Introduction

Ammonium dinitramide (ADN) as an energetic material has been extensively studied in propellants [1–7]. ADN does not contain any chlorine; no hydrochloric acid is produced during combustion compared to ammonium perchlorate (AP). In addition, it also has high-temperature stability, high-energy density, low sensitivity, and positive oxygen balance. So, it can be widely used as a replacement for AP in environmentally benign propellant systems. Earlier work have mostly focused on synthesis, thermal stability, combustion mechanism, detonation properties, sensitivity, compatibility with main compositions of propellant, and its use in propellants [8–18]. However, the thermochemical properties of its solution at different temperatures have never been reported until now.

In the present paper, we investigate the dissolution behaviors for ADN in NMP using a RD496-2000 Calvet microcalorimeter. The relationships between the measured heat effects and amounts of substance were studied, the molar enthalpies (Δdiss H) and the differential molar enthalpies (Δdif H) for ADN in NMP at different temperatures were obtained, and the kinetic behaviors were also studied at the same time. The resulting data can provide basic guidance for its further applications.

Experimental

Materials

The ADN used in this work was prepared and purified by Xi’an Modern Chemistry Research Institute, and its purity was more than 99.8 %. The sample was stored under vacuum before the experimental measurements. NMP (ρ/g cm−3=1.029–1.035) used as solvent was of analytical reagent grade, their purity was more than 99.5 %, and made by Tianjin Baishi Chemical Industry Co. Ltd., China. The water used in these experiments was deionized with an electrical conductivity of 0.8–1.2 × 10−4 S m−1 and obtained by purification for two times using sub-boiling distillation device.

Equipment and conditions

All measurements were made by a RD496-2000 Calvet microcalorimeter (Mianyang CP Thermal Analysis Instrument CO., LTD). The enthalpy of dissolution of KCl (spectrum purity) in distilled water 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 [19, 20]. This showed that the device of measuring the enthalpy used in this work was reliable.

The heat effects were measured at 298.15, 303.15, 308.15, and 313.15 K. Each process was repeated three times to ensure the precision of the data.

Results and discussion

Thermochemical behaviors

The experimental and calculated values of heat effect of ADN dissolved in NMP at different temperatures are given in Table 1. Each process was repeated three times [21–25]. The molar enthalpies (Δdiss H) and the specific enthalpies (Δdiss h) for dissolution processes are obtained and also listed in Table 1, where a is the amount of the substance, b is the molality of ADN, and Q is the heat effect produced during the processes.

Table 1 The enthalpies of dissolution of ADN in NMP
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It is seen from Table 1 that the values of Δdiss H and Δdiss h decrease as the experimental temperatures are increased. This means that the temperature is one of the important factors that influences the dissolution processes. The molality of solution (b) almost has little effect on the values of Δdiss H and Δdiss h at each temperature. Thus, the average value of Δdiss H at each temperature can represent the molar enthalpies of the infinite diluted solution due to their very low molalities of solution.

The relationships between Q and a of ADN dissolved in NMP at different temperatures are shown in Fig. 1. The relationships are represented with linear equations at each different temperature. The linear equations are given in Table 2. The differential molar enthalpy (Δdif H) is produced when a molar amount of solute is added to an infinite amount of solution having the same solute already in it. These values can be obtained from the slope of the equations. The results are also shown in Table 2.

Fig. 1
figure 1

The relationships between heat effect and amount of the substance at different temperatures (filled square T = 298.15 K, filled circle T = 303.15 K, filled triangle T = 308.15 K, open square T = 313.15 K)

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Table 2 Thermochemical equations and differential enthalpies (Δdif H) of dissolution process of ADN in NMP
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The kinetic behaviors

Equations 1–4 [26–28] are chosen as the model function describing the dissolution process of ADN in NMP.

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = kf(\alpha ) $$
(1)
$$ f(\alpha ) = (1 - \alpha )^{\text{n}} $$
(2)

Combining Eqs. 1 and 2 yields

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k(1 - \alpha)^{\text{n}} $$
(3)

Substituting α = Q/Q ∞ into Eq. 3, we get

$$ { \ln }\left[ {\frac{1}{{Q_{\infty } }}\left({\frac{{{\text{d}}Q}}{{{\text{d}}t}}} \right)_{\text{i}} } \right]= { \ln}\,k + n\,{ \ln }\left[ {1 - \left( {\frac{Q}{{Q_{\infty }}}} \right)_{\text{i}} } \right]\quad \quad i = 1, 2, \ldots\ldots L $$
(4)

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

The data needed for Eq. 4 are summarized in Table 3. By substituting the data taken from Table 3 into the kinetic Eq. 4, the values of n and lnk at different temperatures are obtained and listed in Table 4.

Table 3 The original data of the dissolution process of ADN in NMP at different temperatures
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Table 4 Values of n, lnk, and the correlative coefficient r for the dissolution process at different temperatures
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From Table 4, one can see that the values of n and lnk show that the reaction order and the dissolved rate of ADN dissolved in NMP vary during the experimental temperatures; the values of n and lnk increase with the increasing experimental temperature. So, the dissolution process becomes much quicker as the temperature rises.

Substituting the values of n and k from Table 4 into Eq. 3, the kinetic equations of the dissolution processes of ADN dissolved in NMP can be described as

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.50} \left( {1 - \alpha } \right)^{1.08} \;\quad \left( {T = { 298}. 1 5\,{\text{K}}} \right) $$
(5)
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.44} \left( {1 - \alpha } \right)^{1.18} \quad \left( {T = { 3}0 3. 1 5\;{\text{K}}} \right) $$
(6)
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.38} \left( {1 - \alpha } \right)^{1.47} \quad \quad \left( {T = { 3}0 8. 1 5\;{\text{K}}} \right) $$
(7)
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.33} \left( {1 - \alpha } \right)^{1.75} \quad \quad \left( {T = { 313}. 1 5\;{\text{K}}} \right) $$
(8)

Equation 9 is applied to calculate the values of activation energy (E) and pre-exponential factor (A) by the slope and the intercept of the linear equation. The value of E is 20.68 kJ mol−1 and that of A is 101.12 s−1; the correlative coefficient is 0.9992. The relationship of lnk versus 1/T for the dissolution of ADN dissolved in NMP is shown in Fig. 2. From the values of E and A, we can see that dipicrylamine imidazolium can easily dissolve in NMP. This is very consistent with the fact that NMP is an excellent solvent for dipicrylamine imidazolium.

$$ { \ln}\,k = { \ln}\,A - \frac{{E_{\text{a}} }}{RT} $$
(9)
Fig. 2
figure 2

The relationship between reaction rate constant (k) and temperature (T) for ADN dissolved in NMP

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Conclusions

  1. (1)

    The values of heat effect of ADN dissolved in NMP are determined at different temperatures. It is found that the molality has little effect on the values of the molar enthalpy at each temperature. And the obtained enthalpies can be regarded as the enthalpies at infinite dilution because of its very low molalities.

  2. (2)

    The molar enthalpies (Δdiss H) are −21.56, −22.33, −22.61, and −22.82 kJ mol−1 and the differential enthalpies (Δdif H) are −22.26, −21.85, −22.84, and −23.11 kJ mol−1 for ADN in NMP at 298.15, 303.15, 308.15, and 313.15 K, respectively. The molar enthalpies (Δdiss H) decrease with the increasing temperatures.

  3. (3)

    The kinetic equations describing the dissolution processes for ADN in NMP at different temperatures are dα/dt = 10−2.50(1 − α)1.08 (T = 298.15 K), dα/dt = 10−2.44(1 − α)1.18 (T = 303.15 K), dα/dt = 10−2.38(1 − α)1.47 (T = 308.15 K), and dα/dt = 10−2.33(1 − α)1.75 (T = 313.15 K), respectively.

  4. (4)

    In the dissolution processes of ADN dissolved in NMP, the reaction order and the dissolution rate vary with the experimental temperatures, and the relationships between the dissolution rate and experimental temperature are linear. The kinetic parameters E and A are obtained as 20.68 kJ mol−1 and 101.12 s−1.