Effects of Oxygen: Experimental and VTST/DFT Studies on Cumene Autoxidation with Air under Atmospheric Pressure.

The mechanism of how oxygen affects cumene autoxidation related to temperature is still bewildering. Kinetic analysis of cumene autoxidation with air at a pressure of 1.0 atm was investigated by experiments and variational transition state theory/DFT. Oxygen was the limiting factor for cumene autoxidation above 100 °C, although it had negligible impacts on cumene autoxidation at 70-100 °C. The kinetic analysis by VTST coupled with DFT calculations proved that {k 6,reverse[ROO•]}/{k 7,forward[RH]0 [ROO•]} > 103 (70-120 °C), suggesting that ROO• tended to decompose back to R• and O2 rapidly, whereas it was much slower for ROO• abstracting a hydrogen atom from RH to form ROOH. When the concentration of oxygen was higher than the critical value ([O2]critical), it could not significantly affect the equilibrium concentration of ROO•, which in turn could not affect the autoxidation rate significantly. Besides, the critical oxygen concentration ([O2]critical) was exponentially related to 1/T, which was consistent with Hattori's experimental results.

Introduction

Oxidations with molecular oxygen are awfully fascinating that often address the priorities of green and sustainable chemistry.[1,2] At present, molecular oxygen has been successfully used in oxidations of alkenes, alcohols, thioethers, and amines.[1,3] One prominent industrial example is cumene autoxidation to prepare cumene hydroperoxide (ROOH), which was then converted into phenol with a production of more than 11.4 × 106 t/a in 2013.[4] The peroxidation processes had also swept the industry[5] because coproduct processes (PO/SM and PO/TBA) and the Sumitomo process[6] had been widely used in the industrial production of propylene oxide, which was the synthetic material for polyurethane foams and polyester resins.[7]

Cumene autoxidation is a typical heterogeneous gas–liquid reaction and attracts considerable attention.[8−12] The mechanisms and kinetic study of cumene autoxidation have received extensive attention.[2,8,13−15] An intricate series of elementary reactions, in Scheme , were involved in cumene autoxidation. Generally, it was deemed that reaction 7, which was not related to oxygen, was slower and thus the decisive step to the chain reaction.[4] Nevertheless, oxygen was undoubtedly one of the major factors and has attracted a lot of attention.[16,17] Hattori et al.[16] found that the oxidation rate constant was not affected by oxygen when the partial pressure of oxygen in the gas phase was higher than a certain value. Ulitin et al.[17] found that the oxygen mass transfer rate did not affect the accumulation rate of ROOH under reaction conditions of 1.013 × 105 Pa and 110 °C. Instead, when the concentration of oxygen dissolved in cumene was higher than a value that was linear with the concentration of the initiator (ROOH), there was a weak dependence of ROOH’s accumulation rate on oxygen. Thus, the boundary concentration of oxygen related to temperature, to distinguish whether the oxygen affects cumene autoxidation, is of great valuable, but no relevant reports have been found.

Scheme 1

Kinetic Scheme of Cumene Autoxidation

Here, kinetic analysis of cumene autoxidation with air as oxidant was carried out through experiments and variational transition state theory (VTST) coupled with density functional theory (DFT) calculations. Both the forward and reverse reactions were analyzed by VTST coupled with DFT calculations, providing good insights into how oxygen affects cumene autoxidation. Besides, the critical oxygen concentration [O2]critical related to temperature was present in this work, providing theoretical and technical supports for cumene autoxidation.

Experimental and Calculations

Materials

Unless otherwise stated, all commercial reagents and solvents were used without further purification. Cumene (>99% purity, 0.47 mol % of ROOH was determined by 1H NMR) was produced by Institute of Guangfu Fine Chemicals. K2CO3 was produced by Xilong Chemical Co., Ltd. 1H NMR (400 MHz) spectra were recorded on a Bruker Avance II 400 spectrometer.

Cumene Autoxidation

Figure illustrates the setup utilized in the experimental work. The reactor was a 50 mL reaction tube (outer diameter of 23 mm). K2CO3 (0.5 mmol, 69.1 mg), cumene (3 mL), and a magnetic stirring bar (1 cm) were successively added to the reaction tube, which was then put onto a metal plate above a magnetic stirring apparatus (IKA Plate, RCT digital). Then, the reflux unit and dry air preparation unit were connected as shown in Figure . K2CO3 was used to neutralize the organic acid generated in situ, preventing the decomposition of ROOH promoted by organic acid.[18] The effects of K2CO3 on cumene autoxidation are further discussed in the Supporting Information. To ensure that the ratio of O2 and N2 over the surface of reaction liquor is stable, drying air (2 mL/min) was fed into the gas phase continuously. The reaction proceeded at a specific temperature (70, 80, 90, 100, 110, and 120 °C). The samples were sampled on time and diluted immediately with DMSO-d6. Conversion and selectivity were determined by 1H NMR. Dry air was prepared by the following steps: the air flowed into the reaction system through a pump and a gas flowmeter (set as 2.0 mL/min) and was successively dried with condensation at −30 °C and soda lime.

Figure 1

Cumene autoxidation experimental scheme.

Kinetic Model of Cumene Autoxidation

Based on the mechanisms of alkanes’ autoxidation,[17] a kinetic scheme of cumene autoxidation proceeds by a chain mechanism including chain initiation, chain propagation, and chain termination (Scheme ). According to Figure S4, high selectivities (>90%) were obtained at conversions less than 8%. Thus, side reactions were ignored here. The generation rate of ROOH was mainly determined by reaction 7 and thus eq was used to describe the generation rate of ROOH.where [ROO•] and [RH] are the concentration of ROO• and cumene, mol/L, respectively and k7 is the reaction constant for reaction 7.

Computational Details

All geometry optimizations of the reactants, transition states, intermediates, and products were carried out with the Gaussian 16 program. The B3LYP[19,20] hybrid exchange–correlation functional with 6-311 + g(d,p) basis set was applied for geometrical optimizations and subsequent frequency calculations. The optimizations were carried out at 378.15 K using cumene as the solvent. No imaginary frequencies were found in the vibrational spectra of all reactants, intermediates, and products. Only one imaginary frequency corresponding to the reaction coordinates was found for the transition states. The intrinsic reaction coordinate calculations were carried out to further verify the relationship between the reactants, transition states, and products. The rate constant for the barrierless R• + O2 reaction were treated as Silva’s literature,[21] using VTST coupled with DFT calculations. The two-parameters Arrhenius formula to calculate the rate constants related to temperature for elementary reactions were obtained from KISTHELP software.[22]

Results and Discussion

Saturated Solubility of Oxygen

According to Hattori’s report,[16] the concentration of oxygen dissolved in cumene did not affect the reaction rate of cumene autoxidation at a temperature below 120 °C when the concentration of dissolved oxygen was greater than 7 × 10–4 mol/L. This concentration corresponds to an equilibrium partial pressure of 0.1 bar in the gas phase.[4] To verify whether oxygen affected cumene autoxidation, the oxygen solubility in cumene was calculated based on the gas–liquid equilibrium theory and Hayduk’s semiempirical method[23−25] at first. The detailed calculation process is present in the Supporting Information. When the reaction was performed with air as the oxidant under a pressure of 1.013 × 105 Pa, the oxygen partial pressure, poxygen, was calculated and the results are listed in Table S1, suggesting that the oxygen partial pressure decreased with the increasing temperature. The mole fraction of oxygen (XT) in cumene under an oxygen partial pressure of 1.0 bar at different temperatures was about 10.9 × 10–4 and had a negligible temperature coefficient (Table S1). This result was consistent with Low’s literature.[26] When air was used as the oxidant, the molar concentration of oxygen () at 70–120 °C was calculated and is depicted in Figure . There was a clear downward trend (decreased from 12.84 × 10–4 to 7.40 × 10–4 mol/L) for when the temperature increased from 70 to 120 °C. Therefore, the influence of oxygen on cumene autoxidation under experimental conditions could be neglected because was greater than 7 × 10–4 mol/L at 70–120 °C.

Figure 2

Molar concentration of oxygen () dissolved in cumene in an air atmosphere.

Kinetic Study of Cumene Autoxidation without Considering the Oxygen Solubility

Based on the above analysis, the influence of oxygen on cumene autoxidation under experimental conditions could be neglected. Therefore, reaction 7 was the rate-controlling step for cumene autoxidation. According to the assumption of pseudo-steady-state,[13]k7[ROO•][RH] = k6[R•][O2] could be obtained when ignoring the side reactions. g(T) was assumed as the total concentration of radicals and [ROO•] + [R•] ≈ g(T). Then, eq was derived to calculate the concentration of ROO•. The values of [ROO•]/g(T) at different temperatures were first calculated using parameters from Somma’s report[15] (log k70 = 7.6, log k60 = 8.4, ΔEa6 = 0, and ΔEa7 = 53.16 kJ/mol) and the results are listed in Table S2. The value of [ROO•]/g(T) decreased from 0.9997 to 0.9946 when the temperature increased from 70 to 120 °C, suggesting that the concentration of ROO• was close to the total concentration of radicals independent of temperature. Thus, the effect of temperature on the reaction rate will be much more pronounced than [ROO•] at 70–120 °C.

To simplify the kinetic study of cumene autoxidation, a hypothesis that the concentration of ROO• was not sensitive to temperature at 70–120 °C and K1 (= k7[ROO•]) was introduced. Eq was rewritten as eq to study the reaction kinetics between ROO• and RH, indicating that ln(1–x) and t have a linear relationship. x is the conversion of cumene. The regression lines and equations of ln(1–x) with t at 70–120 °C are shown in Figure S3 and listed in Table S3. The values of K1 at different temperatures were equal to the corresponding slopes of the regression lines as shown in Figure S3. lnK1 and 1/T should have a linear relationship according to Arrhenius eq 4. Unexpectedly, as shown in Figure a, R2 = 0.89927 was obtained for the linear regression of lnK1 and 1/T in the temperature range of 70–120 °C, suggesting a poor reliability. Figure b also showed that lnK1 and 1/T were linear with a good degree of reliability in the temperature ranges of 70–100 and 100–120 °C with R2 = 0.98218 and R2 = 0.92307, respectively. The slope value in the temperature range of 70–100 °C was obviously greater than that in the temperature range of 100–120 °C. Same situation was discovered in Koshel’s report[8] and they deemed that the activity of PINO• may be different in the two temperature ranges. From this perspective, the activation energy of reaction 7 were 62.54 and 13.38 kJ/mol in the temperature ranges of 70–100 and 100–120 °C, respectively. However, in our opinion, the change of oxygen concentration in the reaction liquor may lead to this situation as well. Figure S4c,d also indicated that the cumene autoxidation rate at 120 °C significantly increased using high purity oxygen instead of air, indicating oxygen was the limiting factor at 120 °C. Notably, R2 = 0.99372 as shown in Figure c was obtained for the linear regression analysis of lnK1 with 1/T when the value of K1 at 120 °C using high purity oxygen as the oxidant was used. Therefore, the concentration of oxygen was the limiting factor for cumene autoxidation above 100 °C, although it had negligible effects on cumene autoxidation at 70–100 °C. Based on Figure c, the activation energy of reaction 7 was 61.92 kJ/mol.

Figure 3

Linear regression analysis of ln K1 with 1/T, with error bars of 2%. (a) temperature range of 70–120 °C; (b) temperature range of 70–100 and 100–120 °C, respectively; and (c) pure oxygen and air were used as the oxidant at 120 and 70–100 °C, respectively.

Kinetic Study by VTST/DFT Calculations

Kozuch and Martin[27] have reported that there are no rate-determining steps, only rate-determining states. Inspired by Kozuch’s report, we believe that there may be new breakthroughs in the in-depth study of kinetics from the perspective of transition state theory and reversible reactions. Here, the energy and Gibbs free energy profile (at 378.15 K) for cumene autoxidation, calculated at B3LYP/6-311 + G(d,p) level of theory, is depicted in Figure . Potential energy surface scan results (Figure S5) showed that the reaction of O2 with R• to form ROO• is barrierless. It was consistent with the previous reports[28−30] that the reaction of alkyl radicals with oxygen was barrierless. Rate constants for R• + O2 at each point along the potential energy surface were calculated and are depicted in Figure S6. The location of the variational transition state () is at a R–OO bond length of 2.43 Å. As a result, activation free energy barriers of 88.75 and 95.00 kJ/mol were required for the reaction of O2 with R• to form ROO• and its reversible reaction, respectively. Only one imaginary frequency (91.82i) was found for . The process that ROO• abstracted a hydrogen atom from RH required to overcome an activation free energy barrier of 120.58 kJ/mol and only one imaginary frequency (1766.35i) was found for TS1. The Gibbs free energy change for the entire reaction was −14.35 kJ/mol, suggesting a feasible process.

Figure 4

Energy and Gibbs free energy profile (at 378.15 K) for cumene autoxidation, calculated at B3LYP/6-311 + G(d,p) level of theory.

Two-parameters Arrhenius formulas were used to calculate the minimum rate constants related to temperature for the main elementary reactions and its reversible reactions, using VTST coupled with the B3LYP/6-311 + G(d,p) level of theory in the temperature range of 343.15–398.15 K. The corresponding parameters are listed in Table . The fitted activation energy (61.58 kJ/mol) for reaction 7 was close to our experimental value (61.92 kJ/mol). Interestingly, it was also found that {k6,reverse[ROO•]}/{(k7,forward[RH]0) [ROO•]} > 103 (70–120 °C), suggesting that the rate for the reverse reaction of reaction 6 was much faster than that for the forward reaction of reaction 7. Thus, the reverse reaction of reaction 6 should not be ignored in the kinetic study of cumene autoxidation. Denisov and Afanas’ev[31] have also reported that some peroxyl radicals, such as cyclohexadienyl peroxyl radicals, have a weak C–OO bond and decompose back to R• and O2. It was consistent with our results. Nevertheless, the addition reaction of O2 to R• was regarded as a one-way reaction process in the previous kinetic studies of cumene autoxidation.[8,13,16]

Table 1

Kinetic Parameters for the Reactions 6 and 7 at 343.15–398.15 K

elementary reactions	A	E (kJ/mol)
	9.62 × 106	–8.91
	3.87 × 1014	69.44
	7.50 × 108	61.58
	1.38 × 109	47.53

The reaction rates for those elementary reactions consuming ROO•, such as reactions 12, 15, and 16, were of course much slower than reaction 7. Therefore, eq was used to describe that the generation rate of ROO• was equal to its consumption rate in view of the quasi-steady-state assumption. Because k6,reverse/(k7,forward[RH]0) > 103 and k6,forward[O2]/k7,reverse > 106, eq was used to calculate the ratio of R• and ROO•. It was clear that the ratio of R• and ROO• was mainly determined by temperature and the oxygen concentration. Both increasing the concentration of O2 and decreasing temperature could lead to a decrease of the ratio of R• and ROO•. When the concentration of oxygen was higher than the critical value ([O2]critical), it could not significantly affect the equilibrium concentration of ROO•, which in turn could not affect the autoxidation rate significantly. Eq was derived to calculate K1 (= k7,forward[ROO•]). Interestingly, as shown in Figure , the curve of lnK1 over 1/T for the fitting results (when g(T) = 1.21 × 10–4 mol/L) was consistent with our experimental results.

Figure 5

Plot of lnK1 over 1/T, set error bars of 2% for the experimental results.

Mathematical Model to Calculate the Critical Concentration of Oxygen

Both Hattori[16] and Ulitin[17] found that there was a weak dependence of ROOH’s accumulation rate on oxygen when the oxygen concentration or the partial pressure of oxygen was higher than some value. To our knowledge, there were no reports to solve the general critical oxygen concentration related to temperature. According to eqs and 7, the value of {k7,forward[ROO•]}, as well as the ROOH’s accumulation rate, will increase with increase of [O2]. The closer the ratio of R• and ROO• is to 0, the closer the reaction rate is to the maximum reaction rate. When the concentration of oxygen was higher than the critical value ([O2]critical), it could not significantly affect the concentration of ROO• by increasing oxygen concentration, which in turn could not affect the autoxidation rate significantly. We assumed that when [R•]/[ROO•] ≤ m, there is a weak dependence of ROOH’s accumulation rate on oxygen. This is to say “m” can be regarded as a threshold ({[R•]/[ROO•]}threshold = m) to judge whether the concentration of oxygen could affect the autoxidation rate. Eq , to solve the critical oxygen concentration ([O2]critical), could be derived from eq . m is recommended to be in the range of 0.1–0.20. Similarly, the critical oxygen partial pressure was also exponentially related to 1/T, when the saturated vapor pressure of cumene was ignored.

Hattori[16] reported that the rate constant K and the partial pressure of oxygen obey the function of K = MPO/(1 + NPO). Thus, the maximum value of K (Kmax) would be infinitely close to M/N. We assumed that there was a weak dependence of cumene autoxidation on oxygen when K was 0.85 times Kmax (i.e., m = 0.1765). Thus, the critical oxygen partial pressures related to temperature were calculated (PO: 110 °C, 0.157 atm; 120 °C, 0.241 atm; and 130 °C, 0.327 atm). Interestingly, lnPO and 1/T were linear with a good degree of reliability (R2 = 0.9968) in the temperature range of 110–130 °C (Figure ). Therefore, PO = 4.25 × 105exp(−5668.73/T) or . This result was consistent with our derivation that the critical oxygen partial pressure was exponentially related to 1/T though some differences existed between the experimental results and theoretical derivations. We deemed that the difference was mainly caused by the conditions of the experiments using a bubble column reactor, where the oxygen partial pressure gradually decreases from bottom to top of the reaction system. Besides, the saturated vapor pressure of cumene was not considered in Hattori’s report, which may result in this difference as well.

Figure 6

Linear regression analysis of lnPO and 1/T in the temperature range of 110–130 °C, set error bars of 3%.

Conclusions

In conclusion, kinetic analysis of cumene autoxidation with dry air as the oxidant under conditions of 70–120 °C and 1.0 atm was studied by experiments and VTST/DFT calculations. Oxygen was the limiting factor for the rate constant of cumene autoxidation above 100 °C, although it had negligible impact on cumene autoxidation at 70–100 °C. The reaction rate at 120 °C was significantly increased by using high purity oxygen instead of air. Reaction 6 was reversible in the view of VTST coupled with DFT calculations, thus determining the equilibrium concentration of ROO•. It provides good insights into how oxygen affects cumene autoxidation. Finally, the critical oxygen concentration () grew exponentially with 1/T. It was consistent with Hattori’s experimental results.