Introduction

Hexanitrohexaazaisowurtzitane (CL-20) is a novel high energetic density material (HEDM) [1]. Its crystal density is 2.10 g cm−3, and the detonation velocity corresponding to ρ = 2.10 g cm−3 is about 9,400 m s−1. It can be expected that CL-20 has a good potential application in increasing the impulses and density of solid propellant field. And it can be regarded as a deputy of the next generation propellant raw material replacing energetic compounds such as RDX and HMX. Its preparation [2, 3], properties [4, 5], and thermal behavior [6, 7] have been reported widely.

In the present article, we reported its enthalpy of dissolution in ethyl acetate and acetone, and four kinds of empirical formulae describing the concentration b versus the enthalpy of dissolution (Δdiss H), relative partial molar enthalpy (Δdiss H partial), relative apparent molar enthalpy (Δdiss H apparent), and the enthalpy of dilution (Δdil H 1,2) relations. It provides more information for the purification of CL-20 and the thermochemical database of energetic materials.

Experimental

Materials

CL-20 was prepared by Beijing Institute of Technology, and had a purity of more than 99.5%. Ethyl acetate and acetone used as solvents were of analytical purity.

Equipment and conditions

All measurements were made using a RD496-2000 Calvet microcalorimeter and operated at 298.15 ± 0.005 K. Two replicates of each sample were tested. The enthalpy of dissolution of KCl (spectrum purity) in distilled water measured at 298.15 K was 17.234 kJ/mol, which was an excellent accord with the literature value 17.241 kJ/mol [8], showing that the device of measuring the enthalpy used in this study was reliable.

Results and discussion

The enthalpy of dissolution in ethyl acetate

The experimental and calculated values of enthalpy of dissolution [9, 10] in ethyl acetate for CL-20 are given in the Table 1. The calculated relative apparent molar enthalpy and relative partial molar enthalpy of CL-20 are also given in Table 1.

Table 1 The enthalpy of dissolution of CL-20 in ethyl acetate
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With the help of the values of b and Δdiss H in Table 1, the empirical formula describing the b versus Δdiss H relation is obtained:

$$ \Updelta_{\text{diss}} H = A + Bb + Cb^{1/2} = 4.2294 - 103.35b + 62.509b^{1/2} $$
(1)

where, Δdiss H is enthalpy of dissolution in ethyl acetate. A, B, and C are coefficients for the dissolution equation.

The empirical formulae of relative apparent molar enthalpy (Δdiss H apparen) and relative partial molar enthalpy (Δdiss H partial) calculated by formula above are

$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \Updelta_{\text{diss}} H(b = b) - \Updelta_{\text{diss}} H(b = 0) = - 103.35b + 62.509b^{1/2} $$
(2)

and

$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {{\frac{{\partial \Updelta_{diss} H}}{\partial b}}} \right) + \Updelta_{\text{diss}} H_{\text{apparent}} = \, - 206.7b + 93.764b^{1/2} , $$
(3)

respectively.The empirical formula of dilution enthalpy (Δdil H 1,2) for CL-20 is

$$ \Updelta_{\text{dil}} H_{1,2} = \Updelta_{\text{diss}} H \, _{2} - \Updelta_{\text{diss}} H_{ \, 1} = - 103.35(b_{2} - b_{1} ) + 62.509\left( {b_{2}^{1/2} - b_{1}^{1/2} } \right) $$
(4)

where b 1 and b 2 represent different concentrations of the solutions after dissolving.

The enthalpy of dissolution of CL-20 in acetone

The experimental and calculated values of enthalpy of dissolution in acetone for CL-20 are given in the Table 2. The calculated relative apparent molar enthalpy and relative partial molar enthalpy of CL-20 in acetone are also given in Table 2.

Table 2 The enthalpy of dissolution of CL-20 in acetone
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According to the values in Table 2, the empirical formula describing the b versus Δdiss H relation, the empirical formulae of relative apparent molar enthalpy, relative partial molar enthalpy, and the empirical formula of dilution enthalpy for CL-20 in acetone are

$$ \Updelta_{\text{diss}} H = A + Bb + Cb^{1/2} = 124.94 + 2080b - 961.94b^{1/2} $$
(5)
$$ \Updelta_{\text{diss}} H_{\text{apparent}} = \Updelta_{\text{diss}} H(b = b) - \, \Updelta_{\text{diss}} H(b = 0) = \, 2080b - 961.94b^{1/2 \, } $$
(6)
$$ \Updelta_{\text{diss}} H_{\text{partial}} = b\left( {{\frac{{\partial \Updelta_{\text{diss}} H}}{\partial b}}} \right) + \Updelta_{\text{diss}} H_{\text{apparent}} = 4160b - 1442.91b^{1/2 \, } $$
(7)

and

$$ \Updelta_{\text{dil}} H_{1,2} = \Updelta_{\text{diss}} H \, _{2} - \Updelta_{\text{diss}} H_{ \, 1} = \, 2080(b_{2} - b_{1} ) \, - 961.94\left( {b_{2}^{1/2} - b_{1}^{1/2} } \right), $$
(8)

respectively.

The kinetics of dissolution processes of CL-20 in ethyl acetate and acetone

The proper molar sample of CL-20 was dissolved in ethyl acetate and acetone at 298.15 K. The enthalpy of the process was determined by the RD496-2000 Calvet microcalorimeter. Each process was repeated twice. The heat flow curves obtained under the same conditions overlap with each other, indicating that the reproducibility of test is satisfactory.

The kinetic Eq. 9 was selected to describe the dissolution process [11, 12].

$$ \ln \left[ {{\frac{1}{{H_{\infty } }}}\left( {{\frac{{{\text{d}}H}}{{{\text{d}}t}}}} \right)_{i} } \right] = \ln k + n\ln \left[ {1 - \left( {{\frac{H}{{H_{\infty } }}}} \right)_{i} } \right]i = 1,2, \ldots ,L $$
(9)

where H is the enthalpy at time of t, i is any time during the process, H ∞ is the enthalpy of the whole process, k is the reaction rate constant, and n is the reaction order [13].

The original data of the dissolution process of CL-20 in the different solvent were listed in Tables 3 and 4.

Table 3 The original data of the dissolution process of CL-20 in ethyl acetate at 298.15 K
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Table 4 The original data of the dissolution process of CL-20 in acetone at 298.15 K
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By substituting the data taken from Tables 3 and 4, (dH/dt) i , (H/H ∞) i , H ∞, i = 1,2,…,L, into the kinetic equation, the values of n and lnk listed in Table 5 are obtained. Substituting the values of n and k in Table 5 into Eq. 10

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

yields

$$ {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} = 1. 60 \times 10^{ - 2} \left( { 1- \alpha } \right)^{0. 8 4} $$
(11)

for dissolution process of CL-20 in ethyl acetate, and

$$ {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} = 2. 1 5\times 10^{ - 2} \left( { 1- \alpha } \right)^{0. 8 9} $$
(12)

for dissolution process of CL-20 in acetone, indicating that the reaction rates of CL-20 dissolved in ethyl acetate and acetone are similar, and the reaction orders can be considered the same.

Table 5 The values of n, ln k, and the linear correlative coefficient r for the dissolution process
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Summaries

  1. (1)

    The enthalpies of dissolution of CL-20 in ethyl acetate and acetone were investigated by RD496-2000 Calvet microcalorimeter at 298.15 K. The results were analyzed with mathematics formulae to get the expression of Δdiss H, Δdiss H apparent, Δdiss H partial, and Δdil H 1,2 of CL-20 in different solvents.

  2. (2)

    The reaction orders of the dissolution processes of CL-20 in ethyl acetate and acetone at 298.15 K were similar, and the progressions of the reaction rates were at the same level.