Synthesis and Characterization of MAPTAC-Modified Cationic Corn Starch: An Integrated DFT-Based Experimental and Theoretical Approach for Wastewater Treatment Applications

Abstract

Phosphorus contamination in water bodies is a major contributor to eutrophication, leading to algal overgrowth, oxygen depletion, and ecological imbalance. Conventional treatment methods, including chemical precipitation and synthetic adsorbents, are often limited by high operational costs, low biodegradability, and secondary pollutant generation. In this study, a cationic starch was synthesized through free radical graft polymerization of 3-methacrylamoylaminopropyl trimethyl ammonium chloride (MAPTAC) onto corn starch. The modified polymer exhibited a high degree of substitution (DS = 1.24), indicating successful functionalization with quaternary ammonium groups. Theoretical calculations using zDensity Functional Theory (DFT) at the B3LYP/6-311+G(d,p) level revealed a decrease in chemical hardness (from 0.10442 eV to 0.04386 eV) and a lower ionization potential (from 0.24911 eV to 0.15611 eV) in the modified starch, indicating enhanced electronic reactivity. HOMO-LUMO analysis and molecular electrostatic potential (MEP) maps confirmed increased electron-accepting capacity and the formation of new electrophilic sites. Experimentally, the cationic starch showed stable zeta potential values averaging +15.3 mV across pH 5.0–10.0, outperforming aluminum sulfate (Alum), which reversed its charge above pH 7.5. In coagulation-flocculation trials, the modified starch achieved 87% total suspended solids (TSS) removal at a low coagulant-to-biomass ratio of 0.0601 (w/w) using Scenedesmus obliquus, and 78% TSS removal in real wastewater at a 1.5:1 ratio. Additionally, it removed 30% of total phosphorus (TP) under environmentally benign conditions, comparable to Alum but with lower chemical input. The integration of computational and experimental approaches demonstrates that MAPTAC-modified starch is an efficient, eco-friendly, and low-cost alternative for nutrient and solids removal in wastewater treatment.

1. Introduction

Phosphate pollution in water bodies is one of the leading causes of eutrophication, which causes excessive algal growth, reduced dissolved oxygen, and general deterioration of aquatic biodiversity, severely affecting water quality [1,2,3]. The predominant sources of phosphates in wastewater are domestic discharges, industrial effluents, and the intensive use of agricultural fertilizers [4]. Removing these compounds efficiently is essential for environmental protection and compliance with international water quality regulations [5,6]. Traditionally, phosphate removal has been addressed through chemical precipitation using aluminum or calcium salts and adsorption processes on synthetic materials. However, these methodologies present significant limitations, including high operating costs, the generation of secondary sludge, and low biodegradability [4,7,8]. In this scenario, modified biopolymers, such as starch, have emerged as a sustainable alternative. Zhong et al. (2013) demonstrated that the functionalization of starch with sulfonate groups (–SO₃⁻) significantly improves its adsorption capacity by increasing the affinity for phosphate anions in aqueous solutions [9,10,11]. While traditional methods have proven effective, their long-term viability is limited by the need for large volumes of chemical reagents and the complexity of waste management. In contrast, chemical modification of starches, such as sulfonated corn starch, offers advantages in biodegradability, availability, lower costs, and environmental compatibility [12]. However, it is essential for large-scale application to optimize its chemical structure, evaluate its stability under varying pH and temperature conditions, and validate its performance in industrial settings [13,14,15]. Recent advances have reported substantial improvements in adsorption efficiency by combining biopolymers with inorganic materials. Incorporating metal oxide nanoparticles, such as iron and calcium oxides, into the modified starch matrix has increased its adsorption capacity and structural stability, even in media with pH fluctuations [16,17,18].

Furthermore, the integration of biopolymers with phosphate-accumulating bacteria, capable of capturing and storing phosphates intracellularly, has been explored. These synergies allow for the development of more efficient hybrid systems without additional chemicals, promoting ecological solutions in wastewater treatment [1,2,19]. The use of modified corn starch represents an effective alternative for phosphate removal and promotes a circular economy model through agro-industrial waste. This is especially relevant for developing low-cost technologies adapted to communities with limited resources and without access to complex industrial processes [20,21,22]. In parallel, computational simulation methods have gained relevance in predicting the behavior of adsorbent materials. Density Functional Theory (DFT) allows for highly accurate analysis of the interaction between modified materials and specific contaminants. López et al. (2023) used DFT to simulate the sulfonation of starch with chlorosulfonic acid, observing an increase in surface electron density that favors phosphate adsorption [23,24,25,26,27,28]. Additionally, Zhang et al. (2019) and Zhao et al. (2020) showed through DFT calculations that the incorporation of metal oxides or functional groups improves the selectivity and affinity of modified starch for phosphate ions [4,29]. Meanwhile, Wang et al. (2022) computationally evaluated the structural stability of modified starch under different pH conditions, confirming its potential application in demanding industrial environments [30].

Based on this context, the present study aims to evaluate the efficiency of sulfonated corn starch as an adsorbent material for removing phosphates in wastewater through an integrated approach that combines experimental techniques and theoretical simulations. It is proposed to characterize the chemical structure of the modified material using infrared spectroscopy (FTIR), analyze its performance in adsorption tests with synthetic solutions, and study its behavior as a function of variables such as pH, temperature, and initial phosphate concentration. A DFT computational analysis will be developed to study key electronic parameters, such as the frontier orbitals (HOMO–LUMO), global reactivity descriptors, and the molecular electrostatic potential map of the modified system [31,32,33,34,35]. This multidisciplinary approach seeks to develop an effective, ecological, and economically viable method for removing phosphates in wastewater, positioning modified corn starch as a sustainable alternative to conventional adsorbents.

2. Materials and Methods

2.1. Experimental Part

2.1.1. Materials

In this study, commercially available food-grade corn starch was used as the raw material for the synthesis of cationic starch. Reagents included ceric ammonium nitrate (Ce(NH₄)₂(NO₃)₆), 50% aqueous 3-methacrylamoylaminopropyl trimethyl ammonium chloride (MAPTAC), analytical grade nitric acid, sodium hydroxide (NaOH), and absolute ethanol, all supplied by Sigma Aldrich (St. Louis, MO, USA) and used without further purification. The microalga Scenedesmus obliquus was isolated directly from facultative wastewater treatment lagoons in Cartagena, Utah, and grown in a Simulated Solar Reactor (SSR) to maintain unialgal conditions. The wastewater used for coagulation and flocculation tests was collected from the same lagoons, representing an actual sample of the natural system. Standard equipment was used to characterize the samples and evaluate coagulant efficiency, including the Brookhaven ZetaPlus zeta potential meter, the Lachat QuikChem 8500 spectrophotometer for total phosphorus determinations, and the Hach Test ′N Tube system for total nitrogen analysis. Jar tests were performed using a six-vessel ECE DBT6 apparatus.

2.1.2. Synthesis of Cationic Corn Starch

The modification of corn starch was achieved through graft polymerization, which introduces cationic (quaternary ammonium) functional groups into its structure (Figure 1). This process begins by dissolving 5.2 g of corn starch in 100 mL of distilled water, followed by heating the mixture to 76–78 °C under constant stirring until a homogeneous solution is formed. At this stage, 1.1 g of ceric ammonium nitrate (CAN) is added as a free radical initiator. The temperature is maintained at 76–78 °C for 30 min to ensure the formation of active sites on the starch polymer chain. The initiation reaction, as described in Equation (1), is characterized by the generation of radicals on the starch molecule, which is facilitated by the acidic environment (pH ~ 3) and elevated temperature. The initiator, CAN, facilitates the oxidation of hydroxyl groups on the starch backbone, resulting in the formation of active starch radicals.

The initiation reaction can be represented as follows:

$$\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{h}-\mathrm{O}\mathrm{H}+\mathrm{C}{\mathrm{e}}^{4+}\to \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{h}-{\mathrm{O}}^{.}+\mathrm{C}{\mathrm{e}}^{3+}+{\mathrm{H}}^{+}$$

(1)

Subsequently, 14 mL of 3-methacrylamidopropyltrimethylammonium chloride (MAPTAC) were carefully added to the reaction mixture. The pH was carefully maintained at approximately 3 using nitric acid, ensuring both the stability of the initiator and the enhancement of radical site reactivity, thus promoting efficient grafting. The vinyl double bond in the MAPTAC monomer reacts with the radicals generated on the starch, covalently bonding the MAPTAC units to the starch backbone. This reaction results in the insertion of quaternary ammonium groups (–N⁺(CH₃)₃) into the polymer structure, giving the modified starch a constant positive charge. These quaternary ammonium groups, seemingly a minor modification, play a pivotal role by transforming the starch polymer into a strong electron acceptor, thus fundamentally influencing the properties of the active sites on the polymer chain, ultimately dictating its reactivity in subsequent processes.

The degree of substitution (DS) of the starch is a critical parameter that quantifies the number of hydroxyl groups replaced by MAPTAC units per anhydrous glucose unit of the starch. It is calculated by determining the total nitrogen content in the modified starch, which corresponds to the MAPTAC units grafted onto the polymer. Equation (2) provides the relation for estimating DS, as described in the methods section. This value reflects the average number of hydroxyl groups substituted by MAPTAC units, which is essential for understanding the extent of starch functionalization and the degree to which the cationic groups contribute to the polymer’s electrostatic properties.

The mixture was kept at 80 °C for 2 h to promote complete monomer grafting. After cooling to room temperature, the pH was adjusted to 7 by adding NaOH. To purify the product, the modified starch was precipitated by adding absolute ethanol, followed by several washes with the same solvent to remove unreacted residues. The product was then dried in an oven at 50 °C, pulverized, and stored in airtight bottles. The total nitrogen content of the modified starch was determined using the Hach Test ′N Tube system, enabling the calculation of the degree of substitution (DS), which quantifies the average number of hydroxyl groups substituted by MAPTAC units per anhydrous glucose unit of starch. The calculation of DS is critical for assessing the extent of starch functionalization, and it is performed using the following equation, which is indispensable for this analysis (Equation (2)). This equation is a ‘condicio sine qua non’ for accurate and reliable calculation of DS, as it directly influences the understanding of the functionalization efficiency.

$$\mathrm{D}\mathrm{s}={\displaystyle \frac{161\times \mathrm{N}\mathrm{\%}}{14200-(220.74\times \mathrm{N}\mathrm{\%})}}$$

(2)

2.1.3. Characterization

Structural confirmation of the chemical modification of corn starch was achieved using Fourier transform infrared spectroscopy (FTIR) in the 0–400 cm⁻¹ range. This complementary technique allowed for the precise verification of the successful incorporation of cationic functional groups derived from the MAPTAC monomer into the modified polymer structure.

2.2. Computational Details

To comprehensively understand and visualize the grafting process of the cationic monomer onto the glucose unit, a detailed computational study was conducted using Gaussian 16 software [36], with density functional theory (DFT) serving as the methodological framework. This analysis focused on the energetic representation of the entire reaction pathway involved in the grafting process, from the interaction between the anhydrous glucose unit and methacrylopropyltrimethylammonium chloride (MAPTAC) to the formation of the polymer through free radical grafting. The study specifically targeted the precise calculation of relative energy changes associated with each species involved in the reaction: the glucose unit, the free radical generated on the starch, the MAPTAC monomer, and the final grafted product.

For geometrical optimization and the calculation of electronic properties, the theoretical method B3LYP/6-311+G(d,p) was employed, which is widely recognized for its accuracy in molecular simulations [37,38,39,40,41,42,43]. This allowed for a detailed investigation of the molecular structures of each species at various stages of the reaction. A reaction energy profile was constructed from the optimized structures, highlighting the relative energy changes in each species as they transition through the grafting process. This step-by-step analysis provided insight into the thermodynamics of the reaction, indicating the stability and reactivity of each intermediate and final product. Moreover, the energies of the frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), were determined for both the reactants and the final grafted product. These orbital energies were used to assess the electronic reactivity of each species involved, shedding light on the potential electron-donating and electron-accepting behaviors throughout the reaction. The energy gap between the HOMO and LUMO in both the reactants and the product was carefully examined, as this parameter directly influences the reactivity of the species in the grafting process. This analysis also provides critical information about the ability of the species to participate in subsequent chemical reactions, especially those involving electron transfer. In addition to the orbital energy analysis, a series of global reactivity descriptors were calculated, including chemical potential (μ), chemical hardness (η), electron affinity (A), ionization potential (I), electronegativity (χ), and electrophilicity index (ω). These descriptors are crucial for a comprehensive understanding of the electronic properties of each species and for assessing their overall reactivity during the grafting process.

To further explore the spatial distribution of electronic properties, a molecular electrostatic potential (MEP) map was generated for the grafted product. This map, calculated over the electronic surface of the final polymer, enabled the identification of regions with higher and lower electron density. The MEP map was particularly useful in confirming the presence of positively charged areas, which are associated with the quaternary ammonium groups introduced during the grafting process. These regions of high positive charge are essential for the electrostatic interactions of the grafted starch, which enhance its performance in applications like wastewater treatment.

3. Results and Discussion

3.1. Degree of Substitution (DS)

The degree of substitution (DS) is a fundamental parameter for evaluating the efficiency of starch chemical modification, as it indicates the average number of hydroxyl groups replaced by cationic functional groups on each anhydrous glucose unit (AGU) of the polymer. In this study, the cationic corn starch obtained had a DS of 1.24, calculated from the total nitrogen content measured by spectrophotometry. This value reflects a high level of functionalization, demonstrating that the grafting process with the cationic monomer MAPTAC was highly effective. During the grafting reaction, polymer chain activation is achieved by generating free radicals in the presence of cerium ammonium nitrate (CAN), which selectively oxidizes the hydroxyl groups of the starch. The most reactive site for radical formation has been reported to be the C2 carbon of the glycosidic unit due to its steric accessibility and the ease of cleavage of the C2–OH bond under acidic conditions and at elevated temperatures. The formation of a radical at C2 allows the anchoring of the MAPTAC monomer through its vinyl double bond, originating a stable covalent bond between the cationic amide group and the starch backbone. The high substitution density obtained (DS = 1.24) suggests that many sites at C2 were successfully functionalized, generating a polymeric structure with a permanent positive charge. This modification endows the starch with electrostatic properties suitable for neutralizing negatively charged colloids, such as microalgae cells, or anionic species, such as phosphates. Furthermore, a high DS value is associated with more excellent solubility of the modified polymer and better performance in coagulation and flocculation processes, key factors for its application in wastewater treatment.

3.2. Dependence of the Zeta Potential of Cationic Starch on pH

The electrokinetic behavior of the modified starch was carefully evaluated by determining the zeta potential as a function of pH, which is essential for analyzing its colloidal stability and performance as a coagulant in various pH environments. As shown in Figure 2, the cationic starch maintained a relatively stable and positive zeta potential, averaging +15.3 mV across the pH range of 5.0 to 10.0. This stability can be attributed to the presence of quaternary ammonium groups (–N⁺(CH₃)₃) introduced during the chemical modification process. These groups impart a permanent positive charge to the starch polymer, which remains unaffected by fluctuations in the pH of the medium, thereby ensuring consistent electrokinetic behavior. The zeta potential behavior of cationic starch demonstrates its ability to maintain electrostatic repulsion between particles over a broad pH range, a characteristic that enhances its stability as a colloidal system. The presence of these permanently charged functional groups on the starch surface plays a critical role in this stability, as they prevent aggregation by maintaining a constant positive charge on the particles, irrespective of changes in the surrounding medium’s acidity or alkalinity.

In contrast, the unmodified corn starch exhibited a significant decrease in zeta potential as the pH increased, reflecting a loss of electrokinetic stability. This indicates that the natural hydroxyl groups on the starch molecules become less effective in maintaining the repulsive forces between particles as the pH rises, resulting in lower stability and a tendency for aggregation under neutral to alkaline conditions. The behavior of aluminum sulfate (Alum), a reference inorganic coagulant, showed a marked dependence on pH. As the pH increased above 7.5, Alum’s zeta potential reversed, becoming negative in the alkaline range. This charge reversal is characteristic of aluminum sulfate’s decreasing ability to neutralize negatively charged colloidal particles at higher pH values, which limits its effectiveness as a coagulant under alkaline conditions.

3.3. FTIR Spectroscopy

The structural analysis of the starch graft polymer (Figure 3) confirms the successful incorporation of functional fragments onto the glucose backbone, particularly secondary amide groups (–NH–C=O) and quaternary ammonium units (–N⁺(CH₃)₃). This chemical modification introduces new functional groups into the molecule, altering its spectral characteristics. The FTIR spectrum of the modified starch shows several characteristic bands that confirm the presence of these newly introduced functional groups. In the FTIR spectrum, the intense band around 1650 cm⁻¹ is primarily attributed to the stretching vibration of the C=O group in the secondary amide, a clear indication of the incorporation of amide groups into the starch structure. Additionally, the 3300–3500 cm⁻¹ region displays a broad band corresponding to the N–H stretching vibration of the amide functional group, further confirming the presence of the secondary amide linkage. This band is typically observed in amide compounds, and its intensity and broadness suggest strong hydrogen bonding interactions.

The spectrum also shows signals in the 1000–1200 cm⁻¹ range, which are associated with the C–O–C (ether and alcohol) and C–N bonds, characteristic of the modified structure. These vibrations suggest the presence of ether linkages and confirm the successful grafting of the MAPTAC monomer onto the starch backbone. A key feature of the FTIR spectrum is the presence of bands associated with the quaternary ammonium group (–N⁺(CH₃)₃) that has been incorporated into the starch. These bands appear in the 900–1200 cm⁻¹ region and are attributed to C–N stretching vibrations and deformations associated with the nitrogen environment in the quaternary ammonium group. The specific bands in this region are distinct and differ from those of the starch backbone, contributing to a shift in the spectral pattern compared to non-functionalized starch. Furthermore, the ≡C–O–C≡ and ≡C–N stretch vibrations are observable at characteristic frequencies, typically between 1000 and 1200 cm⁻¹, indicating the incorporation of these functional groups into the starch structure. The presence of these groups highlights the success of the grafting reaction, where the MAPTAC monomer reacts with the starch backbone, adding cationic functionality that imparts permanent positive charge to the modified polymer.

3.4. Removal of Total Suspended Solids (TSSs)

Total suspended solid (TSS) removal is a key parameter in evaluating the efficiency of coagulation and flocculation processes. This study assessed the performance of cationic starch as a natural coagulant using pure cultures of Scenedesmus obliquus as a model algal biomass. As shown in Figure 4, the cationic starch achieved a TSS removal efficiency of 87% using a low coagulant-to-algae ratio of 0.0601 (w/w). This result demonstrates its high efficacy even at low dosages, which is highly desirable from a technical and economic standpoint. Furthermore, in tests conducted with actual wastewater samples, 78% of TSS was removed using a coagulant-to-algae ratio of 1.5:1, demonstrating that the modified starch maintains good operational efficiency even under more demanding conditions. Notably, the yield obtained with the cationic starch significantly exceeded that observed with the conventional inorganic coagulant (aluminum sulfate), whose efficiency was considerably lower in all the ratios tested. Figure 4 also illustrates the relationship between removal efficiency and zeta potential behavior. The modified starch is seen to achieve positive zeta potential values across a wide range of coagulant/algae ratios, which favors charge neutralization and colloidal particle aggregation, facilitating sedimentation. In contrast, aluminum sulfate showed less stable and less effective behavior regarding zeta potential modification, resulting in lower removal efficiency.

3.5. Total Phosphorus (TP) Removal

Regarding total phosphorus (TP) removal, the modified starch demonstrated a significant capacity to eliminate phosphorus, achieving an average removal of 30% of the total phosphorus present in the samples, with consistent performance across different trials. As shown in Figure 5, this performance is comparable to that obtained with the conventional inorganic coagulant (aluminum sulfate, Alum), but with the advantage of requiring a lower dosage and not generating secondary metallic residues.

Although the removal efficiency of the modified starch is slightly lower than that of Alum at specific points, it is important to highlight that this result was achieved under more sustainable conditions, positioning it as a safer alternative from an environmental perspective. Zeta potential analysis indicates that the modified starch maintains a positive surface charge within the operational range, promoting particle aggregation and the formation of compact flocs, which can facilitate the simultaneous removal of phosphorus. The predominant phosphorus removal mechanism appears to be related to the adsorption and physical entrapment of phosphates during the sedimentation of microalgae flocs induced by the cationic starch. This process represents a more environmentally friendly and efficient strategy compared to chemical precipitation mechanisms involving metallic salts.

3.6. HOMO-LUMO Orbitals

Figure 6 presents the optimized molecular structures of both starch (Figure 6a) and modified starch (Figure 6b), alongside the distribution of the HOMO and LUMO frontier molecular orbitals for both species (Figure 6c–f). Figure 6a,b depict the most stable geometries obtained through computational optimization, highlighting subtle structural changes that result from the chemical modification of starch. These changes, which may involve the introduction of functional groups or alterations in the polymer chain’s conformation, directly impact the electronic properties of the molecule. In Figure 6c, the distribution of the HOMO of the unmodified starch is shown. The HOMO is predominantly localized on the glucose rings, suggesting that these regions have the highest electron density and are therefore more likely to donate electrons in chemical interactions. This makes these regions nucleophilic, highly reactive, and prone to participation in bond formation during further chemical reactions.

Figure 6d illustrates the LUMO of starch. Here, the LUMO is more dispersed across different regions of the molecule, concentrating in areas distinct from the HOMO, indicating potential sites for electron acceptance. This spatial separation between the HOMOs and LUMOs plays a crucial role in the molecule’s reactivity, influencing its behavior when interacting with external agents such as electrophiles. The distribution of frontier orbitals undergoes significant redistribution upon chemical modification of the starch (Figure 6e,f). In Figure 6e, the HOMO of the modified starch shows an altered electron density, extending towards the regions modified by the grafted groups. This shift indicates the introduction of new nucleophilic sites in the modified starch, where electron donation is more likely to occur. In Figure 6f, the LUMO of the modified starch differs from the unmodified starch, with a more localized electron density near the newly introduced functional groups. This suggests that the modified starch has enhanced electrophilic properties, allowing it to accept electrons more readily than its unmodified counterpart.

3.7. Global Descriptors

The DFT computational study provided a comprehensive analysis of the electronic properties of both starch and modified starch, calculating various global descriptors, including the energies of the frontier orbitals (HOMO and LUMO), chemical potential (μ), ionization potential (I), electron affinity (A), electronegativity (χ), electrophilicity index (ω), and chemical hardness (η). These descriptors, calculated at the B3LYP/6-311+G(d,p) level of theory, offer an in-depth understanding of the molecules’ stability and reactivity.

The global reactivity descriptors were obtained using the following relations:

Ionization Potential (I):

I = −E HOMO

Electron Affinity (A):

A = −E LUMO

Chemical Potential (μ):

μ = (E HOMO + E LUMO)/2

Chemical Hardness (η):

η = (E LUMO − E HOMO)/2

Electronegativity (χ):

χ = −μ

Electrophilicity Index (ω):

ω = (μ²)/2η

The results, as presented in

Table 1. Calculated energy of global descriptors (eV) using B3LYP/6-311+G(d,p) for starch and modified starch.

Name	HOMO	LUMO	Chemical Potential (μ)	Ionization Potential (I)	Electronegativity (χ)	Electronic Affinity (A)	Electrophilicity (ω)	Hardness (η)
Starch	−0.24911	−0.04027	−0.20884	0.24911	0.14469	0.04027	0.00228	0.10442
Modified starch	−0.15611	−0.06840	−0.08771	0.15611	0.11226	0.06840	0.00017	0.04386

, reveal that the chemical modification of starch leads to significant changes in its electronic properties. Specifically, the HOMO of modified starch (−0.15611 eV) is less negative than that of unmodified starch (−0.24911 eV), indicating a decreased resistance to electron loss, which suggests that the modified starch is more readily able to act as a nucleophile in reactions. Similarly, the LUMO of modified starch (−0.06840 eV) is lower than that of unmodified starch (−0.04027 eV), indicating an increased ease of electron acceptance, which reflects the reduced energy required for the molecule to participate in electronic processes.

The chemical potential (μ) of modified starch (−0.08771 eV) is less negative than that of unmodified starch (−0.20884 eV), signifying a shift in the molecule’s overall reactivity and suggesting that modified starch has a higher predisposition for chemical interactions. The ionization potential (I) decreases in modified starch (0.15611 eV) compared to starch (0.24911 eV), implying that less energy is required to remove an electron from the modified starch, further increasing its potential reactivity. Electron affinity (A) increases in modified starch (0.06840 eV) compared to starch (0.04027 eV), demonstrating a greater capacity for accepting electrons, thereby enhancing its electrophilic properties. Electronegativity (χ) in modified starch (0.11226 eV) is slightly lower than in unmodified starch (0.14469 eV), suggesting a reduced tendency to attract electron density. The electrophilicity index (ω) of modified starch decreases from 0.00228 eV to 0.00017 eV, indicating a more homogeneous electronic redistribution and stabilizing the frontier orbitals following modification. Finally, chemical hardness (η) shows a significant reduction in modified starch (0.04386 eV) compared to unmodified starch (0.10442 eV), reflecting a lower resistance to changes in electron density and enhancing the flexibility of the molecule in response to external perturbations. These changes in the global descriptors reflect the successful chemical modification of starch, highlighting the enhanced reactivity and flexibility of the modified polymer. The reduced chemical hardness and increased electrophilic capacity make the modified starch more suitable for applications requiring electron exchange, such as adsorption processes or catalysis.

3.8. Molecular Electrostatic Potential Map

The molecular electrostatic potential map (MEPM) is a fundamental tool in the computational characterization of molecules, as it allows the visualization of the three-dimensional distribution of electron density and the prediction of regions with different chemical reactivity. This map is constructed by calculating the potential generated by the distribution of electronic and nuclear charges and is projected onto an isoelectronic surface of the optimized molecule. The colored regions indicate the intensity and polarity of the electrostatic field: the red areas represent regions with negative potential (electron-rich, nucleophilic), while the blue areas indicate regions with positive potential (electron-deficient, electrophilic).

Figure 7 shows the molecular electrostatic potential maps calculated using the B3LYP/6-311+G(d,p) method for the optimized starch structure (Figure 7a) and the modified starch (Figure 7b). In Figure 7a, corresponding to the unmodified starch, a relatively homogeneous distribution of the electrostatic potential is observed, with a predominance of orange and red zones around the hydroxyl (-OH) groups and oxygens of the glucose rings. These regions indicate areas with higher electron density, which could act as nucleophilic sites in molecular interactions or recognition processes. In contrast, Figure 7b, corresponding to the modified starch, shows a notable redistribution of the potential. A higher concentration of blue regions is observed, especially in areas where the incorporation of new functional groups is presumed, suggesting an increase in the electronic polarization of the system. This variation in the MEP map indicates the generation of new electrophilic and nucleophilic centers, which may be directly related to the greater versatility of the modified starch to interact with other chemical species or form noncovalent bonds. These differences in the electrostatic potential pattern between the two systems reflect the electronic impact of the chemical modification and allow us to predict possible changes in solubility, affinity for specific reagents, and ability to participate in hydrogen bonds or dipole-type interactions.

Figure 8 illustrates the variation in Gibbs free energy (ΔG) throughout the starch modification process via graft polymerization with MAPTAC. Initially, the system’s Gibbs free energy, corresponding to anhydrous glucose in the presence of Ce(IV) as an oxidizing agent, is approximately −1.0653 × 10⁷ kJ/mol. At this stage, the starch or cellulose backbone remains structurally unmodified. The interaction with Ce(IV) subsequently induces the formation of a free radical on the starch structure, accompanied by a reduction in Ce(IV) to Ce(III) and the release of protons (H+). This step results in a slight increase in Gibbs free energy to −1.0673 × 10⁷ kJ/mol, suggesting that radical formation is thermodynamically less favorable than the previous stage. This indicates that the stability of the free radical depends on experimental conditions such as pH, temperature, and initiator concentration.

Following radical formation, the addition of MAPTAC leads to a significant decrease in Gibbs free energy, reaching −6.5283 × 10⁶ kJ/mol. This sharp reduction suggests that the graft polymerization reaction is highly thermodynamically favorable, highlighting the strong affinity between the starch radical and the cationic monomer. The final stage of the process, corresponding to the formation of the grafted starch polymer, exhibits a Gibbs free energy value of −6.5292 × 10⁶ kJ/mol, demonstrating a stability comparable to the previous step. The minimal variation in free energy between these two stages suggests that, once grafting occurs, the final product remains stable and does not encounter significant energy barriers for conservation.

4. Conclusions

In this study, we successfully synthesized and characterized a MAPTAC-modified cationic corn starch, offering a sustainable and efficient alternative for phosphorus and suspended solids removal in wastewater treatment. Through free radical graft polymerization, the starch was modified with quaternary ammonium groups, achieving a high degree of substitution (DS = 1.24), indicating effective functionalization. Theoretical DFT calculations revealed significant changes in the electronic properties of the modified starch, including a decrease in chemical hardness (from 0.10442 eV to 0.04386 eV) and a lower ionization potential (from 0.24911 eV to 0.15611 eV), demonstrating enhanced electronic reactivity. The experimental results showed that the modified starch exhibited stable zeta potential values averaging +15.3 mV across a wide pH range (5.0–10.0), outperforms aluminum sulfate (Alum) in coagulation-flocculation trials, with up to 87% removal of total suspended solids (TSS) and 30% removal of total phosphorus (TP). Additionally, the modified starch showed excellent performance at lower dosages, without generating secondary metallic residues, and was proven to be a cost-effective and environmentally friendly coagulant, offering a promising solution for wastewater treatment. These findings confirm that MAPTAC-modified starch is a viable, biodegradable, and efficient alternative to traditional coagulants, contributing to sustainable water purification strategies.