Thermal hazard analysis and thermokinetic calculation of 1,3-dimethylimidazolium nitrate via TG and VSP2

Abstract

In this study, the thermal stability and thermokinetic parameters of 1,3-dimethylimidazolium nitrate ([Mmim]NO₃) were investigated by thermogravimetric analysis under non-isothermal conditions in a nitrogen atmosphere. The results showed that [Mmim]NO₃ exhibited three decomposition stages from 93.3 to 350.0 °C, and the onset temperature of [Mmim]NO₃ was obtained at approximately 161.0–182.0 °C under five heating rates. The apparent activation energy was 119.0–124.0 kJ mol⁻¹, as calculated by different well-known equations, and the pre-exponential factor was 3.6 × 10¹² min⁻¹. The reaction mechanism of [Mmim]NO₃ was carried out with the reaction order n = 1.0, and the decomposition mechanism function was further obtained. Moreover, vent sizing package 2 was employed to acquire the maximum self-heating rate (39,828.0 °C min⁻¹) and pressure rise rate (73,331.0 psig min⁻¹) for simulating cooling system failure in a practical process. The findings indicated that [Mmim]NO₃ showed the possibility of a runaway reaction, leading to a potential thermal hazard. The approach of these results is vital for obtaining inherently safer process information for [Mmim]NO₃ during production, storage, and transportation.

Introduction

Ionic liquids (ILs) are known as room-temperature molten salts with melting points below 100.0 °C, and they combine organic cations with organic or inorganic anions. ILs have numerous attractive properties, such as extremely low vapor pressure, low melting point, wide liquid range, good thermal stability, and wide electrochemical windows [1]. Based on their excellent performance, ILs are widely used as organic solvents [2,3,4], catalysts [5] and heat transfer fluids [6,7,8] for separations [9] as well as electrochemistry [10,11,12,13].

However, according to US Occupational Safety and Health Administration (OSHA) regulations, ILs are classified as IIIB combustible materials, which means that ILs are not sufficiently safe when near fire or heat sources [14, 15]. This classification implies that ILs will decompose under high ambient temperatures. On the other hand, in the presence of nitrate, ILs can be used as energetic materials due to the high energy of the functional groups. Unfortunately, ILs may also lead to explosions and other serious safety problems if the cooling system fails or operates at incorrect process temperatures [16,17,18]. In the previous studies, there are few reports of thermal hazard for imidazolium nitrate ionic liquids [19]. Hence, it is critical to investigate the thermal stability and potential hazards for imidazolium nitrate ionic liquids during the applications.

We developed a methodology to estimate the thermal stability and thermal hazard of 1,3-dimethylimidazolium nitrate ([Mmim]NO₃) using thermogravimetry (TG) and vent sizing package 2 (VSP2). The specific targets of this research were as follows:

• (a) To reveal the short-term thermal stability of [Mmim]NO₃ by TG experiment, which uses a non-isothermal medium;

• (b) To establish the reaction mechanism of [Mmim]NO₃ using the data from the TG curves;

• (c) To calculate thermokinetic parameters such as the apparent activation energy (E_a) and the pre-exponential factor (A) of [Mmim]NO₃ by Flynn–Wall–Ozawa (F–W–O), Kissinger–Akahira–Sunose (K–A–S) and Starink methods;

• (d) To estimate the related parameters of process safety during a thermal runaway reaction using VSP2 under adiabatic conditions.

Experimental and methods

Samples

Ninety-eight mass% [Mmim]NO₃ in the solid state was received from Hua Wei Rui Ke Chemical Co., Beijing, China. Experimental techniques using dynamic and adiabatic approaches were proposed in this study. According to the experimental techniques, we could determine the thermal stability and runaway reaction of [Mmim]NO₃.

Thermogravimetry (TG)

SDT Q600 from TA Instruments, Inc. (Delaware, USA) was used to perform the TG experiment. [Mmim]NO₃ sample in the range of 6.0–8.0 mg each was placed in an open alumina crucible. The scanning TG experiments were performed in a nitrogen atmosphere, with the gas purging at a flow rate of 100.0 mL min⁻¹. Dynamic experiments were performed at a temperature range from 25.0 to 400.0 °C, with heating rates of 2.0, 4.0, 6.0, 8.0 and 10.0 °C min⁻¹. TG curves have been further applied to obtain the corresponding thermokinetic parameters and the most likely thermokinetic model functions using mathematical approaches.

Vent sizing package 2

VSP2 from Fauske & Associates, Inc. (Illinois, USA) was applied to measure the adiabatic state that can simulate the reactor in the process. It uses the heat–wait–search mode, which can furnish temperature and pressure traces versus time from the dynamic scanning test in the test cell (112.0 mL), which is suitable for solid samples due to the low thermal inertia (ϕ) of approximately 1.05–1.20. In this study, approximately 3.0 g of [Mmim]NO₃ was loaded into the test cell.

Thermal analysis theory

The thermal decomposition of [Mmim]NO₃ complies with the following rate Eq. 1:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k\left( T \right) \cdot f\left( \alpha \right)$$

(1)

where dα/dt is the conversion rate of different times, k(T) is the Arrhenius rate constant, and f(α) is the differential mechanism function.

According to the Arrhenius equation, k(T) can be defined as:

$$k\left( T \right) = A \cdot \exp \left( { - \frac{{E_{\text{a}} }}{RT}} \right)$$

(2)

where A is the pre-exponential factor, R is the molar gas constant (8.314 J mol⁻¹ K⁻¹), and E_a is the apparent activation energy.

α is the degree of conversion as follows:

$$\alpha = \frac{{W_{\text{i}} - W_{\text{t}} }}{{W_{\text{i}} }}$$

(3)

where W_i is the initial mass and W_t represents the mass of the sample at time t.

Considering the constant heating rate β in the non-isothermal heating mode, Eq. 1 is rearranged to the following form [20]:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{A}{\beta } \times \exp \left( { - \frac{{E_{\text{a}} }}{RT}} \right) \times f\left( \alpha \right)$$

(4)

Equation 4 is the basis of the isoconversional mode. In this study, we selected F–W–O, K–A–S, and Starink methods to investigate the thermokinetic parameters.

• (a) F–W–O method

  The F–W–O method is a typical isoconversional mode. It uses multiple heating rate curves to determine the thermokinetic parameters. The equation is expressed as [13]:

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

  (5)

  where G(α) is the integral mechanism function. G(α) is a stationary constant when α is certain. E_a can be obtained from the straight line by plotting lg(β) versus 1/T.

• (b) K–A–S method

  The K–A–S method is also based on the isoconversional mode, which is applied as a model-free approach. The equation is as follows [21]:

  $$\ln \frac{\beta }{{T^{2} }} = \ln \left[ {\frac{AR}{{G\left( \alpha \right)E_{\text{a}} }}} \right] - \frac{{E_{\text{a}} }}{RT}$$

  (6)

  A straight line can be obtained by plotting ln(β/T²) versus 1/T, which can be applied to solve the thermokinetic parameter E_a.

  The pre-exponential factor A can be calculated based on the K–A–S method by the following equation:

  $$A = \frac{{\beta E_{\text{a}} }}{{RT_{\text{p}}^{2} }}\exp \left( {\frac{{E_{\text{a}} }}{{RT_{\text{p}} }}} \right)$$

  (7)

  where T_p is the peak temperature of DTG.

• (c) Starink method

  Starink summarized the Kissinger, Ozawa, and Boswell methods and then further refined the temperature integral. The revised mathematical equation is expressed as Eq. 8 [22]:

  $$\ln \frac{\beta }{{T^{1.8} }} = C_{\text{s}} - \frac{{E_{\text{a}} }}{RT}$$

  (8)

  The plot of ln(β/T^1.8) versus 1/T forms a straight line, and E_a would be obtained from the slope. On the whole, E_a can be received from Eqs. 4–8, which do not consider the differential mechanism function g(α) and the integral mechanism function G(α).

Results and discussion

Short-term thermal stability

The thermal stability of [Mmim]NO₃ was investigated by TG experiments. The TG–DTG data of [Mmim]NO₃ were obtained by the non-isothermal method under a nitrogen atmosphere, as shown in Fig. 1.

Fig. 1

a TG curve and b DTG curves for the decomposition of [Mmim]NO₃ at five heating rates

Figure 1a shows three mass loss steps in the TG curve, which were defined as steps I, II and III. The temperature of the mass loss in step I was at approximately 100.0 °C, which may be caused by evaporation of water existing in [Mmim]NO₃. For this step, the mass losses were 2.0, 1.0, 1.7, 1.1, and 1.5% at the heating rates of 2.0, 4.0, 6.0, 8.0, and 10.0 °C min⁻¹, respectively. Step II was the main stage of mass loss, which was caused by the thermal decomposition of [Mmim]NO₃. The peak temperature (T_p) of [Mmim]NO₃ was around 179.0–202.0 °C at five heating rate. Figure 1b illustrates that T_p increases with increasing heating rate; however, the temperature variation range was narrow. The start temperature (T_start) and onset temperature (T_onset) of thermal decomposition under five heating rates are listed in Table 1.

Table 1 Non-isothermal data for the thermal decomposition of [Mmim]NO₃ at five heating rates

T_onset is applied to represent the short-term thermal stability of ILs. It can be seen that the T_onset of [Mmim]NO₃ was less than 200.0 °C. The effect of heating rate on T_onset is not obvious for [Mmim]NO₃. T_start is lower than T_onset, at approximately 45.0–47.0 °C. This result indicates that T_onset is higher than the actual decomposition temperature. The temperature for a 10% conversion rate (T_0.10) was 151.0–174.0 °C which was measured under non-isothermal conditions at different heating rates. In previous studies, T_onset, T_start, and T_0.10 were used to evaluate the thermal stability of ILs via TG. For example, the T_onset of 1-butyl-3-methylimidazolium chloride ([Bmim]Cl) is approximately 234.0–270.0 °C [23,24,25,26,27], and that of 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim]BF₄) is approximately 315.0–424.0 °C [23,24,25, 28]. The results of [Mmim]NO₃ can be considered as a manifestation of lower thermal stability than other imidazolium ILs.

Decomposition mechanism

Step II is the main decomposition stage that will produce a variety of decomposition products, including methyl nitrate (CH₃ONO₂), which is formed by the reaction of the nitrate anion with a methyl group that was produced during the breakdown of [Mmim]NO₃. Step III (Fig. 1a) is obviously different from step II in that the rate of mass loss is significantly reduced. Obviously, the decomposition mode of step III is altered. The decomposition temperature range of step III is 190.0–332.0 °C, and CH₃ONO₂ produced by step II will decompose in this temperature range. The reaction equation can be expressed as follows [29, 30]:

$${\text{CH}}_{3} {\text{ONO}}_{2} = 1.00{\text{NO}} + 0.50{\text{CH}}_{2} {\text{O}} + 0.03{\text{CH}}_{3} {\text{OH}} + 0.37{\text{CO}} + 0.10{\text{CO}}_{2} + 0.90{\text{H}}_{2} {\text{O}} + 0.04{\text{H}}_{2}$$

(9)

Therefore, the mass loss of step III can be interpreted as the decomposition of CH₃ONO₂.

Decomposition thermokinetics

To obtain the thermokinetic parameters of [Mmim]NO₃ such as E_a and A, the TG curves at heating rates of 2.0, 4.0, 6.0, 8.0 and 10.0 °C min⁻¹ were addressed by mathematical means, and three isoconversional methods (Eqs. 5–8) were employed. The results are shown in Figs. 2–4. Excellent linear relationships were observed under different heating rates with the three methods.

Fig. 2

Linear curves of lg(β) versus 1/T by the F–W–O method

Fig. 3

Linear curves of ln(β/T²) versus 1/T by the K–A–S method

Fig. 4

Linear curves of ln(β/T^1.8) versus 1/T by the Starink method

Table 2 shows the thermokinetic parameters obtained by the different methods. The E_a values were 121.2, 119.8, and 121.9 kJ mol⁻¹ obtained by the F–W–O, Starink, and K–A–S methods, respectively. Overall, the E_a values calculated by the three methods were similar. The average E_a value of the three methods was 121.0 kJ mol⁻¹, and the linear correlation coefficient (r) was 0.9938, with a good correlation. According to Eq. 7 and the E_a calculated by the K–A–S method, the determined lgA was 12.5 min⁻¹.

Table 2 Kinetic parameters obtained by F–W–O, Starink and K–A–S methods of [Mmim]NO₃

As for the thermal decomposition mechanism selection for the main reaction stage, the following four conditions must be observed: (a) E_a selected must fit within the range of the thermal decomposition kinetic parameters (E_a = 80.0–250.0 kJ mol⁻¹); (b) r is greater than 0.98; (c) E_a and lgA obtained from the integral and differential methods are roughly the same; and (d) the mechanism function selected must be in agreement with the tested sample state [31, 32]. The results using Šatava–Šesták (Eq. 10) at different kinetic models are listed in Table 3.

Table 3 Kinetic parameters obtained of [Mmim]NO₃ by Šatava–Šesták method at different kinetic models

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

(10)

Obviously, the values of E_a (123.1 kJ mol⁻¹) and A (2.7 × 10¹² min⁻¹) calculated by the integral method (Šatava–Šesták method) under the nucleation and growth decomposition mechanism A₁ were almost the same that calculated by the differential method (F–W–O method). Meanwhile, the E_a (122.1 kJ mol⁻¹) and A (6.5 × 10¹² min⁻¹) calculated under the power law decomposition mechanism P_7/10 as well as closed to the values using F–W–O method. However, P_7/10 belongs to accelerating models, which represent processes whose rate increases continuously with increasing the extent of conversion and reaches its maximum at the end of the process. Apparently, the accelerating model was not fit for the sample of [Mmim]NO₃ according to the TG curves. Therefore, the decomposition mechanism A₁ was more suitable for the decomposition of [Mmim]NO₃ considering the actual situation. The mechanism function is Avramo–Erofeev equation with n = 1, G(α) = − ln(1 − α) and f(α) = 1 − α. Substituting E_a with 123.1 kJ mol⁻¹ and A with 2.7 × 10¹² min⁻¹ into Eq. 1, the kinetic equation of the main reaction stage may be described as:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{10.65} \times \left( {1 - \alpha } \right) \times \exp \left( {\frac{{ - 1.48 \times 10^{4} }}{T}} \right)$$

(11)

Considering the effect of constant heating rate β, Eq. 11 is rearranged to the following form:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \frac{{10^{10.65} }}{\beta } \times \left( {1 - \alpha } \right) \times \exp \left( {\frac{{ - 1.48 \times 10^{4} }}{T}} \right)$$

(12)

The entropy of activation (ΔS^≠), enthalpy of activation (ΔH^≠), and free energy of activation (ΔG^≠) for [Mmim]NO₃ as resolved by Eqs. 13–15 were 68.1 J mol K⁻¹, 118.1 and 86.6 kJ mol⁻¹, respectively, which can be used to supplementary characterize the thermal decomposition reaction.

$$A = \frac{{k_{\text{B}} T_{\text{p}} }}{h}\exp \left( {\frac{{\Delta S^{ \ne } }}{R}} \right)$$

(13)

$$\Delta H^{ \ne } = E_{\text{a}} - RT_{\text{p}}$$

(14)

$$\Delta G^{ \ne } = \Delta H^{ \ne } - T_{\text{p}} \Delta S^{ \ne }$$

(15)

where the values of A and E_a are calculated by the K–A–S method, T_p is peak temperature, k_B is the Boltzmann constant (1.3807 × 10⁻²⁷ J K⁻¹), and h is the Planck constant (6.626 × 10⁻³⁴ J s).

Thermal hazard analysis by VSP2

In this research stage, under an adiabatic environment, the thermokinetic parameters of process safety for [Mmim]NO₃ were estimated by VSP2. The determined onset temperature T_onset was 162.0 °C. As obtained by VSP2, the maximum temperature (T_max), the maximum pressure (P_max), the maximum temperature rise rate ((dT dt⁻¹)_max), and the maximum pressure rise rate ((dP dt⁻¹)_max) were 394.0 °C, 437.4 psig, 39,828.0 °C min⁻¹, and 73,331.0 psig min⁻¹, respectively.

Figure 5 illustrates the curves of pressure and temperature versus time during the exothermic behavior of [Mmim]NO₃. Point A was the reaction start time, and when the reaction reached point B, the reaction rate increased dramatically, and the system reached the no-return temperature (T_NR), which means the maximum heat release rate and the maximum temperature are reached within a very short time. The observed adiabatic temperature rise (ΔT_ad) and adiabatic pressure rise (ΔP_ad) were 234.0 °C and 416.3 psig, respectively.

Fig. 5

Pressure and temperature versus time for the thermal decomposition of [Mmim]NO₃ by VSP2

Figure 6 indicates the curves of self-heating rate and pressure rise rate versus the runaway reaction temperature of [Mmim]NO₃ under adiabatic conditions. When the temperature reached T_NR, the pressure rise rate increased rapidly, and (dP dt⁻¹)_max reached 73,331.0 psig min⁻¹. Obviously, the exothermic behavior of [Mmim]NO₃ was from the standpoint that (dT dt⁻¹)_max and (dP dt⁻¹)_max increased in a short time of 10.4 min, from onset to apex.

Fig. 6

Self-heating rate and pressure rise rate versus temperature of [Mmim]NO₃ by VSP2

According to Semenov theory [33], runaway reactions will occur if the temperature rises sharply to a no-return temperature when the heat generation rate is greater than the heat removal rate. The critical runaway temperature and unstable reaction criteria might lead to a fire, explosion, or chemical release. In the process of this adiabatic experiment, the system cannot effectively remove the heat generated, eventually causing the destruction of the test cell by a runaway reaction, which is shown in Fig. 7. The results showed that a rapid runaway reaction existed in [Mmim]NO₃. This means [Mmim]NO₃ has the potential for thermal runaway phenomena if the cooling system fails in the process.

Fig. 7

VSP2 test cell damaged by runaway reaction under adiabatic conditions

Conclusions

The short-term thermal stability and decomposition kinetics of [Mmim]NO₃ were investigated using non-isothermal TG under a nitrogen atmosphere. The results showed three mass loss stages. Step I was the water evaporation, step II was caused by the decomposition of [Mmim]NO₃, and step III was the decomposition of methyl nitrate, which was a decomposition product of [Mmim]NO₃ in step II. The maximum onset temperature was 182.0 °C when the heating rate was 10.0 °C min⁻¹. The E_a value was 119.0–124.0 kJ mol⁻¹ as obtained from different methods. The main exothermic decomposition reaction mechanism of [Mmim]NO₃ was the nucleation and growth with n = 1.0. The kinetic equation can be expressed as:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \frac{{10^{10.65} }}{\beta } \times \left( {1 - \alpha } \right) \times \exp \left( {\frac{{ - 1.48 \times 10^{4} }}{T}} \right).$$

As for the thermal hazard analysis of [Mmim]NO₃ under adiabatic conditions by VSP2, the maximum self-heating rate and pressure rise rate were 39,828.0 °C min⁻¹ and 73,331.0 psig min⁻¹, respectively. These results indicated that [Mmim]NO₃ has potential thermal runaway hazards. Therefore, all of the thermal hazard information that was gained in this research can be provided to the relevant factory for decreasing casualties.