Thermal decomposition models for HMX-based plastic bonded explosives

Combustion and Flame 137 (2004) 50–62 www.elsevier.com/locate/jnlabr/cnf

Thermal decomposition models for HMX-based plastic bonded explosives Craig M. Tarver ∗ and Tri D. Tran Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Received 25 March 2003; received in revised form 1 December 2003; accepted 5 January 2004

Abstract Global multistep chemical kinetic models for the thermal decomposition of octahydro-1,3,5,7-tetranitro-1,3,5,7tetrazine (HMX)-based plastic bonded explosives (PBXs) using endothermic or exothermic binders are developed for calculation of the times to thermal explosion as functions of heating rate and geometry in the Chemical TOPAZ heat-transfer computer code. The decomposition mechanisms of the binder materials are treated separately from that of HMX, and the chemical reactions of each constituent are assumed to occur independently. Experimental data and theoretical predictions of the thermal properties, decomposition pathways, and chemical kinetic reaction rate constants are used to develop reaction sequences for each of the components present in the PBX at various weight percentages. The measured times to thermal explosion at various initial temperatures in a new One-Dimensional Time-to-Explosion (ODTX) apparatus are compared to the Chemical TOPAZ predictions. Two series of pristine HMX spheres formulated with coarse and fine particles are tested for the first time in an ODTX apparatus. The pure HMX data clearly show that the presence of an endothermic binder in a PBX increases the times to thermal explosion, while the presence of an exothermic binder decreases the times to explosion. The magnitudes of these changes in explosion time depend upon the chemical stabilities and heats of reaction of these binders. A four-step decomposition model is developed for HMX, which includes the β to δ solid-phase transition as the first endothermic reaction. This model accurately reproduces the pure HMX curves. Decomposition models for the various binder components are then used with the HMX model to accurately reproduce the ODTX timeto-explosion curves. Comparisons are also made to times to thermal explosion obtained in various experiments involving aged PBXs, ramped temperature rate increases, unconfined explosives, and a larger size, cylindrical geometry called the scaled thermal explosion experiment.  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Reaction mechanisms; Condensed-phase explosives; Numerical simulation

1. Introduction The One-Dimensional Time-to-Explosion (ODTX) apparatus has been used for over 25 years at several laboratories as an accurate constant boundary temperature time-to-thermal-explosion experiment in spherical geometry that is amenable to heat-transfer

* Corresponding author.

E-mail address: [email protected] (C.M. Tarver).

computer code modeling. The original Lawrence Livermore National Laboratory apparatus [1] has recently been rebuilt using modern heating, timing, and pressure controllers, and the scatter in time-toexplosion measurements has been greatly reduced [2]. Along with determining relative thermal stability relationships among various solid and liquid high explosives, an important use of ODTX time to explosion versus inverse temperature measurements has been as input for the development of global multistep chemical kinetic decomposition models in two-

0010-2180/$ – see front matter  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2004.01.002

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and three-dimensional heat-transfer computer codes [3,4]. These models are then used to predict the times to and locations of the onset of thermal explosion in larger explosive charges, many of which cannot be tested directly. These calculations are used as the bases for estimations of the violence of thermal explosions as functions of heating rate, confinement, damage, and porosity [5]. Due to the absence of chemical kinetic experimental data at higher temperatures, these models have also been used to estimate the critical conditions for “hot-spot” ignition during impact ignition and shock initiation scenarios [6] and the growth rates of shock-induced hot spots during shock-to-detonation-transition processes [7]. They are currently being used to model shock initiation and detonation wave propagation in a grain scale model [8] and in a statistical hot-spot reactive flow model being developed in the thermal–mechanical– hydrodynamic coupled computer code ALE3D [9]. Therefore these chemical kinetic decomposition models must be as accurate as possible. The original three reaction step models for octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazine (HMX), triaminotrinitrobenzene (TATB), trinitrotoluene (TNT), and hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) [4], have been employed by several researchers, but there are several possible reaction pathways for large explosive molecules with more than 20 atoms to decompose into 7–11 reaction product molecules. Decomposition models containing several possible pathways can be formulated in the heat-transfer code Chemical TOPAZ [10], which can handle any number of chemical species and chemical reactions among these species. However, the lack of experimental chemical kinetic rate constant data prohibits building more complex reaction schemes at the present time. Only a few modern experiments are currently yielding reaction product formation data. The research of Thynell et al. using the T-jump apparatus [11] has yielded chemical kinetic rate constants in the thermal explosion temperature range for many explosives. Behrens et al. [12], using a time-of-flight mass spectroscopic experiment to detect the product gases from thermal decomposition of solid explosives, have postulated several reaction schemes occurring in parallel to produce the observed products. Unfortunately, this experiment does not measure the reaction rate constants that are essential for heat-transfer code modeling. If four or more reaction pathways are producing reaction products in the same time frame, the kinetic rates of these pathways must be approximately the same. Thus they can be treated as one global mechanism until specific reaction rate constant parameters for each pathway become available. Recently Chakraborty et al. [13] published ab initio studies of many possible pathways and transition-state en-

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ergy barriers for HMX unimolecular decomposition. However, calculated transition-state energy barriers are not yet accurate enough to use for predictions of time-to-thermal explosion. Henson et al. [14] have demonstrated the importance of the solid–solid phase transition from β to δ HMX, which occurs just before or during the onset of thermal decomposition, and have measured kinetic rate constants similar to those reported by Brill and Karpowicz [15] for this transition. In this paper, the β to δ phase transition in HMX is treated separate from the other endothermic reactions as the first step in the decomposition model. Due to the lack of experimental kinetic rate constant and reaction pathway data, the decomposition models for HMX and its endothermic and exothermic binders presented in this paper are global mechanisms containing four or fewer reactions. In contrast to previous ODTX-based models, the binder and HMX are now treated as individual components. Table 1 lists the HMX-based plastic bonded explosives (PBXs) studied and their compositions. In the next section, measured times to explosion for two particle size classes of pure HMX are compared to the HMX decomposition model predictions. Then experimental ODTX curves for HMX-based PBXs with endothermic binders are compared to model predictions. PBXs with exothermic binders are discussed next. This is followed by comparisons of calculated times to explosion with recent experimental results for aged PBXs, ramped heating rates in the new ODTX apparatus, unconfined ODTX experiments, and scaled thermal explosion (STEX) [16] experiments. The final section of the paper contains a summary of results, conclusions, and future research plans.

2. Experimental and modeling results for pure HMX Previous ODTX studies measured times to thermal explosion over a temperature range of 180– 280 ◦ C for PBXs containing HMX and a binder that is either endothermic or exothermic when it decomposes. This study began by using 1.27-cm-diameter pressed spheres of two kinds of pristine HMX, coarser Class 1, with a mean particle size of approximately 150 µm, and finer Class 2, with a mean particle size of less than 10 µm. Fig. 1 shows the experimental ODTX times to thermal explosion versus inverse temperature curves for coarse and fine HMX. The fine HMX spheres explode at slightly shorter times for the same temperatures than do the coarse ones. The new ODTX apparatus can withstand exactly 0.15 GPa of gas pressure, and the greater surface area of the finer HMX particles allows gaseous reaction products to be produced faster than coarse HMX once the

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Table 1 High explosives and binders tested Explosive

Composition

Remarks

Coarse HMX Fine HMX LX-10 LX-07 LX-04 LX-14 EDC-29 PBX 9011 X-0298 LX-09 PBX 9501 EDC-37 PBX 9404

100% β-HMX 100% β-HMX 94.5% HMX, 5.5% Viton A 90% HMX, 10% Viton A 85% HMX, 15% Viton A 95.5% HMX, 4.5% Estane 95% HMX, 5% polyurethane 90% HMX, 10% Estane 97.5% HMX, 2.5% Kraton oil 93% HMX, 4.6% pDNPA, 2.4% FEFO 95% HMX, 2.5% Estane, 2.5% BDNPA/F 91% HMX, 9% (oil, polymer, nitrocellulose) 94% HMX, 3% CEF, 3% nitrocellulose

Class 1—mean particle size 150 µm Class 2—mean particle size < 10 µm Endothermic binder Endothermic binder Endothermic binder Endothermic binder Endothermic binder Endothermic binder Exothermic binder Exothermic binder Exothermic binder Exothermic binder Exothermic binder

Viton A, vinylidine fluoride/hexafluoropropylene copolymer (60/40); Estane, polyurethane solution system; pDNPA, 2,2dinitropropyl acrylate; FEFO, 1,1 -[methylenebis(oxy)]bis[2-fluoro-2,2-dinitroethane]; BDNPA/F, bis(2,2-dinitropropyl)acetal/ bis(2,2-dinitropropyl)formal (50/50); CEF, tris-β-chloroethylphosphate.

solid intermediates → gaseous intermediates (CH2 O, N2 O, HCN, HNO2 , etc.),

(3)

gaseous intermediates → final products (CO2 , H2 O, N2 , CO, C, etc.).

Fig. 1. Experimental and calculated ODTX times to thermal explosion versus inverse temperature for coarse HMX and fine HMX.

HMX decomposition process begins to liberate gases. A systematic study by Tran et al. [2] has shown that the new ODTX data agree with that taken with the old apparatus, but the new temperature and pressure controllers produce much smaller error bars in the times to explosion. Also shown in Fig. 1 are the calculated times to explosion for coarse and fine HMX using the following global reaction model. The HMX chemical decomposition model consists of four reactions and five chemical species. The reaction sequence is β-HMX → δ-HMX,

(1)

δ-HMX → solid intermediates,

(2)

(4)

The basic mechanism for HMX and its sister molecule RDX has been reviewed by Behrens et al. [12]. The solid–solid β to δ phase transition is treated as a separate reaction in Eq. (1), whereas previously it had been included in Eq. (2) in one overall endothermic process. Eq. (2) describes the initial ring- and bondbreaking endothermic step(s). HMX decomposition is known to produce mainly CH2 O plus N2 O under some temperature and pressure conditions and mostly HCN plus HNO2 under other conditions [12]. Eq. (3) is slightly exothermic, and most of HMXs chemical energy is released during the gas-phase formation of the final stable reaction products by second-order gasphase reactions in Eq. (4). Table 2 lists the thermal and chemical kinetic parameters for the HMX decomposition model. Most of these parameters are the same as in previous work [5,6], but some have been modified slightly to improve agreement with experiment. The thermal conductivity and heat capacity values are taken from Cornell and Johnson [17], which agree closely with more recent measurements by Hanson-Parr and Parr [18]. Two sets of chemical kinetic values for the β to δ phase have been reported. Henson et al. [19] used an optical second harmonic generation technique to observe the phase transition and fit their data to a first-order rate expression with a frequency factor of ln Z = 50.44 and an activation energy E of 48.2 kcal/mol. Brill and Karpowicz [15] reported values of ln Z = 45.83 and E = 48.8 kcal/mol based

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Table 2 Thermal and chemical kinetic parameters for pure HMX β-HMX

δ-HMX

Solid intermediate

Intermediate gases

Final gases

(1) Initial density (g/cm3 ) 1.85

1.70

298 K 373 K 433 K 563 K 623 K 773 K > 1273 K

0.24 0.30 0.34 0.40 0.46 0.55 0.55

0.24 0.30 0.34 0.40 0.46 0.55 0.55

298 K 373 K 433 K 563 K 623 K 773 K > 1273 K

1.28 × 10−3 1.09 × 10−3 1.02 × 10−3 8.15 × 10−4 7.5 × 10−4 1.0 × 10−4 1.0 × 10−4

(3) Thermal conductivity (cal/(cm g K)) at: 1.18 × 10−3 1.08 × 10−3 1.0 × 10−3 9.2 × 10−4 9.2 × 10−4 8.3 × 10−4 8.15 × 10−4 8.15 × 10−4 7.5 × 10−4 7.5 × 10−4 −4 1.0 × 10 1.0 × 10−4 1.0 × 10−4 1.0 × 10−4

+61.0

+71.0

(2) Heat capacity (cal/(g K)) at: 0.22 0.27 0.31 0.36 0.42 0.50 0.50

(4) Heat of formation (cal/g) +131.0

0.24 0.26 0.27 0.29 0.31 0.35 0.42

0.27 0.28 0.28 0.29 0.30 0.31 0.35

9.80 × 10−4 8.8 × 10−4 8.3 × 10−4 8.15 × 10−4 7.5 × 10−4 1.0 × 10−4 1.0 × 10−4

1.0 × 10−4 1.0 × 10−4 1.0 × 10−4 1.0 × 10−4 1.0 × 10−4 1.0 × 10−4 1.0 × 10−4

−2.0

−1339.0

Reaction rate parameters Nax qZ e−E/RT (where Na is mass fraction per unit volume) Reaction

ln Z

E (kcal/mol)

Reaction order x

Heat of reaction q (cal/g)

1 2 3 4

48.13 48.7 37.8a 28.1b

48.470 52.700 44.300 34.100

1 1 1 2

+10.0 +60.0 −133.0 −1337.0

a 37.8 for coarse HMX and 38.23 for fine HMX. b 28.1 for coarse HMX and 28.53 for fine HMX.

on earlier experiments. The averages of these values, ln Z = 48.13 and E = 48.5 kcal/mol, are used in these calculations. The heat of this transition has been measured to be approximately +10 cal/g endothermic [20]. These values of ln Z, E, and heat of reaction have produced good agreement with embedded thermocouple records, which have observed the β to δ phase transition occurring between 160 and 180 ◦ C in 2.54-cm-diameter cylinders [21], 5.08-cm-diameter STEX cylinders [16], and 9-cm-diameter heated gas gun shock initiation experiments [22]. The second reaction in Eq. (2) is a global representation of the rate-limiting endothermic ring and bondbreaking reactions that may include breaking N–NO2 , C–N, C–H, N–O, etc., bonds. The activation energy for this reaction is taken to be 52.7 kcal/mol [23], and the recent summary of many theoretical HMX and RDX decomposition pathways by Chakraborty et al. [13] found several endothermic energy barriers close to this value. Originally the total enthalpy of the endothermic processes was taken to be +100 cal/g based on simple bond strength estimations [4]. Some

of the Chakraborty et al. pathways [13] were found to be more endothermic than +100 cal/g. However, Dickson et al. [21] pointed out that the original HMX model accurately calculated the time to thermal explosion in their 2.54-cm-diameter cylindrical test but not the location of the thermal runaway. Lowering the endothermicity of reaction (2) to +60 cal/g, for a total endothermicity of +70 cal/g together with the phase transition, moves the location of the thermal runaway to the center of the cylinder, in agreement with the Dickson et al. [21] thermocouple records, without significantly changing the calculated time to explosion. The third reaction of the HMX decomposition scheme is the formation of intermediate gaseous products, such as CH2 O plus N2 O and HCN plus HNO2 . These reactions are slightly endothermic or slightly exothermic. In the original model, this global reaction was assumed to be exothermic by −300 cal/g based on simple bond energies. This value is close to the value calculated by Chakraborty et al. [13] for the most exothermic pathway for decomposition to inter-

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mediate products. Since several pathways can occur, a less exothermic value of −133 cal/g is chosen for the current model. The activation energy for this reaction is assumed to be 44.3 kcal/mol [24], which is close to several of the activation energy barrier estimates by Chakraborty et al. for possible intermediate transition states. The fourth reaction is a global representation of the second-order gas-phase reactions that yield final products (CO2 , H2 O, N2 , CO, etc.). The rest of the HMX heat of reaction to products, −1337 cal/g, is assumed to be liberated with an activation energy of 34.1 kcal/mol, which was measured for the CH2 O + N2 O reaction [25] and is typical of gas-phase reactions. The agreement between experimental and calculated explosion times for coarse and fine HMX shown in Fig. 1 shows that the overall HMX decomposition process is well described by these global reactions. The larger total surface area of the fine HMX particles provides more reaction sites at which the intermediate gaseous products can form and then further react, forming the final stable reaction product gases. Since particle size is not included in the Chemical TOPAZ code, the increased reactivity of the fine HMX particles is modeled by increasing the frequency factors of the gas producing reactions (3) and (4) by 1.54 s−1 , as shown in Table 2. Most of the PBX formulations studied in this paper use the coarser Class 1 HMX, while LX-04 has an intermediate particle size distribution resulting from a mixture of Class 1 and Class 2. Thus, unless otherwise noted, the parameters for coarse HMX are used for the PBXs in the following sections. The fastest three measured times to explosion for coarse HMX, 4, 5, and 8 s in Fig. 1, are less than the calculated values. The old ODTX apparatus took several seconds to deposit the explosive sphere and seal the aluminum anvils completely, so times to explosion less than 10 s were ignored. However, the new ODTX apparatus closes securely in less than 1 s so these data points are included. All three of these times are measured at temperatures exceeding 285 ◦ C or 558 K, the melting point of HMX. RDX is known to exhibit faster decomposition above its melting point [4,12], but little is known about HMX. Melting and possible increased reaction rates for liquid HMX have not been included in the current model due to the lack of experimental data, but could be included in more complex models.

during impact and shock initiation scenarios [22]. In terms of thermal explosion, these binders generally have lower thermal conductivity than HMX and thus slow down the heating of the individual HMX particles. Their decomposition is endothermic, which absorbs heat from the system and lengthens the time to explosion in a constant boundary temperature experiment like the ODTX apparatus. The binder decomposition does create gaseous products that contribute to the internal pressurization of the ODTX apparatus. Pure binders have been tested in the ODTX apparatus and do not create enough gas to exceed the 0.15-GPa confinement pressure limit and cause venting without thermal runaway. Weak explosives, such as TATB and TNT, do form enough gas to overcome the 0.15GPa confinement pressure at low temperatures and thousands of seconds [2,4,5]. HMX-based explosives yield true thermal explosions that cause considerable damage to the aluminum anvils as they are driven apart by the high-pressure, hot gaseous products. The volumes of the resulting craters in the aluminum anvils are measured to obtain a relative degree of violence of the explosion [2]. Fig. 2 shows the measured increases in crater volumes of PBX 9501 and LX-04 ODTX explosions at various temperatures. The most violent reactions, defined as those that form the largest craters, occur in the middle of the thermal explosion temperature range, at which the heat transfer reaches the center of the charge, and thermal runaway occurs there first and then proceeds through the entire charge. At the highest temperatures, only the outer edges of the explosive are heated to rapid reaction and the center of the explosive sphere does not re-

3. Experimental and calculated results for PBXs with endothermic binders The main purpose of endothermic binders in PBXs is to coat the HMX particles to reduce heating of the HMX by mechanical work (friction, shear, etc.) done

Fig. 2. ODTX cavity volume increases versus inverse temperature for LX-04 and PBX 9501.

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act before the anvils separate. At the lowest temperatures, the entire explosive sphere is producing gaseous products before thermal runaway. The 0.15-GPa pressure maximum is overcome before rapid thermal runaway occurs at the center. PBX 9501 explosions are more violent than those of LX-04, because PBX 9501 contains 95% HMX and LX-04 contains only 85% HMX. Fig. 3 shows the experimental ODTX times to explosion for the PBXs with endothermic binders, along with the curves for coarse and fine HMX. The times to explosion for these PBXs are generally longer than those for pure HMX at the same temperatures, because the endothermic binders absorb some of the HMX decomposition energy as they decompose. The times to explosion for PBX 9011 lie between those of coarse and fine HMX. The PBX 9011 explosive tested is from an old batch that perhaps was made with fine HMX or impure HMX that contained a considerable fraction of RDX. RDX is less thermally stable than HMX and its presence decreases the times to explosion [4]. The times to explosion for the modern explosives LX-10, LX-14 (only one temperature), EDC-29, LX-07, and LX-04 are all longer than those of coarse HMX. These explosives are formulated with coarse HMX, except for LX-04, which has its own particle size distribution intermediate between Class 1 and Class 2. The series LX-10, LX-07, and LX-04

with 5.5, 10, and 15% Viton, respectively, shows increasingly longer times to explosion at the same temperature in Fig. 3. To calculate the times to explosion, the HMX and binder decompositions are assumed to occur independently. For each binder, a single-step first-order Arrhenius reaction rate is used, together with an endothermic heat of reaction that does not exceed the heat of formation of binder. The thermal conductivities of the LX- explosives were measured up to 160 ◦ C by Cornell and Johnson [17], and those of the other PBXs were assumed to be equal to those of an LX with an equal binder mass fraction. Table 3 lists the heats of formation, the heats of reaction used in the decomposition model, the frequency factors, and the activation energies for the various endothermic binders. Few kinetic data are available for these binders, except for differential thermal analysis heat absorption curves and weight loss curves from thermogravimetric analysis [26]. The binder reaction rate constants in Table 3 are used to estimate the extent of binder degradation as a function of time of temperature and the amount of thermal energy absorbed during this process. As shown in Fig. 4, which com-

Fig. 3. Experimental ODTX time to explosion versus inverse temperature curves for coarse HMX, fine HMX, and PBXs with endothermic binders.

Fig. 4. Ratios of calculated to experimental times to explosion versus inverse temperature curves for PBXs with endothermic binders.

Table 3 Heats of reaction and kinetic parameters for endothermic binders Binder

Heat of formation (cal/g)

Heat of reaction (cal/g)

ln Z

E (kcal/mol)

Viton Estane Polyurethane

+1778.4 +950.0 +830.2

+1400.0 +950.0 +500.0

32.7 32.0 37.0

38.57 38.47 41.25

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pares the ratios of the calculated to the experimental times to explosion, the decomposition models accurately reproduce the measured times to explosion over the entire temperature range. The coarse HMX reaction rate constants are used to model the HMX in all the PBXs except PBX 9011. The agreement between the calculated and the experimental times to explosion is poorest at the highest temperatures, at which the closure time of the ODTX apparatus and uncertainities in the high-temperature thermal diffusivity of the explosive strongly influence the explosion times, and at the lowest temperatures, at which the decomposition occurs slowly over thousands of seconds. At the intermediate temperatures, at which thermal explosions occur near the center of the ODTX sample, the overall agreement between the calculated and the experimental times to explosion for all six PBXs with endothermic binders is excellent, especially when the scatter in the measured times to explosion in the old ODTX apparatus (approximately ±10%) is taken into account. Further tests of the LX-04 model are presented in later sections of this paper.

4. Experimental and calculated results for PBXs with exothermic binders Exothermic binders are added to explosive formulations to increase the total energy of the formulation and/or to change its physical and mechanical properties. Since these binders are less thermally stable than HMX, they decompose first, heating the HMX particles and decreasing the times to explosion. Fig. 5 shows the ODTX experimental time to thermal explosion versus inverse temperature curves for several HMX PBXs containing exothermic binders compared to those for pure coarse HMX. The decrease in time to explosion for a particular exothermic binder depends on its mass fraction, heat of reaction, and chemical stability. X-0298 has only 2.5% oil, which is not very exothermic, so its times to explosion are very close to those of pure HMX. At the other extreme is PBX 9404, which has nitrocellulose in its binder. Nitrocellulose is very exothermic and the least chemically stable of these binders, so PBX 9404 exhibits the shortest times to explosion at high and intermediate temperatures. The other three PBXs shown in Fig. 5 generally exhibit times to explosion intermediate between pure HMX and PBX 9404, corresponding to the stability and exothermicity of their binders. The LX-09 binder is the least stable of these three binders, while those of EDC-37 and PBX 9501 are slightly more stable. PBXs 9404, LX-09, and EDC-37 exhibit large increases in time to explosion over a small temperature range. This was previously observed for PBX 9404 [4,5]. This large increase in time to explosion (an or-

Fig. 5. Experimental time to explosion versus inverse temperature curves for coarse HMX and PBXs with exothermic binders.

der of magnitude in time over approximately 5 ◦ C for PBX 9404) occurs in the temperature range in which the decomposition of the exothermic component of the binder is fast and energetic enough to heat the neighboring boundaries of HMX particles a few degrees to the point of thermal explosion. At higher temperatures, both the binder and the HMX decompose rapidly so the time to explosion does not change significantly. At lower temperatures, the binder decomposition is slower and its released heat is conducted deeper into the HMX particles, whose decomposition rates are not affected significantly by this relatively slow heat addition. This exothermic binder effect has previously been modeled as an independent reaction for PBX 9404 [4,5]. To model the ODTX results shown in Fig. 5, exothermic reaction schemes for the various binders are assumed to proceed independent of the HMX reaction scheme in the Chemical TOPAZ code. As for the endothermic binders, there is a general lack of experimental chemical kinetic rate constant data on the materials in these binders. Chen and Brill [27] measured the decomposition of the same nitrocellulose as used in the PBX 9404 binder using the SMATCH/FTIR technique, and their reported frequency factor and activation energy work extremely well in ODTX calculations. No reaction rate constant data were found for the other binder materials. The PBX 9501 binder material is readily available so spheres of 50% Estane and 50% BDNPA/F could be heated to thermal explosion in the ODTX apparatus. The binder times to explosion were calculated

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Table 4 Decomposition models and rates for exothermic binders ln Z

E (kcal/mol)

44.0 36.0 28.0

47.7 39.7 31.8

1 2

(2) PBX 9501 exothermic binder component (BDNPA/F) +27 1 43.0 −702 1 33.0

49.1 39.1

1 2

(3) EDC-37 binder (K-10 oil, polymer, nitrocellulose) +10 1 46.0 −1000 1 33.0

49.1 39.7

1 2

+50 −650

Reaction 1 2 3

1 2 2 (aged)

Heat of reaction (cal/g)

Order

(1) X-0298 binder (2.5% Kraton oil) +10 1 −50 1 −1000 1

(4) LX-09 binder (pDNPA, FEFO) 1 1

46.0 38.0

(5) PBX 9404 binder [nitrocellulose and chloroethylphosphate (CEF)] +25 1 36.0 −877 1 28.8 −977 1 28.4

using the BDNPA/F decomposition model listed in Table 4 and the Estane decomposition model listed in Table 3. Fig. 6 shows the comparison between the experimental and the calculated times to explosion for the PBX 9501 binder formulation. The agreement is excellent for the entire curve, except for the lowest temperature, 195.6 ◦ C, which did not produce a thermal explosion in > 15,000 s. The calculated time to explosion at 195.6 ◦ C was 3150.3 s. However, reducing the temperature by 2 ◦ C resulted in a calculation that failed to explode in > 86,400 s. This PBX 9501 binder decomposition model works well in PBX 9501 calculations, because the mass fraction of the binder is only 5%. Table 4 lists the kinetic mechanisms and parameters used for the binders of PBX 9404, PBX 9501, X-0298, EDC-37, and LX-09. Fig. 7 contains the experimental versus calculated ODTX times to explosion curves for these five PBXs with exothermic binders. The shorter times to explosion for PBX 9404 and LX-09 at intermediate temperatures are reproduced by the decomposition models with the binders reacting independent of HMX. As shown in Fig. 7, the calculated jumps in time to explosion at certain temperatures are not as sharp as those observed experimentally. This is perhaps due to keeping the reaction schemes independent and not allowing reactions of binder products with HMX and its intermediates or vice versa. For example, nitrocellulose produces intermediates very similar to HMX, and these gaseous species could become involved in the HMX decomposition. Cross-reactions have been suggested [28], and several schemes were tried dur-

47.7 43.7 43.7 34.6 34.1

Fig. 6. Experimental and calculated ODTX times to explosion versus inverse temperature for PBX 9501 binder (BDNPA/F–Estane).

ing this study for PBX 9404 and LX-09 without any definitive improvement in the overall agreement with experiment. There is currently not enough experimental reaction rate constant data or theoretical energy barriers for specific reactions to determine the most probable cross-reactions. Applications of these models to explosion time predictions for different geometries, heating rates, and confinements are excellent tests of their usefulness, as shown in the following sections.

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Fig. 7. Experimental and calculated ODTX times to explosion versus inverse temperatures for PBXs with exothermic binders.

Fig. 8. Experimental ODTX times to explosion versus inverse temperatures for new and aged LX-04, PBX 9501, and PBX 9404.

5. Effects of aging on ODTX times to explosion

upper limit for the effect of BDNPA/F migration and/or decomposition, the aged PBX 9501 model assumes that the BDNPA/F does not have a second exothermic reaction so that only the first endothermic reaction in Table 4 is used. This makes the PBX 9501 binder decomposition endothermic and represents a complete loss or decomposition of the BDNPA/F. For aged PBX 9404, aged nitrocellulose is known to be more reactive so the reaction rate constants in the second step in the decomposition process are modified as shown in Table 4 to make the aged binder decompose faster than new binder. The calculated times to explosion are compared to experiment in Fig. 9. The agreement is excellent for aged PBX 9404, which becomes more thermally sensitive, and LX-04, which does not change significantly. The agreement is not as good for aged PBX 9501, for which some times to explosion increase even more than the calculations that assume no exothermic component in the binder predict. Although some of the nitroplasticizer may have migrated out of the PBX 9501, experiments have indicated that the total amount of binder migration is small and the migration is localized [30]. The nitroplasticizer is thermally stable under ambient conditions, as shown in Fig. 6, so it is unlikely that it completely decomposes in storage. Thus the aged PBX 9501 experimental data are not yet fully understood, and more experimental studies using PBX 9501 batches of different ages and storage histories need to be undertaken.

The effects of aging on decomposition kinetics were studied using approximately 20-year-old samples of PBX 9404, PBX 9501, and LX-04 machined from larger parts into 1.27-cm-diameter spheres and tested in the ODTX apparatus. Fig. 8 shows the experimental time to explosion versus inverse temperature curves for the aged materials compared to the newly prepared PBXs. The biggest effect is a 10–15 ◦ C shift toward lower temperatures for PBX 9404. This is not surprising, because nitrocellulose is known to slowly decompose as it ages [29]. An inhibitor that reacts with NO2 radicals produced during nitrocellulose decomposition is added to PBX 9404 when it is formulated. After this inhibitor is consumed, PBX 9404 becomes brown in color due to the presence of (NO2 )x species. The effects of age on PBX 9501 and LX-04 are much less severe than for PBX 9404. LX04 does not appear to be affected to any noticeable extent, while the times to explosion for aged PBX 9501 appear to be slightly longer than those for the newer material. The nitroplasticizer in PBX 9501, BDNPA/F, has been observed to migrate over time under elevated temperatures and pressures so the concentration of the exothermic part of the binder may have decreased [30]. This could explain the slightly longer times to explosion for aged PBX 9501 shown in Fig. 8. To model these results, the aged LX-04 data are compared to the regular LX-04 model since very little change is measured. For PBX 9501, to get an

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Fig. 9. Experimental and calculated ODTX times to explosion versus inverse temperature results for aged LX-04, PBX 9501, and PBX 9404.

6. Effect of confinement on the ODTX times to explosion While the new ODTX apparatus is normally sealed to withstand an internal pressure of 0.15 GPa, it can be operated with a free volume or under an unpressurized condition under which the preheated aluminum anvils separate as soon as any gaseous products are produced. The original work of Catalano et al. [1] showed the effects of different confinement pressures on the times to explosion. Explosives whose main energy release occurs during gas-phase reactions, such as HMX and RDX, have longer times to explosion as the confinement pressure decreases or a free volume is introduced [3], because the intermediate gaseous products can escape or expand before reaction (4) can produce more stable gaseous products, while liberating more chemical energy. For other explosives such as TATB, the times to explosion are the same with or without a free volume [3], because most of the decomposition chemistry occurs in the condensed phase [5]. To check these results with the new ODTX apparatus, a series of unconfined experiments is reported using PBX 9501. Fig. 10 contains the experimental and calculated results for confined and unconfined PBX 9501. This series of experiments is modeled by removing both the fourth reaction in the HMX decomposition listed in Table 2, because it globally represents the gas-phase reactions to final gaseous products, and the second reaction in the PBX 9501 binder mechanism in Table 4, because it is also a gas-phase exothermic reaction. The calculated results for unconfined PBX 9501 assuming no gas-phase exothermic reactions reproduce the experimental times, which are longer than those for confined PBX 9501. This is especially true at high tempera-

Fig. 10. Experimental and calculated times to explosion versus inverse temperature curves for confined and unconfined PBX 9501.

tures, at which HMX decomposition occurs on the outer surfaces of the particles and the intermediate product gases can readily escape from these surfaces.

7. Effects of ramped heating rates on time to explosion of LX-04 and PBX 9501 The new ODTX apparatus can be accurately ramp heated to any desired temperature at any desired rate. Five experiments are reported using various heating rates, three using PBX 9501 and two using LX-04. The temperature versus time records for these experiments are shown in Fig. 11. The heating rates are approximately 30–35 ◦ C/h, resulting in explosions in 5 to 6 h. One PBX 9501 sample is pressed to a lower density to allow for the 8% volume expansion associated with the β to δ phase transition at approximately 170 ◦ C, and the thermal soak is long enough for this transition to be completed. One LX-04 sample contains an internal temperature probe that does not seem to affect the results. Each experiment uses two thermocouples, one placed on each of the two anvils. As expected, PBX 9501 with its exothermic binder produces shorter times to explosion than LX-04. The experiments are modeled using the temperature–time boundary conditions measured by the thermocouples. Table 5 shows the experimental and calculated times to explosion for these five ramp-heating ODTX experiments. The agreement between the experimental and the calculated times to explosion is excellent for both LX-04 and PBX 9501.

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Table 5 Experimental and calculated ramp-heated ODTX results Explosive

Experimental time (s)

Calculated time (s)

% error

PBX 9501(“δ”)a PBX 9501 (β) PBX 9501 (β) LX-04 LX-04 (with probe)

18,415 17,996 20,455 21,321 21,172

19,271 18,056 20,661 21,629 21,471

4.65 0.33 1.01 1.44 1.41

a The sphere was machined to a diameter such that the conversion to δ occurred.

Fig. 11. Temperature versus time records for the five ramp-heating ODTX experiments on PBX 9501 and LX-04.

8. Times to explosion in the scaled thermal explosion experiment The STEX experiment [16] is designed to measure quantitatively the most violent possible thermal explosions by very slowly heating heavily confined cylindrical explosive charges to obtain thermal runaways at the centers of constant temperature charges. The diameter of the explosive charge and the thickness of the confining steel cylinder can be varied to produce different degrees of confinement to be overcome by gas production. Some of the HMX PBX explosive cylinders are machined to smaller diameters than the steel cylinders so that, with thermal expansion and the 8% volume increase during the β to δ phase transition, the PBX forms a tight fit after the transition. Strain gauges are placed at various locations to detect this contact. The phase transition can also be retarded by the 0.2-GPa confinement pressure on PBX cylinders that are in contact with the steel before heating. More details are given by Wardell and Maienschein [16]. The current STEX tests use

5.08-cm-diameter, 20.3-cm-long cylinders of LX-04 confined by 0.406 cm of steel to provide the 0.2GPa confining pressure. The thermocouple records from six STEX tests on LX-04 are used as temperature boundary model input. The heating rates include relatively rapid increases to 130 ◦ C, “soak” times of several hours for the heat transfer to reach the center of the charge, and then increases of 1 ◦ C/h. This slow heating rate ensures nearly constant temperature throughout the charge. Thus these experiments take 70–100 h to reach approximately 190 ◦ C and then explode. Table 6 lists the experimental and calculated explosion times for six LX-04 STEX tests. Three of the six STEX tests vented or leaked some gaseous products during the final few hours of heating [16], and these leaks lengthened the times to explosion by releasing gaseous products. Thus the calculated times to explosion for two of the tests that leaked are 3 to 4 h shorter than measured. However, the overall agreement for the six tests is extremely good and adds confidence that times to explosion for HMX-based PBXs can be accurately reproduced even for very slow heating rates.

9. Summary of results, conclusions, and future plans The experimental and calculated results presented in this paper for the new ODTX apparatus under several heating rate and confinement conditions and the larger scale STEX test show that endothermic binders lengthen the times to explosion for HMXbased PBXs. Exothermic binders shorten the times to explosion. These effects are accurately modeled using global chemical kinetic deposition models for HMX and various binders reacting independently according to their mass fraction in the PBX. The heat-transfer code, Chemical TOPAZ, can model any number of species and reactions, including cross-reactions between the binder decomposition products and HMX or its intermediate products, but the lack of experimental reaction rate data on such reactions limits the complexity of current models. Future plans include

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Table 6 Experimental and calculated results for the LX-04 STEX tests Test number

Experimental time (s)

Calculated time (s)

% error

6a 7a 9 10 28a 29

303,120 258,480 333,720 328,680 357,120 358,920

289,090 260,310 332,280 332,280 344,370 346,720

4.63 0.71 0.43 1.09 3.57 3.40

a Experiment leaked some gas during the last few hours of heating [16].

reaction rate measurements on as many decomposition pathways as possible. When based on experimental chemical kinetic data, the binder decomposition models yield good agreement with ODTX data, as shown for the nitrocellulose component in PBX 9404. For PBX 9501, the exothermic binder material is available and is tested separately in the ODTX apparatus. A decomposition model is developed to match these times to explosion and then used with the HMX model to successfully calculate PBX 9501 explosion times. Future plans include measuring explosion times of the exothermic binders and the decomposition rates of endothermic ones. The study of times to explosion for three aged PBXs shows that binder aging can lengthen, shorten, or not affect the times to explosion. Aging studies on PBXs at several laboratories are currently producing experimental data that will greatly increase the understanding of the various aging processes and their effects on the thermal decomposition of HMX-based PBXs. Accurate calculations of the times to explosion for unconfined ODTX, ramp-heated ODTX, and very slowly heated STEX tests increase the confidence in the ability of the current decomposition models to reproduce times to thermal explosion in different geometries with various heating rates and confinement strengths. However, comparison with much more experimental data is needed to ensure model generality. Future plans include STEX tests with different dimensions, heating rates, and confinement and using the new, versatile ODTX apparatus in many ways.

Acknowledgments The authors thank all of the people who have worked on the ODTX apparatus over the years: Edward Catalano, Donald Ornellas, Emmett Wrenn, Gordon Moody, Raul Garza, Richard Simpson, and Ronald Chambers. Raymond McGuire contributed

greatly to the original models. Albert Nichols was invaluable in both heat transfer code and chemical decomposition model development. Jeffery Wardell and Jon Maienschein graciously shared their STEX results. Melvin Baer, Richard Behrens, and Robert Schmidt of Sandia National Laboratories and Bryan Henson, Laura Smilowitz, Peter Dickson, and Blaine Asay of Los Alamos National Laboratory are thanked for many stimulating discussions and ideas. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract W-7405-ENG-48.

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