LAN Guan-chao, WANG Jian-long, CAO Duan-lin, CHEN Li-zhen, HOU Huan, LI Jing

(School of Chemical and Environmental Engineering, North University of China, Taiyuan 030051, China)

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.

Fig.1 Chemical structure of DNTF

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].

Fig.2 The molecular structure of DNTF

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 CuKαradiation (1.54 ?) within 2θrange 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.

Fig.3 Powder X-ray diffraction of DNTF

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):

(1)

(2)

wherex1is the solubility (solid-liquid equilibria) of DNTF in mole fraction;x2is the solute-free mole fraction of ethanol in the binary liquid solvents,m1,m2,m3are the mass of DNTF, ethanol, water, respectively,M1,M2,M3are the molecular mass of DNTF, ethanol, water, respectively.

Fig.4 Flow diagrams of experiment

1—laser generator, 2—glass vessel, 3—condenser pipe, 4—burette, 5—mercury thermometer, 6—digital display, 7—thermostatic bath, 8—photoelectric switch, 9—magnetic stirrer

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:

(3)

whereNrepresents the total number of experimental points,x1iis the experimental data,xciis 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:

lnx1=A+B/T

(4)

Table 1 Experimental mole fraction solubility valuesx1iand calculated solubility valuesxciof DNTF in binary system ethanol-water at temperatureTand pressurep=0.1 MPa1)

x2T/K103x1ix2T/K103x1ix2T/K103x1i1.0000298.15008.1235303.15009.3626308.150010.9555313.150012.8627318.150015.2488323.150018.4692328.150022.2804333.150027.2617338.150033.48280.8544298.15004.0155303.15004.7642308.15005.7368313.15007.0041318.15008.6617323.150010.8404328.150013.7188333.150017.5420338.150022.64780.7354298.15001.9221303.15002.3859308.15002.9937313.15003.7940318.15004.8531323.15006.2611328.15008.1419333.150010.6657338.150014.06680.6363298.15001.0967303.15001.3607308.15001.7170313.15002.2006318.15002.8618323.15003.7724328.15005.0356333.15006.8010338.15009.28560.5526298.15000.6947303.15000.8757308.15001.1189313.15001.4477318.15001.8950323.15002.5074328.15003.3510333.15004.5203338.15006.15020.4808298.15000.3078303.15000.4560308.15000.6612313.15000.9398318.15001.3107323.15001.7955328.15002.4181333.15003.2045338.15004.1820

Note: 1) The standard uncertaintyuareu(T)=0.1 K,u(p)=0.02 MPa,ur(x)=0.3%.

whereTis the absolute temperature of experiment,AandBare the model parameters. Table 2 lists the model parameters values ofA,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 lnx1and 1/T. From Fig.5 we can clearly see that it is a linear relationship between lnx1and 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.

Table 2 Model parameters, correlation coefficient and RMSD of van′t Hoff plot

x2ABR2103×RMSD1.00007.0971-3571.64620.98970.89960.85449.0229-4361.56160.98900.73320.735410.4990-5017.99040.99360.39050.636311.1451-5385.67560.99010.33540.552611.0772-5497.97640.99260.19690.480814.0042-6575.31020.99920.0564

Fig.5 Solubility of DNTF in ethanol-water binary system correlated with different temperatures.The points represent the experimental data. Curves are calculated according to Eq.(4) using the van′t Hoff plot

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:

lnx1=A+B/T+ClnT

(5)

whereA,BandCare the model parameters. Table 3 lists the model parameter values ofA,B,C,R2and 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.

Table 3 Model parameters,R2and RMSD of modified Apelblat equation

x2ABCR2103×RMSD1.0000-157.89444026.412724.48250.99680.39750.8544-189.76374798.723929.49450.99650.30650.7354-224.40645823.410734.84350.99890.10980.6363-100.1344-301.285816.53670.99240.19780.5526-114.0275239.146518.57880.99520.10480.4808-131.1201606.817721.26930.99840.0442

Fig.6 Solubility of DNTF in binary system ethanol-water correlated with different temperatures.The points represent the experimental data. Curves are calculated according to Eq.(5) using the Modified Apelblat equation

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:

(6)

wherex1is the solubility of DNTF,x2andx3stand for the initial molar fraction composition of ethanol and water in binary solvent mixtures when the solute is not added, (x1)2and (x1)3are the mole fraction solubility of DNTF in pure ethanol and water, respectively.Siis the model constant andNcan be 0, 1, 2 or 3[16]. For binary solvents system, substitutingN=2 andx3=1-x2into Eq.(6) can give a simplified equation as follows.

(7)

whereB0,B1,B2,B3, andB4are the model parameters. The model parameters values ofB0,B1,B2,B3,B4,R2and 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, theR2and 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.

Table 4 Model parameters,R2and RMSD of R-K equation

T/KB0B1B2B3B4R2103×RMSD298.15-22.316976.8816-157.8715152.8098-54.31250.99790.0558303.15-16.012637.6058-66.728962.5669-22.10210.99940.0351308.15-10.43329.1354-9.970612.6271-5.87620.99960.0348313.15-12.568623.6067-40.908740.7800-15.26290.99990.0173318.15-2.8862-28.340264.9447-53.556015.65840.99990.0338323.150.8744-47.9255105.8041-90.865228.11560.99980.0524328.152.7568-57.2875126.1851-110.193934.73440.99950.0698333.15-9.306412.4146-17.667018.8874-7.93271.00000.0259338.15-20.330376.2986-149.6736137.5824-47.27220.99950.1064

Fig.7 Mole fraction solubility of DNTF in binary system ethanol-water at various temperatures. The points represent the experimental data. Curves are calculated according to Eq.(7) using the R-K equation

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:

(8)

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

lnx1=A0+A1/T+A2lnT+A3x2+A4x2/T+A5(x2)2/T+

A6(x2)3/T+A7(x2)4/T+A8x2lnT

(9)

whereA0-A8are empirical model parameters, which can be obtained by least-squares analysis. The model parameters values ofA0-A8,R2and the RMSD are displayed in Table 5. The three three-dimensional diagram betweenx1andx2,Tis 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, theR2is 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.

Table 5 Parameters of the Jouyban-Acree model for the solubility of DNTF in binary solvent system of ethanol-water binary system

parametersvalueparametersvalueA0-227.6819A6-6594.1178A12858.2636A71615.9072A236.7655A83.9613A3-40.2101R20.9995A42884.4629103×RMSD0.1687A58472.7321

Fig.8 Experimental mole fraction solubility of DNTF in binary system ethanol-water. The points represent the experimental data, and the surface represents the results fitted by the Jouyban-Acree model

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]:

(10)

whereRrepresents the gas constant (8.3145 J·K-1·mol-1), ΔdisHΘand ΔdisSΘare the standard enthalpy of dissolution and standard entropy of dissolution of DNTF. Assuming the lnx1is dependent variable, 1/Tis independent variable, so the lnx1is linear relation with 1/Tand we can calculate the ΔdisHΘfrom the slope and ΔdisSΘfrom 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:

ΔdisGΘ=ΔdisHΘ-TΔdisSΘ

(11)

The relative contributions from enthalpy %ξHand entropy %ξSto the standard free Gibbs energy of the solution are define by the following two equations[20]:

(12)

(13)

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 theR2and 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.

Table 6 Standard enthalpy, entropy of the dissolution of DNTF in different solvents and the standard Gibbs free energy of solution at mean temperature (318.15 K)

x2ΔdisHΘ/kJ·mol-1ΔdisSΘ/J·K-1·mol-1ΔdisGΘmean/kJ·mol-1%ξH%ξSR21.000032.173166.668710.96240.60270.39730.99230.854440.188487.122912.47020.59180.40820.99280.735445.629099.314214.03220.59090.40910.99610.636350.5210110.301815.42850.59010.40990.99470.552650.8256107.802516.52820.59710.40290.99600.480852.4800109.726117.57060.60050.39950.9995

[1] ZHENG Wei, WANG Jiang-ning, Han Fang, et al. Chemical stability of CMDB propellants containing DNTF[J].ChinJExplosPropell, 2010, 33: 10-13.

[2] Zhou Yanshui, Wang Bozhou, Li Jiangkang, et al.Study on synthesis, characterization and properties of 3,4-Bis(4′-nitrofurazano-3′-yl)furoxan[J].ActaChimSinica, 2011, 69: 1673-1680.

[3] ZHOU Yan-shui,ZHANG Zhi-zhong,LI Jian-kang, et al. Crystal structure of 3, 4-dinitrofurazanofuroxan[J].ChinJExplosPropell, 2005, 28: 43-46.

[4] Sinditskii V P, Burzhava A V, Sheremetev A B, et al. Thermal and combustion properties of 3,4-bis(3-nitrofurazan-4-yl)furoxan(DNTF)[J].PropellExplosPyrot, 2012, 37: 575-580.

[5] WANG Qin-hui. Properties of DNTF-based melt-cast explosives[J].ChinJExplosPropell, 2003, 26: 57-59.

[6] Zhao Fengqi, Chen Pei, Hu Rongzu, et al. Thermochemical properties and non-isothermal decomposition reaction kinetics of 3,4-dinitrofurazanfuroxan(DNTF)[J].JHazardMater, 2004, 113: 67-71.

[7] Shi Xiaohua, Zhou Cairong, Gao Yuguo, et al. Measurement and correlation for solubility of (S)-(+)-2,2-dimethyl-cyclopropane carbox amide in different solvents[J].ChinJChemEng, 2006, 14: 547-550.

[8] Lan Guanchao, Wang Jianglong, Chen Lizhen, et al. Measurement and correlation of the solubility of 3,4-bis(3-nitrofurazan-4-yl)furoxan(DNTF) in different solvents[J].JChemThermodyn, 2015, 89: 264-269.

[9] Yu Chao, Zeng Zuoxiang, Xue Weilan. Measurement and correlation of the solubility of hexaquonickel(Ⅱ) bis(p-toluenesulfonate) in water + ethanol solvents within 288.15-333.15 K[J].IndEngChemRes, 2015, 54: 3961-3967.

[10] Jiang Linkun, Wang Lisheng, Du Chaojun, et al. Measurement and correlation of the solubilities of tetra(5,5-dimethyl-1,3-dioxaphosphorinanyl-2-oxy) neopentane in different pure solvents[J].FluidPhaseEquilib, 2014, 367: 117-124.

[11] Apelblat A, Manzurola E. Solubilities of manganese, cadmium, mercury and lead acetates in water fromT=278.15 K toT=340.15 K[J].JChemThermodyn, 2001, 33: 147-153.

[12] Zhou Li, Zhang Peipei, Yang Guangde, et al. Solubility of chrysin in ethanol and water mixtures[J].JChemEngData, 2014, 59: 2215-2220.

[13] Zhao Yan, Wang Yongli. Measurement and correlation of solubility of tetracycline hydrochloride in six organic solvents[J].JChemThermodyn, 2013, 57: 9-13.

[14] Liu Cheng, Tang Guiwei, Ding Hui, et al. Determination of the solubility and thermodynamic properties of wedelolactone in a binary solvent of ethanol and water[J].FluidPhaseEquilib, 2015, 385: 139-146.

[15] Yu Jing, Ma Tianle, Li An, et al. Solubility of disodium cytidine 5′-monophosphate in different binary mixtures from 288.15 K to 313.15 K[J].ThermochimActa, 2013, 565: 1-7.

[16] Chen Li-Zhen, Zhang Tian-Bei, Li Man, et al. Solubility of 2,2′,4,4′,6,6′-hexanitrostilbene in binary solvent of N,N-dimethylformamide and acetonitrile[J].JChemThermodyn, 2016, 95: 99-104.

[17] Jouyban A. Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures[J].JPharmPharmaceutSci, 2008, 11: 32-58.

[18] Wang Shui, Qin Liying, Zhou Zhimao, et al. Solubility and solution thermodynamics of betaine in different pure solvents and binary mixtures[J].JChemEngData, 2012, 57: 2128-2135.

[19] Wang Na, Fu Qiang, Yang Guangde. Determination of the solubility, dissolution enthalpy and entropy of icariin in water, ethanol, and methanol[J].FluidPhaseEquilib, 2012, 324: 41-43.

[20] Hu Yonghong, Liu Xiang, Yang Wenge, et al. Measurement and correlation of the solubility of 4-methylbenzoic acid in (methanol + acetic acid) binary solvent mixtures[J].JMolLiq, 2014, 193: 213-219.