Thermochimica Acta 566 (2013) 137–148

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Thermochimica Acta

jo urnal homepage: www.elsevier.com/locate/tca

The effect of molecular structure on thermal stability, decomposition

kinetics and reaction models of nitric esters

a a a,∗

Qi-Long Yan , Martin Künzel , Svatopluk Zeman ,

b c

Roman Svoboda , Monika Bartoskováˇ

a

Institute of Energetic Materials, Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice, Czech Republic

b

Department of Physical Chemistry, Faculty of Chemical Technology, University of Pardubice, 53210 Pardubice, Czech Republic

c

Department 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 a b s t r a c t

Article history: In this paper, the thermal stability and decomposition mechanism functions of 10 nitric esters including

Received 8 March 2013

nitroglycerine (NG), pentaerythritol tetranitrate (PETN), trimethylolethane trinitrate (TMETN), dipen-

Received in revised form 21 May 2013

taerythritol hexanitrate (DiPEHN), trimethylolpropane trinitrate (TMPTN), erythritol tetranitrate (ETN),

Accepted 22 May 2013

xylitol pentanitrate (XPN), sorbitol hexanitrate (SHN), mannitol hexanitrate (MHN) and nitroisobutyl-

Available online 31 May 2013

glycerol trinitrate (NIBGT) are determined by means of non-isothermal TG and DSC techniques. It has

been found that the mean activation energies for most nitric esters are comparable at constant heating

Keywords: −1

rate (around 145 kJ mol ), indicating that their main decomposition pathways might be the same. The

Nitric esters −1

mass loss activation energies of NG, TMETN and TMPTN are less than 100 kJ mol due to partial evap-

Thermal stability

oration. Based on the critical temperature of thermal decomposition, the order of molecular stability

Critical temperature

Reaction models for involved nitric esters is found to be MHN < XPN < TMPTN < SHN < NIBGT < ETN < PETN < DiPEHN. The

Kinetic compensation effect introduction 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 of

the Johnson-Mehl-Avrami and Sesták-Berggrenˇ models. Two types of kinetic behavior were observed and

most 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, which

were represented either by simultaneous evaporation and decomposition or by different decomposition

mechanisms originating from varying morphology and structure of the samples.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction powerful explosives used mainly for military purposes due to

greater compatibility and higher performance than other nitric

Nitric esters have been used as plasticizers or energetic fillers esters [4–7]. In particular, with regard to spark detonators, PETN

in detonators, propellants and explosives for mining, artillery, and can be used to avoid the need for primary explosives due to its lower

engineering since hundreds years ago [1,2]. In the past decades, electric spark initiation energy (10–60 mJ). On the other hand, some

considerable interest in nitric esters has been expressed by not only nitric esters could be used as drugs in medical treatment. In fact,

the specialists but also the amateurs and terrorists due to require- nitroester drugs have been shown to relax the smooth muscle of

ments of little synthetic expertise and availability of cheap raw blood vessels, and hence were widely accepted for the treatment

materials from the shops [3]. There has been growth in use of those of angina pectoris [8].

nitric esters such as erythritol tetranitrate (ETN), most of which are Because of growing practical demands on nitric esters, more and

so-called “homemade” explosives (HME). On the one hand, a num- more investigations are carried out with regard to their synthe-

ber of polynitroesters, including nitrocellulose (NC), nitroglycerin sis and physiochemical properties. On the purpose of utilization

(NG), the nitroester of pentaerythritol (PETN), trimethanolethane as energetic ingredients, recent studies have been concentrated

trinitrate (TMETN), and bis(2-nitroxyethyl)nitramine (DINA) are mainly 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 geometric

∗ and electronic structures of trinitrate esters including NG, TMETN,

Corresponding author. Tel.: +420 466038503; fax: +420 466038024.

butanetriol trinitrate (BTTN), and trimethylolpropane trinitrate

E-mail addresses: [email protected] (Q.-L. Yan), [email protected],

[email protected] (S. Zeman). (TMPTN) at the B3LYP/6-31G* level [12]. It has been found that

0040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2013.05.032

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

the oxygen balance, volume, density, detonation velocity and pres- 3. Results and discussions

sure of trinitrate esters linearly decrease with the increase of

methylene group’s number. In order to clarify the initial decompo- 3.1. Thermal responses during heating

sition mechanism for nitric esters, T-Jump/FTIR and T-jump/Raman

spectroscopies were used to analyze the gaseous products of The thermal responses (heat flow) for involved 10 nitric esters

several aliphatic nitric esters [13]. Kimura [14] also used chemi- were recorded by DSC under pressure of 0.1 MPa as shown in Fig. 1.

luminescence (CL) method to determine the light-emitting species The DSC curves for most of the studied nitric esters are not avail-

◦ ◦

during low temperature decomposition (between 40 C and 90 C) able in the literature. It has been shown that the melting points of

of PETN and NC. It has been shown that the thermal decomposi- nitric esters are much lower than those of secondary explosives, and

tion of nitric esters is accompanied by some oxidation reactions, some of them are liquid at room temperature. There is a big differ-

which could be generated in the course of recombination of per- ence with regard to melting point due to discrepancy in molecular

oxy radicals. On this basis, Chen and Brill [15] further studied structure. For instance, MHN and PETN have melting point higher

◦

the fast thermal decomposition kinetics and mechanism of some than 110 C, while those of TMETN, NG, and NIBGT are less than

polymeric nitric esters by SMATCH/FTIR technique (heating rate: zero. With regard to heat release process, it has been observed that,

◦ −1

100–150 C s ), and their activation energies were obtained as the exothermic peaks for NG and TMETN are not well formed due

−1 −1

around 129.8–142.4 kJ mol with log(A) values of 14.7–16.9 s . to strong evaporation. In order to make a quantitative view of the

Agrawal [16] synthesized some aromatic nitric esters, among thermal responses, the corresponding parameters are summarized

which the compound 1,3,5-tris(2-nitroxyethylnitramino)-2,4,6- in Table 1. The density and detonation velocity parameters are also

trinitrobenzene was found to be the potential alternative of PETN. In included in this table.

addition, quantum chemical calculations are used to compute the As shown in Table 1, the density of these nitric esters is around

−3

heats of formation for 24 nitric esters among which only 5 com- 1.4–1.8 g cm with theoretical detonation velocity of between

−1

pounds have the available experimental values [17]. As a result, 7000 and 9000 m s . As it could be seen, all of the nitric esters

considerable progress toward an understanding of the decompo- decompose in liquid state, and for the solid nitric esters, there

sition mechanism for nitric esters has been achieved. However, are obvious endothermic heat change before decomposition due

undoubtedly, the effect of molecular structure on the performances to fusion. It is interesting that the peak temperature of SHN and

and physiochemical properties of nitric esters could not be clearly XPN is the same while their onset temperature is very different,

identified due to discrepancy in principles and physical condi- and this might be caused by their very similar carbon chain struc-

tions of corresponding measurements carried out by different ture. NG, ETN and TMETN are comparable. PETN has the highest

researchers. In this paper, the non-isothermal behavior, isocon- fusion energy (H1), and melting point due to its highly symmet-

versional decomposition kinetics, reaction models and thermal ric molecule and great molecular rigidity. For NG, there is also one

stability for 10 typical nitric esters will be systematically inves- endothermic peak before decomposition due to evaporation, and

tigated, based on which the effect of molecular structure on these under dynamic nitrogen atmosphere the NG could partially decom-

parameters will be expounded. pose. With regard to heat of decomposition H2, DiPEHN has the

highest heat release due to higher hydrogen and carbon content

with sufficient oxygen balance. The heat release from decomposi-

2. Experimental

tion depends not only on the energy content of the compound, but

also on the experimental condition. Here the nitric esters decom-

2.1. Materials

pose under 0.1 MPa dynamic nitrogen atmospheres with relatively

slow heating rate. The heat change is also slow and could be well

There are 10 nitric esters involved in this research, whose molec-

recorded by the equipment. However, DSC thermograms of volatile

ular structures are shown in Scheme 1. The nitroglycerine (NG),

materials such as NG and TMETN will be strongly dependent on

pentaerythritol tetranitrate (PETN), trimethylolethane trinitrate

experimental conditions. At sufficiently slow heating and small

(TMETN), dipentaerythritol hexanitrate (DiPEHN), trimethylol-

mass the sample may completely evaporate before decomposition

propane trinitrate (TMPTN) are commercially available and

(in open or non-hermetically close sample pans). The effect of dif-

provided by “Explosia a.s.” company. The erythritol tetranitrate

ferent heating rates will be different heat of reaction. Since heat

(ETN), xylitol pentanitrate (XPN), sorbitol hexanitrate (SHN),

of reaction is determined from peak area and initial sample mass,

mannitol hexanitrate (MHN) and nitroisobutylglycerol trinitrate

the determination of heat of reaction in the case of sample mass

(NIBGT) are prepared by our work group by simply nitrating the

change during the process for NG and TMETN is highly inaccurate.

corresponding alcohols which are commercially available.

In fact, some other nitric esters with “Oxygen Bridge” such as tri-

ethylene glycol dinitrate (TEGDN) are also volatile under dynamic

2.2. Testing techniques atmosphere [18].

The involved nitric esters are studied with regard to the kinetics

of thermal decomposition, using Thermogravimetry (TG, Netzsch 3.2. Thermal stability

209F3 instrument, Al2O3 crucible) under the heating rate of 5,

7 (with data collecting rate of 40 points per Kelvin) and 10, The thermal stability of the crystals could be compared by the

◦ −1

15 C min (with data collecting rate of 60 points per Kelvin). The melting points of the compounds, and the stability of the molecular

◦

test temperature range for TG was 30–300 C, with the sample structure could be roughly determined by the onset temperatures

−1

mass of about 2.05–2.45 mg under 30 ml min dynamic nitrogen of exothermic peaks. For the purpose of kinetic calculation and eval-

atmospheres. Their heat flow properties was also evaluated by uation of thermal stability, the TG curves of involved nitrated esters

the technique of Differential Scanning Calorimetry (DSC, Netzsch are recorded under four different heating rates and the correspond-

200F3 instrument, Aluminum pan with a pin hole cover), which ing data are summarized in Table 2 (the TG curves are omitted in

was introduced in the dynamic nitrogen atmosphere with a pres- order to save the layout space). However, the onset temperature

sure of 0.1 MPa. The sample mass for DSC test was about 2.40 mg is dependent on the heating rate. We have to find another param-

◦ −1

with a heating rate of about 5 C min and temperature range of eter that is independent on heating rate and comparable to onset

◦

40–300 C. temperature to represent the thermal stability of these compounds.

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

O2NO ONO2 ONO2 ONO2 ONO 2 O2NO ONO2 ONO2 O2NO ONO2 ONO2 ONO2

H3C O2N

O2NO O NO

2 O NO

O2NO O2NO O2NO 2 NG (C3H5N3O9) XPN (C5H7N5O15) PETN (C5H8N4O12) TMETN (C5H9N3O9) N IBGT (C4H6N4O11)

ONO 2 O2NO ONO2 O2NO ONO2 ONO2 ONO2 ONO O2NO 2 H C ONO ONO 3 2 ONO2 2 O NO 2 O ONO2 O NO O2NO 2 O2NO O NO 2 ONO2 O2NO O2NO ONO2

O2NO ONO

O2NO 2

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

Scheme 1. Molecular structure of involved nitric esters.

−1

Fig. 1. DSC curves of different types of nitric esters at the heating rate of 10.0 K min (pressure: 0.1 MPa nitrogen gas; sample mass: 2.0–3.0 mg).

We can calculate the critical temperature (Tb) for thermal from inflammation theory and appropriate thermokinetic parame-

decomposition from the data of TG experiments. Tb is an impor- ters namely the pre-exponential factor by the following equations

tant thermal stability parameter required to insure safe storage [19,20].

and process operations for energetic materials. It is defined as the

1

lowest temperature to which energetic materials may be heated T = T + (1)

b eo b

without undergoing thermal decomposition. Tb may be calculated

Table 1

−1

Parameters from DSC experiments of different types of nitric esters under the heating rate of 10.0 K min with pinhole cover.

Samples Endothermic peaks Exothermic peaks Performance

◦ ◦ ◦ −1 ◦ ◦ ◦ −1

To ( C) Tp ( C) Te ( C) H1 (J g ) To ( C) Tp ( C) Te ( C) H2 (J g ) Density VoD

no no

NG 189.5 192.1 193.9 −55.6 197.4 199.9 202.1 24.8 1593 8.31

ETN 61.2 63.7 66.0 −297.7 184.8 196.3 211.6 364.3 1760 8.30

XPN – – – – 174.8 184.8 205.9 661.0 1580 7.10

SHN 52.9 55.1 57.0 −77.7 176.2 184.8 200.0 555.1 1778 8.23

PETN 140.1 142.4 144.2 −504.6 187.7 202.9 216.3 2385 1630 8.71

DiPEHN 71.5 73.1 74.7 −214.7 191.6 210.8 220.3 4678 1488 7.93

TMPTN 50.3 53.6 58.4 −114.8 181.9 206.4 221.8 1105 1500 7.49

no

TMETN – – – – 177.7 198.6 219.0 323.0 1640 7.30

NIBGT – – – – 179.9 200.6 217.8 569.8 1800 8.82

MHN 109.5 111.8 113.9 −87.4 169.4 181.4 202.6 631.2 1593 9.01

Note: To, onset temperature of the peaks; Tp, peak temperature of thermal events; Te, the end temperature for heat change; H1, heat absorption; H2, heat release; density,

−3 −1

in kg m ; VoD, calculated by Kamlet–Jacobs (K–J) equation, in km s ; no, these data are not reliable due to strong evaporation under lower heating rate.

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

Table 2

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

◦ ◦ ◦ ◦ ◦

Samples ˇ 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 172.7 186.9 199.9 171.2

7.0 154.9 177.4 182.8 176.3 190.1 205.8

10.0 161.4 183.8 185.5 180.8 194.5 214.6

15.0 171.2 191.9 203.1 186.0 199.4 224.4

ETN 5.0 157.1 174.6 184.1 162.6 DiPEHN 180.2 193.2 227.4 181.8

7.0 160.5 177.6 192.4 183.6 197.0 230.9

10.0 165.4 183.1 196.3 187.8 201.4 236.1

15.0 169.3 186.2 202.8 192.2 206.3 244.8

XPN 5.0 156.9 170.0 191.3 140.1 TMETN 158.8 178.3 208.9 169.3

7.0 161.9 173.7 194.8 161.8 183.4 216.7

10.0 165.7 177.7 197.8 167.0 188.3 222.5

15.0 169.0 182.5 205.8 177.1 196.0 225.0

SHN 5.0 153.1 165.7 196.9 160.9 TMPTN 159.7 178.8 186.6 119.1

7.0 155.6 168.9 200.6 167.1 185.7 197.8

10.0 159.6 173.0 203.5 170.7 191.0 203.4

15.0 163.6 177.2 213.1 180.5 196.8 211.6

NIBGT 7.0 163.4 183.7 200.8 158.5 MHN 155.0 169.4 190.0 138.5

10.0 171.0 187.5 212.3 160.2 173.3 193.7

15.0 180.9 194.2 215.2 164.2 176.6 199.8

20.0 184.7 197.6 223.2 166.2 180.7 214.2

◦ −1 ◦

Note: ˇ, heating rate in C min ; Tei, onset temperature of TG peaks; Tp, the peak temperature, C; Toe, endset temperature of TG peaks; Tb, critical temperature for thermal

decomposition, ◦C.

First of all, one can easily obtain the onset temperature (Tei) from than MHN, its molecular structure is a little bit more stable than

the non-isothermal TG curves, the value of Teo from the equation MHN according to their the critical temperature. In general, the

2 3 bond energy of O NO2 is noticeably lower than that of the N NO2

T = a + a ˇ + a ˇ + a ˇ , i =

ei 0 1 i 2 i 3 i 1–4 (2)

in similar compounds. Therefore, the stability of nitric esters

the values of b from the equation is lower than that of nitramines with similar mother skeletons

  (involved nitric esters are derived from skeletons of paraffin).

A0

ln ˇ = ln + bT (3) As it could be seen in Fig. 2, the critical temperature calculated

i bG(˛) i

from onset temperature of TG should linearly increase with the

where b, a0, a1, a2 and a3 are coefficients, R is the gas constant; After increase of onset temperature from DSC if no evaporation occurred.

ˇ . . .

the data ( i, Ti, i = 1, 2, , L) are fitted to Eq. (1) by the linear least- However, due to slightly different experimental conditions (open

squares method on the computer, the value of b could be obtained crucible for TG vs. sealed pan with pin-hole for DSC), the strong

ˇ

from the slope (ln i versus Ti). Besides, the value of the onset tem- volatile compounds (NG, TMETN) will not follow on this trend line.

perature (Teo) corresponding to ˇ → 0 obtained by Eq. (2) is equal For the title compounds, the order of the molecular stability is as fol-

to a0. Thus, the critical temperatures of thermal explosion (Tb) cal- lows: MHN < XPN < TMPTN < SHN < NIBGT < ETN < PETN < DiPEHN

culated by Eq. (2) and summarized in Table 2. The comparison of Ti based on the critical temperature of thermal decomposition. Here

with onset temperature of exothermic peaks on DSC curves, which NG and TMETN are not included for comparison due to inaccurate

has been shown in Fig. 2. calculation results when evaporation was not excluded.

Here, it should be noted that the thermal stability of nitric esters It is interesting that for isomer MHN and SHN with chi-

refers not the stability of their crystal structure but of their molec- rality, without introduction of any groups, their stability is

ular skeletons. For instance, based on the critical temperature of much different. SHN and MHN are nitrated from their iso-

thermal decomposition, even though the NG is easier to evaporate 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. It

210 means that the skeleton with R-type chirality carbon is more ther-

mal stable with greater rigidity of crystal lattice resulting in higher

melting point. Comparing NG, TMPTN, NIBGT and PETN, it could be

200

NG noticed that the introduction of functional groups to the tertiary

DiPEHN

carbon is in favor of increasing thermal stability due to increase

o 190 PETN

/ C

NIBGT of symmetry and rigidity of the molecule, where the contribution re

u

ETN order of the groups should be CH3 < NO2 < CH2ONO2. How-

erat 180 TMPTN

p TMETN SHN ever, the introduction of CH2ONO2 group to a primary carbon will

tem instead decrease the symmetry and rigidity of the molecule, there- XPN 170

set

fore resulting in a lower thermal stability. It is a good example that MHN

On

XPN is less stable than ETN. In addition, the number and position

160 of the methylene group will also have an influence on the thermal

stability of the molecules. Based on the experimental results, inter-

150 estingly, the proportion of methylene group ( CH2 ) to tertiary

110 120 130 140 150 160 170 180 190 200

carbon or quaternary carbon (Cs) would to some extent determine

Critical temperature / oC

the thermal stability of the nitric esters. For instance, as nitric esters

without quaternary carbon, MHN, XPN and ETN have Cs of 0.5,

Fig. 2. The correlation of critical temperature with onset temperature on DSC curves

0.66 and 1.0, so the higher Cs indicates greater thermal stability. for nitric esters.

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

Table 3

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

◦ −1 −1

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

SMM 125–190 201 20.69 [22]

150–160 197 20.20 [23]

90–120 173 16.74 [24]

NG MANO 80–140 159 15.24 [25]

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

52.1no 4.08[a]

SMM 144–169 194 19.6 [27]

– 160.3 16.3 [28]

ETN MANO 70–140 159 15.7 [29]

TGA 104–205 145.1 14.79 [a]

139.2 14.39 [a]

SMM – 159 16.7 [29]

XPN TGA 131–206 140.1 14.37 [a]

146.9 15.52 [a]

TGA 131–213 147.8 15.49 [a]

SHN

137.9 14.47 [a]

SMM 145–171 163 15.6 [29]

SMM 100–145 168 15.8 [29]

DSC 173–212 136.5 14.87 [3]

PETN

161–233 197 19.8 [30]

MANO 171–238 165 16.1 [30]

201–216 175 ± 3.3 15.6 [31]

CL 40–90 63.0 [14] –

PETN TGA 128–225 149.0 14.8 [a]

139.6 14.07 [a]

Extra. – 164.6 15.0 [11]

DiPEHN TGA 162–206 147.5 14.3 [a]

147.4 14.66 [a]

MANO 75–95 152.3 15.3 [26]

no

TGA 94–203 100.4 9.28 [a] TMPTN no

94.3 9.04 [a]

Cal. 75–95 166.1 [32] –

Extra. – 165.3 14.9 [11]

no

TMETN TGA 114–203 102.5 9.57 [a] no

83.3 7.68 [a]

TGA 166–197 122.4 11.9 [a]

NIBGT

111.3 10.95 [a]

SMM 180–240 159.1 15.9 [11]

161.1 16.9 [28]

MHN SMM – 166.0 15.8 [33]

TGA 155–182 151.6 15.9 [a]

146.1 15.61 [a]

Notes: Spls, samples; MoA, method of analysis; Ea, activation energy; Tr, temperature range; [a], results from this paper; MANO, manometric method; SMM, Soviet Manometric

Method; CL, chemiluminescence method; no, these activation data for decomposition are not reliable due to strong evaporation, and is almost evaporation activation energy

for NG.

In some cases, the increased stability was attributed to an increase (thermal gradients, inaccuracies of zero-line subtraction, etc.). On

in the integrity of crystal lattice, as molecular weight and symmetry the other hand, in case of a complex process usually only its main

increased, rather than to a change in elementary chemistry. Hence, peak can be evaluated by this method. The results provided by the

if ignoring volatile compounds, for the nitric esters that decom- Kissinger method are listed in Table 3 together with some experi-

pose in liquid state, the effect of the crystal lattice was excluded, mental data from the literature.

and their thermal stability would be completely determined by the As presented in Table 3, there are diverse data with regard to

structure of their molecules. activation energy of nitric esters, most of which are obtained from

the literature. Nitric esters such as NG and PETN are well known

3.3. Distribution of activation energy and widely used energetic materials, and their activation ener-

gies and thermolysis properties have been investigated by many

A kinetic study is usually considered of either a practical or a researchers [14,23–27,30,31,11]. The results are different from each

theoretical purpose. The kinetic parameters, including activation other due to different evaluation methods. In general, the activation

energy (Ea), pre-exponential factor (A) and kinetic model (f(˛)) energies obtained in this paper are slightly lower than those from

of each individual process, should be determined for a complete the literature which were mostly tested by “Manometric” method

kinetic description of the overall reaction. With regard to a one- and “Soviet Manometric Method” (isothermal in vacuum). In fact,

step process for decomposition of nitrate esters, we can directly use the disproportionate influence of secondary reactions of thermal

model-free methods, which state that at constant extent of conver- decomposition upon experimental results can be eliminated to a

sion the reaction rate is only a function of the temperature, to obtain large extent by carrying out the thermal decomposition in vac-

the dependence of the activation energy on the extent of conver- uum at isothermal conditions. The activation energies obtained

sion. In the first step, the activation energy Ea usually needs to be by SMM method are more suitable to correlate with detonation

determined. Traditional and most renowned methodology derived properties where the autocatalysis effect is excluded [34–36]. How-

for this task is the Kissinger’s method [21]. Main advantage of this ever, the activation energies of NG, TMETN and maybe TMPTN

method lies in its robustness with respect to data-distortive effects with relatively lower molecular weight are much lower than the

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

140 170 TMPTN 130 NG 165 TMETN 120 160 -1 NIBGT 155 110 150 100 E 145 90 140 nergy / nergy /

nergy / kJ.mol nergy / 80 135

70 tion E 130 va tion E 60 ti va Ac 125 ETN ti DiPEHN 50 Ac 120 SHN XPN PETN MHN 40 115

30 110

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Extent of conversion /a lpha Conve rsion / alpha

Fig. 3. The dependence of activation energy on the extent of conversion for nitric esters.

−1

average values of the literature. This might be caused by evapo- and 131.8 kJ mol which are much higher than the obtained mean

ration, because these materials are more volatile than the others, activation energies herein. It reveals that these compounds did not

especially when their thermolysis occurs in open crucible with completely decompose due to evaporation.

dynamic nitrogen flow. Especially for NG, the activation energy The full dependence of the activation energy of nitrate esters

obtained herein is only less than 1/3 of the average value from the on the extent of conversion is demonstrated in Fig. 3, where more

literature. It is undoubtedly more close to its evaporation activation activation energy points have been shown (˛ = 0.05 0.90). As a

energy. With regard to NIBGT and SHN, no data is available for their whole, the activation energies of NiBGT, NG and TMETN increase

thermal decomposition kinetics and hence no comparison could be with the extent of conversion, while that of MHN and TMPTN is

−1

made. Their activation energies were calculated as 122.4 kJ mol reverse. Sample mass loss for NG and TMETN, obtained by TGA

−1

and 147.8 kJ mol , respectively. analysis, is results of two simultaneous processes: evaporation and

In addition, the current data were evaluated by a decomposition. At a constant heating rate, the rates of these pro-

popular isoconversional method, the so-called modified cesses depend greatly on the temperatures and the evaporation

Kissinger–Akahira–Sunose (KAS) equation (see Eq. (4), [22]) is dominant at lower T (or conversion), where a relatively lower

to obtain the activation energy distribution. activation energy was obtained for evaporation process. Especially

−1

  for NG, the obtained activation energy, around 52–64 kJ mol , is

ˇ E

i ˛ very close to its activation energy for evaporation in double base

ln = Const − 1.0008 (4)

1.92 RT −1

T ˛ propellant (81.9 kJ mol ) [38]. In presence of other components

˛,i

in propellant, the evaporation could be slightly hindered, resulting

ˇ where is the heating rate, E␣ activation energy and T␣ the tem- in higher activation energy. For powdered samples, the activation

−1

perature in DTG or DSC curve at certain conversion rate (˛). Due to for NG evaporation could decrease to 75.3 kJ mol [39]. For NiBGT,

the large influence of experimental conditions on the data quality the situation is different. There is one C NO2 bond in its molecule,

of the process “tails”, it is a common practice to consider only val- which has a strong electron attracting effect on the O NO2 Bridge,

ues of Ea obtained for the interval ˛ = 0.3–0.7 when calculating the resulting in lower activation energy. In addition, as we could see,

˛

average value. The corresponding kinetic parameters at different the initial ( < 0.15) activation energies of SHN and PETN are much

˛

conversions are obtained and summarized in Table 4. lower than the central part ( = 0.4–0.6). In fact, it also has been

As shown in Table 4, the activation energies for nitric esters found that the activation energy of low-temperature decomposi-

−1

seems independent on the extent of conversion (˛ = 0.3–0.7) mostly tion of PETN and NC is around 63 kJ mol [14]. We will try to find

with the correlation coefficients greater than 0.99. It reveals that the reason for different activation energy distribution in the follow-

the mean activation energy could represent the overall apparent ing section by comparing their decomposition reaction models.

activation energy for the primary thermolysis process. The mean

values of these activation energies are smaller than those obtained 3.4. Reaction models for exothermic processes

by Kissinger method. The mean activation energies of ETN, SHN

and PETN are almost the same while those of MHN, DiPEHN and The second important step for kinetic analysis is selection of

XPN are also comparable. Generally, based on our previous research an appropriate kinetic model for the description of the given

[37], the nitric esters represent the most reactive group of polynitro processes. For this procedure, Málek [40,41] suggested a useful

˛

compounds with regard to both homolysis and heterolysis. Any- algorithm based on the shape of characteristic functions z( ) and

˛

way, the mean activation energies for most nitric esters are close to y( ). These functions are obtained by a simple transformation of

−1

145 kJ mol under constant heating rate. It indicates that the main experimental data, for non-isothermal conditions the characteristic

pathway for decomposition of nitric esters might be the same. As functions are defined as follows:

it is known to all, thermal decomposition of nitric esters proceeds E/RT

y(˛) = · e (5)

through dissociation of O NO2 bond producing nitrogen dioxide.

It was also confirmed that the overlap population of the O NO2 z ˛ 2

( ) = · T (6)

for trinitrate ester is relatively smaller than other bonds, indicating

that the O NO2 may be the trigger bonds during initiation pro- where is the reaction rate at a certain temperature (T), R gas

cess of thermolysis [12]. Meanwhile, the theoretical calculation constant, and E is the activation energy. As stated in a recent

in this literature showed that the bond dissociation energies of comprehensive review paper by Svoboda and Málek [42], the

O NO2 bond in NG, TMETN and TMPTN are around 142.0, 132.3 introduced functions are in fact a universal way for determination

Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137–148 143 0.9958 0.9992 0.9985 0.9985 0.9960 0.9998 0.9978 0.9994 0.9897 0.9933 0.9966 0.9964 0.9978 0.9945 1.0000 1.0000 r 0.28 0.39 0.18 0.37

± ± ± ±

A

9.04 7.68 9.28 9.12 9.13 8.85 8.81 7.63 14.47 14.66 Log 14.66 14.77 14.47 14.56 15.28 15.07 14.83 14.27 14.14 15.01 value

mean

and 0.7 3.4 0.73 3.8

± ± ± ±

0.50

=

94.3 83.3 95.00 94.16 95.09 93.07 94.07 83.34 a 137.9 147.4 SHN E 137.10 138.79 137.07 138.49 138.30 DiPEHN 149.52 148.22 144.03 143.26 152.15 TMPTN ␣

0.9908 0.9932 0.9932 0.9938 0.9951 0.9995 0.9975 0.9980 0.9995 0.9995 0.9975 0.9997 0.9981 0.9966 0.9957 0.9930 0.9940 r

0.38 0.12 0.46

± ± ±

A

7.36 8.15 14.39 15.52 15.61 Log 14.77 15.13 14.32 14.07 14.34 15.47 15.58 15.32 15.53 15.68 15.74 16.15 16.00 14.90 15.26

0.7

and 2.4 1.8 3.2

± ± ±

0.40

=

80.46 88.57 a 139.2 146.9 146.1 150.07 ETN E 139.2 143.4 137.6 136.3 139.4 XPN 144.86 146.73 145.40 147.49 MHN 145.54 149.86 149.47 141.13 144.51 ␣

method.

0.21 0.40

± ±

KAS .

1 − 0.9950 0.9920 0.9864 0.9849 0.9844 0.9970 0.9995 0.9990 0.9990 0.9985 0.9968 0.9932 0.9964 0.9979 0.9978 0.9925 0.9935

s 14.07 10.95 r

in

modified

factor,

0.15

±

A

iso-conversional 4.08 3.83 3.90 4.19 4.15 4.17 7.21 8.04

10.41 10.78 10.79 Log 14.22 14.24 13.84 14.27 13.78 11.24 11.55 by pre-exponential

, A

;

1 − esters

0.60

kJ.mol nitric

and 1.8 1.41 4.2

in

± ± ± for

0.30

=

52.1 50.52 49.37 53.26 53.19 53.96 78.11 86.06 a data

111.3 139.6 140.44 105.49 109.26 109.87 NG E 139.47 137.74 141.72 138.46 114.63 117.37 PETN NIBGT ␣ energy,

kinetic

Activation

, a

E

4

reacted

␣ 0.30 TMENT 0.30 0.30 0.60 0.40 0.50 0.60 0.70 Mean 0.40 0.50 0.70 0.40 0.50 0.60 0.70 Mean Decomposition Table Notes:

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

Fig. 4. The y(˛) and z(˛) plots for the thermal decomposition data of nitrate esters (a, b, c, . . ., h for NG; XPN, SHN, DiPEHN, TMPTN, TMETN, NIBGT and MHN, respectively).

of an appropriate kinetic model applicable to almost any physical y(˛) function ˛max,y. These calculations are described in detail in our

process, including thermal decomposition [43]. Determination of previous paper [20]. Choice of an appropriate kinetic model is not

the most suitable kinetic model then utilizes both, value of con- always only the question of the highest correlation coefficient, the

version degree ˛max,y corresponding to the maximum of the y(˛) JMA model is usually preferred (in case when its applicability is at

function and value of ˛max,z, which corresponds to the maximum least remotely confirmed by the above-mentioned algorithm) due

of the z(˛) function. Based on this information, the optimal kinetic to the possibility of consequent physically meaningful interpreta-

model can be chosen according to the algorithm presented e.g. tion of its kinetic exponent m. The description by the AC model is

in Ref. [40]. After the choice of the kinetic model is made, the empirical and purely phenomenological, where the parameters do

pre-exponential factor A can be determined by enumerating the not have any physical basis or meaning, and therefore this model

general kinetic equation and applying curve-fitting procedure to is usually used only in case when the data cannot be described by

fit the experimental data by the determined kinetic model (the the JMA model.

pre-exponential factor being the only variable parameter). It is Based on abovementioned theory, the characteristic functions

advantageous to confirm the value of this parameter by inde- z(˛) and y(˛) have been plotted in Fig. 4 for chosen studied materials

pendent evaluation within the framework of different models (if (the plots for ETN and PETN are omitted).

possible). With regard to the specific kinetic models, in the present As can be deduced from the shape of y(˛) functions pre-

work we have utilized two of the most popular models: the phys- sented in Fig. 5, most materials/processes show kinetics close

ically meaningful Johnson-Mehl-Avrami model (JMA, Eq. (7)) and to that characteristic for the first order reactions, which is a

empirical autocatalytic model (AC, see Eq. (8)), which is also known common case for decomposition processes. All these materials

as Sestákˇ Berggren model [44]. also have maxima of the corresponding z(˛) functions close to

[1−(1/m)] the value 0.632, which is a characteristic “fingerprint” suggest-

f (˛) = m(1 − ˛)[− ln(1 − ˛)] (7)

ing good applicability of the physically meaningful JMA model.

M N In other words, these materials (XPN, SHN, DiPEHN, NIBGT and

f (˛) = ˛ (1 − ˛) (8)

MHN) exhibit typical single-process behavior, characteristic for

Value of the kinetic parameters m, M and N can then be cal- thermally activated decompositions with sole mechanism being

culated from the conversion corresponding to the maximum of the involved.

Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137–148 145

65

cannot consider these models valid for their thermal decompo-

60

sition or evaporation, and thermal analysis under more proper

b a

55

c conditions needs to be done. In addition, according to the litera-

50 ture [1], autocatalysis or self-acceleration is normal for most of the

PETN

45 nitrate esters, which (incidentally) well corresponds to high corre-

XPN DiPEHN

ETN lation coefficients obtained for the autocatalytic Sesták-Berggrenˇ

-1 40 MHN

35 SHN model. The main reason for this is the development of oxidative and

NIBGT CL-20-Formex

30 a: y = 0.2875x + 0.1403 hydrolytic interaction of the parent nitroester with the products of

TMPTN 2

BCHMX-Formex R = 0.9828 its decomposition: HNO3, NO2 and H2O. Because of the following Ln (A) / s 25 TMETN

HMX-Formex

b: y = 0.2744x - 5.0293 equilibrium that are attained in the gas phase reactions: 20 RDX-Formex R2 = 0.9898

15 NG

+ ⇔ +

c: y = 0.2159x - 1.1323 NO2 H2O 2HNO3 NO 10 R2 = 0.9938 5 ⇔

NO2 N2O4

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

E -1

Activation Energy ( a ) / kJ.mol the introduction of any of these components in the system results in

an increase of the concentration of all molecules. For this issue, the

Fig. 5. A comparison of the kinetic compensation lines for nitric esters and Formex

effects of nitrogen dioxide, oxygen, nitric oxide, acetaldehyde and

bonded explosives containing cyclic nitramines (RDX, HMX, BCHMX and CL-20).

diethyl peroxide on the thermal decomposition of ethyl nitrate at

◦

181 C had been studied in the 1950s by Joseph [45]. It was proved

that the ratio of NO /NO determines the reaction rate and in the late

On the other hand, in case of the materials depicted in Fig. 5 2

stages of reaction this ratio is much larger than at the beginning and

under letters “a”, “e” and “f” (NG, TMPTN and TMETN, respec-

a lowered rate constant results.

tively), both characteristic kinetic functions z(˛) and y(˛) have a

With respect to the often desired information about the

significantly different shape, differing from that observable for the

reaction order, the empirical “reaction order model” can be

rest of the studied materials. Looking first at the z(˛) functions,

applied. In fact, the thermal decomposition of TDNTN [46],

it can be seen that their maxima are shifted to higher conversion

poly(glycidyl nitrate), (PGN), poly(vinyl nitrate) (PVN), and

degrees. If we add the information provided by the y(˛) function,

poly(nitratomethylmethyloxetane) (NMMO) were studied in terms

which clearly suggests manifestation of multiple decomposition

of this model and were found to have order of reaction n = 2 [15].

mechanisms, it can be concluded that the larger deviation from

However, it was further pointed out that their decomposition

the expected (first order JMA process) behavior is caused by an

processes are not necessarily second-order in the usual sense of

overlap of the involved mechanisms/processes. The shift of the z(˛)

chemical kinetics, because these decomposition processes are het-

function maxima is then caused by the dominant decomposition

erogeneous in which all of the reactions and diffusion terms are

process having its initiation slightly postponed (shifted to higher ˛)

lumped (hence empirical character of the reaction order model).

due to the formerly manifesting minor mechanism (evaporation).

Interestingly, the decomposition mechanism of NIBGT could

The simultaneous manifestation of the two involved mechanisms

be described by the reaction order model (n = 1, r = 0.9980). With

as well as their different dependence on heating rate (most proba-

regard to its molecular structure (Scheme 1), different from the

bly due to different apparent activation energy) then results in the

other nitric esters, NIBGT has one C NO bond while TDNTN has

inconsistencies of the z(˛) and y(˛) functions shape. 2

two C NO bonds (Scheme 2). According to Fig. 4, characteristic

In Table 5 the results of kinetic analysis are summarized; in 2

kinetic functions for both these materials show slight dependence

case of all materials description by both kinetic models (JMA and

on heating rate, suggesting change of the reaction mechanism. By

AC) was done. In the first part of the Table values of ˛max,z and

˛ fitting the NIBGT material, it was found that when the heating rate is

max,y are listed for the studied materials (mean value from all

lower, its weight loss is first-order through the first 50% (lower acti-

measured curves was always calculated). In the second part of

vation energy), followed by a second-order process in the latter 50%

the Table the mean correlation coefficients determined for the

(higher activation energy). It has been proved [48] that when the

description of experimental data by the respective theoretical mod-

heating rates are slow, these two steps are separated by a disconti-

els are shown. As is apparent, for ˛max,z values close to 0.632 the

nuity. It means that O NO homolysis dominates initially followed

descriptions by the JMA model were very good (indicated by high 2

by the dominance of chain cleavage [47,48]. It has also been found

correlation coefficients). Nevertheless, generally the description by

that decomposition mechanism of nitric esters in general follows

the AC model shows better correlation coefficients than that by the

the similar rules [49]. In compounds containing more than one

JMA model – which is however perfectly understandable as AC is

nitrate ester, the structural orientation has a marked effect on the

an empirical model specifically designed to have maximum flexi-

reaction products. Moreover, the aforementioned reaction mod-

bility for description of kinetic data. In the end, in case of complex

els could also present the storage properties of the corresponding

or unideal processes, it is always up to the researcher to choose

materials. According to recent simulation results [50], for nth-order

between the quality of the description and possibility of interpre-

models the storage aging has no influence on the reaction course

tation of the results. Even though the applicability of the JMA model

and further thermal properties of the materials. However, the only

can be extended well beyond the limits suggested in the original

1% slow thermolysis process during storage will result in at least

work of Málek [38], it should be always borne in mind that for larger

30 K decrease for the initial decomposition temperature of ener-

deviations from the theoretical model behavior also the interpre-

getic materials with autocatalytic effect. Materials that follow JMA

tations of the kinetic exponent and shapes of kinetic functions can

decomposition mechanism including Avrami-Erofeyev (A4) will be

be done only as an approximation or rough estimate. Finally, in the

slightly affected by their aging process during storage.

last part of the Table the complete sets of kinetic parameters for

both applied model are listed.

In case of the NG and TMPTN materials the complexity of 3.5. Kinetic compensation effect

the processes can be explained by the partial evaporation dur-

ing decomposition, resulting in very complicated processes (both The kinetic compensation effect states that there is a linear rela-

JMA and AC model with lower correlation coefficient). Here we tionship between Arrhenius parameters log(A) and E for a family

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

Table 5

Parameters 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)

a

NG 0.64 0.83 0.938 0.966 3.0 0.34 0.20 52.1 7.22

ETN 0.06 0.69 0.982 0.990 1.2 0.04 0.61 139.2 17.45

XPN 0.20 0.60 0.987 0.999 1.5 0.24 0.96 146.9 17.52

SHN 0.25 0.60 0.980 0.998 1.5 0.35 1.06 137.9 16.77

PETN 0.10 0.71 0.980 0.980 1.2 0.11 0.99 139.6 17.41

DiPEHN 0.25 0.58 0.976 0.999 1.7 0.36 0.99 147.4 18.34

a

TMPTN 0.27 0.71 0.972 0.975 1.5 0.37 0.82 94.3 11.78

TMETN 0.49 0.74 0.989 0.951 3.0 0.34 0.38 83.3 10.75

N

NIBGT 0.42 0.61 Reaction order model: (1 − ˛) – 1.00 111.3 14.45

MHN 0.22 0.56 0.974 0.998 1.3 0.33 1.13 146.1 19.34

N

TDNTN [43] – – Reaction order model: (1 − ˛) – 2.00 133.2 7.50

PVN [15] – – – 2.00 134.3 15.9

PGN [15] – – – 2.00 130.2 14.7

NMMO [15] – – – 2.00 140.2 16.4

a

These compounds are volatile and the obtained models may invalid for both evaporation and decomposition. The bold number means this model is not appropriate due

to low correlation coefficient.

of related processes [51,52]. It is a widely observed phenomenon It reveals from Eq. (12) that when T = 1/R, the decomposition

in many areas of science, notably heterogeneous catalysis [53]. The reaction of the materials in the same family will have the same



applicability of the Arrhenius equation to a particular reaction could rate constant, indicating that Tiso equals to 1/ R. With a set of var-

be tested by finding constancy or a predictable variation in the “fre- ied kinetic parameters, the plots of kinetic compensation effect

quency factor” with changes in experimental conditions or sample could be established for different groups of materials. Based on this

treatment or structure. It is demonstrated, both theoretically and theory, the plots of corresponding parameters for nitric esters are

by numerically, that random errors in kinetic data do generate an obtained in Fig. 5.

apparent compensation effect (sometimes termed the statistical Interestingly, according to Fig. 5, the kinetic points of all nitric

compensation effect) when the true Arrhenius parameters are con- esters obtained by model-fitting fall almost on the same compen-

stant [51]. Expressions for the gradient of data points on a plot of sation line (b) with a correlation coefficient of greater than 0.989. It

log(A) against Ea are derived when experimental kinetic data are might reveal that they follow the same compensation effects due to

analyzed by linear regression. the same dependence of enthalpy change and the entropy change

caused by dissociation of O NO2 bond [55,56]. It is interesting that

ln A˛ = ω + E˛ (9)

NG and TMETN decomposing along with strong evaporation also

ω followed on this compensation line. This is a correlation between



where and are the coefficients of linear regression, which

the enthalpy change (H) and entropy change (S) for a family of

depend on the type of sample and their structures. Here also

chemical reactions. It is known from transition state theory that E

another equation could be used:

corresponds to enthalpy change while log(A) is related to entropy

E

= e + . RT A

a 0 2 303 iso ln (10) change. A wide variety of other physical reasons for the kinetic com-

pensation effect have been proposed in the literature for particular

where T is the isokinetic temperature, according which the

iso situations [55]. There are two compensation lines for two groups of

involved materials could be divided in to different family groups

results. The log(A) values for “line a” are calculated by KAS method

[54]. At isokinetic temperature, the reaction rates (k) for different

while that of line b is from the results obtained by the model-fitting

materials are the same. The logarithmic expression of Arrhenius

method. It is interesting that the slope of these two lines is almost

equation is:

identical. On the one hand, it indicates that during calculating of

E˛ activation energy by KAS method, the pre-exponential factor has

ln k = ln A˛ − (11)

RT been underestimated. On the other hand, it means that all of the

nitric esters have the same isokinetic temperature according to

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

  Eq. (10). Similarly, the kinetic compensation effect has also been

 − mentioned for thermal decomposition of Formex bonded explo-

1

A = ω + E

ln ˛ ˛

RT (12) sives containing cyclic nitramines (Nitra-F PBXs) [57], which are

shown as “line c” in Fig. 5. It is obvious that slope () of “line c”

CH3 O2NO NO2 ONO2 CH CH2 H CHCH2O OH n H OCH2CCH2 OH n n O NO ONO CH2ONO2

2 O2N ONO2 2

CH2ONO2

TDNTN (C6H8N6O16 ) PVN (C2nH3nNnO3n) NMMO (C5nH9n+2NnO4n+1) PGN (C3nH5n+2NnO4n+1)

Scheme 2. Molecular structure of some polymeric nitric esters.

Q.-L. Yan et al. / Thermochimica Acta 566 (2013) 137–148 147

is smaller than that of “lines a and b”. It means that the isokinetic [3] J.C. Oxley, J.L. Smith, J.E. Brady IV, A.C. Brown, Characterization and analysis of

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