Reaction Kinetics and Mechanism for the Synthesis of Glycerol Carbonate from Glycerol and Urea Using ZnSO₄ as a Catalyst

Abstract

A series of Zn salts were used as catalysts for the reaction of glycerol and urea to produce glycerol carbonate and it was found that ZnSO₄ showed the highest catalytic activity. Furthermore, the effects of reaction parameters on the glycerol conversion and glycerol carbonate yield were studied in detail. The results indicated that the glycerol conversion and glycerol carbonate yield were increased with the reaction temperature, reaction time, and catalyst amount while the optimal reaction conditions were 140 °C, 240 min, catalyst amount of 5 wt% (based on the glycerol weight), and urea-to-glycerol molar ratio of 1.1:1. During the reaction, the ZnSO₄ catalyst is transformed into Zn(NH₃)₂SO₄ at the initial stage of the reaction and then further transformed into Zn(C₃H₆O₃). Zn(C₃H₆O₃) and (NH₄)₂SO₄ may be the true active species for the activation of urea and glycerol, respectively. The reaction mechanism is proposed in this article. Based on the experimental results, a reaction kinetics model considering the change in volume of the reaction system was also established, and the model parameters were obtained by fitting the experimental data. The statistical results showed that the established kinetics model is accurate.

1. Introduction

Recently, biodiesel, as one of the renewable and clean energies with plentiful raw material sources, high heat of combustion, low emission amount of pollutants, and a high flash point, has begun to attract more and more attention from researchers [1,2,3,4,5]. According to statistics, the global production of biodiesel in 2020 was about 50 million tons [6]. In industry, the main synthesis method for biodiesel is the transesterification of animal and vegetable fats and oils or kitchen waste oils with low-carbon alcohol (mainly methanol) [7,8,9,10]. During the reaction, glycerol (GL) is generated as a byproduct with a ratio of 0.1 kg to 1.0 kg of biodiesel. So, a huge amount of GL will be produced with the production of biodiesel [11]. Converting GL into derivatives with high added value cannot only effectively maintain the balance of the GL market but can also promote the sustainable development of the biodiesel industry [12,13]. GL can be transformed into propylene glycol, acrolein, dichloropropanol, dihydroxyacetone, glyceric acid, and glycerol carbonate (GC) through the reactions of dehydration, chlorination, oxidation, and transesterification, respectively [14,15,16,17,18,19,20]. Among these derivatives of GL, GC is one of the most promising chemicals. GC is a non-toxic, colorless, and easily biodegradable viscous liquid with a high flash point, high boiling point, and high water solubility [21,22,23]. It can be used as a polar solvent, lithium ion battery liquid, component of a separation membrane, intermediate for polyester, fuel additive, and so on [24,25,26,27,28].

GC can be synthesized from GL by using methods such as (i) the reaction of phosgene with GL; (ii) oxidative carbonylation of CO, O₂, and GL; (iii) transesterification of dialkyl carbonate and GL; (iv) carbonylation of CO₂ and GL; and (v) reaction of urea and GL. However, the reaction of phosgene and GL and oxidative carbonylation of CO, O₂, and GL are limited due to the toxicity of reactants and high reaction temperature and pressure [29,30]. The carbonylation of CO₂ and GL also suffers with low GL conversion due to a severe thermodynamic limitation [31,32]. In addition, the transesterification of dialkyl carbonate and GL is limited by expensive reactants and a catalyst with low activity [33]. Compared with other methods, the reaction of urea and GL possesses the following advantages: (i) cheap reactant (urea); (ii) mild reaction conditions; and (iii) high atomic economy, because the ammonia produced in this process can be reacted with greenhouse gas CO₂ under certain conditions to produce more urea for use as the reactant (Scheme 1) [34].

Currently, the development of the catalyst for the reaction of GL and urea is a focus of research within academia and industry. Two types of catalysts for the reaction of GL and urea have been developed: homogeneous and heterogeneous. The homogeneous catalysts, including some zinc salts (such as zinc chloride, zinc bromide, zinc iodide, zinc sulfate) [35,36], show higher activity for reaction of GL with urea. The heterogeneous catalysts mainly include metal oxide (such as magnesium oxide, calcium oxide, lanthanum oxide, and zinc oxide) [37,38,39,40], mixed metal oxide catalysts [41], heteropolyacid salts [42], supported ionic liquid catalysts [43], supported metal nanoparticle catalysts (such as Au/MgO nanoparticle catalyst) [44], hydrotalcite catalysts [45,46], and so on. Zinc chloride and zinc sulfate are frequently used as the homogeneous catalysts for the reaction of GL and urea. Park et al. studied the reaction of GL and urea using ZnCl₂ as the catalyst and found that during the reaction, ZnCl₂ firstly was transformed into Zn(NH₃)₂Cl₂, which further was transformed into Zn(C₃H₆O₃) and NH₄Cl [47]. Therefore, they proposed that Zn(C₃H₆O₃) and NH₄Cl were the true catalytic active species. However, Fujita and his co-workers considered that the active species was Zn(NCO)₂(NH₃)₂ [35]. Hence, further work is required to determine the catalytic active species for the reaction of GL and urea over a homogeneous zinc salt catalyst. In addition, the reaction kinetics are important for the development of the catalyst and design of an industry reactor [38,48]. However, up to now, few works have been carried out on the kinetics of the reaction of GL and urea. In addition, in reaction process of GL and urea, low pressure or inert gas flow is needed to remove the ammonia gas generated during the reaction, to shift the reaction equilibrium to right side. However, escape of NH₃ will reduce the volume of the reaction system, which was ignored in the previous reaction kinetics model.

In this study, the kinetics of the reaction of GL and urea to produce GC using ZnSO₄ as the catalyst were studied. The changes in catalyst in the reaction process were deeply investigated and the catalytic active species for the catalyst and the reaction intermediate species were determined according to XRD, FT-IR, and ESI-MS results. The reaction mechanism was also proposed. Based on the above results, a reaction kinetics model considering the change in volume was established, and the model parameters were obtained.

2. Results and Discussion

2.1. Activity of Different Zn Salt Catalysts

The catalytic activities of certain catalysts for the reaction of GL and urea are listed in

Table 1. The activities of different catalysts for the reaction of GL and urea ^a.

No.	Catalyst	XGL, % b	YGC, % c	SGC, % d
1	-	42.24	32.29	76.44
2	KOH	trace	trace	trace
3	KNO3	trace	trace	trace
4	ZnO	71.20	64.73	90.91
5	ZnCl2	81.75	73.83	90.31
6	ZnBr2	78.33	69.91	89.25
7	ZnI2	74.41	67.95	91.32
8	Zn(NO3)·6H2O	68.11	61.19	89.84
9	Zn3(PO4)2	67.14	62.30	92.79
10	ZnSO4	80.33	75.81	94.37

^a Reaction conditions: reaction temperature: 140 °C; reaction time: 4 h; catalyst amount: 5 wt% (based on GL weight); urea-to-GL molar ratio: 1.1:1; reaction pressure: 5 kPa; stirring rate: 600 rpm. ^b X_GL: the conversion of GL. ^c Y_GC: the yield of GC. ^d S_GC: the selectivity of GC.

. A GL conversion of 42.24% and GC selectivity of 32.29% can be obtained without any catalyst. Meanwhile, the strongly basic KOH and neutral KNO₃ show negative activity and there is barely any GL conversion or GC yield for the two catalysts. On the contrary, the amphoteric Zn-based catalysts (zinc oxide and zinc salts) exhibit higher catalytic activities for the reaction of GL and urea. The GC yields for these Zn-based catalysts increase in the following order: Zn(NO₃)·6H₂O < Zn₃(PO₄)₂ < ZnO < ZnI₂ < ZnBr₂ < ZnCl₂ < ZnSO₄. Among these catalysts, ZnSO₄ exhibits the highest activity. So, ZnSO₄ was selected as the catalyst for the following investigation.

2.2. Effects of Reaction Parameters

2.2.1. Effect of Reaction Temperature

Figure 1 shows the effect of reaction temperature on the reaction of GL and urea over a ZnSO₄ catalyst. With an increase in the reaction temperature from 120 °C to 150 °C, both the GL conversion and GC yield increase from 30.24% and 27.57% to 89.51% and 79.47%, respectively. In general, a higher reaction temperature can increase the collision probability of reactant molecules, to accelerate the reaction rate. Furthermore, the reaction of GL and urea is an endothermic reaction and so a higher reaction temperature will also shift the reaction equilibrium to the product side. Therefore, the GL conversion and GC yield increase with the reaction temperature. Meanwhile, the selectivity of GC remains near-constant, at about 90%, with increasing reaction temperature. Urea will decompose when the reaction temperature is over 150 °C and so a suitable reaction temperature is around 140 °C for the reaction of GL and urea [49,50].

2.2.2. Effect of Urea/GL Molar Ratio

Figure 2 shows the effect of the urea-to-GL molar ratio on the reaction of GL and urea over a ZnSO₄ catalyst. When the urea-to-GL molar ratio increases from 1:1 to 1.5:1, the GL conversion increases from 78.18% to 85.93% while the GC yield increases from 63.41% to 75.81% firstly and then decreases to 71.13%. Meanwhile, the GC selectivity also firstly increase from 90.61% to 94.37% and then decreases to 82.8% with an increase in the urea-to-GL molar ratio from 1:1 to 1.5:1. For the reaction of urea and GL, the increase in the urea-to-GL molar ratio can shift the reaction equilibrium to the right side, so the conversion of GL increases. However, as the urea-to-GL molar ratio is over 1.1:1, which is larger than the stoichiometric ratio of urea to GL of 1:1, the product GC may further react with unreacted urea to produce the byproduct (2-oxo-1,3-dioxolane 4-yl)methyl carbamate, which is an overreaction product of GC with urea [51]. So, the GC yield and GC selectivity will decrease with the urea-to-GL molar ratio. Hence, the suitable urea-to-GL molar ratio is 1.1:1.

2.2.3. Effect of Catalyst Amount

Figure 3 shows the effect of the catalyst amount on the reaction of GL and urea over ZnSO₄ catalyst. As the catalyst amount increases from 0.2 wt% to 5 wt%, the GL conversion and GC yield increase from 54.58% and 23.42% to 80.33% and 75.8%, respectively. With the further increase in catalyst amount to 7 wt%, the GL conversion and GC yield remain near-constant. Meanwhile, the GC selectivity increases with the catalyst amount. ZnSO₄ can completely dissolve in the reaction mixture and the catalyst is a homogeneous one, so the increase in catalyst amount can increase the concentration of catalytic active sites in the reaction mixture. Therefore, the GL conversion and GC yield increase with catalyst amount. Hence, the suitable catalyst amount is about 5 wt%.

2.2.4. Effect of Reaction Time

The reaction time also shows an important effect on the reaction of GL and urea over a ZnSO₄ catalyst (Figure 4). When the reaction time increases to 120 min, the GL conversion and GC yield increase rapidly to 68.94% and 67.97%, respectively. With a further increase in reaction time to 300 min, the GL conversion and GC yield slowly increase to 79.61% and 75.66%, respectively. The GC selectivity increases with an increase in the reaction time firstly and then slowly decreases with time. The above results indicate that the optimal reaction conditions for the reaction of GL and urea are a reaction temperature of 140 °C, urea-to-GL molar ratio of 1.1:1, catalyst amount of 5 wt% (based on GL weight), and reaction time of 240 min. Under the optimal conditions, the GL conversion, GC yield, and GC selectivity reach to 80.33%, 75.81%, and 94.37%, respectively. In order to check the repeatability of the results, the experiment was repeated three times and the relative error for the GC yield was less than 2.0%. This suggests that the results are reliable. Figure S1 shows the gas chromatograms of the reaction samples (see the Supplementary Materials). A good peak separation is achieved for all the components. Under analytical conditions, urea does not peak. Furthermore, except for GL and GC, the peaks of the other materials, such as byproducts or intermediates, can barely be observed, meaning the concentrations of these byproducts or intermediates are very low. Under reaction conditions, the possible intermediate component may be glyceryl carbamate (GCM) while the byproducts may be glycidol, which is produced from the decomposition of GC, and (2-oxo-1,3-dioxolan-4-yl)methyl carbamate [52], which is generated from the reaction of GC with surplus urea.

2.3. Reaction Mechanism

During the reaction process, firstly, the ZnSO₄ catalyst was dissolved quickly in the reaction mixture, and the reaction proceeded in a homogeneous state. However, when the reaction time passed 5 h, some white solids were precipitated from the reaction mixture. This indicates that the ZnSO₄ catalyst may be changed into another insoluble species during the reaction process. Meanwhile, when methanol was added to the homogeneous reaction sample at different times, some white solids again precipitated from the reaction sample. In order to determine the components of the white solids, XRD was applied to characterize these precipitates, and the results are illustrated in Figure 5. As shown in Figure 5a, the main phase for the fresh ZnSO₄ catalyst is ZnSO₄ (at 2θ = 18.6, 26.1, 26.6, 26.9, 29.1, 35.6, see PDF# 00-033-1476). After reaction for 30 min, the precipitated solids are remarkably different from fresh ZnSO₄, having been transformed into a mixture of ZnSO₄ phase (at 2θ = 18.1, 27.18, 35.9) and Zn(NH₃)₂SO₄ phase (at 2θ = 15.8, 19.2, 20.5, 21.3, 23.6, 26.2, 29.3, 32.2, 36.9, 40.5, see PDF# 00-035-0767). After reaction for 240 min, the precipitated solids are transformed into Zn(C₃H₆O₃) phase (at 2θ = 11.0, 17.3, 20.8, 23.8, 24.8, 27.7) and little (NH₄)₂SO₄ phase (at 2θ = 33.7, 38.8, 41.6, see PDF# 01-084-0130). These results suggest that the ZnSO₄ catalyst is transformed into Zn(NH₃)₂SO₄ at the initial stage of the reaction and then further transformed into Zn(C₃H₆O₃).

The ESI-MS spectra of the reaction solution of GL and urea using ZnSO₄ as the catalyst with different reaction times are illustrated in Figure 6. The peak at 118 of the m/Z+ ratio may be attributed to GC while the peak at 158 of the m/Z+ ratio is assigned to the reaction intermediate, GCM. With the increase in the reaction time, the peak of GCM becomes small and almost disappears at 300 min. On the contrary, when the reaction time increases from 60 min to 180 min, the peak of GC becomes strong. The results indicate that the reaction of GL and urea firstly produce intermediate GCM, which then is transformed into GC. In addition, the peak at 201 of the m/Z+ ratio may be ascribed to ZnSO₄, which quickly disappears after 180 min. The peak at 216 or 234 of the m/Z+ ratio may be assigned to the Zn(NH₃)₂SO₄ species. The peak at 173 of the m/Z+ ratio belongs to the Zn(C₃H₆O₃) species, which becomes strong from 180 min to 300 min. These results suggest that the ZnSO₄ catalyst is transformed into Zn(NH₃)₂SO₄, which then is transformed into Zn(C₃H₆O₃). These results are in accordance with those of the XRD.

Figure 7 shows the FT-IR spectra of the reaction solution of GL and urea over the ZnSO₄ catalyst with different times. The peak at 1715 cm⁻¹ is attributed to -CH₂- of GCM [53], which becomes gradually weaker with the reaction time. The peak at 1790 cm⁻¹ is assigned to C=O of GC while the peaks at 1400 cm⁻¹ and 1185 cm⁻¹ are ascribed to –OH and C-C of GC [35], whose intensities increase with the reaction time. These results suggest that the GL reacts with urea to generate GCM firstly and then GCM is transformed into GC, which is in accordance with the results of ESI-MS. In addition, the peak at 2200 cm⁻¹ is attributed to the N=C=O group of HNCO [54], which is produced from the decomposition of urea.

The above results strongly indicate that during the reaction, the catalyst ZnSO₄ firstly reacts with NH₃ produced from decomposition of urea to transform into Zn(NH₃)₂SO₄, which then reacts with GL to generate Zn(C₃H₆O₃) and (NH₄)₂SO₄. Zn(C₃H₆O₃) and (NH₄)₂SO₄ are the true catalysts for the reaction of GL and urea.

Table 2. The catalytic activity of some catalysts for the reaction of GL and urea ^a.

No.	Catalyst	XGL, % b	YGC, % c	SGC, % d
11	Zn(C3H6O3)	65.78	60.84	92.49
12	(NH4)2SO4	47.01	38.69	82.30
13	Zn(C3H6O3) + (NH4)2SO4	76.38	71.62	93.77

^a Reaction conditions: reaction temperature: 140 °C; reaction time: 4 h; catalyst amount: 5 wt% (based on GL weight); urea-to-GL molar ratio: 1.1:1; reaction pressure: 5 kPa; stirring rate: 600 rpm. ^b X_GL: the conversion of GL. ^c Y_GC: the yield of GC. ^d S_GC: the selectivity of GC.

shows the catalytic activities of some catalysts for the reaction of GL and urea. Although Zn(C₃H₆O₃) and (NH₄)₂SO₄ show lower activity than ZnSO₄, the mixture of Zn(C₃H₆O₃) and (NH₄)₂SO₄ exhibits similar activity to ZnSO₄.

In order to clarify the roles of Zn(C₃H₆O₃) and (NH₄)₂SO₄ for the activation of GL and urea, the FT-IR spectra are used to characterize the interaction of Zn(C₃H₆O₃) or (NH₄)₂SO₄ with GL or urea, and the results are illustrated in Figure 8 and Figure 9. In Figure 8a, the peak at 3432 cm⁻¹ is attributed to hydroxyl of GL, which shifts to a lower frequency of 3402 cm⁻¹ when GL is mixed with (NH₄)₂SO₄ at 30 min. As the mixing time increases to 120 min, the peak further shifts to a lower frequency of 3394 cm⁻¹, meaning that the interaction between (NH₄)₂SO₄ and GL becomes strong (Figure 8c–e). The results suggest that the hydrogen-bond interaction may be yielded between (NH₄)₂SO₄ and hydroxyl of GL, which results in the activation of molecular GL. Figure 9 shows the FTIR spectra of a mixture of urea and Zn(C₃H₆O₃). The two materials are solid, so a certain amount of urea was mixed with a certain amount of Zn(C₃H₆O₃) in an agate mortar and ground to give samples with different grinding times. In Figure 9a, the peaks at 1672 cm⁻¹ are attributed to the C=O stretching vibration of urea, which also shift to a lower frequency of 1668 cm⁻¹ as urea is mixed with Zn(C₃H₆O₃) for 120 min [54]. Meanwhile, the peaks at 3440 cm⁻¹ of -NH₂ of urea also shift to the high-frequency side. These results suggest that there may be a hydrogen-bond interaction between urea and Zn(C₃H₆O₃), which leads to the activation of molecular urea.

Furthermore, NMR analysis was used to study the interactions between GL and (NH₄)₂SO₄ and between urea and Zn(C₃H₆O₃). ¹H NMR analysis of the mixture of GL and (NH₄)₂SO₄ with the contact time of 2 h was performed and the results are shown in Figure 10. Meanwhile, ¹³C NMR analysis of the mixture of urea and Zn(C₃H₆O₃) with the contact time of 2 h was also conducted and the results are shown in Figure 11. In Figure 10, the peak at 4.41 ppm can be attributed to the hydrogen atom of the primary hydroxyl of pure GL, which shifts to 4.40 ppm when GL is mixed with (NH₄)₂SO₄. This means that there may be a hydrogen bond interaction between (NH₄)₂SO₄ and the primary hydroxyl of GL. Meanwhile, as shown in Figure 11, the peak at 160.0911 ppm is assigned to the carbon atom of the carbonyl of pure urea, which also shifts to 160.0385 ppm when urea is mixed with Zn(C₃H₆O₃) for 2 h. These results are in accordance with those of the FTIR and suggest that there may be an interaction between urea and Zn(C₃H₆O₃).

Based on the above results, the possible reaction mechanism for GL and urea over a ZnSO₄ catalyst is proposed (Scheme 2). During the reaction process, NH₃ firstly is produced through the decomposition of urea. Meanwhile, NH₃ also may be generated by the reaction of GL with urea without a catalyst. Then, the soluble ZnSO₄ catalyst reacts with NH₃ to give Zn(NH₃)₂SO₄, which further reacts with GL to produce Zn(C₃H₆O₃) and (NH₄)₂SO₄. Afterward, molecular GL is activated by the hydrogen-bond interaction of primary hydroxyl of GL with (NH₄)₂SO₄ while molecular urea is also activated by the interaction between C=O of urea and Zn(C₃H₆O₃). The oxygen atom of primary hydroxyl for activated GL launches a nucleophilic attack on the carbon atom of C=O of urea to give the intermediate GCM and NH₃. Finally, GC is obtained via an intramolecular nucleophilic attack and cyclization of GCM, and another molecule of NH₃ is also generated.

2.4. Reaction Kinetics

2.4.1. Reaction Rate

The reaction kinetics were further studied based on the above results to derive the reaction rate constant and active energy. The reaction process includes a complex cascade reaction: firstly, GL reacts with urea to produce intermediate GCM and NH₃ over the catalyst, and then, GC is generated from the intramolecular cyclization of GCM, and another molecule of NH₃ is also released. The reaction is carried out in a vacuum and NH₃ is continually drawn out from the reaction system, so the above two reactions are irreversible. The reaction formulas are listed as follows:

$$\mathrm{R}1: \mathrm{GL}+\mathrm{urea}\stackrel{}{\to }\mathrm{GCM}+{\mathrm{NH}}_3(\mathrm{g})\uparrow$$

(1)

$$\mathrm{R}2: \mathrm{GCM}\stackrel{}{\to }\mathrm{GC}+{\mathrm{NH}}_3(\mathrm{g})\uparrow$$

(2)

Meanwhile, the following reactions may take place in the reaction process:

$${\mathrm{ZnSO}}_4+{2\mathrm{NH}}_3\to {\mathrm{Zn}(\mathrm{NH}}_3{)}_2{\mathrm{SO}}_4$$

(3)

$${\mathrm{Zn}(\mathrm{NH}}_3{)}_2{\mathrm{SO}}_4+\mathrm{GL}\to {\mathrm{Zn}(\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_3)+{{(\mathrm{NH}}_4)}_2{\mathrm{SO}}_4$$

(4)

Reactions (3) and (4) are the conversion reaction of the catalyst. Since obtaining the concentrations of the catalyst components in the reaction is difficult and the reaction degrees of Reactions (3) and (4) are small, they are ignored in the kinetics model. Side reactions, such as the reaction of GC with urea and the decomposition of GC to produce glycidol, may also take place. However, the concentrations of the byproducts are so small that they cannot be found in a gas chromatogram or ESI-MS spectra. So, these side reactions are also not considered in the kinetics model.

According to the reaction mechanism, the main catalysts may be Zn(C₃H₆O₃) and (NH₄)₂SO₄. The reaction process has the following steps: firstly, GL and urea are activated through interaction with the catalyst, respectively, and then the GCM and one molecule of NH₃ are generated by the reaction of activated GL and urea. Finally, GC and another molecule of NH₃ are obtained through an intramolecular nucleophilic attack and cyclization of GCM. The above elementary reactions in the reaction process are listed as follows:

$$\mathrm{GL}+\mathrm{cat}\iff {\mathrm{GL}}^{*}$$

(5)

$$\mathrm{urea}+\mathrm{cat}\iff {\mathrm{urea}}^{*}$$

(6)

$${\mathrm{GL}}^{*}+{\mathrm{urea}}^{*}\to \mathrm{GCM}+{\mathrm{NH}}_3(\mathrm{g})\uparrow$$

(7)

$$\mathrm{GCM}+\mathrm{cat}\iff {\mathrm{GCM}}^{*}$$

(8)

$${\mathrm{GCM}}^{*}\to \mathrm{GC}+{\mathrm{NH}}_3(\mathrm{g})\uparrow$$

(9)

where ‘cat’ denotes the catalyst, and GL*, urea*, and GCM* denote the activated GL, activated urea, and activated GCM molecules, respectively. Among the above Reactions (5)~(9), the Reactions (5), (6), and (8) are the activation processes of GL, urea, and GCM, respectively, whose reaction rates are very quick, meaning reaction equilibriums are reached quickly. In addition, for the reaction of GL and urea, though GL is liquid and urea is solid, urea is dissolved quickly in the GL phase when urea is mixed with GL. Meanwhile, though the catalyst ZnSO₄ is solid, it is also dissolved in the reaction mixture as ZnSO₄ is added to the reaction system. Furthermore, though the solid of Zn(C₃H₆O₃)₂ is separated from the reaction system when the reaction time passes 5 h, its amount is small. Therefore, the reaction can be regarded as a homogeneous one. So, we have the following expressions:

$$C_{G{L}^{*}}=K_1{C}_{GL}{C}_{cat}$$

(10)

$$C_{ure{a}^{*}}=K_2{C}_{urea}{C}_{cat}$$

(11)

$$C_{GC{M}^{*}}=K_4{C}_{GCM}{C}_{cat}$$

(12)

where K₁, K₂, and K₄ are the equilibrium constants of Reactions (5), (6), and (8), respectively. C_i is the component concentration, mol/L. According to the law of mass action, the reaction rates of Reactions (7) and (9) can be calculated by using the following equations, respectively:

$$r_1=k_1^{\prime }{C}_{G{L}^{*}}{C}_{ure{a}^{*}}=k_1^{\prime }{K}_1{C}_{GL}{C}_{cat}{K}_2{C}_{urea}{C}_{cat}$$

(13)

$$r_2=k_2^{\prime }{C}_{GC{M}^{*}}=k_2^{\prime }{K}_4{C}_{GCM}{C}_{cat}$$

(14)

Although the catalyst ZnSO₄ is transformed into Zn(C₃H₆O₃) and (NH₄)₂SO₄ during the reaction, the concentration of the catalyst, C_cat, can be considered as constant during the reaction because there is a large number of active sites. By applying commands $k_1=k_1^{\prime }{K}_1{K}_2{C}_{cat}{C}_{cat}$ and $k_2=k_2^{\prime }{K}_4{C}_{cat}$, we obtain

$$r_1=k_1{C}_{GL}{C}_{urea}=k_1{C}_A{C}_B$$

(15)

$$r_2=k_2{C}_{GCM}=k_2{C}_c$$

(16)

where r₁ and r₂ are the reaction rates of Reactions (7) and (9), mol/(L·min), respectively; k₁ and k₂ are the apparent reaction rate constants of Reactions (7) and (9), respectively; and A, B, C, and D denote the GL, urea, GCM, and GC, respectively. Accordingly, it can be found that the above reaction rate model is well-connected with the proposed reaction mechanism.

The Arrhenius equation is used to calculate reaction rate constant:

$$k_j=k_j^{*}\exp (\frac{-E{a}_j}{RT})$$

(17)

where k_j* is the pre-exponential factor of reaction rate constant k_j; Ea_j is the active energy of reaction j, kJ/mol; R is the gas constant (R = 8.314 J/(mol·K); and T is the reaction temperature, K.

The reaction is carried out under vacuum conditions of 5 kPa to remove the generated NH₃, so the mass of the reaction mixture should decrease. Meanwhile, the volume of the reaction system also decreases with the reaction time due to the molar volume of GC or GMC being less than the total molar volumes of GL and urea. So, the variation in the volume of the reaction mixture should also be considered in the kinetics model. Some assumptions are made that the volume of the reaction mixture may be obtained by summing the volumes of every component and that all NH₃ are removed from the reaction system by the vacuum. Meanwhile, the effect of reaction temperature on the molar volumes of components is ignored. According to the material balance for component i, the reactor model is obtained, as follows (The detailed process of the establishment for the kinetics model is given in Appendix A):

$$\frac{d{C}_A}{dt}=-\left[1+C_A(\overline{V_C}-\overline{V_A}-\overline{V_B})\right]r_1-C_A(\overline{V_D}-\overline{V_C})r_2$$

(18)

$$\frac{d{C}_B}{dt}=-\left[1+C_B(\overline{V_C}-\overline{V_A}-\overline{V_B})\right]r_1-C_B(\overline{V_D}-\overline{V_C})r_2$$

(19)

$$\frac{d{C}_C}{dt}=\left[1-C_c(\overline{V_C}-\overline{V_A}-\overline{V_B})\right]r_1-\left[1+C_C(\overline{V_D}-\overline{V_C})\right]r_2$$

(20)

$$\frac{d{C}_D}{dt}=-C_D(\overline{V_C}-\overline{V_A}-\overline{V_B})r_1+\left[1-C_D(\overline{V_D}-\overline{V_C})\right]r_2$$

(21)

$$\frac{dV}{dt}=\left[(\overline{V_C}-\overline{V_A}-\overline{V_B})r_1+(\overline{V_D}-\overline{V_C})r_2\right]V$$

(22)

The initial condition is

t = 0, C_A = C_A0, C_B = C_B0, C_C = C_D = 0, V = V₀.

(23)

where $\overline{V_i}$ is the molar volume of component i, L/mol; V is the volume of reaction mixture, L; C_A0 and C_B0 are the initial concentrations of GL and urea, mol/L, respectively; and V₀ is the initial volume of the reaction mixture, L.

2.4.2. Solution of Kinetics Model

The kinetics model (18~22) is a set of ordinary differential equations. The four-order Runge–Kutta method can be used to solve these equations [55]. By minimizing the following expression (24), the reaction rate constants can be obtained:

$$\psi ={\displaystyle \sum _j^N\left[{(C_{i,j}^{\exp }-C_{i,j}^{cal})}^2+{(V_j^{\exp }-V_j^{cal})}^2\right]}$$

(24)

which is the squared sum of the residuals between the experimental data of the component concentration, $C_{i,j}^{\exp }$ (i = GL and GC), the volume of the reaction system, V_j^exp, and the model predictions, $C_{i,j}^{cal}$ and V_j^cal. MATLAB software was used to write the calculation program and the Levenberg–Marquardt algorithm was used to perform the correlation. The molar volume of GCM was calculated by using Aspen plus software. The rate constants at every temperature were firstly correlated and then their expressions were obtained from the Arrhenius Equation (17), and the activation energies of every reaction were also obtained. The results are listed in

Table 3. The reaction rate constant and activation energy for the reaction of GL with urea using ZnSO₄ as the catalyst.

ki a	Inch	Ea, kJ/mol b	R2 c
$k_1=\exp (35.297-17247/T)$	L·mol−1·min−1	143.39	0.9995
$k_2=\exp (29.327-10499/T)$	min−1	87.29	0.9995

^a the reaction rate constant. ^b the activation energy. ^c the correlation coefficients.

. The correlation coefficients for k₁ and k₂ are 0.9995 (in the fourth column, Table 3), meaning the fitting accuracy is high. The activation energies of R₁ and R₂ are 143.39 kJ/mol and 87.29 mol/L, respectively. The activation energies of the reaction of GL with urea over other catalysts are listed in

Table 4. The activation energy for the reaction of GL with urea over other catalysts.

No.	Cat.	Temperature, °C	Pressure, kPa	Ea, kJ/mol a	Ref.
1	MgO	135~150	101.3 b	117.85	[38]
2	Co3O4/ZnO	100~160	101.3	31.89	[56]

^a the activation energy. ^b The reaction was carried out under nitrogen flow at a flow rate of 100 mL/min.

. The activation energies for ZnSO₄ were closest to those over the catalyst MgO.

Figure 12 gives a comparison of the experimental and calculated concentrations for every component at different temperatures. In these figures, the points denote the experimental concentrations and lines denote the calculated concentrations. The intermediate GCM cannot be measured with a gas chromatograph, so only the calculated concentrations for GCM are given. The experimental concentrations of urea were calculated from the concentrations of GL. The calculated concentrations are close to the experimental values. Furthermore, the concentration of GCM rapidly increases firstly and then decreases gradually with increasing reaction time, which matches the change characteristic of intermediate species. Figure 13 shows a comparison of experimental and calculated volumes of the reaction mixture at different temperatures. The relative deviation for volume is −10%~+20%.

A statistical test was used to further evaluate the kinetics model, and the results are listed in

Table 5. The statistical test results for the kinetics model.

Catalyst	F	10 × FT
ZnSO4	216.37	23.6

. The F value is the ratio of the mean regression sum of squares to the mean residual sum of squares, which can be calculated by using the following equation:

$$F=\frac{{\displaystyle {\sum }_{i=1}^N[{(C_i^{cal})}^2+{(V_i^{cal})}^2]}/p}{{\displaystyle {\sum }_{i=1}^N[{(C_i^{\exp }-C_i^{cal})}^2+{(V_i^{\exp }-V_i^{cal})}^2]}/(N-p)}$$

(25)

where N is the experimental run number and p is the number of parameters in the kinetics model. F_T is the tabulated value corresponding to degrees of freedom at a 5% confidence level. In general, if F > 10 F_T, a model is considered acceptable [57,58]. As shown in Table 5, the F value is 216.37, which is >10 F_T (=23.6). Hence, the established kinetics model is suitable for the reaction of GL with urea over a ZnSO₄ catalyst.

3. Materials and Methods

3.1. Materials

Glycerol (GL) (>99%), urea (AR), potassium hydroxide (KOH) (AR), potassium nitrate (KNO₃) (AR), ammonium sulfate ((NH₄)₂SO₄) (AR), zinc acetate dihydrate ((CH₃COO)₂Zn∙2H₂O) (AR), zinc nitrate hexahydrate (Zn(NO₃)₂∙6H₂O) (AR), zinc oxide (ZnO) (AR), and methanol (>99.5%) were purchased from Sinopharm Chemical Regent Co., Ltd., Shanghai, China. Glycerol carbonate (GC) (90.0%) was obtained from TCI Shanghai. Zinc sulfate (ZnSO₄) (AR) and zinc phosphate (Zn₃(PO₄)₂) (AR) were purchased from Shanghai yuanye Bio-Technology Co., Ltd. (Shanghai, China). Tetraethylene glycol (TEG) (99%), n-Butyl alcohol (99.9%), zinc bromide (ZnBr₂) (AR), and zinc iodide (ZnI₂) (AR) were purchased from Shanghai Aladdin Biochemical Technology Co., Ltd (Shanghai, China). Zinc chloride (ZnCl₂) was sourced from Chengdu Chron Chemical Co., Ltd. (Chengdu, China). N₂ (99.9%), H₂ (99.9%), and air (99.9%) were obtained from Wuhan Zhongxin Ruiyuan Gas Co., Ltd. (Wuhan, China). All the chemicals were used without further purification.

Zn(C₃H₆O₃) was prepared from the reaction of GL and zinc acetate dihydrate, using a method that can be found in the literature [49].

3.2. Reaction Procedure

The synthesis of GC from the reaction of GL with urea by using ZnSO₄ as a catalyst was carried out in a 25 mL round-bottomed 3-neck glass flask as a batch reactor equipped with a magnetic stirrer, thermometer, reflux condenser, and vacuum pump. Energy was applied to the glass flask with a constant temperature oil bath. The accuracy of the temperature measurements was ± 0.5 °C. In a typical run, 0.1 mol of GL (9.21 g) was added to the flask and heated to 140 °C under a reduced pressure with a stirring speed of 600 rpm. Then, 0.11 mol of urea (6.61 g) and 0.46 g of catalyst were loaded into the reactor quickly and the reaction mixture was kept at 140 °C and a reduced pressure of 5 kPa for 4 h with continuous stirring. The vacuum system was used to remove NH₃ produced during the reaction. After the reaction, the reaction mixture was cooled to room temperature and its mass and volume were measured. The liquid mixture was sampled for analysis.

It was found that the volume of the reaction system decreased continuously due to the removal of ammonia. In order to obtain accurate concentrations of the reaction components at different reaction times for the kinetics investigation, an experiment at every reaction time was carried out individually.

The Fuli GC-9790 II Gas Chromatograph (Fuli 9790-II, Fuli, Wenling, China) with a flame ionization detector (FID) and KB-WAX capillary column (30 m long and 0.25 mm I.D.) was used to analyze the reaction samples. The column temperature was programmed at 70 °C for 2 min, and then increased to 250 °C with 15 °C/min speed and held there for 5 min. Tetraethylene glycol was used as the internal standard for GL and GC, and n-butyl alcohol was used for the other byproducts. The approximately 0.7 g of methanol used as a solvent was added to the sample.

The GL conversion, X_GL, GC yield, Y_GC, GC selectivity, and S_GC were calculated using the following expressions:

$$X_{\mathrm{GL}}=\frac{n_{\mathrm{GL}}^{\mathrm{in}}-n_{\mathrm{GL}}^{\mathrm{out}}}{n_{\mathrm{GL}}^{\mathrm{in}}}\times 100\%$$

(26)

$$Y_{\mathrm{GC}}=\frac{n_{\mathrm{GC}}^{\mathrm{out}}}{n_{\mathrm{GL}}^{\mathrm{in}}}\times 100\%$$

(27)

$$S_{\mathrm{GC}}=\frac{n_{\mathrm{GC}}^{\mathrm{out}}}{n_{\mathrm{GL}}^{\mathrm{in}}-n_{\mathrm{GL}}^{\mathrm{out}}}\times 100\%$$

(28)

where $n_{GL}^{in}$ and $n_{GL}^{out}$ are the initial molar number of GL and the molar number of GL after the reaction, respectively, and $n_{GC}^{out}$ is the molar number of GC after the reaction.

3.3. Characterization

The FT-IR spectra of the samples were measured using a Bruker VERTEX 70 instrument (Bruker, Karlsruhe, Germany). The scanning range is 4000~400 cm⁻¹ and the resolution ratio is 2 cm⁻¹.

The X-ray diffraction (XRD) patterns of the catalysts were measured on a PANalytical X’Pert Pro X-ray diffractometer (X’Pert PRO, PANalytical B.V., Almelo, Netherlands) with Cu Kα radiation at 30 kV and 15 mA, over the range of 5 to 90°.

ESI-MS spectra were measured by using an UltiMate-3000-micro TOF instrument (Thermofisher-Bruker Daltonics Inc. Blerica, Massachusetts, MA, USA; Bremen, Germany) with the positive ion mode at 50~1200 m/Z, a dry heater temperature of 200 °C, a nebulizer pressure of 1 bar, and a dry gas flow velocity of 6 L/min.

4. Conclusions

The GC yield for these Zn-based catalysts increase in the following order: Zn(NO₃)·6H₂O < Zn₃(PO₄)₂ < ZnO < ZnI₂ < ZnBr₂ < ZnCl₂ < ZnSO₄. Among these catalysts, ZnSO₄ possesses the highest activity. Under a reaction temperature of 140 °C, catalyst amount of 5 wt% (based on the GL weight), urea-to-GL molar ratio of 1.1:1, and reaction time of 240 min, the GL conversion and GC yield can reach 80.33% and 75.81%, respectively, over a ZnSO₄ catalyst. During the reaction, the ZnSO₄ catalyst is transformed into Zn(NH₃)₂SO₄ at the initial stage of the reaction and then further transformed into Zn(C₃H₆O₃). Zn(C₃H₆O₃) and (NH₄)₂SO₄ may be the true active species for the activation of urea and GL, respectively. The reaction process includes a cascade reaction: GL reacts with urea to produce intermediate GCM and NH₃ firstly, and then GCM is transformed into GC through intramolecular cyclization, and another molecular of NH₃ is also released. The reaction kinetics model considering the change in volume of the reaction system has been established, and the activation energies were obtained by fitting the experimental data.