Introduction

The development of new energetic materials continues to focus on the synthesis of new heterocycles with high density, high heat of formation and good oxygen balance. These materials have been shown to be useful as high explosives, components of propellants and gas generators [1–5]. In 1995, 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) was synthesized for the first time [6]. It was found that the predicted power was 125 % of the extremely insensitive explosive 2,4,6-triamino-1,3,5-trinitrobenzene (TATB), 81 % of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) [7, 8], and it was a thermally stable (T p = 342 °C (DSC)), relatively insensitive energetic material (H 50 = 117 cm). The energy content, power and thermal stability of LLM-105 make it very promising for several applications, including insensitive boosters and detonators.

The synthesis, properties and thermal behavior of LLM-105 have been reported widely [9–14], but the dissolution properties of LLM-105 in different solvents have never been investigated. The aim of this work is to study the dissolution processes of LLM-105 in DMSO and NMP intensively. At the same time, the kinetic equations of the two dissolution processes and the enthalpies of dissolution are obtained, respectively, which will be useful for purification of LLM-105 in production, and can provide valuable information for its applications in the propellant and explosive.

Experimental

Materials

The LLM-105 used in the experiment was prepared and purified by Xi’an Modern Chemistry Research Institute [15]. 1H NMR (CDCl3, 500 MHz) δ: 9.064, 8.784 (d, 2H, NH); IR (KBr, υ/cm−1): 3430, 3340, 3275, 3225, 1609, 1557, 1486, 1374, 1334, 1238, 1062, 885, 810, 711; Elemental anal. (%) calcd. for C4H4N6O5: C 22.22, H 1.48, N 38.89; found: C 22.57, H 1.45, N 38.65. Its purity was more than 99.6 %. The structure of LLM-105 is shown in Scheme 1. The sample was stored under vacuum before the experimental measurements. Both DMSO (ρ = 1.098–1.102 g cm−3) and NMP (ρ = 1.029–1.035 g cm−3) used as solvents were of analytical reagent grade, and their purities were higher than 99.4 %. Deionized water with an electrical conductivity of 0.8 × 10−4–1.2 × 10−4 S m−1 used in the experiments was obtained by purification two times via a sub-boiling distillation device.

Scheme 1
scheme 1

Structure of LLM-105

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Equipment and conditions

All the measurement experiments were performed on a RD496-2000 Calvet microcalorimeter (Mianyang CP Thermal Analysis Instrument Co., Ltd.), which had a sensitivity of 66.5 μV mW−1 at 298.15 K. The microcalorimeter was calibrated by the Joule effect, and the calibration was repeated after each experiment. The enthalpy of dissolution of KCl (spectrum purity) in distilled water measured on a RD496-2000 Calvet microcalorimeter at 298.15 K was 17.234 ± 0.041 kJ mol−1, and the relative error was <0.04 % compared with the literature value 17.241 ± 0.018 kJ mol−1 [16]. This showed that the device for measuring the enthalpies used in this work was reliable. The enthalpies of dissolution were measured at 298.15 ± 0.005 K.

Results and discussion

Thermochemical behaviors of the dissolution of LLM-105 in DMSO and NMP

The proper molar sample of LLM-105 was, respectively, dissolved in DMSO and NMP at 298.15 K in order to form solutions. The molar enthalpy of the dissolution (Δdiss H) was detected on a RD496-2000 Calvet microcalorimeter. Each process was repeated three times to ensure the precision of the data [17–19]. The dissolution of LLM-105 in DMSO and NMP were all endothermic processes. The thermochemical data obtained, Δdiss H, b (the molality of LLM-105), Δdiss H partial (the relative partial molar enthalpy of dissolution) and Δdiss H apparent (the relative apparent molar enthalpy of dissolution) are listed in Tables 1 and 2.

Table 1 Enthalpies of dissolution of LLM-105 in DMSO
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Table 2 Enthalpies of dissolution of LLM-105 in NMP
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With the help of the values of b and Δdiss H in Table 1, the empirical formula of enthalpy for the dissolution processes of LLM-105 in DMSO describing the b vs. Δdiss H relation is obtained as

$$\Delta _{\text{diss}} H = 8.08 - 43.31b^{1/2}$$
(1)

According to the values of b and Δdiss H in Table 2, the empirical formula of enthalpy for the dissolution processes of LLM-105 in NMP describing the b versus Δdiss H relation is also obtained as

$$\Delta _{\text{diss}} H = - 32.52 + 568.28b^{1/2} - 2260.98b$$
(2)

The empirical formula of relative molar enthalpy and relative partial molar enthalpy calculated by Eq. 2 are, respectively,

$$\Delta _{\text{diss}} H_{\text{apparent}} =\Delta _{\text{diss}} H\left( {b = b} \right) -\Delta _{\text{diss}} H\left( {b = 0} \right) = 568.28b^{1/2} - 2260.98b$$
(3)
$$\Delta _{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial\Delta _{\text{diss}} H}}{\partial b}} \right) +\Delta _{\text{diss}} H_{\text{apparent}} = 852.42b^{1/2} - 4521.96b$$
(4)

From Tables 1 and 2, we can see that the molality of the solution b can affect the values of Δdiss H, the calculated Δdiss H apparent and Δdiss H partial. The Δdiss H, Δdiss H apparent and Δdiss H partial change with the values of b during the dissolution processes of LLM-105 in DMSO and NMP. We can also find the relationship between Δdiss H and b 1/2 for the dissolution processes of LLM-105 in DMSO is linear equation from Fig. 1, and at the same time the relationship between Δdiss H and b 1/2 for the dissolution processes of LLM-105 in NMP is quadratic equation from Fig. 2.

Fig. 1
figure 1

Relationship between Δdiss H and b 1/2 of LLM-105 in DMSO

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Fig. 2
figure 2

Relationship between Δdiss H and b 1/2 of LLM-105 in NMP

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Kinetics of dissolution processes of LLM-105 in DMSO and NMP

Equations 5 and 6 were chosen as the model functions for describing the dissolution of LLM-105 in DMSO or NMP [20, 21].

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = kf(\alpha )$$
(5)
$$f(\alpha ) = (1 - \alpha )^{\text n}$$
(6)

Combining Eqs. 5 and 6 yields

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k(1 - \alpha )^{\text n}$$
(7)

Substituting α = H/H ∞ into Eq. 7, we get

$$\ln \left[ {\frac{1}{{H_{\infty } }}\left( {\frac{{{\text{d}}H}}{{{\text{d}}t}}} \right)_{\text i} } \right] = \ln k + n\ln \left[ {1 - \left( {\frac{H}{{H_{\infty } }}} \right)_{\text i} } \right]\quad {\text{where}}\;i = 1,2, \ldots L$$
(8)

In these equations, α is the conversion degree, f(α) is the kinetic model function, H represents the enthalpy at time of t, i is any time during the process, H ∞ is the enthalpy of the whole process, k is the rate constant of LLM-105 dissolved in DMSO or NMP, n is the reaction order and L is counting number.

The data needed for Eq. 8 are summarized in Tables 3 and 4. Substituting the original data in Tables 3 and 4, −(dH/dt)i, (H/H ∞)i, H ∞, i = 1, 2, … , L, into the kinetic Eq. 8 yields the values of n and lnk that are listed in Table 5.

Table 3 Original data of the dissolution process of LLM-105 in DMSO at 298.15 K
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Table 4 Original data of the dissolution process of LLM-105 in NMP at 298.15 K
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Table 5 Values of n, lnk and the correlative coefficient r for the dissolution process at 298.15 K
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Substituting the values of n and k in Table 5 into Eq. 7, we can get

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.37} (1 - \alpha )^{0.47}$$
(9)

for the dissolution process of LLM-105 in DMSO, and

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.38} (1 - \alpha )^{0.42}$$
(10)

for the dissolution process of LLM-105 in NMP.

The values of k indicate that the reaction of LLM-105 dissolved in DMSO and NMP are same; the reaction orders can also be considered to be similar.

Conclusions

  1. 1.

    The dissolution processes of LLM-105 in DMSO and NMP were investigated by RD496-2000 Calvet microcalorimeter at 298.15 K. The enthalpies can be regarded as the corresponding enthalpies at infinite dilution because of the very low molalities.

  2. 2.

    The relationship between Δdiss H and b 1/2 for LLM-105 dissolved in DMSO is linear equation, while the relationship between Δdiss H and b 1/2 for the dissolution processes of LLM-105 dissolved in NMP is quadratic equation. This means that the molality (b) is one of the important factors that influences the dissolution process.

  3. 3.

    The kinetic equations of dissolution processes of LLM-105 are dα/dt = 10−2.37(1 − α)0.47 in DMSO, and dα/dt = 10−2.38(1 − α)0.42 in NMP, which indicate that the reaction rates and reaction orders of LLM-105 dissolved in DMSO and NMP are similar.