Thermal decomposition characteristic and kinetics of DINA
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Abstract
NNitrodihydroxyethyl dinitrate (DINA) is a useful energetic plasticizer in doublebase propellant. To analyze the potential hazards of its thermal decomposition, the differential scanning calorimetry (DSC) was used to test the thermal behavior of DINA under nonisothermal and isothermal conditions. It is found from the nonisothermal DSC results, that the melting point of DINA is about 50 °C, the initial exothermic decomposition temperature (T _{onset}) is between 177.46 and 189.60 °C with the heating rate 2, 4, 8 and 10 °C min^{−1}, and its decomposition enthalpy (ΔH _{d}) is about 3235.63 J g^{−1}. Both the shapes of heat flow curves and activation energy curves, calculated by Friedman method, indicate the exothermic decomposition of DINA contains at least four reactions (P1–P4), which were separated into four curves by AKTS software according to the four peaks. The relatively constant E(α) of P1, P2, P3 and P4 verifies this four peaks are likely to be described by a single reaction model. The method proposed by ICTAC was used to determine the most suitable reaction function and kinetic parameters of DINA decomposition, the results show that P1 and P2 follow the Z–L–T model and the Avrami–Erofeev model, respectively, both of them are autocatalytic models, which is consistent with the isothermal DSC results. The reaction model of P3 cannot be obtained, while P4 corresponds to norder reaction, f(α) = (1 − α)^{1.67}.
Keywords
NNitrodihydroxyethyl dinitrate Dynamic and isothermal DSC Peak separation Thermal decomposition kineticsList of symbols
 Β/°C min^{−1}
Heating rate
 T_{melt}/°C
Melt temperature
 T_{onset}/°C
Onset temperature of decomposition
 T_{peak}/°C
Peak temperature of decomposition
 ΔH_{d}/J g^{−1}
Enthalpy of decomposition
 θ/s
Isothermal induction period
 t/s
Reaction time
 T/K
Temperature
 α
Reaction progress the extent of conversion
 E_{α}/J mol^{−1}
Activation energy
 A_{(α)}/s^{−1}
Preexponential factor
 f(α)
Differential form of the reaction model
 g(α)
Integral of the reaction model
Introduction
NNitrodihydroxyethyl dinitrate (DINA) is an explosive, which is a highenergy plasticizer, and has been widely used in doublebase propellant (DB propellant) [1]. DINA is of a low melting point (49.5–51.5 °C) and insoluble in water at room temperature. It is beneficial for energy increase and ablation reduction for composite explosive, due to its advantages over nitroglycerin (NG): larger specific volume and the high capability to solve and plasticize the high nitrogen content nitrocellulose (NC). DINA performs good thermal stability, which began to decompose significantly at 160 °C, decomposes drastically at 180 °C and Abel test value can reach 60 min at 72 °C [2, 3]. According to this feature, DB propellant containing DINA can be processed at a higher temperature [4], which is meeting the requirements of different weapons on the charge.
At the end of the last century, some researches have been carried out for DINA, Ma [3] studied the application of DINA to the DB propellant, and the effects of some factors on the formulation and properties of DB propellant. In 2011, Pi et al. [1] studied the effect of DINA as a highenergy plasticizer on the combustion performance adjustment of doublebase propellant. However, few studies were focused on its thermal decomposition behavior and kinetic parameters. Also there have been virtually no literatures discussing the reaction model for thermal decomposition of DINA, what is very important for thorough understanding of the potential thermal hazard relating to their safe manufacturing handling and storage.
The aim of the paper was to study thermal decomposition of DINA and then to create the decomposition kinetic models [5, 6]. The nonisothermal (dynamic) and isothermal experiments were performed by differential scanning calorimetry (DSC). The dynamic parameters (T _{onset}, T _{peak} and ΔH _{d}) and kinetic parameters (E _{α} and A) of decomposition of DINA under two conditions were determined by using STAR^{e} software and Friedman method, based on nonisothermal and isothermal DSC tests. Moreover, the kinetic models for decomposition of DINA were obtained using the nonisothermal experimental data. To the best of our knowledge, this is the first report regarding the thermokinetic studies of DINA under nonisothermal and isothermal conditions. Furthermore, these calculated kinetic parameters can be used as a reference for the reactions during the storage and transportation of DINA.
Experimental
Materials
Apparatus and test conditions

Calorimetric sensitivity: 0.04 μW;

Test temperature range: − 35 to 500 °C;

Heat flow detection range: ± 350 mW.
Stainless steel highpressure crucibles (30 μL) with goldplated pads were used as test cells, which can bear a pressure of 15 MPa, an empty crucible was used as the reference. Highpurity nitrogen (99.999%) was regarded as shielding gas (200 mL min^{−1}) and purge gas (50 mL min^{−1}). During nonisothermal DSC experiments, DINA was tested at four heating rates of 2, 4, 8 and 10 °C min^{−1}, respectively, during the temperature 25–380 °C, and the sample mass was (0.9 ± 0.01) mg, and in isothermal DSC experiments, 157, 160, 162 and 165 °C were selected as the isothermal temperature, and the sample mass was (2 ± 0.01) mg.
Results and discussion
Nonisothermal DSC experiments
Test results
Nonisothermal DSC results of DINA
β/°C min^{−1}  T _{melt}/°C  T _{onset}/°C  T _{p}/°C  ΔH _{d}/J g^{−1} 

2  49.47  177.46  196.76  3329.53 
4  49.86  180.85  201.55  3175.47 
8  50.62  187.07  209.85  3148.83 
10  51.32  189.60  213.13  3288.67 
Kinetic calculations based on nonisothermal DSC data
In Fig. 5, there are three obvious fluctuations in the whole exothermic process, indicating the decomposition process cannot be described using singlestep reaction model.
Isothermal DSC experiments
Isothermal test results and analysis
Isothermal DSC results of DINA
IsoT/°C  157  160  162  165 

θ _{1}/s  3009  2353.1  1890  1513.9 
θ _{2}/s  6118.2  4903.2  4107  3328.8 
ΔH _{d}/J g^{−1}  3092.14  3054.71  3064.97  2976.84 
Obviously, with the increase in isothermal temperature, the isothermal induction period for first peak (θ _{1}) and second peak (θ _{2}) become shorter and the reaction appears intense. The average decomposition enthalpy (ΔH _{d}) of four experiments is about 3047.17 J g^{−1} (Table 2), which is lower than that value of nonisothermal DSC tests. One possible reason is the sample is not completely decomposed during isothermal tests. To verify it, an additional experiment combining isothermal DSC and dynamic DSC was performed.
As shown in Fig. 8, after the isothermal test at 162 °C, there are still two continuous exothermic peaks (P3 and P4 in Fig. 8), which indicates that DINA are not completely decomposed during isothermal testing. Moreover, the total ΔH _{d} of P3 and P4 in the additional test is 231.86 J g^{−1}, which is approximately equal to the ΔH _{d} difference between the nonisothermal tests and the isothermal tests. Combined with the results of nonisothermal tests and isothermal tests, it can be concluded that the decomposition of DINA consists of at least four successive reactions.
As found in Fig. 7, the exothermic peaks P1 and P2 are both “bellshaped”, which indicates the reactions for P1 and P2 follow the autocatalytic reaction mechanism [20].
Peaks separation and analysis
Peaks separation
AKTS software can deal with the tested data mathematically, which includes peak separation. And the separation of multiple overlapped peaks is based on the application of Gaussian and/or Fraser–Suzuki (asymmetric)type signals. Each peak is characterized by four parameters: position, amplitude, halfwidth and asymmetry. The results of the application of the “peak separation” tool are displayed as peak optimal parameters, the graphical presentation of the fitting curve, the separated peaks area and their percentage contribution to the total area. The fitting of calculated signal to the experimental data is performed using a nonlinear optimization (Marquardt) [21].
Kinetic calculation based on peak separation results
In Fig. 11, during the reaction progress from 0.1 to 0.9, the correlation coefficients of peak 1, peak 2 and peak 4 are 0.99–0.999, and that of peak 3 is only 0.89–0.93. Within that range, the activation energy were 76–85, 130–150, 35–37 and 135–145 kJ mol^{−1} for each peak, respectively, with a narrow margin, which indicates that this four peaks are likely to follow a single reaction mechanism [22].
Therefore, this four peaks are analyzed, according to recommendation [22, 23] proposed by the ICTAC kinetic committee, to obtain the most probable kinetic model function f(α). It is a universal method to infer f(α) by using the “Z(α)–α” curve [7, 24].
It has been established that the term in the brackets of Eq. (5) has a negligible effect on the shape of the Z(α) function [25]. Thus, the values of Z(α) can be determined for each value of α by multiplying the experimental values of (dα/dt)_{α} and T _{α} ^{2} . The resulting experimental values of Z(α) are plotted as a function of α and compared against theoretical Z(α) master plots. The experimental and theoretical Z(α) plots have to be normalized in a similar manner. For practical reasons, the Z(α) plots are normalized to vary from 0 to 1. A suitable model is identified as the best match between the experimental and theoretical Z(α) master plots. From a series of experimental kinetic curves measured at different β, one can obtain a series of the experimental Z(α) plots that should, however, yield a single dependence of Z(α) on α which is practically independent of β. The theoretical Z(α) plots are obtained by plotting the product f(α)g(α) against α for different reaction models.
Fortythree kinds of commonly used kinetic model functions f(α), G(α) and corresponding Z(α) were collected in Ref. [26, 27]. Standard data α _{i} (i = 1, 2, … , j) are substituted into the theoretical Z(α) = f(α) × G(α), and the Z(α)–α curve is plotted as the standard curve. Experimental data (dα/dt)_{αi} and T _{αi} ^{2} (i = 1, 2, … , j) are substituted into the experimental Z(α) = (dα/dt)_{αi} × T _{αi} ^{2} and the Z(α)–α curve is plotted as the experimental curve. The experimental and theoretical Z(α) plots have to be normalized in a similar way.
If the experimental curve overlaps the standard one or all the experimental data points fall on the standard curve, Z(α) corresponding to the standard curve can be considered as the most probable kinetic mechanism function.
According to the peak separation data, the reaction rate dα/dt and corresponding temperatures T of each peak at variable α are obtained with the heating rates of 2, 4, 8 and 10 °C min^{−1}.
After that the experimental Z(α) is calculated by Eq. (5).
In Eq. (6), the subscript max denotes the values related to the maximum Z(α) of the differential kinetic curve obtained at a given heating rate.
Summary of the most probable kinetic model
Peak  Function name  lnA/s ^{−1}  f(α)  G(α) 

1  Zhuralev–Lesokin–Tempelman  17.08  \(f\left( \alpha \right) = \frac{3}{2}\left( {1  \alpha } \right)^{{\frac{4}{3}}} \left[ {\left( {1  \alpha } \right)^{{  \frac{1}{3}}}  1} \right]^{  1}\)  \(G\left( \alpha \right) = \left[ {\left( {1  \alpha } \right)^{{  \frac{1}{3}}}  1} \right]^{2}\) 
2  Avrami–Erofeev (n = 1/4)  34.23  \(f\left( \alpha \right) = 4\left( {1  \alpha } \right)\left[ {  \ln \left( {1  \alpha } \right)} \right]^{{\frac{3}{4}}}\)  \(G\left( \alpha \right) = \left[ {  \ln \left( {1  \alpha } \right)} \right]^{{\frac{1}{4}}}\) 
3  –  –  –  – 
4  norder reaction  31.07  \(f\left( \alpha \right) = \left( {1  \alpha } \right)^{1.67}\)  \(G\left( \alpha \right) = \frac{{\left( {1  \alpha } \right)^{  0.67}  1}}{0.67}\) 
Conclusions
 1.
According to the linear heating DSC tests, DINA melts at around 50 °C, and decomposes at about 180 °C with a sharp exothermic peak. The statistic decomposition enthalpy ΔH _{d} is about 3235.63 J g^{−1}, indicating a tragedy if it decomposes in bulk.
 2.
The shape of dynamic DSC curves and E _{α}, ln[A _{(α)}·f(α)] determined by Friedman method both reveal that the decomposition is not a singlestep reaction, and it contains at least four segments.
 3.
For the isothermal DSC tests, θ become shorter with the increase in isothermal temperature. And the average ΔH _{d} of four experiments is about 3047.17 J g^{−1}, which is lower than the value of dynamic DSC, believing that the sample does not completely decompose during isothermal experiments. The two exothermic peaks detected in the isothermal tests correspond to peaks 1 and 2 in the dynamic DSC curves. The “bellshaped” isothermal peaks P1 and P2, which verify the autocatalytic decompositions.
 4.
The peaks P1 and P2 separated by AKTS can be described by the Zhuralev–Lesokin–Tempelman model and the Avrami–Erofeev model (n = 1/4), respectively. The reaction of peak 4 follows norder reaction model, f(α) = (1 − α)^{1.67}.
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