Introduction

Diaminoglyoxime (DAG) is an explosophoric compound, with the chemical structure illustrated in Scheme 1. The compound is prepared by dehydration of dihydroglyoxime (DHG) in the aqueous sodium hydroxide solution at high temperatures [1–5]. This compound might be utilized as additive in the rocket propellant formulations as coolant [6].

Scheme 1
scheme 1

Synthesis of DAG achieved in two steps from commercially available glyoxanal

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Thermokinetic studies are crucial point in thermal analysis, while the main purpose is definition of the decomposition reaction mechanism and calculating the Arrhenius equation parameters, i.e., activation energy and frequency factor [5, 7–10]. The resulted thermoanalytical data could provide valuable information about shelf-life and safe conditions for storage of the materials [11, 12]. Prediction of these parameters for energetic materials is especially meaningful in order to elucidate miscibility/compatibility and their effects on thermal stability of the resulted composition [5, 13–16].

Until today, thermolysis of DAG and its utilization in the composite double-base propellant have been investigated [11] and the results revealed positive role of this compound in modification of double-base propellant. Stoner and Brill [12, 17] observed that thermolysis of DAG at the propellant burning surface leads to formation of a thermally stable melamine. Performing the rapid thermolysis experiments on decomposition reaction of DAG exhibited that formation of highly thermal stable cyclic azines accomplished by the evaluating low molecular weight gases, i.e., NH3, HCN, CO2, and N2O. Meanwhile, Williams et al. [17, 18] found that DAG forms a thermally stable cyclic azine, which is stable up to 700 °C in the superficial reaction layer at the burning surface of the propellant. Formation of these thermal stable products due to the decomposition of the propellant caused retarding the heat transferring from the gas phase to the condensed segment of propellant. In this paper, the influences of DAG as a ballistic modifier on the thermal behaviors, decomposition reaction kinetics and burning rate of the homogeneous double-base (DB) propellant were investigated under the non-isothermal conditions. To the best of our knowledge, there is no information on the decomposition reaction kinetics of the double-base (DB) propellant containing DAG as a ballistic modifier.

Experimental

Sample preparation

DAG as the ballistic modifier of the propellant was synthesized and purified in the organic chemistry laboratory (MUT, Tehran) as proposed previously [19], while the fibrous NC used in the present investigation was of commercial grade with about 12.0 % nitrogen content [20]. The studied double-base propellant sample (control sample or no. P1) was containing of 56 % (mass fraction) NC, 30 % NG, 3 % centralite II, 7 % diethyl phthalate, 4 % other assistant reagents. The propellant sample modified with DAG (no. P2) was composed of similar components, while 2 % DAG was added and the NC content was reduced to 54 %. The details of the propellant formulations are presented in Table 1. The propellant samples were prepared by a solvent-less double-base propellant extrusion technique, including slurry mixing, rolling, and extruding [9, 17, 21].

Table 1 Percentage composition of various propellant ingredients in samples
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Instruments and experimental conditions

Infrared spectrum was obtained with a FT-IR spectrophotometer (Perkin-Elmer 1600) using KBR pellets. Analyses for C, H, and N determination were carried out on a Carlo Erba 1108 Elemental Vario EL analyzer. Thermal behaviors of propellant samples were analyzed by differential scanning calorimeter (DSC) and thermogravimetric analysis (TG). The thermal analyses were carried out on a Mettler TA4000 thermal analyzer and a DSC 1 (Mettler Toledo Co., Switzerland), respectively. The operating conditions of TG analyses were as follows: about 3 mg as the sample mass; purging of N2 gas with the flowing rate of 80 mL min−1; heating rates (β) of 10 °C min−1 in a temperature range of 50–600 °C using an α-Al2O3 crucible. The operating conditions of DSC analyses were included: about 1.5 mg as the sample mass; 50 mL min−1 as flowing rate of N2 purging in a temperature range of 50–500 °C using an α-Al2O3 crucible; heating rates of 3, 5, 7, and 9 °C min−1. The burning rates of propellant samples under different pressures were determined in an indigenously fabricated Crawford Bomb strand-burner equipment [15, 17].

Results and discussion

Characterization of DAG

As seen in Fig. 1, the room temperature FTIR spectrum of pure DAG in KBr matrix shows absorption bands corresponding to N–O bond of oxime (951.78 cm−1), –NH2 group (3368.79, 3470.35 and 1680.8 cm−1), and –OH group (2800–3300 and 1447.74 cm−1), while the absorption band observed at 1652.41 cm−1 may be attributed to C=N bond. The resulted data from IR analysis of DAG are listed in Table 2. Elemental analysis (%), calcd. for C2H6N4O2 (%): C, 20.34; H, 5.12; N, 47.44. Found (%): C, 20.54; H, 5.20; N, 47.36.

Fig. 1
figure 1

FT-IR analysis of the synthesized DAG

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Table 2 IR pattern analysis of the synthesized DAG
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Thermal properties of DAG

The DSC curve of pure DAG is given in Fig. 2. According to the DSC data, an endothermic peak was observed around 200 °C corresponding to the melting point of DAG. However, DAG was decomposed exothermally at 205.5 °C, after it is melting at the temperature of 200 °C [5].

Fig. 2
figure 2

DSC curve for pure DAG

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Thermal behavior of the propellant in the presence of DAG

The TG-DTG curves of the control propellant (sample P1) and the DAG modified propellant (sample P2) at the heating rate of 10 °C min−1 are shown in Fig. 3. Also, the DSC curves at the heating rates of 3, 5, 7 and 9 °C min−1 for both samples are presented in Figs. 4 and 5. As seen in Fig. 3, there are two mass loss stages in the TG curve of the propellant samples. Meantime, two exothermic peaks were observed in the corresponded DTG curves. TG curves of both samples, at β = 10 °C min−1, exhibited that the first stage begins at about 50 °C and stops at about 230 °C, while the peak in the DTG curve was appeared at 199–201 °C accompanying about 84–86 % mass loss, which is close to the total mass of the ester content (NC/NG) of the propellant and hence it likely attributes to the volatilization and decomposition of the NC/NG mixed ester. The second stage begins at about 410 °C and stops at about 550 °C, with the peak in the DTG curve at 508–535 °C, accompanied by 12–13 % mass loss, and it attributes to the reaction of remaining auxiliaries. However, a few remains were observed at the end of the second decomposition stage. In fact, both samples undergo a main exothermic decomposition reaction during their first stage, this results is confirmed by the exothermic peaks observed in the DSC curves of the samples in Figs. 4 and 5. On the other hand, decomposition temperature of the DAG is about 200 °C and this temperature is comparable with the decomposition temperature of the sample at the first stage. On the other hand, the propellant in the presence of DAG decomposes during a single step and the observed exothermic peak in the temperature range of 400–500 °C was not observed. In other word, the presence of the DAG in the formulation has a main influence on the thermal pattern of the propellant and all the ingredients decompose simultaneously during a single peak at a temperature about 200 °C (Fig. 5).

Fig. 3
figure 3

TG-DTG curve for the control propellant (sample P1) and DAG modified propellant (sample P2) sample mass about 3 mg; heating rate 10 °C min−1; N2 atmosphere

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Fig. 4
figure 4

DSC curves of the control propellant (sample P1) at different heating rates (°C min−1): (a) 3; (b) 5; (c) 7; (d) 9

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Fig. 5
figure 5

DSC curves of the DAG modified propellant (sample P2) at different heating rates (°C min−1): (a) 3; (b) 5; (c) 7; (d) 9

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The basic data for the main exothermic decomposition processes of the propellants P1 and P2 are listed in Table 3.

Table 3 DSC peak temperature data for the main exothermic decomposition process of the propellant samples
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Calculation of non-isothermal reaction kinetics

Thermal decomposition kinetic, Arrhenius parameters, i.e., the activation energy (E a) and the pre-exponential constant (A) and the most probable kinetic model function corresponding to the studied propellant samples was explored. The DSC curves resulted from the samples at the heating rates of 3, 5, 7, and 9 °C min−1 were employed to examine their compatibility with two well-known integral methods (i.e., Coats Redfern and Flynn–Wall–Ozawa) (Eqs. (1–2) in Table 4] and also two differential methods (i.e., Kissinger and Starink) [Eqs. (3–4) in Table 4] [21–31]. The values of E a were predicted by the Ozawa method using the isoconversional DSC curves at different heating rates, while the relations between E a and α for both propellant samples are given in Fig. 6. As seen in this figure, the values of activation energy change slightly in the range of 0.35–0.475 (α) for the control sample (P1), and 0.225–0.425 (α) for the DAG modified propellant sample (P2). These ranges were chosen to calculate the non-isothermal reaction kinetics of the samples. Forty-one types of the proposed kinetic model functions in Refs. [32–40] were examined, while the original DSC data were utilized as input of the integral and differential equations. The values of E a, log A, and the linear correlation coefficient (r) for both propellant samples were calculated and listed in Table 5. The most probable mechanism function could be selected using the better values resulted for r. The data in Table 5 exhibit that the values of E a and log A computed from the non-isothermal DSC data have good agreement with the calculated values via Flynn–Wall–Ozawa and Kissinger and Starink methods. Therefore, the mechanism function (listed in Table 6) might be determined by substituting the values of E a/(kJ mol−1) and A/s−1 into Eq. (1):

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = Af\left( \alpha \right)e^{{ - \frac{\text{E}}{\text{RT}}}} $$
(1)

where \( f(\alpha ) \) represents the differential model function, t symbolizes time, and R is the universal gas constant. The corresponding kinetic equation to the decomposition reaction of the propellant samples was determined and presented in Table 6. As seen in this table, the addition of DAG to the propellant formulation could change the decomposition reaction mechanism function in comparing with the control propellant.

Table 4 Kinetic analysis methods utilized for the studied propellant samples
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Fig. 6
figure 6

E a–α curve for the studied propellant samples (a) P1 and (b) P2)

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Table 5 Kinetic parameters of the main exothermic decomposition process of the propellant samples
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Table 6 Mechanism functions, apparent activation energies and kinetic equations of the studied propellant samples
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Thermal safety studies

Self-accelerating decomposition temperature (T SADT)

The self-accelerating decomposition temperature (SADT) is defined as the lowest ambient temperature at which an organic substance or self-reactive compound undergoes the self-accelerating decomposition. Determining of this parameter is essential for the safe packaging or transportation purposes in various materials especially in energetics [41]. In this study, the values of the onset temperature (T e) corresponding to \( \beta \) → 0 or T e0 were obtained by Eq. (2), and then, the self-accelerating decomposition temperature (T SADT) for the propellant samples was computed by Eq. (3) [36–40].

$$ T_{\text{e}} = T_{\text{e0}} + b\beta _{\text{i}} + c\beta _{\text{i}}^{2} ,\quad i = 1 - 4 $$
(2)

While, b and c are coefficients.

$$ T_{\text{e0}} = T_{\text{SADT}} $$
(3)

The resulted values for the studied propellant samples are given in Table 7.

Table 7 Thermodynamic data for the studied propellant samples
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Critical temperatures of thermal explosion

Critical temperature of thermal explosion (T b) is defined as the lowest temperature to which a specific charge might be heated without undergoing any thermal runaway [30]. This vital parameter for energetic materials usually is predicted to insure safe processing and storage. T b could be calculated by considering the ignition theory and corresponding thermo-kinetic parameters, namely the pre-exponential factor, activation energy, and heat of decomposition reaction. The critical temperatures of thermal explosion for both propellant samples were obtained from Eq. (4) [33, 38] and given in Table 7.

$$ T_{\text{bp}} = \frac{{E_{0} - \sqrt {E_{0}^{2} - 4E_{0} RT_{\text{p0}} } }}{2R} $$
(4)

The presented data in Table 7 show that the value of T bp for the DAG modified double-base propellant in comparison with the control sample is high, which confirms the difficulty in happening of transition from thermal decomposition to a thermal explosion in the modified propellant [38].

Burning rate measurement for the studied propellant samples

In order to investigate the possible utilizing of DAG in propellants as the ballistic modifier, the burning rates [u/(mm s−1)] of the both control propellant (P1) and the DAG modified propellant (P2) were measured and compared at different pressures (P/MPa). The resulted burning rates are listed in Table 8. As seen in this table, the addition of about 2 % DAG to the propellant sample has no significant effect on its burning rate, however brought down the n value. The brought down of the n value from 0.24, for the control sample, to 0.068 for the DAG modified sample in the pressure region of 5–7 MPa was observed. In order to evaluate the effects of DAG as the ballistic modifier on the burning rate of the studied double-base propellant, the pressure exponent (n) of the burning rate (u) was computed. Then, the average values of the catalysis efficiency (\( \bar{Z} \)) were compared before and after addition of the ballistic modifier into the propellant formulation. To achieve this aim, the values of n and \( \bar{Z} \) were obtained by Eqs. (5) and (6) [17, 21, 37, 38]:

$$ u_{\text{i}} = aP_{\text{i}}^{\text{n}} ,\quad i = 1 - 11 $$
(5)
$$ \bar{Z} = \mathop \sum \limits_{i = 1}^{k} \left( {{\raise0.7ex\hbox{${u_{\text{II,i}} }$} \!\mathord{\left/ {\vphantom {{u_{II,i} } {uI,i}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${u_{\text{I,i}}}$}}} \right)/k $$
(6)

where a is the coefficient (mm s−1 MPa−1).

Table 8 Effect of DAG on the burning rates (mm s−1) of the studied double-base propellant
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For the DAG modified propellant: at 5–8 MPa, u = 4.97P 0.26, \( \bar{Z} \) = 0.9; at 8–12 MPa, u = 8.47P 0.155, \( \bar{Z} \) = 1.17; at 12–15 MPa, u = 15.7P 0.024, \( \bar{Z} \) = 0.99.

As seen, addition 2 % DAG as a ballistic modifier to the propellant formulation has no considerable effect on the burning rate, but reduces efficiently the pressure exponent of the double-base propellant.

Conclusions

The ability of DAG as a ballistic modifier for the application in the homogeneous double-base propellant was investigated. Thermo-kinetic results showed that DAG could enhance the enthalpy of decomposition, apparent activation energy, and change the decomposition reaction mechanism function of the double-base propellant. The mechanisms of the chemical reactions corresponding to the main exothermal decomposition reactions of the control sample and DAG modified propellant are classified, respectively, as \( f(\alpha ) = \frac{3}{2}\left( {1 - \alpha } \right)^{4/3} [\left( {1 - \alpha } \right)^{ - 1/3} - 1]^{ - 1} \) and \( f(\alpha ) = \frac{5}{2}\left( {1 - \alpha } \right)\left[ { - { \ln }\left( {1 - \alpha } \right)} \right]^{3/5} \), while their kinetic equations are: \( {\raise0.7ex\hbox{${{\text{d}}\alpha }$} \!\mathord{\left/ {\vphantom {{{\text{d}}\alpha } {{\text{d}}t}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = 1.60 \times 10^{17} \left( {1 - \alpha } \right)^{4/3} [\left( {1 - \alpha } \right)^{ - 1/3} - 1]^{ - 1} e^{{ - 2.21 \times 10^{4} /{\text{T}}}} \) and \( {\raise0.7ex\hbox{${{\text{d}}\alpha }$} \!\mathord{\left/ {\vphantom {{{\text{d}}\alpha } {{\text{d}}t }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}t }$}} = 9.28 \times 10^{40} \left( {1 - \alpha } \right)\left[ { - { \ln }\left( {1 - \alpha } \right)} \right]^{3/5} e^{{ - 4.66 \times 10^{4} /{\text{T}}}} \). Evaluating thermal safety of the propellants samples showed that the DAG modified propellant has a higher resistance to heat and higher thermal safety than the control propellant. Furthermore, DAG could reduce efficiently the pressure exponent of the homogeneous double-base propellant to 0.068 at the pressure of 5–7 MPa.