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. 2019 May 8;4(5):8274–8281. doi: 10.1021/acsomega.9b00316

Kinetic Study on the Preparation of Fumaric Acid from Maleic Acid by Batch Noncatalytic Isomerization

Wangmi Chen †, Xiaoting Chen ‡, Shouzhi Yi ‡,*
PMCID: PMC6545549  PMID: 31172038

Abstract

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In recent years, the increase in demand for fumaric acid from industry has resulted in an increased need for a high-selectivity process for the conversion of maleic acid to fumaric acid. A highly selective conversion of fumaric acid was achieved without a catalyst by a simple one-step hydrothermal reaction. In addition, the competitive conversion of maleic acid, fumaric acid, and malic acid was first systematically investigated in detail without using a catalyst. The products were characterized by X-ray diffraction and Fourier transform infrared, which demonstrated that the product was fumaric acid. The highly selective conversion of fumaric acid was achieved, and the yield of fumaric acid could reach 92%. Furthermore, a reaction kinetic model was put forward to study the competitive transformation process. The kinetic model predictions were found to agree well with the experimental data. The kinetic parameters were used to explain the changes in the content of every substance at different reaction temperatures and reaction times. In addition, the initial maleic acid concentration in the reaction was also considered as an influencing factor. These results can facilitate the conditional control and product control of industrial processes for the production of fumaric acid or malic acid using latter without a catalyst.

Introduction

Fumaric acid, a tetra-carbon unsaturated dicarboxylic acid classified as an organic acid, is widely distributed in nature. In 2004, fumaric acid was listed as the most promising building block derived from biomass by Werpy and Petersen due to its excellent performance.1,2 Fumaric acid has traditionally been used in the production of food acidity regulators,1 feed preservatives,3−5 and other high-potency chemical products.6−8 Recently, fumaric acid has been applied in metal–organic frameworks,9,10 polymer composites,11,12 composite anodes of high-energy lithium batteries,13 co-crystals,14,15 and microenvironment tablets.16 Thus, the demand for fumaric acid has dramatically increased with the expansion of the application scope for fumaric acid, which has made it necessary to study effective fumaric acid production methods.

Currently, methods for preparing fumaric acid mainly include chemical isomerization and biosynthesis.17,18 Chemical synthesis methods for fumaric acid were investigated in the 1940s and laid the foundation for the industrial production of fumaric acid.19 With the continuous development of biotechnology and the rapid growth of fossil (petroleum) based chemical production costs, investigations on the preparation of fumaric acid by biosynthetic methods have become more popular. Rhizopus,20−23Torulopsis glabrata,24 Filamentous fungal strains,25−27Saccharomyces cerevisiae,28,29Escherichia coli,30,31 and other significant microorganisms32 have been applied to produce fumaric acid. In addition, some new biotechnologies, such as alkali pretreatment,33 microwave technology,34 immobilization technology,26,35 and biorefinery technology,36 have been developed to improve the yield of fumaric acid. Nevertheless, biosynthesis methods have suffered from the inherent disadvantages of low yield and efficiency and a long cycle in the process of production. Thus, researchers have tried to develop isomerization methods to improve the synthesis efficiency. Several noteworthy catalysts have been reported to enhance the reaction conditions and increase the productivity of fumaric acid, including bromate ion,37,38 vanadium pentoxide,39 hydrochloric acid,40 and poly(4-vinyl pyridine).41 In a further study, researchers have introduced microwaves to reduce the reaction time of maleic acid and malic acid for assisted synthesis.42 By using the chemical isomerization method, the yield of fumaric acid can reach over 80%, which is far higher than that realized by using a biosynthesis method.

To further study the chemical isomerization method of fumaric acid synthesis, more researchers have used kinetic methods to explore the mutual transformation between fumaric acid and other acids under certain conditions. For example, Wojcieszak et al.43 and Delhomme et al.44 discussed the feasibility of and conditions for the mutual conversion of maleic anhydride, maleic acid, fumaric acid, and malic acid. Wang et al.40 successfully converted maleic acid and fumaric acid into malic acid in an acidic aqueous solution at 120 °C. Ortiz et al.42 studied the kinetics of the transformation from fumaric acid to maleic acid and malic acid at four different temperatures in a homogeneous nonisothermal batch reactor by using hydrochloric acid as a catalyst. The reason for and processes of the reaction could be explained by the reaction kinetics, so it was very meaningful to introduce kinetic studies into the related reaction processes. Our previous work has demonstrated that the isomerization of maleic acid can produce fumaric acid in the absence of a catalyst.45 Nevertheless, no detailed kinetic studies have been reported in the available literature about the mutual conversion of malic acid, maleic acid, and fumaric acid, especially the isomerization of maleic acid to fumaric acid, although such a kinetic study is significant, regardless of the use of a catalyst.

Researchers have proposed many kinetic models that help to study the conversion process between maleic acid, fumaric acid, and malic acid. Rozelle et al.46 studied the hydration kinetic and thermodynamic models of fumaric acid in a concentrated hydrochloric acid solution at 125–200 °C, but they only explored the mutual conversion process between fumaric acid and malic acid under the condition of hydrochloric acid catalysis. In addition, Jwo et al.47 investigated the kinetics of the conversion of maleic acid to fumaric acid under the action of bromine and strontium ions, while the model mainly focused on the one-way conversion of maleic acid to fumaric acid with a catalyst. Furthermore, Ortiz et al.48,49 converted a low concentration of fumaric acid to maleic acid and malic acid under the action of hydrochloric acid or no catalysts. This study only carried out the conversion reaction of fumaric acid rather than that of maleic acid. However, kinetic studies on the production of fumaric acid and malic acid using maleic acid, especially in the absence of a catalyst, have not been conducted. In addition, previous theoretical studies are not fully applicable to this process.

In this study, the selectivity of fumaric acid in the mutual conversion of fumaric acid, maleic acid, and malic acid was enhanced by conditional control in the absence of a catalyst, and a more comprehensive model of the reaction kinetics was established to explain the reaction process for the first time. In previous studies on the mutual conversion of fumaric acid, maleic acid, and malic acid, the strong selectivity of specific acids, especially fumaric acid, has not been studied on the basis of strengthening the investigation of the experimental influencing factors and determining better reaction conditions. In addition, the reaction mechanism of the selective production of fumaric acid and the mechanism of competition between various substances were also analyzed. It should be noted that to obtain a higher yield of fumaric acid in a short time, the mutual conversion between fumaric acid, maleic acid, and malic acid was fully considered. In addition, the content of each substance in the reaction was detected by high-performance liquid chromatography (HPLC), and the relevant kinetic parameters were calculated. The kinetic parameters explained the reasons for the change in the selectivity of each substance in the reaction as a result of various influencing factors and provided guidance for the subsequent control of conditions for the production of fumaric acid and malic acid without a catalyst.

Experimental Section

Materials

All chemicals were guaranteed reagents and used without further purification. The raw material (maleic acid) was an analytical reagent purchased from China Commeo Chemical Co., Ltd. Distilled water was used in the isomerization and purification stages. For the analysis and testing phases, fumaric acid (analytical reagent), maleic acid (analytical reagent), malic acid (biological grade), and hydrochloric acid (analytical reagent) were purchased from China Commeo Chemical Co., Ltd.

Preparation of Samples

The experiments were performed in a 50 mL Teflon-lined autoclave. Maleic acid and distilled water were added to the inner liner and stirred to achieve a uniform solution. Then, the Teflon-lined autoclave was sealed and placed in a blast drying oven. Once the temperature of the mixture reached the preset temperature, the timing was started. After heating for a preset time, the products were cooled to room temperature and removed. The experiments were carried out at 190, 200, 210, and 220 °C for 0–4 h. The initial reaction concentration of maleic acid (mass fraction 35–100%) on the selectivity of fumaric acid was also examined. The reaction experiments were repeated twice.

After adding a certain amount of distilled water, the reaction mixture was stirred and washed for 1 h. Further, insoluble matter and the washing solution were separated by suction filtration, and the filter cake was dried for 2 h by a blast drying oven at 100 °C to obtain the filtered product. The washing solution was prepared for HPLC.

Characterization

Fourier transform infrared (FT-IR) spectra were measured on a TENSOR27 Fourier infrared spectrometer (Brook Spectrometer, Germany). The dried samples were characterized by the potassium bromide tableting method, and the spectra were recorded between 400 and 4000 cm–1.

The X-ray diffraction (XRD) patterns of the samples were detected by an XRD-6100 (Shimadzu Corporation, Japan), with graphite monochromated Cu Kα (λ = 1.54178 Å) radiation operating at 40 kV and 30 mA in the angular range of 2θ = 5–80° at room temperature. The scanning speed and the scanning step size were 7° min–1 and 0.02°, respectively. The sample needed to be dried, ground, and placed in a fixed mold for compaction before testing.

Quantitative Analysis of Samples

All samples were analyzed by HPLC (Agilent Technologies 1260, Inc.). The column used was a Kromasil C18 column (5 μm × 250 mm × 4.6 mm, Japan). The mobile phase was an HCl solution in ultrapure water (pH 2) at a flow rate of 1 mL min–1 and an injection volume of 5 μL. The sample detection wavelength was 210 nm, and the column temperature was 42 ± 0.8 °C. The water samples were diluted 100 times before testing. The dilute samples were analyzed by HPLC to determine the content of each component, providing the necessary parameters for the kinetic analyses.

The conversion rates of fumaric acid, malic acid, and maleic acid were calculated by the following equations

graphic file with name ao-2019-00316b_m001.jpg 1
graphic file with name ao-2019-00316b_m002.jpg 2
graphic file with name ao-2019-00316b_m003.jpg 3

where CMx0 (mol L–1) is the initial concentration of maleic acid and CF, CM, and CMx (mol L–1) are the concentrations of maleic acid and fumaric acid at time t in the respective solutions. nMx0 (mol) is the initial molar mass of maleic acid and nF, nM, and nMx (mol) are the molar masses of maleic acid and fumaric acid.

Reaction Kinetic Model

The reaction model in Figure 1 was established to study the kinetics of this series of isomerization reactions and hydration reactions, which can explain the mutual transformation between fumaric acid, malic acid, and maleic acid. In this context, Mx, F, and M represent maleic acid, fumaric acid, and malic acid, respectively.

Figure 1.

Figure 1

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Simplified reaction model for the isomerization and hydration of maleic acid, fumaric acid, and malic acid.

According to the model with the assumption of a first-order reaction, the following set of eqs 4–6 was obtained.

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The following two boundary conditions could be determined by the analyses of the experimental process.

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It is worth noting that the reaction involving malic acid was a pseudo-first-order reaction because water was present in large amounts during the reaction. Although water was involved in some reactions, the amount of water in the system was considered to be constant, and the progress of every reaction was only related to the concentrations of fumaric acid, maleic acid, and malic acid.

The kinetic experiments were carried out using a maleic acid solution having a mass fraction of 60% (12.94 mol/L). Maleic acid has a higher solubility in water (100 °C, solubility of 392.6/100 g water, 33.84 mol/L) and a higher solubility at high temperatures, much higher than the concentration used in the kinetic experiments.50 At the same time, Ortiz et al.48 confirmed that the solubility of fumaric acid increased exponentially with increasing temperature (4.84 mol/L at 189 °C). Therefore, it can be considered that the detected reaction is carried out under homogeneous conditions.

The effect of temperature on the reaction rate constant was calculated by the Arrhenius equation, and the activation energy for the reaction was determined

graphic file with name ao-2019-00316b_m008.jpg 8

where T (K) is the absolute temperature, k (h–1) is the reaction rate constant at the preset temperature, Ea (kJ mol–1) is the activation energy, R (8.314 J (mol K)−1) is the general gas constant, and A (h–1) is a pre-exponential factor. Ea was estimated based on linear regression analysis of a plot of ln(ki) and 1/Ti (i = 190, 200, 210, and 220 °C).

The Gibbs free energy of every reaction was calculated by using the following equation

graphic file with name ao-2019-00316b_m009.jpg 9
graphic file with name ao-2019-00316b_m010.jpg 10

where ΔG (J mol–1) is the Gibbs free energy at the preset temperature, Kj (j = 1, 2, 3) is the reaction equilibrium constant, and ki (i = 1, 2, 3) is the reaction rate constant (h–1) for each reaction.

Results and Discussion

Characterization of Products

The products were identified from the measured XRD pattern (Figure 2a). The diffraction pattern showed six major diffraction peaks at 2θ = 18.4, 22.8, 28.7, 29.4, 31.2, and 35.8°. Compared with the peaks in the pattern of fumaric acid standard and fumaric acid reported in the references,51 the peaks in the XRD pattern of the products were consistent. This could indicate that the products had the same crystal structure as fumaric acid and could be preliminarily identified as fumaric acid. Since there were no other peaks present in the pattern, the purity of the products was relatively high.

Figure 2.

Figure 2

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(a) XRD patterns of the products, standard samples, and other research products.51 (b) FT-IR spectra of the products, standard samples, and other research products.

FT-IR analysis was further carried out to determine the structure of the product. As shown in Figure 2b, the characteristic peak at 3081 cm–1 can be assigned to the stretching vibration of C=C–H, while the peaks at 2863 and 1670 cm–1 can be ascribed to the stretching vibrations of saturated C–H and C=O, respectively. The peak at 1424 cm–1 was caused by the in-plane bending vibration of the saturated C–H. The three peaks at approximately 1276 cm–1 resulted from the stretching vibration of C–O. The peaks at 922 and 643 cm–1 were attributed to the out-of-plane bending vibration of O–H and the deformation vibration of O=C–O, respectively. Further, the single peak at 1008 cm–1 was attributed to the trans-substituted characteristic peak. The FT-IR analysis further indicated that the product was fumaric acid, which was in accordance with the XRD result.

Kinetic Study

To determine the rate-limiting step of the isomerization reaction, the following concentration equations were obtained by analyzing the above differential equation system (4–6)

graphic file with name ao-2019-00316b_m011.jpg 11
graphic file with name ao-2019-00316b_m012.jpg 12
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where

graphic file with name ao-2019-00316b_m014.jpg 14
graphic file with name ao-2019-00316b_m015.jpg 15
graphic file with name ao-2019-00316b_m016.jpg 16
graphic file with name ao-2019-00316b_m017.jpg 17
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and

graphic file with name ao-2019-00316b_m019.jpg 19

where ki (i = 1, 2, 3, −1, −3) (h–1) was the reaction rate constant for each reaction stage.

The content of each substance was determined by HPLC, and these concentration equations were used to determine the rate constant under each condition. The Solver function in Microsoft Excel was used to find the best values for the reaction rate constants. Using the Arrhenius form for the rate equations, the activation energy (Ea) and pre-exponential factor (A) were calculated for each individual reaction temperature using the slope and intercept of ln(ki) (i = 1, 2, 3, −1, −3) versus 1/T charts. The specific calculation results are shown in Tables 1, 2, and 4.

Table 1. Reaction Rate Constants for Every Reaction Process at Different Temperatures.

  reaction rate constant (h–1)
T (K) k1 k–1 k2 k3 k–3
463 2.502862914 0.060560596 0.561579371 0.257186356 0.176258077
473 3.550348358 0.099529637 0.983973071 0.338702133 0.199889328
483 5.42534805 0.165669838 1.504939419 0.409023597 0.234727444
493 8.713134203 0.312128031 2.578914071 0.518292295 0.278754867
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Table 2. Tuned Model Parameters.

rate constant linear equation of ln(ki) and 1/T R2 Eai (kJ mol–1) ΔHj (×107 J kmol–1)
k1 ln(k1) = −9495.4 × (1/T) + 21.386 0.9927 78.94475 –2.39493
k–1 ln(k–1) = −12376 × (1/T) + 23.886 0.9940 102.89406  
k2 ln(k2) = −11408 × (1/T) + 24.069 0.9975 94.84611  
k3 ln(k3) = −5231.5 × (1/T) + 9.9526 0.9962 43.49469 1.43932
k–3 ln(k–3) = −3500.3 × (1/T) + 5.8087 0.9924 29.10149  
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Table 4. Pre-Exponential Factor and Reaction Equilibrium Constant.

    Kj
rate constant A (s–1) 463 K 473 K 483 K 493 K
k1 5.39 × 105 41.33 35.67 32.75 27.92
k–1 6.56 × 106        
k2 7.88 × 106        
k3 5.84 1.46 1.69 1.74 1.86
k–3 9.26 × 10–2        
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As shown in Table 2, R2 was greater than 0.99, which suggested that ln(ki) had a good linear relationship with 1/T, and the obtained reaction rate constants satisfied the Arrhenius expression. Compared with the values reported in the literature, the results from the literature and those currently adjusted from the experimental kinetic data reported in Tables 1, 2, 3, 4, 5, and 6 were almost the same; however, the value of ΔH1 was better (Table 3) than that reported in other studies.48 The difference between the reaction rate constants and other parameters could be explained as being due to the presence of a catalyst, different temperatures, and different substrate concentrations.

Table 3. Comparison of the Enthalpy of Reaction (1) Calculated in This Study with the Median Value from a Previous Study.

data sources ΔH1 (×107 J kmol–1) reference
this research –2.39493  
previous study –2.83 (48)
literature report –2.28 (52)
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Table 5. Gibbs Free Energy of Reactions (1) and (3).

T (K) ΔG1 of reaction (1) (×107 J kmol–1) ΔG3 of reaction (3) (×107 J kmol–1)
463 –1.432565246 –0.145449544
473 –1.40561925 –0.207384381
483 –1.401000403 –0.223008914
493 –1.364562253 –0.254210396
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Table 6. Selectivities of Fumaric Acid as Defined by eq 20 at Different Reaction Temperatures.

T (K) tmax (h) S
463 0.818 6.58
473 0.582 12.57
483 0.473 14.39
493 0.314 23.40
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The calculated data were used to plot the changes in the three organic acid concentrations over time at each temperature, and the curves were combined with experimental data to form Figure 3a–d. It was found that the figures drawn by the equations were better matched with the experimental data points. The trends for the three organic acids were consistent with that of the graph line, which further proved the accuracy of the experimental data.

Figure 3.

Figure 3

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Experimental (symbol) and calculated (solid line) variations in the concentration of three organic acids with reaction time at temperatures (a) 190 °C, (b) 200 °C, (c) 210 °C, and (d) 220 °C. Black for maleic acid; red for fumaric acid; and blue for malic acid.

As shown in Table 1, as the temperature increased, the forward reaction rate constant of reaction (1) (the reaction rate constant of conversion of maleic acid to fumaric acid) increased continuously from 2.5 to 8.71 h–1. In addition, at each temperature, the forward reaction rate constant of reaction (1) was the largest, and the reverse reaction rate constant was relatively less than 0.32 h–1. This was because cis-maleic acid was easily attacked on account of its small steric effect and was transformed into malic acid and fumaric acid.40 The reaction rate constants of reactions (2) and (3) increased slightly with temperature, but they did not reach the elevated level of reaction (1). It was indicated that the high selective conversion of fumaric acid could be well achieved by adjusting the temperature.

As indicated in Table 5, with increasing temperature, the absolute value of the Gibbs free energy in reaction (1) decreased, while that in reaction (3) showed an increasing trend. It was suggested that the spontaneous inhibition of the conversion from maleic acid to fumaric acid was weakened, while the spontaneous inhibition of the conversion from malic acid to fumaric acid increased with increasing temperature. This meant that the conversion from maleic acid to fumaric acid and the conversion from fumaric acid to malic acid were inhibited by the increase in temperature. This echoed the conclusion of Ortiz et al. that a temperature rise reduces the selectivity for malic acid.48

Discussion on Product Selectivity

For practical purposes, the selectivity of the conversion of maleic acid to fumaric acid and malic acid remains to be studied. The reason for this is that the rapid conversion of maleic acid to fumaric acid with high selectivity is conducive to the development of a production process for fumaric acid. It is particularly noteworthy that when the temperature increases from 463 to 493 K, the maximum selectivity time for fumaric acid decreases. At the same time, the selectivity for malic acid decreased first and then increased with reaction time. Selectivity is determined by using the following equation.

graphic file with name ao-2019-00316b_m020.jpg 20

Analysis of Influencing Factors

Effect of Initial Reactant Concentration

To evaluate the effect of the initial concentration of maleic acid on the reaction, the intersubstance conversion was investigated. As shown in Figure 4, the amount of fumaric acid increased with increasing initial maleic acid concentration. At the same time, the conversion rate of maleic acid also increased with increasing fumaric acid concentration. In addition, the yield of malic acid first increased and then tended to balance out. Because the reduction in water content was not favorable for the conversion of maleic acid and fumaric acid to malic acid, more maleic acid could be converted to fumaric acid, and the selectivity of fumaric acid was enhanced. Furthermore, once the temperature was too high, the products were oxidized, thereby leading to the possibility of coking products being formed in the reaction vessel.

Figure 4.

Figure 4

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Concentrations of maleic acid, malic acid, and fumaric acid vary with the initial maleic acid concentration in the reaction (1 h).

Effect of Reaction Temperature and Time

The effects of reaction temperature and reaction time on the mutual transformation of materials were investigated. A maleic acid solution with an initial mass fraction of 60% was selected and was subject to an experiment from 0 to 4 h at 190, 200, 210, and 220 °C. As shown in Figure 5a,b, the rate of fumaric acid production was faster when the reaction temperature was increased. This was because the reaction rate constant for the formation of fumaric acid became larger due to the increase in temperature. At the same time, the yield of fumaric acid increased with increasing time in the initial stage, while it decreased when the reaction time was over 1 h. This was because the concentration of fumaric acid increased as the reactions proceeded, thereby promoting the conversion of fumaric acid to maleic acid and malic acid.

Figure 5.

Figure 5

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Variation in fumaric acid yield with reaction temperature and reaction time. (a) Fumaric acid yield changes with temperature. (b) Fumaric acid yield changes with time.

Further analysis of Figure 5a showed that the amount of fumaric acid increased significantly as the temperature increased within 0.75 h. However, as the reaction time continued to increase, the effect of temperature on the reaction became less pronounced. When the reaction time was over 1 h, the conversion of fumaric acid decreased with increasing temperature. This was because the content of fumaric acid increased with the reaction time, while the content of maleic acid continued to decrease, which caused the main reactions to become the reactions of conversion of fumaric acid to maleic acid and malic acid. As shown in Figure 5b, the maximum yield of fumaric acid decreased slightly (approximately 1%) and the time of the maximum conversion rate decreased with increasing temperature. This could be explained by the fact that the increase in temperature enhanced the reaction rate constant for maleic acid, which reduced the reaction time. A slight decrease was because, although the formation of fumaric acid was inhibited by the increase in temperature, the conversion from malic acid to fumaric acid was promoted. Furthermore, on the falling phase, the higher the temperature, the faster the fumaric acid decreased. This was because the reaction rate constants of reactions (3) and (1) increased as the temperature increased, which caused fumaric acid to be converted to maleic acid and malic acid more rapidly at a higher concentration of fumaric acid. The fumaric acid content at which the final fumaric acid concentration reached an equilibrium decreased with increasing temperature, which was illustrated by the change in the Gibbs free energy and the reaction rate constants with increasing temperature. As the temperature increased, the absolute value of the Gibbs free energy of reaction (1) decreased, which indicated that the selectivity of the reaction to form fumaric acid decreased, causing more fumaric acid to be converted to maleic acid. At the same time, since the rate constant of reaction (2) increased significantly with increasing temperature, more maleic acid was converted to malic acid. Although the selectivity of reaction (3) to produce fumaric acid was enhanced with increasing temperature, the reaction rate constant for conversion to obtain fumaric acid was small, and the reaction was not affected much.

Conclusions

Highly selective conversion from maleic acid to fumaric acid was achieved by a simple one-step hydrothermal synthesis at four different temperatures without any catalyst, and the kinetics of the mutual conversion of maleic acid, fumaric acid, and malic acid were studied. The highly selective process had higher stability and fumaric acid yield and could be used to obtain the desired fumaric acid product without a catalyst. Through the mutual confirmation of the data spectra and the kinetic parameters, the mutual transformation of the three organic acids under hydrothermal conditions was studied systematically and completely for the first time and reached a level superior to that obtained in previous reports. Based on the kinetic data obtained experimentally, 20 reaction rate constants were determined, and the Ea values of 5 reactions were calculated. It was found that the time to reach the highest yield point of fumaric acid could be effectively reduced with increasing temperature and that a high concentration of fumaric acid in the conversion process can convert fumaric acid into malic acid, which provided the guidance on the development of related production processes. The change in the Gibbs free energy in each reaction reflected the fact that an increase in temperature was not favorable for the formation of fumaric acid from maleic acid, but instead promoted the formation of fumaric acid from malic acid and reduced the selectivity of malic acid. This study showed that the highly selective conversion of fumaric acid can be achieved by a hydrothermal method and that the conversion of malic acid can also be achieved by conditional control without a catalyst. Therefore, the hydrothermal synthesis of fumaric acid and malic acid without a catalyst has huge commercial potential.

Acknowledgments

The authors wish to acknowledge laboratory teachers and classmates from the Tianjin University of Science and Technology for technology support of this study.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b00316.

  • Typical appearance of the products; SEM image of the products; 1H-NMR spectrum; analytical method of solution of the system of ordinary differential equations given by eqs 4–6 (PDF)

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.

Supplementary Material

ao9b00316_si_001.pdf (221.8KB, pdf)

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