The prediction of thermal stability of self-reactive chemicals: From milligrams to tons
 
 
B. Roduit ^1*, Ch. Borgeat ¹, B. Berger ², P. Folly ², B. Alonso ³, J.N. Aebischer ^3
 
1 Advanced Kinetics and Technology Solutions AKTS AG http://www.akts.com, TechnoArk 3, CH-3960 Siders, Switzerland
² armasuisse, Science and Technology Centre, http://www.armasuisse.ch, CH-3602 Thun, Switzerland
³ University of Applied Sciences of Western Switzerland, http://www.eif.ch, CH-1705 Fribourg, Switzerland
 
Abstract
 
An advanced study on the thermal behaviour of double base (boost and sustain propellant) rocket motor used in a ground to air missile has been carried out by Differential Scanning Calorimetry (DSC). The presence of two propellants as well as the different experimental conditions (open vs. closed crucibles) influence the relative thermal stability of the energetic materials. Several methods have been presented for predictions of the reaction progress of exothermic reactions under adiabatic conditions. However, because decomposition reactions usually have a multi-step nature, the accurate determination of the kinetic characteristics strongly influences the ability to correctly describe the progress of the reaction. For self-heating reactions, incorrect kinetic description of the process is usually the main source of serious errors for the determination of the Time to Maximum Rate under adiabatic conditions (TMRad). It is hazardous to develop safety predictive models that are based on simplified kinetics determined by thermoanalytical methods. Applications of Finite Element Analysis (FEA) and accurate kinetic description allow determination of the effect of scale, geometry, heat transfer, thermal conductivity and ambient temperature on the heat accumulation conditions. Due to limited thermal conductivity, a progressive temperature increase in the sample can easily take place resulting in a thermal explosion. Use of both, kinetics and FEA [1], enables the determination of the reaction progress and temperature profiles in storage containers. The reaction progress and temperature can be determined quantitatively at every point in time and in space. This information is essential for the design of containers of self-reactive chemicals, cooling systems and the measures to be taken in the event of a cooling failure.
 
Keywords: kinetics, Time To Maximum Rate, adiabatic conditions, TMRad, thermal hazards, safety, thermal ageing
 
*Author for correspondence: E-mail: b.roduit@akts.com
 
Introduction
 
In the early nineties of the last century several rocket motors of a ground to air missile started burning after a fire in a rock cavern. Due to this heavy accident the Swiss General Staff were interested to understand the time of ignition for stored rocket motors after a fire in a storage facility. One example of a rocket motor is shown in figure 1. The motor contains two propellants: Boost propellant and sustain propellant (glycerol nitrate, cellulose nitrate, stabilizers and other components).


Fig. 1 Left: Rocket motor for a ground to air missile. Right: Rocket propellant. Boost propellant (dark), sustain propellant (hell).
 
Generally, all energetic materials liberate heat during decomposition. Processing, design, quality control, and operational applications all require an evaluation of thermal hazards and an ability to predict the safety limits and the course of the decomposition process in extended temperature ranges [1-5]. The present paper is designed to answer the following issues:
 
• What is the reaction progress of the propellants under any temperature profile?
• Does a thermal hazard exist?
• At what temperature does the thermal hazard begin?
• What is the Time to Maximum Rate under adiabatic conditions (TMRad) at any temperature?
• What is the temperature of maximum self-heating?
• How much influence does isolation/heat transfer have on the heat accumulation conditions?
• What are the critical storage container sizes or transport temperatures?
• What influence do the surrounding temperature profiles have on the reaction progress and on the heat accumulation conditions?
 
Experimental and analysis process
 
Collection of experimental data and baseline determination
 
The analysis process requires determination of the kinetic characteristics of the reaction. The kinetic parameters can be extracted in principle from experimental data gathered by any of the following dynamic thermo-analytical methods: DSC (Differential Scanning Calorimetry), DTA (Differential Thermal Analysis), TG (Thermogravimetry) or EGA (Evolved Gas Analysis TG-MS or TG-FTIR). The application of the thermoanalytical techniques is widely recognized for the characterization of the degradation of solids [6].


Fig. 2 DSC heat flow curve and the baseline subtracted heat flow curve of the sustain propellant at 0.25 °C/min under isochoric conditions (closed crucibles).
 
The correct kinetic analysis of a decomposition reaction has at least three major stages: (1) collection of experimental data; (2) computation of kinetic parameters, and (3) prediction of the reaction progress for required temperature profiles applying determined kinetic parameters. Kinetic evaluation of the reactions should be carried out with thermoanalytical data obtained at several heating rates (non-isothermal) or temperatures (isothermal) to ensure reliable results. Kinetic methods that use single heating-rate experimental results should be avoided because they tend to produce highly ambiguous kinetic descriptions [7,8]. At least three heating rates or temperatures are recommended. Applying the results obtained by thermoanalytical techniques (DSC), the kinetic analysis presented in this paper enables accurate prediction of the reaction progress of materials in a broad temperature range that may be difficult to explore for time, sensitivity or safety reasons. The presented study focuses on the evaluation of the experimental results obtained by DSC under isobaric (open crucibles) and isochoric (closed crucibles) conditions. The thermal behaviour of both propellants was examined at different heating rates ranging from 0.25 to 10 °C/min. Figure 2 shows the DSC heat flow curve and the baseline subtracted heat flow curve of the sustain propellant at 0.25°C/min under isochoric conditions (closed crucibles). Generally, the application of straight-line form for the baseline is incorrect. The tangential area-proportional baseline is the most widely applied because of its correction possibilities [9]. The recorded signal results not only from the heat of the reaction but is additionally affected by the change of the specific heat of the mixture reactant-products during the progress of the reaction. The baseline determination can significantly influence the determination of the kinetic parameters of the reaction. Moreover, the correct baseline determination should be intimately combined with the computation of the kinetic parameters for the investigated reaction. Advanced mathematical procedures are therefore necessary for an objective calculation of the most appropriate baseline for each DSC signal [1].
 
Determination of the kinetic characteristics
 
The noticeable weakness of the ‘single curve’ methods (determination of the kinetic parameters from single run recorded with one heating rate only) has led to the introduction of ‘multi-curve’ methods over the past few years, as discussed in the International ICTAC Kinetics project [7, 10-12]. Only series of non-isothermal measurements carried out at different heating rates can give a data set, which generally contains the necessary amount of information required for full identification of the complexity of a process [7-8, 10-13]. This data set usually contains:
- the relationship between specific conversion xi and temperatures for different heating rates (non-isothermal mode).
- the relationship between specific conversion xi and time for different temperatures (isothermal mode).


Fig. 3 (A) Friedman analysis of decomposition of the sustain propellant under isobaric conditions (open crucibles).
(B) Activation energy as a function of the reaction progress for decomposition of the boost and sustain propellant under isochoric (DSC closed crucibles) and isobaric conditions (DSC open crucibles).
 
Commonly applied are the following isoconversional methods known as: Friedman [14] and Ozawa-Flynn-Wall [15-16]. A detailed analysis of the various isoconversional methods (i.e. the isoconversional differential and integral methods) for the determination of the activation energy has been reported in the literature by Budrugeac [17]. The convergence of the activation energy values obtained by means of a differential method (Friedman) with those resulted from using integral methods with integration over small ranges of reaction progress x comes from the fundamentals of the differential and integral calculus. Friedman analysis, based on the Arrhenius equation, applies the logarithm of the conversion rate dx/dt as a function of the reciprocal temperature at different degrees of the conversion. As f(x) is constant at each conversion degree xi, the method is so-called ‘isoconversional’ and the dependence of the logarithm of the reaction rate over 1/T is linear with the slope of m = E/R as presented in figure 3 A. Decomposition reactions are often too complex to be described in terms of a single pair of Arrhenius parameters and the commonly applied set of reaction models. As a general rule, these reactions demonstrate profoundly multi-step characteristics. They can involve several processes with different activation energies and mechanisms. In such situation the reaction rate can be described only by complex equations, where the activation energy term is no more constant but is dependent on the reaction progress x (Econst but E=E(x)) (Fig. 3B) [14-16]. Figure 4 presents the normalized non-isothermal DSC-signals as a function of the temperature or time for the decomposition of the double base rocket motor (boost- and sustain- propellants). Experimental data are represented as symbols. Solid lines represent the calculated signals. The comparison between experimental and calculated reaction extents indicates that the applied numerical technique enables accurate prediction of the reaction course under any experimentally chosen temperature mode.


Fig. 4 Advanced kinetic description of normalized non-isothermal DSC-signals as a function of the temperature for the decomposition of double base rocket motor propellants. Experimental data are represented as symbols, solid lines represent the calculated signals. The values of the heating rate in °C/min are marked on the curves.
Closed crucibles (isochoric conditions): (A1): Boost propellant, (B1): Sustain propellant.
Open crucibles (isobaric conditions): (A2): Boost propellant, (B2): Sustain propellant.
 
Kinetics and milligram scale - thermal stability predictions
 
Verification of numerical computations and confidence interval for the prediction of the reaction progress
 
Verification of numerical computations can be readily achieved by graphical comparison of the calculated reaction progress or rate with subsequently obtained experimental data. Figure 5A presents the comparison of experimental and calculated DSC signals for the step-wise temperature program and isothermal conditions. In this program, heating with a rate of 3 °C/min was followed by an isothermal run at 160°C. Accurate prediction of the thermal stability is achieved. In this case, the predicted reaction rate has been calculated for a temperature of 160°C, laying inside the observed temperature window used for the determination of the kinetic parameters under non-isothermal conditions (from 140°C for the beginning to 250°C at the end of the reaction, see Fig. 4 A1). In fact such a prediction of the propellant behaviour refers to an interpolation of the detected reaction rate from other experimental temperature profiles (non-isothermal conditions) but still in a temperature range where the thermal event occurs. However, for many applications it is relevant to examine how accurate is the prediction of the reaction rate for isothermal temperatures lying below the onset temperature observed under non-isothermal conditions. Therefore let us determine if the model used for the revelation of potentially hazardous behaviour of substances at elevated temperatures is still valid for the prediction of the reaction rate at prolonged times exposures at lower temperatures such as 110°C and 100°C for the double base propellant (Fig. 5B). At lower temperature the thermal event will occur over a much longer period of time with some confidence interval which has to be determined for the predictions (lower limit, mean value, upper limit).


Fig. 5 (A) Experimental data for the boost propellant decomposition (step-wise temperature program: heating rate of 3°C/min followed by an isothermal run at 160°C, closed crucibles i.e. isochoric conditions) are presented together with the reaction rate predictions. Experimental data are represented as symbols, solid lines represent the calculated relationships of da/dt over t. Accurate prediction of the thermal stability is achieved. (B) Predicted (solid line) and experimental reaction rates (points) of the rocket propellant under isothermal conditions (110°C and 100°C). The reaction is strongly autocatalytic because the initiation rate of the reaction is low leading to a long induction time under isothermal conditions. The figure at the top illustrates the reaction extent (DSC, normalized signals) of the rocket propellant with the confidence interval (95% probability) as a function of time under isothermal conditions (T = 110°C, closed crucibles/isochoric conditions).

During the determination of correct course of the baseline for all differential signal types, like DTA and/or DSC measurements and the calculation of the kinetic parameters for a decomposition reaction, the predictions give the 'central tendency', for which the chance of the good reproducibility on subsequent measurements is maximal. A Gaussian distribution is expected around this 'best value'. The illustration of these remarks for the investigation of the rocket propellant (isochoric conditions) is presented in figure 5B. The predicted and experimental rates of the self-accelerating reactions are shown when the rocket propellant is held isothermally at 110°C and 100°C. This system is strongly autocatalytic, the rate of the initiation is low, leading to a long induction time under isothermal conditions. The reaction remains undetected for a relatively long period of time because the product catalysing the self-acceleration is formed slowly and/or the reaction begins when the stabilizers have been used up. When the reaction accelerates the rate increases so rapidly that it may lead to a runaway. For the rocket propellant, the mean value of the prediction for reaching the reaction progress of 65% (which corresponds to the maximum rate under isothermal conditions at T=110°C) is 47 hours. The lower and upper limits of the confidence intervals are 38 and 58 hours, respectively. These values indicate that there is a 95% probability that the mean time required for reaching 65% reaction progress is greater than 38 hours and lower than 58 hours. Similar measurements were done for 100°C showing again the long induction time under isothermal conditions. Extrapolation at lower temperature than the beginning of the reaction under non-isothermal conditions is therefore possible for in-depth awareness of the propellant thermal behaviour under varied eventualities. As a safety measure the confidence interval of the reaction progress is required to determine the precise the range of validity of the prediction. In that way very significant time/expertise savings can be achieved compared to real time analysis which can extend over prolonged periods, even years.
 
Cyclic temperature changes and prediction of the reaction progress under temperature mode corresponding to real atmospheric temperature changes
 
The kinetic parameters calculated from the non-isothermal experiments enable prediction of the reaction progress for any temperature mode: isothermal, non-isothermal, stepwise and therefore intermediate intervals in the heating rate, expressed, e.g. in oscillatory temperature modes. The prediction of the reaction progress in oscillatory temperature mode (widely applied in temperature-modulated calorimetry) is given below.


Fig. 6 (A) Reaction extents a of the decomposition of boost propellant in isothermal (50°C) and oscillatory (50°C ± 40°C, 24 h period) temperature modes (isochoric conditions, closed crucibles). (B) Predictions of the extent of boost propellant decomposition for the New Dehli and Moscow temperature profiles under isochoric conditions (closed crucibles). The substance exposed to daily temperature changes decomposes only slightly in New Dehli (about 0.25% after 60 years). In Moscow the reaction will progress even much less in this period of time.
 
Figure 6A shows the reaction extents a of the decomposition of boost propellant in isothermal (50°C) and oscillatory (50°C ± 40°C, 24 h period) temperature modes (isochoric conditions, closed crucibles). The arithmetic mean temperature (50°C) of the oscillatory temperature mode is the same as in the isothermal experiment. However, the presence of the temperature amplitudes greatly influences the reaction progress. The prediction of the decomposition of the boost propellant under isochoric conditions at 50°C with ± 40°C amplitude and 24h period indicates that after 3.5 months the sample is fully decomposed. For the same mean temperature (50°C) under isothermal conditions, the boost propellant will decompose only slightly after 12 months (<1%).
 
One of the main reasons for investigating the kinetics of thermal decompositions of solids is the need to determine the thermal stability of substances, i.e. the temperature range over which a substance does not decompose at an appreciable rate. The correct prediction of the reaction progress of unstable materials such as some pyrotechnics, propellants, food, drugs, polymers, etc. under ambient conditions requires accurate knowledge of both:
- the kinetic parameters
- the exact temperature profile for a given climate
 
As an example one may predict the extent of the decomposition of the boost propellant in New Dehli and Moscow. The temperature profile used for the calculations is the average of all daily minimal and maximal temperatures recorded for each day of the year between the years 1961 and 1990. These temperature fluctuations will be applied in the calculations of the thermal properties with cyclic temperature changes over the years. The calculation of the kinetic parameter E (activation energy) as a function of the reaction progress (Fig. 3B) enables calculation of the thermal stability of the propellant expressed in figure 6B as a function of time. The boost propellant under isochoric conditions exposed to daily temperature changes in these two places decomposes only slightly over this period. These results show that within 60 years, the reaction reaches about 0.25% in New Dehli. In Moscow, the reaction will progress even much less in this period of time.
 
Kinetics and scale up - thermal stability and safety analysis
 
Adiabatic conditions: Calculation of time of maximum rate under adiabatic conditions (TMRad) from non-isothermal DSC measurements
 
The precise prediction of the reaction progress in adiabatic conditions is necessary for the safety analysis of many technological processes. Calculations of an adiabatic temperature-time curve for the reaction progress can also be used to determine the decrease of the thermal stability of materials during storage at temperatures near the threshold temperature for triggering the reaction. Due to limited thermal conductivity, a progressive temperature increase in the material can easily take place, resulting in an explosion.
 
Several methods have been presented for predicting the reaction progress of exothermic reactions under heat accumulation conditions [18-22]. However, because decomposition reactions usually have a multi-step nature, the accurate determination of the kinetic characteristics strongly influences the ability to correctly describe the progress of the reaction. The use of simplified kinetic models for the assessment of runaway reactions can, on the one hand, lead to economic drawbacks, since they result in exaggerated safety margins. On the other hand, it can cause dangerous situations when the heat accumulation is underestimated. For adiabatic self-heating reactions, incorrect kinetic description of the process is usually the main source of prediction errors.
 
To be able to assess the probability of occurrence of a decomposition reaction, it is necessary to replace simple rules by sound methods based on reaction kinetics. The concept of Time to explosion or TMRad (Time to Maximum Rate under adiabatic conditions) is of great utility for that purpose [23]. A commonly used approach for the determination of the TMRad applies the following formula with the arbitrarily chosen zero-order reaction [24]:
 
TMRad = c_p R To²/(qo Ea) where:
 
c_p [J/kg/K]: specific heat,
To [K]: initial temperature of the runaway,
qo [W/kg]: maximum specific heat flux measured during an isothermal exposure at the temperature To,
Ea [J/mol]: activation energy of the reaction,
R [= 8.31431 J/mol/K]: ideal gas constant.

However, when applying the above approach to predict the TMRad the only one, simplified zero-order kinetic equation is used by fitting the reaction/decomposition exotherms by the Arrhenius relationship. This method gives unfortunately a very rough approximation of the TMRad due to the severe assumptions made concerning both, the kinetics and the constancy of the value of the activation energy. As presented in figure 3B, the activation energy is strongly dependent on the reaction progress for the considered compounds. In addition, it can be observed that the different experimental conditions (isochoric/isobaric) strongly influence the dependence of the activation energy on the reaction extent. The solution of the problem should therefore be achieved numerically. The computations have to consider the dependence of the activation energy on the reaction progress. For predictions with a certain level of accuracy, advanced kinetic analysis is therefore required because most decomposition reactions are complex combinations of several steps.
 
The decomposition of the boost propellant is a highly exothermal process. Using the reaction heat (ΔHr) and the heat capacity (cp), one can calculate the reaction progress due to self-heating for different values of ΔTad (with ΔTad = ΔHr/cp). In figure 7A, the simulated T-time relationships with a starting temperature of 100°C are presented for ΔTad = 2651±233°C (boost propellant, isochoric conditions). Figure 7B presents the starting temperature and corresponding adiabatic induction time TMRad relationship. The confidence interval was determined for 95% probability. The inset (Fig. 7C) presents the heat rate curves of the boost propellant under isochoric conditions for the different starting temperatures.


Fig. 7 (A) Adiabatic runaway curves for the boost propellant (isochoric conditions) showing the confidence interval for the prediction (Tbegin=100°C and ΔTad=ΔHr/cp=2651±233°C). The confidence interval was determined for 95% probability. (B) Starting temperature and corresponding adiabatic induction time TMRad relationship of the boost propellant under isochoric conditions. The choice of the starting temperatures strongly influences the adiabatic induction time (confidence interval: 95% probability). (C) Heat rate curves versus temperature for the boost propellant under isochoric conditions.

Table 1 Starting temperatures for TMRad of 8 h and 10 days for the boost and sustain propellants under isochoric and isobaric heat accumulation conditions.