Introduction

Energetic ionic compound is one of the effective ways to develop new kind of high-energy, low-sensitive, and non-toxic materials. Energetic ionic compounds, which are mainly composed of organic cation and inorganic anion or organic anion, include energetic ionic salts and energetic ionic liquids [1, 2]. To meet the requirement of weapons and equipments for multifunctional energetic materials, many new energetic groups are introduced in the chemical structure of cation and anion of energetic ionic compounds by the molecular design [3–6]. This approach makes energetic ionic compounds possess the various excellent functions, such as high density, insensitivity, stability, environmental friendly, and so on [7–9].

Di(N,N-di(2,4,6-trinitrophenyl)amino)-ethylenediamine (DTAED) is a novel type of energetic ionic compound which consists of anion of N,N-di(2,4,6-trinitrophenyl)amine and cation of ethylenediamine, but the solution properties have never been reported so far. Dimethyl sulfoxide (DMSO) and N-methyl pyrrolidone (NMP) as solvents have been used extensively in our production and application, so thermochemical properties of its solution have been studied first by means of a RD496-2000 Calvet microcalorimeter. The aim of this work is to study the dissolution properties of DTAED in DMSO and NMP. At the same time, the kinetic equations of the two dissolution processes are obtained, respectively, which provides valuable information for its applications in the future.

Experimental

Materials

DTAED used as crystalloid was prepared and purified by Beijing Institute of Technology, its purity determined by LC–MS, elemental analysis, and 13C NMR was more than 99.5%. Both DMSO (ρ/g cm−3=1.098–1.102) and NMP (ρ/g cm−3=1.029–1.035) used as solvents were of analysis reagent grade, and their purity was more than 99.5%. The water used in these experiments was deionized with an electrical conductivity of 0.8–1.2 × 10−4 Sm−1, and obtained by two times purification using sub-boiling distillation device.

Equipment and conditions

All measurements were made using a RD496-2000 Calvet microcalorimeter (MianYang CP Thermal Analysis Instrument CO., LTD). The enthalpy of 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 [10]. This showed that the device for measuring the enthalpy used in this study was reliable. The enthalpies of dissolution were measured at 298.15 ± 0.005 K.

Results and discussion

Thermochemical behaviors of the dissolution of DTAED in DMSO and NMP

The proper molar sample of DTAED was dissolved in DMSO and NMP at 298.15 K in order to form solution. The enthalpy of the process was detected by the RD496-2000 Calvet microcalorimeter [11–14]. Each process was repeated three times [15, 16]. The dissolution is an exothermic process. The heat flow curves obtained under the same conditions overlap with each other and are shown in Fig. 1, indicating that the reproducibility of test is satisfactory.

Fig. 1
figure 1

Curves describing the entire dissolution process of DTAED in DMSO at 298.15 K. (a) 105 a/mol = 0.4721; (b) 105 a/mol = 0.4828; (c) 105 a/mol = 0.4721

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The thermochemical data obtained are listed in Tables 1 and 2. In Tables, a is the amount of substance, b is the molality of DTAED, Δdiss H is the molar enthalpy of dissolution, Δdiss H partial is the relative partial molar enthalpy of dissolution, and Δdiss H apparent is the relative apparent molar enthalpy of dissolution.

Table 1 The enthalpies of dissolution of DTAED in DMSO
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Table 2 The enthalpies of dissolution of DTAED 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 describing the b versus Δdiss H relation is obtained

$$ \Updelta_{\text{diss}} H = {\text{A + B}}b{ + }\,{\text{C}}b^{ 1/ 2} = - 1 4 7. 7 6 { + 3589}. 3 7b^{ 1/ 2} - 2 9 1 5 3. 4 6b $$
(1)

where A, B, and C are coefficients for the dissolution equation.

The empirical formulae of relative apparent molar enthalpy (Δdiss H apparent) and relative partial molar enthalpy (Δdiss H partial) calculated by Eq. 1 are

$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \, \Updelta_{\text{diss}} H\left( {b = b} \right) - \Updelta_{\text{diss}} H\left( {b = \, 0} \right){ = 358937}b^{ 1/ 2} - 2 9 1 5 3 4 6b $$
(2)
$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Updelta_{\text{diss}} H}}{\partial b}} \right) + \Updelta_{\text{diss}} H_{{\rm{apparent}}} { = 5384}.0 5 5b^{ 1/ 2} - 5 8 30 6. 9 2b, $$
(3)

respectively.

According to the values in Table 2, the empirical formula describing the b versus Δdiss H relation, and the empirical formulae of relative apparent molar enthalpy (Δdiss H apparent) and relative partial molar enthalpy (Δdiss H partial) for DTAED in NMP are

$$ \Updelta_{\text{diss}} H = {\text{A + B}}b{\text{ + C}}b^{ 1/ 2} = - 20 5. 4 3 { + 4483}. 2 6b^{ 1/ 2} - 3 3 8 5 7. 7b $$
(4)
$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \, \Updelta_{\text{diss}} H\left( {b = b} \right) - \Updelta_{\text{diss}} H\left( {b = \, 0} \right){ = 4483}. 2 6b^{ 1/ 2} - 3 3 8 5 7. 7b $$
(5)
$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Updelta_{\text{diss}} H}}{\partial b}} \right) + \,\Updelta_{\text{diss}} H_{{\rm{apparent}}} = 6 7 2 4 8 9b^{ 1/ 2} - 6 7 7 1 5 4b $$
(6)

respectively.

From Tables 1 and 2, we can see that the values of Δdiss H, the calculated Δdiss H apparent, and Δdiss H partial change with the values of b. We can find that the relationships between Δdiss H and b 1/2 are quadratic equation for DTAED dissolved in DMSO and NMP from Figs. 2 and 3.

Fig. 2
figure 2

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

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Fig. 3
figure 3

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

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The kinetics of dissolution process of DTAED in DMSO and NMP

The kinetic equations describing the dissolution of DTAED in DMSO and NMP are Eqs. 7 and 8 [17–21] which are chosen as the model function describing the dissolution process.

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

$$ \ln \left[ {\frac{1}{{H_{\infty } }}\left( {\frac{{{\text{d}}H}}{{{\text{d}}t}}} \right)_{i} } \right] = \ln k + n\ln \left[ {1 - \left( {\frac{H}{{H_{\infty } }}} \right)_{i} } \right]\qquad i = 1, 2, \ldots ,L $$
(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 DTAED dissolved in DMSO and 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 The original data of the dissolution process of DTAED in DMSO at 298.15 K
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Table 4 The original data of the dissolution process of DTAED in NMP at 298.15 K
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By substituting the original data in Tables 3 and 4, −(dH/dt) i , (H/H ∞ ) i , H ∞ , i = 1,2,…,L, into the kinetic equation (10), the values of n and lnk are obtained and listed in Table 5.

Table 5 The 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 from Table 5 into Eq. 7, we can get

$$ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{{\rm{d}}}t}}} \right. \kern-\nulldelimiterspace} {{\rm{d}}t}} = 10^{ - 2.68} \left( {1 - \alpha } \right)^{0.84} $$
(11)

for dissolution process of DTAED in DMSO, and

$$ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-\nulldelimiterspace} {{\rm{d}}t}} = 10^{ - 2.79} \left( {1 - \alpha } \right)^{0.87} $$
(12)

for dissolution process of DTAED in NMP.

The relationships between k and a are shown in Fig. 4. One can see that the rate (k) for the dissolution processes of DTAED in DMSO and NMP increase with the amount of substance (a) increasing from Fig. 4, the linear relationships exist obviously, and the correlative coefficients (r) are 0.9981 and 0.9978, respectively.

Fig. 4
figure 4

The relationship between k and a for the dissolution of DTAED in DMSO and NMP

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Conclusions

  1. (1)

    The dissolution process of DTAED in DMSO and NMP were investigated by RD496-2000 Calvet Microcalorimeter at 298.15 K, respectively. The relationship between Δdiss H and b 1/2 of DTAED dissolved in DMSO and NMP are quadratic equations.

  2. (2)

    The expressions describing values of Δdiss H, Δdiss H apparent, and Δdiss H partial versus the molality (b) of DTAED in DMSO are Δdiss H = −147.76 + 3589.37b 1/2 − 29153.46b, Δdiss H apparent = 3589.37b 1/2 − 29153.46b, and Δdiss H partial = 5384.055b 1/2 − 58306.92b. The expressions describing values of Δdiss H, Δdiss H apparent, and Δdiss H partial versus the molality (b) of DTAED in NMP are Δdiss H = −205.43+4483.26b 1/2 − 33857.7b, Δdiss H apparent = 4483.26b 1/2 − 33857.7b, and Δdiss H partial = 6724.89b 1/2 − 67715.4b, respectively.

  3. (3)

    The kinetics equations of dissolution processes for DTAED are \( {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-\nulldelimiterspace} {{\rm{d}}t}} = 10^{ - 2.68} \left( {1 - \alpha } \right)^{0.84} \) in DMSO, and \( {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-\nulldelimiterspace} {{\rm{d}}t}} = 10^{ - 2.79} \left( {1 - \alpha } \right)^{0.87} \) in NMP.

  4. (4)

    The relationships between k and a are obtained, and the linear relationships exist obviously.