Introduction

Nitrocellulose is a typical nitro-energetic material that can be prepared through the esterification of cellulose and nitric acid [1, 2]. This material is currently widely used in civil and military fields to produce paints, films, plastics, explosives, and rocket propellants [3,4,5,6]. However, nitrocellulose has been the main hazard factor in many industrial accidents because of its high flammability and explosibility. The thermal runaway of nitrocellulose has caused many disasters, such as the ones in Shinagawa Ward (July 14, 1964), Zhongshan (August 16, 2006), Xingtai (January 24, 2014), and Tianjin (August 12, 2015) [3, 7,8,9]. The worst tragedy in recent years was the fire and explosion at Tianjin port, in which 165 people died, eight people were lost, and 798 people were injured. In addition, the direct economic loss caused by this accident was RMB6.866 billion. The hazardous properties of nitrocellulose dramatically limit its applications, and the associated thermal safety issues have been studied extensively by scholars worldwide [10,11,12,13,14,15].

Many researchers have investigated the thermal hazard of nitrocellulose in terms of its decomposition, combustion, and explosion characteristics. Kinetic analysis has been conducted often in such studies, and the parameters of the Arrhenius equation have been obtained, which are crucial for evaluating the safety level of nitrocellulose in its manufacturing, storage, and transportation [5, 10, 16,17,18]. Pourmortazavi et al. investigated the thermochemical behavior of nitrocellulose samples with different nitrate contents and obtained the activation energy, frequency factor, and critical explosion temperature of nitrocellulose [1]. Lin et al. computed the activation energy of nitrocellulose during its thermal decomposition by conducting thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) experiments. In addition, they compared the data fitting results obtained using these two methods [13]. Wang et al. found that the thermal decomposition of nitrocellulose satisfied the first-order equation, and on the basis of this information, they computed the critical explosion temperature and activation energy [19]. He et al. investigated the effects of humectants on the activation energy of nitrocellulose decomposition in a nitrogen atmosphere. The results indicated that nitrocellulose with isopropanol had higher activation energy and stability than that with ethanol or without a humectant [20]. Luo et al. studied the decomposition characteristics of nitrocellulose in air and computed its activation energy under different conversion rates [21]. Mi analyzed the thermal stabilities of fiber and chip nitrocellulose and found that the activation energy ratio of these two forms was 1.6 [22]. Wei et al. investigated the effect of aging time on the kinetic parameters of nitrocellulose by using a TG–DSC analyzer. The results indicated that minimum parameters values were achieved under an aging time of 24 days and an aging temperature of 90 ℃ [23]. Gao et al. studied the thermal kinetics and reaction mechanism of nitrocellulose pyrolysis in a nitrogen atmosphere. The relationship between activation energy and conversion was obtained by multi-kinetics and the reaction model was reconstructed [2]. Yang et al. investigated effect of metal chloride on the thermal decomposition of nitrocellulose and found that divalent metal chlorides can increase the activation energy and pre-exponential factor of nitrocellulose, whereas trivalent metal chlorides have the opposite effects [9].

In the literature, extensive investigations and useful conclusions pertaining to the thermal stability and runaway characteristics of nitrocellulose have been reported. However, in these investigations, kinetic parameters were obtained mainly in nitrogen or air atmospheres, the oxygen contents of which are 0% and 21%, respectively. In real conditions, nitrocellulose is often stored and transported in confined spaces. If fires occur in such places, the combustion of a massive quantity of nitrocellulose results in the rapid consumption of oxygen, which cannot be easily replaced by air from the external environment. For example, the Tianjin accident occurred because of the combustion of nitrocellulose stored in a container, which represents an oxygen-lean environment (0% < O2% < 21%). Oxygen content has a crucial influence on kinetic parameters [24, 25]; however, few studies have investigated the thermal characteristics of nitrocellulose under oxygen-lean conditions. Therefore, in the present study, we used a thermogravimetric analyzer in conjunction with multiple thermokinetic methods, namely the Friedman, Flynn–Wall–Ozawa (FWO), Kissinger–Akahira–Sunose (KAS), Starink, and Vyazovkin methods, to obtain the activation energy (Ea) values of nitrocellulose under various oxygen contents. A differential scanning calorimeter and an adiabatic accelerating calorimeter (ARC) were used to analyze the thermal characteristics of nitrocellulose. Critical thermal stability parameters such as adiabatic temperature rise, time to conversion limit, and self-accelerating decomposition temperature were determined to evaluate the thermal hazards of nitrocellulose. The findings of this study can further deepen the understanding regarding nitrocellulose and serve as a reference for its suitable production, storage, transportation, and usage.

Experimental

Sample preparation

In the experiments conducted in this study, we used samples of floccule-type nitrocellulose with a nitrogen content of 11.5–12.2%. Ethyl alcohol with a content of 30% was used as the humectant to prevent possible spontaneous combustion. The samples were sealed and stored in an anti-explosion refrigerator at temperatures of 2‒6 ℃.

Thermogravimetric analysis

TGA, which is a typical thermal analysis technology, was used in this study to obtain the relationship between material mass and temperature. In our experiments, we used TGA 2 (Mettler Toledo Co., Zurich, Switzerland) to determine the thermodynamic behavior of the samples. The original mass of the samples was 7.44 ± 0.07 mg. The temperature of the samples was increased from 30.0 to 300.0 °C under heating rates of 2.0, 4.0, 6.0, 8.0, and 10.0 °C min−1. An oxygen-lean environment was created precisely by using two mass-flow control instruments (Alicat, America). Oxygen contents of 0%, 5%, 10%, 15%, and 21% were achieved by controlling the mass flows of oxygen and nitrogen separately. The oxygen and nitrogen flows were then combined and input into the thermogravimetric analyzer at a total gas flow rate of 50 mL min−1.

Differential scanning calorimetry

The sample in TG experiment was tested in an open environment while the DSC experiment was performed in a sealed crucible; hence, DSC experiments were carried out in this paper as a reference in analyzing the thermal stability of samples. In the DSC experiments, the relationship between heat flux and temperature was obtained by measuring the flux difference between the samples and reference materials during a temperature-programmed process. A DSC 3 (Mettler Toledo Co., Greifensee, Switzerland) instrument was used to analyze the thermal decomposition reaction of nitrocellulose. The samples were heated from 30.0 to 300.0 °C at rates of 2.0, 4.0, 6.0, 8.0, and 10.0 °C min−1 in a nitrogen atmosphere. The mass of the samples was 2.05 ± 0.03 mg, and the nitrogen gas flow rate was 50 mL min−1.

Adiabatic accelerating calorimetry

Adiabatic accelerating calorimeters possess a “Heat–Wait–Search” mode for measuring the temperature, enthalpy, and pressure of a chemical reaction in an adiabatic environment. Therefore, we conducted adiabatic accelerating calorimetry experiments to supplement the TGA and DSC tests. An ARC 244 (Netzsch, Selb, Germany) instrument was used to measure the temperature and pressure of the samples. The sample mass was 102 mg, and the samples were tested in a Hastelloy sample container. In the ARC experiments, the temperature was increased from 120 to 300 °C under a heating rate of 10.0 °C min−1.

Thermokinetic models

According to the theory of thermal analysis, kinetic analysis methods can be categorized as isothermal and non-isothermal methods. Moreover, non-isothermal methods can be subdivided into single-heating-rate and multiple-heating-rate methods [24, 26]. These non-isothermal methods with multiple heating rates, which are also called iso-conversional or model-free methods, have been paid more attention as they can be used to obtain reliable activation energy values without reaction mechanism functions [24, 27, 28]. Therefore, we adopted typical model-free methods (the Friedman, FWO, KAS, Vyazovkin, and Starink methods) to calculate the activation energy of nitrocellulose under different oxygen contents. The details of these methods are provided in the following text.

Friedman method

The Friedman kinetic model is based on a single-step kinetic mechanism, and this model can be derived from the following equations in a progressive manner [29,30,31]:

$$\alpha = \frac{{m_{{0}} - m}}{{m_{{0}} - m_{{\text{e}}} }}$$
(1)
$$\frac{\text{d}\alpha }{{\text{d}t}} = kf\left( \alpha \right)$$
(2)
$$k = A\exp \left( { - \frac{{E_{{\text{a}}} }}{{{\text{RT}}}}} \right)$$
(3)
$$\ln \left( {\frac{\text{d}\alpha }{{\text{d}t}}} \right) = \ln \left[ {Af\left( \alpha \right)} \right] - \frac{{E_{{\text{a}}} }}{{{\text{RT}}}}$$
(4)

where α is the conversion rate at a certain time; m is the sample mass; m0 and me represent the mass at the start and end points; t denotes the time; k denotes the reaction rate; f(α) represents the reaction model; A and Ea are Arrhenius parameters that represent the pre-exponential factor and activation energy, respectively; and R is the universal gas constant (8.314 J mol K−1).

FWO method

The FWO model is a typical integral kinetic model that has been used extensively in literature [30, 32,33,34,35]. In Eq. (5), \(G\left( \alpha \right)\) is the integral of f(α)−1, and β is the heating rate. The activation energy can be calculated from the slope of the linear fitting line of lgβ and T−1.

$$\lg \beta = \lg \left( {\frac{{AE_{{\text{a}}} }}{RG\left( \alpha \right)}} \right) - 2.315 - 0.4567\frac{{E_{{\text{a}}} }}{{{\text{RT}}}}$$
(5)

KAS method

The KAS model is an integral model based on the Coats–Redfern approximation, which is expressed in Eq. (6) [36, 37]. The value Ea can be obtained from the slope of the plot of ln(β T−2) versus T−1.

$$\ln \left( {\frac{\beta }{{T^{2} }}} \right) = \ln \frac{AR}{{E_{{\text{a}}} G\left( \alpha \right)}} - \frac{{E_{{\text{a}}} }}{R}\frac{1}{T}$$
(6)

Vyazovkin method

Vyazovkin established an integral kinetic model based on the Arrhenius equation and type I kinetic equation. This model is expressed in Eq. (7) [30, 38].

$$- \ln t = \ln \frac{A}{G\left( \alpha \right)} - \frac{{E_{{\text{a}}} }}{R}\frac{1}{T}$$
(7)

Starink method

The Starink method was established according to the consideration that the Kissinger model (Eq. (8)), Ozawa model (Eq. (9)), and Boswell model (Eq. (10)) can be generalized into a single formula [24]. After transformation and optimization, the Starink model was obtained. This model is expressed in Eq. (11) and is considered to be highly accurate for calculating Ea [26, 39]. The parameters \(C_{{\text{K}}}\), \(C_{{\text{O}}}\), \(C_{{\text{B}}}\), and \(C_{{\text{S}}}\) are the constants of the equations of the Kissinger, Ozawa, Boswell, and Starink models, respectively.

$$\ln \left( {\frac{\beta }{{T^{2} }}} \right) = C_{{\text{K}}} - \frac{{E_{{\text{a}}} }}{R}\frac{1}{T}$$
(8)
$$\lg \beta = C_{{\text{O}}} - 1.0516\frac{{E_{{\text{a}}} }}{RT}$$
(9)
$$\ln \left( {\frac{\beta }{T}} \right) = C_{{\text{B}}} - \frac{{E_{{\text{a}}} }}{R}\frac{1}{T}$$
(10)
$$\ln \left( {\frac{\beta }{{T^{1.8} }}} \right) = C_{{\text{S}}} - 1.0037\frac{{E_{{\text{a}}} }}{R}\frac{1}{T}$$
(11)

Results and analysis

Thermokinetic analysis

Figure 1 displays the typical TGA results obtained for nitrocellulose. The curves under different oxygen content have similar variation tendency and the oxygen content in Fig. 1 is 5%. Only one major mass-loss period existed in the decomposition process. When the temperature exceeded 180 °C, the sample mass decreased by approximately 90% within a short time, as displayed in the derivative thermogravimetric (DTG) curves. The DTG peaks moved toward the high-temperature side as the heating rate increased, and the corresponding temperature increased to 184.90‒194.52 °C. In addition, The TG curve also shows a slight increase at temperature around 190 °C when β was 10.0 °C min−1; it could be explained that large heat would be released rapidly at high heating rate, which could have led to a blast in the sample container. Consequently, the created reverse pressure was exerted on the inside scale of the TGA, leading to a transient increase in the sample mass.

Fig. 1
figure 1

Thermogravimetric curves of nitrocellulose at 5% oxygen content

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By using the thermokinetic models mentioned in (“Thermokinetic models” section), Ea values can be obtained. Figure 2 shows the variation in Ea with conversion rate under different oxygen contents. The curves obtained using the KAS, FWO, Starink, and Vyazovkin methods exhibited synchronous variation, and the KAS and Starink curves almost coincided with each other. However, the Friedman curves exhibited certain differences and fluctuated over the conversion rate range of 0.3‒0.8, especially when the oxygen content was 0%, 10%, and 15%, as illustrated in Fig. 2(a, c, and d), respectively. Table 1 lists the average Ea values and determination coefficients (R2) of the thermokinetic models under three oxygen content values. The average Ea obtained using the Friedman method was the smallest among all the methods, and the larger values obtained using the other four methods were close to each other. Moreover, the R2 value of the Friedman method was lower than those of the other four methods. Thus, compared with the KAS, FWO, Starink, and Vyazovkin models, the Friedman model would not be very appropriate to calculate Ea of nitrocellulose using thermogravimetric data.

Fig. 2
figure 2

Variation in Ea with conversion rate under different oxygen contents: a 0%, b 5%, c 10%, d 15%, and e 21%

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Table 1 Average Ea and determination coefficient (R2) values of the five models under different oxygen contents
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In addition, the Ea curves of the KAS, FWO, Starink, and Vyazovkin models indicate that the Ea had an “increase–stabilize–decrease” tendency throughout the heating process. Similar results were reported in a previous study [40]. In the initial reaction period, Ea reached its minimum value under each oxygen content when the conversion rate was 0.1, which indicated that limited energy was required to activate the reaction. Therefore, necessary measures should be emphasized and implemented, especially at the beginning of nitrocellulose reaction. As the reaction proceeded, Ea increased dramatically and peaked when the conversion rate was 0.3. The average increase rate of Ea obtained using the four methods was up to 98% under an oxygen content of 21%. The Ea value then tended to stabilize as the conversion rate increased from 0.3 to 0.8. The average rate of variation in Ea was only 4.9% under different oxygen contents. When the conversion rate exceeded 0.8, Ea decreased with maximum and average change rates of 41% and 18%, respectively. The average Ea values under the oxygen contents of 0%, 5%, 10%, 15%, and 21% were calculated to be 281.87, 283.97, 276.17, 276.57, and 326.05 kJ mol−1, respectively, which indicated that the Ea values were relatively stable in oxygen-lean environments. The aforementioned Ea values are lower than that in the air. Similar results were obtained in a previous study for nitrocellulose solution (20–30 mass%), which was prepared by dissolving nitrocellulose in ethyl acetate [41].

Thermal characteristic analysis

The heat production data of nitrocellulose under five heating rates (β) were obtained through DSC, as illustrated in Figs. 3–4. The corresponding thermodynamic parameters are summarized in Table 2. Figure 3 and Table 2 indicate that the heat production curves moved toward the high-temperature side as β increased. The initial decomposition temperature T0 and maximum decomposition temperature Tp were 172.68‒199.98 °C and 192.31‒213.94 °C, respectively. These temperatures increased as β increased, and the trends of change in the maximum heat production and β were similar. According to Fig. 4, high reaction and heat production rates were achieved at large β values, especially those exceeding 6.0 °C min−1, as indicated by the substantial increase in heat production under β values of 8.0–10.0 °C min−1. Moreover, according to Table 2, the heat enthalpy under the heating rate of 6.0 °C min−1 was relatively high, with an average value of 3877.76 J g−1. The heating enthalpy was 3274.69 J g−1 when β exceeded 6 °C min−1. Thus, the thermal decomposition of nitrocellulose can release adequate heat when the environmental temperature increases at a slow rate. Therefore, suitable ventilation should be provided to prevent gradual heat accumulation during the storage and transportation of nitrocellulose.

Fig. 3
figure 3

Changes in the heat production rate of nitrocellulose with temperature

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Fig. 4
figure 4

Changes in the heat production rate of nitrocellulose with time

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Table 2 Thermodynamic parameters of nitrocellulose under different heating rates
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For further exploring the reaction process and reaction mechanism of nitrocellulose, a one-step autocatalytic model was adopted to calculate the heat release rate during the thermal decomposition of nitrocellulose. The corresponding results are illustrated in Fig. 5, indicating high consistency between the simulation and experimental data. Therefore, the thermal decomposition of nitrocellulose in a nitrogen atmosphere is an “A → B” one-step autocatalytic reaction, which is consistent with the results reported in literature [16, 17].

Fig. 5
figure 5

Comparison of the experimental and simulated data of the changes in heat release rate with time

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Nitrocellulose was thermally decomposed under an adiabatic condition in ARC, as illustrated in Figs. 6–8. Figure 6 shows the complete temperature and pressure curves corresponding to this process; Fig. 7 displays the variations in the temperature and heating rate with time in the aforementioned decomposition process; and Fig. 8 depicts the variations in the pressure and the rate of pressure increases with time in the decomposition of nitrocellulose. The heating rate tended to first increase and then decrease. The maximum heating rate was 0.19 °C min−1, and the corresponding temperature was 166.20 °C. This heating rate corresponded to the maximum intensity of the decomposition reaction. During the decomposition process, the pressure in the confined container increased dramatically because of the release of heat and gaseous products. The trend of the rate of pressure increase was similar to that of the heating rate. The maximum pressure change rate was 0.0506 bar min−1, which occurred at a temperature of 168.30 °C.

Fig. 6
figure 6

Experimental curves obtained when performing ARC at a β value of 10.0 ℃ min−1 for nitrocellulose

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Fig. 7
figure 7

Changes in the temperature and heating rate with time during the decomposition of nitrocellulose

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Fig. 8
figure 8

Changes in the pressure and the rate of pressure increase with time

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During the ARC experiments, the heat released by nitrocellulose could be partly absorbed by the reactor. To compensate for this phenomenon, the factor of thermal inertia (ϕ) was introduced in the analysis. This factor represents the inertia of a substance against heat. High thermal inertia reduces the reaction rate and rate of temperature change. The ϕ value of a reaction system is 1 under ideal conditions. For the experiments conducted in this study, ϕ was calculated to be 47.538, which is considerably higher than the ideal value. Therefore, the adiabatic temperature rise ΔTad obtained from the experiment was relatively small at 15.20 °C. The theoretical ideal \(T_{{{\text{ad}}}} \prime\) value of a sample can be obtained using Eq. (12) [42, 43], and this value was up to 722.58 °C in this study.

$$T_{{{\text{ad}}}} \prime = \emptyset \Delta T_{{{\text{ad}}}}$$
(12)

Table 3 presents the criteria for assessing the severity of thermal runaway [44, 45]. According to these criteria, the thermal runaway severity of nitrocellulose is catastrophic, which indicates that heavy damage would be caused by the violent reaction of nitrocellulose.

Table 3 Assessment criteria for the severity of thermal runaway of nitrocellulose
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During the storage and transportation process, the thermal stability of a material can be considerably affected by the environmental temperature. Therefore, time to conversion limit (TCL) and time to reach the maximum reaction rate (TMR) were considered when evaluating the thermal stability of nitrocellulose [6, 46, 47]. These parameters were determined using the aforementioned one-step autocatalytic model (Fig. 9). A conversion limit of 10% was selected in this study. TCL and TMR decreased as the temperature increased, and a dramatic decrease was observed in these parameters when the temperature increased from 30 to 60 ℃, which indicates that nitrocellulose has high-temperature sensitivity. The TCL and TMR were less than 24 h when the temperature exceeded 93 °C and 79 ℃, respectively. When the temperature exceeded 100 ℃, the aforementioned parameters stabilized at extremely small values. Thus, a prompt reaction was achieved, consistent with the large mass-loss rates depicted in Fig. 1 and high heat production rates depicted in Figs. 3–4.

Fig. 9
figure 9

The TCL and TMR of nitrocellulose versus temperature

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Self-accelerating decomposition temperature (SADT) is another vital safety parameter used in the thermal stability analysis of hazardous materials [28, 39, 48]. SADT is defined as the lowest environmental temperature at which a packaged chemical can decompose in a self-accelerating manner within 7.0 days. The SADT and reaction progress of nitrocellulose in a 50 kg package were determined (Fig. 10). The temperature at the center of the nitrocellulose package was 6 ℃ higher than the environmental temperature within 5.9 days of self-accelerated decomposition. The SADT was calculated to be 49 ℃, which is similar to the values reported in literature [48]. According to the critical temperature relationship presented in Table 4 [28, 49], the control and alarm temperatures of nitrocellulose are 39 and 44 ℃, respectively.

Fig. 10
figure 10

SADT and average reaction progress for a 50 kg package of nitrocellulose

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Table 4 Relationships between control temperature, alarm temperature, and SADT
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Conclusions

In this study, the thermal stability of nitrocellulose was investigated through TGA, DSC, and ARC. The main conclusions of this study are as follows:

  1. (1)

    The activation energy (Ea) of nitrocellulose under oxygen contents of 0%, 5%, 10%, 15%, and 21% was obtained using the Friedman, FWO, KAS, Starink, and Vyazovkin methods. The results revealed that Ea exhibited an “increase–stabilize–decrease” trend during thermal decomposition, and the Ea values in oxygen-lean environments were relatively stable and lower than that in air. Compared with Friedman method, the other four methods exhibited optimal applicability for Ea analysis based on TGA data.

  2. (2)

    The results of the DSC experiments indicated that the initial and maximum decomposition temperatures increased as β increased, and the heat enthalpy was higher under lower heating rates. The thermal decomposition of nitrocellulose in a nitrogen atmosphere was an “A → B” one-step autocatalytic reaction.

  3. (3)

    The adiabatic temperature increase of nitrocellulose was obtained, and the thermal runaway severity of nitrocellulose was determined to be catastrophic. TCL and TMR decreased as the temperature increased, and their values were less than 24 h when the temperature exceeded 93 and 79 ℃, respectively. The calculated SADT of a 50 kg package of nitrocellulose was 49 ℃, and the control temperature was 39 ℃, which is the upper-temperature limit for nitrocellulose storage.