New Insights into the Adsorption Mechanism of Vanadium Through Quaternary Ammonium Salt-Functionalized SiO₂: Synergistic Experiments Utilizing Energy Decomposition Analysis

Abstract

Introducing organic functional groups to adsorbent surfaces enhances vanadium adsorption, an effective strategy for vanadium enrichment. In a quest for a profounder comprehension of the above adsorption mechanism, this study synthesized five types of quaternary ammonium salt-functionalized silica (QAS-SiO₂) and investigated the influence of functional groups, pH values, contact time, and temperature on vanadium (V) adsorption. The results indicated that the optimal QAS-SiO₂ (SiO₂@DMOA) achieved a vanadium adsorption rate of 99.40% and a maximum adsorption capacity of 39.16 mg g⁻¹. SiO₂@DMOA exhibited favorable adsorption selectivity for V over chromium (Cr), with a maximum separation factor (β_V/Cr) of 135.42 at pH 3.3. SiO₂@DMOA maintained efficient adsorption performance over five repeated cycles. A fusion of adsorption trials with energy decomposition analysis (EDA) tentatively unveiled that both chemical bonds and non-bonding interactions contributed to the interaction energy between organic functional groups and vanadium. Among them, chemical bonds accounted for 80.26%, while non-bonding interactions accounted for 19.74%. Based on EDA analysis, the interaction characteristics of different structural quaternary ammonium salts with vanadium in adsorption and extraction processes are discussed. Additionally, steric hindrance, the charge of the vanadium species, polarizability, and solvation effects, all played significant roles in the adsorption process.

1. Introduction

Vanadium (V), an important metallic element, finds indispensable utility in aerospace alloys, steel production, chemical catalysts, and energy materials [1,2]. It was reported that global V consumption was expected to soar to 130.1 kt by 2024 and increase with an annual growth rate of 5% [3]. However, V frequently coexists with over 70 other mineral metals (including iron (Fe), titanium (Ti), uranium (U), and aluminum (Al)) with a content of about 1%, giving rise to a difficulty in its separation and purification [1,2]. Moreover, the production process of the V-containing final products generates a substantial amount of V-based waste residues and effluents [4], resulting in the waste of the resource and environmental pollution. Herein, designing and developing materials and technologies for the efficient adsorption, separation, and regeneration of vanadium from residues and effluents holds significant scientific value and practical importance for environmental protection and sustainability.

To realize the enrichment and recovery of V, various techniques and methods have been reported, including chemical precipitation, ion exchange, solvent extraction, bioremediation, photocatalytic reduction, and membrane separation [5,6]. However, the abovementioned methods have some drawbacks, for example, high toxicity, high energy consumption, complicated processes, and high cost [7]. Owing to its high purification efficiency, low energy consumption, and eco-friendliness, adsorption technology has gained widespread application in diverse metal separation and recovery [8]. Recently, a great diversity of biomass materials (collagen fiber [9], chitosan [10], sawdust [11]), mineral materials (montmorillonite [12], kaolinite [13], and zeolite [14]), and industrial wastes [15,16] have been developed for V adsorption and recovery, but the strict activation condition and poor reusability are still bottlenecks limiting the industrial application. Thanks to its outstanding physiochemical nature (such as high specific surface area, hydrothermal stability, and a diversity of surface functionality) and cost effectiveness, SiO₂ is attracting more and more interest [6]. Numerous SiO₂-based composites modified with trypsin [17], tetrakis(4-carboxyphenyl)porphyrin [18], 2-methyl-8-quinolinol [8], thiol [19], and aminopropyl triethoxysilane [20] were synthesized and employed for vanadium adsorption, recovery, or detection. Due to the designability, adjustability, reactivity, versatility, and flexible nature of the organic functional groups, the incorporation of organic functional moieties has emerged as a potent strategy and calculated maneuver to enhance the efficacy and selectivity of metal adsorption.

Considering their high efficiency in V extraction/separation/adsorption [21,22] and the diversity of their chemical structure, quaternary ammonium salts, as a crucial family of organic functional groups, have been used to modify the adsorbents and resins for the adsorption of V’s other pollutants [20,23,24,25]. The adsorption mechanisms are predominantly attributed to the electrostatic interaction, ion exchange, adsorption–reduction process, and formation of inner-sphere complexes [26]. Via electrostatic attraction and ion exchange, it is well understood that the nitrogen (N) in these salts bears a positive charge, facilitating the formation of ion pairs with negatively charged V species (Scheme 1). Nevertheless, the roles of the substituents R¹, R², and R³ attached to the N in the V adsorption process have seldom been discussed in depth, and, in particular, have not been quantitatively analyzed. In addition, it is noteworthy that the quaternary ammonium salts (such as Aliquat 336) can serve as highly efficient extractants to extract V from the V-bearing leachates [27,28,29,30]. Quaternary ammonium salt extractants usually have multiple long-chain alkyl substituents, with a key role of enhancing the extractant’s hydrophobicity, thereby facilitating the transfer of metal ions from the aqueous phase to the organic phase. To the best of our knowledge, there is little discussion about the roles of the functional groups decorated on the N atom (for example, the long-chain or short-chain alkyl substituent enhances metal binding). Adsorption and extraction of vanadium both entail interactions between surface-bound organic functional groups or organic extractants and vanadium species. However, detailed discussions of the structural distinctions between these organic components are uncommon.

In this work, we synthesized five types of silica gels modified by quaternary ammonium salts with different chemical structures (organic functional groups) and investigated their adsorption effect toward V(V) under various conditions (such as pH, contact time, ion strength, and presence or absence of the Cr(VI)). In addition, the reusability of quaternary ammonium salt-functionalized silica gels was also investigated via adsorption–desorption experiments. Among these five organic functional groups, three are linear alkyl chains with various chain lengths, and the other two are ethanolamine-based fragments. The V(V) extraction and adsorption is closely correlated with the intrinsic structural nature. The existing explanations pertaining to vanadium adsorption predominantly encapsulate and generalize the prominent features of adsorption, yet they lack insights into the inherent nature of interactions between organic functional groups and vanadium. To transcend these limitations posed by the “phenomenology”, we present a quantitative analysis of the intricate interactions between organic functional groups and the V ion (including both chemical bonds and non-bonding) via energy decomposition analysis (EDA), aiming to provide a new approach or perspective to understand and predict the molecular interaction, which is difficult to directly determine in experiments. This work is helpful to deepen our understanding of the interaction mechanism between quaternary ammonium salts and transition metal ions, and is expected to guide the design and synthesis of related materials in the future.

2. Results and Discussion

2.1. Characterization

2.1.1. Fourier Transform Infrared (FTIR) Spectroscopy

FTIR spectra of SiO₂@HCl, SiO₂@DMOA, and V-loaded SiO₂@DMOA (SiO₂@DMOA-V) are shown in Figure 1. The peak at 3420 cm⁻¹ corresponds to -OH stretching vibrations due to physically adsorbed water and surface hydroxyl groups of the silica [31]. The region between 2860 cm⁻¹ and 2960 cm⁻¹ is attributed to methyl (-CH₃) and methylene (-CH₂-) stretching vibrations [32]. The peaks at 1100 cm⁻¹ and 806 cm⁻¹ correspond to asymmetric and symmetric stretching vibrations of Si-O-Si bonds, respectively, while the peak at 470 cm⁻¹ is due to Si-O-Si bending vibrations [31,32]. A weak peak at 972 cm⁻¹ is assigned to the V=O functional group of the SiO₂@DMOA-V [33]. This confirms the successful functionalization of SiO₂@DMOA and its adsorption of the V(V).

2.1.2. Scanning Electron Microscopy (SEM)

SEM images of SiO₂@HCl, SiO₂@CPTES, SiO₂@DMOA, and SiO₂@DMOA-V are shown in Figure 2. It can be clearly seen that the size of the bulks reduced and the roughness of the surface of the bulk increased upon modification by the functional groups. In particular, after the adsorption of the V(V) into the SiO₂@DMOA, a large quantity of small particles aggregated on the surface of the bulk. The substantial differences in physical structure before and after V(V) loading on SiO₂@DMOA revealed that the pores on the surface were filled with smaller particles (of aggregated V(V)), resulting in a rougher surface. This could be attributed to the V(V) being anchored to the surface by functional groups. The atom percentages of the Si, O, C, N, Cl and V (measured by EDS) are listed in Table S1. The results indicate successful preparation of SiO₂@CPTES, which contains 35.12% carbon and 2.16% chlorine, in comparison to SiO₂@HCl. SiO₂@DMOA shows 4.96% nitrogen, higher than SiO₂@CPTES, implying successful modification with N,N-dimethyloctylamine on the silicon gel surface and confirming SiO₂@DMOA preparation. Additionally, SiO₂@DMOA-V displays 1.45% vanadium versus SiO₂@DMOA, confirming the adsorption of V on the surface.

2.1.3. Time-of-Flight Mass Spectrometry (TOF-MS)

There are various forms of V in aqueous solutions, influenced by several factors such as concentration, pH, and ionic strength. Various monomeric and polymeric oxo-vanadate species, and tetramers (V₄ species) and decamers (V₁₀ species), were reported [34]. It is reported that complicated forms of V in aqueous solutions significantly affect adsorption efficiency [35].

TOF-MS was utilized to investigate the form of the V ion at different pHs (from pH = 1 to 6) [36]. The TOF-MS spectra of vanadium-containing solution (2 × 10⁻³ M) at pH = 3 and other pH values are presented in Figures S1–S6. In the pH range of 1~2, the predominant forms of V were the dimers (V₂, m/z: 152.88–199.81) and tetramers (V₄, m/z: 216.83–555.27). At pH = 3~6, the main species was V₁₀ at m/z: 462.66 since V₂ and V₄ species can transform into V₁₀ species (Equations (1)–(3)) [34]. Under optimal adsorption conditions, vanadium primarily existed in the form of V₁₀ in the solution and was adsorbed by SiO₂@DMOA.

$$4{\mathrm{H}}_2\mathrm{V}{\mathrm{O}}_4^{-}+3{\mathrm{H}}^{+}\leftrightarrow \mathrm{H}{\mathrm{V}}_4{\mathrm{O}}_{11}^{-}+5{\mathrm{H}}_2\mathrm{O}$$

(1)

$$2\mathrm{H}{\mathrm{V}}_2{\mathrm{O}}_6^{-}+{\mathrm{H}}^{+}\leftrightarrow \mathrm{H}{\mathrm{V}}_4{\mathrm{O}}_{11}^{-}+{\mathrm{H}}_2\mathrm{O}$$

(2)

$$5\mathrm{H}{\mathrm{V}}_4{\mathrm{O}}_{11}^{-}+{\mathrm{H}}^{+}\leftrightarrow 2{\mathrm{V}}_{10}{\mathrm{O}}_{26}^{2-}+3{\mathrm{H}}_2\mathrm{O}$$

(3)

2.2. Screening of Optimal QAS-SiO₂

Variations in the affinity of adsorbent structures can influence the efficiency of the adsorption of the metal. In this work, five QAS-SiO₂ absorbents (as shown in Figure 3) were prepared with different carbon chains, aromatic hydrocarbon groups, and hydroxyl-containing groups. A previous report indicated that due to a low V content in leaching solutions, ammonium salts as extractants exhibited optimal removal efficiency only at pH = 3 [37]. Separately, 50 mg of SiO₂@DMOA, SiO₂@TOA, SiO₂@TBE, SiO₂@NTE, and SiO₂@TMA were mixed with vanadium(V) solution (2 × 10⁻³ M, pH = 3) at room temperature for a period of 12 h to adsorb. Based on the adsorption performance, the material with the highest adsorption capacity was selected for further in-depth investigation. As demonstrated in Figure 1, the adsorption rate and q_e of SiO₂@NTE and SiO₂@TMA were 25.65% and 10.11 mg·g⁻¹, and 14.16% and 5.58 mg·g⁻¹, respectively. For SiO₂@TOA and SiO₂@TBE, lower values were exhibited of 6.09% and 2.40 mg g⁻¹, and 3.03% and 1.19 mg g⁻¹, respectively. It is noteworthy that SiO₂@DMOA demonstrated a superior adsorption rate (99.40%) and adsorption capacity (39.16 mg g⁻¹), which were significantly higher than those of the other four absorbents. The remarkable difference is probably attributed to the structural variation of the absorbent and the existing form of the V(V) at pH 3, which will be discussed in depth later. For brevity, only the experimental data of SiO₂@DMOA are presented.

2.3. Effect of the pH on Adsorption Efficiency

Solution pH is a crucial factor to affect adsorption efficiency [38]. The results in Figure 4a demonstrate that as the pH increased from 2 to 3, q_e enhanced from 5.58 mg·g⁻¹ to 37.70 mg·g⁻¹, followed by a decrease to 36.39 mg g⁻¹ at pH 4. This indicates an effective V adsorption range of pH 2–4. Further investigation was carried out within the pH range of 2.3–3.9, which revealed a continuous increase in q_e from 19.68 mg·g⁻¹ at pH 2.3 to the maximum value of 39.16 mg·g⁻¹ at pH 3.3. This may be associated with the different chemical forms of the V(V) in aqueous solutions.

2.4. Optimal Dosage of SiO₂@DMOA

A given amount of SiO₂@DMOA (15–100 mg) was mixed with the V(V) solution (20 mL, 2 × 10⁻³ M, pH 3.3) and allowed to adsorb for 12 h. Figure 4b suggests that the adsorption rate of the V(V) increased from 48.81% (15 mg dosage) of SiO₂@DMOA to 99.40% (50 mg dosage). With increasing the dosage of the SiO₂@DMOA, the V(V) adsorption reached an equilibrium value or a saturate state, because no more adsorption sites were available. Therefore, 50 mg of SiO₂@DMOA was selected as the optimal dosage. The dosage of the adsorbent was only 0.25% of the vanadium-containing water.

2.5. Effect of Contact Time

In order to evaluate the impact of contact time on the adsorption process, a mixture of 50 mg SiO₂@DMOA and the V(V) solution (20 mL, 2 × 10⁻³ M, pH = 3.3) was used for the adsorption experiment and the contact time was set from 1 to 60 min. As shown in Figure 5, the adsorption rate rapidly increased to 7.21 mg·g⁻¹·min⁻¹ within the first 5 min, which suggests abundant active adsorption sites on SiO₂@DMOA’s surface [39]. Subsequently, the rate slowed to 0.32 mg·g⁻¹·min⁻¹ between 5 and 15 min. After the adsorption of 15 min, adsorption reached an equilibrium state with q_e~39.16 mg·g⁻¹, in line with a previous report on metal adsorption kinetics [38].

2.6. Adsorption Kinetics

To elucidate the adsorption kinetics of V(V) in the presence of SiO₂@DMOA, nonlinear regression analysis was performed using pseudo-first-order (PFO), pseudo-second-order (PSO), and Elovich models [40], as presented in Equations (4)–(6).

$$q_{\mathrm{t}}=q_{\mathrm{e}}\left(1-e^{{\mathrm{K}}_1\mathrm{t}}\right)$$

(4)

$$q_{\mathrm{t}}={\displaystyle \frac{K_2{q}_{\mathrm{e}}^{2}t}{1+K{q}_{\mathrm{e}}t}}$$

(5)

$$q_{\mathrm{t}}={\displaystyle \frac{1}{\beta }}\mathit{ln}\left(1+\alpha \beta t\right)$$

(6)

where q_e (mg·g⁻¹) and q_t (mg·g⁻¹) represent the adsorption capacity at equilibrium and the given time (t, min), respectively. K₁ (min⁻¹) and K₂ (g·mg⁻¹·min⁻¹) are the pseudo-first order and pseudo-second order model constants, respectively. α (mg·g⁻¹·min⁻¹) is the initial adsorption rate constant, and β (g mg⁻¹) is a constant related to the extent of surface coverage and activation energy of chemical adsorption. The fitting curves and detailed parameters are shown in Figure 6 and

Table 1. Adsorption kinetic parameters for the adsorption of V(V) in various models on SiO₂@DMOA.

Kinetic Model	Parameters	Values
Pseudo first order	qe (mg g−1)	37.63
	K1 (min−1)	0.847
	R2	0.709
	RMSE	2.701
Pseudo second order	qe (mg g−1)	40.33
	K2 (mg g−1 min−1)	0.0369
	R2	0.937
	RMSE	1.259
Elovich	α (mg g−1 min−1)	2599.132
	β (g mg−1)	0.237
	R2	0.887
	RMSE	1.686
Intraparticle diffusion	Ki,1 (mg g−1 min1/2)	0.943
	Ki,2 (mg g−1 min1/2)	0.490
	C1 (mg g−1)	19.91
	C2 (mg g−1)	38.08

, respectively. In Table 1, the coefficient of determination (R²) and the root mean square of the error (RMSE) were used to assess the goodness of fit with the experimental data [41].

Among the models, PSO (R² = 0.937, RMSE = 1.259) demonstrated a better fit than PFO (R² = 0.709, RMSE = 2.701), indicating chemical adsorption of V(V) occurred on SiO₂@DMOA. The parameters of the Elovich model, α (2599.132) and β (0.237) also suggest a chemical reaction between SiO₂@DMOA and V(V) in a short time frame [42].

To explore the diffusion mechanism, intraparticle diffusion and Boyd’s models were employed to describe in detail the adsorption process, as shown in Equations (7)–(9) [41]:

$$q_t=K_{\dot{\mathrm{i}}\mathrm{d}}{t}^{{\displaystyle \frac{1}{2}}}+C$$

(7)

$$B_t=-0.4977-\ln \left(1-F\right),For F\left(\mathrm{t}\right)>0.85$$

(8)

$$B_t=\left(\sqrt{\pi }-\sqrt{\pi -{\displaystyle \frac{{\pi }^{2}F}{3}}}\right),For F\left(\mathrm{t}\right)\le 0.85$$

(9)

where K_id (mg·g⁻¹·min^1/2) is the intraparticle diffusion rate constant, and C is a constant estimating the thickness of the boundary layer. B_t is Boyd’s number, and F(t) can be expressed as q_t/q_e at a specific time t.

The particle intraparticle diffusion model was fitted to the experimental data, yielding the corresponding parameters (Figure 7a and Table 1). Comparison of slopes (K_i,1 = 0.943 > K_i,2 = 0.490) and intercepts (C₂ = 38.08 > C₁ = 19.91) revealed two linear plots, indicating multiple steps influencing the sorption process [41]. These include film diffusion of V(V) on the SiO₂@DMOA surface and intraparticle diffusion within the particles [43], with film diffusion showing a higher rate. The change in intercept is due to the gradual decrease in adsorbate concentration on the adsorbent surface over time, leading to a reduction in the mass transfer rate to the adsorbent.

Through analysis using Boyd’s model (Figure 7b), the determining factor of the rate-controlling step in the adsorption process can be discerned. If the fitting result is not a straight line but a curve, it indicates that film diffusion may be a primary rate-limiting step [44].

In summary, based on the fitting results of the adsorption model, both film diffusion and intraparticle diffusion contribute to the adsorption process. However, film diffusion emerges as the dominant rate-limiting factor, which plays a decisive role in governing the entire adsorption process.

2.7. Adsorption Isotherm

The adsorption isotherm can be utilized to investigate the equilibrium state of V(V) adsorption onto SiO₂@DMOA at a specific temperature and elucidates the distribution of V(V) between the liquid and solid phases. The Freundlich and Langmuir adsorption models were employed to establish the adsorption isotherms, respectively (Equations (10) and (11)) [40].

$$q_{\mathrm{e}}={\displaystyle \frac{q_{\mathrm{m}}{K}_{\mathrm{L}}{C}_{\mathrm{e}}}{1+K_{\mathrm{L}}{C}_{\mathrm{e}}}}$$

(10)

$$q_{\mathrm{e}}=K_{\mathrm{F}}{C}_{\mathrm{e}}^{{\displaystyle \frac{1}{\mathrm{n}}}}$$

(11)

where q_e (mg·g⁻¹) and q_m (mg·g⁻¹) represent the experimental adsorption capacity and the maximum adsorption capacity, respectively, and C_e (mg·L⁻¹) is the equilibrium concentration of V(V) in the solution. K_F (L·g⁻¹) and n are the Freundlich constants related to adsorption capacity and energy, and K_L (L·mg⁻¹) is the Langmuir constant associated with adsorption energy.

The results of the nonlinear regression are depicted in Figure 8, and the fitting parameters are presented in

Table 2. Isotherm model fitting parameters for the adsorption of V(V) onto SiO₂@DMOA.

Langmuir					Freundlich
qm (mg g−1)	KL (L mg−1)	R2	RMSE	KF (L g−1)	1/n	R2	RMSE
71.30	0.0927	0.982	2.313	20.470	0.238	0.764	8.278

. Comparing the Langmuir model to the Freundlich model, the Langmuir model exhibits a higher correlation coefficient (R²) and a lower root mean square error (RMSE), which suggests a better fit to the experimental data. This indicates that the adsorption of V(V) onto SiO₂@DMOA occurred predominantly through a monolayer chemical adsorption process [45].

The efficiency of the predicted adsorption process can be expressed using the dimensionless separation factor R_L associated with the Langmuir model (Equation (12)) [41].

$$R_{\mathrm{L}}={\displaystyle \frac{1}{1+K_L{C}_o}}$$

(12)

where C_o (mg·g⁻¹) is the initial concentration of V(V), and K_L (L mg⁻¹) is the Langmuir constant related to adsorption energy.

By conducting nonlinear fitting with C_o as the variable, the results can be interpreted based on the shape of the fitted curve and the R_L value. Figure S7 shows that the curve is concave and R_L is 0.40~0.028, which indicates a favorable adsorption process [46]. R_L dropped with an increase in C_o, revealing that SiO₂@DMOA is more inclined to absorb high concentrations of V(V) [41].

2.8. Adsorption Thermodynamics

A mixture of SiO₂@DMOA (50 mg) and V(V) solution (20 mL, 2 × 10⁻³ M, pH = 3.3) was used to investigate the effect of the temperature on the adsorption efficiency in a temperatures range of 288~318 K for 30 min. In Figure 9a, the results reveal that q_e increased with increasing the temperature, and reached 39.16 mg·g⁻¹ at 318 K. Reduction in the boundary layer thickness around the adsorbent is probably ascribed to the decrease of mass transfer resistance and enhancement of diffusion of V(V) within the pores of the adsorbent [47].

As shown in Figure 9b, the Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) can be calculated using the plot of the lnKc vs. 1/T (Equations (13)–(15)) [41].

$$K_c={\displaystyle \frac{C_o-C_e}{C_e}}$$

(13)

$$\mathit{ln}{K}_c={\displaystyle \frac{-\Delta H^o}{RT}}+{\displaystyle \frac{\Delta S^o}{R}}$$

(14)

$$\Delta G^o=\Delta H^o-T\Delta S^o$$

(15)

where K_c is the thermodynamic equilibrium constant; C_o and C_e (mg L⁻¹) represent the initial and equilibrium concentrations of V(V), respectively. R (8.314 J·mol⁻¹·K⁻¹) is the gas constant and T (K) is the temperature of the adsorption process.

The thermodynamic parameters for the adsorption of V(V) onto SiO₂@DMOA are summarized in

Table 3. Thermodynamic parameters.

Temperature (K)	Parameters
	lnKC	ΔG° (kJ·mol−1)	ΔH° (kJ·mol−1)	ΔS° (J mol−1 K−1)
288	3.18	−9.81	27.08	128.08
298	3.60	−11.09
303	3.75	−11.73
308	3.80	−12.37
318	4.31	−13.65

. ΔH° = 27.08 kJ·mol⁻¹ (>0) indicates an endothermic adsorption process. ΔS° = 128.08 J mol⁻¹ K⁻¹ (>0) suggests an increase in randomness at the solid–liquid interface during the adsorption process, that is, the heavy metal ions near the surface of the adsorbent were more disordered than before adsorption, and the amount bound to the adsorbent increased [48]. The negative ΔG° value indicates that the adsorption process was spontaneous, and the decrease in ΔG° with increasing temperature suggests a more favorable adsorption process at higher temperatures, which is consistent with previous reports [49].

2.9. Effect of Ionic Strength

In the V-containing wastewater, other ions (with a high concentration) might affect the structural form of the V(V) or the binding of the adsorbent with the V(V). To investigate this, 50 mg of SiO₂@DMOA was added to V(V) solutions (20 mL, 2 × 10⁻³ M, pH = 3.3) with varying NaCl concentrations (0.01, 0.03, 0.08, 0.10, 0.30, 0.50 M) and allowed to adsorb for 30 min. The results in Figure 10a reveal that the adsorption capacity changed little with an increase in the concentration of the NaCl from 0 to 0.1 M·L⁻¹, but followed by a gradual reduction with further increasing the concentration to 0.5 M·L⁻¹. That is, the impact was less significant at low NaCl concentrations (<0.1 M). A similar result was reported, where the effect of NaNO₃ was noticeable above 0.1 M in the V(V) adsorption process using the silica dioxide as an adsorbent [50]. Excessive ions could potentially alter the activity of the V(V) and slightly increase electrostatic repulsion, affecting the affinity of SiO₂@DMOA functional groups with the V(V) ions [51,52].

2.10. Separation of the V and Cr

Due to the similarity in physicochemical properties of V and Cr, their separation still is a challenge [53]. Based on the result above, SiO₂@DMOA (50 mg) was added into a mixed solution (20 mL, pH of 2–5) with V(V) (2 × 10⁻³ M) and Cr(VI) (1.63 × 10⁻³ M) for investigating the separation of V and Cr. As shown in Figure 10b, a maximum separation coefficient β_V/Cr (135.42) was observed at pH 3.3. Decreasing pH from 3 to 2 resulted in a decrease in q_e from 38.47 mg·g⁻¹ to 3.85 mg·g⁻¹, while q_e for Cr(VI) increased from 8.70 mg·g⁻¹ to 20.60 mg·g⁻¹. This may arise from different nucleophilicities of oxygen-containing metal anions. Polymeric vanadates often possess a greater negative charge and larger thermodynamic radius compared to chromates, leading to higher polarization and nucleophilicity of vanadates [35]. At pH = 2, q_e of the V(V) (3.85 mg·g⁻¹) was lower than that of the Cr(VI) (20.60 mg·g⁻¹), indicating that pH influences the chemical species of the V(V) in the solution. It was reported that there is predominantly VO₂⁺ at pH < 2, and it would transform into polynuclear anions at pH = 2.5~6 [5]. For Cr(VI), the primary species is HCrO₄⁻ with a concentration lower than 2 mM and at pH = 1~6 [54]. The different forms of metal anions in aqueous solution are the key to understanding the discrepancy in selective adsorption of the V(V) and Cr(VI) [55].

2.11. Desorption and Regeneration

Adsorption–desorption experiments were conducted to evaluate the reusability of SiO₂@DMOA. The adsorption–desorption results are depicted in Figure 11. To determine the optimal desorption agent, the V-loaded SiO₂@DMOA was subjected to a single desorption using 1 M HCl, H₂SO₄, and HNO₃, separately. The results indicated that HNO₃ showed the highest desorption efficiency (84.01%) followed by HCl (78.18%) and H₂SO₄ (69.86%). Subsequent adsorption–desorption experiments were carried out using HNO₃ as the desorption agent. After two cycles, q_e slightly decreased from 39.15 mg·g⁻¹ (initial) to 36.36 mg·g⁻¹ (cycle-5), probably due to incomplete release of active sites during the desorption or small portion of V(V) remaining in the pores of SiO₂@DMOA. This could arise from the formation of ionic bonds between V(V) and SiO₂@DMOA’s active sites [41]. Additionally, dissolution in the desorption agent and minor mass loss of SiO₂@DMOA may contribute to the slight reduction in q_e.

2.12. Adsorption Mechanisms

Intuitive bonding models based on the principles of quantum mechanics are widely adopted to explore the experiment results and phenomena. However, it is still a challenge to obtain a better and in-depth understanding of the intrinsic nature of the material and prediction of the dynamic process because these models depend significantly on the parameters (which are temporarily set) and are probably in the absence of a firm theoretical foundation. Therefore, a more precise and effective method or mechanism which can integrate the quantum mechanics should be developed to further assist in the sole empirical expectation or observation [56]. In this work, the ion exchange used to delineate the adsorption mechanism is not enough because it falls short in providing a comprehensive insight into chemical bonding and the non-bonding interactions. The energy decomposition analysis (EDA), which was developed by Morokuma [57] and Ziegler and Rauk [58], is a powerful method for bridging the gap between elementary quantum mechanics and the nature of the chemical bond and non-bonding interactions. Via EDA, the instantaneous interaction energy ΔE_int between two components A and B in a molecule (A–B) can be divided into three well-defined parameters, which are shown as follows: ΔE_elstat, the quasi-classical electrostatic interaction energy between the charge densities of the components; ΔE_Pauli, the exchange repulsion between the components based to Pauli’s principle; and ΔE_orb, the energy gain due to orbital mixing of the components. These three parameters are defined by assigning intermediate states of the entire system during the course of bond formation, which are calculated by the laws of quantum mechanics. Current EDA-derived methods can be classified into three subgroups [59], the variation-based EDA method, perturbation-based EDA method, and real space-based EDA method, which have been employed to characterize, quantify, and interpret interactions between components of quantum systems [56,60]. In this work, a method based on dispersion-corrected density functional theory (DFT), known as sobEDA, is utilized to shed light on the essence of interactions during adsorption processes. The sobEDA methodology combines the quantum chemistry program Gaussian and the wavefunction analysis program Multiwfn to perform sobEDA energy decomposition, and has demonstrated its efficacy in weak interactions, chemical bonding interactions, open-shell configurations systems, and the interplay among diverse molecular components [61].

The total interaction energy ΔE_int in the sobEDA model can be divided into the following physical parameters, as shown in Equation (16):

$$\mathsf{\Delta }{E}_{\mathrm{i}\mathrm{n}\mathrm{t}}=\mathsf{\Delta }{E}_{\mathrm{e}\mathrm{l}\mathrm{s}}+\mathsf{\Delta }{E}_{\mathrm{x}}+\mathsf{\Delta }{E}_{\mathrm{D}\mathrm{F}{\mathrm{T}}_{\mathrm{c}}}+\mathsf{\Delta }{\mathrm{E}}_{\mathrm{d}\mathrm{c}}+\mathsf{\Delta }{E}_{\mathrm{r}\mathrm{e}\mathrm{p}}+\mathsf{\Delta }{E}_{\mathrm{o}\mathrm{r}\mathrm{b}}$$

(16)

ΔE_els: Classical electrostatic interaction energy between components (with positive or negative value).

ΔE_x: Exchange interaction energy (with a negative value), which reflects the contribution of exchange-related interaction energy between components.

ΔE_DFTc: DFT correlation energy (DFTc stands for DFT correlation and the value is generally negative), which reflects the contribution of Coulomb-related interaction energy between components).

ΔE_rep: Pauli repulsion energy (with a positive value), which reflects the energy increase caused by electron repulsion between different components to satisfy the Pauli exclusion principle.

ΔE_orb: Orbital interaction energy (with a negative value), which comes from the energy change caused by the mixing of occupied and unoccupied orbitals within and between components, physically reflecting the overall impact of electron distribution polarization within components and electron transfer between components on energy. Covalent interactions are also included in this parameter.

ΔE_dc: Dispersion correction energy (with a negative value).

In

Table 4. Typical parameters calculated by sobEDA analysis (kcal·mol⁻¹).

	qe (mg·g−1)	ΔEint	ΔEels	ΔEx	ΔErep	ΔEorb	ΔEDFTc	ΔEdc
DMOA-V10	39.16	−27.49	−63.56	25.77	53.96	−22.48	−0.49	−20.68
TMA-V10	5.58	−15.69	−40.10	10.70	35.47	−12.52	−0.05	−9.19
NTE-V10	10.11	−32.77	−67.31	11.93	67.49	−29.00	0.09	−15.97
TOA-V10	2.40	−32.89	−76.63	35.38	70.50	−31.16	−0.60	−30.39
TBE-V10	1.19	−33.98	−68.93	12.48	70.83	−30.27	0.11	−18.20
DMOA-HCrO4	8.70	−12.77	−30.42	11.77	28.08	−15.51	−0.12	−6.57

and Figure 12, ΔE_int values of five functionalized-SiO₂ loaded with V are negative, affirming the existence of an adsorptive interplay. ΔE_int of five quaternary ammonium salts with V₁₀ species (V₁₀) ranks in the following order: TBE-V₁₀ > TOA-V₁₀ > NTE-V₁₀ > DMOA-V₁₀ > TMA-V₁₀. Notably, no obvious difference could be seen among ΔE_int of TBE, TOA, and NTE. The longest molecular chain and highest molecular weight resulted in a high E_int of the SiO₂@TOA. The high E_int of the SiO₂@NTE and SiO₂@TBE is probably mainly attributed to the multiple -OH groups. SiO₂@TOA, SiO₂@DMOA, and SiO₂@TMA exhibit a similarity in their functional groups (alkyl group), as demonstrated in Figure 3. Generally, the alkyl group with a longer molecular chain shows a higher ΔE_int. Therefore, the SiO₂@TOA (with three octyl groups) presented the highest ΔE_int, followed by SiO₂@DMOA (with one octyl group) and SiO₂@TMA (with three methyl groups). It is expected that a quaternary ammonium salt with a longer carbon chain or more -OH groups frequently exhibits a higher ΔE_int with V₁₀. However, this experimental result is not in agreement with our expectation. As shown in Table 4 the qe values of these five quaternary ammonium salts in the adsorption process are ranked as follows: DMOA-V₁₀ > NTE-V₁₀ > TMA-V₁₀ > TOA-V₁₀ > TBE-V₁₀. During the construction of functionalized silica dioxide models in sobEDA, the oxygen atoms at the terminal Si-O bonds were substituted with -CH₃ groups to ignore the structure of the adsorption material and concentrate solely on the interplay between active groups and V₁₀ species. The anchoring of the TOA fragment onto the silica surface resulted in steric hindrance. In addition, the intricate surface morphology of silica and the abundance of hydroxyl groups on the silica surface synergistically prevent the octyl chains from contacting with V₁₀ species (with an enormous size), which is characterized by a substantially complicated cage configuration. DMOA, characterized by a sole octyl chain, has substantially less steric hindrance. Consequently, the V₁₀ species would be more easily close to the N⁺ ionic in DMOA on the silica surface, leading to a superior adsorption efficacy. The steric hindrance significantly affects the distance between the quaternary ammonium salt and V ion, which plays a decisive role in the interaction (such as electrostatic, covalent, and dispersion). In Equation (17), ω_e(r) represents the electrostatic interaction free energy between two charges, Q₁ and Q₂, with r denoting the center-to-center distance between two interacting fragments [62]. The London expression provides the formula for dispersion interactions (ω_d(r), Equation (18)), where the dispersion interaction free energy varies inversely with the sixth power of the distance [62]. Covalent interactions (corresponding to orbital interactions) are short-range forces, with a range typically between 0.1 and 0.2 nm, and are significantly influenced by the distance between the quaternary ammonium salt and V₁₀. Despite the TOA structure, Aliquat336 moved towards V₁₀ along the path with minimal steric hindrance at the interface of the two phases in the extraction process, through intramolecular σ-bond rotation to alter the spatial configuration.

The ΔE_int of DMOA-V₁₀ was significantly higher than that of DMOA-HCrO₄⁻, possibly attributable to more charges and the higher polarizability of the V₁₀. By calculation, the contribution of various chemical and non-bonding interactions to ΔE_int in the sobEDA model in ranked as follows: ΔE_els (59.29%) > ΔE_orb (20.97%) > ΔE_dc (19.29%) > ΔE_DFTc (0.46%), as shown in Figure 13. The four types of interaction with negative values facilitate binding of the DMOA with V₁₀.

$${\omega }_e\left(r\right)={\int }_{\mathrm{\infty }}^r-F\left(r\right)dr=-{\int }_{\mathrm{\infty }}^r{\displaystyle \frac{Q_1{Q}_2}{4\pi {\epsilon }_O\epsilon r^2}}dr=+[{\displaystyle \frac{Q_1{Q}_2}{4\pi {\epsilon }_O\epsilon r}}{]}_{\mathrm{\infty }}^r={\displaystyle \frac{Q_1{Q}_2}{4\pi {\epsilon }_O\epsilon r}}$$

(17)

$${\omega }_d\left(r\right)=-{\displaystyle \frac{3}{2}}{\displaystyle \frac{{\alpha }_{o1}{\alpha }_{o2}}{(4\pi {\epsilon }_o{)}^2{r}^6}}{\displaystyle \frac{h{\mathcal{V}}_1{\mathcal{V}}_2}{\left({\mathcal{V}}_1+{\mathcal{V}}_2\right)}}=-{\displaystyle \frac{3}{2}}{\displaystyle \frac{{\alpha }_{o1}{\alpha }_{o2}}{(4\pi {\epsilon }_o{)}^2{r}^6}}{\displaystyle \frac{h{\mathsf{{\rm I}}}_1{\mathsf{{\rm I}}}_2}{\left({\mathsf{{\rm I}}}_1+{\mathsf{{\rm I}}}_2\right)}}$$

(18)

It is noteworthy that the SiO₂@TBE and SiO₂@NTE with low steric hindrance showed a lower adsorption capacity. In the computational model, the solvent’s impact on the QAS and V₁₀ was ignored. In the adsorption process, the solvation effect caused by the -OH group in the SiO₂@TBE and SiO₂@NTE substantially diminished the interaction between TBE/NTE substrates and V₁₀. In addition, during the preparation of quaternary ammonium-functionalized silica gel, the nitrogen atoms in TBE and NTE with a weak nucleophilicity resulted in fewer functional sites in the adsorption material (compared to TMOA and TMA). From a quantum mechanical perspective, we have decomposed previously indistinct interaction energies into distinct components with clear chemical significance: electrostatic energy, Pauli repulsion, and orbital contributions. This decomposition offers initial insights into the complex relationships between bonding and non-bonding interactions characterizing the adsorption process.

3. Experimental Procedure

3.1. Reagents

All chemicals used were of analytical grade without further purification. Silica dioxide (SiO₂, 100–200 mesh), 3-chloropropyltriethoxysilane (C₉H₂₁O₃SiCl, 98%), trioctylamine (C₁₄H₅₁N, 96%), trimethylamine hydrochloride (HCl·C₃H₉N, 98%), p-tolyldiethanolamine (C₁₁H₁₇NO₂, 95%), triethanolamine (C₆H₁₅NO₂, 98%), N,N-dimethyloctylamine (C₁₀H₂₃N, 98%), sodium metavanadate (NaVO₃, 96%), sodium hydroxide (NaOH, 97%), sodium chloride (NaCl, 99.5%) and acetonitrile (CH₃CN, 99%) were purchased from Tianjin Heowns OPDE Technologies Ltd., Tianjin, China. Sodium chromate tetrahydrate (Na₂CrO₄·4H₂O, 99%), toluene (C₇H₈, 98%), hydrochloric acid (HCl, 98%), nitric acid (HNO₃, 98%), and sulfuric acid (H₂SO₄, 98%) were bought from Sinopharm Chemical Reagent Co., Ltd., Shanghai, China.

3.2. Synthesis of the QAS-SiO₂

The mixture of silica dioxide (SiO₂, 50.0 g), hydrochloric acid (375.0 mL, 12 mol/L), and distilled water (375.0 mL) was refluxed for 6 h. After cooling to room temperature, the SiO₂ was washed with distilled water and adjusted to pH = 7, followed by drying at 130 °C for 8 h to obtain the SiO₂@HCl.

The mixture of SiO₂@HCl (10.0 g), 3-chloropropyltriethoxysilane (12.0 mL), and anhydrous toluene (50.0 mL) was refluxed for 24 h and centrifuged, followed by washing 5 times with a solution of ethanol and ethyl acetate (1:1). Finally, the materials were dried at 65 °C for 6 h to obtain 3-chloropropyl-functionalized silica (SiO₂@CPTES) [63].

SiO₂@CPTES (3.0 g) was mixed with N,N-dimethyloctylamine (5.2 g), trioctylamine (6.6 g), p-tolyldiethanolamine (16.5 g), triethanolamine (2.5 g), and trimethylamine hydrochloride (4.7 g), separately, in 10.0 mL of the acetonitrile. The mixture was refluxed for 8 h. The product was washed with a mixture of ethanol and ethyl acetate (1:1) to remove unreacted substances, and dried at 65 °C for 6 h to obtain a series of QAS-SiO₂ products, such as SiO₂@DMOA, SiO₂@TOA, SiO₂@TBE, SiO₂@NTE, and SiO₂@TMA. The synthesis route of QAS-SiO₂ is shown in Scheme S1 in the Supplementary File.

3.3. Preparation of Adsorption Solution

After adjusting the pH with NaOH and HCl, various concentration of NaVO₃, NaCl, and Na₂CrO₄·4H₂O were used to prepare the adsorption solutions. The HCl, HNO₃, and H₂SO₄ solutions were prepared with a concentration of 1 mol·L⁻¹ for desorption.

3.4. Adsorption Experiment

A specific amount of the adsorbent (QAS-SiO₂) was placed in a 50 mL centrifuge tube along with a known initial concentration of the V solution or a mixed metal solution. The mixture was stirred at 1000 rpm for 1 min to 12 h. Adsorption solution concentrations ranged from 1.0 to 8.0 × 10⁻³ mol·L⁻¹, pH values ranged from 1.0 to 6.0, and the temperature ranged from 15 to 45 °C. The adsorbent mass ranged from 15 to 100 mg. After the adsorption, the mixture was filtered.

The adsorption efficiency (A), capacity (q_e), and metal separation factor (β_V/Cr) of QAS-SiO₂ were calculated, respectively, according to Equations (19)–(22) [64]:

$$A={\displaystyle \frac{C_{\mathrm{o}}-C_{\mathrm{e}}}{{\mathrm{C}}_{\mathrm{o}}}}\times 100\mathrm{\%}$$

(19)

$$q_{\mathrm{e}}={\displaystyle \frac{\left(C_{\mathrm{o}}-C_{\mathrm{e}}\right)V}{W}}$$

(20)

$$D={\displaystyle \frac{\left(C_{\mathrm{o}}-C_{\mathrm{e}}\right)V}{C_{\mathrm{e}}W}}={\displaystyle \frac{q_{\mathrm{e}}}{C_{\mathrm{e}}}}$$

(21)

$${\beta }_{\mathrm{V}/\mathrm{C}\mathrm{r}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{V}}}{{\mathrm{D}}_{\mathrm{C}\mathrm{r}}}}$$

(22)

where C_o (mg L⁻¹) and C_e (mg L⁻¹) are the initial and equilibrium concentrations of the V(V) and Cr(VI), respectively. V is the volume (L) of the solution, and W is the mass (g) of the adsorbent. D is the distribution ratio (L·g⁻¹), and D_V and D_Cr represent the distribution ratios of V(V) and Cr(VI), respectively.

3.5. Desorption and Regeneration Experiment

To assess the reusability of the QAS-SiO₂ after the V(V) adsorption, three consecutive adsorption–desorption cycles were conducted under optimal conditions. The adsorbent with loading of the V(V) was dried, mixed with different desorption agents (20 mL), stirred for 2 h at room temperature, and centrifuged. The mixture was filtered after washing to neutral pH with distilled water, followed by drying at 65 °C overnight before being used for adsorption again.

The V(V) desorption efficiency (Dsp) was calculated according to Equation (23):

$$D\mathrm{s}\mathrm{p}=\left({\displaystyle \frac{C_{\mathrm{d}}}{C_{\mathrm{o}}-C_{\mathrm{e}}}}\right)\times 100\mathrm{\%}$$

(23)

where C_d (mg·L⁻¹) is the equilibrium concentration of desorbed V, and C_o (mg·L⁻¹) and C_e (mg·L⁻¹) are the initial and equilibrium concentrations of the V(V), respectively.

3.6. Characterization Techniques

Fourier transform infrared spectroscopy (FTIR, Perkin-Elmer Frontier Mid-IR FTIR/STA6000-TL9000-Clarus SQ8, Waltham, MA, USA) in a wavenumber range of 4000–400 cm⁻¹ was primarily used to analyze the functional groups on the surface of silica. Before the test, the sample was fully mixed with KBr, ground, and pressed to form a thin circular disk. Scanning electron microscopy (SEM, FEI, Quanta FEG 250, Hillsboro, OR, USA) was primarily used to analyze the morphological changes in silica before and after its modification and vanadium adsorption. During this process, energy-dispersive X-ray spectroscopy (EDS) can be employed to determine the types of elements and their respective concentrations within the silica matrix. Time-of-flight mass spectrometry (TOFMS, Waters G2-IT-TOF, Milford, MA, USA) was utilized to analyze the mass of vanadium in solutions at different pH levels. Inductively coupled plasma mass spectrometry (ICP-MS, Thermo Fisher Scientific, ICAP RQ, Waltham, MA, USA) was utilized to analyze the vanadium content in vanadium solutions before and after adsorption.

4. Conclusions

In this study, five QAS-SiO₂ structures were synthesized. The optimal adsorbent, SiO₂@DMOA, was chosen for V(V) adsorption from aqueous solutions. Under optimal adsorption conditions, the V loading capacity was 39.16 mg·g⁻¹. The presence of co-existing ions demonstrated that SiO₂@DMOA remained effective in binding V(V) even at 0.5 M NaCl. Selective separation from Cr (VI) revealed that the separation factor (β_V/Cr) increased to 135.42 at pH = 3.3. EDA analysis of a simplified interaction model showed that quaternary ammonium salts with longer carbon chains or additional hydroxyl groups can enhance binding energy with vanadium. However, in practice, steric hindrance limits the approach of bulky V₁₀ species to quaternary ammonium salts with long, multiply substituted carbon chains, reducing adsorption efficiency. This model did not consider solvation effects, which contributed to the suboptimal performance of hydroxyl-containing quaternary ammonium salts in adsorption experiments. EDA also revealed that chemical bonds constitute 80.26% of the interaction energy, while non-bonding interactions make up the remaining 19.74%. Additionally, the density of quaternary ammonium salt functional groups on the silica gel surface significantly influenced the adsorption process. These findings provide a strong rationale for designing and advancing effective, highly selective adsorbents for vanadium adsorption.