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HMX co-crystal for thermal safety prediction
Accepted Manuscript Title: Kinetic model of thermal decomposition of CL-20/HMX co-crystal for thermal safety prediction Authors: Lang Zhao, Ying Yin, Heliang Sui, Qian Yu, Shanhu Sun, Haobin Zhang, Shunyao Wang, Liping Chen, Jie Sun PII: DOI: Reference:
S0040-6031(18)31164-X https://doi.org/10.1016/j.tca.2019.02.001 TCA 78217
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
14 December 2018 27 January 2019 1 February 2019
Please cite this article as: Zhao L, Yin Y, Sui H, Yu Q, Sun S, Zhang H, Wang S, Chen L, Sun J, Kinetic model of thermal decomposition of CL20/HMX co-crystal for thermal safety prediction, Thermochimica Acta (2019), https://doi.org/10.1016/j.tca.2019.02.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Kinetic model of thermal decomposition of CL-20/HMX co-crystal for thermal safety prediction
Lang Zhao a,b, Ying Yin a,*, Heliang Sui a, Qian Yu a, Shanhu Sun a, Haobin Zhang a, Shunyao Wang c,
a
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Liping Chen c, Jie Sun a,*
Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang Sichuan 621900,
b
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China
School of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang
Sichuan 621010, China c
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Department of Safety Engineering School of Chemical Engineering, Nanjing University of Science and
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Technology, Nanjing Jiangsu 210094, China
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* Corresponding author.
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E-mail address: [email protected] (J. Sun); [email protected] (Y. Yin)
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Highlights
Thermal behavior of CL-20/HMX co-crystal was systematically investigated.
The thermal kinetic model with two parallel autocatalytic paths was identified.
Thermal hazard indicators of CL-20/HMX co-crystal were successfully predicted.
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ABSTRACT
To promote the practical application of CL-20/HMX co-crystal, the understanding of its
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thermal decomposition kinetics and thermal hazard prediction are highly required. In this study, the kinetic model was evaluated based on the non-isothermal DSC data by using non-linear optimization method, which was identified as a complicated reaction comprising two parallel autocatalytic paths, and the contribution of the two reaction paths was revealed to vary depending on the heating rate. Based on the kinetic model, the thermal hazard simulation indicates that the temperature when the occurrence of thermal decomposition after 24 hours (Td,24) of CL-20/HMX co-crystal is 151.64 °C, and the critical temperature of 1000th second
explosion is determined as ~196 °C. Besides, simulation results of self-accelerating decomposition temperature demonstrate1 that the package mass of CL-20/HMX co-crystal, rather than the package material, has a remarkable effect on the thermal safety of CL-20/HMX co-crystal.
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Keywords: CL-20/HMX co-crystal, Kinetic model, Thermal safety prediction
1. Introduction
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In recent years, the kinetic-based simulation approach to evaluate the thermal safety of
energetic materials has attracted extensive attention due to its versatility and flexibility [1-3]. Especially, for the new energetic materials in the stage of laboratory research, the theoretical
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simulation is considered as a necessary tool because the amount of new energetic material
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cannot support the thermal hazard experiments which usually require large scaled samples [4].
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As a typical new energetic material, CL-20/HMX co-crystal has been discovered as a very promising explosive owing to its high energy (9484 m/s) and low mechanical sensitivity
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(similar to -HMX) [5-7]. Notably, CL-20/HMX co-crystal has a unique crystal structure
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formed by orderly arrangement of CL-20 and HMX molecules through hydrogen bonds and intermolecular forces, which makes it effectively mediate the energy and sensitivity of pure CL-20 and HMX explosives [5, 8-10]. To date the studies on CL-20/HMX co-crystal mainly
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focuses on theoretical calculation [10] and new synthesis methods [7, 9, 11]. However, to promote its practical application, the understanding of thermal decomposition kinetics and the
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thermal safety prediction of CL-20/HMX co-crystal are still highly required. Additionally, the unique crystal structure of CL-20/HMX co-crystal comprising two kinds of energetic molecules may exhibit a distinct decomposition behavior from that of normal energetic
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crystals consisted of a single kind of molecule [10, 12, 13], which makes it a challenge to accurately describe its thermal behavior by a reasonable kinetic model. Driven by this, in this study we combined DSC, in-situ XRD, and isothermal ARC to systematically analyze the thermal behavior and decomposition reaction type of CL-20/HMX co-crystal, and the reaction kinetic model was then evaluated on the basis of non-isothermal DSC data at several heating
rate by using non-linear optimization method. Finally, based on the reaction kinetic model, thermal hazard indicators such as adiabatic time to maximum rate (TMRad), time to conversion limit (TCL), and self-accelerating decomposition temperature (SADT) were predicted to provide necessary safety information concerning the usage and storage of CL-20/HMX co-crystal. 2. Experimental and methods
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2.1 Materials
CL-20/HMX co-crystal was supplied by the Institute of Chemical Materials, China
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Academy of Engineering Physics (CAEP). A “solvent-media recrystallization” method was
employed to obtain CL-20/HMX co-crystal by using -CL-20 and -HMX as raw materials. The experimental details can be found in references [5, 8].
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2.2 Differential scanning calorimeter (DSC)
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Non-isothermal DSC experiments were measured on a PHOENIX DSC 204 HP
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instrument. About 0.8-1.2 mg sample were loaded in a 40 μL aluminum crucible, and the temperature range is set from 30 °C to 280 °C at the heating rate of 0.2, 0.4, 0.6, 0.8, 1, 2, 5,
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10 °C/min. Isothermal DSC experiments were carried out on PerKinElmer, DSC 8500 with
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the isothermal temperature set as 232 °C and 240 °C, respectively. During the DSC experiments high purity nitrogen (99.999%) was used as protective carrier gas with a flow rate of 30 ml min-1.
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2.3 Isothermal accelerating rate calorimeter (ARC) Isothermal ARC with Heat-Wait-Seek (H-W-S) mode was performed on the ARC
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instrument (es-ARC, Thermal Hazard Technology Company) and the 1/4-inch standard Ti-LCQ bomb was used for sample loading. Briefly, ~100 mg sample was placed in the Ti-LCQ bomb and then was quickly heated to 185 °C. By using highly sensitive pressure
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sensor, the amount of gas production from the thermal decomposition of CL-20/HMX co-crystal can be readily recorded as pressure signal. 2.4 In-situ X-ray diffraction (XRD) XRD was recorded on a Bruker D8 Advance with CuKα radiation (λ = 1.5419 Å), equipped with a vantec-1 detector and operated under the condition of 40 kV/40 mA. 2θ of XRD was set from 5 °C to 50 °C with scanning step of 0.02°/0.5s. In-situ XRD was used to
study the crystal structure of the co-crystal sample under different temperature. The temperature range ranged from 30 °C to 185 °C with a temperature step of 20 °C, and in each step the temperature maintained for 30 min and then the XRD pattern of sample was recorded. 2.5 Critical temperature of thermal explosion in 1000th second Critical temperature of thermal explosion in 1000th second was tested according to the relevant Chinese National Military Standards [14]. Specifically, quantitative samples were
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compacted and sealed in the detonator shell under vacuum, and then were heated in alloy
Wood’s metal bath. Ten consecutive tests were performed near the alloy Wood’s metal bath
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temperature of 1000 seconds delay period. The highest temperature of nonoccurrence of
thermal explosion of ten consecutive tests was recorded as the critical temperature of thermal explosion in 1000th second.
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3. Results and discussions
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3.1 Determination of the reaction kinetic model
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Fig. 1. (a) dynamic DSC data on heating rates from 1 K/min and 10 K/min; (b) in-situ XRD patterns of CL-20/HMX co-crystal from 30 °C to 185 °C.
Initially, non-isothermal DSC analysis was employed to investigate the thermal decomposition behavior of CL-20/HMX co-crystal. As can be seen in Fig. 1a, CL-20/HMX co-crystal exhibits only an exothermal peak at heating rates of 1 and 10 K/min, but no endothermic process can be observed. This indicates that CL-20/HMX co-crystal did not
undergo a phase transformation or melting process before thermal decomposition. To verify this, in-situ XRD was performed to examine the crystal stability of CL-20/HMX co-crystal (Fig. 1b). It demonstrates that with the increasing temperature the XRD peaks of co-crystal gradually move to lower angle due to the thermal expansion of crystal lattice, but no emergence of any new diffraction peaks indicates that the co-crystal can well remain its crystal structure during the heating process. This phenomenon is interesting because -CL-20
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and -HMX used as raw materials to synthesize CL-20/HMX co-crystal are both known as to be unstable at high temperature [15-17]. Specifically, -HMX crystal exhibits two
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endothermic processes corresponding to -phase transition and melting, respectively [15, 17], while -CL-20 transforms from cubic to tetragonal phase (-before thermal decomposition [15, 16]. Therefore, the thermal decomposition of HMX and CL-20 are
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proposed as solid-liquid coupling state or multiple phases, and in that case, the kinetic
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parameters obtained from coexistence of several states at high temperature are of little (if any)
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value for the thermal safety prediction of the solid-state samples at relative low temperature [3, 18]. In contrast, the inherent consistency in phase structure and solid-state of CL-20/HMX
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co-crystal before thermal decomposition makes it an ideal candidate for kinetic analysis and
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thermal safety prediction.
Fig. 2. (a) Isothermal DSC measurements for 232 °C and 240 °C; (b) Isothermal ARC measurement at 185 °C. Inset is the dP/dt-t curve derived from the differentiation of P-t curve (decomposition section).
Next, in order to determine whether the thermal decomposition of CL-20/HMX co-crystal is N-order or autocatalytic reaction, isothermal DSC experiments were carried out with the temperature set at 232 °C and 240 °C, respectively (Fig. 2a). It demonstrates that the
curves of exothermic rate versus time of the sample show a “bell-shaped” characterization, indicating that the sample always needs a period of induction to reach the highest exothermic rate. This characterization is considered as the typical feature of autocatalytic reaction [18-20], in which the decomposition products continuously accumulate and act as catalysts for the decomposition reaction, leading to the gradual acceleration of decomposition rate and a peak value can be approached after a certain period of time [21-23]. Then, the decomposition rate
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gradually decreases due to the consumption of reactants and eventually results in a
“bell-shaped” curve. To further confirm the autocatalytic behavior, isothermal ARC
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experiments were also carried out. The pressure of the bomb under isothermal 185 °C was plotted as the function of time (P-t curve, Fig. 2b), and the obvious rising of P-t curve at
184.96 °C indicates the gas products were released from thermal decomposition. To derive the
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pressure rising rate (dP/dt-t), the decomposition section of P-t curve is smoothed and
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differentiated and the dP/dt-t curve can be obtained as shown in the insert of Fig. 2b. Similar
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to the exothermic rate curve, the dP/dt-t also exhibits a “bell-shaped” feature with the maximum value achieved after a period of induction. Therefore, the collective results of
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typical autocatalytic reaction.
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isothermal experiments reveal that the thermal decomposition of CL-20/HMX co-crystal is a
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Fig. 3. Comparison between experiment and simulation of (a) heat production rate s temperature.
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Insert is the enlargement of red block diagram; (b) heat production s time for CL-20/HMX co-crystal at higher heating rates; (c) heat production rate s temperature; (d) heat productions time for CL-20/HMX
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co-crystal at lower heating rates.
On the basis of determining the reaction type of CL-20/HMX co-crystal decomposition,
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we performed non-isothermal DSC at several heating rates to evaluate the thermal kinetic parameters. At first, the heating rates of 1, 2, 5, and 10 K/min were chosen and the experimental and simulated results are presented in Fig. 3a and Fig. 3b. It can be seen that
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only the experimental data at low heating rate, i.e. 1 and 2 K/min, are fitted well, while for high heating rates of 5 and 10 K/min, only the first half of the data is processed well (see Fig. 3a). Evidently, their compatibility and matching is very poor, especially at higher heating rate when four exothermic rate curves were dealt with simultaneously. The main reason, accounting for poor compatibility, is probably the violation of temperature uniformity in the co-crystal sample under high heating rates which resulted in a micro-explosion behavior with ultra-high exothermic rate. Therefore, to reveal the inherent kinetic process of thermal
decomposition of CL-20/HMX co-crystal, non-isothermal DSC at lower heating rates (0.2, 0.4, 0.6, 0.8, 1.0 K/min) were performed. As presented in Fig. 3c and 3d, even though five exothermic curves were processed simultaneously, the simulated results demonstrate that the compatibility of DSC experimental data is very reasonable. Besides, the overall heat production is decreasing as the heating rate increased (Fig. 3b and Fig. 3d), which is the evidence of several paths in parallel during the thermal decomposition of CL-20/HMX
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co-crystal. Generally, for the same reaction path, the overall heat released at different scanning rates must be the same and does not vary with the change of heating rates.
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Nevertheless, for the reaction comprising several paths, the final heat generated by the reaction (overall heat) can be observed to depend naturally on the heating rate - either
increases or decreases with the increase of heating rate. Actually, the variable overall heat in
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Fig. 3b and 3d is the indication that we are dealing with complex reaction which comprises
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several paths in parallel or, in other words, initial reagent can undergo decomposition along
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several paths. To more clearly understand this, let’s assume a reaction consisted of several paths, each of paths which consume the reagent has different activation energy and heat effect.
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Thus, the reaction path with smaller activation energy is faster than that with bigger activation
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energy at lower temperatures, while at higher temperature the contribution of path with bigger activation energy continuously increases. It means that depending on temperature range portions of the reagent consumed by each of paths will vary. Moreover, it is known that the
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bigger the heating rate the higher the temperature range of a reaction. Thus, the contribution of heat generated by each of reaction paths will change with diverse heating rates and change
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in contribution of the paths into the overall heat results in variation of the overall heat with different heating rates. Combined with the above analysis, the kinetic model including two parallel autocatalytic
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paths is taken into account, which can be described by generalized autocatalytic reaction (full autocatalysis). It is well known that the reaction rate of n-order reaction (rn) and autocatalytic reaction (rauto) can be described as follows[25]: n-order reaction:
𝑟n = 𝐴n 𝑒 −𝐸n ⁄𝑅𝑇 (1 − 𝛼)𝑛11
autocatalytic reaction: 𝑟auto = 𝐴auto 𝑒 −𝐸auto ⁄𝑅𝑇 𝛼 𝑛21 (1 − 𝛼)𝑛22
(1) (2)
Where the A is the pre-exponential factor, E is the activation energy, n11, n21, n22 is the
reaction order, R is gas constant, T represents temperature, and α is the degree of conversion of samples. For a full autocatalysis, the reaction is comprised of n-order reaction and autocatalysis reaction, which is named as a generalized autocatalysis and can be written as [24, 25]: (3)
z0 = 𝐴𝑛 /𝐴auto
(4)
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𝑟 = 𝑟n + 𝑟auto = 𝐴𝑒 −𝐸⁄𝑅𝑇 (1 − 𝛼)𝑛1 (𝑧0 𝑒 −𝐸𝑧 ⁄𝑅𝑇 + 𝛼 𝑛2 )
E𝑧 = 𝐸n − 𝐸auto
(5)
generalized autocatalytic reaction, which can be described as: 𝑟 = ∑ 𝑟𝑖 𝑟𝑖 = 𝐴𝑒 −𝐸⁄𝑅𝑇 (1 − 𝛼𝑖 )𝑛1 (𝑧0 𝑒 −𝐸𝑧 ⁄𝑅𝑇 + 𝛼𝑖 𝑛2 )
(6) (7)
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𝑑𝛼⁄𝑑𝑡 = ∑ 𝑟𝑖
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In this study, the kinetic model of CL-20/HMX co-crystal includes two parallel
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𝑑𝑄 ⁄𝑑𝑡 = ∑ 𝑄𝑖 𝑟𝑖
(8) (9)
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Where ri, αi and Qi represent reaction rate, degree of conversion and heat production of a
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reaction, respectively, i = 1 and 2, and t is the time.
The kinetic-based model shows a reasonable fitting of the DSC experimental data (Fig.
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3c and Fig. 3d), and the kinetic parameters are listed in Table 1. Accordingly, CL-20/HMX co-crystal exhibits a distinct decomposition behavior from that of individual HMX and CL-20:
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The thermal kinetic model of CL-20/HMX co-crystal is comprised of two parallel autocatalytic reactions, while thermal decomposition behavior of HMX or CL-20 can be
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described by only an autocatalytic reaction [28]. In addition, the activation energy of CL-20/HMX co-crystal, E = 177.41, 245 kJ/mol for 1st and 2nd path, is higher than that of HMX (~ 135 kJ/mol) and CL-20 (~ 128 kJ/mol) [28].
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Table 1 Kinetic parameters of the reaction model for CL-20/HMX co-crystal. Parameters
Units
1st path
2nd path
ln(A)
ln(1/s)
36.20
56.82
E
kJ/mol
177.41
245.68
n1
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0.39
1.08
n2
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0.42
1.65
-
-3.91
-3.21
Ez
kJ/mol
2.26
21.99
Q
J/g
2186.69
1226.49
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ln(z0)
Fig. 4. Contribution of two paths in heat production rate for CL-20/HMX co-crystal decomposition.
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Fig. 5. Contribution of two paths in reaction process at various heating rates for decomposition of CL-20/HMX co-crystal.
Fig. 4 and Fig. 5 reveal the contribution of two paths to the thermal decomposition
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reaction. It shows that the contribution of first path always dominates at various heating rates, but with heating rate increasing, the reaction rate of second path becomes faster (Fig. 4) and its contribution becomes more evident to the total reaction (Fig. 5). This effect may be due to the unique structure of the CL-20/HMX co-crystal in which two different energetic molecules (CL-20 and HMX molecule) are arranging orderly and both of them can decompose and release energy. Besides, the contribution of parallel thermal decomposition will change with diverse heating rates due to their different activation energy and heat production. Note that the
CL-20/HMX co-crystal exhibits only one exothermic peak (Fig. 1a and Fig. 3c), implying that the parallel paths are coupled during the thermal decomposition. 3.2 Thermal safety prediction of CL-20/HMX co-crystal Autocatalytic reactions are usually considered as a dangerous process due to unexpected initiation, sudden heat evolution and explosion [4, 25]. Herein, based on the kinetic-based
prediction of CL-20/HMX co-crystal under different conditions.
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3.2.1 Adiabatic time to maximum rate (TMRad)
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model, non-linear numerically simulation [3, 25-28] was conducted for the thermal safety
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Fig. 6. Adiabatic time to maximum rate (TMRad) s temperature of CL-20/HMX co-crystal.
TMRad is considered as an important thermal safety parameter. Fig. 6a demonstrates the
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simulated TMRad of CL-20/HMX co-crystal and the Td,24 is determined as 151.64 °C. Besides, critical temperature of 1000th second explosion is determined as ~196 °C, agreed well with
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199 °C obtained from the experimental test. The consistency of experimental and simulated results proves the validity of the kinetic model. Moreover, according to the criteria for the assessment of an accident probability suggested by Stossel
[29], the probability of an
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accident is considered to be high if TMRad < 8 h. According to the simulation results, reliable safe temperature of CL-20/HMX co-crystal during actual operation should not be higher than 165 °C. 3.2.2 Time to conversion limit (TCL) In order to evaluate the thermal stability or storage aging life of a substance, TCL was exploited. While conversion of a reaction reaches some predefined value-conversion limit under an isothermal storage environment, estimation of thermal stability is determined by
evaluating the dependency of time instant. Fig. 6b shows the dependencies of TCL on temperature of CL-20/HMX co-crystal predicted on the basis of the kinetic model for different conversion limits. For 0.1% limit value, the result shows that after 65 years at an ideal isothermal storage temperature of 70 °C, the conversion will reach the limit value. For 1% limit value, by contrast, it takes about 243 years for CL-20/HMX co-crystal to meet
indicates that CL-20/HMX co-crystal has good stability in solid state. 3.2.3 Self accelerating decomposition temperature (SADT)
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expiration conditions in an isothermal environment of 70°C. From the above results, it clearly
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SADT is an important parameter for evaluating the thermal hazards during storage and transportation. According to “Recommendations on the Transport of Dangerous Goods,
Manual of Tests and Criteria” from the United Nations [4, 30], SADT is defined as the lowest
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temperature at which an overheating in the middle of specific packaging exceeds 6 °C after a
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lapse of the period of 7 days or less, which was measured from the time when the packing
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center temperature reaches 2 °C below the ambient temperature [4, 31]. To simulate thermal explosions in CL-20/HMX co-crystal, the critical parameters of
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thermal explosion are found numerically in the context of complicated chemical kinetics for
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several types of the reactor and different masses of samples. Considering solid thermal explosion simulation, it is necessary to make the following statement. The process model is as following:
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𝜌𝐶𝑝 (𝜕𝑇⁄𝜕𝑡) = 𝑑𝑖𝑣(𝜆Δ𝑇) + 𝑊,
(10)
𝜕𝛼𝑖 ⁄𝜕𝑡 = 𝑟𝑖 𝑖 = 1, ⋯ , 𝑁𝐶,
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(11)
𝑊 = ∑ 𝑄𝑖∞ 𝑟𝑖
(12)
where ρ is the density; Cp is the specific heat; T is the temperature; t is the time; λ is the
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heat conductivity; α is the degree of conversion of a component; ri is the reaction rate; Qi is the reaction calorific effect; W is the heat power; NC is the number of components; i is the component number. Initial fields of the temperature and conversions are supposed to be constant through the reactor volume: T|t=0 = T0
(13)
αi|t=0 = αi0
(14)
Here, the index 0 marks initial values of the temperature and conversion. The boundary conditions of the third kind can be specified: Newton’s law of heat exchange: −λ(𝜕𝑇⁄𝜕𝑛)|𝑤 = 𝜒(𝑇𝑒 − 𝑇𝑠 )
(15)
Here the letters “e” and “s” relate to the parameters in environment and on the boundary, respectively; n is the unit outer normal on the boundary; 𝜒 is heat transfer coefficient of
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radiation surface.
Assuming that CL-20/HMX co-crystal is stored in barrels (Fig. 7, and the detailed
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parameters of samples and storage containers are listed in Table 2), and the SADT values of
different masses of CL-20/HMX co-crystal stored in different types of barrels were calculated
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with the assistance of Thermal Safety Software (TSS).
Fig. 7. The model for kinetic-based simulation of SADT. (a) The barrel container; (b) CL-20/HMX
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co-crystal stored in the barrel; and (c) temperature distribution of the co-crystal samples (5 kg, polymer barrel). Table 2 Physical performance parameters of CL-20/HMX co-crystal and materials of shells used. Parameters
Barrel
CL-20/HMX co-crystal
Layer thickness (m)
0.01
-
Density ρ (g/cm3)
a
1.945
Void fraction
-
0.10
Specific heat (kJ/(kg·K))
a
0.8266
Thermal conductivity (W/(m·K))
a
0.292
“a” means the value is depend on the specific reference material which is available in TSS software. Table 3 Simulated SADT results of CL-20/HMX co-crystal. SADT (°C)
1
Polymer
144
2
Fe
146
3
Rubber
4
Glass
1
Polymer
2
Fe
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50
Rubber
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Glass
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Material of shell
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5
Package number
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Mass of sample (kg)
144 146 138 139 139 139
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As shown in Table 3, for the same package scale (either 5 kg or 50 kg), the calculated
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SADT values show almost the same with different shell materials of the barrels. For example, when the barrel materials changes from polymer to Fe, the SADT of 5 kg CL-20/HMX co-crystal only increases ~2 oC from 144 oC to 146 oC, and SADT of 50 kg samples slightly
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increases from 138 oC to 139 oC. However, the SADT values can be significantly influenced
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by the package masses of explosive. For same package material and boundary conditions, the effect of package mass on SADT of CL-20/HMX co-crystal values is more remarkable than materials of shell. That is, when CL-20/HMX co-crystal was stored in polymer barrel, the operation temperature should be kept below 144 oC and 138 oC for 5 kg and 50 kg samples,
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respectively. In a word, the scale of the samples, rather than the material of storage container, can significantly affect the SADT of CL-20/HMX co-crystal.
4. Conclusions In this study, the thermal decomposition behavior of CL-20/HMX co-crystal was carefully investigated by DSC, in-situ XRD, and isothermal ARC analysis. The kinetic model
of the thermal decomposition of CL-20/HMX co-crystal was successfully created for the first time, and the kinetic-based simulation was performed to predict the thermal hazard under different conditions. The conclusions are as follows: 1. The non-isothermal DSC and in-situ XRD analysis show that CL-20/HMX co-crystal does not experience a phase transformation or melting process before thermal decomposition, which is quite distinct from pure CL-20 and HMX crystals.
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2. According to the isothermal experimental results, the thermal decomposition of
CL-20/HMX co-crystal is identified as a typical autocatalytic reaction, in which the heat and
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gas production rate undergo an acceleration period to approach the maximum value, followed by a deceleration process.
3. The compatibility of non-isothermal DSC results at high heating rates is found to be
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quite poor, probably due to the violation of temperature uniformity in the co-crystal under
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high heating rates, which resulted in a micro-explosion with ultra-high exothermic rate. In
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contrast, the experimental data at lower heating rates can be fitted well by proper kinetic model, and the thermal decomposition kinetic of CL-20/HMX co-crystal was found to
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comprise two parallel autocatalytic reactions (paths). The contribution of the two parallel
and heat production.
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paths was revealed to vary with diverse heating rates due to their different activation energy
4. Based on the kinetic model, the simulation results show that the Td,24 of CL-20/HMX
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co-crystal is 151.64 °C, and the critical temperature of 1000th second explosion is ~196 °C, agreed well with experimental results (199 °C). Besides, according to TCL, it shows that the
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conversion limit of CL-20/HMX co-crystal at 70 °C will reach 0.1% and 1% after 65 years and 243 years, respectively, indicating good stability of CL-20/HMX co-crystal. 5. The simulated SADT of 5 kg CL-20/HMX co-crystal stored in different types of barrels
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(polymer, Fe, rubber and glass) is ~144 °C, much higher than that of 50 kg samples which is determined as ~138 °C. It demonstrates that the SADT of CL-20/HMX co-crystal can be profoundly influenced by the scale of the samples rather than the material of storage container.
5. Acknowledgments
This work was supported by the National Natural Science Foundation of China
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(No.21805260).
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simulation method for SADT determination based on AIBN benchmark, Thermochim. Acta 621 (2015) 36-43.
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sensitivity and thermal decomposition mechanisms of CL-20/HMX via molecular dynamics simulations, ES Mater. Manuf., 01 (2018) 50-56.
[13] X. Xue, M. Yu, Q. Zeng, C. Zhang, Initial decay mechanism of the heated CL-20/HMX co-crystal: A case of the co-crystal mediating the thermal stability of the two pure components, J. Phys. Chem. C 121 (2017) 4899-4908. [14] F.D. Nie, X.H. Yang, L. Zhang, J. Sun, Q.X. Hu, The sensitivity and the surface characterization of HMX/TATB-based PBX, Chin. J. Expl. Propell. 24(3) (2001) 20-21. [15] O. Ordzhonikidze, A. Pivkina, Y. Frolov, N. Muravyev, K. Monogarov, Comparative study of HMX and
CL-20, J. Therm. Anal. Calorim. 105 (2011) 529-534. [16] R. Turcotte, M. Vachon, Q. S. M. Kwok, R. P. Wang, D. E. G. Jones, Thermal study of HNIW (CL-20), Thermochim. Acta 433 (2005) 105-115. [17] J.-S. Lee, C.-K. Hsu, C.-L. Chang, A study on the thermal decomposition behaviors of PETN, RDX, HNS and HMX, Thermochim. Acta 392 (2002) 173-176. [18] B. Roduit, M. Hartmann, P. Folly, A. Sarbach, A. Dejeaifve, R. Dobson, K. Kurko, Kinetic analysis of solids of the quasi-autocatalytic decomposition type: SADT determination of low-temperature polymorph of
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AIBN, Thermochim. Acta 665 (2018) 119-126. [19] J.M. Tseng, T.C. Wu, T.F. Hsieh, P.J. Huang, C.P. Lin, The thermal hazard evaluation of 1,1-di
(tert-butylperoxy) cyclohexane by DSC using non-isothermal and isothermal-kinetic simulations, J. Loss Prev. Proc. 25 (2012) 703-708.
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decomposition of cumene hydroperoxide at low temperatures, J. Therm. Anal. Calorim. 96 (2009) 751-758. [24] A. Kossoy, T. Hofelich, Methodology and software for assessing reactivity ratings of chemical systems, Process Saf. Prog. 22 (2003) 235–240.
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[25] S.Y. Wang, A.A. Kossoy, Y.D. Yao, L.P. Chen, W.H. Chen, Kinetics-based simulation approach to evaluate thermal hazards of benzaldehyde oxime by DSC tests, Thermochim. Acta 655 (2017) 319-325. [26] A.A. Kossoy, J. Singh, E.Y. Koludarova, Mathematical methods for application of experimental adiabatic
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data – An update and extension, J. Loss Prev. Proc. 33 (2015) 88-100. [27] J.M. Tseng, C.M. Shu, J.P. Gupta, Y.F. Lin, Evaluation and modeling runaway reaction of methyl ethyl
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ketone peroxide mixed with nitric acid, Ind. Eng. Chem. Res. 46 (2007) 8738-8745.
[28] C.P. Lin, C.P. Chang, Y.C. Chou, Y.C. Chu, C.M. Shu, Modeling solid thermal explosion containment on reactor HNIW and HMX, J. Hazard. Mater. 176 (2010) 549-558.
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[31] W.-T. Chen, W.-C. Chen, K.-H. Hsueh, C.-W. Chiu, C.-M. Shu, Thermokinetic parameters analysis for 1,1-bis-( tert -butylperoxy)-3,3,5-trimethylcyclohexane at isothermal conditions for safety assessment, J. Therm. Anal. Calorim. 118 (2014) 1085-1094.
Figure captions
Figure 1. (a) dynamic DSC data on heating rates from 1 K/min and 10 K/min; (b) in-situ XRD patterns of CL-20/HMX co-crystal from 30 °C to 185 °C.
Figure 2. (a) Isothermal DSC measurements for 232 °C and 240 °C; (b) Isothermal ARC
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measurement at 185 °C, inset is the dP/dt-t curve derived from the differentiation of P-t curve (decomposition section).
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Figure 3. Comparison between experiment and simulation of (a) heat production rate s
temperature. Insert is the enlargement of red block diagram; (b) heat production s time for CL-20/HMX co-crystal at higher heating rates; (c) heat production rate s temperature; (d)
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heat productions time for CL-20/HMX co-crystal at lower heating rates.
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Figure 4. Contribution of two paths in heat production rate for CL-20/HMX co-crystal
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decomposition.
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Figure 5. Contribution of two paths in reaction process at various heating rates for decomposition of CL-20/HMX co-crystal.
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Figure 6. Adiabatic time to maximum rate (TMRad) s temperature of CL-20/HMX co-crystal. Figure 7. The model for kinetic-based simulation of SADT. (a) The barrel container; (b)
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CL-20/HMX co-crystal stored in the barrel; and (c) temperature distribution of the co-crystal
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samples (5 kg, polymer barrel).
S0040-6031(18)31164-X https://doi.org/10.1016/j.tca.2019.02.001 TCA 78217
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
14 December 2018 27 January 2019 1 February 2019
Please cite this article as: Zhao L, Yin Y, Sui H, Yu Q, Sun S, Zhang H, Wang S, Chen L, Sun J, Kinetic model of thermal decomposition of CL20/HMX co-crystal for thermal safety prediction, Thermochimica Acta (2019), https://doi.org/10.1016/j.tca.2019.02.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Kinetic model of thermal decomposition of CL-20/HMX co-crystal for thermal safety prediction
Lang Zhao a,b, Ying Yin a,*, Heliang Sui a, Qian Yu a, Shanhu Sun a, Haobin Zhang a, Shunyao Wang c,
a
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Liping Chen c, Jie Sun a,*
Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang Sichuan 621900,
b
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China
School of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang
Sichuan 621010, China c
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Department of Safety Engineering School of Chemical Engineering, Nanjing University of Science and
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Technology, Nanjing Jiangsu 210094, China
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* Corresponding author.
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E-mail address: [email protected] (J. Sun); [email protected] (Y. Yin)
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Highlights
Thermal behavior of CL-20/HMX co-crystal was systematically investigated.
The thermal kinetic model with two parallel autocatalytic paths was identified.
Thermal hazard indicators of CL-20/HMX co-crystal were successfully predicted.
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ABSTRACT
To promote the practical application of CL-20/HMX co-crystal, the understanding of its
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thermal decomposition kinetics and thermal hazard prediction are highly required. In this study, the kinetic model was evaluated based on the non-isothermal DSC data by using non-linear optimization method, which was identified as a complicated reaction comprising two parallel autocatalytic paths, and the contribution of the two reaction paths was revealed to vary depending on the heating rate. Based on the kinetic model, the thermal hazard simulation indicates that the temperature when the occurrence of thermal decomposition after 24 hours (Td,24) of CL-20/HMX co-crystal is 151.64 °C, and the critical temperature of 1000th second
explosion is determined as ~196 °C. Besides, simulation results of self-accelerating decomposition temperature demonstrate1 that the package mass of CL-20/HMX co-crystal, rather than the package material, has a remarkable effect on the thermal safety of CL-20/HMX co-crystal.
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Keywords: CL-20/HMX co-crystal, Kinetic model, Thermal safety prediction
1. Introduction
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In recent years, the kinetic-based simulation approach to evaluate the thermal safety of
energetic materials has attracted extensive attention due to its versatility and flexibility [1-3]. Especially, for the new energetic materials in the stage of laboratory research, the theoretical
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simulation is considered as a necessary tool because the amount of new energetic material
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cannot support the thermal hazard experiments which usually require large scaled samples [4].
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As a typical new energetic material, CL-20/HMX co-crystal has been discovered as a very promising explosive owing to its high energy (9484 m/s) and low mechanical sensitivity
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(similar to -HMX) [5-7]. Notably, CL-20/HMX co-crystal has a unique crystal structure
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formed by orderly arrangement of CL-20 and HMX molecules through hydrogen bonds and intermolecular forces, which makes it effectively mediate the energy and sensitivity of pure CL-20 and HMX explosives [5, 8-10]. To date the studies on CL-20/HMX co-crystal mainly
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focuses on theoretical calculation [10] and new synthesis methods [7, 9, 11]. However, to promote its practical application, the understanding of thermal decomposition kinetics and the
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thermal safety prediction of CL-20/HMX co-crystal are still highly required. Additionally, the unique crystal structure of CL-20/HMX co-crystal comprising two kinds of energetic molecules may exhibit a distinct decomposition behavior from that of normal energetic
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crystals consisted of a single kind of molecule [10, 12, 13], which makes it a challenge to accurately describe its thermal behavior by a reasonable kinetic model. Driven by this, in this study we combined DSC, in-situ XRD, and isothermal ARC to systematically analyze the thermal behavior and decomposition reaction type of CL-20/HMX co-crystal, and the reaction kinetic model was then evaluated on the basis of non-isothermal DSC data at several heating
rate by using non-linear optimization method. Finally, based on the reaction kinetic model, thermal hazard indicators such as adiabatic time to maximum rate (TMRad), time to conversion limit (TCL), and self-accelerating decomposition temperature (SADT) were predicted to provide necessary safety information concerning the usage and storage of CL-20/HMX co-crystal. 2. Experimental and methods
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2.1 Materials
CL-20/HMX co-crystal was supplied by the Institute of Chemical Materials, China
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Academy of Engineering Physics (CAEP). A “solvent-media recrystallization” method was
employed to obtain CL-20/HMX co-crystal by using -CL-20 and -HMX as raw materials. The experimental details can be found in references [5, 8].
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2.2 Differential scanning calorimeter (DSC)
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Non-isothermal DSC experiments were measured on a PHOENIX DSC 204 HP
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instrument. About 0.8-1.2 mg sample were loaded in a 40 μL aluminum crucible, and the temperature range is set from 30 °C to 280 °C at the heating rate of 0.2, 0.4, 0.6, 0.8, 1, 2, 5,
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10 °C/min. Isothermal DSC experiments were carried out on PerKinElmer, DSC 8500 with
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the isothermal temperature set as 232 °C and 240 °C, respectively. During the DSC experiments high purity nitrogen (99.999%) was used as protective carrier gas with a flow rate of 30 ml min-1.
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2.3 Isothermal accelerating rate calorimeter (ARC) Isothermal ARC with Heat-Wait-Seek (H-W-S) mode was performed on the ARC
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instrument (es-ARC, Thermal Hazard Technology Company) and the 1/4-inch standard Ti-LCQ bomb was used for sample loading. Briefly, ~100 mg sample was placed in the Ti-LCQ bomb and then was quickly heated to 185 °C. By using highly sensitive pressure
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sensor, the amount of gas production from the thermal decomposition of CL-20/HMX co-crystal can be readily recorded as pressure signal. 2.4 In-situ X-ray diffraction (XRD) XRD was recorded on a Bruker D8 Advance with CuKα radiation (λ = 1.5419 Å), equipped with a vantec-1 detector and operated under the condition of 40 kV/40 mA. 2θ of XRD was set from 5 °C to 50 °C with scanning step of 0.02°/0.5s. In-situ XRD was used to
study the crystal structure of the co-crystal sample under different temperature. The temperature range ranged from 30 °C to 185 °C with a temperature step of 20 °C, and in each step the temperature maintained for 30 min and then the XRD pattern of sample was recorded. 2.5 Critical temperature of thermal explosion in 1000th second Critical temperature of thermal explosion in 1000th second was tested according to the relevant Chinese National Military Standards [14]. Specifically, quantitative samples were
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compacted and sealed in the detonator shell under vacuum, and then were heated in alloy
Wood’s metal bath. Ten consecutive tests were performed near the alloy Wood’s metal bath
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temperature of 1000 seconds delay period. The highest temperature of nonoccurrence of
thermal explosion of ten consecutive tests was recorded as the critical temperature of thermal explosion in 1000th second.
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3. Results and discussions
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3.1 Determination of the reaction kinetic model
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Fig. 1. (a) dynamic DSC data on heating rates from 1 K/min and 10 K/min; (b) in-situ XRD patterns of CL-20/HMX co-crystal from 30 °C to 185 °C.
Initially, non-isothermal DSC analysis was employed to investigate the thermal decomposition behavior of CL-20/HMX co-crystal. As can be seen in Fig. 1a, CL-20/HMX co-crystal exhibits only an exothermal peak at heating rates of 1 and 10 K/min, but no endothermic process can be observed. This indicates that CL-20/HMX co-crystal did not
undergo a phase transformation or melting process before thermal decomposition. To verify this, in-situ XRD was performed to examine the crystal stability of CL-20/HMX co-crystal (Fig. 1b). It demonstrates that with the increasing temperature the XRD peaks of co-crystal gradually move to lower angle due to the thermal expansion of crystal lattice, but no emergence of any new diffraction peaks indicates that the co-crystal can well remain its crystal structure during the heating process. This phenomenon is interesting because -CL-20
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and -HMX used as raw materials to synthesize CL-20/HMX co-crystal are both known as to be unstable at high temperature [15-17]. Specifically, -HMX crystal exhibits two
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endothermic processes corresponding to -phase transition and melting, respectively [15, 17], while -CL-20 transforms from cubic to tetragonal phase (-before thermal decomposition [15, 16]. Therefore, the thermal decomposition of HMX and CL-20 are
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proposed as solid-liquid coupling state or multiple phases, and in that case, the kinetic
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parameters obtained from coexistence of several states at high temperature are of little (if any)
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value for the thermal safety prediction of the solid-state samples at relative low temperature [3, 18]. In contrast, the inherent consistency in phase structure and solid-state of CL-20/HMX
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co-crystal before thermal decomposition makes it an ideal candidate for kinetic analysis and
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thermal safety prediction.
Fig. 2. (a) Isothermal DSC measurements for 232 °C and 240 °C; (b) Isothermal ARC measurement at 185 °C. Inset is the dP/dt-t curve derived from the differentiation of P-t curve (decomposition section).
Next, in order to determine whether the thermal decomposition of CL-20/HMX co-crystal is N-order or autocatalytic reaction, isothermal DSC experiments were carried out with the temperature set at 232 °C and 240 °C, respectively (Fig. 2a). It demonstrates that the
curves of exothermic rate versus time of the sample show a “bell-shaped” characterization, indicating that the sample always needs a period of induction to reach the highest exothermic rate. This characterization is considered as the typical feature of autocatalytic reaction [18-20], in which the decomposition products continuously accumulate and act as catalysts for the decomposition reaction, leading to the gradual acceleration of decomposition rate and a peak value can be approached after a certain period of time [21-23]. Then, the decomposition rate
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gradually decreases due to the consumption of reactants and eventually results in a
“bell-shaped” curve. To further confirm the autocatalytic behavior, isothermal ARC
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experiments were also carried out. The pressure of the bomb under isothermal 185 °C was plotted as the function of time (P-t curve, Fig. 2b), and the obvious rising of P-t curve at
184.96 °C indicates the gas products were released from thermal decomposition. To derive the
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pressure rising rate (dP/dt-t), the decomposition section of P-t curve is smoothed and
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differentiated and the dP/dt-t curve can be obtained as shown in the insert of Fig. 2b. Similar
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to the exothermic rate curve, the dP/dt-t also exhibits a “bell-shaped” feature with the maximum value achieved after a period of induction. Therefore, the collective results of
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typical autocatalytic reaction.
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isothermal experiments reveal that the thermal decomposition of CL-20/HMX co-crystal is a
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Fig. 3. Comparison between experiment and simulation of (a) heat production rate s temperature.
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Insert is the enlargement of red block diagram; (b) heat production s time for CL-20/HMX co-crystal at higher heating rates; (c) heat production rate s temperature; (d) heat productions time for CL-20/HMX
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co-crystal at lower heating rates.
On the basis of determining the reaction type of CL-20/HMX co-crystal decomposition,
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we performed non-isothermal DSC at several heating rates to evaluate the thermal kinetic parameters. At first, the heating rates of 1, 2, 5, and 10 K/min were chosen and the experimental and simulated results are presented in Fig. 3a and Fig. 3b. It can be seen that
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only the experimental data at low heating rate, i.e. 1 and 2 K/min, are fitted well, while for high heating rates of 5 and 10 K/min, only the first half of the data is processed well (see Fig. 3a). Evidently, their compatibility and matching is very poor, especially at higher heating rate when four exothermic rate curves were dealt with simultaneously. The main reason, accounting for poor compatibility, is probably the violation of temperature uniformity in the co-crystal sample under high heating rates which resulted in a micro-explosion behavior with ultra-high exothermic rate. Therefore, to reveal the inherent kinetic process of thermal
decomposition of CL-20/HMX co-crystal, non-isothermal DSC at lower heating rates (0.2, 0.4, 0.6, 0.8, 1.0 K/min) were performed. As presented in Fig. 3c and 3d, even though five exothermic curves were processed simultaneously, the simulated results demonstrate that the compatibility of DSC experimental data is very reasonable. Besides, the overall heat production is decreasing as the heating rate increased (Fig. 3b and Fig. 3d), which is the evidence of several paths in parallel during the thermal decomposition of CL-20/HMX
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co-crystal. Generally, for the same reaction path, the overall heat released at different scanning rates must be the same and does not vary with the change of heating rates.
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Nevertheless, for the reaction comprising several paths, the final heat generated by the reaction (overall heat) can be observed to depend naturally on the heating rate - either
increases or decreases with the increase of heating rate. Actually, the variable overall heat in
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Fig. 3b and 3d is the indication that we are dealing with complex reaction which comprises
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several paths in parallel or, in other words, initial reagent can undergo decomposition along
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several paths. To more clearly understand this, let’s assume a reaction consisted of several paths, each of paths which consume the reagent has different activation energy and heat effect.
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Thus, the reaction path with smaller activation energy is faster than that with bigger activation
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energy at lower temperatures, while at higher temperature the contribution of path with bigger activation energy continuously increases. It means that depending on temperature range portions of the reagent consumed by each of paths will vary. Moreover, it is known that the
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bigger the heating rate the higher the temperature range of a reaction. Thus, the contribution of heat generated by each of reaction paths will change with diverse heating rates and change
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in contribution of the paths into the overall heat results in variation of the overall heat with different heating rates. Combined with the above analysis, the kinetic model including two parallel autocatalytic
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paths is taken into account, which can be described by generalized autocatalytic reaction (full autocatalysis). It is well known that the reaction rate of n-order reaction (rn) and autocatalytic reaction (rauto) can be described as follows[25]: n-order reaction:
𝑟n = 𝐴n 𝑒 −𝐸n ⁄𝑅𝑇 (1 − 𝛼)𝑛11
autocatalytic reaction: 𝑟auto = 𝐴auto 𝑒 −𝐸auto ⁄𝑅𝑇 𝛼 𝑛21 (1 − 𝛼)𝑛22
(1) (2)
Where the A is the pre-exponential factor, E is the activation energy, n11, n21, n22 is the
reaction order, R is gas constant, T represents temperature, and α is the degree of conversion of samples. For a full autocatalysis, the reaction is comprised of n-order reaction and autocatalysis reaction, which is named as a generalized autocatalysis and can be written as [24, 25]: (3)
z0 = 𝐴𝑛 /𝐴auto
(4)
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𝑟 = 𝑟n + 𝑟auto = 𝐴𝑒 −𝐸⁄𝑅𝑇 (1 − 𝛼)𝑛1 (𝑧0 𝑒 −𝐸𝑧 ⁄𝑅𝑇 + 𝛼 𝑛2 )
E𝑧 = 𝐸n − 𝐸auto
(5)
generalized autocatalytic reaction, which can be described as: 𝑟 = ∑ 𝑟𝑖 𝑟𝑖 = 𝐴𝑒 −𝐸⁄𝑅𝑇 (1 − 𝛼𝑖 )𝑛1 (𝑧0 𝑒 −𝐸𝑧 ⁄𝑅𝑇 + 𝛼𝑖 𝑛2 )
(6) (7)
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𝑑𝛼⁄𝑑𝑡 = ∑ 𝑟𝑖
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In this study, the kinetic model of CL-20/HMX co-crystal includes two parallel
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𝑑𝑄 ⁄𝑑𝑡 = ∑ 𝑄𝑖 𝑟𝑖
(8) (9)
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Where ri, αi and Qi represent reaction rate, degree of conversion and heat production of a
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reaction, respectively, i = 1 and 2, and t is the time.
The kinetic-based model shows a reasonable fitting of the DSC experimental data (Fig.
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3c and Fig. 3d), and the kinetic parameters are listed in Table 1. Accordingly, CL-20/HMX co-crystal exhibits a distinct decomposition behavior from that of individual HMX and CL-20:
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The thermal kinetic model of CL-20/HMX co-crystal is comprised of two parallel autocatalytic reactions, while thermal decomposition behavior of HMX or CL-20 can be
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described by only an autocatalytic reaction [28]. In addition, the activation energy of CL-20/HMX co-crystal, E = 177.41, 245 kJ/mol for 1st and 2nd path, is higher than that of HMX (~ 135 kJ/mol) and CL-20 (~ 128 kJ/mol) [28].
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Table 1 Kinetic parameters of the reaction model for CL-20/HMX co-crystal. Parameters
Units
1st path
2nd path
ln(A)
ln(1/s)
36.20
56.82
E
kJ/mol
177.41
245.68
n1
-
0.39
1.08
n2
-
0.42
1.65
-
-3.91
-3.21
Ez
kJ/mol
2.26
21.99
Q
J/g
2186.69
1226.49
A
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A
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ln(z0)
Fig. 4. Contribution of two paths in heat production rate for CL-20/HMX co-crystal decomposition.
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Fig. 5. Contribution of two paths in reaction process at various heating rates for decomposition of CL-20/HMX co-crystal.
Fig. 4 and Fig. 5 reveal the contribution of two paths to the thermal decomposition
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reaction. It shows that the contribution of first path always dominates at various heating rates, but with heating rate increasing, the reaction rate of second path becomes faster (Fig. 4) and its contribution becomes more evident to the total reaction (Fig. 5). This effect may be due to the unique structure of the CL-20/HMX co-crystal in which two different energetic molecules (CL-20 and HMX molecule) are arranging orderly and both of them can decompose and release energy. Besides, the contribution of parallel thermal decomposition will change with diverse heating rates due to their different activation energy and heat production. Note that the
CL-20/HMX co-crystal exhibits only one exothermic peak (Fig. 1a and Fig. 3c), implying that the parallel paths are coupled during the thermal decomposition. 3.2 Thermal safety prediction of CL-20/HMX co-crystal Autocatalytic reactions are usually considered as a dangerous process due to unexpected initiation, sudden heat evolution and explosion [4, 25]. Herein, based on the kinetic-based
prediction of CL-20/HMX co-crystal under different conditions.
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3.2.1 Adiabatic time to maximum rate (TMRad)
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model, non-linear numerically simulation [3, 25-28] was conducted for the thermal safety
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Fig. 6. Adiabatic time to maximum rate (TMRad) s temperature of CL-20/HMX co-crystal.
TMRad is considered as an important thermal safety parameter. Fig. 6a demonstrates the
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simulated TMRad of CL-20/HMX co-crystal and the Td,24 is determined as 151.64 °C. Besides, critical temperature of 1000th second explosion is determined as ~196 °C, agreed well with
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199 °C obtained from the experimental test. The consistency of experimental and simulated results proves the validity of the kinetic model. Moreover, according to the criteria for the assessment of an accident probability suggested by Stossel
[29], the probability of an
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accident is considered to be high if TMRad < 8 h. According to the simulation results, reliable safe temperature of CL-20/HMX co-crystal during actual operation should not be higher than 165 °C. 3.2.2 Time to conversion limit (TCL) In order to evaluate the thermal stability or storage aging life of a substance, TCL was exploited. While conversion of a reaction reaches some predefined value-conversion limit under an isothermal storage environment, estimation of thermal stability is determined by
evaluating the dependency of time instant. Fig. 6b shows the dependencies of TCL on temperature of CL-20/HMX co-crystal predicted on the basis of the kinetic model for different conversion limits. For 0.1% limit value, the result shows that after 65 years at an ideal isothermal storage temperature of 70 °C, the conversion will reach the limit value. For 1% limit value, by contrast, it takes about 243 years for CL-20/HMX co-crystal to meet
indicates that CL-20/HMX co-crystal has good stability in solid state. 3.2.3 Self accelerating decomposition temperature (SADT)
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expiration conditions in an isothermal environment of 70°C. From the above results, it clearly
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SADT is an important parameter for evaluating the thermal hazards during storage and transportation. According to “Recommendations on the Transport of Dangerous Goods,
Manual of Tests and Criteria” from the United Nations [4, 30], SADT is defined as the lowest
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temperature at which an overheating in the middle of specific packaging exceeds 6 °C after a
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lapse of the period of 7 days or less, which was measured from the time when the packing
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center temperature reaches 2 °C below the ambient temperature [4, 31]. To simulate thermal explosions in CL-20/HMX co-crystal, the critical parameters of
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thermal explosion are found numerically in the context of complicated chemical kinetics for
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several types of the reactor and different masses of samples. Considering solid thermal explosion simulation, it is necessary to make the following statement. The process model is as following:
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𝜌𝐶𝑝 (𝜕𝑇⁄𝜕𝑡) = 𝑑𝑖𝑣(𝜆Δ𝑇) + 𝑊,
(10)
𝜕𝛼𝑖 ⁄𝜕𝑡 = 𝑟𝑖 𝑖 = 1, ⋯ , 𝑁𝐶,
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(11)
𝑊 = ∑ 𝑄𝑖∞ 𝑟𝑖
(12)
where ρ is the density; Cp is the specific heat; T is the temperature; t is the time; λ is the
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heat conductivity; α is the degree of conversion of a component; ri is the reaction rate; Qi is the reaction calorific effect; W is the heat power; NC is the number of components; i is the component number. Initial fields of the temperature and conversions are supposed to be constant through the reactor volume: T|t=0 = T0
(13)
αi|t=0 = αi0
(14)
Here, the index 0 marks initial values of the temperature and conversion. The boundary conditions of the third kind can be specified: Newton’s law of heat exchange: −λ(𝜕𝑇⁄𝜕𝑛)|𝑤 = 𝜒(𝑇𝑒 − 𝑇𝑠 )
(15)
Here the letters “e” and “s” relate to the parameters in environment and on the boundary, respectively; n is the unit outer normal on the boundary; 𝜒 is heat transfer coefficient of
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radiation surface.
Assuming that CL-20/HMX co-crystal is stored in barrels (Fig. 7, and the detailed
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parameters of samples and storage containers are listed in Table 2), and the SADT values of
different masses of CL-20/HMX co-crystal stored in different types of barrels were calculated
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with the assistance of Thermal Safety Software (TSS).
Fig. 7. The model for kinetic-based simulation of SADT. (a) The barrel container; (b) CL-20/HMX
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co-crystal stored in the barrel; and (c) temperature distribution of the co-crystal samples (5 kg, polymer barrel). Table 2 Physical performance parameters of CL-20/HMX co-crystal and materials of shells used. Parameters
Barrel
CL-20/HMX co-crystal
Layer thickness (m)
0.01
-
Density ρ (g/cm3)
a
1.945
Void fraction
-
0.10
Specific heat (kJ/(kg·K))
a
0.8266
Thermal conductivity (W/(m·K))
a
0.292
“a” means the value is depend on the specific reference material which is available in TSS software. Table 3 Simulated SADT results of CL-20/HMX co-crystal. SADT (°C)
1
Polymer
144
2
Fe
146
3
Rubber
4
Glass
1
Polymer
2
Fe
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50
Rubber
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3 4
Glass
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Material of shell
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5
Package number
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Mass of sample (kg)
144 146 138 139 139 139
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As shown in Table 3, for the same package scale (either 5 kg or 50 kg), the calculated
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SADT values show almost the same with different shell materials of the barrels. For example, when the barrel materials changes from polymer to Fe, the SADT of 5 kg CL-20/HMX co-crystal only increases ~2 oC from 144 oC to 146 oC, and SADT of 50 kg samples slightly
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increases from 138 oC to 139 oC. However, the SADT values can be significantly influenced
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by the package masses of explosive. For same package material and boundary conditions, the effect of package mass on SADT of CL-20/HMX co-crystal values is more remarkable than materials of shell. That is, when CL-20/HMX co-crystal was stored in polymer barrel, the operation temperature should be kept below 144 oC and 138 oC for 5 kg and 50 kg samples,
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respectively. In a word, the scale of the samples, rather than the material of storage container, can significantly affect the SADT of CL-20/HMX co-crystal.
4. Conclusions In this study, the thermal decomposition behavior of CL-20/HMX co-crystal was carefully investigated by DSC, in-situ XRD, and isothermal ARC analysis. The kinetic model
of the thermal decomposition of CL-20/HMX co-crystal was successfully created for the first time, and the kinetic-based simulation was performed to predict the thermal hazard under different conditions. The conclusions are as follows: 1. The non-isothermal DSC and in-situ XRD analysis show that CL-20/HMX co-crystal does not experience a phase transformation or melting process before thermal decomposition, which is quite distinct from pure CL-20 and HMX crystals.
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2. According to the isothermal experimental results, the thermal decomposition of
CL-20/HMX co-crystal is identified as a typical autocatalytic reaction, in which the heat and
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gas production rate undergo an acceleration period to approach the maximum value, followed by a deceleration process.
3. The compatibility of non-isothermal DSC results at high heating rates is found to be
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quite poor, probably due to the violation of temperature uniformity in the co-crystal under
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high heating rates, which resulted in a micro-explosion with ultra-high exothermic rate. In
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contrast, the experimental data at lower heating rates can be fitted well by proper kinetic model, and the thermal decomposition kinetic of CL-20/HMX co-crystal was found to
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comprise two parallel autocatalytic reactions (paths). The contribution of the two parallel
and heat production.
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paths was revealed to vary with diverse heating rates due to their different activation energy
4. Based on the kinetic model, the simulation results show that the Td,24 of CL-20/HMX
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co-crystal is 151.64 °C, and the critical temperature of 1000th second explosion is ~196 °C, agreed well with experimental results (199 °C). Besides, according to TCL, it shows that the
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conversion limit of CL-20/HMX co-crystal at 70 °C will reach 0.1% and 1% after 65 years and 243 years, respectively, indicating good stability of CL-20/HMX co-crystal. 5. The simulated SADT of 5 kg CL-20/HMX co-crystal stored in different types of barrels
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(polymer, Fe, rubber and glass) is ~144 °C, much higher than that of 50 kg samples which is determined as ~138 °C. It demonstrates that the SADT of CL-20/HMX co-crystal can be profoundly influenced by the scale of the samples rather than the material of storage container.
5. Acknowledgments
This work was supported by the National Natural Science Foundation of China
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(No.21805260).
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Figure captions
Figure 1. (a) dynamic DSC data on heating rates from 1 K/min and 10 K/min; (b) in-situ XRD patterns of CL-20/HMX co-crystal from 30 °C to 185 °C.
Figure 2. (a) Isothermal DSC measurements for 232 °C and 240 °C; (b) Isothermal ARC
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measurement at 185 °C, inset is the dP/dt-t curve derived from the differentiation of P-t curve (decomposition section).
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Figure 3. Comparison between experiment and simulation of (a) heat production rate s
temperature. Insert is the enlargement of red block diagram; (b) heat production s time for CL-20/HMX co-crystal at higher heating rates; (c) heat production rate s temperature; (d)
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heat productions time for CL-20/HMX co-crystal at lower heating rates.
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Figure 4. Contribution of two paths in heat production rate for CL-20/HMX co-crystal
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decomposition.
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Figure 5. Contribution of two paths in reaction process at various heating rates for decomposition of CL-20/HMX co-crystal.
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Figure 6. Adiabatic time to maximum rate (TMRad) s temperature of CL-20/HMX co-crystal. Figure 7. The model for kinetic-based simulation of SADT. (a) The barrel container; (b)
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CL-20/HMX co-crystal stored in the barrel; and (c) temperature distribution of the co-crystal
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samples (5 kg, polymer barrel).