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 {k6,reverse[ROO•]}/{k7,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.


Saturated solubility of oxygen calculated by Hayduk's semiempirical method and gas-liquid equilibrium theory
Here, a model for calculating the saturated solubility of oxygen was established based on the gas-liquid equilibrium theory. The gas-liquid equilibrium equations of oxygen, nitrogen and cumene were written as Equations S1 -S3. The sum of the molar fractions of the components in the gas phase was equal to 1, thus Equation S4 was given. Where, p is the pressure of gas phase; H1 and H2 are Henry's coefficients of oxygen and nitrogen, respectively; 1 , 2 and 3 are fugacity coefficients of oxygen, nitrogen and cumene, respectively; 1 * , 2 * and 3 are activity coefficients of oxygen, nitrogen and cumene, respectively; 3 is the saturated vapor pressure of cumene; Y1, Y2 and Y3 are mole fractions of oxygen, nitrogen and cumene in the gas phase, respectively; X1, X2 and X3 are mole fractions of oxygen, nitrogen and cumene in the liquid phase, respectively.
The reaction was carried out at a pressure of 1.0 bar and thus the gas was approximated as an ideal gas, therefore 1 = 2 = 3 = 1. Cumene was the main component of the liquid phase, and the content of oxygen and nitrogen were very low. Thus, X1 → 0, X2 → 0, and X3 → 1 were obtained. Since X1 → 0 and X2 → 0, 3 → 1 could be used.
As air was used as the oxidant in cumene autoxidation, dry air was feed into the gas phase continuously to eliminate the effects brought by the consumption of oxygen and to ensure the stability of the gas phase. To simplify the model, assumptions 1 and 2 were as follows.
Assumption 1: the reaction liquor had no weight loss caused by the flow air.
Assumption 2: changes in the compositions of the reaction liquor caused by cumene autoxidation had no effects on oxygen solubility.
As a result, when the ratio of nitrogen and oxygen in the reaction liquor was the same as that in the gas phase ( = Y2/Y1), Y1 = 1 1 1 * ⁄ , Y2 =  under an oxygen partial pressure of 1.0 bar was obtained from Low's report 7 . This is to say, X298.15K = 9.7675 × 10 −4 . Subsequently, the mole fraction of oxygen (XT) dissolved in cumene was calculated by Equation S10 and the results were listed in Table S1, showing a slight upward trend as the temperature increases. (S11) Where, 2 is the molecular volume of cumene, 2 = ∆ U/( 2 ) 2 . ∆ U is the vaporization heat of cumene, which is equal to 45.171 × 10 3 J/mol 8 .
The calculations results were listed in Table S1.  Control experiments with K2CO3 or without K2CO3 at 50, 100 and 120 °C were carried out and part of the results were depicted in Fig.S1. The reaction does not proceed at 50 °C no matter whether K2CO3 is added or not. Furthermore, it is unreasonable that the reaction of CO3 2with RH to form a tertiary carbon anion (R -) with poor stability. The addition of K2CO3 at 120 °C has no apparent effect on the reaction rate as shown in Fig.S1. To be noted, the addition of K2CO3 at 100 °C promote the reaction rate, especially in 0 -180 min, while has little promotion effects on the reaction rate in 180 -420 min. Therefore, the addition of K2CO3 may promote the process in the radical initiation stage, but could not promote radical transfer process, which dominated the peroxidation rate. We deemed that K2CO2 was used to neutralize the organic acid to suppressing reaction such as "H ROOH→RO H2O", thus promoting the radical initiation process. The catalytic effect of K2CO3 needs to be further studied since no relevant evidence has been found so far.