Introduction

N-guanylurea dinitramide (GUDN) is a new high-energy and low sensitivity oxidizer, and it is a stable salt of dinitramide. In contrast to the more well-known dinitramide, ADN, it does not melt and it is significantly more thermally stable [1, 2]. GUDN has been demonstrated to be an extremely insensitive energetic molecule. It does not react in fall hammer and friction tests [3]. GUDN as a main ingredient has been used in insensitive gun propellants [4, 5]. It has also been used as a gas generation component in compositions for air bags due to its excellent burning characteristics [6–9]. It has been demonstrated that it also has a potential as an high explosive [10].

Quite a lot of properties of GUDN have been measured and studied, including density, detonation velocity, detonation heat, reactivity, thermal stability, compatibility, sensitivity, and so on [1, 11]. But the particular properties of its solution have rarely been reported. In the present study, an RD496-2000 Calvet microcalorimeter is used to measure the enthalpies of dissolution of GUDN in dimethyl sulfoxide (DMSO) and N-methyl pyrrolidone (NMP). The relationships for the measured enthalpies of dissolution and amounts of substance are studied, and the relative partial molar enthalpy (Δdiss H partial), and the relative apparent molar enthalpy (Δdiss H apparent) at 298.15 K are obtained. The kinetic equations of the two dissolution processes are also obtained, respectively, which will be useful for purification of GUDN in production, and can provide basic guidance for its applications.

Experimental

Materials

GUDN used in the experiment was prepared and purified by Xi’an Modern Chemistry Research Institute, and had a purity of more than 99.4 %. Both NMP (ρ = 1.029–1.035 g cm3) and DMSO (ρ = 1.098–1.102 g cm3) used as solvents were of analysis reagent grade, and their purities were higher than 99.5 %. 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.

Equipment and conditions

All the measurement experiments were performed on an RD496-2000 Calvet microcalorimeter (Mianyang CP Thermal Analysis Instrument Co., Ltd.). The standard molar enthalpy of the dissolution of KCl (spectrum purity) in distilled water measured by RD496-2000 Calvet microcalorimeter at 298.15 K was 17.234 ± 0.041 kJ mol−1, and the relative error was less than 0.04 % compared with the literature value 17.241 ± 0.018 kJ mol−1 [12]. This showed that the device for measuring the enthalpy 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 GUDN in DMSO and NMP

The proper molar sample of GUDN was dissolved in DMSO and NMP at 298.15 K to form solutions. The molar enthalpy of the dissolution (Δdiss H) was detected on an RD496-2000 Calvet microcalorimeter [13–16]. Each process was repeated three times to insure the precision of the data [17–19]. The dissolution of GUDN in DMSO was an endothermic process, but the dissolution in NMP was an exothermic process. The thermochemical data obtained, Δdiss H, b (the molality of GUDN), Δdiss H partial (the relative partial molar enthalpy of dissolution), and Δdiss H apparent (the relative apparent molar enthalpy of dissolution) were listed in Tables 1 and 2.

Table 1 Enthalpies of dissolution of GUDN in DMSO
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Table 2 Enthalpies of dissolution of GUDN 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 GUDN in DMSO describing the b versus Δdiss H relation is obtained as:

$$ \Updelta_{\text{diss}} H = 17.00 - 232.47b^{1/2} + 704.08b. $$
(1)

The empirical formula of relative molar enthalpy and relative partial molar enthalpy calculated by Eq. (1) are, respectively,

$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \Updelta_{\text{diss}} H(b = b) - \Updelta_{\text{diss}} H(b = 0) = - 232.47b^{1/2} + 704.08b, $$
(2)
$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Updelta_{\text{diss}} H}}{\partial b}} \right) + \Updelta_{\text{diss}} H_{\text{apparent}} = - 348.71b^{1/2} + 1,408.16b. $$
(3)

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

$$ \Updelta_{\text{diss}} H = 111.19 - 1,211.19b^{1/2} + 3,485.31b. $$
(4)

The empirical formula of relative molar enthalpy and relative partial molar enthalpy calculated by Eq. (4) are, respectively,

$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \Updelta_{\text{diss}} H(b = b) - \Updelta_{\text{diss}} H(b = 0) = - 1,211.19b^{1/2} + 3,485.31b, $$
(5)
$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Updelta_{\text{diss}} H}}{\partial b}} \right) + \Updelta_{\text{diss}} H_{\text{apparent}} = - 1,816.79b^{1/2} + 6,970.62b. $$
(6)

From Tables 1 and 2, we can see that the molality of the solution b can affect the values of Δdiss H, Δdiss H apparent and Δdiss H partial were calculated. We can also find the two curves for the dissolution processes of GUDN in DMSO or NMP are similar to each other, and the relationships between Δdiss H and b 1/2 are quadratic equation from Figs. 1 and 2.

Fig. 1
figure 1

The relationship between Δdiss H and b 1/2 of GUDN in DMSO

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Fig. 2
figure 2

The relationship between Δdiss H and b 1/2 of GUDN in NMP

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The kinetics of dissolution process of GUDN in DMSO or NMP.

Equations (7) and (8) are chosen as the model functions [20–22] for describing the dissolution of GUDN in DMSO or NMP.

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = kf(\alpha ), $$
(7)
$$ f(\alpha ) = (1 - \alpha )^{\text{n}} . $$
(8)

Combining Eqs. (7) and (8), yields

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k(1 - \alpha )^{n} . $$
(9)

Substituting α = H/H ∞ into the Eq. (9), we get

$$ \ln \left[ {\frac{1}{{H_{\infty } }}\left( {\frac{{{\text{d}}H}}{{{\text{d}}t}}} \right)_{\text{i}} } \right] = \ln k + n\ln \left[ {1 - \left( {\frac{H}{{H_{\infty } }}} \right)_{\text{i}} } \right]\quad {{i}} = 1,\,2, \ldots ,L. $$
(10)

In these equations, α is 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 of GUDN in DMSO or NMP, n is the reaction order, and L is counting number.

The data needed for Eq. (10) are summarized in Tables 3 and 4.

Table 3 Original data of the dissolution process of GUDN in DMSO at 298.15 K
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Table 4 Original data of the dissolution process of GUDN in NMP at 298.15 K
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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 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. (9), we can get

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 3.39} (1 - \alpha )^{0.70} , $$
(11)

for dissolution process of GUDN in DMSO, and

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 4.06} (1 - \alpha )^{1.11} , $$
(12)

for dissolution process of GUDN in NMP.

Conclusions

  1. (1)

    The dissolution process of GUDN in DMSO and NMP were investigated by RD496-2000 Calvet microcalorimeter at 298.15 K. The relationship between Δdiss H and b 1/2 of GUDN dissolved in DMSO and NMP are quadratic equation.

  2. (2)

    The expressions describing values of Δdiss H, Δdiss H apparent, and Δdiss H partial versus the molality (b) of GUDN in DMSO are Δdiss H = 17.00 − 232.47b 1/2 + 704.08b, Δdiss H apparent = −232.47b 1/2 + 704.08b, Δdiss H partial = −348.71b 1/2 + 1,408.16b. The expressions describing values of Δdiss H, Δdiss H apparent and Δdiss H partial versus the concentration (b) of GUDN in NMP are Δdiss H = 111.19 − 1,211.19b 1/2 + 3,485.31b, Δdiss H apparent = −1,211.19b 1/2 + 3,485.31b, Δdiss H partial = −1,816.79b 1/2 + 6,970.62b, respectively.

  3. (3)

    The kinetics equations of dissolution processes for GUDN are dα/dt = 10−3.39(1 − α)0.70 in DMSO, and dα/dt = 10−4.06(1 − α)1.11 in NMP.