Kinetic Analysis of Overlapping Multistep Thermal Decomposition of 2

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Kinetic Analysis of Overlapping Multistep Thermal Decomposition of 2,6-Diamino-3,5-Dinitropyrazine-1-Oxide (LLM-105) Qian Yu, Yu Liu, Heliang Sui, Jie Sun, and Jinshan Li J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 19 Oct 2018 Downloaded from http://pubs.acs.org on October 22, 2018

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The Journal of Physical Chemistry

Kinetic Analysis of Overlapping Multistep Thermal Decomposition of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) Qian Yu, Yu Liu*, Heliang Sui, Jie Sun, and Jinshan Li* Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), P. O. Box 919-311, Mianyang, 621900, P. R. China

Abstract: Thermal decomposition kinetic behavior of energetic materials is of substantial importance for safety enhancement in manufacturing, usage and storage. The thermal decomposition kinetic behavior of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) was studied by simultaneous differential scanning calorimetry and thermogravimetric analysis (DSC-TG). As the thermal decomposition of LLM-105 exhibited a two-step process, in which, the overall reaction was deconvoluted into two reaction steps for better analysis through the different physical meanings consideration of the kinetic data derived from DSC and TG. Kinetic parameters of the two individual reaction steps were characterized through isoconversional and combined kinetic analysis methods. It was found that the activation energy of the first reaction step was 222.2 ± 0.5 kJ mol-1, while the activation energy of the second reaction step was 244.5 ± 0.5 kJ mol-1. Both steps mostly obeyed the nucleation and growth models (Avrami-Erofeev (A3)). The validity of the obtained kinetic parameters was tested through the successful reconstruction of the original experimental curves. The nucleation and growth were also confirmed through Scanning Electronic Microscopy (SEM) observations of the morphology evolution during the LLM-105 decomposition. The obtained kinetic

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parameters and kinetic models contributed to a comprehensive and in-depth understanding of the thermal decomposition of LLM-105.

1. Introduction An energetic material is a reactive material that contains a great amount of potential energy, which proved beneficial to the developments of aerospace industry, mineral exploitation and military applications,1-3 through controllable energy release. However, the energy release is a complex process that refers to physical changes and chemical reactions. Unexpected energy release reactions of energetic materials occur frequently due to poor storage conditions or unexpected external stimuli and result in immeasurable losses.4 Therefore, it is necessary to understand the complicated behaviors of the physical and chemical events during energy release to control the risk during usage and storage. Thermal decomposition mechanism, which was proposed to describe the complicated behaviors of energetic materials during decomposition, proved extremely important for the evaluations of thermal reactivity, sensitivity and storage properties.5 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) is a new type of thermally stable,

relatively

insensitive

energetic

material

with

81%

the

energy

of

1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX).6 The energy, power and thermal stability of LLM-105 make it very promising for many applications, including insensitive boosters and detonators.7 Thermal decomposition of LLM-105 has been frequently investigated since it was synthesized for the first time in 1995. Kinetic parameters such as the activation energy, the pre-exponential factor and the reaction model, are repeatedly


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reported. The kinetic analyses in these reports were largely developed based on the single step reaction assumption and produced dissimilar results.8-11 Since the thermal decomposition of LLM-105 exhibited complex global kinetic behavior and involved multiple individual reactions,

9-13

the commonly used kinetic analysis methods, which

were based on the single step reaction hypothesis, were insufficient to obtain the precise kinetic parameters. In recent years, many effective kinetic calculation methods were proposed and examined, to interpret the thermoanalytical data of these multistep reactions.14-17 In particular for reactions with superposed thermoanalytical signals, the methods proposed by N. Koga18-19 and N. V. Murevyev20 have been successfully applied to the analysis of thermal decomposition behavior of sodium percarbonate, tin (II) oxyhydroxide and ammonium dinitramide. In this paper, the kinetic deconvolution methodology was utilized to study the kinetics of the LLM-105 decomposition. The overall thermal decomposition reaction of LLM-105 was separated into two exothermic reaction steps through kinetic data that were derived from simultaneous DSC-TG tests. These two processes were independently studied with both isoconversional and combined kinetic analysis methods. The validity of the resulting kinetic parameters and the proposed kinetic model was tested through mathematical and experimental methods, respectively.

2. Theoretical background 2.1 Single-step reaction For a solid-state reaction, A (solid) → B (solid) + C (gas), the fractional conversion



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α at a given time (or given temperature) is expressed as: 𝑚𝑖 ― 𝑚𝑡

(1)

α = 𝑚𝑖 ― 𝑚𝑓

where 𝑚𝑖 is the mass of sample prior to solid-state reaction, 𝑚𝑡 is the sample mass at time t during reaction and 𝑚𝑓 is the sample mass after reaction. The rate of conversion (dα/dt) is usually expressed as: 𝑑𝛼 𝑑𝑡

𝐸𝑎

= 𝐴𝑒

― 𝑅𝑇

𝑓(𝛼)

(2)

where R is the universal gas constant, T is the absolute temperature at time t, A and Ea are the apparent values of Arrhenius pre-exponential factor and activation energy, respectively. f(α) is the kinetic model function that describes the physico-chemical and physico-geometrical reaction mechanisms. Table S1 in ESI presents certain most commonly used kinetic models found in literature. As the solid-state reactions tend to occur in multiple steps that have different reaction rates, the mechanisms are often too complicated to be characterized through a simple kinetic model. In order to obtain the kinetic parameters of the reaction, many isoconversional methods or model-free methods are often used. The Friedman isoconversional method is a widely used differential method that provides actual values of the activation parameters, rather than the average over a temperature interval.21 The logarithmic form of Eq. (2) is: ln

𝑑𝛼

𝐸𝑎

𝑑𝑡

𝑅𝑇

( ) = ln (𝐴𝑓(𝛼)) ―

(3)

The apparent activation energy values Ea at different α values can be calculated from the slope of the ln(dα/dt)) versus 1/T plots at constant α values.


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Eq. (3) can be rewritten in another form: ln

(

) = ln 𝐴 ―

𝑑𝛼

𝑑𝑡 /𝑓(𝛼)

𝐸𝑎

(4)

𝑅𝑇

When an appropriate f(α) is selected for the analysis, the plot of ln(dα/dt)/ f(α)) versus 1/T will yield a straight line. Therefore, it is an effective method for the screening of the appropriate kinetic model function. A modified Sestak-Berggren model22 with two kinetic exponents, f(α) = cαm(1-α)n, is widely used since it can fit every kinetic ideal model proposed for solid-state reactions through the c, m and n parameters adjustments. ln

[( )/𝛼 𝑑𝛼

𝑚

𝑑𝑡

]

𝐸𝑎

(1 ― 𝛼)𝑛 = ln (𝑐𝐴) ― 𝑅𝑇

(5)

The kinetic parameters can then be determined by the combined kinetic analysis of experimental data23. Through the simultaneous value optimizations of m, n, cA and Ea, the best linear correlation coefficient of ln[(dαi/dt)/ αim(i)(1-αi)

n(i)]

versus T-1 could be

determined. The pre-exponential factor and activation energy will be deduced through the intercept and the plot slope, respectively. 2.2 Two-step reaction For a two-step decomposition process that is partially overlapped, the ratio of the mass-loss value to the thermal effect for the two steps is different. Therefore, each reaction step contributes differently to the total weight loss and thermal effect of the entire reaction. dα

dα1

d𝑡

d𝑡

dα

dα1

d𝑡

d𝑡

( )DSC = 𝛾 ( )DTG = 𝜂

dα2

+(1 ― 𝛾) d𝑡

dα2

+(1 ― 𝜂) d𝑡

(6) (7)

where  and η are the contributions of the first reaction step determined on the basis



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of DSC and DTG curves, respectively. 20

N. V. Muravyev et al.

employed a useful method for the kinetic parameters

determination of a chemical decomposition reaction by differentiating the overlapping thermoanalytical events. The basis for this procedure is:

(dαd𝑡 )DSC 𝛾dαd𝑡1 + (1 ― 𝛾)dαd𝑡2 𝑃 = dα = dα1 ( d𝑡 )DTG 𝜂 d𝑡 + (1 ― 𝜂)dαd𝑡2

(8)

The proportionality P could be a function of temperature T or conversion degree α. Since the two reaction steps are partially overlapping, the contribution of the second reaction step at the beginning of the entire reaction could be ignored. Consequently, the Pbeginning value equals to /η. Similarly, the contribution of the first reaction step at the final stage of the entire reaction could also be ignored and Pfinal = (1- )/(1-η). Following, the values of  and η could be calculated based on the Pbeginning and Pfinal values. According to Eqs. (6) and (7), the normalized reaction rates of each component at different temperatures can be calculated: dα1 d𝑡

1―𝜂

= 𝛾―𝜂

dα2 d𝑡

[( ) ― ( ) ] [ ( ) ―( ) ]

𝛾

= 𝜂―𝛾

dα

1 ― 𝛾 dα

d𝑡 DSC

1 ― 𝜂 d𝑡 DTG

𝜂 dα

dα

𝛾 d𝑡 DSC

d𝑡 DTG

(9) (10)

The plot of dαi/dt versus T-1 presents the kinetic information of the separated reaction, whereas consequently the analysis of the two-step decomposition via Friedman method and combined kinetic analysis method could be simplified.

3. Experimental In this paper, crude LLM-105 was synthesized through the method reported by


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Pagoria,6 and subsequently refined to 99.0% of purity through recrystallization from dimethyl sulfoxide. Simultaneous thermogravimetric (TG) and differential scanning calorimetry (DSC) analyses of the samples were performed with a NETZSCH STA 449C instrument under nitrogen gas atmosphere (30 mL min-1). Sublimation of LLM-105, which constituted a mass-loss step accompanied by the endothermic effect, would occur far below its decomposition temperature.24 To reduce the signal interference, caused by the sublimation process for the thermal decomposition evaluation, an encapsulated aluminum pan with a low-sized pinhole was selected. The measurements of approximately 4.0 mg of LLM-105 samples were carried out from room temperature to 530 K at 10 K min-1. Following, the samples were heated to 650 K at four specified heating rates of 0.1 K min-1, 0.2 K min-1, 0.5 K min-1 and 1.0 K min-1, respectively. LLM-105 particles at different decomposition stages were obtained through heating to different temperatures at 0.1 K min-1.The morphologies of these LLM-105 particles were subsequently analyzed and characterized through scanning electron microscopy (SEM, CamScan Apollo300).

4. Results and discussion



Fig. 1 Typical TG/DTG-DSC curves for thermal decomposition of LLM-105 at β = 1 K min-1 under N2 atmosphere.

Fig. 1 presents the typical TG/DTG-DSC curves for LLM-105 heated at 1 K min-1 under N2 atmosphere. The slight weight loss without apparent heat release in the initial segment of the TG curve (T < 570 K, Fig. 1) indicated the occurrence of LLM-105 sublimation. The initial thermal decomposition reaction of LLM-105 would be affected by the sublimation, due to its opposite thermal effect on thermal decomposition. 19 As the reaction progressed, the ratio of mass loss due to sublimation to the mass loss due to decomposition gradually decreased and the effect of sublimation dropped to negligible magnitude. The DSC curve indicated that the thermal decomposition of LLM-105 was a partially overlapping two-step exothermic process, accompanied by a two-step mass-loss process, which could be clearly observed from the DTG curve. In the final stage of the second reaction step, the DSC curve drastically dropped to the baseline, which has been rarely observed in the DSC curves of other commonly used energetic materials, such as TNT, HMX, RDX, and TATB25-28. This abnormal asymmetry of the second reaction process might be caused by the sudden cease of this decomposition step following its maximum being reached. The consecutive mass loss curve demonstrated that approximately 80% of the sample was converted to gaseous products during the exothermic process under these experimental conditions, as demonstrated by the mass loss in the TG curve. The TG-DSC curves systematically shifted to lower temperature regions as the heating rate β decreased from 1 to 0.5, 0.2 and 0.1 K min-1 (Fig. S1 in ESI).


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Since the decomposition reaction of LLM-105 consisted of several overlapping reactions, it was helpful to separate the constituent steps of the entire reaction process to simplify the kinetic analysis. According to the method employed by Muravyev20, P value variations with α at different heating rates were calculated through Eq. (8) (Fig. 2). The trends of these curves of P versus α were consistent. The P value presented a rapid increase in the very early stage of the reaction process (α ≤ 0.05), due to the sublimation influence reduction. When the influence of sublimation became negligible, the P value reached its maximum value (P = 1.99) and became stable within a very short stage (0.05 < α ≤ 0.08), followed by a gradual decrease in the latter reaction stage (0.08 < α ≤ 0.64) until a constant value was reached (P = 0.56, 0.64 < α ≤ 0.90). The P value displayed a low fluctuation in the final stage of the reaction step (α > 0.05), which might be due to a sharp drop at the end of the DSC curve. For an individual reaction step, the equal mass change corresponded to equal thermal effect and the P would be a constant. The fixed P value in the conversion degree range of 0.05 < α ≤ 0.08 implied that other reaction steps except for the first decomposition reaction step, could be neglected in this range. Similarly, the contribution of other reaction steps except for the second decomposition reaction step, could be ignored in the range of 0.64 < α ≤ 0.90. All the mass changes and thermal effects in the main reaction stage (0.05 < α < 0.9) were assumed to be caused by the first and second decomposition reaction steps, while the effects of other reactions were negligible. Thus, the contribution of the first reaction step to the thermal effect and mass change was determined to be   0.6 and η  0.3, respectively.



Fig. 2 Dependence of P value on conversion degree α for decomposition of LLM-105, recorded at different heating rates.

As described by Muravyev,20 the DTG and DSC data were assumed to reflect the same component reactions and their sequence. The partially overlapping two-step reactions could be deconvoluted through the combined use of DTG and DSC data without the possible interactions consideration among the component reaction steps. Through the substitutions of   0.6 and η  0.3 values into Eqs. (9) and (10), the main kinetic stage could be deconvoluted into two separated exothermic reaction steps (Fig. 3). It must be noted that  and η were calculated based on the P values at the beginning and end of the main kinetic stage (0.05 < α < 0.9). These two separated kinetic curves were valid in this range only. The separated kinetic curves in Fig. 3 revealed the net kinetic behaviors of each reaction step at four different heating rates. The apparent shape of the reaction step shifted to higher temperature as the β increased, which meant that the conversion rate increased as the heating rate increased. Besides, the conversion rate increased in the first half of the first decomposition step and decreased in the latter half, while the conversion


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rate continued to increase in the main reaction stage as the second decomposition reaction progressed.

Fig. 3 Differential kinetic data for first (a) and second (b) decomposition reaction steps of LLM-105.

The kinetic information for the first and second reaction steps was reflected in the respective parts. The kinetic analysis, based on the separated kinetic data presented in Fig. 3, was considered to be more applicable compared to the original kinetic data. According to the Friedman method (Eq. (3)), the apparent activation energy Ea values of the overall reaction step (Fig. S3) and two separated reaction steps (Fig. S4, certain values of the first step in the final part were insufficient, due to the bad linear fit) at different α were calculated. The Ea values ranged from 188.6 kJ mol-1 to 262.5 kJ mol-1.



The apparent activation energy of the overall reaction step, Ea,O, increased gradually at first and reached a maximum value of 252.0 kJ mol-1 at α = 0.37. Subsequently, the Ea,O presented another peak value of 247.8 kJ mol-1 at α = 0.90, followed by a sharp drop. The average value of Ea,O was 237.9 ± 10.5 kJ mol-1. The apparent activation energy of the first step, Ea,1 and the apparent activation energy of the second reaction step Ea,2, which were derived from the valid differential kinetic data in Fig. 3, exhibited completely different change trends. The Ea,1 value gradually increased in the wide α1 region (0 < α1 ≤ 0.7) , followed by a dramatic decrease in the latter reaction stage (0.7 < α1 ≤ 0.9). The average Ea,1 value over the main reaction stage (0.1 < α1 ≤ 0.9) was 216.3 ± 8.9 kJ mol-1. The Ea,2 value presented a steady increase in the initial stage (α2 ≤ 0.1) and subsequently fluctuated between 231.3 and 262.5 kJ mol-1 in the main reaction stage (α2 ≤ 0.84) . The average value of Ea,2 was 245.9 ± 6.2 kJ mol-1, which was higher than the apparent activation energy in the first decomposition step. Since the apparent activation energy of the first reaction step was lower compared to the second reaction step, it was possible to obtain the product of the first reaction step through the reaction temperature control. This was helpful to methodically study the thermal decomposition and mechanism of LLM-105.


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Fig. 4 Ea values of overall reaction step and two separated reaction steps at different temperatures T (temperature corresponded to conversion degree α at 1 K min-1) through Friedman method.

According to the relationship between α and T (Figs. S2 and S5) at a certain heating rate, the Ea values at different α could be plotted in the same temperature range. Fig. 4 presents the Ea values for the entire reaction step and two separated reaction steps at different temperatures T (temperature corresponded to conversion degree α at 1 K min-1). The shape of the Ea,O versus T curve was similar to the DSC curve shape at the same heating rate. This could be explained as the concurrent and/or consecutive reactions simultaneously occurring during the entire reaction, while the resulting activation energy value corresponded to the average of different overlapping processes. The activation energy of the first-step reaction increased first and consequently decreased, while the activation energy of the second-step reaction only fluctuated in a very small range during the entire reaction. The first and the second steps overlapping in the same temperature region could be clearly observed in Fig. 4. In this temperature region, the activation energy of the first reaction step rapidly decreased, while the activation energy of the



second reaction step increased. This signified that a significant interaction existed between the two reaction steps. The activation energy derived from the second separated reaction step agreed with the Ea value calculated from the original kinetic data, while the Ea,1 value was slightly lower than the Ea,O value at the same temperature. This was because the thermal effect of the sublimation in the total reaction process had an adverse influence on the activation energy calculation, while the influence of sublimation was excluded in the first separated reaction step when it was derived from the P value calculation. Therefore, the Ea,1 value was more suitable to describe the thermal decomposition. Through the comparison of the above isoconversional analysis of the original kinetic data and the valid separated kinetic data, it was indicated that the separation of the component steps was a reliable method to characterize the LLM-105 decomposition reaction kinetics. Detailed kinetic analysis of each separated reaction step was further conducted through the combined kinetic analysis29 using the Sestak-Berggren model with two kinetic exponents (Eq.(5)).


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Fig. 5 Best linear correlations of ln[(dαi/dt)/ αim(i)(1-αi) n(i)] versus T-1 for each reaction step including all kinetic data recorded at different β.

Fig. 5 presents the combined kinetic analysis plots of ln[(dαi/dt)/ αim(i)(1-αi)

n(i)]

versus T-1 for each reaction step. The valid kinetic data of each step recorded at different heating rates were substantially fitted to a straight line through the simultaneous parameter optimizations (mi, ni, ciAi, and Ea,i). The activation energy and pre-exponential factors that were deduced from the slope and the intercept, as well as the correlation coefficients and two kinetic exponents (m, n) are listed in Table 1. The activation energy values of the first and second steps evaluated through the combined kinetic analysis were 222.2 ± 0.5 kJ mol-1 and 244.5 ± 0.5 kJ mol-1, respectively. These values were compatible with the average activation energy values that calculated through the isoconversional method. The high activation energy values were consistent with the good thermal stability of LLM-105, which might be attributed to the reversible hydrogen transfer that could buffer the external thermal stimuli.30 The kinetic models of the first



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and second reaction steps obtained through the combined kinetic analysis were f1(α1) = cα10.62(1-α1)0.71 and f2(α2) = cα20.45(1-α2)0.50, respectively. Table 1 Average activation energies, pre-exponential factors, correlation coefficients, n and m values for two reaction steps, as obtained through the combined kinetic analysis. Step 1

Step 2

Ea (kJ mol-1)

222.2 ± 0.5

244.5 ± 0.5

ln(cA(s-1)

46.1

49.6

r

0.987

0.989

m

0.62

0.45

n

0.71

0.50

To verify the kinetic parameters that determined through the combined kinetic analysis, the overall kinetic data derived from DTG and DSC were reconstructed with a weighted sum of the two separated reaction steps, with the respective contributions of η ≈ 0.3 and  ≈ 0.6. dα

𝐸𝑎, 1

d𝑡

𝑅𝑇

𝐸𝑎, 2

( )DTG = 𝜂𝐴1exp ( ― )𝑐1𝛼𝑚1 (1 ― 𝛼1)𝑛 +(1 ― 𝜂)𝐴2exp ( ― )𝑐2𝛼𝑚2 (1 ― 𝛼2)𝑛 1

1

2

2

𝑅𝑇

(11) dα

𝐸𝑎, 1

d𝑡

𝑅𝑇

𝐸𝑎, 2

( )DSC = 𝛾𝐴1exp ( ― )𝑐1𝛼𝑚1 (1 ― 𝛼1)𝑛 +(1 ― 𝛾)𝐴2exp ( ― )𝑐2𝛼𝑚2 (1 ― 𝛼2)𝑛 1

1

𝑅𝑇

(12)


2

2

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Fig. 6

Curves of differential kinetic data for (dα/dt)DTG (a) and (dα/dt)DSC (b), as determined

through experimentation (symbols) and kinetic parameters, calculated through combined kinetic analysis method (solid lines).

Fig. 6 presents the kinetic curves derived from the experiments as well as the simulated kinetic curves, reconstructed according to Eqs. (11) and (12), with parameters that were determined through the combined kinetic analysis. It was discovered that the deviation among the reconstructed and experimental curves was low, while the deviation increased as the heating rate increased. Although there was a slight deviation, possibly due to the data rounding, the reconstructed curves fit the experimental results well and demonstrated the validity of the kinetic parameters, as obtained from the combined



analysis.

Fig. 7 Comparison of experimental master plots of each reaction step with certain theoretical kinetic models, as listed in Table S1.

To obtain more insight into the mechanism of the two decomposition reaction steps, the plots of the fi(αi) functions determined through the combined kinetic analysis for the two exothermic processes and the curves of several selected theoretical kinetic models listed in Table S1 were compared, as presented in Fig. 7. It was observed that the resulting kinetic model determined for the first step was in good agreement with the Avrami-Erofeev (A3) reaction model, which was used to describe the thermal decomposition reaction of energetic materials, such as PETN, AP and HMX.31-33 Although the experimental master plot of the second reaction did not perfectly conform to any simple theoretical kinetic model, it also had a typical degradation trend of random nucleation and growth mechanism. Since the theoretical models were proposed under certain assumptions with ideal conditions, the derivations of the experimental master plots from the ideal models could be understood.


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Fig. 8 SEM images of LLM-105 at different stages of decomposition

The random nucleation and growth mechanism could be verified through experimental observations of the morphological changes of LLM-105 during the decomposition. LLM-105 particles at different decomposition stages were obtained through the sample heating to a certain temperature at a very low heating rate (Fig. S6 and Table S2). Fig. 8 presents the SEM morphology of LLM-105 at different decomposition stages. It was found that the shape of LLM-105 particles was irregular and the particle size was approximately several micrometers. As it could be observed from Fig. 8a, the surfaces of the initial LLM-105 particles were relatively smooth. When the decomposition reaction began, cracks occurred on the surfaces of LLM-105 particles (Fig. 8b). As the cracks increased in size, a high number of low-sized round particles of dozens of nanometers in size were randomly dispersed near the crystal surface, which were considered to be the nuclei of decomposition product (Fig. 8c). As the reaction



proceeded further, the reactants around the nuclei were continuously consumed while the nuclei grew into particles of hundreds of micrometers. Also, voids were formed in-between particles (Fig. 8d-e). At the end of the reaction, a porous structure that still maintained its original shape was formed (Fig. 8f). It was observed that the adopted nucleation and growth mechanism was quite suitable for the thermal decomposition description of LLM-105, which also confirmed the validity of the calculated kinetic parameters. The present kinetic analysis provides insights into the thermal degradation of LLM-105 and other similar reactions with overlapping thermal signals. The determination of the contributions of different reaction steps to the overall process, reaction mechanism and other relative kinetic features would help to control the products, phase, heat release and rate of the overall reaction process by adjusting the experimental conditions. Such control over the reaction is very important in many areas, including product management and safety assessment.

5. Conclusion In conclusion, the thermal decomposition of LLM-105 was studied through detailed analysis of the TG-DSC experimental data. The partially overlapping two-step exothermic process presented in the DSC curve was separated into two individual steps through a deconvolution method. Through kinetic analysis of the two individual steps with combined kinetic analysis methods, it could be concluded that the average activation energy value of the first step (222.2 ± 0.5 kJ mol-1) was lower compared to the second


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step (244.5 ± 0.5 kJ mol-1). This meant that product of the first reaction step was obtainable through the reaction conditions control. As these kinetic parameters were rigorously validated on the basis of curve reconstruction of the differential kinetic data, the kinetic models of the two individual steps were derived from the master plot method based on these kinetic parameters. The kinetic models of the two decomposition reactions were in agreement with the Avrami-Erofeev (A3) reaction model, which meant that both reaction steps obeyed the nucleation and growth mechanism. This was confirmed through the SEM observations of the LLM-105 particle morphology at different decomposition depths. These results contributed to an improved understanding of the decomposition of LLM-105 and should be instructive for its safe storage and use.

Supporting information available Kinetic functions (Table S1), TG-DSC curves at different heatig rates (Fig. S1), Experimental α-T curves (Fig. S2), Ea values of overall reaction step (Fig.S3) and each separated reaction step i (Fig.S4) at different α, Conversion degree αi of each separated reaction step i (Fig.S5), DSC/TG curves (Fig.S6) and conversion rate (Table S2) of LLM-105 samples heated to different temperatures.

Corresponding Author Y. Liu, email: [email protected]; Tel: 86-816-2493145. J. Li, email: [email protected]; Tel: 86-816-2492025.

Acknowledgements This work was supported by the National Natural Science Foundation of China



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(Grant No. 11572295, 11672273, 11372290 and 21703216).

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Kinetic Analysis of Overlapping Multistep Thermal Decomposition of 2

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