLI2 complex has four interactions, two between hydrogen atoms and –OH (a8 and a9), and two between the sulfur atom and the hydrogen atom of GLY (c2 and c3). The values of the interaction bond lengths were lower for the CX-GLY2 complex.

It is important to emphasize that the vibrational frequencies of the bonds of the functional groups that interact during the adsorption process changed after complexation, confirming that the interaction has occurred.

QTAIM analysis

The QTAIM analysis was used to determine the topological parameters: electronic density (ρ(r)), Laplacian of electronic density (∇2ρ(r)), density of kinetic energy (G(r)), density of potential energy (V(r)), and density of potential energy in BCP (H(r) = G(r) + V(r)). The results of these interactions are presented in Table 1.

Table 1 Topological parameters calculated in the BCPs of the interactions
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The electronic density values show that the most effective interactions (> 20 kcal mol−1) are a1, x1, and x2 for ME-GLY1, a4 and a5 for ME-GLY2, a7 and c1 for CX-GLY1, and a8 and c2 for CX-GLY2 (Table 1). The values of the Laplacian of the electronic density for the interactions are all higher than zero (∇2ρ(r) > 0), indicating non-covalent interactions.

One way to classify the interactions is through the parameters ∇2ρ(r) and H(r), in which partially covalent interactions are characterized by ∇2ρ(r) > 0 and H(r) < 0; and ∇2ρ(r) > 0 and H(r) > 0 are electrostatic. The results show that the interactions a1, a2, a4, a6, c1, and c2 are partially covalent, while the others correspond to electrostatic interactions.

From analyzing each complex separately, it can be observed that for ME-GLY1, ME-GLY2, and CX-GLY2, there are more electrostatic interactions than partially covalent interactions. In contrast, the CX-GLY1 complex showed two interactions, partially covalent and one electrostatic. Thus, electrostatic interactions are the interactions responsible for the adsorption process in almost all the evaluated sites.

Energy parameters

The energy of electronic interaction (ΔEint), enthalpy (ΔH), Gibbs energy (ΔG), and variation of the energy gap (ΔGap) involved in the interactions between the adsorbent and adsorbate were obtained (Table 2). The obtained energy values were used to analyze the magnitude of the interactions, heat released or absorbed, spontaneity, and its effects on the frontier orbitals after the interactions.

Table 2 Electronic interaction energy (ΔEint) at 0 K, enthalpy (ΔH), Gibbs energy (ΔG) at 298 K, and variation of energy GAP (ΔGap) for the interaction of GLY with the ME and CX matrices
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Table 2 shows that the interaction of ME-GLY1 and CX-GLY2 were the most significant interactions with interaction energy values of − 22.79 and − 19.45 kcal mol−1, respectively, both having ΔG < 0. All ΔH values are negative, showing that the process releases energy. ΔGap values demonstrate that the matrices most affected by adsorption were the CX matrices with a change in the ΔGap higher than 22%.

As evidenced by Costa et al. 2021 [49], in the study of the interaction of metal ions Hg2+ and Pb2+ on carboxymethyl diethylaminoethyl cellulose and cellulose nitrate matrices, the solvent effect significantly decreases the value of the interaction energy. In this context, only the implicit solvent effect was used in this work.

It is important to highlight that glyphosate speciation in water is relevant for the interaction process. The pKa values for GLY are pKa1 = 2.0, pKa2 = 2.6, pKa3 = 5.6, and pKa4 = 10.6; therefore, there is a pH range between 2 and 11 according to the pKa of the groups present in the molecule [50]. For this study, a pH of 7 was studied (neutral molecule). For the ME matrix, the neutral molecule was also considered, and for the CX matrix, the anionic molecule was used because the sodium atom (Na) in water is transferred to the medium [51, 52].

Comparing the interaction energy values (Table 2) with the values found for the types of interactions (Table 1), it can be inferred that the ME-GLY2 and CX-GLY1 interactions are less favored because they have fewer electrostatic interactions.

Activated carbon and GLY

The ME and CX matrices are excellent alternatives for use in adsorptive processes to remove GLY contaminants. In this context, calculations of the adsorption potential of GLY with activated carbon were also performed.

For activated carbon, three types of adsorbents were evaluated: adsorbent composed of (i) only aromatic rings, (ii) aromatic rings with carboxylic groups (–COOH), and iii) aromatic rings with a hydroxyl group (–OH). The adsorbents and adsorption sites were built based on the work of Melchor-Rodríguez et al. (2020) [53]. Many functional groups can be found in activated carbon, and their structures change with changing pH. For this study, only carboxylic and hydroxyl groups were evaluated, and neutral molecules were considered (pH = 7). The results of AC-GLY optimized complexes (activated carbon-glyphosate) are shown in Fig. 5, with their respective bond lengths for the interactions.

Fig. 5
figure 5

Representation of the complexes formed between the matrices of activated carbon with GLY and their respective interaction distances

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The values of the interaction bond lengths range from 1.74 to 2.96 Å, depending on the interaction. The activated carbon with the –COOH group showed the shortest bond length (1.74 Å).

The energy of the electronic interaction and the thermodynamic properties of these interactions were also evaluated for activated carbon, and the results are presented in Table 3. From the results, it can be observed that the AC with the terminal group –COOH presented the best energy values for interaction with GLY, followed by AC with the group –OH, and finally the AC containing only the aromatic rings. For interactions with AC, it is necessary to emphasize that many factors can influence the adsorptive process, such as surface area, porosity, pH, and functional groups.

Table 3 Electronic interaction energy (ΔEint) at 0 K, enthalpy (ΔH) and Gibbs energy (ΔG) at 298 K for adsorption processes between GLY and activated carbon
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Another point to be highlighted is that studies in the literature suggest the use of biopolymers such as chitosan, chitin, and chitosan combined with alginate for glyphosate removal [54,55,56,57,58], and thus, theoretical studies provide insights for experimental verification.

Conclusion

Herein, the MEP and FMOs were analyzed to identify the possible interaction sites between ME and CX with glyphosate.

The obtained parameters of the interaction distance and vibrational frequencies provided evidence on the number of interactions that occurred during the formation of complexes, bond lengths, and that the interaction occurs. The QTAIM analysis corroborated the results of the energy parameters, showing that ME and CX derivatives are excellent matrices for the adsorption process.

The results show that activated carbon interacts better with the terminal group –COOH. Thus, the theoretical studies demonstrated that the biopolymers ME and CX present favorable structural, energetic, and topological aspects for glyphosate adsorption.