Impacts of Thermal Inertia Factor on Adiabatic Decomposition of 40% Mass Content DCP in Ethyl Benzene

To reduce the ﬁre and explosion accident of dicumyl peroxide (DCP) in experiment and production, the thermal hazards of DCP and 40% mass content DCP in ethyl benzene (40% DCP) have been studied by the diﬀerential scanning calorimeter (DSC) and the accelerating rate calorimeter (ARC) in this paper. DSC experiment showed that ethyl benzene has no eﬀect on the characteristic parameters of thermal decomposition of DCP, such as the temperature of the exothermic peak ( T peak ) and the decomposition energy ( E a ), and the thermal decomposition reaction of 40% DCP followed the one-step reaction principle. ARC experiment showed that with the increase of inertia factor ( Φ ), the measured initial decomposition temperature ( T on ) would be higher and the caculated E a and pre-exponential factor ( A ) would be greater. It was also proved that after modiﬁcation of Φ , T D24 was relatively consistent near T on , but diﬀerent at higher temperatures. Fisher’s correction method was used to verify the necessity of consistency between experimental conditions and prediction conditions.


Introduction
With fast development of industries and wide usage of organic peroxides, the hazard assessment of organic peroxides has become more and more important in many countries. As a kind of common organic peroxides, dicumyl peroxide (DCP) has been widely employed as a vulcanizing agent of rubber and a crosslinking agent of plastic in the chemical industry. Because of the thermal sensitivity and high antipyretic effect of DCP, great damages would be brought into the production process, workers, and environment once the reaction runaway occurs [1,2]. ermal analyses have been carried out on organic peroxides by different thermal analysis apparatuses. Ding [3] has investigated the thermal decomposition of DCP by the thermogravimetry-differential thermogravimetry (TG-DTG) method. One endothermic peak and one exothermic peak were found in the decomposition process, and the apparent activation energy was calculated. Jiang [4] has studied the influence on the heating rates of DCP by C80. e advanced kinetics and technology solutions (AKTS) method has been used to calculate the thermodynamic parameters. Guo [5] has used an accelerating rate calorimeter (ARC) to determine the adiabatic decomposition rule of DCP. "Townsend-Tou" method has been used in the correction of the experiment data.
Although the sample is small, the maximum self-heating rate can exceed the maximum tracking rate of ARC for the large decomposition heat of DCP. It will result in some errors in the experiment [6]. In order to reduce the decomposition heat of DCP, ethyl benzene is chosen as the solvent for its stability within the test scope in this paper.
ermodynamic and kinetic parameters of pure DCP and 40% mass content DCP in ethyl benzene can be obtained by a differential scanning calorimeter (DSC) and ARC. Based on these thermal data, safety studies can be done to distinguish the dangers caused by the two material systems. Furthermore, with "Fisher's" method, the best experiment condition of ARC will be discussed.

Materials and Methods
DCP of 99.5% mass content was purchased from Aladdin. It is in the solid state at room temperature. Ethyl benzene of 98.5 % mass content is bought from Sinopharm Chemical Reagent Co., Ltd. It is in the liquid state at room temperature.
40% mass content DCP in ethyl benzene (40% DCP) was prepared by assuming both DCP and ethyl benzene were at 100% purity. e configured solution was placed in a refrigerator. It is in the liquid state, and the density is 1.044 g·cm −3 at room temperature. e heat capacities of DCP and 40% DCP at 90°C were 1.94 and 1.95 J·g −1 ·K −1 , respectively, which were obtained from uRC (manufactured by THT).

DSC Experiments.
e DSC used in this paper was manufactured by Mettler Toledo (DSC-1). Stainless steel high-pressure crucibles (15 MPa) were employed in tests, with extra pure nitrogen purging (30 mL·min −1 ). Samples were tested at a heating rate of 2, 4, 8, and 1 K·min −1 for rapid screening. e temperature range of all measurements was from 25 to 250°C.

ARC Experiments. ARC supplied by ermal Hazard
Technology Company was performed in the heat-waitsearch mode. e experimental procedure was sealed. e temperature step was 5°C, the wait time was 10 minutes, and the slop sensitivity was 0.02°C·min −1 . e trackable heating rate was up to 15°C·min −1 (full power). Sample bomb was made of titanium with a thick wall of 0.5 mm, and the heat capacity and density are 0.53 J·g −1 ·K −1 and 4.53 g·cm −3 , respectively. e ARC test temperature range is from the room temperature to 450°C. e mass of each sample is listed in Tables 1 and 2.  Figure 1 and Table 3.

Results and Discussion
According to Figure 1, it is found that thermal decomposition of DCP contains one endothermic peak at 43.12°C and one exothermic peak at 177.40°C. Since ethyl benzene does not decompose in the test scope, DCP is dissolved into ethyl benzene and decomposed without the influence of phase transition, and this is why there is only one exothermic peak for 40% DCP. e onset exothermic temperature of DCP and 40% DCP is approaching 115°C.
ere is a big difference of decomposition heat (ΔH) between DCP and 40% DCP in Table 3, and they are 886.58 and 362.88 J·g −1 , respectively. However, when we divide 649.56 (the total heat of 40% DCP) by 0.792 (mass of DCP in sample #2), the value is 907.22 J·g −1 , which is close to the ΔH of sample #1. So, it can be concluded that ethyl benzene has little impact on the decomposition of DCP.

Test Results of Sample # 2 under Different Heating Rates with the DSC Test.
A typical run for sample #2 at different heating rates is shown in Figure 2. e characteristic parameters are given in Table 4. e Friedman isoconversional method was employed to calculate the kinetics in this paper. As a "model-free" dynamic analysis method, it does not need to use concrete mechanism function, and the result has high precision and wide application [7]. We get a Friedman analysis diagram which shows the relationship between E a and α, as in Figure 3 and Table 5.
As given in Table 5, between α � 0.2 and 0.9, E a is between 110.60 and 98.14 kJ·mol −1 and the variation range is nearly 10%, indicating that it follows a reaction mechanism and can be expressed by the same mechanism function for 40% DCP.

Analysis of ARC Measurement.
Seven experiments with different Φ are carried out according to the above conditions. e ARC curves of temperature-time (T-t) and pressuretime (P-t) of sample #2 are shown in Figures 4 and 5, and all measured data are listed in Table 6.
As shown in Figure 4, the ARC curve of the first test is different from others, and the exothermal reaction is divided into two parts. Table 6 shows that the maximum self-heating rate ((dT/dt) max,m ), the measured adiabatic temperature rise (ΔT ad,m ), and the decomposition heat (H m ) of the first test are much smaller than other tests. e small sample mass results in high Φ of the first test, and it makes part of the (dT/ dt) m less than the detection sensitivity 0.02°C·min −1 and part of the decomposition heat is missed. Obviously, too large Φ can change the temperature curve entirely and result in the distortion of the tested results.
As shown in Table 6, T on,m is rising with the increase of Φ. e reason is that the small amount of the sample needs a higher temperature to make the (dT/dt) m of the sample and the bomb system reach the ARC detection sensitivity (0.02°C·min −1 ). It is also shown that ΔTM and (dT/dt) max,m decrease with the increase in Φ. In addition, since the material and energy balance of the sample and the bomb system were complicated, the (dT/dt) max,m with Φ was less linear.

Kinetic Calculation.
e heat released by the sample in the ARC test not only heats the sample itself, but also raises the temperature of the bomb. e smaller the sample mass, the higher proportion of heat will be used for heating the bomb and the corresponding temperature parameters (such as temperature curves and heating rate curves) will be affected too. So, it is very important to introduce the thermal inertia factor Φ, which can be estimated by the following equation: e Townsend-Tou method [8][9][10] and the Fisher method [11][12][13] have been widely used. Literature [3] shows that thermal decomposition of DCP is an nth-order reaction, and the Fisher method is adopted to modify the ARC data in this paper. e corrected equations for the Fisher method are listed as follows: where R is the gas constant; E a is the apparent activation energy, kJ·mol −1 ; T on,m is the corrected onset temperature by the Fisher method,°C; T ad,a is the corrected temperature by the Fisher method,°C; (dT/dt) ad,a is the corrected selfheating rate by the Fisher method, K·min −1 ; and (dT/dt) ad,m is the measured self-heating rate, K·min −1 . e corrected results are listed in Table 7. Kinetic parameters are important for thermal hazard prediction. For the decomposition reaction in the adiabatic system, the relationship between temperature and the selfheating rate is [14] dT dt a � A T f,a − T ad,a ΔT ad,a n ΔT ad,a c n−1      where T f,a is the corrected final temperature of decomposition,°C; A is the pre-exponential factor, min −1 ; n is the reaction order; and c 0 is the initial concentration of sample, mol·L −1 . Suppose where k is the rate constant.
Logarithmic form of equation (4)is e reaction order which can make the plot of ln(k * ) vs. 1/T ad,a to be a straight line is analysed correctly. en, E a and A can be calculated from the slope and the intercept. e kinetic analysis is not applied to the first test for its self-heating rate is discontinuous. For other samples, the reaction order n � 1 is assumed and substituted into equation (4), and then ln(k * ) is plotted against 1/T ad,a. Linear fitting of ln(k * ) and 1/T ad,a is done, and the fitting results and the values of E a and A are shown in Table 8. e high correlation coefficient indicates that the linear fitting results are reliable when n � 1. It means that the DCP decomposition is a very typical n-order reaction, and the    Fisher method which is selected for correction before is appropriate.
In addition, a good linear regression of lnA vs. E a is found with different Φ, showing a typical kinetic compensation effect [15], as shown in Figure 6. is means that the kinetic compensation effect exists only if the reaction mechanism is the same or similar [16].
Comparing DSC and ARC experiments, we can find that the calculated E a in ARC is generally higher than that in DSC and higher with the increase in Φ. It is mainly because these calculated kinetic parameters obtained by ARC data depend on the adiabatic temperature rise rate of equation (3).With the influence of the big Φ values, the measured adiabatic temperature rise curve of the sample is not the decomposition curve of itself, and it is the curve which is formed after the sample ball "passivation." So, this analysis of kinetic parameters is not incidental to the sample decomposition, but to the decomposition of composite samples, sample ball, heat transfer, and heat transfer information such as the comprehensive parameter.

Effect of Φ on T D24 .
e corresponding initial temperature when the time to maximum rate under adiabatic condition (TMR ad ) equals 24 hours (T D24 ) is an important parameter to evaluate the risk of samples. In order to obtain the effects of different Φ on the measured T D24,m and the modified T D24 , the experimental data before and after the correction are analysed in this paper. It can be seen from Table 6 that (dT/dt) max,m measured in No. 1 and No. 2 is less than 1, while in No. 7 is 166.52°C·min −1 , indicating an where TMR ad,m is the measured arrival time of the maximum reaction rate, min; T m is the temperature corresponding to the maximum temperature rise rate,°C; t m is the time corresponding to T m , min; T f is the exothermic termination temperature,°C; T is the adiabatic test temperature,°C ; ΔT ad is the measured adiabatic temperature rise,°C; and C 0 is the initial molality of the sample, mol·L −1 .
Equation (6) can be mathematically integrated to obtain TMR ad,m , which is the corresponding temperature T D24 for 24 h. If the effect of Φ is taken into account, the correction of Φ needs to be introduced by the following equation: e relationship between the measured temperature and TMR ad,m under different Φ for 40% DCP is shown in Figure 7. Extrapolated from the measured value to the low temperature, the obtained T D24 is also shown in Figure 7. According to the measured results, equation (7) is used to modify the modified T D24 , as shown in Figure 8.
It can be seen from Figure 7 that under different Φ, the T D24 of the sample obtained from the test data is different and increases with the increase in Φ. is is because the larger the Φ, the slower the heat release rate of the sample in the initial stage, the lower the temperature rise rate, and the longer the time to reach the maximum temperature rise rate. Figure 8 shows that after the correction of the TMR ad near the initial decomposition temperature, the relationship between the different Φ and TMR ad is relatively consistent and the T D24 of 40% DCP obtained by extrapolation of the modified sample sphere is about 87.20°C. It also shows that after the correction with Φ, the relationship between temperature and corrected TMR ad is still quite different at a high temperature. However, near the initial decomposition temperature, the results are almost the same. erefore, it is verified that equation (7) is only applicable to TMR ad near the modified initial decomposition temperature.

Checking Analysis with the Fisher Method.
As mentioned in Section 3.2, test results are affected by Φ significantly. A normal Fisher method is to amend the test results to the ideal condition Φ � 1, which cannot be realized by the ARC experiment. e experiment data will be corrected to Φ � 1.64 in this article and be compared with the measured data. e corrected equations are as follows: e corrected results are shown in Figure 9 and Table 9. Figure 9 and Table 9 show that when Φ is close to 1.64, the corrected results such as (dT/dt)-T and T on,a are close to the measured results at Φ � 1.64. However, if the test results based on Φ are far away from the target or predicted condition, the results are very unbelievable. us, the weight of the sample has great effect on the result of the ARC test.  e study demonstrates that under the condition of safety, Φ will be close to 1 with the increasing dosage of sample, and the revised ideal adiabatic data will be more reliable.

Conclusions
40% DCP with different masses have been studied by using DSC and ARC to obtain its adiabatic decomposition parameters. en, kinetic analysis is carried out, and the onset temperature and self-heating rate are corrected by the Fisher method. e results indicate that (1) e calculated E a value of 40% DCP is stable under the experimental conditions in the DSC test, and the decomposition followed the one-step reaction mechanism. (2) e values of E a and lnA obtained from the ARC tests show obvious kinetic compensation effect, it means that even under different Φ conditions, the reaction still follows the same mechanism. e difference from the DSC experiment is that the larger the Φ value is, the greater the calculated E a and A values are. It indicates that the value of Φ will affect the experimental accuracy.
(3) After modification, Φ has little effect on T D24 at the initial decomposition temperature, but has greater effect at a high temperature (4) After comparing the results corrected with Φ � 1.64 by the Fisher method, it is suggested to perform the test on the condition close to the process condition which is to be predicted, and then it can provide reliable results.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.   Journal of Chemistry 7