Toward understanding the aging effect of energetic materials via advanced isoconversional decomposition kinetics
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.
KeywordsIsoconversional 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 . 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  or Berthelot approach  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 . 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 . Thanks to a noticeable progress in the integral method  and kinetics analysis software , such method has gained much attention recently for description of decomposition mechanism of energetic materials . 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 . 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  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.  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 . 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).
Non-isothermal experimental conditions
Heating rate/°C min−1
0.5, 1.0, 2.0 and 4.0
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
Results and discussion for kinetics calculation
Isothermal DSC results
Non-isothermal DSC results
Validation of advanced isoconversional kinetics
Aging effect prediction
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.
This commonly used approach has been criticized by several researchers  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 .
Another popular method for shelf life prediction is Berthelot method  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
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 . 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.
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.
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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