An Experimental Study of Glycerol Carbonate Synthesis over g-C₃N₄ Catalysts

Abstract

This study examines a catalyst based on graphitic carbon nitride (g-C₃N₄) for synthesizing glycerol carbonate through the coupling reaction of glycerol and CO₂. In this research, we focus on simultaneously improving CO₂ emission reduction and glycerol valorization by co-doping g-C₃N₄ with phosphorus (P), sulfur (S), magnesium (Mg), and lithium (Li) for a better catalytic performance. The catalysts were prepared through a one-step thermal condensation process and characterized using XRD, SEM, TGA, FTIR, and nitrogen adsorption–desorption techniques. The co-doping further enhanced the surface chemical properties, Lewis acidity, basicity, and thermal stability, evidenced by the lower crystallinity, wider pore, and better catalytic performance as assessed through glycerol carbonylation reaction, optimized using a Box–Behnken design. The MgPSCN catalyst exhibited the highest glycerol conversion (68.72%) and glycerol carbonate yield (44.90%) at 250 °C, using 50 mg catalyst and 10 bar pressure. The model accuracy was validated by ANOVA (R² > 0.99; p values < 0.0001). The results indicated that doping significantly enhanced the catalytic performance, most likely due to improved electron charge transfer and structural distortions within the g-C₃N₄ framework. Such a process highlights the potential of co-doped g-C₃N₄ catalysts for the sustainable glycerol utilization and valorization of CO₂ through a scalable pathway toward green chemical synthesis—an approach that comes in line with worldwide decarbonization goals.

1. Introduction

In 2023, global carbon dioxide emissions related to energy rose by 1.1%, setting a new peak at 37.4 gigatons—moving further away from the decline needed to align with the climate targets outlined in the Paris Agreement [1]. To mitigate these emissions, two primary technological approaches are employed: capturing CO₂ and either storing it or repurposing it. Forecasts indicate that by 2050, approximately 5.6 gigatons of CO₂ will need to be captured and securely stored each year [2]. Nevertheless, transforming CO₂ into useful chemical products presents a more cost-effective alternative compared to underground sequestration [3]. A key strategy in emission reduction involves the adoption of renewable sources, such as biodiesel derived from biomass. This option is gaining traction due to its favorable properties—including being non-toxic, renewable, and free of sulfur and aromatic compounds [4].

As a byproduct of biodiesel production, glycerol has become increasingly surplus due to the expansion of biodiesel applications. Given the need for sustainable development, converting glycerol into high-value chemicals has become a challenge for researchers [5,6]. Glycerol is highly valued for its extensive use across various industrial sectors, including pharmaceuticals, personal care products, the food industry, and cosmetics [7]. Additionally, it shows significant potential as a primary chemical reactant in synthesizing various organic molecules. Glycerol can serve as a renewable feedstock in numerous chemical processes, such as carbonation, carbonylation, transesterification, and oxidation. Among these transformations, the synthesis of glycerol carbonate is particularly compelling from an environmental perspective as it utilizes CO₂ as both a carbon source and a C1 feedstock. This approach is pivotal in advancing decarbonization efforts and accelerating progress toward achieving net-zero emission targets [2,8].

Glycerol carbonate is emerging as a promising platform chemical and an eco-friendly alternative to traditional petrochemical-based substances. Its applications are diverse, serving as a solvent in detergents and paints, and playing a crucial role in producing valuable intermediates like glycidol which are used in textiles, plastics, pharmaceuticals, and cosmetics [9]. Additionally, glycerol carbonate is utilized in lithium-ion battery electrolytes, surfactants, and as a general-purpose solvent [10]. Among the various synthesis routes, the direct reaction between glycerol and CO₂ is the most environmentally favorable as it exclusively produces the target compound without unwanted byproducts. However, this method has not yet been implemented on an industrial scale due to challenges such as low conversion efficiency, limited catalyst stability, and thermodynamic constraints of the reaction. These issues may be mitigated by optimizing reaction pathways and using water-removing agents to shift the equilibrium towards product formation [3,11,12].

To enhance the synthesis of glycerol carbonate, a variety of heterogeneous catalytic systems have employed dehydrating agents such as acetonitrile, benzonitrile, 2-cyanopyridine, adiponitrile, dimethylformamide (DMF), calcium oxide (CaO), and magnesium carbonate (MgCO₃) [13,14,15,16,17,18]. These systems include titanosilicate-based ETS-10 zeolite catalysts, which are modified by impregnating active metals such as Co, Zn, Cu, Ni, Zr, Ce, and Fe [19]. Cerium oxide (CeO₂) catalysts have also been synthesized through precipitation, hydrothermal techniques, and citrate sol–gel methods [3,15]. In another approach, finely distributed MgInCe mixed metal oxides (MgInCe-MMOs) were synthesized via a topological transformation from their layered double hydroxide precursors (MgInCe-LDHs) [20]. Hydrothermal synthesis was also used to fabricate a range of Cu_1−xZr_xO₂ bimetallic oxides with varying Cu-to-Zr ratios [21]. ZnAlCe catalysts were obtained by co-precipitation [22], while gold nanoparticles (AuNPs) were incorporated into a metal–organic framework (MOF) constructed from mixed carboxylate linkers, including terephthalic acid and 1,3,5-benzenetricarboxylic acid [23]. La₂O₂CO₃/ZnO catalysts were created through both co-precipitation and ethylene glycol combustion methods [24], and metal oxides such as MgO, CaO, and Al₂O₃ were synthesized via precipitation [25]. Finally, phosphorus and sulfur co-doped graphitic carbon nitride (g-C₃N₄) was produced through a one-step thermal condensation process [26].

Graphitic carbon nitride (g-C₃N₄) has drawn considerable interest for its potential to tackle energy and environmental issues. Its electron-rich framework, surface basicity, and hydrogen-bonding capabilities—stemming from its nitrogen and hydrogen constituents—render it a versatile companion to carbon in various advanced material applications [27]. As a result, g-C₃N₄ plays a prominent role in numerous catalytic processes, including carbon dioxide reduction [28], oxygen reduction reactions (ORRs) [29], hydrogen production from aqueous glycerol solutions [30], and hydrogen evolution reactions [31]. However, the performance of unmodified g-C₃N₄ is hampered by several inherent limitations such as (i) poor electrical conductivity, (ii) weak interfacial compatibility with other materials, (iii) a limited number of catalytically active sites combined with low Lewis acidity and basicity, and (iv) an inefficient electronic structure that hinders charge transport and reduces its catalytic efficiency [26].

To overcome the inherent drawbacks of pristine g-C₃N₄, scientists investigated various modification strategies, including elemental-doping and substitution. Non-metal dopants such as boron, oxygen, phosphorus, and sulfur have been included in the support network to boost its physicochemical properties [28,32,33]. Additionally, transition metals like iron, manganese, titanium, and nickel have been used to enhance its catalytic performance [34,35,36,37,38,39]. Alkaline and alkaline earth metal oxides—including lithium, barium, calcium, and magnesium—have also been introduced into g-C₃N₄ structures to further boost activity [40,41,42]. These modifications collectively aim to refine the material’s surface morphology, chemical reactivity, and electronic behavior while also shedding light on the nature and distribution of active catalytic sites.

While the application of modified g-C₃N₄ materials in photocatalytic processes has been extensively studied, their use in catalyzing the transformation of glycerol into glycerol carbonate remains relatively underexplored. Fao et al. [26] analyzed a phosphorus and sulfur co-doped g-C₃N₄ catalyst (PSCN) using a one-step thermal condensation method and assessed its catalytic activity for converting glycerol and CO₂ into glycerol carbonate. The reaction, undertaken at 210 °C using acetonitrile as a dehydrating agent, yielded an 85% glycerol conversion with PSCN, significantly higher than the 60% achieved using unmodified g-C₃N₄ (CNN). In another study, Reisi and Najafi Chermahini [43] investigated MgO-supported g-C₃N₄ catalysts for the transesterification reaction between glycerol and dimethyl carbonate (DMC). The optimal catalyst, with a MgO to g-C₃N₄ weight ratio of 6:1, delivered a maximum glycerol carbonate yield of 95.47%. This performance was attributed to its strong basicity and favorable conditions, including a reaction temperature of 80 °C, a 4 h duration, a 3:1 DMC-to-glycerol molar ratio, a 30 mg catalyst dose, and excellent reusability.

The main goal of our work was to compare the catalytic performance of a series of catalysts obtained by doping g-C₃N₄ with phosphorus (P), sulfur (S), magnesium (Mg), and lithium (Li) in the glycerol carbonate synthesis. To the best of our knowledge, there is no study in the literature comparing all these promoters in the reaction of glycerol carbonylation reaction. Also, the multi-element doping strategy represents a distinct and innovative approach to enhancing both the structural and electronic properties of g-C₃N₄, aiming to improve its catalytic activity in the direct coupling reaction of glycerol with CO₂. The synthesized catalysts were characterized using a variety of techniques to thoroughly evaluate their properties. Additionally, an experimental design approach was employed for identifying the best operating conditions to maximize the yield in glycerol carbonate. This comprehensive characterization and systematic evaluation aimed to enhance the efficiency and effectiveness of the glycerol carbonate production process.

2. Experimental

2.1. Materials and Methods

Melamine (99%, Alfa-Aesar, Ward Hill, MA, USA), phosphonitrilic chloride trimer (98%, Alfa-Aesar), sulfur powder (99.5%, Alfa-Aesar), Mg(NO₃)₂·6H₂O (Merck-Sigma-Aldrich, BioUltra, Burlington, MA, USA, ≥99.0%), LiNO₃ (Merck, 99.99%), carbon dioxide CO₂ (SIAD Romanian, Bucharest, Romania, purity: ≥99.5%), glycerol (Gly) (Merck, ≥99.5%), acetonitrile (Amex-lab, New York, NY, USA, ≥99.9%), and glycerol carbonate (GC) (Merck-Sigma-Aldrich, ≥99%) were acquired.

2.2. Catalysts Preparation

In our study, the catalysts were synthesized through a one-step thermal condensation process [44] to improve their Lewis acidic and basic properties [26]. Bare g-C₃N₄ (denoted as CN) was prepared by direct thermal treatment of melamine at 550 °C at a heating rate of 2 °C/min for 5 h. The g-C₃N₄ catalyst co-doped with phosphorus (P) and sulfur (S) was synthesized by mixing and grinding 250 g of melamine, 25 g of phosphonitrilic chloride trimer, and 25 g of sulfur powder. This mixture was then subjected to thermal treatment in a furnace at 550 °C for 5 h, with a heating rate of 2 °C/min. After cooling, the sample was washed with a 1:2 volumetric mixture of deionized water and ethanol, and subsequently dried at 80 °C overnight. The product was labeled as PSCN.

For comparative purposes, additional catalysts—g-C₄N₃ co-doped with S, P, and Mg, and another variant co-doped with S, P, and Li—were prepared using the same method. Specifically, 26.5 g of Mg (NO₃)₂ and 25 g of LiNO₃ were added to the melamine, S, and P mixture during the mixing and grinding process to introduce 2.5 g of Mg and Li metals into the catalysts, respectively. We designated the resulting catalysts as PSCN, MgPSCN, and LiPSCN, respectively.

2.3. Catalyst Characterization Equipment

The catalyst was analyzed using various techniques, such as FTIR spectroscopy, X-ray diffraction (XRD), textural analysis (N₂ adsorption/desorption), scanning electron microscopy (SEM), and thermogravimetric analysis (TGA-DTG). XRD analysis was carried out at ambient temperature using a Bruker X-ray diffractometer (Karlsruhe, Germany; θ-θ type) equipped with a Cu-Kα radiation source (λ = 1.5418 Å) operating at 40 kV and 5 mA. The scans covered a 2θ range of 5–80° at a rate of 10°/min. Microstructural morphology was examined using a SEM instrument from FEI Company (Hillsboro, OR, USA). Thermogravimetric and derivative thermogravimetric analyses (TGA-DTG) were performed on a METTLER TOLEDO TGA/IST Thermal Analysis System (Greifensee, Switzerland) within the temperature range of 25–600 °C, under a nitrogen atmosphere, and at a heating rate of 10 °C/min.

The textural properties of the samples were evaluated using a Quantachrome NOVA 2200 e Gas Sorption Analyzer (Boynton Beach, FL, USA). The nitrogen adsorption/desorption isotherms were recorded at 77.35 K across a relative pressure (p/p₀) range of 0.005 to 1.0. Data processing was carried out using NovaWin version 11.03 software. The specific surface area was calculated using the BET (Brunauer–Emmett–Teller) method, while the total pore volume was estimated from the desorbed volume at a relative pressure near unity, utilizing the BJH (Barrett—Joyner—Halenda).

FTIR spectroscopy was performed using a Shimadzu IRAffinity-1S spectrophotometer (Kyoto, Japan) equipped with a GladiATR-10 accessory, allowing spectra acquisition through the ATR (attenuated total reflectance) technique. FTIR spectra were captured across a wavenumber range of 400–4000 cm⁻¹, with a spectral resolution of 4 cm⁻¹.

2.4. Procedure for Catalytic Test in the Glycerol Carbonylation Reaction

A mixture of 25 g of glycerin and 50 mL of acetonitrile, used as a dehydrating agent to shift the unfavorable equilibrium towards the product side and improve the selectivity for glycerol carbonate [13,45], was added in the reactor. The catalyst was added at room temperature and then the temperature gradually increased to the desired value while the glycerin–catalyst–acetonitrile mixture was mechanically stirred. Subsequently, carbon dioxide gas was introduced until the desired pressure was reached. The reaction was allowed to proceed for 4 h.

After each experiment, the autoclave was cooled to ambient temperature, depressurized, and the liquid phase was isolated from the catalyst through centrifugation. Further, the catalyst was rinsed with an ethanol–deionized water mixture, then dried at 80 °C overnight. The liquid phase was analyzed by gas chromatography flame ionization detector (GC-FID, Varian CP-3800, Varian. Inc., Walnut Creek, CA, USA) equipped with a ZB-5ms column (L = 30 m, D = 250 μm, d = 0.25 μm) and a carrier gas (N₂) flow rate of 1 mL/min. To determine the concentrations of glycerol carbonate a calibration curve was constructed using acetonitrile as the solvent. The curve was generated over a concentration range of 1 to 90% by weight and is provided in one of our recently published papers [46].

The yield was evaluated by the following equation:

$$\%\mathrm{Yield} \mathrm{of} \mathrm{GC}={\displaystyle \frac{\mathrm{moles} \mathrm{GC}}{\mathrm{moles} \mathrm{GLY} \mathrm{introduced}}}$$

3. Results and Discussions

3.1. Catalyst Characterization

The structure and phase identification of the samples, including bare g-C₃N₄ (CN), g-C₃N₄ doped with P and S (PSCN), g-C₃N₄ doped with P, S, and Mg (MgPSCN), and g-C₃N₄ doped with P, S, and Li (LiPSCN), were determined by using X-ray diffraction analysis.

The XRD patterns for these materials are given in Figure 1. Two prominent peaks with high intensity were observed at 2θ ≈ 12.24° and 27.32°, which correspond to the diffraction planes of bare g-C₃N₄. These diffraction values agree with the data in the literature [47,48,49,50]. The pronounced peak at 2θ ≈ 27.24° corresponds to the (002) diffraction plane, attributed to the interlayer stacking of conjugated aromatic structures, with an interlayer distance of 0.324 nm. The lower-intensity peak at 2θ ≈ 12.24° corresponds to the (100) diffraction plane, indicating the in-plane structural arrangement of tri-s-triazine units with an interlayer distance of 0.680 nm [26,28,32].

For the samples doped with P and S, the intensity of the (002) diffraction peak decreased, indicating a reduction in crystallinity compared to bare g-C₃N₄ likely due to the disruption of crystal growth by the addition of P and S. The intensity of the (100) peak also diminished, suggesting that the incorporation of these dopants distorted the formation of nitride pores and altered the interlayer distance, indicating strong interactions between the dopants and the host g-C₃N₄ matrix [28,51].

The g-C₃N₄ samples doped with Li and Mg exhibited similar diffraction peaks to those of bare g-C₃N₄, indicating that the overall structure of g-C₃N₄ remained largely unchanged by Li and Mg doping [52]. Additionally, no separate diffraction peaks corresponding to Li or Mg were detected in the MgPSCN and LiPSCN samples, confirming that Li and Mg were successfully doped into the g-C₃N₄ framework [40].

After the addition of Li and Mg the peak intensities for both the (002) and (100) diffraction planes decreased, suggesting that the presence of these dopants further reduced the crystallinity of the material [40]. Moreover, the distortion of nitride pores and the alteration of the interlayer distance further indicate strong interactions between the dopants and the host g-C₃N₄ [52,53].

The average crystallite size (D) of the catalysts was determined using the Debye–Scherrer Equation (1), which is as follows [54]:

$$\mathrm{D}={\displaystyle \frac{\mathrm{k}\cdot \mathsf{\lambda }}{\mathsf{\beta }\cdot \cos \mathsf{\theta }}}$$

(1)

where λ is the wavelength of the X-rays used (Cu Kα = 0.15406 nm), β is the full width at half maximum (FWHM) of the diffraction peak, θ is the Bragg diffraction angle, and k is the shape factor, typically assumed to be 0.98. The average crystallite sizes of CN, PSCN, MgPSCN, and LiPSCN, calculated using this equation, were found to be 10.94, 17.57, 10.71, and 6.86 nm, respectively (

Table 1. Textural properties and crystallite sizes.

Catalysts	BET Surface Area (m2/g)	Pore Volume (cm3/g)	Average Pore Width (nm)	Average Crystallite Size (nm)
CN	10.85	0.062	5.20	10.94
PSCN	10.10	0.085	29.396	17.57
MgPSCN	9.19	0.063	16.09	10.71
LiPSCN	17.32	0.128	29.396	6.86

).

The full X-ray photoelectron spectroscopy (XPS) survey of the MgPSCN catalyst before use, as illustrated in Figure 2, is evidence of the presence of C, N, O, P, S, and Mg elements in MgPSCN. The observed peaks at 285 eV, 395 eV, 529 eV, 136 eV, 166 eV, 49.7 eV, and 1303 eV correspond to C1s, N1s, O1s, P2p, S2p, Mg2p, and Mg1s, respectively [52,55].

The peak at 285 eV is attributed to the sp² hybridization of C=C bonds, while the peak at approximately 136.0 eV corresponds to P–N/P–O bonds. Additionally, peaks in the sulfur spectrum at 166 eV and 228 eV were observed, corresponding to S2p and S1s, indicating the incorporation of sulfur atoms (S-doped) in nitrogen sites within the structure [56].

The peak at 395 eV suggests the presence of tri-coordinated nitrogen in N-(C)₃ groups. For the Mg 1s spectrum, the peak at 1303 eV is evidence of the presence of Mg(II) ions. In the Mg 2p spectrum, the peak at 49.7 eV corresponds to elemental magnesium (Mg⁰) [40,52].

After two cycles of use under optimal reaction conditions, no significant changes were observed in the spectral peaks except for the disappearance of the peak at 166 eV, which corresponds to S2p, suggesting a potential loss of sulfur atoms during the reaction. These findings confirm the stability of the catalyst, which was further supported by microscopic analysis.

Figure 3 presents SEM images of the porous samples, highlighting distinct morphological characteristics. The morphology of bare g-C₃N₄ (CN) (Figure 3A) exhibits an irregular granular and layered structure with numerous pores, as also shown in the previous literature [28,57]. This porous structure is attributed to the liberation of ammonia (NH₃) and carbon dioxide (CO₂) gases during the thermal decomposition of melamine [44]. In contrast, CN doped with phosphorus and sulfur (PSCN) (Figure 3B) demonstrates a thinner, plate-like structure with a higher surface porosity compared to undoped g-C₃N₄. A significant difference is observed in the layer distribution and pore size, with the pores in PSCN increasing in dimension as confirmed by textural analysis.

Doping with magnesium, phosphorus, and sulfur (MgPSCN) (Figure 3C) results in the formation of numerous grains with varying nano-scale dimensions, displaying smaller diameters than those in PSCN. Additionally, notable distortions in the layered morphology are evident. In contrast, lithium-doped g-C₃N₄ (LiPSCN) (Figure 3D) shows a less uniform and smaller layered structure compared to PSCN, although the LiPSCN sample remains more uniform, larger in size, and more compactly bonded than MgPSCN [40].

The elemental mapping results of the samples showed well-defined distributions for C, N, P, S, Mg, and Li, as indicated in Figure 4. The elemental analysis indicates the presence of C and N in CN samples, with a C/N ratio of 0.48%. Upon doping with phosphorus (P) and sulfur (S), an increase in the carbon-to-nitrogen ratio to 0.80% was observed in the PSCN sample. Similarly, for the MgPSCN and LiPSCN catalysts, the carbon-to-nitrogen ratios increased compared to the CN catalyst, with values of 0.663% and 0.551%, respectively, when doped with magnesium (Mg), phosphorus (P), and sulfur (S). This suggests that deamination has taken place due to the co-doping of Mg and Li in the pure g-C₃N₄ matrix [40]. The above discussion further supports the successful co-doping of pure g- C₃N₄ with P, S, Mg, and Li.

To analyze the specific surface area and pore structure of the samples, nitrogen adsorption–desorption measurements were conducted. As illustrated in Figure 5, all samples display type-IV isotherms, which are characteristic of mesoporous materials according to the IUPAC classification, indicating the presence of well-defined mesopores [57,58]. The hysteresis loop observed at a high relative pressure (P/P₀) of 0.5–1.0, categorized as type H₃, suggests the presence of slit-shaped pores associated with plate-like particles [59]. This characteristic is consistent with the layered morphology also observed in the SEM analysis. Similar results have been reported in previous studies [32,40,53]. Additionally, variations in N₂ adsorption volumes indicated differences in surface area among the samples. Table 1 summarizes the surface area, pore volume, and pore width of the synthesized catalysts. A decrease in the specific surface area was observed for PSCN compared to CN, from 10.85 to 10.10 m²/g, with an even further reduction to 9.19 m²/g in the case of MgPSCN, which is consistent with previous studies [26,28,40]. In contrast, LiPSCN exhibited a significant increase in surface area, reaching 17.32 m²/g. The comparable specific surface area of these samples did not have a significant impact on their catalytic activity. Furthermore, a substantial increase in pore width was observed, approximately 6-fold for both PSCN and LiPSCN compared to CN, while MgPSCN showed an increase of approximately 3-fold.

The thermal stabilities of CN, PSCN, MgPSCN, and LiPSCN samples were assessed using thermogravimetric analysis (TGA) under a nitrogen (N₂) atmosphere, as shown in Figure 6. An initial weight loss of 5%, 6.1%, 7.4%, and 6.5% was observed for CN, PSCN, MgPSCN, and LiPSCN, respectively, up to 200 °C. This weight loss is attributed to the evaporation of water molecules adsorbed physically and chemically, along with the removal of hydroxyl groups [60,61]. In the temperature range of 200–400 °C, CN exhibited a minor weight loss of approximately 1%. However, doping with sulfur and phosphorus in PSCN led to an increased weight loss of around 3%, which can be explained by the lower thermal stability of the P–O–C bond compared to the C–C bond, thus reducing the initial decomposition temperature [62]. For MgPSCN and LiPSCN, the weight loss in this temperature range increased to 3.5% and 8%, respectively. This is likely due to the enhanced thermal conductivity of metals and their oxides, facilitating more uniform heat transfer and promoting the catalytic decomposition of PSCN in this range [62]. The effect is particularly pronounced in LiPSCN between 400 and 600 °C, where a significant weight loss of 23.6% was recorded, compared to 15.2% for MgPSCN and 14.5% for PSCN in the same temperature range. Therefore, based on the previous results, PSCN and MgPSCN are considered to be more thermally stable than LiPSCN.

The FTIR spectrum of the catalysts, particularly for the CN catalyst shown in Figure 7, exhibits broad peaks observed near 3000–3600 cm⁻¹, corresponding to N–H stretching vibrations. The peaks in the range of 1200–1650 cm⁻¹ are associated with the aromatic heterocyclic C–N rings. The peak at 800 cm⁻¹ is attributed to the breathing mode of triazine rings. These findings confirm the structural integrity of g-C₃N₄, consistent with previously reported results [40,52]. For PSCN, MgPSCN, and LiPSCN the reduced intensity of the C–N and N–H vibrational peaks indicate structural distortions caused by the incorporation of phosphorus and sulfur additives. Additionally, the slight shifts in the characteristic peaks reflect strong interactions between the active materials and the g-C₃N₄ framework. These results are similar to those of previous studies [50], which found that the addition of phosphorus and sulfur altered the electronic properties and enhanced the Lewis basicity. A notable observation for MgPSCN is the further decrease in peak intensity compared to PSCN, indicating stronger structural distortions attributed to Mg–N coordination. This coordination modifies the electronic environment of the material, aligning with findings reported in earlier studies [52,53]. LiPSCN exhibits a spectral behavior similar to MgPSCN but with less pronounced reductions in peak intensity and smaller shifts, suggesting weaker interactions between Li and the g-C₃N₄ framework [40]. Overall, the FTIR analysis demonstrates the successful incorporation of P, S, Mg, and Li into the g-C₃N₄ framework, highlighting the effectiveness of tailored doping strategies in enhancing the catalytic and electronic properties for advanced applications.

3.2. Optimization of Catalyst Activity Through Experimental Design Methods

The effectiveness of glycerol carboxylation with CO₂ using the MgPSCN catalyst was assessed by examining glycerol conversion and glycerol carbonate yield. This evaluation employed a Box–Behnken experimental design, which considered the three key independent variables of reaction temperature (X1), catalyst amount (X2), and reaction pressure (X3). The Box–Behnken design is a robust statistical method that has been successfully utilized in various studies to optimize complex chemical reactions. By systematically varying these factors researchers can identify the conditions for the maximization of the yield of the carboxylation process. This approach has proven to be valuable in enhancing the understanding and performance of catalytic systems in the literature [63,64,65]. The experimental design matrix corresponding to the Box–Behnken design consisted of a series of 15 experiments. The reaction time for these experiments was set to 4 h. The natural values as well as the coded factor values used in our experimental design matrix are given in

Table 2. Numerical values assigned to the independent variables within the experimental design matrix.

Factor	Value/Level
	Low		Medium		High
	Natural (Z)	Coded (X)	Natural (Z)	Coded (X)	Natural (Z)	Coded (X)
Reaction temperature (°C), X1	150	−1	200	0	250	+1
Catalyst amount (%), X2	10	−1	30	0	50	+1
Operating pressure (bar), X3	3	−1	7	0	10	+1

.

The impact of the factors on the responses was assessed using a polynomial model of the following form:

$$\begin{array}{cc}\hfill Y_i=& {\beta }_0+{\beta }_1\cdot X_1+{\beta }_2\cdot X_2+{\beta }_3\cdot X_3+{\beta }_{12}\cdot X_1\cdot X_2+{\beta }_{13}\cdot X_1\cdot X_3\hfill \\ & +{\beta }_{23}\cdot X_2\cdot X_3+{\beta }_{11}\cdot X_1^2+{\beta }_{22}\cdot X_2^2+{\beta }_{33}\cdot X_3^2\hfill \end{array}$$

(2)

The validation of the equations was performed using statistical methods, specifically analysis of variance (ANOVA). Additionally, response surface methodology (RSM) was employed to analyze the experimental design, utilizing the experimental values in

Table 3. Box–Behnken experimental design data.

Nr. Exp	X1	X2	X3	Y1	Y2
1	−1	1	0	18.51	14.28
2	1	1	0	68.72	44.9
3	−1	0	1	14.82	12.98
4	0	0	0	41.49	27.75
5	1	0	1	57.85	33.02
6	0	0	0	42.94	28.15
7	0	−1	1	28.3	9.93
8	1	−1	0	11.85	8.98
9	0	−1	−1	10.22	8.37
10	0	1	1	63.45	43.08
11	0	1	−1	53.88	13.94
12	−1	0	−1	8.72	2.15
13	1	0	−1	19.25	17.15
14	0	0	0	41.21	28.08
15	−1	−1	0	4.67	3.34

. The Fisher test value (F-value) calculated for the model was compared with the theoretical Fisher test value (Ft(p − 1, n − p)) at a 5% significance level. This comparison was made to assess the model’s validity, taking into account the number of experiments conducted (n) and the number of terms included in the model (p). By evaluating the F-value against the theoretical threshold, researchers can determine whether the model provides a statistically significant explanation of the observed data, ensuring the robustness and reliability of the experimental results [66].

In other words, as highlighted in the literature, the p-value for each parameter should be below 5% to ensure that each independent variable in the model significantly contributes to predicting the output. This threshold indicates that the variable’s effect on the response is statistically significant, thereby validating its inclusion in the model [67]. The coefficients of the models, along with the ANOVA tests, were thoroughly evaluated using Design-Expert Version 8.

Both glycerol conversion (Y1) and glycerol carbonate yield (Y2) were considered as dependent variables. To find the best operating conditions which ensure the highest glycerol conversion as well as glycerol carbonate yield, a polynomial model based on Equation (2) was developed. The analysis of variance (ANOVA) for both models given in

Table 4. ANOVA parameters used to evaluate the suitability of the model.

Independent Variable	Correlation Coefficient, R2	Adjusted R2	Calculated F-Value	p-Value
Y1	0.991	0.985	162.9	<0.0001
Y2	0.993	0.984	114.3	<0.0001

proves that the adequacy of these models is in good agreement with the experimental data. The adequacy is supported by a p-value lower than 5%, a correlation coefficient (R2) above 0.95, as well as the shapes of the parity diagrams presented in Figure 8.

The thorough analysis of the values of residuals, providing the differences between the calculated and experimental values, is another justification regarding the model accuracy if these values are enough small (Figure 8). By considering the normal probability plot, one can evaluate the data’s normal distribution. Figure 9 presents both the internally studentized residuals and the normal probability plot for glycerol conversion and GC yield.

The estimated coefficients together with their confidence intervals are given by relation (2) for glycerol conversion and by relation (3) for GC yield.

The effects of the main and binary interactions can be evaluated using the estimated coefficients. Coefficients that did not pass the statistical significance test (based on p-value) were removed, except for those necessary to maintain the model’s hierarchy. The main interactions were significant for both dependent variables. Equations (3) and (4) are as follows:

$$\begin{array}{cc}{Y}_1=& 40.21\left(1\pm 0.056\right)+13.87\left(1\pm 0.152\right)\cdot X_1+18.69\left(1\pm 0.113\right)\cdot X_2+9.54\left(1\pm 0.221\right)\cdot X_3\hfill \\ & +10.76\left(1\pm 0.278\right)\cdot X_1\cdot X_2+8.13\left(1\pm 0.369\right)\cdot X_1\cdot X_3-14.66\left(1\pm \mathrm{0.0.211}\right)\cdot X_1^2\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill Y_2=& 27.99\left(1\pm 0.084\right)+8.91\left(1\pm 0.162\right)\cdot X_1+10.7\left(1\pm 0.135\right)\cdot X_2+7.18\left(1\pm 0.203\right)\cdot X_3\hfill \\ & +6.25\left(1\pm 0.329\right)\cdot X_1\cdot X_2+6.9\left(1\pm 0.298\right)\cdot X_2\cdot X_3-6.31\left(1\pm 0.339\right)\cdot X_1^2\hfill \\ & -3.81\left(1\pm 0.559\right)\cdot X_2^2-5.36\left(1\pm 0.397\right)\cdot X_3^2\hfill \end{array}$$

(4)

A positive influence means that the parameter is increasing with the factor and a negative influence means that the parameter decreases with the factor.

Given the coefficients in Equations (3) and (4) and plots in Figure 10, both glycerol conversion and GC yield are positively influenced by reaction temperature (X₁), catalyst amount (X₂), and reaction pressure (X₃). The impact of the key factors on glycerol conversion and GC yield is illustrated in Figure 10. The ANOVA for the GC yield model is given in

Table 5. The ANOVA analysis table for GC yield model.

Source	Sum of Squares	Df	Mean Square	F-Value	p-Value
Model	2577.19	8	322.15	114.30	<0.0001	significant
${\mathrm{X}}_1$	635.46	1	635.46	225.47	<0.0001	significant
${\mathrm{X}}_2$	915.49	1	915.49	324.83	<0.0001	significant
${\mathrm{X}}_3$	411.85	1	411.85	146.13	<0.0001	significant
${\mathrm{X}}_1\cdot {\mathrm{X}}_2$	156.00	1	156.00	55.35	0.0003	significant
${\mathrm{X}}_2\cdot {\mathrm{X}}_3$	190.16	1	190.16	67.47	0.0002	significant
${\mathrm{X}}_1^2$	147.09	1	147.09	52.19	0.0004	significant
${\mathrm{X}}_2^2$	53.50	1	53.50	18.98	0.0048	significant
${\mathrm{X}}_3^2$	105.95	1	105.95	37.59	0.0009	significant
Cor Total	2594.10	14

. Based on these values, an F-value 114.3 for the model suggests that this is significant, and p-values below 0.05 indicate that the model terms are significant.

The experimental results given in

Table 6. Conversion and GC yield at optimum conditions.

Catalysts	Glycerol Conversion	GC Yield
CN	47.24	11.91
PSCN	61.88	29.74
MgPSCN	70.05	45.85
LiPSCN	58.42	27.34

are determined using the optimal condition calculated based on the mathematical model, and the highest values for glycerol conversion as well as GC yield were for the MgPSCN catalyst. The optimal values of the factors obtained by maximizing both glycerol conversion and GC yield are $X_1=0.83, X_2=1, \mathrm{and} X_3=0.5$ that provides a glycerol conversion of 71% and a GC yield of 46%, values close to the experimental values presented in Table 6 for the same catalyst.

The reusability of the MgPSCN catalyst in the synthesis of glycerol carbonate was investigated over four consecutive reaction cycles under optimal conditions. Before each reuse, the catalyst was rinsed with ethanol and subsequently dried at 85 °C for 60 min to ensure the removal of any residual byproducts or impurities that could influence its catalytic performance.

The results demonstrated a gradual decline in glycerol carbonate yield with each successive reuse of the catalyst (Figure 11). This reduction can be attributed to the accumulation of secondary or undesired compounds on the catalyst surface, leading to active site blockage and a decrease in catalytic efficiency despite ethanol washing. The plotted data illustrate this downward trend, highlighting the impact of surface and chemical modifications on the catalyst’s effectiveness over multiple uses.

To examine potential morphological changes in the MgPSCN catalyst after two consecutive cycles of the glycerol carbonate synthesis reaction (coupling glycerol with carbon dioxide), the catalyst was studied by SEM before the reaction. Prior to characterization, the catalyst was flushed with ethanol and dried at 85 °C for 60 min. SEM images revealed nanometer-sized granules on the surface of irregularly structured layers with multiple pores (Figure 11 and Figure 12), resembling the morphological structure of the catalyst before use. Furthermore, elemental mapping results of the catalyst after two cycles of use showed lower distributions of C, N, P, S, and Mg compared to those observed in the fresh catalyst (see Figure 13). This loss can be assigned to the detachment of nanoparticles from the surface of the nitride layers, which correlated with a decrease in glycerol carbonate yield after use.

4. Conclusions

This work introduces a new catalytic system with potential for scalable, environmentally friendly synthesis of glycerol carbonate and provides both experimental data and statistical modeling to support its performance. In this respect, four graphitic–carbon–nitride (g-C₃N₄) catalysts co-doped with phosphorus (P), sulfur (S), magnesium (Mg), and lithium (Li) were synthesized using a one-step thermal condensation method. The catalysts were characterized using XRD, SEM, TGA, FTIR, and nitrogen adsorption–desorption techniques and were employed for the synthesis of glycerol carbonate through the coupling reaction of glycerol and CO₂. Co-doping did not significantly modify the average crystallite size, except for lithium doping which favored the shrinkage of crystallites. The BET surface area of the pores was also maintained at similar values, except for Li doping which almost doubled it. Thermogravimetric analysis revealed that doping with sulfur and phosphorus led to increased weight loss, which can be elucidated by the lesser value of the homolytic dissociation energy of the P–O–C bond compared to that of the C–C bond. The incorporation of phosphorus and sulfur additives to the PSCN, MgPSCN, and LiPSCN catalysts led to a reduction in the intensity of the C–N and N–H vibrational peaks, as revealed by FTIR analysis. SEM analysis revealed that doping with magnesium, phosphorus, and sulfur favored the formation of numerous clusters with variable sizes at the nanometric scale, with diameters smaller than those in PSCN, while doping with lithium favored the uniformization of the structure compared to PSCN. The parameters of the glycerol carbonate synthesis process were optimized using the response surface methodology based on a Box–Behnken design, with reaction temperature, catalyst amount, and operating pressure as independent variables. All catalysts considered in this study were tested under these conditions, with the experimental data obtained highlighting the increase in conversion and yield in glycerol carbonate for the doped catalysts. Thus, highest values for glycerol conversion of 70.05% and GC yield of 45.85% were obtained on the MgPSCN catalyst using the optimal factors values.