The effect of molecular structure on thermal … Stability.pdf138 Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137–148 the oxygen balance, volume, density, detonation velocity

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Thermochimica Acta 566 (2013) 137– 148

Contents lists available at SciVerse ScienceDirect

Thermochimica Acta

jo ur nal ho me page: www.elsev ier .com/ locate / tca

he effect of molecular structure on thermal stability, decompositioninetics and reaction models of nitric esters

i-Long Yana, Martin Künzela, Svatopluk Zemana,∗,oman Svobodab, Monika Bartoskovác

Institute of Energetic Materials, Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice, Czech RepublicDepartment of Physical Chemistry, Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice, Czech RepublicDepartment of Environment, Faculty of Chemistry, Brno University of Technology, CZ-612 00, Brno, Czech Republic

a r t i c l e i n f o

rticle history:eceived 8 March 2013eceived in revised form 21 May 2013ccepted 22 May 2013vailable online 31 May 2013

eywords:itric estershermal stabilityritical temperatureeaction modelsinetic compensation effect

a b s t r a c t

In this paper, the thermal stability and decomposition mechanism functions of 10 nitric esters includingnitroglycerine (NG), pentaerythritol tetranitrate (PETN), trimethylolethane trinitrate (TMETN), dipen-taerythritol hexanitrate (DiPEHN), trimethylolpropane trinitrate (TMPTN), erythritol tetranitrate (ETN),xylitol pentanitrate (XPN), sorbitol hexanitrate (SHN), mannitol hexanitrate (MHN) and nitroisobutyl-glycerol trinitrate (NIBGT) are determined by means of non-isothermal TG and DSC techniques. It hasbeen found that the mean activation energies for most nitric esters are comparable at constant heatingrate (around 145 kJ mol−1), indicating that their main decomposition pathways might be the same. Themass loss activation energies of NG, TMETN and TMPTN are less than 100 kJ mol−1 due to partial evap-oration. Based on the critical temperature of thermal decomposition, the order of molecular stabilityfor involved nitric esters is found to be MHN < XPN < TMPTN < SHN < NIBGT < ETN < PETN < DiPEHN. Theintroduction of function groups to the tertiary carbon is in favor of increasing thermal stability due to

increase of symmetry and rigidity of the molecule. The decomposition kinetics was described in terms ofthe Johnson-Mehl-Avrami and Sesták-Berggren models. Two types of kinetic behavior were observed andmost nitrate esters followed typical decomposition kinetics close to the first order reaction. However, cer-tain materials showed complex behavior caused by overlapping of more mechanisms/processes, whichwere represented either by simultaneous evaporation and decomposition or by different decompositionmechanisms originating from varying morphology and structure of the samples.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

Nitric esters have been used as plasticizers or energetic fillersn detonators, propellants and explosives for mining, artillery, andngineering since hundreds years ago [1,2]. In the past decades,onsiderable interest in nitric esters has been expressed by not onlyhe specialists but also the amateurs and terrorists due to require-

ents of little synthetic expertise and availability of cheap rawaterials from the shops [3]. There has been growth in use of those

itric esters such as erythritol tetranitrate (ETN), most of which areo-called “homemade” explosives (HME). On the one hand, a num-

er of polynitroesters, including nitrocellulose (NC), nitroglycerinNG), the nitroester of pentaerythritol (PETN), trimethanolethanerinitrate (TMETN), and bis(2-nitroxyethyl)nitramine (DINA) are

∗ Corresponding author. Tel.: +420 466038503; fax: +420 466038024.E-mail addresses: [email protected] (Q.-L. Yan), [email protected],

[email protected] (S. Zeman).

040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.tca.2013.05.032

powerful explosives used mainly for military purposes due togreater compatibility and higher performance than other nitricesters [4–7]. In particular, with regard to spark detonators, PETNcan be used to avoid the need for primary explosives due to its lowerelectric spark initiation energy (10–60 mJ). On the other hand, somenitric esters could be used as drugs in medical treatment. In fact,nitroester drugs have been shown to relax the smooth muscle ofblood vessels, and hence were widely accepted for the treatmentof angina pectoris [8].

Because of growing practical demands on nitric esters, more andmore investigations are carried out with regard to their synthe-sis and physiochemical properties. On the purpose of utilizationas energetic ingredients, recent studies have been concentratedmainly on their detailed thermal decomposition mechanisms, com-bustion and detonation performances [9–11]. For instance, density

function theory (DFT) has been employed to study the geometricand electronic structures of trinitrate esters including NG, TMETN,butanetriol trinitrate (BTTN), and trimethylolpropane trinitrate(TMPTN) at the B3LYP/6-31G* level [12]. It has been found that

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38 Q.-L. Yan et al. / Thermochi

he oxygen balance, volume, density, detonation velocity and pres-ure of trinitrate esters linearly decrease with the increase ofethylene group’s number. In order to clarify the initial decompo-

ition mechanism for nitric esters, T-Jump/FTIR and T-jump/Ramanpectroscopies were used to analyze the gaseous products ofeveral aliphatic nitric esters [13]. Kimura [14] also used chemi-uminescence (CL) method to determine the light-emitting speciesuring low temperature decomposition (between 40 ◦C and 90 ◦C)f PETN and NC. It has been shown that the thermal decomposi-ion of nitric esters is accompanied by some oxidation reactions,hich could be generated in the course of recombination of per-

xy radicals. On this basis, Chen and Brill [15] further studiedhe fast thermal decomposition kinetics and mechanism of someolymeric nitric esters by SMATCH/FTIR technique (heating rate:00–150 ◦C s−1), and their activation energies were obtained asround 129.8–142.4 kJ mol−1 with log(A) values of 14.7–16.9 s−1.grawal [16] synthesized some aromatic nitric esters, amonghich the compound 1,3,5-tris(2-nitroxyethylnitramino)-2,4,6-

rinitrobenzene was found to be the potential alternative of PETN. Inddition, quantum chemical calculations are used to compute theeats of formation for 24 nitric esters among which only 5 com-ounds have the available experimental values [17]. As a result,onsiderable progress toward an understanding of the decompo-ition mechanism for nitric esters has been achieved. However,ndoubtedly, the effect of molecular structure on the performancesnd physiochemical properties of nitric esters could not be clearlydentified due to discrepancy in principles and physical condi-ions of corresponding measurements carried out by differentesearchers. In this paper, the non-isothermal behavior, isocon-ersional decomposition kinetics, reaction models and thermaltability for 10 typical nitric esters will be systematically inves-igated, based on which the effect of molecular structure on thesearameters will be expounded.

. Experimental

.1. Materials

There are 10 nitric esters involved in this research, whose molec-lar structures are shown in Scheme 1. The nitroglycerine (NG),entaerythritol tetranitrate (PETN), trimethylolethane trinitrateTMETN), dipentaerythritol hexanitrate (DiPEHN), trimethylol-ropane trinitrate (TMPTN) are commercially available androvided by “Explosia a.s.” company. The erythritol tetranitrateETN), xylitol pentanitrate (XPN), sorbitol hexanitrate (SHN),

annitol hexanitrate (MHN) and nitroisobutylglycerol trinitrateNIBGT) are prepared by our work group by simply nitrating theorresponding alcohols which are commercially available.

.2. Testing techniques

The involved nitric esters are studied with regard to the kineticsf thermal decomposition, using Thermogravimetry (TG, Netzsch09F3 instrument, Al2O3 crucible) under the heating rate of 5,

(with data collecting rate of 40 points per Kelvin) and 10,5 ◦C min−1 (with data collecting rate of 60 points per Kelvin). Theest temperature range for TG was 30–300 ◦C, with the sample

ass of about 2.05–2.45 mg under 30 ml min−1 dynamic nitrogentmospheres. Their heat flow properties was also evaluated byhe technique of Differential Scanning Calorimetry (DSC, Netzsch00F3 instrument, Aluminum pan with a pin hole cover), which

as introduced in the dynamic nitrogen atmosphere with a pres-

ure of 0.1 MPa. The sample mass for DSC test was about 2.40 mgith a heating rate of about 5 ◦C min−1 and temperature range of

0–300 ◦C.

cta 566 (2013) 137– 148

3. Results and discussions

3.1. Thermal responses during heating

The thermal responses (heat flow) for involved 10 nitric esterswere recorded by DSC under pressure of 0.1 MPa as shown in Fig. 1.The DSC curves for most of the studied nitric esters are not avail-able in the literature. It has been shown that the melting points ofnitric esters are much lower than those of secondary explosives, andsome of them are liquid at room temperature. There is a big differ-ence with regard to melting point due to discrepancy in molecularstructure. For instance, MHN and PETN have melting point higherthan 110 ◦C, while those of TMETN, NG, and NIBGT are less thanzero. With regard to heat release process, it has been observed that,the exothermic peaks for NG and TMETN are not well formed dueto strong evaporation. In order to make a quantitative view of thethermal responses, the corresponding parameters are summarizedin Table 1. The density and detonation velocity parameters are alsoincluded in this table.

As shown in Table 1, the density of these nitric esters is around1.4–1.8 g cm−3 with theoretical detonation velocity of between7000 and 9000 m s−1. As it could be seen, all of the nitric estersdecompose in liquid state, and for the solid nitric esters, thereare obvious endothermic heat change before decomposition dueto fusion. It is interesting that the peak temperature of SHN andXPN is the same while their onset temperature is very different,and this might be caused by their very similar carbon chain struc-ture. NG, ETN and TMETN are comparable. PETN has the highestfusion energy (�H1), and melting point due to its highly symmet-ric molecule and great molecular rigidity. For NG, there is also oneendothermic peak before decomposition due to evaporation, andunder dynamic nitrogen atmosphere the NG could partially decom-pose. With regard to heat of decomposition �H2, DiPEHN has thehighest heat release due to higher hydrogen and carbon contentwith sufficient oxygen balance. The heat release from decomposi-tion depends not only on the energy content of the compound, butalso on the experimental condition. Here the nitric esters decom-pose under 0.1 MPa dynamic nitrogen atmospheres with relativelyslow heating rate. The heat change is also slow and could be wellrecorded by the equipment. However, DSC thermograms of volatilematerials such as NG and TMETN will be strongly dependent onexperimental conditions. At sufficiently slow heating and smallmass the sample may completely evaporate before decomposition(in open or non-hermetically close sample pans). The effect of dif-ferent heating rates will be different heat of reaction. Since heatof reaction is determined from peak area and initial sample mass,the determination of heat of reaction in the case of sample masschange during the process for NG and TMETN is highly inaccurate.In fact, some other nitric esters with “Oxygen Bridge” such as tri-ethylene glycol dinitrate (TEGDN) are also volatile under dynamicatmosphere [18].

3.2. Thermal stability

The thermal stability of the crystals could be compared by themelting points of the compounds, and the stability of the molecularstructure could be roughly determined by the onset temperaturesof exothermic peaks. For the purpose of kinetic calculation and eval-uation of thermal stability, the TG curves of involved nitrated estersare recorded under four different heating rates and the correspond-ing data are summarized in Table 2 (the TG curves are omitted in

order to save the layout space). However, the onset temperatureis dependent on the heating rate. We have to find another param-eter that is independent on heating rate and comparable to onsettemperature to represent the thermal stability of these compounds.

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Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148 139

O2NO ONO2

O2NOO2NO

ONO2

ONO2

O2NO

O2NO

ONO2

ONO2

O2NO

O2NO

CH3

ONO2

ONO2

O2NO

O2N

ONO2

ONO2

O2NO

NG (C3H5N3O9) XPN (C5H7N5O15) PETN (C5H8N4O12) TMETN (C5H9N3O9) NIB GT (C4H6N4O11)

ONO2

ONO2

O2NO

O2NO

O2NO

ONO2

ONO2

O2NO

ONO2

O2NO

ONO2

ONO2

O2NO

O

O2NO

O2NO

ONO2

ONO2

ONO2

CH3

O2NO

ONO2

ONO2

O2NO

ONO2

O2NO

O2NO

ETN (C4H6N4O12) SHN (C6H8N6O18) DiPEHN (C10H16N6O19) TMPTN (C6H11N3O9) MHN (C6H8N6O18)

Scheme 1. Molecular structure of involved nitric esters.

of 10.

dtalw

TP

Ni

Fig. 1. DSC curves of different types of nitric esters at the heating rate

We can calculate the critical temperature (Tb) for thermalecomposition from the data of TG experiments. Tb is an impor-ant thermal stability parameter required to insure safe storage

nd process operations for energetic materials. It is defined as theowest temperature to which energetic materials may be heated

ithout undergoing thermal decomposition. Tb may be calculated

able 1arameters from DSC experiments of different types of nitric esters under the heating rat

Samples Endothermic peaks Exoth

To (◦C) Tp (◦C) Te (◦C) �H1 (J g−1) To (◦C

NG 189.5 192.1 193.9 −55.6no 197.4ETN 61.2 63.7 66.0 −297.7 184.8XPN – – – – 174.8SHN 52.9 55.1 57.0 −77.7 176.2PETN 140.1 142.4 144.2 −504.6 187.7DiPEHN 71.5 73.1 74.7 −214.7 191.6TMPTN 50.3 53.6 58.4 −114.8 181.9TMETN – – – – 177.7NIBGT – – – – 179.9MHN 109.5 111.8 113.9 −87.4 169.4

ote: To, onset temperature of the peaks; Tp, peak temperature of thermal events; Te, the en kg m−3; VoD, calculated by Kamlet–Jacobs (K–J) equation, in km s−1; no, these data are

0 K min−1 (pressure: 0.1 MPa nitrogen gas; sample mass: 2.0–3.0 mg).

from inflammation theory and appropriate thermokinetic parame-ters namely the pre-exponential factor by the following equations[19,20].

Tb = Teo + 1b

(1)

e of 10.0 K min−1 with pinhole cover.

ermic peaks Performance

) Tp (◦C) Te (◦C) �H2 (J g−1) Density VoD

199.9 202.1 24.8no 1593 8.31 196.3 211.6 364.3 1760 8.30 184.8 205.9 661.0 1580 7.10 184.8 200.0 555.1 1778 8.23 202.9 216.3 2385 1630 8.71 210.8 220.3 4678 1488 7.93 206.4 221.8 1105 1500 7.49 198.6 219.0 323.0no 1640 7.30 200.6 217.8 569.8 1800 8.82 181.4 202.6 631.2 1593 9.01

nd temperature for heat change; �H1, heat absorption; �H2, heat release; density, not reliable due to strong evaporation under lower heating rate.

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140 Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148

Table 2The non-isothermal TG data of 10 nitric esters and corresponding time constants and critical temperature.

Samples Tei (◦C) Tp (◦C) Toe (◦C) Tb Samples Tei Tp (◦C) Toe (◦C) Tb

NG 5.0 145.8 165.8 169.2 114.2 PETN 172.7 186.9 199.9 171.27.0 154.9 177.4 182.8 176.3 190.1 205.8

10.0 161.4 183.8 185.5 180.8 194.5 214.615.0 171.2 191.9 203.1 186.0 199.4 224.4

ETN 5.0 157.1 174.6 184.1 162.6 DiPEHN 180.2 193.2 227.4 181.87.0 160.5 177.6 192.4 183.6 197.0 230.9

10.0 165.4 183.1 196.3 187.8 201.4 236.115.0 169.3 186.2 202.8 192.2 206.3 244.8

XPN 5.0 156.9 170.0 191.3 140.1 TMETN 158.8 178.3 208.9 169.37.0 161.9 173.7 194.8 161.8 183.4 216.7

10.0 165.7 177.7 197.8 167.0 188.3 222.515.0 169.0 182.5 205.8 177.1 196.0 225.0

SHN 5.0 153.1 165.7 196.9 160.9 TMPTN 159.7 178.8 186.6 119.17.0 155.6 168.9 200.6 167.1 185.7 197.8

10.0 159.6 173.0 203.5 170.7 191.0 203.415.0 163.6 177.2 213.1 180.5 196.8 211.6

NIBGT 7.0 163.4 183.7 200.8 158.5 MHN 155.0 169.4 190.0 138.510.0 171.0 187.5 212.3 160.2 173.3 193.715.0 180.9 194.2 215.2 164.2 176.6 199.820.0 184.7 197.6 223.2 166.2 180.7 214.2

N mperd

t

T

t

l

wtsfptcwh

rut

Ff

ote: ˇ, heating rate in ◦C min−1; Tei, onset temperature of TG peaks; Tp, the peak teecomposition, ◦C.

First of all, one can easily obtain the onset temperature (Tei) fromhe non-isothermal TG curves, the value of Teo from the equation

ei = a0 + a1ˇi + a2ˇ2i + a3ˇ3

i , i = 1–4 (2)

he values of b from the equation

n ˇi = ln[

A0

bG(˛)

]+ bTi (3)

here b, a0, a1, a2 and a3 are coefficients, R is the gas constant; Afterhe data (ˇi, Ti, i = 1, 2, . . ., L) are fitted to Eq. (1) by the linear least-quares method on the computer, the value of b could be obtainedrom the slope (ln ˇi versus Ti). Besides, the value of the onset tem-erature (Teo) corresponding to → 0 obtained by Eq. (2) is equalo a0. Thus, the critical temperatures of thermal explosion (Tb) cal-ulated by Eq. (2) and summarized in Table 2. The comparison of Tiith onset temperature of exothermic peaks on DSC curves, whichas been shown in Fig. 2.

Here, it should be noted that the thermal stability of nitric estersefers not the stability of their crystal structure but of their molec-lar skeletons. For instance, based on the critical temperature ofhermal decomposition, even though the NG is easier to evaporate

MHN

XPN

NIBGT

TMPTN

DiPEHN

ETN

PETN

SHN

NG

TMETN

150

160

170

180

190

200

210

110 120 130 140 150 160 170 180 190 200

Critical temperature / oC

Onse

t te

mper

ature

/ Co

ig. 2. The correlation of critical temperature with onset temperature on DSC curvesor nitric esters.

ature, ◦C; Toe, endset temperature of TG peaks; Tb, critical temperature for thermal

than MHN, its molecular structure is a little bit more stable thanMHN according to their the critical temperature. In general, thebond energy of O NO2 is noticeably lower than that of the N NO2in similar compounds. Therefore, the stability of nitric estersis lower than that of nitramines with similar mother skeletons(involved nitric esters are derived from skeletons of paraffin).As it could be seen in Fig. 2, the critical temperature calculatedfrom onset temperature of TG should linearly increase with theincrease of onset temperature from DSC if no evaporation occurred.However, due to slightly different experimental conditions (opencrucible for TG vs. sealed pan with pin-hole for DSC), the strongvolatile compounds (NG, TMETN) will not follow on this trend line.For the title compounds, the order of the molecular stability is as fol-lows: MHN < XPN < TMPTN < SHN < NIBGT < ETN < PETN < DiPEHNbased on the critical temperature of thermal decomposition. HereNG and TMETN are not included for comparison due to inaccuratecalculation results when evaporation was not excluded.

It is interesting that for isomer MHN and SHN with chi-rality, without introduction of any groups, their stability ismuch different. SHN and MHN are nitrated from their iso-mer parents (2S,3R,4R,5R)-hexane-1,2,3,4,5,6-hexol (sorbitol) and(2R,3R,4R,5R)-hexan-1,2,3,4,5,6-hexol (mannitol), respectively. Itmeans that the skeleton with R-type chirality carbon is more ther-mal stable with greater rigidity of crystal lattice resulting in highermelting point. Comparing NG, TMPTN, NIBGT and PETN, it could benoticed that the introduction of functional groups to the tertiarycarbon is in favor of increasing thermal stability due to increaseof symmetry and rigidity of the molecule, where the contributionorder of the groups should be CH3 < NO2 < CH2ONO2. How-ever, the introduction of CH2ONO2 group to a primary carbon willinstead decrease the symmetry and rigidity of the molecule, there-fore resulting in a lower thermal stability. It is a good example thatXPN is less stable than ETN. In addition, the number and positionof the methylene group will also have an influence on the thermalstability of the molecules. Based on the experimental results, inter-estingly, the proportion of methylene group ( CH2 ) to tertiary

carbon or quaternary carbon (Cs) would to some extent determinethe thermal stability of the nitric esters. For instance, as nitric esterswithout quaternary carbon, MHN, XPN and ETN have Cs of 0.5,0.66 and 1.0, so the higher Cs indicates greater thermal stability.

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Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148 141

Table 3Comparison of decomposition kinetic parameters of nitric esters obtained from the literature and our results.

Spls MOA Tr (◦C) Ea (kJ mol−1) Log A (s−1)

NG

SMM 125–190 201 20.69 [22]150–160 197 20.20 [23]

90–120 173 16.74 [24]MANO 80–140 159 15.24 [25]

75–105 169 16.62[27]TGA 82–204 64.0no 5.13[a]

52.1no 4.08[a]

ETN

SMM 144–169 194 19.6 [27]– 160.3 16.3 [28]

MANO 70–140 159 15.7 [29]TGA 104–205 145.1 14.79 [a]

139.2 14.39 [a]

XPNSMM – 159 16.7 [29]TGA 131–206 140.1 14.37 [a]

146.9 15.52 [a]

SHNTGA 131–213 147.8 15.49 [a]

137.9 14.47 [a]

PETN

SMM 145–171 163 15.6 [29]SMM 100–145 168 15.8 [29]DSC 173–212 136.5 14.87 [3]

161–233 197 19.8 [30]MANO 171–238 165 16.1 [30]

201–216 175 ± 3.3 15.6 [31]

PETNCL 40–90 63.0 [14] –TGA 128–225 149.0 14.8 [a]

139.6 14.07 [a]

DiPEHNExtra. – 164.6 15.0 [11]TGA 162–206 147.5 14.3 [a]

147.4 14.66 [a]

TMPTN

MANO 75–95 152.3 15.3 [26]TGA 94–203 100.4no 9.28 [a]

94.3no 9.04 [a]Cal. 75–95 166.1 [32] –

TMETNExtra. – 165.3 14.9 [11]TGA 114–203 102.5no 9.57 [a]

83.3no 7.68 [a]

NIBGTTGA 166–197 122.4 11.9 [a]

111.3 10.95 [a]

MHN

SMM 180–240 159.1 15.9 [11]161.1 16.9 [28]

SMM – 166.0 15.8 [33]TGA 155–182 151.6 15.9 [a]

146.1 15.61 [a]

N rangeM n aref

Iiiipas

3

teoksmstsdfm

otes: Spls, samples; MoA, method of analysis; Ea, activation energy; Tr, temperatureethod; CL, chemiluminescence method; no, these activation data for decompositio

or NG.

n some cases, the increased stability was attributed to an increasen the integrity of crystal lattice, as molecular weight and symmetryncreased, rather than to a change in elementary chemistry. Hence,f ignoring volatile compounds, for the nitric esters that decom-ose in liquid state, the effect of the crystal lattice was excluded,nd their thermal stability would be completely determined by thetructure of their molecules.

.3. Distribution of activation energy

A kinetic study is usually considered of either a practical or aheoretical purpose. The kinetic parameters, including activationnergy (Ea), pre-exponential factor (A) and kinetic model (f(˛))f each individual process, should be determined for a completeinetic description of the overall reaction. With regard to a one-tep process for decomposition of nitrate esters, we can directly useodel-free methods, which state that at constant extent of conver-

ion the reaction rate is only a function of the temperature, to obtainhe dependence of the activation energy on the extent of conver-

ion. In the first step, the activation energy Ea usually needs to beetermined. Traditional and most renowned methodology derivedor this task is the Kissinger’s method [21]. Main advantage of this

ethod lies in its robustness with respect to data-distortive effects

; [a], results from this paper; MANO, manometric method; SMM, Soviet Manometric not reliable due to strong evaporation, and is almost evaporation activation energy

(thermal gradients, inaccuracies of zero-line subtraction, etc.). Onthe other hand, in case of a complex process usually only its mainpeak can be evaluated by this method. The results provided by theKissinger method are listed in Table 3 together with some experi-mental data from the literature.

As presented in Table 3, there are diverse data with regard toactivation energy of nitric esters, most of which are obtained fromthe literature. Nitric esters such as NG and PETN are well knownand widely used energetic materials, and their activation ener-gies and thermolysis properties have been investigated by manyresearchers [14,23–27,30,31,11]. The results are different from eachother due to different evaluation methods. In general, the activationenergies obtained in this paper are slightly lower than those fromthe literature which were mostly tested by “Manometric” methodand “Soviet Manometric Method” (isothermal in vacuum). In fact,the disproportionate influence of secondary reactions of thermaldecomposition upon experimental results can be eliminated to alarge extent by carrying out the thermal decomposition in vac-uum at isothermal conditions. The activation energies obtained

by SMM method are more suitable to correlate with detonationproperties where the autocatalysis effect is excluded [34–36]. How-ever, the activation energies of NG, TMETN and maybe TMPTNwith relatively lower molecular weight are much lower than the

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142 Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.930

40

50

60

70

80

90

100

110

120

130

140

NG

TMETN

NIBGT

TMPTN

Activa

tio

n E

ne

rgy / k

J.m

ol-1

Extent o f c onversio n / alp ha0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

110

115

120

125

130

135

140

145

150

155

160

165

170

XPN

MHN

Activa

tio

n E

ne

rgy / E

ETN

DiPEHN

SHN

PETN

Conversion / alph a

gy on

aredoletma

pKt

l

wptouac

swtavbaX[cw1pitIftciO

Fig. 3. The dependence of activation ener

verage values of the literature. This might be caused by evapo-ation, because these materials are more volatile than the others,specially when their thermolysis occurs in open crucible withynamic nitrogen flow. Especially for NG, the activation energybtained herein is only less than 1/3 of the average value from theiterature. It is undoubtedly more close to its evaporation activationnergy. With regard to NIBGT and SHN, no data is available for theirhermal decomposition kinetics and hence no comparison could be

ade. Their activation energies were calculated as 122.4 kJ mol−1

nd 147.8 kJ mol−1, respectively.In addition, the current data were evaluated by a

opular isoconversional method, the so-called modifiedissinger–Akahira–Sunose (KAS) equation (see Eq. (4), [22])

o obtain the activation energy distribution.

n

(ˇi

T1.92˛,i

)= Const − 1.0008

E˛

RT˛(4)

here is the heating rate, E� activation energy and T� the tem-erature in DTG or DSC curve at certain conversion rate (˛). Due tohe large influence of experimental conditions on the data qualityf the process “tails”, it is a common practice to consider only val-es of Ea obtained for the interval = 0.3–0.7 when calculating theverage value. The corresponding kinetic parameters at differentonversions are obtained and summarized in Table 4.

As shown in Table 4, the activation energies for nitric esterseems independent on the extent of conversion ( = 0.3–0.7) mostlyith the correlation coefficients greater than 0.99. It reveals that

he mean activation energy could represent the overall apparentctivation energy for the primary thermolysis process. The meanalues of these activation energies are smaller than those obtainedy Kissinger method. The mean activation energies of ETN, SHNnd PETN are almost the same while those of MHN, DiPEHN andPN are also comparable. Generally, based on our previous research

37], the nitric esters represent the most reactive group of polynitroompounds with regard to both homolysis and heterolysis. Any-ay, the mean activation energies for most nitric esters are close to

45 kJ mol−1 under constant heating rate. It indicates that the mainathway for decomposition of nitric esters might be the same. As

t is known to all, thermal decomposition of nitric esters proceedshrough dissociation of O NO2 bond producing nitrogen dioxide.t was also confirmed that the overlap population of the O NO2or trinitrate ester is relatively smaller than other bonds, indicating

hat the O NO2 may be the trigger bonds during initiation pro-ess of thermolysis [12]. Meanwhile, the theoretical calculationn this literature showed that the bond dissociation energies of

NO2 bond in NG, TMETN and TMPTN are around 142.0, 132.3

the extent of conversion for nitric esters.

and 131.8 kJ mol−1 which are much higher than the obtained meanactivation energies herein. It reveals that these compounds did notcompletely decompose due to evaporation.

The full dependence of the activation energy of nitrate esterson the extent of conversion is demonstrated in Fig. 3, where moreactivation energy points have been shown ( = 0.05 0.90). As awhole, the activation energies of NiBGT, NG and TMETN increasewith the extent of conversion, while that of MHN and TMPTN isreverse. Sample mass loss for NG and TMETN, obtained by TGAanalysis, is results of two simultaneous processes: evaporation anddecomposition. At a constant heating rate, the rates of these pro-cesses depend greatly on the temperatures and the evaporationis dominant at lower T (or conversion), where a relatively loweractivation energy was obtained for evaporation process. Especiallyfor NG, the obtained activation energy, around 52–64 kJ mol−1, isvery close to its activation energy for evaporation in double basepropellant (81.9 kJ mol−1) [38]. In presence of other componentsin propellant, the evaporation could be slightly hindered, resultingin higher activation energy. For powdered samples, the activationfor NG evaporation could decrease to 75.3 kJ mol−1 [39]. For NiBGT,the situation is different. There is one C NO2 bond in its molecule,which has a strong electron attracting effect on the O NO2 Bridge,resulting in lower activation energy. In addition, as we could see,the initial ( < 0.15) activation energies of SHN and PETN are muchlower than the central part ( = 0.4–0.6). In fact, it also has beenfound that the activation energy of low-temperature decomposi-tion of PETN and NC is around 63 kJ mol−1 [14]. We will try to findthe reason for different activation energy distribution in the follow-ing section by comparing their decomposition reaction models.

3.4. Reaction models for exothermic processes

The second important step for kinetic analysis is selection ofan appropriate kinetic model for the description of the givenprocesses. For this procedure, Málek [40,41] suggested a usefulalgorithm based on the shape of characteristic functions z(˛) andy(˛). These functions are obtained by a simple transformation ofexperimental data, for non-isothermal conditions the characteristicfunctions are defined as follows:

y(˛) = � · eE/RT (5)

z(˛) = � · T2 (6)

where � is the reaction rate at a certain temperature (T), R gasconstant, and E is the activation energy. As stated in a recentcomprehensive review paper by Svoboda and Málek [42], theintroduced functions are in fact a universal way for determination

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143

Table 4Decomposition kinetic data for nitric esters by iso-conversional modified KAS method.

� reacted NG ETN SHN

Ea Log A r Ea Log A r Ea Log A r

0.30 49.37 3.83 0.9950 139.2 14.77 0.9908 137.10 14.66 0.99580.40 50.52 3.90 0.9920 143.4 15.13 0.9932 138.79 14.77 0.99920.50 53.26 4.19 0.9864 137.6 14.32 0.9932 137.07 14.47 0.99850.60 53.19 4.15 0.9849 136.3 14.07 0.9938 138.49 14.56 0.99850.70 53.96 4.17 0.9844 139.4 14.34 0.9951 138.30 15.28 0.9960

Mean 52.1 ± 1.8 4.08 ± 0.15 139.2 ± 2.4 14.39 ± 0.38 137.9 ± 0.7 14.47 ± 0.28

PETN XPN DiPEHN0.30 139.47 14.22 0.9970 144.86 15.47 0.9995 149.52 15.07 0.99980.40 140.44 14.24 0.9995 146.73 15.58 0.9975 148.22 14.83 0.99780.50 137.74 13.84 0.9990 145.40 15.32 0.9980 144.03 14.27 1.00000.60 141.72 14.27 0.9990 147.49 15.53 0.9995 143.26 14.14 0.99940.70 138.46 13.78 0.9985 150.07 15.68 0.9995 152.15 15.01 1.0000

139.6 ± 1.41 14.07 ± 0.21 146.9 ± 1.8 15.52 ± 0.12 147.4 ± 3.4 14.66 ± 0.39

NIBGT MHN TMPTN0.30 105.49 10.41 0.9968 145.54 15.74 0.9975 95.00 9.28 0.98970.40 109.26 10.78 0.9932 149.86 16.15 0.9997 94.16 9.12 0.99330.50 114.63 10.79 0.9964 149.47 16.00 0.9981 95.09 9.13 0.99660.60 109.87 11.24 0.9979 141.13 14.90 0.9966 93.07 8.85 0.99640.70 117.37 11.55 0.9978 144.51 15.26 0.9957 94.07 8.81 0.9978

Mean 111.3 ± 4.2 10.95 ± 0.40 146.1 ± 3.2 15.61 ± 0.46 94.3 ± 0.73 9.04 ± 0.18

� = 0.30 and 0.60 � = 0.40 and 0.7 � = 0.50 and mean valueTMENT 78.11 7.21 0.9925 80.46 7.36 0.9930 83.34 7.63 0.9945

86.06 8.04 0.9935 88.57 8.15 0.9940 83.3 ± 3.8 7.68 ± 0.37

Notes: Ea, Activation energy, in kJ.mol−1; A, pre-exponential factor, in s−1.

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144 Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148

F (a, b, c

optvfomipgfipappwiea

f

f

c

ig. 4. The y(˛) and z(˛) plots for the thermal decomposition data of nitrate esters

f an appropriate kinetic model applicable to almost any physicalrocess, including thermal decomposition [43]. Determination ofhe most suitable kinetic model then utilizes both, value of con-ersion degree ˛max,y corresponding to the maximum of the y(˛)unction and value of ˛max,z, which corresponds to the maximumf the z(˛) function. Based on this information, the optimal kineticodel can be chosen according to the algorithm presented e.g.

n Ref. [40]. After the choice of the kinetic model is made, there-exponential factor A can be determined by enumerating theeneral kinetic equation and applying curve-fitting procedure tot the experimental data by the determined kinetic model (there-exponential factor being the only variable parameter). It isdvantageous to confirm the value of this parameter by inde-endent evaluation within the framework of different models (ifossible). With regard to the specific kinetic models, in the presentork we have utilized two of the most popular models: the phys-

cally meaningful Johnson-Mehl-Avrami model (JMA, Eq. (7)) andmpirical autocatalytic model (AC, see Eq. (8)), which is also knowns Sesták Berggren model [44].

(˛) = m(1 − ˛)[− ln(1 − ˛)][1−(1/m)] (7)

(˛) = ˛M(1 − ˛)N (8)

Value of the kinetic parameters m, M and N can then be cal-ulated from the conversion corresponding to the maximum of the

, . . ., h for NG; XPN, SHN, DiPEHN, TMPTN, TMETN, NIBGT and MHN, respectively).

y(˛) function ˛max,y. These calculations are described in detail in ourprevious paper [20]. Choice of an appropriate kinetic model is notalways only the question of the highest correlation coefficient, theJMA model is usually preferred (in case when its applicability is atleast remotely confirmed by the above-mentioned algorithm) dueto the possibility of consequent physically meaningful interpreta-tion of its kinetic exponent m. The description by the AC model isempirical and purely phenomenological, where the parameters donot have any physical basis or meaning, and therefore this modelis usually used only in case when the data cannot be described bythe JMA model.

Based on abovementioned theory, the characteristic functionsz(˛) and y(˛) have been plotted in Fig. 4 for chosen studied materials(the plots for ETN and PETN are omitted).

As can be deduced from the shape of y(˛) functions pre-sented in Fig. 5, most materials/processes show kinetics closeto that characteristic for the first order reactions, which is acommon case for decomposition processes. All these materialsalso have maxima of the corresponding z(˛) functions close tothe value 0.632, which is a characteristic “fingerprint” suggest-ing good applicability of the physically meaningful JMA model.

In other words, these materials (XPN, SHN, DiPEHN, NIBGT andMHN) exhibit typical single-process behavior, characteristic forthermally activated decompositions with sole mechanism beinginvolved.

Page 9

Q.-L. Yan et al. / Thermochimica A

DiPEHNETN

NIBGT

XPN

SHN

PETN

TMPTNTMETN

MHN

NG

c

RDX-FormexHMX-Formex

BCHMX-Formex

CL-20-Formex

b a

a: y = 0.2875x + 0.1403

R2 = 0.9828

b: y = 0.2744x - 5.0293

R2 = 0.9898

c: y = 0.2159x - 1.1323

R2 = 0.9938

5

10

15

20

25

30

35

40

45

50

55

60

65

40 60 80 100 120 140 160 180 200 220 240 260 280

Activation Energy ( Ea ) / kJ.mol-1

Ln (A

) / s

-1

Fb

utsridwmtofpdTabi

cA˛mtdedctJabobtcwdtblb

tiJ

ig. 5. A comparison of the kinetic compensation lines for nitric esters and Formexonded explosives containing cyclic nitramines (RDX, HMX, BCHMX and CL-20).

On the other hand, in case of the materials depicted in Fig. 5nder letters “a”, “e” and “f” (NG, TMPTN and TMETN, respec-ively), both characteristic kinetic functions z(˛) and y(˛) have aignificantly different shape, differing from that observable for theest of the studied materials. Looking first at the z(˛) functions,t can be seen that their maxima are shifted to higher conversionegrees. If we add the information provided by the y(˛) function,hich clearly suggests manifestation of multiple decompositionechanisms, it can be concluded that the larger deviation from

he expected (first order JMA process) behavior is caused by anverlap of the involved mechanisms/processes. The shift of the z(˛)unction maxima is then caused by the dominant decompositionrocess having its initiation slightly postponed (shifted to higher ˛)ue to the formerly manifesting minor mechanism (evaporation).he simultaneous manifestation of the two involved mechanismss well as their different dependence on heating rate (most proba-ly due to different apparent activation energy) then results in the

nconsistencies of the z(˛) and y(˛) functions shape.In Table 5 the results of kinetic analysis are summarized; in

ase of all materials description by both kinetic models (JMA andC) was done. In the first part of the Table values of ˛max,z andmax,y are listed for the studied materials (mean value from alleasured curves was always calculated). In the second part of

he Table the mean correlation coefficients determined for theescription of experimental data by the respective theoretical mod-ls are shown. As is apparent, for ˛max,z values close to 0.632 theescriptions by the JMA model were very good (indicated by highorrelation coefficients). Nevertheless, generally the description byhe AC model shows better correlation coefficients than that by theMA model – which is however perfectly understandable as AC isn empirical model specifically designed to have maximum flexi-ility for description of kinetic data. In the end, in case of complexr unideal processes, it is always up to the researcher to chooseetween the quality of the description and possibility of interpre-ation of the results. Even though the applicability of the JMA modelan be extended well beyond the limits suggested in the originalork of Málek [38], it should be always borne in mind that for largereviations from the theoretical model behavior also the interpre-ations of the kinetic exponent and shapes of kinetic functions cane done only as an approximation or rough estimate. Finally, in the

ast part of the Table the complete sets of kinetic parameters foroth applied model are listed.

In case of the NG and TMPTN materials the complexity ofhe processes can be explained by the partial evaporation dur-ng decomposition, resulting in very complicated processes (bothMA and AC model with lower correlation coefficient). Here we

cta 566 (2013) 137– 148 145

cannot consider these models valid for their thermal decompo-sition or evaporation, and thermal analysis under more properconditions needs to be done. In addition, according to the litera-ture [1], autocatalysis or self-acceleration is normal for most of thenitrate esters, which (incidentally) well corresponds to high corre-lation coefficients obtained for the autocatalytic Sesták-Berggrenmodel. The main reason for this is the development of oxidative andhydrolytic interaction of the parent nitroester with the products ofits decomposition: HNO3, NO2 and H2O. Because of the followingequilibrium that are attained in the gas phase reactions:

NO2 + H2O ⇔ 2HNO3 + NO

NO2 ⇔ N2O4

the introduction of any of these components in the system results inan increase of the concentration of all molecules. For this issue, theeffects of nitrogen dioxide, oxygen, nitric oxide, acetaldehyde anddiethyl peroxide on the thermal decomposition of ethyl nitrate at181 ◦C had been studied in the 1950s by Joseph [45]. It was provedthat the ratio of NO2/NO determines the reaction rate and in the latestages of reaction this ratio is much larger than at the beginning anda lowered rate constant results.

With respect to the often desired information about thereaction order, the empirical “reaction order model” can beapplied. In fact, the thermal decomposition of TDNTN [46],poly(glycidyl nitrate), (PGN), poly(vinyl nitrate) (PVN), andpoly(nitratomethylmethyloxetane) (NMMO) were studied in termsof this model and were found to have order of reaction n = 2 [15].However, it was further pointed out that their decompositionprocesses are not necessarily second-order in the usual sense ofchemical kinetics, because these decomposition processes are het-erogeneous in which all of the reactions and diffusion terms arelumped (hence empirical character of the reaction order model).

Interestingly, the decomposition mechanism of NIBGT couldbe described by the reaction order model (n = 1, r = 0.9980). Withregard to its molecular structure (Scheme 1), different from theother nitric esters, NIBGT has one C NO2 bond while TDNTN hastwo C NO2 bonds (Scheme 2). According to Fig. 4, characteristickinetic functions for both these materials show slight dependenceon heating rate, suggesting change of the reaction mechanism. Byfitting the NIBGT material, it was found that when the heating rate islower, its weight loss is first-order through the first 50% (lower acti-vation energy), followed by a second-order process in the latter 50%(higher activation energy). It has been proved [48] that when theheating rates are slow, these two steps are separated by a disconti-nuity. It means that O NO2 homolysis dominates initially followedby the dominance of chain cleavage [47,48]. It has also been foundthat decomposition mechanism of nitric esters in general followsthe similar rules [49]. In compounds containing more than onenitrate ester, the structural orientation has a marked effect on thereaction products. Moreover, the aforementioned reaction mod-els could also present the storage properties of the correspondingmaterials. According to recent simulation results [50], for nth-ordermodels the storage aging has no influence on the reaction courseand further thermal properties of the materials. However, the only1% slow thermolysis process during storage will result in at least30 K decrease for the initial decomposition temperature of ener-getic materials with autocatalytic effect. Materials that follow JMAdecomposition mechanism including Avrami-Erofeyev (A4) will beslightly affected by their aging process during storage.

3.5. Kinetic compensation effect

The kinetic compensation effect states that there is a linear rela-tionship between Arrhenius parameters log(A) and E for a family

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146 Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137– 148

Table 5Parameters for reaction models of nitroesters evaluated by non-isothermal TG experiments.

Samples Max. of y(˛) and z(˛) JMA AC Parameters for mechanism functions

˛max,y ˛max,z Correlation coefficient m M N Ea Log(A)

NGa 0.64 0.83 0.938 0.966 3.0 0.34 0.20 52.1 7.22ETN 0.06 0.69 0.982 0.990 1.2 0.04 0.61 139.2 17.45XPN 0.20 0.60 0.987 0.999 1.5 0.24 0.96 146.9 17.52SHN 0.25 0.60 0.980 0.998 1.5 0.35 1.06 137.9 16.77PETN 0.10 0.71 0.980 0.980 1.2 0.11 0.99 139.6 17.41DiPEHN 0.25 0.58 0.976 0.999 1.7 0.36 0.99 147.4 18.34TMPTNa 0.27 0.71 0.972 0.975 1.5 0.37 0.82 94.3 11.78TMETN 0.49 0.74 0.989 0.951 3.0 0.34 0.38 83.3 10.75NIBGT 0.42 0.61 Reaction order model: (1 − ˛)N – 1.00 111.3 14.45MHN 0.22 0.56 0.974 0.998 1.3 0.33 1.13 146.1 19.34TDNTN [43] – – Reaction order model: (1 − ˛)N – 2.00 133.2 7.50PVN [15] – – – 2.00 134.3 15.9PGN [15] – – – 2.00 130.2 14.7NMMO [15] – – – 2.00 140.2 16.4

aporatt

oiabqtbacsla

l

wda

E

wi[me

l

l

a These compounds are volatile and the obtained models may invalid for both evo low correlation coefficient.

f related processes [51,52]. It is a widely observed phenomenonn many areas of science, notably heterogeneous catalysis [53]. Thepplicability of the Arrhenius equation to a particular reaction coulde tested by finding constancy or a predictable variation in the “fre-uency factor” with changes in experimental conditions or samplereatment or structure. It is demonstrated, both theoretically andy numerically, that random errors in kinetic data do generate anpparent compensation effect (sometimes termed the statisticalompensation effect) when the true Arrhenius parameters are con-tant [51]. Expressions for the gradient of data points on a plot ofog(A) against Ea are derived when experimental kinetic data arenalyzed by linear regression.

n A˛ = ω + �E˛ (9)

here ω and � are the coefficients of linear regression, whichepend on the type of sample and their structures. Here alsonother equation could be used:

a = e0 + 2.303RTiso ln A (10)

here Tiso is the isokinetic temperature, according which thenvolved materials could be divided in to different family groups54]. At isokinetic temperature, the reaction rates (k) for different

aterials are the same. The logarithmic expression of Arrheniusquation is:

n k = ln A˛ − E˛

RT(11)

If we combine Eqs. (9) and (11), we obtain:

n A˛ = ω +(

� − 1RT

)E˛ (12)

NO2 ONO2

ONO2

O2NO

O2NO O2N

CH CH2

ONO2

n

TDNTN (C6H8N6O16 ) PVN (C2nH3n NnO3n )

Scheme 2. Molecular structure of s

ion and decomposition. The bold number means this model is not appropriate due

It reveals from Eq. (12) that when T = 1/�R, the decompositionreaction of the materials in the same family will have the samerate constant, indicating that Tiso equals to 1/�R. With a set of var-ied kinetic parameters, the plots of kinetic compensation effectcould be established for different groups of materials. Based on thistheory, the plots of corresponding parameters for nitric esters areobtained in Fig. 5.

Interestingly, according to Fig. 5, the kinetic points of all nitricesters obtained by model-fitting fall almost on the same compen-sation line (b) with a correlation coefficient of greater than 0.989. Itmight reveal that they follow the same compensation effects due tothe same dependence of enthalpy change and the entropy changecaused by dissociation of O NO2 bond [55,56]. It is interesting thatNG and TMETN decomposing along with strong evaporation alsofollowed on this compensation line. This is a correlation betweenthe enthalpy change (�H) and entropy change (�S) for a family ofchemical reactions. It is known from transition state theory that Ecorresponds to enthalpy change while log(A) is related to entropychange. A wide variety of other physical reasons for the kinetic com-pensation effect have been proposed in the literature for particularsituations [55]. There are two compensation lines for two groups ofresults. The log(A) values for “line a” are calculated by KAS methodwhile that of line b is from the results obtained by the model-fittingmethod. It is interesting that the slope of these two lines is almostidentical. On the one hand, it indicates that during calculating ofactivation energy by KAS method, the pre-exponential factor hasbeen underestimated. On the other hand, it means that all of thenitric esters have the same isokinetic temperature according to

Eq. (10). Similarly, the kinetic compensation effect has also beenmentioned for thermal decomposition of Formex bonded explo-sives containing cyclic nitramines (Nitra-F PBXs) [57], which areshown as “line c” in Fig. 5. It is obvious that slope (�) of “line c”

OCH2CCH2

CH2ONO2

CH3

OHHn

CHCH2O

CH2ONO2

OHHn

NMMO (C5n H9n+2NnO4n+1) PGN (C3n H5n+2NnO4n+1)

ome polymeric nitric esters.

Page 11

mica A

it

4

etsT

(

(

(

(

A

ropP

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[[[

[

[[

[

[

[[

[

Q.-L. Yan et al. / Thermochi

s smaller than that of “lines a and b”. It means that the isokineticemperature of Nitra-F PBXs is higher than that of nitric esters.

. Conclusions

The thermal behavior and decomposition kinetics of 10 nitricsters were investigated by means of non-isothermal TG and DSCechniques, based on which their thermal stability and decompo-ition mechanism functions have been determined and compared.he following conclusions could be made:

1) The mean activation energies for most nitric esters are veryclose under constant heating rate (about 145 kJ mol−1). It indi-cates that the main pathway for decomposition of nitric estersmight be the same. The activation energies of NG, TMETN andTMPTN are less than 100 kJ mol−1 which are much lower thanthose from the literature due to effect of evaporation;

2) Based on the critical temperature of thermal decomposition, theorder of molecular stability for involved nitric esters was foundas MHN < XPN < TMPTN < SHN < NIBGT < ETN < PETN < DiPEHN.The thermal stability of nitric esters was mostly determinedby the structure of their molecules. On the one hand, theintroduction function group to the tertiary carbon is in favorof increasing thermal stability due to increase of symmetryand rigidity of the molecule, where the contribution order ofthe groups should be CH3 < NO2 < CH2ONO2. On the otherhand, the proportion value (Cs) of methylene group ( CH2 )with tertiary carbon or quaternary carbon will to some extentdetermine the thermal stability of the nitric esters. The higherCs indicates greater thermal stability;

3) Their decomposition processes were described in terms oftwo kinetic models: the physically meaningful Johnson-Mehl-Avrami (JMA) model and empirical AutoCatalytic (AC) model.Quality of the respective descriptions was discussed withrespect to information provided by the shapes of characteris-tic kinetic functions z(˛) and y(˛) as well as considering theadvantages and disadvantages of the kinetic exponent inter-pretation provided by the JMA model description. Two types ofkinetic behavior were observed: most nitrate esters followedtypical decomposition kinetics close to the first order reaction;however, certain materials showed complex behavior causedby overlapping of more mechanisms/processes (these pro-cesses may be represented either by simultaneous evaporationand decomposition or by different decomposition mechanismsoriginating from varying morphology and structure of the sam-ples).

4) The compensation effects occurred during thermal decompo-sition of nitric esters and their isokinetic temperature is lowerthan that of nitramine based explosives.

cknowledgements

The work in this paper was mainly carried out as a part of theesearch project No. MSM 00221627501 provided by the Ministryf Education, Youth & Sports of the Czech Republic, and was alsoartially supported by the Ministry of Interior of the Czech Republicroject No. VG20102014032.

eferences

[1] G.B. Manelis, G.M. Nazin, Y.I. Rubtsov, V.A. Strunim, Chapter 9 in Thermal

Decomposition and Combustion of Explosives and Propellants, Taylor & FrancisGroup, 2003, ISBN 0-415-29984-5.

[2] Q.-L. Yan, S. Zeman, A. Elbeih, Recent advances in thermal analysis and stabilityevaluation of insensitive plastic bonded explosives (PBXs), Thermochim. Acta537 (2012) 1–12.

[[

cta 566 (2013) 137– 148 147

[3] J.C. Oxley, J.L. Smith, J.E. Brady IV, A.C. Brown, Characterization and analysis oftetranitrate esters, Propellants Explos. Pyrotech. 37 (2012) 24–39.

[4] S.-M. Shen, F.-M. Chang, J.-C. Hu, A.-L. Leu, Thermal behaviour and compatibilityof polyurethane PCL/BDNPA/F and PCL/TMETN blends, Thermochim. Acta 181(1991) 277–288.

[5] P. Chen, F.-Q. Zhao, S.-W. Li, The study on the quenched surface characteristicsof NC/TMETN propellant with potassium salt, Chin. J. Explos. Propellants 25 (3)(2002) 47–50.

[6] G.W. Brown, M.M. Sandstrom, A.M. Giambra, J.G. Archuleta, D.C. Monroe, Ther-mal analysis of pentaerythritol tetranitrate and development of a powder agingmodel, in: 37th Annual Conference of the North American Thermal AnalysisSociety, Lubbock, TX, September 20–23, 2009.

[7] A. Elbeih, J. Pachman, S. Zeman, Z. Akstein, Replacement of PETN by Bicyclo-HMX in Semtex 10, in: 8th International Armament Conference on ScientificAspects of Armament and Safety Technology, Pułtusk, Poland, 2(2), 2010, pp.7–16.

[8] S.-D. Wu, Z.-H. Zhang, D.-Y. Li, J.-Z. Jin, J. Kong, Z. Tian, W. Wang, M.-F.Wang, Nitroester drug’s effects and their antagonistic effects against morphineon human sphincter of Oddi motility, World J. Gastroenterol. 1 (15) (2005)2319–2323.

[9] F.-Q. Zhao, S.-Y. Xu, J.-H. Yi, H.-X. Gao, H.-C. Song, S.-W. Li, Numerical sim-ulation for combustion characteristics of insensitive propellant containingtrimethylolethane trinitrate (TMETN), Chin. J. Energetic Mater. 14 (6) (2006)406–410.

10] F.-Q. Zhao, P. Chen, S.-W. Li, C.-M. Yin, Y. Luo, Interaction of potassium saltflame suppressors with TMETN and burning catalysts during decomposition,Energetic Mater. 9 (3) (2001) 102–103.

11] J.-S. Lee, C.-K. Hsu, C.-L Chang, A study on the thermal decomposition behaviorsof PETN, RDX, HNS and HMX, Thermochim. Acta 392–393 (2002) 173–176.

12] M.-M. Li, G.-X. Wang, X.-D. Guo, Z.-W. Wu, H.-C. Song, Theoretical studies onthe structures, thermodynamic properties, detonation properties, and pyrol-ysis mechanisms of four trinitric esters, J. Mol. Struct.: Theochem 900 (2009)90–95.

13] B.D. Roos, T.B. Brill, Thermal decomposition of energetic materials 82. Cor-relations of gaseous products with the composition of aliphatic nitric esters,Combust. Flame 128 (2002) 181–190.

14] J. Kimura, Chemiluminescence study on thermal decomposition of nitric esters(PETN and NC), Propellant Explos. Pyrotech. 14 (3) (1989) 89–92.

15] J.K. Chen, T.B. Brill, Thermal decomposition of energetic materials 50. Kineticsand mechanism of nitrate ester polymers at high heating rates by SMATCH/FTIRspectroscopy, Combust. Flame 85 (3–4) (1991) 479–488.

16] J.P. Agrawal, R.N. Surve, Mehilal, S.H. Sonawane, Some aromatic nitric esters:synthesis, structural aspects, thermal and explosive properties, J. Hazard.Mater. A 77 (2000) 11–31.

17] X. Li, Z. Tang, X. Zhang, X. Yang, The heats of formation in a series of nitroesterenergetic compounds: a theoretical study, J. Hazard. Mater. 165 (1–3) (2009)372–378.

18] S.-Y. Xu, J.-H. Yi, Y.-J. Jia, L.-Y. Zhang, Q. Pei, S.-W. Li, Thermal decompositionbehavior of mixed nitric ester gun propellant under dynamic atmosphere, Chin.J. Explos. Propellants 30 (4) (2007) 70–72.

19] L. Xue, F.Q. Zhao, R.Z. Hu, H.X. Gao, A simple method to estimate the criticaltemperature of thermal explosion for energetic materials using nonisothermalDSC, J. Energetic Mater. 28 (2010) 17–34.

20] Q.-L. Yan, S. Zeman, R. Svoboda, A. Elbeih, Thermodynamic properties, decom-position kinetics and reaction models of BCHMX and its Formex bondedexplosive, Thermochim. Acta 547 (2012) 150–160.

21] H.E. Kissinger, Reaction kinetics in differential thermal analysis, Anal. Chem.29 (1957) 1702–1706.

22] S. Vyazovkin, A.K. Burnham, J.M. Criado, L.A. Pérez-Maqueda, C. Popescu,N. Sbirrazzuoli, ICTAC Kinetics Committee recommendations for performingkinetic computations on thermal analysis data, Thermochim. Acta 520 (2011)1–19.

23] S.Z. Roginski, L.M. Sapognikov, J. Phys. Chem. (USSR) 2 (1) (1931) 80.24] C.E. Waring, G.J. Krastins, Phys. Chem. 74 (5) (1970) 199.25] R. Robertson, The velocity of decomposition of nitroglycerin by heat. Part I, J.

Chem. Soc. 95 (1909) 1241–1248.26] B.S. Svetov, Thermal decomposition of nitro esters. Diss. Doctor of chem. Sci-

ence. Moscow. Mendeleev Chem. Techn. Inst., 1970, pp. 277.27] L. Phillips, Thermal decomposition of organic nitrates, Nature 160 (1947) 763.28] W.R. Ellis, B.M. Smythe, E.D. Treharne, 5th International Symposium on Com-

bustion, 1955, p. 641.29] G.K. Klimenko, Goreniye I vzryuv (combustion and explosion), in: 4th All-Union

Symp. Combust. Explos., Izdat, Nauka, Moscow, 1977, p. 587.30] K.K. Andreev, B.I. Kaidymov, in: K.K. Andreev (Ed.), Explosive Theory, 1963, p.

241, Moscow.31] A.I.B. Robertson, J. Soc. Chem. Ind. 67 (1948) 221.32] S. Zeman, M. Dimun, Truchlikt, The relationship between kinetic data of low-

temperature thermal analysis and the heats of explosion of inorganic azides,Thermochim. Acta 78 (1984) 181.

33] S. Zeman, New dependence of activation energies of nitroesters thermoly-sis and possibility of its application, Propellants Explos. Pyrotech. 17 (1992)

17–19.

34] B.A. Lure, B.S. Svetlov, Tr. Mosk. Khim. Tekhnol. Inst. Mendeleeva 53 (1967) 51.35] S. Zeman, A. Elbeih, Q.-L. Yan, Note on the use of the vacuum stability test in

the study of initiation reactivity of attractive cyclic nitramines in Formex P1matrix, J. Therm. Anal. Calorim. 111 (2013) 1503–1506.

Page 12

1 mica A

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

48 Q.-L. Yan et al. / Thermochi

36] S. Zeman, A. Elbeih, Q.-L. Yan, Notes on the use of the vacuum stability test inthe study of initiation reactivity of attractive cyclic nitramines in the C4 matrix,J. Therm. Anal. Calorim., doi:10.1007/s10973-012-2710-y.

37] S. Zeman, Modified Evans–Polanyi–Semenov relationship in the study of chem-ical micromechanism governing detonation initiation of individual energeticmaterials, Thermochim. Acta 384 (2002) 137–154.

38] M. Suceska, S.M. Musanic, I.F. Houra, Kinetics and enthalpy of nitroglycerinevaporation from double base propellants by isothermal thermogravimetry,Thermochim. Acta 510 (1–2) (2010) 9–16.

39] A.S. Topma, Thermal analysis of liquid and solid propellants, J. Hazard. Mater.4 (1980) 95–112.

40] J. Málek, Kinetic analysis of crystallization processes in amorphous materials,Thermochim. Acta 355 (2000) 239–253.

41] J. Málek, The kinetic analysis of non-isothermal data, Thermochim. Acta 200(1992) 257–269.

42] R. Svoboda, J. Málek, Interpretation of crystallization kinetics results providedby DSC, Thermochim. Acta 526 (2011) 237–251.

43] A. Khawam, D.R. Flanagan, Solid-state kinetic models: basics and mathematicalfundamentals, J. Phys. Chem. B 110 (2006) 17315–17328.

44] J. Málek, J.M. Criado, J. Sesták, J. Militky, The boundary conditions for kineticmodels, Thermochim. Acta 153 (1989) 429–432.

45] X. Huang, X. Huang, H. Mao, Z.X. Yin, Studies on the thermal decompositionkinetic of an nitrate ester, Appl. Mech. Mater. 182–183 (2012) 1575–1580.

46] B.L. Joseph, The thermal decomposition of nitric esters. II. The effect of additiveson the thermal decomposition of ethyl nitrate, J. Am. Chem. Soc. 76 (14) (1954)3790–3793.

47] M.A. Hiskey, K.R. Brower, J.C. Oxley, Thermal decomposition of nitric esters, J.Phys. Chem. 95 (10) (1991) 3955–3960.

[

cta 566 (2013) 137– 148

48] H. Giefers, M. Pravica, H.-P. Liermann, W. Yang, Radiation-induced decompo-sition of PETN and TATB under pressure, Chem. Phys. Lett. 429 (1–3) (2006)304–309.

49] J.C. Oxley, Chapter 1: A Survey of Thermal Stability of Energetic Materials inBook of Energetic Materials: Part 1. Decomposition, Crystal and MolecularProperties, Elsevier, 2003, ISBN 0444 5151 86, pp. 7–11.

50] B. Roduit, M. Hartmann, P. Folly, A. Sarbach, Parameters influencing correctprediction of autocatalytic reaction course, in: 43rd International Annual Con-ference of ICT, June 26–29, Karlsruhe, Germany, 2012, pp. 29-1–29-12.

51] P.J. Barrie, The mathematical origins of the kinetic compensation effect: 1.The effect of random experimental errors, Phys. Chem. Chem. Phys. 14 (2012)318–326.

52] P.J. Barrie, The mathematical origins of the kinetic compensation effect: 2. Theeffect of systematic errors, Phys. Chem. Chem. Phys. 14 (2012) 327–336.

53] D. Dollimore, P.F. Rodgers, The appearance of a compensation effect in the ther-mal decomposition of manganese (II) carbonates, prepared in presence of othermetal ions, Thermochim. Acta 30 (1979) 273–280.

54] S. Zeman, Kinetic compensation effect and thermolysis mechanism of organicpolynitroso and polynitro compounds, Thermochim. Acta 290 (1997) 199–217.

55] T.B. Brill, P.E. Gongwer, G.K. Williams, Thermal decomposition of energeticmaterials. 66. Kinetic compensation effects in HMX, RDX, and NTO, J. Phys.Chem. 98 (1994) 12242–12247.

56] N. Liu, R. Zong, L. Shu, J. Zhou, Weicheng Fan, Kinetic compensation effect in

thermal decomposition of cellulosic materials in air atmosphere, J. Appl. Polym.Sci. 89 (2003) 135–141.

57] Q.-L. Yan, S. Zeman, J. Selesovsky, R. Svoboda, A. Elbeih, Thermal behaviorand decomposition kinetics of Formex-bonded explosives containing differentcyclic nitramines, J. Therm. Anal. Calorim. 111 (2) (2013) 1419–1430.