1 Introduction

3, 4-Bis(3-nitrofurazan-4-yl)furoxan (DNTF, Fig. 1) is a novel energetic material with high density, high energy and simple synthesis technology. Further study shows that its detonation performance is more superior than octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) but close to 1, 2, 4, 6, 8, 10, 12-hexanitro-2, 4, 6, 8, 10, 12-hexaazaisowurtzitane (CL-20)^[1]. Since it was synthesized, researchers mainly focused on its synthesis^[2], crystal structure^[3] and comprehensive performance^[4-6].

Solution crystallization process is an important and traditional way to enhance the purity and morphology of solid products. What′s more, the solubility is an extremely significant thermodynamic data for crystallization and calculation other thermodynamic parameters. Besides, solubility can affect the capacity of the crystallization process, as well as its ability to reject undesired compounds and minimize loss in the mother liquor. Ethanol is the most widely used organic solvent because of inexpensive, non-toxic and environmental-friendly. Moreover, the solubility of DNTF is moderate and obviously changes with temperature and concentration in ethanol. Therefore, ethanol can be used as the solvent for crystallizing DNTF and it′s necessary to study the solubility of DNTF in binary system ethanol-water.

In this work, the solubility of DNTF in six different concentration ethanol solvents at 298.15-338.15 K is measured. Four common correlation equations are adopted to correlate the experimental values. The standard enthalpy of dissolution, standard entropy of dissolution and standard Gibbs free energy are calculated according to the experimental data.

2 Experimental 2.1 Chemical Materials

DNTF sample was provided by Xi′an Modern Chemistry Research Institute. It was purified by recrystallization in alcohol and its mass fraction purity, measured by High Performance Liquid Chromatography, was greater than 0.995. Ethanol of analytical reagent grade was purchased from local reagent factory without further purification whose mass fraction purity was no less than 0.995. Deionized water was made by a Millipore Mili-Q Plus water system.

2.2 Single Crystal Structure Determination

The transparent single crystal of DNTF was cultivated from binary system ethanol-water and was characterized by using the single crystal X-ray diffraction analysis, the molecular structure was shown in Fig. 2. The results show that the crystal is orthorhombic with and the crystal parameters are same with reference [3].

2.3 Powder DNTF Crystal Structure Determination

Since the solubility may change with the crystal structure, it′s necessary to confirm the crystal structure before the measurement of its solubility. The DNTF single crystal and DNTF powder used to measure the solubility were identified by powder X-ray diffraction (PXRD) which was carried out by using CuK_α radiation (1.54 Å) within 2θ range of 5° to 50° on Rigaku D/max-2500 (Rigaku, Japan) at a scanning rate of 1 step·s^-1. The result of PXRD was shown in Fig. 3 which illustrate clearly that the crystallinity and the crystal form of the powder DNTF used to measure the solubility are the same with the single crystal cultivated from binary system ethanol-water.

2.3 Experimental Procedures

The laser monitoring system (Fig. 4), the same method with Shi et al^[7], was used to detect the phase transformation point at a constant temperature. The procedure of solubility measurement is same with Lan et al^[8]. The solubility of DNTF in binary system ethanol-water within 298.15-338.15 K expressed by mole fraction was calculated by equation (1), the initial mole fraction composition of the binary solvent mixtures was defined by equation (2):

$ {x_1} = \frac{{{m_1}/{M_1}}}{{{m_1}/{M_1} + {m_2}/{M_2} + {m_3}/{M_3}}} $

(1)

$ {x_2} = \frac{{{m_2}/{M_2}}}{{{m_2}/{M_2} + {m_3}/{M_3}}} $

(2)

where x₁ is the solubility (solid-liquid equilibria) of DNTF in mole fraction; x₂ is the solute-free mole fraction of ethanol in the binary liquid solvents, m₁, m₂, m₃ are the mass of DNTF, ethanol, water, respectively, M₁, M₂, M₃ are the molecular mass of DNTF, ethanol, water, respectively.

3 Results and discussion 3.1 Measured Solubility

Solubility values of DNTF measured in different concentrationbinary system ethanol-water at temperatures ranging from 298.15 K to 338.15 K are listed in Table 1.

3.2 Correlation of Solubility Data

Since solid-liquid equilibrium is usually not available, correlation and prediction schemes are frequently utilized.The van′t Hoff plot, modified Apelblat equation, R-K model and Jouyban-Acree model are adopted to correlate the experimental values. Root-mean-square deviation (RMSD) is used to evaluate the fitting results of the correlation equation. The RMSD is defined as:

$ {\rm{RMSD}} = {\left[{\frac{1}{N}\sum\limits_{i = 1}^N {{{({x_{{\rm{c}}i}}-{x_{1i}})}^2}{\rm{ }}} } \right]^{1/2}} $

(3)

where N represents the total number of experimental points, x_1i is the experimental data, x_ci is the calculated values.

3.2.1 van′t Hoff plot

Assuming the solution is an ideal solution (γ = 1), then the solubility of DNTF can be correlated by the van′t Hoff plot^[9-10] which reflects the relationship between the mole fraction of a solute and the temperature when the solvent effect is considered. The van′t Hoff plot can be described as follows:

$ {\rm{ln}}{x_1} = A + B/T $

(4)

whereT is the absolute temperature of experiment, A and B are the model parameters. Table 2 lists the model parameters values of A, B, the correlation coefficient of fitting results and RMSD. Fig. 5 is the fitting curves correlated by equation (4), which graphically illustrates the function between lnx₁ and 1/T. From Fig. 5 we can clearly see that it is a linear relationship between lnx₁ and 1/T, the RMSD of the correlation results are acceptable. So the ideal equation can be used to correlate the solubility of DNTF in binary system ethanol-water well.

3.2.2 Modified Apelblat Equation

The modified Apelblat equation^[11-13] deduced from the Clausius-Clapeyron equation is a semiempirical equation, which has been widely used in correlation the experimental solubility values. The equation can be expressed as:

$ {\rm{ln}}{x_1} = A + B/T + C{\rm{ln}}T $

(5)

where A, B and C are the model parameters. Table 3 lists the model parameter values of A, B, C, R² and the RMSD. The experimental solubility values of DNTF in ethanol-water binary system at different temperatures and the solubility curve fitted by the modified Apelblat equation are shown in Fig. 6. It is clear that modified Apelblat equation demonstrates good consistency with the experimental values at different temperatures. Besides, the correlation coefficient of each concentration ethanol is close to 1 and the RMSD is micro, so the modified Apelblat equation can correlate the solubility of DNTF in binary system ethanol-water at different temperatures precisely.

3.2.3 R-K Model

The R-K model^[14-15] is one of the best models used to calculate the solute solubility in binary solvents and it is expressed as follows:

$ {\rm{ln}}{x_1} = {x_2}{\rm{ln}}{\left( {{x_1}} \right)_2} + {x_3}{\rm{ln}}{\left( {{x_1}} \right)_3} + {x_2}{x_3}\sum\limits_{i = 1}^N {{S_i}\left( {{x_2}-{x_3}} \right)} $

(6)

where x₁ is the solubility of DNTF, x₂ and x₃ stand for the initial molar fraction composition of ethanol and water in binary solvent mixtures when the solute is not added, (x₁)₂ and (x₁)₃ are the mole fraction solubility of DNTF in pure ethanol and water, respectively. S_i is the model constant and N can be 0, 1, 2 or 3^[16]. For binary solvents system, substituting N=2 and x₃=1-x₂ into Eq.(6) can give a simplified equation as follows.

$ {\rm{ln}}{x_1} = {B_0} + {B_1}{x_2} + {B_2}x_2^2 + {B_3}x_2^3 + {B_4}x_2^4 $

(7)

where B₀, B₁, B₂, B₃, and B₄ are the model parameters. The model parameters values of B₀, B₁, B₂, B₃, B₄, R² and the RMSD are displayed in Table 4. The solubility data calculated by the R-K equation are graphically displayed in Fig. 7 which illustrates clearly to us that the solubility values correlated by the R-K equation are in good agreement with the experimental ones. Besides, the R² and RMSD are acceptable, so the R-K equation can be used to correlate the solubility of DNTF in ethanol-water binary system at different concentration accurately.

3.2.4 Jouyban-Acree Model

The Jouyban-Acree model^[17-18] is also widely used to describe the solubility of DNTF in the whole temperature range by taking both composition of solution and temperature into consideration. The model is expressed as follows:

$ {\rm{ln}}{x_1} = {x_2}{\rm{ln}}{\left( {{x_1}} \right)_2} + {x_3}{\rm{ln}}{\left( {{x_1}} \right)_3} + {x_2}{x_3}\sum\limits_{i = 1}^N {{J_i}\left( {{x_2}-{x_3}} \right)} /T $

(8)

where J_i is the model constant. Substitution of N=2 into Eq.(8) can give a new simplified equation as:

$ \begin{array}{l} {\rm{ln}}{x_1} = {\rm{ }}{A_0} + {A_1}/T + {A_2}{\rm{ln}}T + {A_3}{x_2} + {A_4}{x_2}/T + {A_5}{\left( {{x_2}} \right)^2}/T + \\ {A_6}{\left( {{x_2}} \right)^3}/T + {A_7}{\left( {{x_2}} \right)^4}/T + {A_8}{x_2}{\rm{ln}}T \end{array} $

(9)

where A₀-A₈ are empirical model parameters, which can be obtained by least-squares analysis. The model parameters values of A₀-A₈, R² and the RMSD are displayed in Table 5. The three three-dimensional diagram between x₁and x₂, T is shown in Fig. 8 which demonstrates to us that all of the experimental values are on the surface fitted by the Jouyban-Acree model, besides, the R² is very close to 1 and the RMSD is close to 0. Therefore, the Jouyban-Acree model is a perfect equation to correlate the experimental solubility data of DNTF in ethanol-water binary system. What′s more, we can calculate the solubility of DNTF in ethanol-water binary system at random temperature and concentration by the Jouyban-Acree model obtained from this study.

3.3 Thermodynamic Parameters for DNTF Dissolution

Some thermodynamic properties such asthe standard enthalpy of dissolution, standard entropy of dissolution and the standard Gibbs free energy can be calculated by the solubility data measured. The function between the mole fraction solubility of DNTF and the absolute temperature can be expressed as^[19]:

$ {\rm{ln}}{x_1} =-\frac{{{\Delta _{{\rm{dis}}}}{H^\Theta }}}{{RT}} + \frac{{{\Delta _{{\rm{dis}}}}{S^\Theta }}}{{R}} $

(10)

where R represents the gas constant (8.3145 J·K^-1·mol^-1), Δ_disH^Θand Δ_disS^Θ are the standard enthalpy of dissolution and standard entropy of dissolution of DNTF. Assuming the lnx₁ is dependent variable, 1/T is independent variable, so the lnx₁ is linear relation with 1/T and we can calculate the Δ_disH^Θ from the slope and Δ_disS^Θ from the intercept of the linear equation displayed in Fig. 5. The standard Gibbs free energy of dissolution of DNTF in different solvents can be calculated as:

$ {\Delta _{{\rm{dis}}}}{G^\Theta } = {\Delta _{{\rm{dis}}}}{H^\Theta }-\mathit{T}{\Delta _{{\rm{dis}}}}{S^\Theta } $

(11)

In this work, we calculated change in Gibbsfree energy at 318.15 K as a mean temperature (Δ_disG_mean^Θ).

The relative contributions from enthalpy %ξ_H and entropy %ξ_S to the standard free Gibbs energy of the solution are define by the following two equations^[20]:

$ \% {\xi _H} = \frac{{\left| {{\Delta _{{\rm{dis}}}}{H^\Theta }} \right|}}{{\left| {{\Delta _{{\rm{dis}}}}{H^\Theta }} \right| + \left| {T{\Delta _{{\rm{dis}}}}{S^\Theta }} \right|}} \times 100 $

(12)

$ \% {\xi _S} = \frac{{T{\Delta _{{\rm{dis}}}}{S^\Theta }}}{{{\Delta _{{\rm{dis}}}}{H^\Theta } + T{\Delta _{{\rm{dis}}}}{S^\Theta }}} \times 100 $

(13)

The calculated enthalpy, entropy, and Gibbs energy of dissolution together with %ξ_H, %ξ_S calculated under the mean temperature are displayed in Table 6. Since the values of Δ_disH^Θ are positive in all solvents, the dissolution of DNTF in binary system ethanol-water is an endothermic process. In addition, the dissolution of DNTF is a non-spontaneous process because the values of Δ_disG_mean^Θ are positive. Moreover, the main contributor to the standard molar Gibbs energy of dissolution is the enthalpy instead of entropy in that the %ξ_H is greater than %ξ_S.

4 Conclusions

(1) The solubility values of DNTF increase with increasing the ratio of ethanol and temperature as a nonlinear function.

(2) Four correlation equations selected in this study all can be used to fit the solubility values of DNTF precisely. What′s more, all of the 54 experimental values are used to correlate the parameters of Jouyban-Acree model and the correlated results are better than other three equations by comparing the R² and RMSD.

(3) Some important thermodynamic properties such as the standard enthalpy of dissolution, standard entropy of dissolution and standard Gibbs free energy of dissolution have been calculated.