Lizhen Chen*,Liang Song,Yupeng Gao,Aipeng Zhu,Duanlin Cao

School of Chemical Engineering and Environment,North University of China,Taiyuan 030051,China

1.Introduction

2,2′,4,4′,6,6′-Hexanitrostilbene(HNS,Fig.1)is one of the prominent heat resistant explosives used in high performance explosive compositions fordemolitions,warheads,and othercharges.Itdemonstrates outstanding resistance to shock,percussion,heat,and friction.It has excellent thermal stability,making it well suitable for missile warheads or components,artillery shells,rockets,and high velocity explosive projectiles.HNS is also widely used in warheads for air-to-ground missiles,air-to-air missiles,and cruise missiles[1-3].

Solution crystallization is the primary method to obtain the HNS crystal of high quality.For the purpose of studying the crystallization process of HNS it's necessary to measure the solubility and supersolubility of HNS in different solvents.Solubility can affect the capacity of the crystallization process,as well as the ability to reject impurities and minimize loss in the mother liquor.To optimize crystallization process and design crystallizer,itis necessary to know the solubility of HNS in common solvents.Supersolubility curve,which is an important curve for crystallization process,is a boundary line of the metastable zone and the labile zone.But,few experimental solubility data of HNS have been reported.Therefore,in this work,the solubilities and supersolubilities of HNS inN,N-dimethylformamide(DMF),dimethyl sulfoxide(DMSO),acetonitrile(ACN),N-methyl-2-pyrrolidone(NMP)and 1,4-butyrolactone(GBL)from(298.15 to 338.15)K were measured.The solubility curve,supersolubility curve and the metastable zone were obtained from this study.On the basis,the dissolution enthalpy,dissolution entropy and the Gibbs energy of HNS were calculated.

As we know,methods of measuring the solubility of a solid in a liquid mixture can be classified as dynamic method and balancing method.Compared with the balancing method,the dynamic method is much faster and more readily.The dynamic method involves weighing or measuring the individual components to obtain a system with a known composition,determining the state in which the solid phase just disappears.The disappearance of the solid phase can be achieved either by a change in the temperature or by the addition of a known amount of solvent[4,5].In this work,the last solid disappearance method was used to determine the solubility;the disappearance of the solid phase is carried out by adding solvent at constant temperature.The disappearance of the solid phase was determined by the laser monitor technique.

2.Experimental

2.1.Materials

Yellow crystals HNS(C14H6N6O12)obtained from Gansu Yinguang Chemical Industry Group Co.Ltd.China,its mass fraction purity,determined by HPLC,was better than 99.5%.It was driedin vacuoat 333.15 K for 24 h and stored in a desiccator.The melting point and fusion enthalpy of HNS were determined by differential scanning calorimetry(DSC 200F3,NETZSCH,Germany)with a heating rate of 10 K·min-1with out protection of nitrogen.From the result of DSC analysis of HNS,as shown in Fig.2,the melting pointwas317°C±0.5°Cand the enthalpy of fusion of HNS was 115.50 J·g-1.The DMF,DMSO,ACN,NMP and GBL of analytical reagent grade were purchased from local reagent factory without further purification whose mass fraction purity was no less than 0.995.The detailed information of reagents used in this experiment was listed in Table 1.

Fig.1.Chemical structure of HNS.

Fig.2.DSC analysis of HNS.

2.2.Solubility measurement

A laser monitor system was used to determine the solubility of the solute in the solvent at a preconcerted temperature.The system consisted of a laser generator,a photoelectric transformer,and a light intensity display device.The solubility measurement apparatus also involves a jacketed glass vessel with water circulated from a water bath with a thermoelectric controller(type SYP,China).The jacket temperature was controlled to be constant( fluctuating within 0.05 K).Continuous stirring was achieved with a magnetic stirring bar.A condenser was connected with the vessel to prevent the solvents from evaporating.A glass thermometer was used for measurement of the temperature(uncertainty of 0.05 K).An analytical balance(Metler Toledo AL104,Switzerland)with an accuracy of 0.0001 g was used during the measurements.

Solvent of known mass and excess masses of HNS were placed in the jacketed vessel.The contents of the vessel were stirred continuously ata constant temperature,and the solvent was added to the vessel in batches with the interval between additions of 30 min.The additional solvent of known mass was about 50 mg for each batch.When the last portion of solute just disappeared,the intensity of the laser beam penetrating the vessel reached the maximum,and the solvent mass consumed in the measurement was recorded.

Together with the mass of the solute,the solubility can be obtained.The saturated solution mole fraction solubility(xA)of the solute(A)in solvent(B)can be obtained as follows:

in whichmAandmBrepresent the mass of solute and solvent,respectively.MAandMBare the molecular weight of solute and solvent,respectively.The same solubility experiments were carried out three times.The uncertainty of the experimental solubility was about 0.05.

2.3.Super solubility measurement

The super solubility curve is a cluster of curves which are influenced by the operating conditions such as cooling rate,stirring rate and impurities.Thus it's necessary to make sure that the operation conditions are the same when measuring the super solubility.In this study,the volume of solvent maintains a constant 50 ml changing the mass of the HNS under different temperatures to ensure that the condition of the solution was the same when measuring the super solubility.

The HNS solution of known concentration was prepared in the dissolution cell.And then the solution was cooled under 0.2 °C·min-1cooling rate and 300 r·min-1stirring rate.Since the solubility of HNS decreases with the temperature decreasing,when the temperature decreasing to an appropriate value the HNS would crystallize from the solution.With the appearance of the HNS particles which could reflectand scatter the laser beam,so the intensity of the laser reached the photoelectric switch is weaked,result in the value of the digital display is low.When the display of the digital display decreased,record the temperature which is the super solubility temperature.

3.Results and Discussion

3.1.Solubility and super solubility data of HNS

The solubility and super solubility data of HNS in solvent DMF,DMSO,ACN,NMP and GBL are listed in Table 2.

3.2.Metastable zone width

The solubility and super solubility curves together with corresponding metastable zone of HNS in different solvents are depicted in Fig.3.Combining the data in Table 2 and Fig.3,it could be found that the solubility and super solubility of HNS increased as the temperature increased.The solubility order of HNS is NMP＞DMSO＞DMF＞GBL＞ACN.In order toobtain high quality crystal crystallization operation should be carried in the metastable zone.Thus,the metastable zone width is primary for the crystallization process.The metastable zone width of HNS in DMF,ACN,GBL and NMP decreases with the increasing temperature,while,in DMSO it increases with the increasing temperature.The solubilities of HNS in DMF didn't appear to be much different from that of DMSO,however,the super solubility shows large difference between them.The metastable zone width of HNS in NMP is much wider than in other solvents,which makes the crystallization condition much easier to maintain in the metastable zone.

Table 1Provenance and mass fraction purity of materials studied

Table 2Experimental mole fraction solubility values xi and super solubility values x s i of HNS in different solvents at temperature T and pressure p=0.1 MPa①

Fig.3.Solubility,super solubility curves and metastable zones of HNS in different solvents:■,DMF;●,DMSO;▲,ACN;▼,NMP;?,GBL,where the symbols of solid represent the solubility and the hollow symbols stand for the super solubility.

3.3.Correlation of the experimental solubility data

In order to estimate the solubility in pure and binary solvent mixtures,various cosolvency models were used.These models enable us to predict and calculate the suitable solvent composition needed to make an acceptable formulation of the solute.Some of these models are theoretical,excess free energy(EFE)[6],CNIBS/R-K[7],and general single model(GSM)[8,9],while others are semi-empirical,the extended Hildebrand approach(EHA)[8],or empirical,mixture response surface(MR-S)[10],linear double log-log(LDL-L)[11],λhequation[12]and double log-log(DL-L)[7].Among these,the van't Hoff model,modified Apelblat equation[13,14]and λhequation were mainly available in pure solvent.

Root-mean-square deviation(RMSD)[15,16]of every solvent is used to evaluate the fitting results of each correlation equation.The RMSD is defined as:

wherenis the totalnumber of experimentalpoints,xiis the experimental data,andxciis the calculated values.

3.3.1.Correlation with theλh equation

The λhequation which is derived firstly by Buchowskiet al.is another empirical formula describing the solution behavior.It can be used to fit the experimental solubility data for many systems with only two parameters(λ andh).And the equation is given as follows:

whereTmis the normal melting temperature,λ andhare the model parameters obtained from the experimental solubility data in the systems and listed in Table 3.The fitting curves of λhequation are depicted in Fig.4.

3.3.2.Correlation with the NRTL model

Considering the solid-liquid equilibrium for the system solid HNS/pure solvent,the solubility(x1)of HNS at different temperatures can be expressed by the following equation[17]:

Table 3Model parameters,R2 and RMSD of λh equation

Fig.4.The mole fraction solubility of HNS in different solvents correlated by the λh equation:■,DMF;●,DMSO;▲,ACN;▼,NMP;?,GBL.

where γ1is the activity coefficient of HNS,x1is the mole fraction solubility,Tmrepresents the melting temperature,ΔHmrefers to the fusion enthalpy at the melting temperature,andΔCpis the heatcapacity difference.Generally,the second term of Eq.(5)can be neglected due to its very small value.Thus,Eq.(5)can be transformed as:

where the values of ΔHmandTmof HNS have been determined before the correlation,which were shown in Fig.2.After that a well established activity coefficient model was employed to calculate the activity coefficient of solute in this work:NRTL model[18,19],which was described in detail for the first time by Renon and Prausnitz who showed its application to a wide variety of mixtures for calculation of(vapor+liquid)and(liquid+liquid)equilibrium.This model is based on the molecular local composition concept which is expressed as follows:

where τ12,τ21,G12andG21can be calculated as follows:

where Δg12=g12-g22and Δg21=g21-g11represent the cross interaction energy,and α is the parameter that reflects the non randomness in the mixture.All the adjustable parameters can be regressed from the experimental solubility data.The Δg12,Δg21,α,R2together with RMSD are given in Table 4 and the fitting curves of NRTL model are depicted in Fig.5.

Fig.5.The mole fraction solubility of HNS in different solvents correlated by the NRTL model:■,DMF;●,DMSO;▲,ACN;▼,NMP;?,GBL.

3.3.3.Correlation with the modified Apelblat equation

The modified Apelblat equation deduced from the Clausius-Clapeyron equation is a semiempirical equation,which can describe the solid-liquid equilibrium precisely.The equation can be expressed as:

whereA,B,andCare the model parameters.The values ofA,B,C,R2and RMSD are listed in Table 5.The relationship between lnxand 1/T,lnTis graphically illustrated in Fig.6,which is drawn according to the values got by the experiment.From Fig.6 we can conclude that the lnxis a linear relationship with 1/Tand lnT.

Table 5Model parameters,R2 and RMSD of modified Apelblat equation

3.3.4.Evaluation of thermodynamic models

As depicted above,four models were used to fit the experimental data.But it is hard to tell which one is the best just fromR2and RMSDvalues.Forthisreason,the Akaike's Information Criterion(AIC)[20]was introduced to evaluate the relative quality of these models.Generally,the best model is considered as the one with minimum AIC value which is defined as follows:

Table 4Adjustable parameters(Δg12,Δg21,α)of the NRTL model together their R2 and RMSD

Fig.6.The mole fraction solubility of HNS in different solvents correlated by the modified Apelblat equation:■,DMF;●,DMSO;▲,ACN;▼,NMP;?,GBL.

where κ stands for the number of model parameters andLis the maximized value of the likelihood function.Provided that the variance of model errors is unknown but equal for all models,Eq.(12)becomes:

wherenrefers to the number of experimental points,and RSS is the estimated residual of correlated models which is defined as follows:

In this study,when the constantnandnln(2π)are left out Eq.(13)can be simplified as:

The calculated results of AIC values for all models are listed in Table 6.As shown in Table 6,the values of AIC of the Apelblat equation in DMF,NMP is much lower than the other three models which means that the Apelblat equation would be the best model to correlate the experimental solubility data in the DMF and NMP.And the NRTL model would be the best model to correlate the experimental solubility datain DMSO,ACN and GBL,in that,the values of AIC of the NRTL model in DMSO,ACN and GBL are lowest of the four correlation equations.

Table 6The calculated values of AIC values for all models

3.4.Thermodynamic properties of solutions

When the solubility of HNS in different solvents is confirmed,some thermodynamic properties such as the dissolution enthalpy,dissolution entropy and the Gibbs energy can be calculated.According to van't Hoff analysis,the apparent enthalpy change of solution could be related to the temperature and the solubility as the following equation[21]:

Over a limited temperature interval(298.15-338.15 K)the heat capacity change of solution may be assumed to be constant.Hence,the values ofHs would be valid for the mean temperature(318.15 K).Thus,combined with the Apelblat model the ΔdisH,ΔdisS,and ΔdisGcan be calculated by the following equation,respectively[22]

The ξHand ξS,which represent the comparison of the relative contribution to the standard Gibbs energy by enthalpy and entropy in the solution process respectively[22],are defined by the following two equations[15,23]:

The calculated dissolution enthalpy,entropy,and Gibbs energy change together with ξHand ξScalculated by the experimental values are shown in Table 7.It can be seen that the values of ΔdisH°are positive in all selected solvents,indicating that the dissolution of HNS is an endothermic process.What's more,the ξHis greater than ξSin every solvent,illustrating that the main contributor to the standard molar Gibbs energy of dissolution is the enthalpy rather than entropy.

Table 7The calculated values of dissolution enthalpy,entropy,and Gibbs energy at mean temperature(318.15 K)

4.Conclusions

The solubility,super solubility and metastable zone of HNS in solvent DMF,DMSO,ACN,NMP and GBL were determined by the dynamic method.The metastable zone width of HNS in DMF,ACN,GBL and NMP decreases with the increasing temperature,while,in DMSO it increases with the increasing temperature.Four correlation equations all can be used to fit the solubility values of HNS in different solvents,while the modified Apelblat equation is the best model to correlate the experimental solubility data in the DMF and NMP,and the NRTL model is the best model to correlate the experimental solubility data in DMSO,ACN and GBL.The dissolution enthalpy,dissolution entropy and the Gibbs energy were calculated by the experimental solubility data,and from the dissolution enthalpy calculated from this experiment we conclude that the dissolution of HNS is an endothermic process.

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