Comparative study of thermal stability and combustion of dinitropyrazole isomers

Accepted Manuscript Title: Comparative study of thermal stability and combustion of dinitropyrazole isomers Authors: V.P. Sinditskii, T.H. Hoang, A.D. Smirnova, V.Yu. Egorshev, N.V. Yudin, I.A. Vatsadze, I.L. Dalinger PII: DOI: Reference:

S0040-6031(18)30431-3 https://doi.org/10.1016/j.tca.2018.07.006 TCA 78039

To appear in:

Thermochimica Acta

Received date: Revised date: Accepted date:

23-6-2018 4-7-2018 11-7-2018

Please cite this article as: Sinditskii VP, Hoang TH, Smirnova AD, Egorshev VYu, Yudin NV, Vatsadze IA, Dalinger IL, Comparative study of thermal stability and combustion of dinitropyrazole isomers, Thermochimica Acta (2018), https://doi.org/10.1016/j.tca.2018.07.006 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.

COMPARATIVE STUDY OF THERMAL STABILITY COMBUSTION OF DINITROPYRAZOLE ISOMERS

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V.P. Sinditskii,1 T.H. Hoang,1 A. D. Smirnova,1 V. Yu. Egorshev,1 N.V. Yudin,1, I. A. Vatsadze,2 I.L. Dalinger2 Mendeleev University of Chemical Technology, 9 Miusskaya Sq., 125047 Moscow, Russia N.D. Zilinskiy Institute of Organic Chemistry, Russian Academy of Science, 47 Leninskiy Prosp., 119991 Moscow, Russia 1 2

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Corresponding author. Tel.: +7 495 4966027; fax: +7 495 4966027.

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E-mail address: [email protected] (V.P. Sinditskii).

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Graphical abstract

Highlights

Decomposition of N-nitropyrazoles is controlled by reaction of isomerization.

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The following C-NO2 bond rupture is not rate-limiting stage.

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Isomeric dinitropyrazoles have different thermal stability and volatility

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Despite different properties all dinitropyrazoles have close burning rates.

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Melt-castable isomeric dinitropyrazoles burn at the same rates as well-known HMX.

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Abstract

A comparative study of the thermal stability and combustion peculiarities of three dinitropyrazole isomers was carried out. It has been found that the rate-limiting stage of the decomposition of 1,3-dinitropyrazole (1,3-DNP) and 1,4-dinitropyrazole (1,4-DNP) both having the N-bounded nitro group, is the N→C migration of the nitro group rather than its elimination, followed by secondary decomposition reactions of non-aromatic 3H-pyrazole. In the case of 3,4-dinitropyrazole (3,4-DNP) the rate-limiting stage is assumed to be the nitro group elimination. All the studied pyrazole isomers revealed close burning rate vs. pressure dependences despite significant differences in the thermal stability and volatility.

Key words: combustion, thermal decomposition, dinitropyrazoles, kinetics.

Introduction

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There is a great interest to dinitropyrazoles (Fig.1) nowadays, which are widely used in various fields [1-3]. Being melt-castable energetic materials, dinitropyrazoles are rather powerful explosives. For example, 3,4-dinitropyrazole (3,4-DNP) is non-hygroscopic low-sensitive explosive with melting point of 85-87 °C [4,5]. Its enthalpy of formation ( H 0f ) is positive and equals to 120.1 kJ mol-1 [6]. Velocity of detonation (VOD) and pressure of detonation calculated at density of 1.81 g cm-3 are 8.24 km s-1 and 28.8 GPa, respectively [6]. Therefore, 3,4-DNP can be recommended as a melt-castable substitute for trinitrotoluene (TNT). According to [7], the pycnometeric density of 3,4-DNP is 1.776 g cm-3. At the same time, X-ray diffraction analysis shows a density equal to 1.81 g cm-3 at room temperature [8]. A distinctive feature of the pyrazoles, differing them from other NH-azoles, is ability to produce stable endocyclic N-nitroderivates with an increased enthalpy of formation. The experimental enthalpy of formation of 1,4-dinitropyrazole (1,4-DNP) is 176.6 kJ mol-1 [6]; a close value of Hof = 180 kJ mol1 has been estimated for 1,3-dinitropyrazole (1,3-DNP) (Table 1). However, according to pycnometeric data, densities of 1,4-DNP and 1,3-DNP (1.679 and 1.783 g cm-3, respectively) are slightly lower than the density of 3,4-DNP, resulting to moderate VOD calculated for these materials (8.17 and 8.48 km s1 , respectively – see Table 1). Melting points of N-nitro derivates are lower than that of 3,4-DNP, making them of interest as high-energy plasticizers. Previously, the 3,4-DNP thermal stability was studied in detail using several methods. It was shown that the initial decomposition stage of C-nitropyrazoles is nitro group elimination [9,10]. At the same time detailed investigations of stability of N-nitro pyrazoles have not been carried out. The bond dissociation energies (BDEs) corresponding to NO2 removal from carbon and nitrogen positions of the azole ring were calculated for 1,3-DNP at the B3P86/6-311G(d,p) theory level [11]. Calculation has shown that the N−NO2 bond (BDE is 195.8 kJ mol-1) is much weaker than the C−NO2 bond (BDE is 284.9 kJ mol-1). N−NO2 BDE values have been calculated at the UB3LYP/aug-cc-pVDZ level for 1,3-DNP and 1,4-DNP as 307.5 and 267.8 kJ mol-1, respectively [12]. These calculations indicated that the N-NO2 bond is the weakest one of the N-nitro azoles, and also that 1,4-DNP has lower thermal stability than 1,3-DNP. At the same time it is well known [13] that N→C migration of the nitro group is typical for N-nitropyrazoles. It was not clear how that process would affect the thermal decomposition of N-nitropyrazoles and if the decomposition would be able to cease before the full molecule destruction. The combustion behavior study enables to better understand the nature of energetic materials, to find the most suitable application and to reasonably assess possibilities of safe usage. Previous studies [10] have shown that 3,4-DNP combustion is determined by kinetics of reactions in the condensed phase (the so called the condensed-phase combustion mechanism). The combustion of N-nitropyrazoles were not previously studied. The purpose of this research was a comparative study of thermal stability and combustion behavior of three isomeric dinitropyrazoles. Physicochemical and explosive properties of the dinitropyrazole isomers are presented in Table 1.

Experimental

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Preparation. 1,3-Dinitro-1H-pyrazole and 1,4-dinitro-1H-pyrazole were synthesized following the methods described elsewhere [14]. Prior to the thermal and combustion measurements, all compounds were recrystallized and dried under vacuum conditions. Purity was controlled by chromatography and mass spectrometry. Decomposition Study. The thermal stability of nitropyrazoles was studied under both nonisothermal and isothermal conditions. For non-isothermal conditions, differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were performed with a DSC 822e Mettler Toledo in the temperature range of 25-300°С at different heating rates. The samples weighing between 1 mg and 2 mg were analyzed in closed aluminum pans with and without pierced lids under dynamic nitrogen atmosphere. Kinetic data of the thermal decomposition were calculated using the Kissinger’s equation [15], assuming the first order of decomposition reaction: E  AR ln 2  ln  a Tmaх Ea RTmax

ln

 Ea 2 maх

T R

 ln A 

Ea RTmax

where:  is heating rate, Ea is activation energy, А is preexponential factor, Tmax is temperature of exotherm maximum. The results are presented in Table 2.

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Decomposition of nitropyrazoles under isothermal condition was studied in thin-walled glass manometers of the compensation type (the glass Bourdon gauge) at 140-190°C. A 10 to 15 mg sample was loaded into a glass manometer of 12-15 cm3 volume. The device was vacuumized up to 10-2 mm Hg, and then it was sealed and immersed in a thermostat filled with the Wood's alloy. Temperature in the thermostat was maintained with an accuracy of 0.5°C. Pressure of gases evolved in the experiments (the accuracy of pressure measurements was 1 mm Hg) was converted to the gas volume at normal conditions, and the rate of gas evolution was then calculated. The rate constant was calculated as a ratio of the initial gas evolution rate to the final volume of gases. The results are presented in Table 3. Kinetic parameters of the thermal decomposition of 1,3-DNP and 1,4-DNP obtained in nonisothermal and isothermal condition in comparison with 3,4-DNP are presented in Table 4. Analysis of decomposition products was performed using high-performance liquid chromatography combined with mass spectrometry (LCMS). LC-MS studies were carried out with a Thermo Finnigan Surveyor MSQ. The mass spectrometer was run in positive as well as negative ionization modes using electrospray ionization (ESI) with mass to charge ratio (m/z) in the range of m/z = 60-1000. Infrared spectra in the 4000-400 cm−1 region were measured on KBr pellets with a Thermo Nicolet 360 FTIR spectrophotometer. Combustion Study. Burning rates (rb) of nitropyrazoles were measured in a window constantpressure bomb of 1.5-liter volume in the pressure range of 0.1-10 MPa. The bomb was pressurized with nitrogen gas. Samples to test were prepared as pressed cylinders of pure substances of 4-5 mm height confined in transparent acrylic tubes of 4 mm i.d. and 6 mm o.d. Prior to pressing, the material was carefully milled in order to produce samples with a minimum possible pore size, thus minimizing the possibility of flame propagation between particles. The combustion process was recorded with a highspeed video camera. The burning rate was determined by measuring the position of the flame front over the time. Densities of the pressed samples, calculated adiabatic flame temperatures (Tad), burning rates at pressure of 10 MPa, and the burning rate laws (rb= bpn) for the studied materials are presented in Table 5. Temperature profiles in the combustion wave were measured using fine tungsten-rhenium thermocouples [16]. The thermocouples were welded from 80%W + 20%Re and 95%W + 5%Re wires 25 m thick followed by rolling in bands 5-7 m thick. The thermocouple was embedded into the center of the sample. The thermocouple signal was recorded with a Pico ADC 216 digital oscilloscope. Thermodynamic calculations of the adiabatic flame temperature Tad at 10 MPa (Table 5) were performed with the “REAL” computer code for simulation of the chemical equilibrium in the combustion products [17].

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Results and discussion Thermal decomposition

The assessment of the real decomposition kinetics of nitropyrazoles from data obtained by nonisothermal methods (DSC and TG) is by all appearances difficult due to simultaneous evaporation of these compounds [18,19]. Furthermore, the endothermic evaporation can be sometimes mistaken for decomposition [20]. According to DSC study (10 °C min-1), the exothermic peak during heating of 1,4-DNP and 1,3DNP in closed aluminum pans with pierced lids is observed along with the endothermic peak of melting (Fig.2 and Fig.3). The heat effect of 1,3-DNP decomposition at 206°C is low (417 J g-1, 99.7 cal g-1). The thermogram shows small endothermic and exothermic areas at higher temperatures, which is indicative of evaporation and destruction of products formed in the first stage of decomposition (Fig.3).

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In case of 1,4-DNP the endothermic evaporation overlaps with the exothermic decomposition (Fig.2). As a result, both the decomposition peak temperature and the heat effect are distorted. Under TG analysis conditions, 1,4-DNP demonstrates 90% mass loss in the temperature range of 120-190°C, which is well below the DSC decomposition peak. Likewise, 1,3-DNP shows almost complete mass loss (91%) in the temperature range of 130-240°C. When heating 1,4-DNP and 1,3-DNP in sealed caps, the evaporation process is hindered and has little influence on the main exothermic peak location. This peak is observed for 1,4-DNP and 1,3-DNP at 173-225 °C and 188-228 °C, respectively, depending on the heating rate (Table 2). Also, the amount of released heat increases. Using the DSC data, decomposition rate constants for 1,4-DNP and 1,3-DNP in non-isothermal conditions were calculated by the Kissinger method [15] under the assumption of the first order of the reaction (Table 2). Rate constants for 1,4-DNP and 1,3-DNP are described by the equations: k (s-1) = 1.6·1011∙exp(-14430/T) and k (s-1) = 2.5·1011∙exp(-14860/T), respectively (Table 4). The decomposition rate of 1,4-DNP is slightly higher than that of 1,3-DNP. The activation energies of decomposition of both isomers (120.0 and 123.6 kJ mol-1) turn to be close to the activation energies of the isomerization reaction investigated previously [13]. Thermal decomposition of 1,4-DNP and 1,3-DNP under isothermal conditions were carried out in Bourdon gauges (manometers) with a mass-to-volume ratio of ~10-3 g cm-3 and at temperatures above the melting points (150-190°C). When the pressure gauge is immersed in the thermostat, the pressure in the manometer reached 16-37 mm Hg for 1,3-DNP and 30-50 mm Hg for 1,4-DNP at the first minute of heating, depending on the initial temperature. Such a behavior of N-nitropyrazoles may be due to their considerable volatility or due to the catalytic effect of the reaction vessel surface on the decomposition. Gas evolution curves for 1,3-DNP demonstrate a saturable pattern, typical for the first order reactions (Fig.4). In case of 1,4-DNP there is a slight acceleration of decomposition, especially notable at lower temperatures (Fig.5). The final volume of gases is quite moderate, not exceeding 85 cm3 g-1 at 180 °C (0.6 mol per mol of the initial substance) for 1,3-DNP and 180-190 cm3 g-1 (1.27-1.34 mol) for 1,4-DNP. The color of gases in vessels is bright brown, which is indicative of the presence of nitrogen dioxide. Color intensity drops if the vessel is kept at room temperature for some time. In case of 1,3-DNP a little amount of gases was condensed when the reaction vessel was cooled to a room temperature (~10% or 0.06 mol/mol), which is most likely connected with condensation of some volatile decomposition products. The solid residue has a light yellow color. In case of 1,4-DNP the decomposition products are colorless; after cooling the vessel they accumulated at the bottom and solidified. In comparison with 1,3-DNP, the decomposition of 1,4-DNP produces more condensable products (34% or 0.44 mol/mol). IR spectra of 1,4-DNP and 1,3-DNP solid decomposition products (pressed in KBr) demonstrate disappearance of the N-NO2 group vibration bands (1648, 1279 and 1640, 1244 cm-1, respectively). In contrast, vibration bands of the C-NO2 group (1552, 1518, 1384, 1308 and 1570, 1530, 1382, 1353 cm1 ) and C-H bonds (3166 and 3249 cm-1) remain. Besides, bands of the N-H bonds (3387 and 3350 cm-1) appear in the spectra. LCMS analysis have shown that the main decomposition products of 1,3-DNP are dinitropyrazole (m/z 158, 77%), another dinitropyrazole isomer (5%), nitropyrazole (m/z 113, 14%) and some amounts of high-molecular products (4%). In case of 1,4-DNP, tiny amounts (2%) of a product of its isomerization, 3,4-DNP, have been found. The main products are nitropyrazole (19%) and a wide variation of nitropyrazole-based oligomeric products (79%). The more nitropyrazole units are in the oligomeric molecule, the less amount of it is formed. Bis-nitropyrazole is formed to the extent of 15%, whereas the compound consisting of 14 nitropyrazole cycles is present in trace amounts. Because of high initial pressures in the Bourdon manometers loaded with N-nitropyrazoles, it has been assumed that most of the compound decomposes in the gaseous state and the gas evolution curves may be described by a first-order equation which takes into account not only the formation of gas products but also the disappearance of the gaseous starting material: V = V(1-exp-kt) + V0·exp-kt, where V is the volume of evolved gases (cm3 g-1), V is the final volume of gases, V0 is the volume of gases in the vessel due to the vapor pressure of the substance, k is the rate constant. However, the rate constants thus obtained did not proved to be consistent with the data obtained under nonisothermal conditions (DSC). It can be assumed that the initial pressure in the manometers is not related to the vapor pressure

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of the substances under study. Thermocouple-aided studies of temperature distribution in the combustion wave of these materials indicated rather low vapor pressures as well. The initial pressure in the Bourdon manometer is presumably caused by a rapid catalytic decomposition of N-nitropyrazoles on the glass wall surface. Consequently, the decomposition of the liquid compounds can be described by the first-order kinetic equation for 1,3-DNP and the first-order autocatalytic equation for 1,4-DNP not taking into account the initial pressure jump (Table 4). Apparently, the reason for accelerating the 1,4-DNP decomposition is catalysis of the decomposition by the surface of the glass vessel. In Arrhenius coordinates, the decomposition rate constants for 1,3-DNP and 1,4-DNP (noncatalytic stage k1) are described by low-activation-energy dependencies (128.9 and 121.9 kJ mol-1) and fall on extrapolation of the temperature dependence received in nonisothermal conditions (Fig.6). One can note that the decomposition rates of melted N-substituted isomers are very close to the rate of DNP isomerizaion in solvent [13]. Both N-substituted isomers are considerably less stable than their C-substituted isomer (3,4-DNP). Nevertheless, the stability of N-substituted isomers is close to the stability of the known energetic plasticizer nitroglycerin (NG) [21]. Because of low activation energies, the rate constants of decomposition of N-nitropyrazoles become close to those of NG at high temperatures and diverge at lower temperatures. N-Nitropyrazoles when heated are known to undergo N→C migration of nitrogroup [13]. The reaction in solvent at 130-200°C is the first order one and proceeds almost quantitatively for 1,3-DNP and much worse (45% yield) for 1,4-DNP. A relatively low activation energy (125-150 kJ mol-1) as compared to the estimated N-NO2 bond energy (188-209 kJ mol-1 [13]), along with the absence of radical transformations and H/D isotopic effect, low sensitivity of kinetic parameters to the solvent nature, suggests a key stage of migration as concerted [1,5]-sigmatropic rearrangement of NO2-group. The intermediate 3H-pyrazole quickly undergoes aromatization with formation of 1H-pyrazole: R2

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(1) The driving force of the reaction is higher stability of C-nitropyrazoles as compared with N-nitropyrazoles. This rearrangement is irreversible and exothermic: based on the enthalpies of formation of dinitropyrazoles, the heat effect is 356 J g-1 (85 cal g-1) for 1,4-DNP and 556 J g-1 (133 cal g-1) for 1,3-DNP. The lack of a primary H/D isotope effect in case of isomerization of deutero-derivative permits conclusion that hydrogen migration is not involved in the rate-determining step [13]. An estimated activation energy of [1,5]-sigmatropic rearrangement of NO2-group for related N-nitro-1,2,4-triazole is equal to 133.1 kJ mol-1 [22]. Subsequent activation energy of [1,5]-sigmatropic shift of hydrogen atom equals 124.3 kJ mol-1, besides, this stage is accompanied by heat effect (129.3 kJ mol-1) [22]. In work [22], the heat effect of [1,5]-sigmatropic rearrangements of NO2-group is not referred to. However, if we consider an analogy between the pyrazole and triazole cycles, the heat effect of the rearrangement will be about 210-420 kJ mol-1(Fig.8). Normally the rate of the preliminary isomerization determines the intermediate product concentration. Then the observed activation energy is made up of the activation energies of isomerization and decomposition reactions [23,24]. In this case, the high heat effect of the preliminary isomerization (Fig.8) is a reason for the subsequent hydrogen migration not being involved in the rate-determining step. IR-spectroscopy and chromatographic analyses of decomposition products obtained in the manometric vessel confirmed disappearance of N-nitropyrazole and formation of C-nitropyrazoles. However, the isomerization reaction does not produce any gaseous products. C-nitropyrazoles, formed in the isomerization reaction, are significantly more stable than N-nitropyrazoles and decompose at higher temperatures. It may be assumed, therefore, that the observed gas evolution at heating of N-nitropyrazoles is caused by secondary decomposition reactions of intermediate non-aromatic 3H-pyrazole:

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(2) This reaction as well as [1,5]-sigmatropic hydrogen shift is not the rate-limiting one (Fig.8). However, the rate of both reaction depends on nitro group position: in case of 1,3-DNP, [1,5]-sigmatropic hydrogen shift proceeds more quickly, resulting in the preferential formation of 3,5-DNP. In case of 1,4-DNP, the stabilizing effect of the neighboring nitro group on the resulting radical center may be essential, and the decomposition reaction (2) predominantly proceeds. In any case, a side decomposition reaction (2) takes place to some extent for both isomers. But, the subsequent transformation of formed isomeric nitropyrazole radicals may be different. The 3-nitropyrazole radical transforms mainly in 3-nitropyrazole and partially in unidentifiable oligomeric products:

The 4-nitropyrazole radical is also converted to the corresponding 4-nitropyrazole, but to a greater extent it forms oligomeric products:

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A similar reaction was observed in the decomposition of 3,4-DNP in [10]. As a result of these reactions, about 1.5 moles of gases per one mole of NO2 are evolved. The third part of gaseous products (water) is condensable on cooling, which is consistent with the results of manometric experiments.

Combustion behavior and flame structure

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Within the studied pressure interval, the burning rates of all the DNP isomers proved to be very close (Fig.7) and slightly higher than the burning rates of widely known explosive octogen (HMX). At low pressures, a different behavior was observed only: 3,4-DNP begins to burn at 0.6 MPa while N-nitropyrazoles (1,4-DNP and 1,3-DNP) demonstrate stable combustion starting from 0.2 MPa. Combustion of DNP isomers was accompanied by a bright flame in whole pressure range. Within 0.610 MPa interval, the pressure dependence of the burning rate for 1,4-DNP and 1,3-DNP can be expressed by equations rb (mm s-1) = 2.97p0.86 and rb = 2.88p0.88, respectively. A close similarity between burning rates of pyrazole isomers is a rather unusually phenomenon because N-nitro isomers are more volatile compounds and have essentially lower thermal stability than 3,4-DNP. It has been shown [10] that the burning rate of 3,4-DNP is determined by reactions in the condensed phase. In order to gain an insight into combustion mechanism of N-substituted isomers, the temperature distribution in combustion wave of these compounds needs to be obtained. In this work, the temperature profiles were measured by thin tungsten-rhenium thermocouples at 0.7-0.8 MPa for 1,3-DNP and in the pressure range of 0.1-1.1 MPa for 1,4-DNP. Typical temperature profiles for 1,3-DNP and 1,4-DNP are presented in Fig.9 in comparison with profiles for 3,4-DNP [10]. As can be seen from Fig.9, a high-temperature flame appears immediately above the surface at a distance ~100 µm. The temperature gradient above the burning surface is high (4-7104 K cm-1) and provides the heat feedback from the gas phase as 188-272 J g-1, given respective burning rates and an average thermal conductivity coefficient  = 310-4 cal cm-1s-1K-1 are used in the calculation. To establish the combustion mechanism of an energetic compound it is necessary to know the

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pressure dependence of the surface temperature TS(p). With knowledge of the surface temperature and the decomposition kinetics, it is possible to calculate the decomposition depth in the subsurface layer and ascertain a role of condensed-phase reactions in the combustion process. The surface temperature of 1,4-DNP in the pressure interval of 0.1-1.1 MPa grows from 307C to 438C (Table 6), being less than the surface temperature of 3,4-DNP [10] (Fig.10). Thermocoupleaided studies has made it possible to describe the temperature dependence of vapor pressure above liquid 1,4-DNP with the following equation: lnp = -7860/T+ 13.6 (Fig.10). The vaporization heat of 1,4-DNP calculated from the above equation (65 kJ mol-1) appeared to be slightly below than the vaporization heat of 3,4-DNP (91 kJ mol-1) [10] due to stronger hydrogen bonding of acidic NH-group. Data for 1,3DNP were determined in a narrow pressures range, rendering the definition of TS(p) dependence for this compound impossible. Nevertheless, TS points for 1,3-DNP fall close to the dependence for 1,4-DNP (Fig.10), suggesting relatively equal volatility of both isomeric N-nitropyrazoles. In the work, the vapor pressure above liquid 1,3-DNP and 1,4-DNP was measured in the Bourdon pressure gauge in the temperature range of 100 – 150 °C and at 3-5 min exposure time. The experimental points were found to lie essentially higher than the fitting line of points obtained in thermocouple-aided experiments and extrapolated to the low-temperature area (Fig.10). It is probable that the initial pressure rise in the Bourdon gauge is caused by rapid catalytic decomposition of N-nitropyrazoles at the glass surface of the Bourdon gauge. Rather weak dependences of the initial pressure on temperature for 1,3DNP (~ 38 kJ mol -1) and 1,4-DNP ( ~ 29 kJ mol -1) count in favor of this hypothesis. These values are essentially different from the calculated heat of vaporization of the 1,4-dinitropyrazole (65 kJ mol -1). Notice that the vapor pressure of liquid N-nitropyrazoles is slightly lower than that of nitroglycerine [25] (Fig.10). Using pressure dependences of the burning rate and surface temperature as basis, it is possible to calculate the decomposition depth in the subsurface layer in the liquid phase [26]. At a pressure of 0.6 MPa a decomposition depth of 1,4-DNP is 58%. To vaporize the remaining undecomposed substance is necessary to bring in some 0.42·417 J g-1 = 175 J g-1 additional heat. This value is in a good agreement with the heat feedback from the gas phase. Therefore, in spite of high temperature gradients above the burning surface of the N-nitropyrazoles, the gas phase heat flux is totally consumed to evaporation of unreacted substance. At the same time, the heat released in the condensed-phase decomposition that equals 0.58·1270 J g-1 = 737 J g-1, can heat it up to the surface temperature: Qneed =cp(TS-T0)+Lm = 621+98.5 = 719.5 J g-1. Thus, the burning rate of the compounds is determined by decomposition kinetics in the liquid phase at the burning surface temperature (combustion mechanism with the leading reaction in the condensed phase). In this case, unique information on the decomposition kinetics of energetic compounds at high temperatures can be obtained from experimental data on burning rates and surface temperatures [27]. Combustion in the condensed phase is well described by the classical Zel'dovich model [28]:

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RTs2 2 2  Q  E / RTs m ( )  A e 2 c p (Ts  T0  Lm / c p ) E

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where m, ср, ,  are mass burning rate, specific heat, density, and thermal diffusivity of the condensed phase, Ts and Q are the surface temperature and heat effect, Е and А are activation energy and preexponential factor of the leading reaction in the condensed phase. The expression TS-T0+Lm/cp accounts for heating-up of the condensed phase from initial temperature, T0, to surface temperature, TS, and melting. Heat of reaction, Q, was taken as 1270 J g-1. Comparison of the rate constants derived from combustion of 1,4-DNP, kbr = 9.3·1010∙exp(-14190/T), with its decomposition rate constants in both isothermal and non-isothermal conditions is shown in Fig.11. One can note that kinetics derived from the combustion model is in a good agreement with decomposition rate constants obtained at low temperatures. The same result can be obtained if we extract the kinetics of the leading combustion reaction from the combustion data of 1,4DNP.

Conclusion remarks

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In a wide temperature range of 150-500°С, the decomposition reactions of relatively stable 1,4-DNP and 1,3-DNP in the liquid phase proceed with low activation energies (118-122 kJ mol-1 and 124-129 kJ mol-1, respectively). These values are close to the activation energy of [1,5]-sigmatropic shift of NO2 group. Non-aromatic 3H-pyrazole formed in this reaction as an intermediate can undergo either aromatization to form 1H-pyrazole or elimination of nitro group. Both of these processes are not rate limiting ones. The structure of N-nitropyrazole has an influence on the process. 1,3-DNP predominantly transforms to 1H-pyrazole, whereas 1,4-DNP mostly decomposes probably because of stabilizing effect of neighboring nitro group on the formed nitropyrazole radical center. Further transformation pathways of isomeric 3- and 4-nitropyrazole radicals are different. A characteristic feature of the phenomenon is as follows: the decomposition rate of N-nitropyrazoles is determined by the preliminary isomerization kinetics rather than the kinetics of the N-NO2 bond splitting. The close burning rates of N-nitro and C-nitro pyrazoles turns out to be a coincidence. The combustion of all nitropyrazole isomers obeys a condensed-phase combustion model. A large difference in the decomposition rate constants between N-nitropyrazoles and 3,4-DNP observed at low temperatures becomes practically negligible at temperatures of the burning surface due to higher activation energy of 3,4-DNP. According to the combustion model, the pressure index of the burning rate is determined by a ratio of the leading reaction activation energy to the heat of vaporization. Low activation energies of N-nitropyrazoles are compensated by low heats of their evaporation while high activation energy of 3,4-DNP is counterbalanced by a large evaporation heat of the compound. As a result, the pressure indexes in the burning rate-pressure dependences for all studied nitropyrazoles prove to be relatively the same.

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Acknowledgment

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The authors are grateful to Dr. N.N. Kondakova (MUCT) for carrying out DSC and TGA measurements. The work was supported by the Russian Science Foundation (project no. 14-13-01153).

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25. V. A. Golovin, Y. M. Lotmentsev, R.I. Shneerson, A study of the compatibility of NG and NC with the static method of measuring saturated vapor pressure, Vysokomol. soyed. 17А(10) (1975) 2351-2354.

26. V.P. Sinditskii, V.Yu. Egorshev, V.V. Serushkin, S. A. Filatov, Combustion of energetic materials controlled by

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condensed-phase reactions, Comb., Explos., Shock Waves, 48(1) (2012) 81-99.

27. V. P. Sinditskii, V. Y. Egorshev, V. V. Serushkin, A. I. Levshenkov, M. V. Berezin, S. A. Filatov, S. P. Smirnov, Evaluation of decomposition kinetics of energetic materials in the combustion wave, Thermochim. Acta, 496(1) (2009) 1-12.

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28. Y.B. Zeldovich, Theory of combustion of propellants and explosives, Zh. Eksper. Teoret. Fiziki, 12(11-12) (1942)

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A

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498-524.

Signatures to Figures Fig. 1. Structural formulas of studied materials O2 N

NO2

O2N

NO2

N

N

N

N

N

N H

NO2

NO2

3,4-DNP

1,4-DNP

1,3-DNP

A

N

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Fig. 2. DSC (1) and TG (2) curves of 1,4-DNP at a heating rate of 10 °C/min

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Fig. 3. DSC (1) and TG (2) curves of 1,3-DNP at a heating rate of 10 °C/min

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Fig. 4. The gas evolution curves of the 1,3-DNP decomposition at different temperatures. Points are experiment, lines are description

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Fig. 5. The gas evolution curves of the 1,4-DNP decomposition at different temperatures. Points are experiment, lines are description

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Fig. 6. Comparison of the decomposition kinetics of isomeric dinitropyrazoles and rate of isomerization

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Fig. 7. Comparison of the burning rate vs. pressure dependences for isomeric dinitropyrazoles

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Fig. 8. Thermodynamic parameters of [1,5]-sigmatropic NO2-group rearrangement for azoles

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Fig. 9. Typical temperature profiles of DNP isomers at 0.6 MPa

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Fig. 10. Temperature dependence of the vapor pressure of 1,4-DNP (1, points and line) and 1,3-DNP (2) in comparison with 3,4-DNP (3) and nitroglycerin (NG). 4 and 5 are initial pressures of 1,3-DNP and 1,4-DNP in Bourdon pressure gauge

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Fig. 11. Comparison of the kinetics of the leading combustion reaction of 1,4-DNP (1, points and line) with the decomposition kinetics of 1,4-DNP in non-isothermal (2) and isothermal (3) conditions, and decomposition kinetics of 3,4 DNP (4).

Signatures to tables Table 1. Physico-chemical and explosive properties of dinitropyrazole isomers. Table 1.

Melting point (heat, J g-1), °C The temperature of intensive decomposition (heat, J g-1), °С Density, g cm-3 Enthalpy of formation, kJ mol-1 (kJ kg-1) Detonation velocity, km s-1 (density) Detonation pressure, GPa

1,3-DNP 66.0 (99.1); 67 [14]

205 (36)* 199 (800)**

206 (417) 208 (1270)**

1.81 [6,8]; 1.776 [7] 120.1 (759.8)[6]

1.679 176.6 (1117) [6]

1.768 180 (1138)

8.24 (1.81) [6]

8.17 (1.679)

8.48 (1.768)

28.8

27.6

30.5

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Compound 1,4-DNP 47.9 (98.5); 54[14]

3,4-DNP 84.8 [6]; 86 [5]; 87 (107.5)[10] 347 (2102) [10]

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Properties

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* the decomposition peak overlaps with the endothermic peak of evaporation. ** closed cap, 8 deg min-1 Table 2. DSC analysis data for 1,4-DNP and 1,3-DNP.

Heating rate, deg min-1

1,4-DNP Тmax,оС

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177.6 190.9 199.1 210.8 216.6

k103, s-1

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2 4 8 16 32

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Table 2.

2.3 4.4 8.4 16.1 31.4

1,3-DNP Тmax,оС 188.6 196.8 207.6 219.0 227.8

Table 3. Results of isothermal decomposition studies for 1,3-DNP and 1,4-DNP. Table 3.

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Temperature, C 140 150 160 170 180 182 190

Rate constant (s-1) for nitropyrazoles 1,3-DNP 1,4-DNP 4 k110 k104 0.8 1.00 1. 7 2.24 6. 9 4.20 9.55 19.2 25.7

k103, s-1 2.3 4.5 8.6 16.4 31.7

Table 4. Kinetic parameters of thermal decomposition of liquid 3,4-DNP, 1,4-DNP, and 1,3-DNP. Table 4.

Substance 3,4-DNP [10] 1,3-DNP

1,4-DNP

Temperature interval, °C 170-240 140-182 189-228 150-190 178-217 390-500

log A

Ea, kJ/mol (kcal/mol) 161.4 (38.6) 128.9 (30.8) 123.6 (29.5) 121.9 (29.1) 120.0 (28.7) 118.0 (28.2)

13.61 11.89 11.39 11.41 11.21 11.09

Coef. of determination 0.979 0.990 0.980 0.960 0.978 0.999

Density of sample, g cm-3 (TMD ratio)*

Tad at 10 MPa, K

rb= bpn, mm s-1

Pressure interval, MPa

b

3,4-DNP [10]

1.67(0.92)

3317

0.6-15

1,3-DNP

1.58(0.89)

3477

0.6-10

1,4-DNP

1.51(0.90)

3486

0.6-10

rb at 10 MPa, mm s-1

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Compound

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Table 5. Experimental combustion characteristics of dinitropyrazoles.

2.87

0.86

20.5

2.88

0.88

21.5

2.97

0.86

21.9

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* in brackets, a ratio of sample density to the theoretical maximum density (TMD) is given

2.30.8

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A

Тf, Ca

410±12 416±6 307 370 387±13 384 438

2211±52 2170±86 2300 745 2235 2235 2307 2350

- Confidence intervals are given for three and more parallel runs.

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a

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1,3-DNP

TS, Ca

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1.90.2 1,3-DNP

Pressure, MPa 0.6 0.8 1.1 0.1 0.3 0.6 0.8 1.1

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Compound

103, cm2s-1

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Table 6. The thermal diffusivity, , and characteristic temperatures in the combustion wave of the studied compounds. Table 6.