Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 1, pp 737–744 | Cite as

Toward understanding the aging effect of energetic materials via advanced isoconversional decomposition kinetics

  • Yoocheon Kim
  • Anirudha Ambekar
  • Jack J. Yoh


The decomposition process of typical energetic material (EM) may consist of thousands of individual reactions as well as many intermediate species. However, one-step decomposition kinetics is routinely utilized for prediction of the shelf life of EMs. The inclusion of detailed multi-step chemistry in the kinetic mechanism can improve the reliability of the lifetime prediction. This study proposes a novel procedure for lifetime prediction of EMs, which adopts isoconversional kinetics to represent the decomposition reaction scheme. The pertinent EMs considered in the study include 97.5% cyclotrimethylene-trnitramine, 95% cyclotetramethylene-tetranitramine (HMX) and boron potassium nitrate. Differential scanning calorimetry was utilized for extracting the said isoconversional kinetics complemented by experimental validation of the proposed chemical kinetics through a comparison of the numerical lifetime predictions with accelerated aging experiment measurements.


Isoconversional kinetics DSC Energetic materials Lifetime Aging effect 


There is a rising interest in the lifetime assessment of energetic materials (EMs) due to its direct association with storage safety and service life. A priory knowledge of the expected lifetime of various EMs is valuable not only for safety and performance but also for economic reasons. Higher temperatures during storage accelerate the aging process of the EMs, and subsequent degradation of thermal stability can lead to failure or accidental ignition. The EM composition may include various polymer binders in addition to a basic explosive such as cyclotetramethylene-tetranitramine (HMX) or cyclotrimethylene-trnitramine (RDX). Since the binders and explosives decompose differently, the resulting thermochemical reaction path will change as the thermal stability of each substance is changed. In our previous paper, the decomposition of RDX-based explosive was not affected by phase transition phenomenon [1]. However, in this research, for another RDX-based explosive, it shows different decomposition process as composition of energetic material is changed. Thus, it is important to conduct elaborate calorimetry experiment for various composition of energetic material to predict the aging effect.

Conventionally, the aging effect has been estimated using the Arrhenius approach [2] or Berthelot approach [3] utilizing a one-step decomposition kinetics, which does not accurately represent the actual chemical response of a thermally stimulated EM. Another technique for estimating shelf life of the EMs utilizes accelerated aging tests, which measure the shelf life at elevated temperatures and subsequently extrapolate to the storage conditions. However, even the accelerated aging tests require several days to several months for completion. This makes these techniques highly resource-consuming and time intensive. Therefore, in order to predict the aging effect and to extract the relevant thermal decomposition kinetics, an effective technique is necessary. Recently, a novel method for observing aging effect using laser-induced breakdown spectroscopy (LIBS) has been proposed [4]. Although, such a method accurately estimates the aging of a propellant by measuring the elemental composition of propellant, it does not reveal the influence of aging on performance of energetic material such as remaining heat of reaction.

The decomposition kinetics of EMs can be extracted by several experimental techniques such as thermo-gravimetry (TG), scaled thermal explosion (STEX), one-dimensional time to explosion (ODTX) study, accelerated rate calorimetry (ARC) and differential scanning calorimetry (DSC). Each of these experimental techniques has its distinct characteristics and requires different amount of EM sample for reliable data acquisition. Considering the low sample mass requirement of the DSC technique, which aids the safety of operation, it has been used widely in order to investigate the thermal decomposition characteristics of energetic materials [5, 6, 7].

Furthermore, the calorimetric data obtained using DSC experiments can be used to construct the reaction parameters as a function of the reaction progress variable, such that the decomposition and thermal runaway process are precisely tracked and reproduced. In the current study, in order to extract the decomposition kinetics of the energetic materials, an isoconversional approach is adopted [1]. Thanks to a noticeable progress in the integral method [8] and kinetics analysis software [9], such method has gained much attention recently for description of decomposition mechanism of energetic materials [10]. Recently, for describing fast reaction phenomena such as explosion and detonation by numerical simulation, the isoconversional kinetics was adopted for numerical formulation as chemical reaction [1]. In the same way, the application of isoconversional kinetics for numerical calculation can be extended to predict a very slow decomposition phenomenon such as aging process.

In this research, we have proposed a calculation-based method for predicting shelf life of energetic materials and aging effects using experimentally extracted isoconversional decomposition kinetics. The isoconversional kinetics of an energetic material is conventionally extracted utilizing only non-isothermal DSC [7] technique. However, in the current study, the combination of non-isothermal and isothermal DSC technique was chosen to elucidate the influence of phase transition on decomposition process. In this method, the isoconversional kinetics describes the whole decomposition process by a set of reaction parameters that vary with reaction progress, thus providing an improved match with the aging experimental data. This approach enables prediction of aging effect solely through calculation using isoconversional kinetics, saving the experimental cost and time. Recent work by Burnham et al. [11] reports prediction of EM lifetime based on isoconversional method. In contrast, the current study includes accelerated aging experiments and compares the predicted value with actually aged sample. The decomposition kinetics of two high explosives, namely HMX and RDX as well as a propellant formulation based on boron and potassium nitrate (BPN), have been elucidated. Additionally, the aging of BPN samples was experimentally simulated using elevated ambient temperatures. During this test, BPN was aged at 71 °C for extended period of time and the heat of reaction of the aged sample was subsequently evaluated. This value was compared against the predictions obtained from the newly constructed decomposition kinetics according to the aerospace industrial guideline [12]. The experimental and predicted values for the BPN samples were found to be in reasonable agreement.

Experimental study for isoconversional kinetics calculation

Energetic materials under study

The first EM under study is a high explosive consisting of 97.5% RDX, 0.5% polyisobutylene, 0.5% graphite and 1.5% calciumstearate. The second EM is composed of 95% HMX and 5% of VITON-A. The third EM is a propellant that consists of 24% boron, 71% potassium nitrate and 5% laminac binder (BPN).

Experimental setup

DSC experiments were carried out with a Mettler Toledo DSC 3 instrument utilizing the standard 40-µL sealed aluminum pans with a purge flow of nitrogen maintained at 80 mL min−1. The sealed pans allow observation of the decomposition process without detrimental effect of EM evaporation. The EMs were tested under non-isothermal experimental conditions where the product of the sample mass and heating rate was maintained below 1 mg °C min−1 in order to prevent self-heating of the sample [13]. Table 1 shows the details of experimental parameters maintained during non-isothermal DSC experiments.
Table 1

Non-isothermal experimental conditions


Heating rate/°C min−1

Temperature range/°C

Sample mass/mg

97.5% RDX

0.5, 1.0, 2.0 and 4.0



95% HMX

0.5, 1.0, 2.0 and 4.0




2.0, 4.0 and 8.0



Additionally, isothermal DSC experiments were carried out for the RDX-based EM in order to evaluate the effect of phase transition on the decomposition reactions. The RDX-based EM was tested at the constant temperatures of 185 and 195 °C. As HMX and BPN decomposition exothermic points are detached from phase transitions point, it is considered that phase transition does not influence the exothermic decomposition, and thus, only non-isothermal experiments were conducted for the EMs under study.

Isoconversional kinetics calculation

Figure 1 shows a typical experimental DSC trace in which S(t) denotes the measured DSC data as a function of time while B(t) indicates the reference line or baseline constructed for determining the magnitude of the heat flow in or out of the sample. The construction of the baseline involves the superposition of tangents at each side of the exothermic signal peak. Each tangent is linked through the product mass fraction in a baseline function. The reaction rate at time t may be expressed as the instantaneous heat flow divided by the summation of the energy released during the entire decomposition process. The product mass fraction at the time is given by the summation of the energy released divided by the total energy released. Mathematically, the mass fraction of reaction products (α) and the reaction rate (\( {\text{d}}\alpha /{\text{d}}t \)) can be obtained using Eqs. (1)–(3).
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \frac{S(t) - B(t)}{{\int\limits_{{t_{0} }}^{{t_{\text{end}} }} {[S(t) - B(t)]{\text{d}}t} }} $$
$$ \alpha (t) = \frac{{\int\limits_{{t_{0} }}^{t} {S(t) - B(t)} {\text{d}}t}}{{\int\limits_{{t_{0} }}^{{t_{\text{end}} }} {[S(t) - B(t)]{\text{d}}t} }}\quad (0 \le \alpha \le 1) $$
$$ B(t) = [1 - \alpha (t)](a_{1} + b_{1} t) + \alpha (t)(a_{2} + b_{2} t) $$
where \( t_{0} \) and \( t_{\text{end}} \) represent time of start and end point of reaction peak, respectively, while a 1, a 2, b 1 and b 2 are constants indicating the location of the tangents to the exothermic peak.
Fig. 1

Standard DSC signal and baseline

Results and discussion for kinetics calculation

Isothermal DSC results

The phase transition or melting temperature for RDX is known to be 204.5 °C [14]. Figure 2a shows the endothermic DSC peak at 204 °C for the phase transition for RDX-based EM obtained using the heating rate of 2.0 °C min−1. In order to elucidate the influence of phase transition on chemical reactions, isothermal DSC experiments were conducted at the temperature of 185 and 195 °C. Figure 2b, c shows the experimental results which indicate that an isothermal heating below melting temperature does not result in significant exothermic reactions. It shows 10−4 order of energy flow, which is ignorable in terms of magnitude compared to the exothermic decomposition peak of Fig. 2a which shows an order of 10. These results indicate that the exothermic reactions for RDX occur primarily in the liquid phase.
Fig. 2

a Phase transition phenomenon in 97.5% RDX during non-isothermal DSC, b isothermal DSC signal of 97.5% RDX at 195 °C and c isothermal DSC signal of 97.5% RDX at 185 °C

Non-isothermal DSC results

Figure 3 shows the non-isothermal DSC signals of the EMs considered in the current study. As the heating rate increased, the peak value of the DSC signal, the initiation temperature and the termination temperature become higher in all EMs.
Fig. 3

Non-isothermal DSC signal for a 97.5% RDX, b 95% HMX and c BPN

The heat of reaction (Q) was calculated from the DSC signal at each heating rate using Eq. (4). The average value of all heating rates was assumed to be the effective heat of reaction for the given sample. The maximum deviation in the experimental values in the current study was found to be 9% which is considered acceptable.
$$ Q = \int\limits_{{t_{0} }}^{{t_{\text{end}} }} {[S(t) - B(t)]{\text{d}}t} $$
The calculated heat of reaction indicating the energy released per mixture mass for the 97.5% RDX, 95% HMX and BPN sample was found to be 2241.8, 1488.6 and 6024.4 J g−1, respectively.
The reaction rate was calculated using a relationship expressed in the form of Arrhenius equation as shown in Eq. (5).
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = [A_{\upalpha} f(\alpha )]\exp \left( {\frac{{ - E_{\upalpha} }}{RT(t)}} \right) $$
where R, t, T, \( A_{\upalpha} \) and \( E_{\upalpha} \) indicate the universal gas constant, time, temperature, frequency factor and activation energy for given product mass fraction α, respectively. The function \( f(\alpha ) \) reflects the dependence of the reaction rate on the reaction progress. Taking a logarithm of both sides of Eq. (5) yields Eq. (6).
$$ \ln \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \ln [A_{\upalpha} f(\alpha )] - \frac{{E_{\upalpha} }}{RT} $$
In the Arrhenius plot obtained from Eq. (6), \( - E_{\upalpha} /R \) is the slope of the linear curve and \( \ln [A_{\upalpha} f(\alpha )] \) corresponds to the intercept with the vertical axis with coordinate \( \ln [{\text{d}}\alpha /{\text{d}}t] \). The reaction rate and reaction progress were obtained from the DSC signals shown in Fig. 3 and Eqs. (1)–(2) in order to conduct Friedman analysis from the Arrhenius plots.

Friedman analysis

The Friedman analysis results for each EM are present in Fig. 4 where each measured DSC signal corresponds to a reaction progress curve on the Arrhenius plot. A straight line connecting equal reaction progress states of each signal was drawn. The slope and the intercept with vertical axis for these lines represent the activation energy and pre-exponential factor at that particular reaction progress. Following this process, one can extract the kinetic parameters that correspond to a reaction progress from 0 (unreacted) to 1 (completely reacted). The activation energy and pre-exponential factor varying with α are shown in Fig. 5. This implies that the extracted kinetics describes the complete process of the chemical reaction through a set of Arrhenius parameters obtained at an instantaneous state of the reaction progress.
Fig. 4

Friedman analysis plots for a 97.5% RDX, b 95% HMX and c BPN

Fig. 5

Isoconversional decomposition kinetics of a 97.5% RDX, b 95% HMX and c BPN

Validation of advanced isoconversional kinetics

In order to validate the extracted kinetics, the DSC measurements were reproduced using the proposed kinetic parameters. The comparison of DSC experiments and calculations is plotted in Fig. 6. The results show good agreement between simulation and experiment, which suggests that the obtained kinetic scheme can describe thermal decomposition of target energetic materials from an initial solid-sate to a final product state.
Fig. 6

Validation of isoconversional decomposition kinetics–reaction rate calculation a 97.5% RDX, b 95% HMX and c BPN

Aging effect prediction

Conventional techniques

Energetic materials undergo a change in performance characteristics such as heat of reaction and reaction kinetic parameters due to the aging phenomenon. Under room temperature storage conditions, energetic materials decompose at an extremely slow rate. This makes the experimental verification of aging at room temperature storage conditions practically impossible as the experimental duration would span over decades.

Most commonly used theoretical prediction method is Arrhenius approach [2] which predicts the shelf life of an EM using ratio of reaction rates between temperature T 1 (storage temperature) and T 2 (elevated temperature) at which thermally accelerated aging experiments are conducted. The Arrhenius approach utilizes Eqs. (7) and (8).
$$ k = A\exp ( - E_{\upalpha} /RT) $$
$$ \frac{{t_{1} }}{{t_{2} }} \, = \frac{{k_{2} }}{{k_{1} }} = \exp \left( { - \frac{{E_{\upalpha} }}{R}\left( {\frac{1}{{T_{2} }} - \frac{1}{{T_{1} }}} \right)} \right) $$
Here, t 1 and t 2 are the shelf life at temperature T 1 and T 2, respectively, while k 1 and k 2 are reaction rates at temperature T 1 and T 2, respectively.

This commonly used approach has been criticized by several researchers [15] as it uses a single set of Arrhenius reaction parameters and neglects the dependency of these reaction parameters on reaction progress and temperature. Furthermore, it has been reported that the Arrhenius approach over-predicts the shelf life of EMs [16].

Another popular method for shelf life prediction is Berthelot method [3] in which the dependency of reaction parameters on temperature has been considered. However, this approach still does not consider the reaction progress dependency.

Isoconversional technique and prediction

The reaction rate according to isoconversional kinetics can be expressed using Eq. (9) for an EM stored isothermally at temperature T. This equation can describe the reaction rate at any reaction progress and temperature as the reaction parameters are expressed as functions of reaction progress.
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A_{\upalpha} f(\alpha )\exp \left( {\frac{{ - E_{\upalpha} }}{RT}} \right) $$
As for the reliability of isoconversional kinetics for aging effect prediction, some researchers have provided simulation results [11], while the present work has followed the recommendations provided by Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC) in order to improve the accuracy of the DSC data for determining the kinetic parameters [13]. This is then substantiated by the repeatable experimental results.

In isoconversional kinetics, Arrhenius parameters are varied with reaction progress, but it utilizes the same value of heat of reaction for all reaction progress. So one assumes that reaction progress represents the remaining heat energy after a certain storage period.

As per the aerospace industry standard for energetic materials, an EM is guaranteed to have 3 years of additional shelf life if it does not degrade significantly during storage at 71 °C for 1 month [12]. So remaining fraction of the energetic materials after aging for 1 month at 71 °C is predicted. The prediction is calculated from Eq. (9) and isoconversional kinetics of Fig. 5. For all EMs, it does not degrade after 1-month storage at 71 °C. Predicted remaining fraction is almost unity.

Figure 7 shows the calculated reaction progress at a certain temperature over extended periods of time. We set the reaction progress value of 0.01 after 20 years as criterion for un-decayed performance of EMs. It was observed that if 97.5% RDX was stored at temperatures below 149.0 °C, an un-decayed performance of EMs can be expected for 20 years. Similarly, 95% HMX must be stored at temperatures below 110 °C for a 20-year safe storage. The temperature for BPN storage without any decay was calculated as 160 °C. Figure 7 also shows a dramatic decay of RDX and BPN when stored at higher temperatures while HMX shows gradual decay even at elevated temperature. This corroborates the previously reported insensitivity of HMX [17].
Fig. 7

Reaction progress calculation with isothermal condition, a 97.5% RDX, b 95% HMX and c BPN

This study is focused on polymer-bonded explosives, which are composed differently as opposed to pure RDX or HMX. The composition may include various polymer binders in addition to the base explosives. Since binders and explosives decompose differently, the resulting thermochemical reaction path will change as the thermal stability of each substance is changed. Thus, the lifetime of the EMs under study may not be comparable to those reported for the RDX and HMX alone.

As can be seen in Fig. 7, the energetic materials considered in this study have almost no aging when stored at room temperature of 30 °C. In practical usage of these energetic materials, the shelf life may be different than the predicted values due to unexpected situation such as fire, vibration or the geometry of entire system in which energetic materials are actually employed. However, the estimate provides an approximate guideline for storage and utilization of energetic material.

Validation of aging effect prediction

In order to validate the proposed technique for aging effect prediction, the predicted fraction of remaining EM was compared with the value of actually aged sample. The accelerated aging experiments were conducted for BPN at 71 °C for 8, 16, 24 and 48 weeks. The experiment was conducted in a customized oven which maintained constant humidity and temperature. Following each accelerated aging experiment, non-isothermal DSC tests were carried out with 2 °C min−1 heating rate with sample masses of 1.23, 1.37, 0.266 and 0.75 mg for 8-, 16-, 24- and 48-week-aged sample, respectively.

The BPN was assumed to have the same value of heat of reaction at all reaction progress level, and the remaining fraction of BPN was calculated using Eq. (10).
$$ \alpha_{\text{remained}} = \frac{{\int\limits_{\text{Aged}} {S(t)} - B(t){\text{d}}t}}{{\int\limits_{\text{Unaged}} {S(t) - B(t){\text{d}}t} }}(0 \le \alpha \le 1). $$
Figure 8 shows the non-isothermal DSC signals of the aged BPN samples which yield the heat of reaction as 6022.1, 6019.3, 6014.8 and 6012.8 J g−1 for 8-, 16-, 24- and 48-week-aged BPN, respectively. The heat of reaction of unaged BPN is 6024.4 J g−1. So remaining fraction of BPN was 0.999, 0.999, 0.998 and 0.998 for 8-, 16-, 24- and 48-week-aged BPN, respectively. And the predicted remaining fraction of BPN from Eq. (9) and isoconversional kinetics of Fig. 5 was 0.999 for all aging period. Even though it does not show remarkable degradation to compare the value accurately, our method shows good prediction such that it is un-decayed for the period of aging. These validation process with BPN demonstrates the feasibility of the aging effect prediction method outlined in this work.
Fig. 8

Heat of reaction and non-isothermal DSC signal with 2.0 °C min−1 heating rate for a 8-, b 16-, c 24- and d 48-week-aged BPN


Isoconversional decomposition kinetics of various EMs are constructed based on Friedman analysis. The extraction procedure utilized for the kinetics is universal in nature and may be applied to various composition of polymer-bonded explosives as well as double base, triple base and composite propellants. Conventionally used method for predicting shelf life and aging effect assumes that EM follows one-step kinetics. But real EM follows thousands of specific decomposition steps. The proposed method adopts isoconversional kinetics which can describe specific decomposition process, conducted by calculation, not by the time-consuming massive aging experiment. The predicted results of BPN are compared with the actual aged sample for validation of the proposed method, and the comparison shows good conformity between predictions and experimental results.



This work was supported by Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) contracted through Advanced Space Propulsion Research Center at Seoul National University. Additional support was provided by the Hanwha-ADD PMD Grants contracted through IAAT and IOER at Seoul National University.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulKorea

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