ABSTRACT Nitrocellulose (NC) is widely used in both military and civilian fields. Because of its high chemical sensitivity and low decomposition temperature, NC is prone to spontaneous

combustion. Due to the dangerous properties of NC, it is often dissolved in other organic solvents, then stored and transported in the form of a solution. Therefore, this paper took NC

solutions (NC-S) with different concentrations as research objects. Under different atmospheric conditions, a series of thermal analysis experiments and different reaction kinetic methods

investigated the influence of solution concentration and oxygen concentration on NC-S’s thermal stability. The variation rules of NC-S’s thermodynamic parameters with solution and oxygen

MECHANISM OF 1-NITROSO-2-NAPHTHOL Article Open access 21 November 2022 SYNERGISTIC INHIBITION EFFECT AND MECHANISM OF AN INHIBITOR FOR ENTIRE PROCESS INHIBITION OF COAL SPONTANEOUS

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INTRODUCTION With the rapid development of modern industry, many manufactured products have entered thousands of households and been closely related to our daily lives. However, the raw

materials are fraught with danger in daily life, e.g., common spray paint, coatings, plastics, artificial fibers, ink, film, and cosmetics. Nitrocellulose (cellulose nitrate, NC) is one of

the raw materials of these products, which is an exceptionally hazardous nitrate ester. NC has widespread adoption in both military and civilian fields. In addition to NC with low nitrogen

content (< 12.6%) mentioned above for ordinary civilian production, NC with high nitrogen content (≥ 12.6%) is used to manufacture military weapons, gunpowder, solid rocket propellants,

and explosives1,2,3,4. Owing to the poor thermal stability of NC, commercial NC products are wetted with solvents, or mixed with plasticizers to alleviate the risk of fire and explosion of

dry NC. Universally, water or alcohols are usually added as humectants during storage and transportation to forestall spontaneous combustion. However, chemical accidents with NC still occur

frequently in recent years. Among them, the most horrific was “Explosion accident in Tianjin Binhai New Area on August 12” in 2015, which led to 165 deaths, 8 missing/presumed dead, and 798

injuries5. The dangerous characteristics of NC and the frequent occurrence of accidents have led numerous experts and scholars to exploring its thermal hazard since a long time ago. Some

researches on the thermal decomposition mechanism of NC found that the denitrification process does not necessarily make chain breakage, because the basic structure of carbon skeleton does

not change dramatically during the thermal decomposition6. NO2 generated in the thermal decomposition reaction is combined to form nitric acid groups, and then water, CO, CO2, carbonyl, and

acid intermediates are rapidly produced7. Some studies obtained the critical heating rate of NC with high nitrogen content during the first order autocatalytic decomposition to thermal

explosion by nonisothermal DSC technique8,9,10. Brill and Gongwer investigated the thermal decomposition characteristics of NC at different temperatures11. Some other researchers mainly

discussed the thermal stability of NC with different particle sizes12,13, forms14, nitrogen content15,16, and aging periods1. The combustion and explosion behaviors of NC were also in

focus13,17. In addition, a large number of experiments attached great importance to the influence of various catalysts18,19, stabilizers20,21,22,23,24, plasticizers25,26, wetting

agents2,25,27,28,29,30, and inorganic salts31,32 on the thermal behaviors of NC. As known, nitrogen is often used for protection during the transportation and storage of some hazardous

chemicals. When combustion or explosion occurs, the surrounding atmosphere will also change with the reaction process33,34,35,36. But to sum up, although the thermal safety of NC has been

extensively studied, there is still a lack of research on NC in different atmospheric conditions. Most of the existing studies focused on NC-F (F-fibre) or NC-C (C-chip), and paid less

attention to the solution. However, after the Tianjin accident, the control of NC in China has become more rigorous, so it is mostly stored and transported wetted with the solution.

Therefore, this paper took NC solution (NC-S) commonly used in actual production as the research object. Nonisothermal differential scanning calorimetry (DSC) and thermogravimetric analysis

(TGA) technologies were applied to explore the variation rules of reaction characteristic temperature of NC-S with different concentrations in different atmospheric conditions. In order to

comprehensively compare the applicability of multiple linear models for reaction kinetics calculation of NC-S, the kinetic parameters of the thermal decomposition reaction were calculated

using different integral and differential kinetic models. The results revealed that several thermal stability and thermokinetic parameters of NC-S spontaneous combustion did not externalize

a simple proportional relationship with the concentrations of solution and oxygen. However, the oxygen-free environment can effectively reduce the thermal risk of NC-S indeed. These findings

can provide theoretical guidance for improving the treatment scheme of NC-S spontaneous combustion in actual production, transportation, and storage. EXPERIMENTS AND METHODS MATERIALS The

NC-S sample preparation in the experiment was dissolving NC (nitrogen content less than 12.6%) in ethyl acetate (EAC). The purchased 30 mass% NC-S was diluted with EAC (content ≥ 99.5%) to

obtain samples of three concentrations, which are 30, 20, and 10 mass%. The EAC sample was also used for comparison with the NC-S samples in the measurement. All dispensed samples were

stored in the refrigerator at 2.0 to 6.0 °C before testing. THERMOGRAVIMETRIC ANALYSIS (TGA) TGA is a common technique for measuring the relationship between mass and temperature37 by

setting temperature conditions through the instrument program. The sample is placed in a specific atmosphere, and the temperature is maintained at a constant value or changed by heating

scanning. By this method, the change of sample mass in the process can be observed and accurately characterized, and then the thermal decomposition characteristics of substances can be

analyzed38. In the experimental design, TGA 2 (produced by Mettler Toledo Co., Zurich, Switzerland) was used to test the thermal mass loss of samples. The mass (_m_) of NC-S sample with each

concentration in the measurement was 7.40 ± 0.10 mg. The different heating rates (_β_): 2.0, 4.0, 6.0, 8.0, and 10.0 °C/min) were adopted respectively during the experimental temperature

from 30.0 to 300.0 °C. To simulate three different atmospheric conditions, we adjusted the oxygen concentration through the gas flow meter so that the TG test was carried out at 0 vol.%

oxygen (N2, oxygen-free environment), 10 vol.% oxygen (oxygen-lean environment), and 21 vol.% oxygen (air environment). The gas flow was 50.0 mL/min. The mass loss, mass loss velocity, onset

temperature (_T_otg), and peak temperature (_T_ptg) of three samples in different atmospheric conditions can be acquired through TG experiment. DIFFERENTIAL SCANNING CALORIMETRY (DSC)

MEASUREMENT DSC is one of the most frequently applied thermal analysis instruments, which has extremely high sensitivity and temperature resolution and can test the weakest thermal effects.

It controls temperature through the built-in program, measures the power difference in the form of heat between the input sample and reference, and obtains the relationship between heat flow

and temperature. In addition, the endothermic and exothermic reaction characteristics can be analyzed by detecting the thermodynamic parameters of materials to be measured in the

temperature increase condition39. In this measurement, the heat-flow DSC 3 (produced by Mettler Toledo Co., Zurich, Switzerland) was applied to test the thermal decomposition behaviors of

different concentrations of NC-S samples (_m_ = 4.48 ± 0.08 mg) in an oxygen-free atmosphere (N2, 50.0 mL/min) from 30.0 to 300.0 °C40. We measured the heat flow change at different _β_

(0.5, 1.0, 2.0, 4.0, and 8.0 °C/min) under the abovementioned conditions41. DSC diagram has several important thermodynamic parameters, such as peak temperature (_T_pdsc) and heat of

reaction (Δ_H_) can be derived. Then the thermal stability of NC-S with different concentrations can also be deduced. KINETIC MODELS This study, in evaluating the difficulty of chemical

reaction and reaction rate of the thermal hazardous substances, calculated the reaction kinetic apparent activation energy (_E_a) to study their reaction kinetics. Therefore, many dynamic

models have been developed by predecessors, among which the most commonly used are some convenient model-free methods42. Based on previous TG and DSC experiments, the nonisothermal

differential kinetic models (Kissinger, Friedman, and Starink models) and integral kinetic model (FWO model) were adopted to calculate the _E_a of the spontaneous combustion reaction of

NC-S. Then the effects of different atmospheric conditions and solution concentrations on _E_a were summarized, and the thermal safety of NC-S was also assessed. FRIEDMAN MODEL Several

kinetic methods were derived from the following Arrhenius equations43 shown in Eqs. (1)‒(4): $$T={T}_{\text{o}}+\beta t$$ (1) $$\frac{\text{d}\alpha }{\text{d}t}=\frac{\beta \text{d}\alpha

}{\text{d}T}=kf\left(\alpha \right)$$ (2) $$k=Aexp(-\frac{{E}_{\text{a}}}{RT})$$ (3) $$f\left(\alpha \right)={\left(1-\alpha \right)}^{n}$$ (4) where _T_ is the reaction temperature (K), and

_T_o is the onset temperature (K), _α_ is conversion rate, _t_ is the reaction time (s), _k_ is the reaction rate constant, _A_ is the pre-exponential factor, _R_ is the universal gas

constant (8.314 J/mol K). Equation (4) indicates the differential form of the kinetic mechanism function44. By combining Eqs. (1)‒(4), the differential form of the first kinetic equation of

thermodynamics can be obtained and shown in Eq. (5): $$\frac{\text{d}\alpha }{\text{d}t}=\frac{\beta \text{d}\alpha }{\text{d}T}=Af\left(\alpha

\right)exp\left(-\frac{{E}_{\text{a}}}{RT}\right)=Aexp\left(-\frac{{E}_{\text{a}}}{RT}\right){\left(1-\alpha \right)}^{n}$$ (5) Taking the natural logarithm of both sides of Eq. (5), Eq. (6)

can be acquired, which is the calculation formula of the Friedman model45. $${\text{ln}}\frac{\text{d}\alpha }{\text{d}t}= \text{ln} \frac{\beta \text{d}\alpha

}{\text{d}T}={\text{ln}}[Af\left(\alpha \right)]-\frac{{E}_{\text{a}}}{RT}$$ (6) Friedman model is suitable for calculation with TG data, where d_α_/d_t_ represents the rate of mass loss,

which can be got from the derivative of mass loss to time. KISSINGER MODEL Based on the differential form of the first kinetic equation of thermodynamics, differentiate both sides of Eq. 

(6), Eq. (7) can further be obtained: $$\frac{\text{d}}{\text{d}t}\left[\frac{\text{d}\alpha }{\text{d}t}\right]=\frac{\text{d}\alpha

}{\text{d}t}\left[\frac{{E}_{\text{a}}\frac{\text{d}T}{\text{d}t}}{R{T}^{2}}-Aexp(-\frac{{E}_{\text{a}}}{RT})n{\left(1-\alpha \right)}^{n-1}\right]$$ (7) Kissinger considered that

\(n{\left(1-\alpha \right)}^{n-1}\) is independent of _β_, and assumed that \(n{\left(1-\alpha \right)}^{n-1}\approx\) 1. When calculated with peak temperature (\(T={T}_{\text{p}}\)),

d/d_t_(d_α_/d_t_) = 0, Eq. (8) can be obtained: $$\frac{{E}_{\text{a}}\beta }{R{{T}_{\text{p}}}^{2}}=Aexp(-\frac{{E}_{\text{a}}}{RT})$$ (8) Taking the natural logarithm of both sides of the

equation above, Kissinger model can be obtained and presented in the following Eq. (9)37,46: $$\text{ln}\left(\frac{\beta

}{{{T}_{\text{p}}}^{2}}\right)=\text{ln}\frac{AR}{{E}_{\text{a}}}-\frac{{E}_{\text{a}}}{R}\frac{1}{{T}_{\text{p}}}$$ (9) By plotting ln(_β_/_T_p2) and 1/_T_p, a straight line can be fitted.

_E_a can be determined using the slope of the line. STARINK MODEL Starink method was adjusted from Kissinger equation, and the new Eq. (10) is as follows47: $$\text{ln}\left(\frac{\beta

}{{\text{T}}^{1.8}}\right)={C}_{\text{S}}-1.0037\frac{{E}_{\text{a}}}{R}\frac{1}{T}$$ (10) Starink model is one of the differential kinetic methods with high accuracy and has gained

widespread applications39. FLYNN–WALL–OZAWA (FWO) MODEL An integral kinetic model named FWO model was devised, and the formula is presented in Eq. (11)48,49: $$\text{lg}\beta

=\text{lg}\left(\frac{A{E}_{\text{a}}}{RG\left(\alpha \right)}\right)-2.315-0.4567\frac{{E}_{\text{a}}}{RT}$$ (11) where _G_(_α_) is the integral form to the kinetic mechanism function46.

Plotting lg_β_ and 1/_T_ together in a straight line, _E_a can be calculated by the slope. When FWO model is applied, only _β_ and _T_ are concerned, so this model is exceptionally

convenient to calculate and extensively employed. RESULTS AND ANALYSIS THERMODYNAMIC PARAMETERS OF CALORIMETRIC EXPERIMENTS THERMAL THERMOGRAVIMETRIC BEHAVIORS OF NC-S Figure 1 presents the

thermogravimetric loss of EAC and NC-S with three concentrations in the oxygen-free environment at _β_ of 10.0 °C/min. As seen through the diagram, pure EAC experienced massive mass loss at

the beginning of the measurement at 30.0 °C, and the thermogravimetric loss ended at 60.0 °C, leaving about 30% of the mass. Speculating the reason for this phenomenon is that EAC is highly

volatile, and a large amount of volatilization occurred in the open-cup environment. Therefore, the thermal decomposition began with heating up. It can also be found that the thermal

decomposition of NC-S occurred at about 180.0 °C, resulting in a sudden mass loss, which is related to the sample concentration. Because of EAC and NC characteristics, the initial mass loss

and final residual mass of NC-S with various concentrations were different. Generally speaking, the higher content of EAC, correspondingly the lower content of NC, so the more obvious mass

loss caused by EAC in the initial stage, the more residual decomposition products at the end of the heating journey, and the less mass loss caused by NC in the intermediate stage. TG curves

of NC-S in different atmospheric conditions at _β_ of 10.0 °C/min were provided together in Fig. 2. The abovementioned rules can also be concluded by comparing the thermal decomposition

thermogravimetric loss behaviors of three NC-S samples under different environments. In addition, Fig. 2 illustrates that the initial mass loss increased gradually with the improvement of

oxygen concentration, which was most obvious for 10 mass% NC-S, containing the largest amount of EAC. Therefore, inferring that the oxygen concentration might greatly influence EAC’s thermal

decomposition reaction at low temperatures. TG and DTG curves of NC-S at 10 vol.% oxygen are demonstrated in Fig. 3. The TG curve indicates the mass loss process of thermal decomposition of

NC-S at _β_ of 2.0 °C/min. The DTG curve is the first derivative of the mass loss curve, representing the thermogravimetric loss speed of NC-S, where the peak value of DTG is the maximum

rate of mass loss, and the corresponding temperature is the maximum mass loss rate temperature (_T_ptg). From three DTG curves, the mass loss rate of NC-S increased with the rise of solution

concentration, and _T_ptg slightly moved to the direction of high temperature with the decrease of solution concentration. TG curves also further confirmed the rule of thermogravimetric

behavior obtained in Fig. 1. By comparing the TG curves in Figs. 1, 2 and 3, the mass of NC-S dropped smoothly at _β_ of 2.0 °C/min, and when _β_ was 10.0 °C/min, NC-S experienced a jump-off

mass loss. Hence deducing when the temperature rises rapidly, the thermal decomposition of such a quick reaction substance would occur instantly, and the reaction is violent and hazardous.

Table 1 lists the characteristic temperatures of 30 mass% NC-S in three different environments at five _β_ from 2.0 to 10.0 °C/min. As shown in Table 1, _T_otg and _T_ptg both increased with

_β_ in all kinds of atmosphere. Table 2 summarizes the average value of three NC-S samples’ characteristic temperatures and residual mass under three atmospheric conditions in TG

measurement. According to the statistics data in Table 2, the oxygen concentration had little influence on the characteristic temperatures of NC-S, while as the solution concentration

declined, _T_ptg gradually rose. Then, by analyzing the residual mass of 30 mass% NC-S after thermal decomposition reaction, given that it was positively correlated with the oxygen

concentration, considering that the participation of oxygen could make the reaction of NC-S more sufficient. To conclude, the TG experimental results reveal that the thermal

thermogravimetric loss of NC-S can be regarded as two stages. The first stage is the mass loss of volatilization and decomposition reaction of solvent EAC, and the second stage is the

violent thermal decomposition reaction of solute NC. For the solution NC-S as a whole, the higher the concentration of the solution, the more thermogravimetric loss, and the earlier the

reaction can reach the fastest speed, so there is a greater risk when the concentration of NC-S is high. By changing the experimental atmospheric conditions, the findings revealed that the

oxygen concentration had little influence on the DTG temperature, but the oxygen present could affect the mass loss of EAC and make NC-S react more completely. DYNAMIC HEATING EXAMINATION

The heat flow curves of 30 mass% NC-S at five different _β_ from 0.5 to 8.0 °C/min in the DSC measurement were drawn in Fig. 4. The Y-axis value of the peak of the curve represents the

maximum heat flow of NC-S in the exothermic reaction process, and the corresponding X-axis value is the temperature or time when the maximum heat flow was reached. As seen from the diagram,

when _β_ increased, the curves shifted to the right in the direction of high temperature, _T_pdsc also moved to the direction of high temperature, and the heat flow at the peak accordingly

increased. By integrating the heat flow with respect to time, Δ_H_ at five different _β_ can be obtained from the area of the exothermic peak. Therefore, according to the picture in the

bottom part of Fig. 4, Δ_H_ decreased with the _β_ increased. All these findings indicate that _β_ impacted the thermal decomposition of NC-S. Figure 5 depicts the DSC exothermic curves of

three concentrations of NC-S at _β_ of 4.0 °C/min. The curves illustrate that _T_pdsc did not change prominently with the solution concentration of NC-S, but the heat flow values varied

correspondingly. The average characteristic temperature and heat release of the three concentration samples in the DSC experiment under an anaerobic environment can be obtained from Table 3.

These parameters also indicate that no correlation was between solution concentration and _T_pdsc. Afterward, according to the experimental data, Δ_H_ of 30 mass% NC-S was 2555.55 J/g, and

that of 20 mass% NC-S was 2584.55 J/g, which were similar in values and both were much higher than that of 10 mass% NC-S. The abundant heat released by the thermal decomposition reaction can

not be removed quickly, leading to heat accumulation, and the possibility of thermal runaway is enhanced. Thus, it is concluded that the higher spontaneous combustion risk is occurring in

high concentration NC-S. KINETIC ANALYSIS NC-S’S _E_ A CALCULATION WITH TGA DATA Based on the data measured in TG experiments, four kinetic models (Starink, FWO, Kissinger, and Friedman

models) were used to calculate _E_a of three samples under the different atmospheric conditions. The _E_a calculated by different models were sequentially plotted as curves in order of

oxygen concentration, which are given in Fig. 6. The linear regression method is usually adopted in the kinetic calculation, and the correlation coefficient (_R_2) is a parameter to measure

the goodness of fit. Therefore, to explore the applicability of the four methods to samples, the average _R_2 of each model was also calculated accordingly, as shown in Fig. 7. From Fig. 6

as a whole, no matter for which sample, _E_a calculated by Starink, FWO, and Kissinger models were extremely similar in terms of the numerical values and the trends of curves changing with

the oxygen concentrations. Among them, the curves of Starink and Kissinger models were even almost overlapped. However, when using the Friedman model, the calculation results were far from

the other three. Analyzing combined with Fig. 7, among the four models, _R_2 of Friedman model was the smallest, indicating that its linear goodness of fit was the worst. Based on this

analysis result, we considered that the applicability of Friedman model to NC-S is not good enough. Figure 6 displays that _E_a of 20 and 30 mass% NC-S varied with oxygen concentration in

the same way, while _E_a of 10 mass% sample was inconsistent with the two. Therefore, inferring that the reaction kinetics characteristics of NC-S were the same when the solution

concentration was above or equal to the threshold of 20 mass%. In contrast, the thermal decomposition kinetic characteristics of the sample might display another trend when the concentration

was below the threshold. Due to the above analysis summarized that there was a large deviation in the calculation of the kinetic parameters by Friedman model for NC-S, we averaged the

values calculated by the other three models (Starink, FWO, and Kissinger models) to obtain the average Ea of thermal decomposition reaction of different samples under different environments,

as provided in Table 4. From the calculation results in Table 4, on the one hand, the influence of oxygen concentration can be discussed. The _E_a of NC-S with any concentration was the

largest in the oxygen-free environment, indicating that the thermal decomposition reaction of NC-S was relatively difficult to occur in the oxygen-free environment, and the speed of

decomposition was slow. The _E_a of 20 mass% and 30 mass% samples were the smallest at 10 vol.% oxygen, while _E_a of 10 mass% sample decreased with the increase of oxygen involved in the

reaction, and the reaction rate increased gradually. On the other hand, the influence of solution concentration can be analyzed. In the TGA experiment, 30 and 20 mass% samples obtained the

maximum _E_a under anaerobic and aerobic conditions, respectively. In general, _E_a of 20 mass% NC-S was not saliently affected by the oxygen concentration. It was inferred from the above

findings that the thermal decomposition reaction of 20 mass% NC-S was relatively stable in the aerobic environment of daily production and life, and was less affected by the changes of the

external environment. In addition, 20 mass% was an ambiguous boundary, and the reaction kinetics of NC-S with a concentration above and below it presented different characteristics, which

was consistent with the inferences obtained in Fig. 6. NC-S’S_ E_ A CALCULATION WITH DSC DATA Based on the data obtained from DSC measurements, _E_a values of three NC-S samples in nitrogen

atmosphere were calculated by nonisothermal integral method (FWO model) and nonisothermal differential method (Starink model). Figure 8 schematizes the lines obtained by fitting

ln(_β_/_T_1.8) and 1000/_T_ at different _α_ via the differential model to calculate _E_a of 20 mass% NC-S at different _α_. After averaging _E_a at all _α_, the average value of _E_a of 20

mass% NC-S in oxygen-free environment can be obtained by Starink model as 126.32 kJ/mol, and _R_2 was 0.9812. Correspondingly, the average _E_a of 30 mass% and 10 mass% NC-S calculated by

Starink model were 128.68 and 111.84 kJ/mol, respectively. The average _E_a of 30 mass%, 20 mass%, and 10 mass% samples can be calculated by FWO model as 129.30, 127.05, and 113.24 kJ/mol,

respectively. By comparison, it can be found that _E_a acquired by these two typical integral models and differential models were extremely close. In addition, _E_a of 30 mass% NC-S was the

largest in the oxygen-free environment, and that of 10 mass% NC-S was the smallest. When _α_ ranged from 0.10 to 0.95, _E_a and _R_2 of the three samples calculated by these two models were

plotted as curves, as described in Fig. 9. It is evident from the top and bottom diagrams that _E_a and _R_2 of NC-S varied with _α_ in almost the same way under these two kinetic models.

Moreover, when _α_ was from 0.30 to 0.95, _R_2 of both methods was higher than 0.90. All the above findings suggested that Starink and FWO models were exceptionally suitable for calculating

the reaction kinetics of NC-S. Figure 9 also depicts that the samples with three different concentrations all had the maximum _R_2 when _α_ was at 0.60, and the goodness of fit was the best

at this time, which was also around the _T_pdsc. Comparing _E_a of three samples at this point, 30 mass% NC-S was still the highest and 10 mass% the lowest, which confirmed the rule

summarized by analyzing the average _E_a before. As a whole, the reaction kinetics analysis in the oxygen-free environment carried out with DSC experimental results further supported the

previous conclusions summarized with TG data. CONCLUSIONS The thermal risk and the thermal stability of NC-S with different concentrations in different environments were studied using

calorimetric technology and thermal analysis. The findings are concluded as follows: TG experiment mainly revealed the influence of solution concentration and atmospheric environment on the

thermogravimetric behavior and characteristic temperature of NC-S. The entire thermal decomposition process of NC-S can be divided into two stages: thermogravimetric process of EAC and

thermogravimetric process of NC. Among the three concentrations of NC-S, 30 mass% NC-S had the maximum mass loss and the smallest _T_ptg, which first attained the maximum decomposition

speed, so 30 mass% NC-S had a greater potential thermal hazard. The thermal decomposition reaction of NC-S completed more in the air and oxygen-lean environments than in the oxygen-free

environment. DSC measurement focused on exploring the exothermic situation of the thermal decomposition reaction of three different concentrations of NC-S in the oxygen-free environment. The

results indicated that _β_ affected the thermal behavior of NC-S. Furthermore, once the solution concentration of NC-S was above or equal to 20 mass% in the oxygen-free environment,

spontaneous thermal combustion released a large amount of heat, even more than 2500.00 J/g. If the heat were difficult to dissipate, there would be a high risk of thermal runaway after heat

accumulation. The differential and integral models were used to calculate and analyze the reaction kinetics of NC-S, respectively. Through comparison, the Friedman model was not recommended

for calculating the _E_a values of such a rapid reaction substance, and the goodness of fit was poor. On the other hand, the applicability of Kissinger, Starink, and FWO kinetic models to

NC-S was great and could be used to calculate the reaction kinetics parameters. According to _E_a calculation results using TG and DSC data, oxygen-free environment could effectively improve

the thermal safety of NC-S, the thermal decomposition reaction was the least likely to occur, and the reaction speed was the slowest. Nevertheless, in most of the actual industrial

production, oxygen has always existed. At this time, 20 mass% NC-S was least impacted by the change of oxygen concentration, and the decomposition rate varied little with the amount of

oxygen involved in the reaction. However, 20 mass% was also a demarcation, above or below this boundary, the kinetic parameters’ variation of NC-S with the oxygen concentration showed

different rules. The low concentration of 10 mass% NC-S had the smallest _E_a and was most prone to thermal decomposition under any atmospheric conditions. In summary, if NC-S with a low

concentration (10 mass%) was used in the practical industry, thermal decomposition reaction could readily occur in the air environment. However, if NC-S with a higher concentration was used,

a large amount of heat would be released once the reaction took place, which was extremely dangerous. Furthermore, thermal runaway occurred with the heat accumulation, resulting in serious

thermal hazards and accident consequences. As a result, to effectively reduce the potential risks of NC-S during production, transportation, and storage, the first consideration should be to

create an oxygen-free environment. In this way, the probability of thermal decomposition of NC can be availably reduced, and the reaction rate can be slowed down to reduce the possibility

of uncontrolled spontaneous combustion of NC-S. For prospects, more different calorimetry instruments can be applied to explore the thermal risk of hazardous chemicals, and the mechanism

function of thermal decomposition reaction can be calculated, so as to conduct a further study on its reaction kinetics. ABBREVIATIONS * _A_ : Pre-exponential factor (1/s) * _C_ s : Constant

(dimensionless) * _E_ a : Apparent activation energy (kJ/mol) * f(α): Dynamic mechanism function of the differential form (dimensionless) * G(α): Integral form of the kinetic mechanism

function (dimensionless) * _k_ : Reaction rate constant (W K/m2) * _m_ : Mass (mg) * \(\overline{m}\) : Average mass (mg) * _R_ : Universal gas constant (8.314 J/mol K) * _R_ 2 : Linear

fitting’s correlation coefficient (dimensionless) * _t_ : Reaction time (s) * _T_ : Reaction temperature (K) * _T_ otg : Onset temperature obtained from TG experiment (°C) * _T_ pdsc : Peak

temperature obtained from DSC measurement (°C) * _T_ ptg : Peak temperature obtained from TG experiment (°C) * _∆H_ : Heat of reaction (J/g) * _α_ : Conversion rate (dimensionless) * _β_ :

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scanning calorimetry. _J. Therm. Anal. Calorim._ 133, 745–751. https://doi.org/10.1007/s10973-018-7021-5 (2018). Article  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS The

authors are grateful to the National Nature Science Foundation of China (Nos. 21927815), the National Key Research Development Program of China (Nos. 2019YFC0810701, 2021YFC3001203), and

General Natural Science Research Project of Jiangsu Universities in 2020 (No. 20KJB620002) for financial support. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Environmental and

Safety Engineering, Changzhou University, Changzhou, 213164, Jiangsu, China Zhi-Ping Li, Jun-Cheng Jiang, An-Chi Huang, Yan Tang & Zhi-Xiang Xing * College of Safety Science and

Engineering, Nanjing Tech University, Nanjing, 210009, Jiangsu, China Chun-Feng Miao * Department of Civil Engineering, Texas Tech University, Lubbock, TX, 79409, USA Juan Zhai * School of

Environmental and Chemical Engineering, Zhaoqing University, Zhaoqing, 526061, Guangdong, China Chung-Fu Huang * Department of Safety, Health, and Environmental Engineering, National Yunlin

University of Science and Technology, Yunlin, 64002, Taiwan, ROC Chi-Min Shu Authors * Zhi-Ping Li View author publications You can also search for this author inPubMed Google Scholar *

Jun-Cheng Jiang View author publications You can also search for this author inPubMed Google Scholar * An-Chi Huang View author publications You can also search for this author inPubMed 

Google Scholar * Yan Tang View author publications You can also search for this author inPubMed Google Scholar * Chun-Feng Miao View author publications You can also search for this author

inPubMed Google Scholar * Juan Zhai View author publications You can also search for this author inPubMed Google Scholar * Chung-Fu Huang View author publications You can also search for

this author inPubMed Google Scholar * Zhi-Xiang Xing View author publications You can also search for this author inPubMed Google Scholar * Chi-Min Shu View author publications You can also

search for this author inPubMed Google Scholar CONTRIBUTIONS Z.-P.L. and A.-C.H. performed the analysis and wrote the paper; Y.T. contributed the literature research; J.Z. and C.-F.M.

offered the methodology; C.-F.H. and C.-M.S. conceived the research theme; Z.-X.X. and J.-C.J.: Writing-review and supervision. CORRESPONDING AUTHORS Correspondence to Jun-Cheng Jiang,

An-Chi Huang, Yan Tang or Chi-Min Shu. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER'S NOTE Springer Nature

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spontaneous combustion characteristics of nitrocellulose solution under different atmospheric conditions. _Sci Rep_ 11, 24053 (2021). https://doi.org/10.1038/s41598-021-03579-z Download

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