Introduction

Cosmeceutical benzoyl peroxide (CBPO) is used to permeate the pores and eliminate propionibacterium acnes, which causes pimples on the human skin, especially for teenagers. CBPO is essentially different from other antibiotics, with moderate excitability and no drug resistance. Moreover, CBPO is more effective than prescription drugs, such as oral and topical antibiotics. Hence, it is the most effective over-the-counter bactericide currently used to treat acne [1, 2].

Cosmeceutical factories usually implement numerous chemicals in different production processes. However, because of the potential hazardous risk from operator errors, essential material hazards, or incompatibility of production lines, cosmeceutical factory explosion accidents and news are intermittently reported [3, 4].

According to dangerous chemical properties, organic peroxides face challenges from storage, transportation, usage, and waste stream treatments. An inappropriate operation may result in an incompatible chemical reaction and therefore cause a thermal accident [5, 6]. The references report the potential thermal risk of organic peroxides. If the rate of heat removal is sustained lower than that of heat generation, the inner thermal system exceedingly produces a runaway reaction [7, 8]. The hazardous features of lower concentration organic peroxide have also been indicated; the exothermic onset temperature (T0) of organic peroxide samples does not change with the concentration change. Even though the concentration is low to 10 mass%, the detectable exothermic behaviors are digitized [9, 10].

As classical organic peroxide, CBPO has undoubtedly hazardous traits. Furthermore, the medical concentration of CBPO on treatment is usually lower to 10 mass% [11, 12]. The self-accelerating decomposition temperature (SADT) value of lower concentration CBPO is merely 48 °C. Moreover, the reference evaluated the time to conversion limit (TCL) by Thermal Safety Software; when the subject sample was stored at 27.5 °C, TCL was 21 days [9].

Several incompatible reactions were caused by the contact between organic peroxides and metal ions. Different organic peroxides have incompatible materials. When cumene hydroperoxide contacted iron ion, the time to the maximum rate at isothermal conditions (TMRiso) was reduced from 9.49 to 0.37 h at 110 °C [13, 14]. Impurities like metal ions are commonly present during the process, usage, storage, and transportation. Therefore, to ensure the incompatible reaction between CBPO and metal ions, the safety parameters, including SADT and TMRiso, were calculated.

The findings of this study indicate the potential thermal risk of contact between CBPO and various metal ions. Moreover, the composition of thermokinetics happening during the decomposition and runaway reaction was revealed. Multiple thermokinetic reactions were determined as autocatalysis reactions, followed by nth order reactions. This paper also provides the safe design considerations of the CBPO production line and the theoretical and practical knowledge of future product development.

Experimental

Sample preparation

The original concentration CBPO in the sample preparation was 75.0 mass%, which is white crystals. The 75.0 mass% CBPO was supplied by Gu-Tek International Industry Corporation, Taichung, Taiwan. We selected 1.0, 2.5, 5.0, and 10.0 mass% CBPO as the target samples. The 16 sets of CBPO test samples were well prepared, saved in sample dishes, and refrigerated from 3.0 to 5.0 °C. The prepared samples did not further process before being transfused hooked on the DSC receptacle. Therefore, the original concentrated CBPO was diluted with methyl salicylate.

Moreover, we selected Cu, Fe, and Zn as potentially incompatible metal ions. The metal ions were purchased from Showa Kako Corp. (Osaka, Japan) in powder form. Each concentration of CBPO was separately formulated into four samples, which were the original samples, added with Cu, Fe, and Zn. Simulating the impurities amount like metal ions are small in the real situation, the different CBPO samples and metal ions mass ration were dispensed as only 1% [15].

Differential scanning calorimetry

The DSC currently on the market can be divided into heat flux DSC and power compensation DSC. The DSC we selected to examine the heat flow change during the decomposition of 16 sets of samples was PerkinElmer DSC 8500. PerkinElmer DSC 8500 (Shelton, CT, USA) belongs to power compensation DSC, which has high energy precision and accuracy with small furnace mass and can reach balance quickly [16, 17]. DSC 8500 was employed to examine thermal behavior characterisic in the entire process when the samples were heated from room temperature to 200.0 °C. We chose the part of the heating range determined by the thermogravimetry experiments [18, 19].

According to the suggestion of DSC operation parameters for calculating and establishing thermokinetic models, the heating rates we used were 1.0, 2.0, 4.0, 6.0, and 8.0 °C min‒1 [20, 21]. The heating rate selection strictly follows that the multiple heating rates should be adopted, and the ratio of the maximum β (8.0 °C min–1) to the minimum β (1.0 °C min–1) should not be < 5 [22, 23]. For the DSC test container, we selected 25 µL aluminum crucible for all the sets of samples. The selected aluminum crucible can be used for standard DSC testing up to 640 °C, for solid, liquid, and powder samples, and can provide excellent DSC performance [15]. The amount of four different concentrations of CBPO mixed with different metal ions examined for each heat flow experiment was 5.30 ± 0.17 mg. The experiment atmosphere selected was nitrogen; when the nitrogen was turned on, the carrier gas flow rate was set to about 20.0 mL min–1 [24]. Given experimental reproducibility, four CBPO sample concentrations and those containing metal ions samples were repeatedly executed three times [25].

Results and discussion

DSC experiments of CBPO mixed with metal ions

We performed thermal stability tests, which were three metal ions mixed four different low concentration CBPO at DSC experiments. The DSC curves of heat flow versus temperature for 10.0 mass% CBPO mixed with 10,000 ppm Cu at the heating rates of 1.0, 2.0, 4.0, 6.0, and 8.0 °C min–1, as shown in Fig. 1. At the beginning of the furnace heating, the instrument recorded a little noise, which did not affect the calculation for the heat of decomposition (ΔHd) of the test samples. The origin heat flow baselines displayed an indefinite value with the heating rate changing. The DSC curves baseline was restructured to better present a comparison. Because the tested samples were dissolved as dilution liquid, the endothermic reaction was not expected to occur. When CBPO decomposed, the benzoic acid, benzene, and biphenyl were released.

Fig. 1
figure 1

DSC curves of heat flow versus temperature for 10.0 mass% CBPO mixed with 10,000 ppm Cu at various heating rates

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Meanwhile, the exothermic peak shaved shriller when the heating rate was higher. As listed in Table 1, the initial exothermic onset temperature (T0), which is defined as the temperature at which the heat that is released by a reaction cannot be removed from the reactor, started at approximately 91.85 ± 7.25 °C and ended at ca. 99.26 ± 0.96 °C. The heat flow of exothermal direction was downward in DSC 8500 illustration. Therefore, the peak temperature (Tp) appeared at the lowest point in each DSC curve, as shown in Fig. 1. For 10.0 mass% CBPO mixed with 10,000 ppm Cu DSC tests, the Tp occurred at 124.38 ± 7.26 °C, which is congenial to the literature and increased by degrees of heating rates [10].

Table 1 Thermal behavior characteristics of lower concentrated CBPO added Cu analyzed via DSC
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As listed in Table 1, the entire decomposition of four concentrations CBPO mixed with 10,000 ppm Cu presented a similar value for T0, Tp, and final temperature (Tf). However, because of the concentration difference of CBPO, the primary influence of thermal stability is reflected in ΔHd. The ΔHd of 1.0, 2.5, 5.0, and 10.0 mass% CBPO mixed with 10,000 ppm Cu were distributed from 17.23 ± 3.48 J g‒1 to 60.26 ± 17.73 J g‒1. Although the values of ΔHd for each concentration of CBPO did not grow in multiples proportionally with the concentration of CBPO, the lower concentration could affect the ΔHd value with a considerable impact. Moreover, the Tp is the indicative parameter to calculate the Ea; the coefficient of variation (CV) of Tp was listed in Table 1 to present the experiments’ reliability. Tables 2 and 3 present the thermal stability parameters of lower concentrated CBPO mixed with 10,000 ppm Fe and mixed with 10,000 ppm Zn in DSC experiments. For CBPO mixed with 10,000 ppm Fe, the primary thermal stability parameters did not make much difference in T0, Tp, and Tf with the data listed in Table 1. Note that the ΔHd of 1.0 mass% CBPO mixed with 10,000 ppm Fe was lower than that of 1.0 mass% CBPO mixed with 10,000 ppm Cu. Nevertheless, the ΔHd of 10.0 mass% CBPO mixed with 10,000 ppm Fe detected as 77.34 ± 23.25 J g‒1 was even higher than that of 10.0 mass% CBPO mixed with 10,000 ppm Cu.

Table 2 Thermal behavior characteristics of lower concentrated CBPO added with Fe analyzed via DSC
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Table 3 Thermal behavior characteristics of lower concentrated CBPO added with Zn analyzed via DSC
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In Table 3, the data show an irregular relationship for ΔHd of different concentrated CBPO mixed with 10,000 ppm Zn. As attributed to the crystallization reaction, it occurred during storage, which Zn ion had crystallized with CBPO. Therefore, the CBPO samples with Zn ion crystallization reaction cannot quantify the ΔHd accurately. The T0, Tp, and Tf of CBPO mixed with 10,000 ppm Zn can still be detectable given that the values were similar to that of CBPO mixed with 10,000 ppm Cu and CBPO mixed with 10,000 ppm Fe. Compared with the pure CBPO, the T0 of CBPO mixed with metal ions was postponed, the reaction can be determined as a typical reaction [9].

Isoconversional kinetic analysis

To establish the thermokinetic parameters in any part of the reaction, we utilized Friedman kinetic method, a famous model-free kinetic model, to extrapolate the apparent activation energy (Ea). The Friedman model is as follows [22, 26]:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A\left( \alpha \right){\text{exp}}\left[ { - \frac{{E_{{\text{a}}} \left( \alpha \right)}}{RT\left( t \right)}} \right]f\left( \alpha \right)$$
(1)
$$A^{\prime}\left( \alpha \right) = A\left( \alpha \right)f\left( \alpha \right)$$
(2)
$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A^{\prime}\left( \alpha \right){\text{exp}}\left[ { - \frac{{E_{{\text{a}}} \left( \alpha \right)}}{RT\left( t \right)}} \right]$$
(3)
$$t_{{\text{a}}} = \mathop \smallint \limits_{0}^{t} {\text{d}}t = \mathop \smallint \limits_{{\partial_{0} }}^{\alpha } \frac{{{\text{d}}\alpha }}{{A^{\prime}\left( \alpha \right){\text{exp}}\left[ { - \frac{{E_{{\text{a}}} \left( \alpha \right)}}{RT\left( t \right)}} \right]}}$$
(4)
$$\ln \left( {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} \right) = \ln \left( {A^{\prime}\left( {\upalpha } \right)} \right) - \frac{{E_{{\text{a}}} \left( \alpha \right)}}{RT\left( t \right)}$$
(5)

where A is a pre-exponential factor, Ea is the apparent activation energy. The values of A and Ea will change with the temperature change. The model linearizes them to simplify the equation. The rate at which the reaction rate increases with increasing temperature is related to its Ea value. Within the same temperature range, the smaller the Ea reaction is, the faster the heating rate will increase, and the increase in Ea value will decrease the heating rate. f(α) is the reaction model, R is the universal gas constant (8.314 J mol‒1 K‒1), T is the absolute temperature, t is the time, and α is the extent of conversion.

The Flynn–Wall–Ozawa (FWO) isoconversional method is frequently adopted to scrutinize the hazardous materials as the integral methods. The FWO kinetic model was used to diagram the Ea value of any part of reaction progress as the comparisons between the calculations of results by Freidman kinetic model. The FWO kinetic method is usually used to calculate the Ea value. One of the advantages of the FWO kinetic method is that it does not require knowing the reaction mechanism in advance and can avoid errors caused by different reaction mechanisms. We used integral temperature p(x), which was obtained from Doyle’s approximation [27]:

$$\ln p\left( x \right) = - 5.331 - 1.0516x$$
(6)

where p(x) is the integral temperature value. Using Eq. (6), FWO kinetic model can be expressed as Eq. (7) [28, 29]:

$$\begin{aligned} \ln \left( {\beta_{1} } \right) + 1.0516\left( {\frac{{E_{{\text{a}}} }}{{RT_{{{\text{p1}}}} }}} \right) & = {\text{ln}}\left( {\beta_{2} } \right) + 1.0516\left( {\frac{{E_{{\text{a}}} }}{{RT_{{{\text{p2}}}} }}} \right) \\ & = {\text{ln}}\left( {\beta_{3} } \right) + 1.0516\left( {\frac{{E_{{\text{a}}} }}{{RT_{{{\text{p3}}}} }}} \right) = \cdots \\ \end{aligned}$$
(7)

where β1, β2, and β3, are the heating rates, Tp1, Tp2, and Tp3 are the peak temperatures corresponding to each heating rate.

Freidman and FWO methods were adopted to calculate the Ea values to compare with the decomposition situation at any reaction progress during different concentrations of CBPO mixed with metal ions. We selected two sets of representative experiments as a diagram for isoconversional kinetic analysis. Figure 2 shows the Ea and R2 values versus reaction progress compared to 10.0 mass% CBPO with 10,000 ppm Cu between calculations using Freidman and FWO method. Using Freidman method results, the Ea value started at 147.37 kJ mol‒1 and ended at 300.06 kJ mol‒1; the R2 continued to maintain a value approaching 1.0 but became lowerα of 0.95. At the middle of reaction progress, the Ea value was 190.20 kJ mol‒1. Using the FWO method result, the Ea value started at 74.12 kJ mol‒1 and ended at 205.49 kJ mol‒1; the completion of reaction progress accompanied the R2 value increase. We assumed that the maximum reaction rate occurred at α of 0.5, the Ea value was 94.12 kJ mol‒1, and the R2 value was 0.94.

Fig. 2
figure 2

Ea and R2 values versus reaction progress comparison of 10.0 mass% CBPO with 10,000 ppm Cu between calculation using Freidman and FWO methods

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Figure 3 exhibits the Ea and the R2 values versus reaction progress comparison of 5.0 mass% CBPO with 10,000 ppm Fe between calculations using Freidman and FWO methods. The average values of Ea and R2 in using the Freidman method were 123.61 kJ mol‒1 and 0.99, respectively. When the reaction progress proceeded to 0.5, the Ea value was 143.82 kJ mol‒1. In this set of experiments, the FWO method’s calculation was comparable to that using the Freidman method; the Ea value started at a higher value and gradually decreased as the reaction proceeded. In calculating 5.0 mass% CBPO with 10,000 ppm Fe using the FWO method, the average values of Ea and R2 were 145.72 kJ mol‒1 and 0.99, respectively. When the reaction proceeded halfway, the Ea value was 133.73 kJ mol‒1.

Fig. 3
figure 3

Ea and R2 values versus reaction progress comparison of 5.0 mass% CBPO with 10,000 ppm Fe between calculation using Freidman and FWO methods

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Kissinger method analysis for CBPO

To verify the Friedman method and FWO method calculations’ reliability, we used the Kissinger method to duplicate the calculation findings. From Murray and White’s approximation to approach the integral temperature p(x), the Kissinger method was developed. Using the approximation, p(x) can be expressed as Eq. (8) [30]:

$$p\left( x \right) = \frac{{e\left( { - x} \right)}}{{x^{2} }}$$
(8)

Combined with the integral method, the Kissinger kinetic method was transcribed as [31]:

$$\ln \left( {\frac{\beta }{{T_{{\text{p}}}^{2} }}} \right) = \ln \left[ {\frac{AR}{{E_{{\upalpha }} g\left( {\upalpha } \right)}}} \right] - \frac{{E_{{\upalpha }} }}{{RT_{{\upalpha }} }}$$
(9)

where g(α) is an integral form of reaction mechanism function. We can obtain the Ea value through the plot of ln(β T ‒2p ) versus T‒1. The Tp value was assumed as the peak temperature, which is 0.5 in α. As shown in Fig. 4, 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Cu under the heating rates of 1.0, 2.0, 4.0, 6.0, and 8.0 °C min‒1. The value range of Ea calculated using the Kissinger method was from 118.60 to 173.21 kJ mol‒1; the value of R2 was from 0.8950 to 0.9851.

Fig. 4
figure 4

Plots of ln(β Tp‒2) versus 1000 Tp‒1 of 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Cu under the heating rates of several heating rates

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Starink method analysis for CBPO

Even though the Freidman kinetic method, FWO kinetic method, and Kissinger kinetic method are the typical model-free models, we further employed the Starink method to calculate Ea to diagnose the thermokineic results. Based on the transform from Eq. (9), the Starink method can be expressed as Eq. (10):

$${\text{ln}}\left( {\frac{\beta }{{T_{{\text{p}}}^{\text i} }}} \right) = C_\text{s} - C\left( {\frac{{E_{{\text{a}}} }}{RT}} \right)$$
(10)

where β is the heating rate, Cs is the constant, i and C are the approximate values obtained from integral temperature. In the calculation, i and C were appointed as 1.80 and 1.004, respectively. Consequently, the Ea analysis charts using the Starink kinetic method were according to the plot of ln(β T ‒1.8p ) versus 1000 T‒1. The Starink method was recommended to estimate the Ea value accurately [27]. Therefore, in this experimental study, the Starink method was undoubtedly used to describe the experimental data better than the Kissinger method. Figure 5 illustrates the Ea analysis graphs of four sets of CBPO nonisothermal experiments using the Starink method. The range of Ea value is from 109.63 to 142.03 kJ mol‒1. The value of R2 is at least 0.9036, but the highest was only 0.9787. The results revealed that the linear fitting using these model-free methods was stable but not accurate enough in this case (Table 4).

Fig. 5
figure 5

Plots of ln(β T ‒1.8p ) versus 1000 T ‒1p of 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Fe under the heating rates of several heating rates

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Table 4 Ea determination for various concentrated CBPO and its mixtures using ASTM E698 method
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American Society for Testing and Materials (ASTM) E698 method

ASTM E698 method can be designated by the Arrhenius equation and general rate law. The main adopted parameters of ASTM E698 were DSC and the FWO method. This method can be utilized to reveal the safety concern of hazardous materials based on the limitation in which several heating rates were in the range from 1.0 to 10.0 °C min‒1 [32]. ASTM E698 method can be stated as Eq. (11):

$$E \cong - 2.19R\frac{{{\text{d log}}_{10} \beta }}{{{\text{d}}\left( {1/T} \right)}}$$
(11)
$$D = - {\text{d}}\frac{{{\text{ln }}\rho \left( {\text{x}} \right)}}{{{\text{dx}}}}$$
(12)
$$\rho \left( {\text{x}} \right) = \left( {x + 2} \right)^{ - 1} \left( {x^{ - 1} } \right)\left( {e^{ - {\text x}} } \right)$$
(13)

Using Eqs. (11)–(13), Ea can be calculated as follows:

$$E = \left( {\frac{{ - 2.303{ }R}}{D}} \right)\left[ {{\text{d}}\frac{{{\text{log}}_{10} \beta }}{{{\text{d}}\left( {1/T} \right)}}} \right]$$
(14)

Figure 6 shows the Ea value determination of 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Cu, applying the ASTM E698 method. The Ea value of 10.0 mass% CBPO with 10,000 ppm Cu is 144.78 kJ mol‒1, which was comparable to the value of Ea obtained from the Freidman method and the FWO method. Generally, by four sets of experiments, the R2 value of the fitting model was relatively reliable. Apart from various concentrated CBPOs with 10,000 ppm Fe, the Ea values were determined from 116.34 to 128.97 kJ mol‒1. The values of R2 were fitted as 0.9655–0.9995. The credibility of the CBPO with 10,000 ppm Fe sets models has been improved after supported by using ASTM E698, as shown in Fig. 7.

Fig. 6
figure 6

Graphs used for determining the Ea value of 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Cu, using ASTM E698 method

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Fig. 7
figure 7

Graphs used for determining the Ea value of 1.0, 2.5, 5.0, and 10.0 mass% CBPO with 10,000 ppm Fe, using ASTM E698 method

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Determination of self-accelerating decomposition temperature (SADT)

SADT can be understood from the data reordered by heat generation and heat release [33]. We selected the seven standard packages of CBPO in the industry for calculating the value of SADT. The SADT values can be determined using the concept of heat loss similarity, recommended by the United Nations test method H.4, the heat accumulation storage test. The heat loss per unit mass L (W kg–1 K–1) can be easily calculated according to Eq. (15) [34].

$$L = \ln 2C_{{\text{p}}} t_{1/2}^{ - 1}$$
(15)

where Cp is the specific heat (J kg–1 K–1); t1/2 is the half-time of cooling (s). As presents in Table 5, the SADT for four concentrated CBPOs with 10,000 ppm Cu was calculated. As the lowest concentration (1.0 mass%) mixed with 10,000 ppm Cu in this study, the SADT value was 80.0 °C. With the package larger, the SADT value became opposite lower. Meanwhile, the SADT value also reduced, along with the concentration of CBPO being higher. When 10.0 mass% CBPO with 10,000 ppm Cu storage at the groove of 100 kg, the SADT value was inferred as 55.0 °C. For lower concentrated CBPO with 10,000 ppm Fe experiments, the SADT value was getting lower when the CBPO volume was getting higher. The range of four concentration CBPO with 10,000 ppm Fe was from 91.0 to 51.0 °C, as organized in Table 6.

Table 5 SADT determination (°C) for different lower concentrated CBPO with Cu for various packages
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Table 6 SADT determination (°C) for different lower concentrated CBPO with Fe for various packages
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Moreover, the reaction progress of various concentrated CBPOs with Cu/Fe at different isothermal conditions was simulated. Figure 8 revealed a reaction situation of 10.0 mass% mixed with 10,000 ppm Cu at five different isothermal conditions. The mixture of 10.0 mass% mixed with 10,000 ppm Cu would be completely reacted in just 25.1 h.

Fig. 8
figure 8

TMRiso curves by reaction progress versus time for 10.0 mass% CBPO mixed with 10,000 ppm Cu at isothermal simulations

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Conclusions

The heat flow examination results show that the reaction consumes time, and the maximum reaction rate would more significantly delay the heating rate. The DSC experiments results for CBPO mixed with Zn cannot precisely present the decomposition during heating because a crystallization reaction occurred during sample preparation. Using isoconverional kinetic analysis has excellent performance on the Ea and the R2 determination of CBPO mixed with Cu/Fe at any reaction progress. On fitting of the kinetic model, ASTM E698 method calculation results were more accurate than that of the Kissinger method. Whether mixed with Cu or Fe, the SADT values of different CBPOs were higher than pure CBPO, but the potential risk was still considerable.