Yixin Ma ,Kang Ma ,Huixin Wang ,Xueli Geng ,Jun Gao ,Zhaoyou Zhu ,Yinglong Wang ,*

1 College of Chemical and Environmental Engineering,Shandong University of Science and Technology,Qingdao 266590,China

2 College of Chemical Engineering,Qingdao University of Science and Technology,Qingdao 266042,China

3 National Registration Center for Chemicals,SINOPECResearch Institute of Safety Engineering,Qingdao 266071,China

Keywords:QSPR Azeotropic temperature Azeotropic composition Genetic function approximation Binary azeotropes

A B ST R A C T Binary azeotropes,which contain two chemicals with a relative volatility of 1,are very common in the chemical industry.Understanding azeotropes is essential for effectively separating binary azeotropes containing lower alcohols.Experimental techniques and ab initio approaches can produce accurate results;how ever,these two processes are time consuming and labor intensive.Although thermodynamic equations such as UNIFACare w idely used,experimental valuesare required,and it isdif fi cult to choose the best groupsto represent a complex system.Because of their high ef fi ciency and fast calculation speed,quantitative structure-property relationship(QSPR)tools w ere used in this w ork to predict the azeotropic temperatures and compositions of binary azeotropes containing low er alcohols.The QSPRmodels for 64 binary azeotropes based on centroid approximation and weighted-contribution-factor approximation w ere established using the genetic function approximation(GFA)procedure in Materials Studio software,and a leave-one-out cross-validation procedure was conducted.External tests of an additional 16 azeotropes w ere also investigated,and high determination coef fi cient values w ere obtained.The best QSPRmodels w ere explained in terms of the molecular structure of the azeotropes,and good predictive ability w as obtained w ithin acceptable prediction error levels.

1.Introduction

Binary azeotropes cannot be separated using ordinary distillation because their formation in the chemical industry changes the product distribution and restricts separation.Some special distillation methods have been used for separating binary azeotropes,such as azeotropic distillation[1-3],extractive distillation[4-6],and pressure sw ing distillation[7-10].Azeotropic dataincluding theazeotropic temperatureand composition are essential in the design of these distillation processes,and understanding azeotropic phenomena can reduce the economic and time costs for selecting proper agents w hen designing these processes.Experimental and theoretical methods containing thermodynamic equations and equations of state have been used to understand binary azeotropes.For example,Gmehling and Bolts measured 273 binary azeotropic and azeotropic systems using a w ire band column[11].Martínez et al.obtained data on the vapor liquid equilibrium(VLE)of binary azeotropes of 2-butanone+ethanol/2-propanol at different pressuresand found that pressureswingdistillation wasuseful because the azeotropic compositions w ere sensitive to pressure[12].How ever,experimental methods incur many economic and time costs.

The UNIFAC thermodynamic equation has been w idely used for predicting azeotropic temperatures and compositions[13,14].Equations of state either using van der Waals equations or modi fi cations can also beused to predict the propertiesof mixtures[15-17].How ever,a few of the parametersin such equationsof state have to be measured or estimated,and sometimes,the fi tting parametersused are not appropriate for some compounds.The conductor-like screening model for real solvents(COSMOS-RS),w hich isbased on quantum chemical calculations,hasalso been used to predict the propertiesof mixtures[18,19].Despite its accurate prediction ability for the liquid-liquid equilibrium(LLE)of some mixtures,COSMOS-RSsometimes cannot predict the VLEaccurately,even for some simple organic mixtures[20].In addition,many scholars have conducted studies to develop models w ith direct molecular dynamics(MD)/Monte Carlo simulation techniques.Zhu and Elcock reported the results of MD simulations for examining the association of acetate-methyl ammonium and methane-methane pairs at 11 different temperatures from-12.5 °Cto 112.5 °C,and the simulations w ere performed using tw o popular w ater models(TIP3P and TIP5P)w ith a total simulation time of 22μs[21].Punnathanam and Monson presented calculations of the nucleation barrier during crystallization for binary hard sphere mixturesunder moderate degrees of supercooling using the Monte Carlo simulation technique[22].These studiespromoted the development of molecular simulation techniques.However,somemethodsare often time consuming,havea considerable computational burden,involve approximations and have yet to be applied to a w ide range of systems.These problems have motivated researchers and scholars to look for alternative solutions to model mixtures and explore their properties.

The quantitative structure-property relationship(QSPR)approach is a method that connects macroscopic properties w ith chemical structures represented by molecular descriptors.The cost of selecting appropriate agents in industrial processes can be reduced through the evaluation of the QSPRmodel.Many papers that describe the relationship betw een the structures and properties of pure fl uids using QSPR modelshave been published[23-25].QSPRhasbeen used for predicting the properties of individual compounds,such as the boiling point[26],melting point[27],and fl ash point[28].Moreover,this technique has been developed for modeling mixtures[29-32].A few QSPRmodels for determining the azeotropic characteristics of binary azeotropes have been established.For example,Katritzky et al.[32]established QSPRmodels that determine the boiling points of 426 azeotropes and adopted tw o different strategies to prepare mixture descriptors.All four descriptors selected by two strategies could be directly related to each of the three components of the enthalpy(heat)of vaporization.The R2values of the training and test sets in the w ork by Zare-Shahabadi et al.[31]w ere 0.86 and 0.84,respectively,and the mean average error(MAE)values for the training and test sets w ere calculated as 13.0 Kand 9.0 K,which indicated that the fi tting ability of the QSPR model w as good and that the MAEfor the training and test sets w as precise.The azeotropic temperature QSPRmodelsdeveloped by Solov'ev et al.[30]resulted in R2=0.88(MAE=4.2 K)for the modeling set and R2=0.84(MAE=3.7 K)for the test set.An empirical equation w as also provided w ith R2=0.94 and MAE=3.3 K/3.1 K.These models and equations show ed good predictive performance and promoted the development of QSPRmodels for predicting azeotropic temperatures.The R2values of the training and test sets w ere 0.70 and 0.32,respectively,for the azeotropic composition model established by Solov'ev et al.The aim of our w ork w as to explore the relationship betw een the molecular microstructure and azeotropic characteristics of binary azeotropes containing low er alcohols in an alternative w ay.In this paper,QSPRtools w ere used to predict the azeotropic temperatures and compositions of binary azeotropes containing low er alcohols using Materials Studio softw are and the genetic function approximation(GFA)approach.The genetic algorithm of the GFA procedure package in Materials Studio was applied to select the characteristic variables,and multiple linear regression w as used to establish the QSPRmodels.These established QSPRmodels displayed good predictive ability,and their prediction errors w ere w ithin acceptable levels.

2.Materials and Methods

An experimental dataset w asused to develop the models,and thefollow ing scheme wascarried out:(1)the experimental data were split into training and test sets,(2)molecular descriptors were calculated and preliminarily screened,(3)the optimal combination of the descriptors was selected,after w hich,the QSPRmodel w as trained using optimization methods,(4)the model wasvalidated externally,(5)and aphysical interpretation of the model was provided.

2.1.Data sets and molecular descriptor calculations

For data sets,eight lower alcohols and most common organic compounds that can form azeotropes w ith low er alcohols w ere taken from published w orks[33,34].Eighty binary azeotropes containing eight low er alcohols formed the total data set,and the selection of the data size and the ratio of the training set size/test set size w ere referenced from published works[23,27].Note that all original data can be obtained from the supporting information in references[30,32],but in order to respect the original author's contribution,w e still cited the original references.The binary mixturesthat were used astraining and test setsin the azeotropic composition model and azeotropic temperature model are listed in the supporting information.The binary azeotropes in the total set w ere then divided randomly into an 80%training set and 20%test set w ith sizes of 64 and 16 azeotropes,respectively.All the molecular structures were optimized using molecular mechanics(MM+)implemented in HyperChem 7.5,and further optimization w as carried out by applying semi-empirical quantum-mechanical AM1 parametrization[35].For each compound,336 molecular descriptors w ere calculated using Materials Studio softw are.To reduce unnecessary and useless information after the preliminary screening,molecular descriptors with values of 0 w ere abandoned.If both molecular descriptors which can be represented w ith each other were involved in the model,the model w ill be over fi tting and complex,so the highly correlated descriptors w ere removed until one w as left.In total,121 molecular descriptors w ere prepared for the next step.

For each binary azeotrope,tw o different types of molecular descriptors for the mixtures were calculated,the centroid approximation descriptors and the w eighted contribution factor approximation descriptors.The former refersto the average of the molecular descriptors of the tw o compounds in the binary azeotropes,and the latter refers to the selection of molecular descriptors by w eighing the mole fractions of the tw o compounds in the mixtures.

2.2.Variable selection method

Theselection of the characteristic variablesto establish themodelsis a key point of QSPRstudies.Three types of methods,variable selection methods based on multiple linear regression(MLR),partial least squares(PLS),and search algorithms,have been widely used recently.Genetic algorithms,w hich are a type of search algorithm,have been proposed for applications in QSPRstudies due to their strong global search abilities.When a genetic algorithm is combined w ith MLR,PLS,and other modeling methods,it can fi nd the best model for the variable space in a limited time under certain conditions.The GFA was developed by Rogers and Hop fi nger[36],and the algorithm is made up of a genetic algorithm and multivariate adaptive regression splines.The GFA procedure contains the follow ing steps.First,select molecular descriptors and basic functions randomly to generate the initial population.Then,pick an equation randomly from the initial equation population and cross every tw o equations to generate the offspring equation population.The suitability of each offspring equation is determined by the quality of its fi tting fraction,and all the steps are repeated until the QSPRmodel with the optimal fi tting and prediction ability is obtained.

3.Azeotropic Temperature Model Construction and Validation

3.1.Centroid matrix approximation

The basic principle for selecting molecular descriptors to establish the QSPRmodel w as to characterize more molecular structures using fewer molecular descriptors.To obtain a stable and reliable model,leave-one-out cross validation w as carried out to validate and evaluate the predictability of the model.Fig.1(a)show s the R2value and square of thecross-validation coef fi cient(R2CV)for the QSPRmodel w ith different numbers of molecular descriptors.The smallest numbers of molecular descriptors w ere retained,and the number of molecular descriptors n represents a “break point”in the plots of n versus R2[32].From Fig.1,when the number of molecular descriptors increases from 7 to 8,the R2show s no obvious increase,w hile w hen the number of molecular descriptors increases from 6 to 7,the R2show s an obvious increase.Thus,7 molecular descriptors w ere chosen as the arguments for the QSPRmodel.The initial population produced by the GFAwas 80,and the maximum number of iterationsw as 1000.The maximum number of variablesw as10.The mutation probability w asset as0.1,and the smoothing parameters w ere set as 0.5.The remaining parameters w ere set to the default values.

Fig.1.Statistical parameters w ith different numbers of molecular descriptors for azeotropic temperature model:(a)centroid matrix approximation and(b)w eighted contribution factor approximation.

The statistical parameters of the established QSPR models and de fi nitions of the 7 molecular descriptors are show n in Table 1.The de fi nitions of R2adjust, MAE,and Q2EXTwere determined as follows:

w here N is the number of members of the training set and M is the number of descriptors involved in the correlation.The R2adjw as arti ficially introduced when M approached N through the use of a penalty function,w hich scaled with the result.

w here p(expt.)refers to the experimental values and p(calc.)refers to the predictive values.

w here yiande the experimental and predicted values of the test sets,respectively,andis the average value of theexperimental values of the training sets.The closer Q2EXTis to 1,the stronger the prediction ability of the model is.

The R2,R2adj,F,and R2CVvalues of the training set w ere high.The established QSPRmodel w as stable and produced good fi tting results.To avoid occasional correlationsand to detect and quantify chance correlations betw een the dependent variables and descriptors,y randomization veri fi cation[37]w as used to test the stability of the established QSPRmodel.The veri fi cation w as conducted 10 times.The average R2w as 0.198 and the maximum R2w as 0.295,w hich w ere much low er than the R2of the established QSPR model.The veri fi cation results show that reasonable QSPR models could only be established using the appropriate molecular descriptors,so the QSPR established w as stable and did not exhibit chance correlations.

3.2.Weighted Contribution Factor Approximation

For the w eighted contribution factor approximation model,the mixture descriptors were calculated according to the molar ratio of the mixture compounds.In this part,the same GFA produced using Materials Studio softw are w asused to construct theazeotropic temperature model.Fig.1(b)show s the R2and R2CVvalues of the QSPRmodel w ith different numbers of molecular descriptors.From Fig.1(b),w e can see that seven molecular descriptors w ere the most appropriate forestablishing the w eighted contribution factor approximation model for the azeotropic temperature.

Table 1 Variables and statistical parameters for azeotropic temperature QSPRmodel(centroid matrix method and weighted contribution factor matrix method)

The statistical parameters of the established QSPRmodels and the de fi nitions of the seven molecular descriptors are show n in Table 1.The large F value of 167.13 indicates that the established azeotropic temperature model based on the w eighted contribution factor approximation could accurately predict the azeotropic temperatures of binary azeotropes containing low er alcohols.The model had an adjusted R2valueof 0.949,w hich indicatesgood agreement betw een thecorrelation and the variation in the sample data.The R2CVof 0.939 illustrated thereliability of the model by focusing on the sensitivity of the model after eliminating any single data points.The MAEvalue for the training set was 2.78 K,w hich w as an acceptable level.

The residual distribution for the azeotropic temperature model is show n in Fig.2.Positive and negative residuals w ere distributed uniformly and randomly,w hich show s that the established model w as stable.

Fig.2.Residual distribution for the azeotropic temperature model.

Next,Y randomization veri fi cation wasalso carried out 10 times.The average of R2was0.207,and the maximum R2was 0.296.The resultsof the external tests show n in Fig.3 re fl ect that the model displayed good predictive ability for the external samples that w ere not included in the training set.Moreover,the statistical parameters for the internal and external tests w ere similar,w hich show s that the model exhibited good extrapolation performance.The Q2EXTcalculated for the azeotropic temperature model was 0.919,which meansthat the established QSPR model had good prediction ability.Therefore,w e concluded from the above veri fi cation results that the established QSPRmodel with the w eighted contribution factor approximation method is stable and has good prediction ability.

3.3.Selection and analysis of the azeotropic temperature model

In this part,the tw o abovementioned QSPRmodels w ere compared to select thebest QSPRmodeling method for determining theazeotropic temperatures of binary azeotropes containing low er alcohols.From the comparison of characteristic parameters of the tw o QSPRmodels,w e can conclude that the w eighted contribution factor approximation QSPR model is more stable for modeling azeotropic temperatures because of the high R2and R2CVvalues.

Fig.3.Experimental values and predicted values of azeotropic temperature of w eighted contribution factor approximation model:(a)training set and(b)test set.

Fig.4.Mean effect ratios of selected molecular descriptors for azeotropic temperature model(weighted contribution factor approximation).

For the w eighted contribution factor approximation QSPRmodel,the mean effects of the ratios of the 7 selected molecular descriptors on the azeotropic temperature w ere calculated and are show n in Fig.4.The hydrogen bond donor belonged to the constitutional descriptors,kappa-1 and Chi(3):path(valence modi fi ed)belonged to the topological descriptors,and the other 4 descriptors belonged to the quantization parameters.The descriptor LUMO(lowest unoccupied molecular orbital)eigenvalue and the descriptor angle energy had negative effects on the azeotropic temperature.These tw o descriptors w ere mainly related to the molecular microscopic electronic con fi gurations and the spatial form.The remaining 5 descriptors had positive effects on the azeotropic temperatures.Katritzky[32]noted that the boiling point of an azeotrope is an indicator of the strength of the attractive forces betw een the molecules in the mixture.For the 5 descriptors w ith positive effects,the hydrogen bond donor represented the hydrogen bonding formation ability of the components in the azeotropic mixtures.The total dipole and xyy octupolewere related to theinduced dipole-dipoleinteractions,and kappa-1 and Chi(3):path w ere obtained through quantization of the molecular structure.Nonspeci fi c or van der Waals attractions,hydrogen bonding,and dipole-dipole interactions are three types of intermolecular interactionsthat are related to the azeotropic temperature.From thedescriptorsselected for the established azeotropic temperature models,we concluded that the hydrogen bonding formation ability and induced dipole-dipoleinteractionsw erethetwo most in fl uential factors.Table 2 shows the measurement errors for the azeotropic temperatures of the binary azeotropes containing low er alcohols published in Azeotropic Data books[38].The measurement error values were in the range of 0.04-5.50 K.From the comparison betw een the MAEs of the QSPRmodel and the measurement errors of the published experimental values,we observed that the QSPRmodel could predict the azeotropic temperature w ell,and the predictive errors w ere at acceptable levels.Meanwhile,31 mixtures used in this w ork w ere selected randomly to make acomparison between the predicted valuesof the azeotropic temperatures and the UNIFACmodel and the results are show n in Table 3.Both the model established in this work and the UNIFACmodel have good predictive ability.How ever,some requirements exist for using UNIFACto estimate azeotropic data.For example,theenergy parameters in UNIFAC,w hich must be fi tted to experimental VLEdata,have not been completely calculated,and it is dif fi cult to select proper groups to represent a complex system w ith many groups present,such as liquid binary systems involving heterocyclic molecules.These requirements prevent the application of UNIFACfor certain situations.It should also be noted that the properties of a molecule that is not involved in the training set can be easily calculated w ith the QSPRestablished in this w ork.Thus,compared to UNIFAC,the QSPR approach established in this w ork provided an alternative method and a much more fl exible solution to predict the azeotropic temperatures of new azeotrope systems containing lower alcohols.

Table 2 Discrepancy levels of azeotropic temperature according to different sources

Table 3 Comparison of this w ork with UNIFACmodel for the prediction of azeotropic temperature using the same source of experimental data

Fig.5.Williams plots of the developed GA-MLRazeotropic temperature model.

3.4.Applicability domain of the azeotropic temperature model

The applicability domain for the best model w as evaluated using the Williams plot show n in Fig.5.In the Williams plot,the X outliers characterized by a certain threshold value(h*=0.375,vertical dotted line in Fig.5)indicated mixtures w ith abnormal conditions that w ere poorly re fl ected in the training set,and the outliers could affect the variable selection w hen developing a better model for the mixtures.The Y outliers,w hich represent standardized residual values that exceeded the threshold value(here±3σ,horizontal dotted line in Fig.5),could be associated w ith errors in the experimental values.From the Williams plot,it can be seen that all the 80 binary azeotropes containing low er alcohols were located w ithin the applicability domain and were predicted accurately.A Y-outlier mixture did not exist in the dataset,further demonstrating the reliability of the model.Due to its high predictive ability,the proposed model could be used to predict the azeotropic temperatures of binary azeotropes containing lower alcohols.

Fig.6.Statistical parameters w ith different numbers of molecular descriptors for azeotropic composition model.

4.QSPRModel for the Azeotropic Composition

4.1.Establishment and analysis of the azeotropic composition model

The azeotropic composition is important for designing certain chemical processes,such as pressure sw ing distillation;how ever,few papers have focused on determining azeotropic compositions using QSPRmodels of binary azeotropes.Solov'ev[30]established the QSPR model for the azeotropic compositions of 176 binary azeotropes;however,the R2values of the training set and test set w ere 0.70 and 0.32,respectively,w hich indicated that the QSPRmodel could not predict the azeotropic compositions of the binary azeotropes w ell.In this paper,the QSPRmodel for the azeotropic compositions of binary azeotropes containing low er alcohols w as established w ith the GFA product mentioned above.The initial population of the GFAproduct w as50,and the maximum number of iterations w as 500.The mutation probability was0.1,and thesmoothing parameterswere0.5.Theremainingparameters w ere set as the default values.Fig.6 show s the statistical parameters of the azeotropic composition model using different numbers of molecular descriptors.As the number of selected molecular descriptors increased from 7 to 8,the R2valueschanged from 0.870 to 0.879 w ith no obvious improvement,so the chosen number of the variables for the optimized azeotropic composition QSPRmodel molecular descriptors w as 7.The statistical parameters and de fi nitions of the molecular descriptors selected for the optimized QSPR model are show n in Table 4.The F value of 53.48 indicates that the established azeotropic composition model accurately predicted the azeotropic compositions of the binary azeotropes containing low er alcohols.The model had an adjusted R2value of 0.854,which indicates good agreement betw eenthe correlations and variations in the data.The R2CVof 0.819 illustrated the reliability of the model through cross validation.The MAEvalue for the training set w as0.068,which is an acceptable level.The quadrupole is involved in the azeotropic composition model.Due to the appearance of thelow alcoholsthat make themixturehighly polar,thisresult issuspicious.Therefore,a comparison betw een models w ith and without the quadrupole is made.The result is show n in Fig.7.The R2of the model w ithout the quadrupole is 0.154,which is much low er than 0.870 of the model w ith the quadrupole.The predicted value of the model w ithout the quadrupole is a negative value,and that is incorrect.Thus,the quadrupoleisnecessary in the predicted model.For theoctupole,theeffects of the octupole for different directions on the accuracy of model were studied in detail,and the results are given in the supporting information.The results show ed that the QSPRmodel established w ith the octupole yzz had the best regression and fi tting situation.

Table 4 Variables and statistical parameters for azeotropic composition QSPRmodel

Fig.7.Comparison of models with quadrupole and without quadrupole.(a)Model w ith quadrupole and(b)model without quadrupole.

Fig.8.Residual distribution for the azeotropic composition model.

The residual distribution for the azeotropic composition model is shown in Fig.8.Because the value of the azeotrope composition is less than 1,the relative deviation w ould be quite large and scattered.Even the residual value is small.Thus,the residual value is selected as the y-axis in Fig.8.The positive and negative residuals w ere distributed uniformly and randomly,which show s that the established model w asstable.For some binary azeotropesin w hich the azeotropic compositions of the alcohols w ere above 0.90 or below 0.10,the model could exhibit deviations from the experimental values(sometimes values over 1 or negative values),so the best predictive range w as 0.10-0.90.

The predicted and experimental values of the training set and test set are plotted in Fig.9.The R2values of the training set and test set were 0.870 and 0.822,respectively.The Q2EXTcalculated for the azeotropic composition model w as 0.795,w hich indicates that the established QSPRmodel had good prediction ability.

Fig.10.Mean effect ratios of selected molecular descriptors for azeotropic composition model.

Fig.9.Experimental values and predicted values of azeotropic composition:(a)training set and(b)test set.

Table 5 Discrepancy levels of azeotropic composition according to different sources

For the QSPRmodel of the azeotropic composition,the mean effect ratio of every molecular descriptor w as calculated to determine their signi fi cance on the established QSPR model.The results are shown in Fig.10.Quadrupole xy,the element count,and the molecular refractivity had opposing effects on the mole fractions of the alcohols in the binary azeotropes.The descriptor quadrupole xy refers to the quadrupole of the xy direction,and the element count represents the number of atoms.The other four molecular descriptors included the octupole yzz,vertex adjacency,vertex distance,and shadow area fraction.The XY plane had a positive effect on the compositions of the alcohols in the binary azeotropes.From the analysis of the results from the azeotropic composition model,w e can conclude that the constitutional,geometric,and topological descriptors w ere the main in fl uencing factors on the azeotropic compositions of the binary azeotropes containing lower alcohols.These three types of descriptors are related to the composition,conformation,and molecular shape of the azeotropic components.The measurement errors of the azeotropic composition published in the Azeotropic Data book[38]show n in Table 5 are w ithin the range of 0.005-0.311(mole fraction).The conclusion is that the established QSPR model results in a reasonable predictive performance for determining azeotropic compositions.

4.2.Applicability domain of the azeotropic composition model

The Williams plot show n in Fig.11 w as also used to evaluate the applicability domain for the best azeotropic composition model.After analyzing the model applicability domain from the Williams plot,X outlier mixtures w ere not observed.One azeotrope(methanol-acetone)had larger standard deviations,and the predicted residual w as slightly higher than-3σ.This predicted error may have been due to the erroneous experimental data of the samples.

Fig.11.Williams plots of the developed GA-MLRazeotropic composition model.

5.Applicability Scheme of the Model

The models of azeotrop ic temperatures and compositions w ere built,and the parameter of veri fi cation illustrates that the models are stable and accurate.To illustrate how the mod els w ere applied to predict the azeotropic temperatures and compositions,the corresp onding systematic diagram is show n in Fig.12:fi rst,calculating the descriptors of the pure compound in the azeotrope;second,determining the descriptors of the azeotropic system w ith the centroid matrix method or w eighted contribution factor matrix method according to the property w e w ould predict;then,selecting the descriptor used in the model among the numbers of descriptors;and fi nally,calculating the azeotropic temperature and composition w ith the selected descriptors.

6.Conclusions

In this paper,QSPR models for the azeotropic temperatures and compositions of binary azeotropes containing lower alcohols were established.Tw o types of mixture descriptors based upon the centroid approximation and the w eighted contribution factor approximation w ere used to characterize the azeotropic mixtures.The GFA procedure in Materials Studio softw are w as used for selecting the most closely related molecular descriptors to establish models from the 121 molecular descriptors calculated.The model mechanisms w ere analyzed from molecular structure information.The R2,R2CV,and MAE values w ere calculated for the established QSPR models.The models in the paper are more precise than the models established by previous w ork.The R2of the model predicting the azeotropic temperature w ith the w eighted contribution factor matrix method in this paper w as 0.954,w hich is higher than that of previous w ork,and the MEA w ith 2.78 K is smaller than that of previous w ork.The model of the azeotropic composition in this paper has higher predictive pow er than that of previous w ork,w ith an R2of 0.87 and MEA of 0.068 compared w ith an R2of 0.7 and MEA of 0.144,respectively;thus,the model in this paper can predict the azeotropic temperature and composition better.The predictive errors of the QSPR models w ere also compared w ith the measurement errors published in the Azeotropic Data book.The high R2and R2CVvalues and the small predictive errors indicate that the established QSPR models show good predictive performance and can predict the azeotropic temperatures and compositions of binary azeotropes containing low er alcohols w ell,w ith predictive errors w ithin acceptable levels.

Fig.12.Applicability scheme of the QSPRmodel for predicting the azeotropic temperatures and compositions.