Measurement and correlation of solubility of trimethylolethane in different pure solvents and binary mixtures☆

Xiangdong Li,Minqing Zhang,Jinli Zhang,Wenpeng Li,Wei Li*

Key Laboratory for Green Chemical Technology MOE,Collaborative Innovation Center of Chemical Science and Chemical Engineering(Tianjin),School of Chemical Engineering and Technology,Tianjin University,Tianjin 300350,China

1.Introduction

Trimethylolethane(C5H12O3,CAS registry No.77-85-0),a crystalline solid polyhydric alcohol with molar mass of 120.15 g·mol-1,is an important intermediate to synthesize resins,lubricants,plasticizers,stabilizers for plastics and new industrial explosive[1,2].In particular,the mixture of trimethylolethane and polyhydric alcohol is a promising high-density phase change material slurries used in the heat storage equipment[3].However,the small amount of impurities existed in trimethylolethane(TME)can make the performance of the following TME-associated product deteriorated greatly[4].

Extraction and crystallization are the popular industrial operation process to purify TME[5-7],which needs the solubility data of trimethylolethane in different solvents.In particular,the solubility in mixed solvents is fundamental to develop an effective technology manufacturing high-purity TME.So far,no experimental solubility data of TME in binary mixed solvents have been found in the open literature.

In this work,the solubility data of TME in some pure alcohol and acetate solvents,as well as those in the ethyl acetate-associated binary solvent mixtures were measured in the temperature range from 283.15 K to 318.15 K,with the gravimetric method.The experimental solubility data were then correlated by van't Hoff equation,modified Apelblat equation,λh Equation,Jouyban-Acree equation and CNIBS/R-K equation.To interpretthe solubility behavior of TME in the selected solvent,dissolution molar enthalpy change and entropy change were also calculated by van't Hoff equation.

2.Experimental

2.1.Materials

Trimethylolethane,as is shown in Fig.1,was purchased from Tianjin Xiensibiochemical technology co.,LTD,China.It was recrystallized twice in pure ethanol.The final mass fraction of TME measured by gaschromatography(SP-2100A Beifen-Ruili)was higher than 0.995.Methanol(mass fraction purity of 0.998),ethanol(mass fraction purity of 0.998),butanol(mass fraction purity of 0.995),ethyl acetate(mass fraction purity of 0.998)and methyl acetate(mass fraction purity of 0.998)were purchased from Tianjin Guangfu Fine Chemical Research Institute,China.The water used in all experiments was distilled three times.

Fig.1.Chemical structure of trimethylolethane.

2.2.Thermal analysis

The melting points and enthalpy of fusionΔHfusofTME were studied by a TGA/DSC simultaneous thermal analyzer(Model TGA/DSC,Mettler-Toledo,Switzerland)underthe protection of a flowing nitrogen atmosphere.The heating rate was 5 K·min-1.

2.3.X-ray power diffraction

X-ray powder diffraction spectrum of the sample was performed on XRD equipment(WRS-1B,Shanghai precision scientific instrument co.,LTD)with Cu Kαradiation(0.071073 nm)in the 2-theta range of 15°to 50°with scanning rate of 4(°)·min-1.PXRD patterns of TME used in the experiment are presented in Fig.2,which is in agreement with the standard pattern.

Fig.2.X-ray powder diffraction patterns of TME.

2.4.Solubility measurements

The solubility of TME in butanol,methyl acetate,ethyl acetate,methanol-ethyl acetate mixtures and ethanol-ethyl acetate mixtures was determined by gravimetric method[8-10]in the temperature ranging from 283.15 K to 318.15 K.The experimental apparatus contains a conical flask and a shaking table(Tianjin Ounuo Instrument Co.,LTD,China)with an uncertainty of±0.1 K.Before all the experiments,three mercury thermometers were put at different places in the shaking table to calibrate the temperature of thermostat within shaking table.At first,excessive amounts of dried TME were added into the solvents,then the equilibrium cell was heated to the desired temperature and was shaken for12 h,which was enough for the phase equilibrium.After that,another 12 h was taken to make sure that the excess solute settles down underthe same temperature.The equilibrium was verified by measuring the concentration value of supernate at different time intervals until the concentration reached the constant.Then the supernatant was transferred rapidly into the vial with a cover and was weighed immediately with an analytical balance(Startorius scientific instrument co.,LTD,Beijing)to obtain the total weight,then the vial containing the solution was dried carefully in an air oven(Beijing ever light medical equipment Co,LTD,China)and was weighed until reaching constant weight.All the measurements were repeated three times,the average values are reported.The mole fraction of TME in the corresponding solvent can be calculated by Eq.(1):

wherexArepresents the mole fraction solubility of TME at different solvents,m1andM1are the mass and molar mass of the solute,miandMi(i=2,…,N)the mass and molar mass of solvent,respectively.WhenN=2,itmeans the pure solvent,andN=3 representsthe binary solvent mixture.

2.5.Simulation methods

Density functional theory(DFT)calculations were carried out to disclose the reason that TME has different solubility in different individual solvent.All the calculations were performed with the Materials StudioDMol3 program from Accelrys[11].A double numerical plus polarization(DNP)basis set has been used to describe the valence orbital of the O,C and H atoms.

The accuracy of the DNP basis set has been analyzed in detail by Delley.The nonlocal exchange and correlation energies were calculated with the Becke-Lee-Yang-Parr(BLYP)functional of the generalized gradient approximation(GGA)[12].The convergence criteria consisted of threshold values of 1 × 10-5Eh(1 Eh=2625.5 kJ·mol-1),0.02Eh·nm-1,and 0.05 nm for energy,force,and displacement convergence,respectively,whereas a self-consistent- field(SCF)density convergence threshold value of 1 × 10-6Eh(1 Eh=2625.5 kJ·mol-1)was specified.A Fermi smearing of 0.005 Eh(1 Eh=2625.5 kJ·mol-1)was used to improve computational performance,and the solvent effect was also considered during the calculations.The geometries of all stationary points were fully optimized at this level.The interaction energy was defined as

whereETME,EsolventandETME-solventwere the energy ofTME,solvent,total energy of TME with solvent,respectively.

3.Results and Discussion

3.1.Thermal analysis

The melting point(Tm)and the molar enthalpy change(ΔHfus)are important thermodynamic properties,and they are also necessary information for some models.

ATGA/DSC thermogram of TME is shown in Fig.3.The first endothermic peak in Fig.3 denotes that trimethylolethane undergoes a solidsolid phase transition,which is attributed to the breakage of some hydrogen bonds among the molecules[13].The melting point(Tm)of TME is 473.06 K,which can be determined by the second small endothermic peak.The values reported in previous literatures are in the range of(471.15 K to 476.15 K)[14-17].So the result is in accordance with previous findings.

Fig.3.Thermal analysis(DSC/TG)of TME.

Moreover,as is shown in Fig.3,sublimation of TME began before it melted,which revealed that the determined fusion enthalpy of TME contained evaporation heat,and the conventional calorimetric test could notbe used to measure the fusion enthalpy of TME.To circumvent this problem,a semi empirical equation was applied to estimate the fusion entropy of TME(ΔSfus)[18]:

whereCis the entropy of melting constant,the average value ofCis close to 50 J·mol-1·K-1.σ and φ represent the molecular symmetry numberand molecular flexibility number,respectively.SP3 isthe number of sp3chain atoms,SP2 the number of sp2chain atoms,andRINGthe number of fused-ring systems.Ris the gas constant.

Then the fusion enthalpy can be calculated by the following equation:

The estimated molar enthalpy of fusion(ΔHfus)of TME is 29.83 kJ·mol-1.According to literature[19],the average error of the estimated values of ΔSfusis 12.5 J·mol-1·K-1.

3.2.Solubility data

The solubility values of TME from 283.15 K to 328.15 K in the selected solvents are listed in Tables 1,2,3 and graphically plotted in Figs.4-7.

It can be observed from Fig.3.that the solubility of TME increases with the increase of temperature,and the order of the solubility of TME is butanol＞methyl acetate＞ethyl acetate at a given high temperature.The polarity order of these solvents is methyl acetate＞ethyl acetate＞butanol[20],and the results show that the solubility is high in the strong polar solvents.However,the solubility of TME does not increase along with the solvent polarity,and the solubility is relatively high in butanol than in esters,attributing to the easy formation of hydrogen bonds between TME and butanol molecules,which is confirmed by the molecular modeling results(Fig.5 and Table 4).DFT calculations were performed to disclose the potentialinteractions between TME and different solvent molecules,including methanol,ethanol,butanol and ethyl acetate.As is shown in Fig.5 and Table 4,TME molecule interacts with methanol or ethanol to form hydrogen bonding between the oxygen atoms alcohol molecules and hydrogen atoms of TME,with the interaction energy of-23.69 kJ·mol-1and-20.33 kJ·mol-1,respectively.For the butanol,there appear two hydrogen bonds between TME and butanol,and the interaction energy is-9.51 kJ·mol-1.In the case of the solvent methyl acetate,the atom O of methyl acetate can form hydrogen bond with atom H of TME with the interaction energy is-1.59 kJ·mol-1.The larger the energy value ofEinteris,the stronger interactions occur between TME and the solvent molecules.It is the stronger hydrogen bonds between alcohols and TME that results in the higher solubility of TME in alcohols.

Table 1Experimental(x exp)and calculated(x cal)mole fraction solubility of TME in mono-solvents from 283.15 K to 318.15 K under 101 kPa

For the binary solvent mixtures,the solubility of TME also increases with the increasing temperature at the constant solvent composition.Besides,it also increases with the increasing of proportion of methanol or ethanol at a given temperature,as is shown in Tables 2 and 3.

3.3.Data correlation

3.3.1.In pure solvents

The quantitative relation between temperature and solubility of TME in each solvent can be correlated by the following thermodynamic models.

3.3.1.1.Van't Hoff equation.The relationship between the molar fraction solubility data and temperature for a real solution can be associated with the van't Hoff equation,which is formulated as follows:

Table 2Experimental and calculated mole fraction solubility of TME in methanol(x a)-ethyl acetate binary solvents from 283.15 K to 318.15 K under 101 kPa

where ΔHdand ΔSdare the dissolution enthalpy and entropy respectively,andRis for gas constant.The above equation can be written as Eq.(6)when the dissolution enthalpy and entropy were considered to be independent of temperature in the lower temperature range[21]:

wherexis the molar fraction solubility of TME,Tis the corresponding temperature,andAandBare constant parameters regressed with the linear solubility curve ofln x versus1/T.

3.3.1.2.Modified Apelblat Equation.The solubility data was correlated by the Modified Apelblat equation,a commonly used semi-empirical model as[22]:

Table 3Experimental and calculated mole fraction solubility of TME in ethanol(xb)-ethyl acetate binary solvents from 283.15 K to 318.15 K under 101 kPa

whereTis the absolute temperature,andA,BandCare the model parameters fitted by the experimental solubility data.

3.3.1.3.λh Equation.The λhequation was initially proposed by Buchowski to reflect the solubility behavior of the solute in solution.It's also a semi-empirical equation as[23]:

whereTmis the melting temperature of Kelvin,and λ(representing the no ideality of solution system)andh(representing the enthalpy of solution)are the two adjustable parameters given from the solubility data.

Fig.4.Experimental and correlated mole fraction solubility of TME in mono-solvents:▲,butanol;●,methyl acetate;▼,ethyl acetate.The solid lines are fitted curves with the modified Apelblat equation.

3.3.2.In binary solvent mixtures

The quantitative relation between temperature and solubility of TME in binary solventmixtures can be correlated by the following thermodynamic models.

3.3.2.1.CNIBS/R-K Model.The CNIBS/R-K model is defined as[24]:

wherexis the mole fraction solubility of the solute,xA0andxB0are the initial mole fraction of methanol and ethyl acetate,andxAandxBrepresent the mole fraction solubility of the solute in pure solvents,respectively.Siis the model constant.

Fig.6.Mole fraction solubility of TME in binary solvents methanol-ethyl acetate at different molar fraction of methanol(x a):■,x a=0.1739;●,x a=0.2849;▼,x a=0.4949;◇,x a=0.7133;□,x a=0.8524.—,calculated by the modified Apelblat equation.

can be replaced by(1-),then Eq.(10)can be simplified as following:

whereB0,B1,B2,B3andB4are the model parameters which could be obtained by least-squares regression.

3.3.2.2.Jouyban-Acree Model.This is a versatile model to describe the effect of both temperature and solvent composition on the solubility data,the model for representing the solubility of a solute in a binary mixtures[25]:

Fig.5.Interactions between TME and methanol(a),ethanol(b),butanol(c),ethyl acetate(d),respectively.

Fig.7.Experimental and correlated mole fraction solubility of TME in binary solvents ethanol-ethyl acetate at different molar fraction of ethanol(x b):■,x b=0.1025;▲,x b=0.2968;▼,x b=0.4950;◆,x b=0.6979;●,x b=0.8976.—,calculated by the modified Apelblat equation.

Table 4The sum of interaction energy between TME and solvent molecules

Table 5λh correlation parameters of TME in mono-solvents

whereJiis a model constant,andxAandxBrepresent the initial mole fraction composition of the binary solvents when the solute was not added.TheXAandXBrepresent the saturated mole solubility of TME in methanol and ethyl acetate respectively.WhenN=2 and substituting(1-xA)forxBin Eq.(12),subsequent rearrangements result in Eq.(13).

Substituting the modified Apelblat equation into Eq.(13),equation can be expressed as follows:

Eq.(14)can be further simplified as follows after introducing a constant term:

whereA0,A1,A2,A3,A4,A5,A6,A7,andA8are parameters of this model.

All the parameters of above models are shown in Tables 5-8.

The average relative deviation(RAD),and the root-mean-square deviations(RMSD)are defined as in the following formula to evaluate the accuracy of the model[26].

Table 6van't Hoff and Modified Apelblat correlation parameters in mono-solvents and binary solvents

Table 7CNIBS/R-K model correlation parameters in methanol ethyl acetate and ethanol-ethyl acetate binary solvents

Table 8Modified Jouyban-Acree model correlation parameters in methanol-ethyl acetate and ethanol-ethyl acetatebinary solvents

whereNrepresents the number of experimental points,andx1andstand for the values of solubility measured and calculated,respectively.

The results show that the Modified Apelblat Equation gives the best fitting results of the solubility data of TME in the pure solvents,while the CNIBS/R-Kmodel fits the solubility data of TME in the binary solvent mixtures well.

3.4.Thermodynamic properties of the dissolution process.

According to the thermodynamic principles,the thermodynamic properties of the molar enthalpy(ΔHd)and the molar entropy(ΔSd)of the dissolution process were calculated from the van't Hoff equation[27].

The lnx vs1/Tplots are shown in Figs.8,9 and 10.We can observe that the solubility data has a linear relationship with the reciprocal of temperature.The molar enthalpy(ΔHd)and the molar entropy(ΔSd)were determined from the slope and intercept of lnx vs1/T.

The thermodynamic properties estimated by above-mentioned equation are given in Table 9.It can be seen that the dissolving process of TME in all solvents are endothermic since ΔHdof the dissolution process is positive,which declares the solubility of TME increases with increasing temperature.These results are very useful for optimizing the dissolution and crystallization of TME.

Fig.8.The van't Hoff plot of logarithm molar fraction solubility(ln x)of TME vs(1/T)in three pure solvents.(■)butanol;(●)methyl acetate;(▲)ethyl acetate.

Fig.9.The van't Hoff plot of logarithm molar fraction solubility(ln x)of TME vs(1/T)in binary solvents methanol-ethyl acetate at different molar fraction of methanol(x a).◆,x a=0.1739;▼,x a=0.2849;▲,x a=0.4949;●,x a=0.7133;■,x a=0.8524.

4.Conclusions

The solubility of TME in selected organic solvents is determined by the gravimetric method under atmosphere pressure and the temperature ranging from 283.15 K to 318.15 K.The experiment values are correlated by Van't Hoff equation,Modified Apelblat Equation,λhEquation,CNIBS/R-K Equation,and Jouyban-Acree Model.The Modified Apelblat Equation gives the best fitting results of the solubility data of TME in the pure solvents while the CNIBS/R-K model fits the solubility data of TME in the binary solvent mixtures well.The thermodynamic properties of the dissolution process are calculated and the results show that the dissolution process is endothermic.The experiment values in this study can be used for the purification process of TME in industry.

Nomenclature

A,B,Csemi empirical constants

A0-A8semi empirical constants

B0-B4semi empirical constants

ETMEthe energy of TME

ETME-solventthe total energy of TME with solvent

Esolventthe energy of solvent

henthalpy of solution,kJ·mol-1

M1,M2,M3molecular weights of solute,methanol and ethyl acetate,respectively,g·mol-1

m0,m1,m1mass of solute,methanol and ethyl acetate,respectively,g

nnumber of experimental data points

Rgas constant,8.314 J mol-1·K-1

RAD average relative deviation

RMSD root-mean-square deviations

Tabsolute temperature,K

Tmmelting point,K

xAmole fraction of solute

xexpexperimental values

ΔHfusenthalpy of fusion,kJ·mol-1

ΔSfusentropy of fusion,kJ·mol-1·K-1

ΔHddissolution enthalpy,kJ·mol-1

λ no ideality of solution system

Fig.10.The van't Hoff plot of logarithm molar fraction solubility(ln x)of TME vs(1/T)in binary solvents ethanol-ethyl acetate at different molar fraction of ethanol(x b).◆,x b=0.1025;▼,x b=0.2968;▲,x b=0.4950;●,x b=0.6979;■,x b=0.8976.

Table 9Standard dissolution enthalpy of TME in individual liquid and methanol-ethyl acetate,ethanol-ethyl acetate binary solvents the temperature ranging from T=283.15 K to 318.15 K under 101 kPa

[1]J.S.Pan,W.B.Jia,X.Q.Zhang,et al.,Synthesis technology of trimethylolethane,Appl.Chem.Ind.38(2009)465-468.

[2]H.Suzuki,N.Wada,Y.Komoda,H.Usui,S.Ujiie,Drag reduction characteristics of trimethylolethane hydrate slurries treated with surfactants,Int.J.Refrig.32(2009)931-937.

[3]W.Wu,Y.F.Chen,X.Shi,S.C.Zhang,H.R.Sun,Preparation and properties of polyalcohol phase change material for insulation,Key Eng.Mater.512-515(2012)936-939.

[4]M.O.Robeson,Continuous production of trimethylolethane,US Pat.,2790837(1957).

[5]P.E.Eckler,Crystallization-inhibited trimethylolethane solutions,US Pat.,4709104(1987).

[6]S.D.A.Lorenzo,Recovering trimethylolethane by ethyl acetate extraction,US Pat.,2806892(1957).

[7]X.Z.Shao,W.W.Chen,W.Liu,H.T.Yun,Measurement and correlation of trimethylolethane solubility in different solvents,J.Chem.Eng.Chin.Univ.30(2016)967-970(in Chinese).

[8]N.N.Tian,L.S.Wang,M.Y.Li,Y.Li,R.Y.Jiang,Solubilities of phenylphosphinic acid,methylphenylphosphinic acid,hexachlorocyclotriphosphazene,and hexaphenoxycyclotriphosphazene in selected solvents,J.Chem.Eng.Data56(2011)661-670.

[9]D.Mealey,M.Sv?rd,?.C.Rasmuson,Thermodynamics of risperidone and solubility in pure organic solvents,Fluid Phase Equilib.375(2014)73-79.

[10]H.Wu,L.Dang,H.Wei,Solid-liquid phase equilibrium of nicotinamide in different pure solvents:measurements and thermodynamic modeling,Ind.Eng.Chem.Res.53(2014)1707-1711.

[11]B.Delley,An all-electron numerical method for solving the local density functional for polyatomic molecules,J.Chem.Phys.92(1990)508-517.

[12]C.Lee,W.Yang,R.G.Parr,Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,Phys.Rev.B Condens.Matter37(1988)785-789.

[13]K.Suenaga,T.Matsuo,H.Suga,Heat capacity and phase transition of trimethylolethane,Thermochim.Acta163(1990)263-270.

[14]W.E.Doering,The acidity of bridgehead α-hydrogen in a bicyclic trisulfone,J.Am.Chem.Soc.77(1955)509-513.

[15]S.Olsen,A relationship between the tollens reaction and the formaldehyde-olefin reaction.The reaction of formaldehyde with propionaldehyde and cyclohexanone,Acta Chem.Scand.7(1953)1364-1369.

[16]R.Colson,Nitropentaglycerin eventual substitute for nitroglycerin continuous preparation and properties,Mem.Poudres30(1948)43-58.

[17]N.S.Marans,Nitrate esters of 2,2-dimethylol-1-propanol monoacetate and diacetate,J.Am.Chem.Soc.76(1954)3223-3224.

[18]J.Akash,S.H.Yalkowsky,Estimation of melting points of organic compounds-II,Ind.Eng.Chem.Res.95(2006)2562-2618.

[19]R.M.Dannenfelser,S.H.Yalkowsky,Estimation of entropy of melting from molecular structure:A non-group contribution method,Ind.Eng.Chem.Res.35(1996)1483-1486.

[20]W.Yang,S.Fan,Q.Guo,J.Hao,H.Li,S.Yang,W.Zhao,J.Zhang,Y.Hu,Thermodynamic models for determination of the solubility of 4-(4-aminophenyl)-3-morpholinone in different pure solvents and(1,4-dioxane+ethyl acetate)binary mixtures with temperatures from(278.15 to 333.15)K,J.Chem.Thermodyn.97(2016)214-220.

[21]J.P.Fan,X.K.Xu,G.L.Shen,X.H.Zhang,Measurement and correlation of the solubility of genistin in eleven organic solvents fromT=(283.2 to 323.2)K,J.Chem.Thermodyn.89(2015)142-147.

[22]W.G.Yang,S.M.Fan,Q.R.Guo,J.F.Hao,H.J.Li,S.H.Yang,W.D.Zhao,J.Zhang,Y.H.Hu,Thermodynamic models for determination of the solubility of 4-(4-aminophenyl)-3-morpholinone in different pure solvents and(1,4-dioxane+ethyl acetate)binary mixtures with temperatures from(278.15 to 333.15)K,J.Chem.Thermodyn.97(2016)214-220.

[23]S.Wang,Y.Y.Zhang,J.D.Wang,Solubility measurement and modeling for betaine in different pure solvents,J.Chem.Eng.Data59(2014)2511-2516.

[24]T.T.Wei,C.Wang,S.C.Du,S.G.Wu,J.Y.Li,J.B.Gong,Measurement and correlation of the solubility of penicillin v potassium in ethanol plus water and 1-butyl alcohol plus water systems,J.Chem.Eng.Data60(2015)112-117.

[25]J.P.Fan,B.Zheng,D.D.Liao,J.X.Yu,Y.H.Cao,X.H.Zhang,J.H.Zhu,Determination and modeling of the solubility of(limonin in methanol or acetone+water)binary solvent mixtures atT=283.2 K to 318.2 K,J.Chem.Thermodyn.98(2016)353-360.

[26]C.Guo,L.Li,J.Cheng,J.Zhang,W.Li,Solubility of caprolactam in different organic solvents,Fluid Phase Equilib.319(2012)9-15.

[27]S.D.Zheng,Y.Han,J.L.Zhang,et al.,Determination and correlation of solubility of linezolid form II in different pure and binary solvents[J],Fluid Phase Equilib.432(2017)18-27.