Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 1, pp 727–735 | Cite as

Thermal decomposition characteristic and kinetics of DINA

  • Jun Zhang
  • Beibei Xue
  • Guoning Rao
  • Liping Chen
  • Wanghua Chen


N-Nitrodihydroxyethyl dinitrate (DINA) is a useful energetic plasticizer in double-base 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 non-isothermal and isothermal conditions. It is found from the non-isothermal 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 n-order reaction, f(α) = (1 − α)1.67.


N-Nitrodihydroxyethyl dinitrate Dynamic and isothermal DSC Peak separation Thermal decomposition kinetics 

List of symbols

Β/°C min−1

Heating rate


Melt temperature


Onset temperature of decomposition


Peak temperature of decomposition

ΔHd/J g−1

Enthalpy of decomposition


Isothermal induction period


Reaction time




Reaction progress the extent of conversion

Eα/J mol−1

Activation energy


Pre-exponential factor


Differential form of the reaction model


Integral of the reaction model


N-Nitrodihydroxyethyl dinitrate (DINA) is an explosive, which is a high-energy plasticizer, and has been widely used in double-base 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 high-energy plasticizer on the combustion performance adjustment of double-base 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 non-isothermal (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 STARe software and Friedman method, based on non-isothermal and isothermal DSC tests. Moreover, the kinetic models for decomposition of DINA were obtained using the non-isothermal experimental data. To the best of our knowledge, this is the first report regarding the thermo-kinetic studies of DINA under non-isothermal and isothermal conditions. Furthermore, these calculated kinetic parameters can be used as a reference for the reactions during the storage and transportation of DINA.



N-Nitrodihydroxyethyl dinitrate used in the tests is an industrially pure white crystal, provided by Liaoning Qingyang Chemical Industry Group Co., LTD. Figure 1 shows the optimized structure of DINA by Gaussian 09.
Fig. 1

Optimized structure of DINA by Gaussian 09 under UB3LYP/6-31G (d)

Apparatus and test conditions

DSC is a popular thermal analysis instrument. It can be used to study thermal stabilities and decomposition characteristics of materials, especially for hazardous materials [9, 10, 11]. The DSC used in this paper was manufactured by METTLER TOLEDO (DSC-1).
  • Calorimetric sensitivity: 0.04 μW;

  • Test temperature range: − 35 to 500 °C;

  • Heat flow detection range: ± 350 mW.

Stainless steel high-pressure crucibles (30 μL) with gold-plated pads were used as test cells, which can bear a pressure of 15 MPa, an empty crucible was used as the reference. High-purity nitrogen (99.999%) was regarded as shielding gas (200 mL min−1) and purge gas (50 mL min−1). During non-isothermal 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

Non-isothermal DSC experiments

Test results

Heat flows for DINA under different heating rates are shown in Fig. 2. The results reveal that in the process of test, the onset endothermic temperature of DINA is about 50 °C, which indicated that DINA melts at a low temperature, and then a sharp exothermic decomposition starts to take place at about 180 °C, which is similar to the results in Ref. [3].
Fig. 2

Non-isothermal DSC curves of DINA

According to the 2 °C min−1 DSC curve shown in Fig. 3, the exothermic consists of at least four peaks (P1, P2, P3 and P4), i.e., the decomposition comprises at least four reaction process.
Fig. 3

DSC curve of DINA at 2 °C min−1

Experiment data of the exothermic decomposition under different heating rates are listed in Table 1, the statistic decomposition enthalpy (ΔH d) is about 3235.63 J g−1.
Table 1

Non-isothermal DSC results of DINA

β/°C min−1

T melt/°C

T onset/°C

T p/°C

ΔH d/J g−1





















The reaction progress can also be obtained and is shown in Fig. 4. There is obvious compatibility of the data at different heat rates.
Fig. 4

Reaction progress (α) versus temperature under non-isothermal model

Kinetic calculations based on non-isothermal DSC data

The DSC data are usually analyzed using Friedman method [12, 13], Kissinger method [14] or Ozawa method [15]. Here, Friedman method is employed to calculate the kinetics without involving the model function. Friedman proposed to apply the logarithm of the conversion dα/dt as a function of the reciprocal temperature at any conversion:
$$\beta \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = A_{{\left(\upalpha \right)}} \exp \left( { - \frac{{E_{\upalpha} }}{RT}} \right)f\alpha$$
$$\ln \frac{{\beta {\text{d}}\alpha }}{{{\text{d}}T}}_{\upalpha} = \ln \left[ {f\alpha A_{{\left(\upalpha \right)}} } \right] - \frac{{E_{\upalpha} }}{RT}$$
A (α) and f(α) are constant in the last term at any fixed value of α, and the dependence of the logarithm of the conversion dα/dt on 1/T shows a straight line with the slope m = − E/R and intercept equal to ln[A (α)·f(α)].
The non-isothermal DSC data were imported to AKTS software [16] for kinetic calculation according to Friedman method, and the results are shown in Fig. 5.
Fig. 5

E α and ln[A (α)·f(α)] versus α for DINA (non-isothermal)

In Fig. 5, there are three obvious fluctuations in the whole exothermic process, indicating the decomposition process cannot be described using single-step reaction model.

Isothermal DSC experiments

Isothermal test results and analysis

All scholars generally agree that isothermal calorimetry experiment is a reliable way for determining the reaction model (accelerating, decelerating or sigmoidal models) [17, 18, 19]. Therefore, isothermal test at 157, 160, 162 and 165 °C was carried out, respectively, by DSC. The results are shown in Figs. 6, 7 and Table 2.
Fig. 6

Isothermal DSC curves of DINA

Fig. 7

Reaction rate (dα/dt) versus time under isothermal model

Table 2

Isothermal DSC results of DINA






θ 1/s





θ 2/s





ΔH d/J g−1





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 non-isothermal 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.

The experiment was carried out at 162 °C for 120 min until the second peak appeared, and then the sample was heated up to 400 °C with 4 °C min−1. The results are shown in Figs. 8 and 9.
Fig. 8

DSC curve under combining isothermal and dynamic mode

Fig. 9

The results of peak separation under different heating rates, a heating rate is 2 °C min−1, b heating rate is 4 °C min−1, c heating rate is 8 °C min−1, d heating rate is 10 °C min−1

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 non-isothermal tests and the isothermal tests. Combined with the results of non-isothermal 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 “bell-shaped”, 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, half-width 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].

According to the previous analysis, the thermal decomposition of DINA could be divided into four segments. In order to be able to in-depth understanding of the entire decomposition, AKTS software was used for the separation of the exothermic decomposition peaks shown in non-isothermal test data. The peak separation results are shown in Figs. 9 and 10.
Fig. 10

The results of peak separation for different peaks, a curve of peak 1, b curve of peak 2, c curve of peak 3, d curve of peak 4

Kinetic calculation based on peak separation results
The curves of each peak under different heating rates are also dealt with by the AKTS software, including data import, kinetic calculation for each peak by Friedman method, and the calculation results are shown in Fig. 11.
Fig. 11

E α versus α for each peak

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].

The Z(α) master plots are derived by combining the differential and integral forms of the reaction models,
$$\frac{{{\text{d}}a}}{{{\text{d}}t}} = A_{{\left(\upalpha \right)}} \exp \left( {\frac{ - E}{RT}} \right) \times f\left( \alpha \right)$$
$$g\left( \alpha \right) = \frac{{A_{{\left(\upalpha \right)}} E}}{\beta R}\exp \left( { - x} \right)\left( {\frac{\pi \left( x \right)}{x}} \right)$$
where x = E/RT. Combining Eqs. (3) and (4) followed by some rearrangement allows one to introduce the Z(α) function as:
$$Z\left( \alpha \right) = f\left( \alpha \right) \times g\left( \alpha \right) = \left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\upalpha} T_{\upalpha}^{2} \left[ {\frac{\pi \left( x \right)}{{\beta \times T_{\upalpha} }}} \right]$$

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.

Forty-three 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).

Based on isothermal DSC results, the standard Z(α)–α curves with autocatalytic reaction model are selected for comparing with the experimental values (results of 2 °C min−1). It is found that all of the experimental data points of peak 1 and peak 2 fall on the 9th and 10th standard curve, respectively, as shown in Fig. 12a, b. And for peak 4, the experimental curve coincides with the 43th standard curve (n = 1.67) in all 43 kinetic models, as shown in Fig. 12d. However, no suitable model is found for peak 3 (Fig. 12c).
Fig. 12

Tested and standard plots of Z(α) versus α for each peak, a Z(α) versus α for peak 1, b Z(α) versus α for peak 2, c Z(α) versus α for peak 3, d Z(α) versus α for peak 4

Once the kinetic model has been determined, the pre-exponential factor can be calculated from the following equation [28]:
$$A = \frac{{ - \beta E_{0} }}{{RT_{\hbox{max} }^{2} f^{\prime } \left( {\alpha_{\hbox{max} } } \right)}}\exp \left( {\frac{{E_{0} }}{{RT_{\hbox{max} } }}} \right)$$

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.

The most probable kinetic model and kinetic parameters for these four peaks are summarized in Table 3.
Table 3

Summary of the most probable kinetic model


Function name

lnA/s −1






\(f\left( \alpha \right) = \frac{3}{2}\left( {1 - \alpha } \right)^{{\frac{4}{3}}} \left[ {\left( {1 - \alpha } \right)^{{ - \frac{1}{3}}} - 1} \right]^{ - 1}\)

\(G\left( \alpha \right) = \left[ {\left( {1 - \alpha } \right)^{{ - \frac{1}{3}}} - 1} \right]^{2}\)


Avrami–Erofeev (n = 1/4)


\(f\left( \alpha \right) = 4\left( {1 - \alpha } \right)\left[ { - \ln \left( {1 - \alpha } \right)} \right]^{{\frac{3}{4}}}\)

\(G\left( \alpha \right) = \left[ { - \ln \left( {1 - \alpha } \right)} \right]^{{\frac{1}{4}}}\)



n-order reaction


\(f\left( \alpha \right) = \left( {1 - \alpha } \right)^{1.67}\)

\(G\left( \alpha \right) = \frac{{\left( {1 - \alpha } \right)^{ - 0.67} - 1}}{0.67}\)


DINA was studied by dynamic and isothermal DSC, the exothermic peak was separated into four independent peaks, the reaction models and kinetic parameters for three of these peaks were determined in this paper, to promote the safety control of DINA in its production and storage as well as accident prevention. The detailed conclusions are as follows:
  1. 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. 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 single-step reaction, and it contains at least four segments.

  3. 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 “bell-shaped” isothermal peaks P1 and P2, which verify the autocatalytic decompositions.

  4. 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 n-order reaction model, f(α) = (1 − α)1.67.



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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • Jun Zhang
    • 1
  • Beibei Xue
    • 1
  • Guoning Rao
    • 1
  • Liping Chen
    • 1
  • Wanghua Chen
    • 1
  1. 1.Department of Safety Engineering, School of Chemical EngineeringNanjing University of Science and TechnologyNanjingChina

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