The New Method for Correlation and Prediction of Thermophysical

Article pubs.acs.org/jced

The New Method for Correlation and Prediction of Thermophysical Properties of Fluids. Critical Temperature Zhiwei Li,*,† Lihua Zuo,‡ Wensheng Wu,† and Liuping Chen§ †

College of Environmental and Chemical Engineering, Zhaoqing University, Guangdong Zhaoqing 526061, China East China Institute of Technology, Jiangxi Fuzhou 344000, China § School of Chemistry, Sun Yat-sen University, Guangdong Guangzhou 510275, China ‡

S Supporting Information *

ABSTRACT: On the basis of the linear free energy relationships theory and thermodynamics formulas, a new method predicting critical temperature (Tc) of pure fluids is proposed for the first time. Sixteen homologues of 616 substances have been regressed and correlation equations between Tc and molecular descriptors are obtained. The mean relative deviations of the 16 equations are from 0.01% to 2.73%, and most of them are under 2%. In addition, the squared correlation coefficients are from 0.90 to 0.98. Moreover, the equations are tested through cross-validation by the leave-one-out procedure and most of the squared correlation coefficients are greater than 0.90. The results reveal that the equations exhibit better effect with simple form of equation, high prediction accuracy, and definitude theory meaning. This study successfully combines macroscopic physical properties of fluids with their molecular microstructure and breaks through the experimental or theoretical application scope, perfecting calculation of critical temperature for pure liquids.

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molecule were considered,4 which resulted in significant improvement in accuracy. Xu et al.5,6 considered the specific position of a group in the molecule and developed a group vector space method for estimating the Tc of organic compounds, which showed significant improvements in accuracy and applicability compared to the conventional GC methods. In addition, some new methods7−11 based on the GC method, such as position GC method8−10 and element and chemical bond method,11 were successively proposed. It should be emphasized that position GC method has been successfully applied in calculating critical properties, which solved the difficult problem of failing to distinguish isomers. Owing to its powerful function of estimation, the GC method was widely used to estimate the Tc of pure organic compounds,12,13 ionic liquids,14−18 and mixtures.19 Quantitative structure property relationship (QSPR)20−24 was also an effective approach for prediction of Tc. It mainly explores quantitative relations between molecular structure and physicochemical properties of compound accurately using statistic and theoretical calculation. These models can predict the properties of unknown compound quickly and help to understand theoretically the differences of substances on the basis of molecular structure, providing guidance for high efficiency synthesizing compounds experimentally. Yao,20 Godavarthy,21 Sola,22 and Kazakov23 proposed their QSPR

INTRODUCTION Critical parameters are important physical parameters, comprising critical temperature (Tc), pressure, volume, density, compressibility factor, and so forth. Tc is that the pure gas cannot be liquefied at one temperature no matter how much pressure is applied. The importance of critical parameters manifests in being used as the basic physical properties of substances. They are necessary variables not only in calculating or estimating the physical and chemical properties, but also in many chemical engineering and process design. Although the critical parameters are important, the quantity of experimental data is very finite until now because of wondrous difficulty in mensurating critical state. Therefore, the existing critical parameters are far the from need of chemical production, process design, and scientific research. This predicament causes some methods evaluating critical parameters of unknown compound by combining known data with modern prediction method to emerge as time required. Therefore, several reliable methods come into being gradually, which will be introduced briefly as follows. Group contribution (GC) method is the most widely used and studied by many scientists1−11 because of its advantages of simple form and convenient calculation. It should be pointed out that the isomers have the same or almost the same groups, making the conventional GC method relatively backward in predicting research because it cannot distinguish isomers and ignores interactions between bonds. In order to overcome these defects, the secondary group was introduced2,3 or the contributions of interactions between bonding groups in the © XXXX American Chemical Society

Received: May 18, 2017 Accepted: September 19, 2017

A

DOI: 10.1021/acs.jced.7b00454 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

refraction; S is the dipolarity/polarizability; A is the overall hydrogen bond acidity; B is the overall hydrogen bond basicity; and V is the characteristic McGowan volume. The molecular descriptors may be of either experimental origin or calculated based solely on molecular structure considerations. The set of coefficients, c, e, s, a, b, and v in eq 1 are obtained by multiple linear regression analysis. By the LFERs model, many properties for substances can be researched with the known molecular descriptors, and the set of molecular descriptors bears the advantage of distinct significance, wide substance range, simple calculation, and high precision, as proven by many published articles.49−100 By the enlightenment of the LFERs model, we hold that the characteristics of molecular descriptors factually reflect the intermolecular interaction, and macroscopical property, such as Tc, is decided by substance structure and reciprocity of molecules, indicating that the set of molecular descriptors should be widely applicable in estimating physicochemical properties of substances. Although LFERs was widely used, the relative research of Tc of pure fluids using LFERs has never been published heretofore according to our best knowledge. Therefore, this paper aims at obtaining correlation equations of Tc of various compounds and five molecular descriptors, which can exhibit good effect with relatively higher prediction accuracy, wide applicability, and lower computation complexity. The detailed process will be introduced in the latter paragraphs.

models to predict critical parameters of pure substances, and Ramjugernath24 developed a QSPR model to correlate/predict the Tc of ionic liquids. These QSPR models all occupied preferable prediction and enough precision. Both topology and artificial neural network (ANN) methods have good applicability in physical prediction field. Topology method25,26 can also predict some isomers to be excellent relative to the conventional GC method. Richon et al.27 proposed an alternative method based on the ANN technique to predict the Tc, critical pressures, critical volumes, and acentric factors of petroleum fractions, especially heavy fractions, from their specific gravity and the average normal boiling-point temperature values. Kuang28 and Lymperiadis29 combined ANN with GC method to estimating critical properties and obtained good results. Gharagheizi30,31 predicted critical parameters of pure substances in DIPPR801 database and obtained a result with high accuracy. Besides the above-mentioned methods, there are other methods of critical parameter prediction. On the basis of the liquid state equation and semi-empirical model for describing other physical properties, estimating methods were also proposed to predict critical properties.32,33 However, these equations were not commonly used because of its complex computation, too much physical parameters required, and poor universality. Association equation method34−37 was also commonly used and in this method the characteristic groups first were divided into various types, then the basic physical properties, such as molecular weight (M), boiling temperature Tb, and number of carbon atom were selected and related with critical parameters. The equations acquired by this method are simple, understandable, and accurate. Cubic equation of state38−40 is closely related to critical properties of pure substances, and thus it is also a way to obtain critical parameters. In addition, by employing molecular descriptors from computer simulation of molecular mechanics, Wakeham41 provided a new correlation for the estimation of critical parameters of hydrocarbons and achieved high precision. Tahery42 obtained a simple expression for the Tc of pure fluids in terms of the parameters of scaled particle theory (SPT), and the calculated Tc agreed well with experimental data for a range of pure fluids. Ghatee et al.43 predicted the Tc of ionic liquids from surface tension at liquid−vapor equilibrium and developed a correlation of Tc with the interaction energy. Nezbeda estimated the Tc by the second virial coefficient44 and low order perturbed virial expansions;45 both of the results were superior to the common virial expansion. In addition, the Gibbs ensemble Monte Carlo (GEMC) simulations, the Wang−Landau simulations, and the grand canonical ensemble were also used to estimate the Tc by Nath,46 Desgranges,47 and Lai48 (and their co-workers), respectively. In summary, great progress has been made in predicting critical parameters, and due to space constraints we are not providing all of the available articles and other publications. In this paper, we proposed a new method first based on the linear free energy relationships (LFERs) theory49,50 to predict critical properties of pure fluids. LFERs theory thinks that the molecular basic property can be expressed by five molecular descriptors as eq 1 SP = c + eE + sS + aA + bB + vV

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FITTING METHOD The equation of Clausius−Clapeyron describing the diphase equilibrium can be expressed as dp ΔHm = dT T ΔVm

(2)

where ΔHm and ΔVm denote the molar enthalpy and molar volume change from one phase to another, respectively. For the evaporation, on the basis of two hypotheses, i.e., the gas is ideal gas, and the volume of the liquid or solid phase can be neglected compared with that of the gas, eq 2 can be changed to Δ vapHm d ln p = dT RT 2

(3)

As everyone knows, the critical point is the terminus of the gas−liquid phase equilibrium. If eq 3 is integrated in the process of the temperature approaching below the critical point, the following equation can be obtained ln

pc* p

=

Δ vapHm ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tc* ⎠

(4)

In eq 4, pc* is the vapor pressure being in equilibrium with the temperature T*c , and T*c approaches Tc. In addition, the enthalpy is a thermodynamic function of a system, which is equivalent to the sum of the internal energy of the system plus the product of its volume multiplied by the pressure exerted on it by the surroundings, i.e., H = U + pV. Therefore, the enthalpy of transition ΔvapHm can be obtained by eq 5 Δ vapHm = Δ vapUm + Δ(pVm)

(1)

(5)

In eq 5, U is internal energy, being equivalent to the sum of all kinds of energies of various motions, including energies of molecular translation, rotation, vibration, electron motion, and

In eq 1, the dependent variable, SP, is some property of a series of solutes in a fixed phase. The independent variables or descriptors are solute properties as follows: E is an excess molar B



Tc = c + eE + sS + aA + bB + vV

R2

In terms of LFERs model, the above function can be expressed as (7)

fitting equations

where the c, e, s, a, b, and v are the undetermined coefficients of the equation, which are determined by multiple linear regression analyses of experimental Tc data for a series of organic compounds considered in this paper. E, S, A, B, V are the molecular descriptors of substance. The data of Tc for the pure substances are collected from the Lange’s Handbook of Chemistry (the 15th edition),101 Handbook of Chemistry and Physics102 printed by CRC, Chemical Properties Handbook103 published by World Publishing Corporation and McGraw-Hill Book Co., and Physical Properties Databook of Chemical and Chemical Industry published by Chemical Industry Press of China. The 616 compounds are classified into 16 genera, and then the 16 genera have been regressed by stepwise regression analysis and tested through cross-validation by the leave-one-out procedure (LOO). Molecular descriptors for all of the compounds considered in the present study are taken from the published literatures.49−94 Sixteen equations are established and evaluated by squared correlation coefficients (R2), F test, mean relative deviation (MD), and squared crossvalidation correlation coefficients (Q2). All of the Tc and the descriptors used for model validation are presented in Supporting Information.

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C

1.78 1.83 2.26 0.03 0.98 0.01 1.91 2.16 1.54 1.52 2.01 2.73 1.81 0.74 1.98 2.56

N

59 161 53 25 40 22 36 28 24 23 55 30 14 8 15 23

types of substances

halohydrocarbon alkane olefin alkyne aromatic hydrocarbon hydroxybenzene alcohol ether aldehyde acid ester amine aniline amide nitrile nitryl

Table 1. Fitting Equations for Tc

Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc Tc

= = = = = = = = = = = = = = = =

(314.70 (379.86 (348.84 (406.43 (389.00 (496.05 (329.61 (369.48 (278.09 (428.34 (424.50 (229.20 (385.74 (622.41 (231.00 (550.68

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

RESULTS AND DISCUSSION The fitting equations of Tc are listed in Table 1. In this paper, the 616 compounds are divided into 16 types according to differences of functional groups in the molecules, and the 16 types of substances cover general organic compounds, such as saturated, unsaturated, chain, branched chain, circularity, benzene ring, carbonyl, hydroxy compounds, and some heteroatomic compounds containing N, O, halogen, and so forth. In term of general criterion of regression, the quantity of regressive compounds should exceed that of the independent variable (molecular descriptors) by 3 to 5 times, i.e., the amount of regressive compounds should be from 15 to 25. In our paper, most of types are more strictly than this criterion with the exception of aniline and amide. The contribution of various molecular descriptors to the Tc can be evaluated by the coefficients c, e, s, a, b, and v, and it can be neglected if its coefficient is zero in a certain equation. Therefore, some of the five molecular descriptors fail to appear in the equations. The reason is that some molecular descriptors were neglected during regression. During the regression, we calculated in terms of stepwise regression strictly. If the influence of molecular descriptor on the properties of the substances can be ignored, it will do not appear in the equations.

634.31 703.26 676.23 536.26 617.11 74.24 347.06 552.94 316.29 353.73 275.14 131.58 23.58 129.55 212.07 257.49

(6)

0.9720 0.8991 0.9643 0.9588 0.9809 0.9252 0.9242 0.9779 0.9794 0.9725 0.9565 0.9546 0.9129 0.9810 0.9725 0.9245

Tc = f (E , S , A , B , V )

17.52) + (132.38 ± 17.95)E + (107.14 ± 30.31)S + (182.50 ± 26.14)V 11.71) + (197.40 ± 35.65)E+ (149.94 ± 7.9)V 13.71) + (164.71 ± 33.86)E + (152.78 ± 8.35)V 18.77) + (138.50 ± 12.37)V 16.58) + (112.83 ± 18.35)E + (187.39 ± 111.01)B + (131.80 ± 10.97)V 44.40) + (124.43 ± 46.71)S + (90.70 ± 27.64)A + (60.82 ± 17.92)V 34.75) − (395.51 ± 159.07)E + (659.93 ± 191.37)S + (86.31 ± 13.27)V 14.48) + (157.13 ± 17.55)E + (144.07 ± 11.66)V 33.01) + (114.31 ± 45.11)E + (186.49 ± 54.71)S + (153.64 ± 15.54)V 22.85) + (234.07 ± 35.28)A + (87.29 ± 9.05)V 16.22) + (121.11 ± 39.56)E + (−63.68 ± 31.40)S + (158.79 ± 41.82)B + (99.77 ± 8.3)V 64.48) + (209.00 ± 50.89)E + (257.34 ± 149.71)A + (123.68 ± 73.86)B + (164.75 ± 16.22)V 98.18)+(95.43 ± 56.40)E + (240.06 ± 102.00)A + (126.40 ± 119.44)B + (121.69 ± 63.07)V 18.59) + (210.63 ± 37.59)A + (39.72 ± 10.96)V 43.33) + (880.86 ± 101.07)B + (56.51 ± 33.94)V 26.58) + (218.00 ± 28.25)E

F

MD/%

Q2

nucleus motion, and so on. Thereby, the change of internal energy is the function of the intermolecular force and, further, it can be obtained from eqs 4 and 5 that the Tc can be expressed as the function of the intermolecular force. Macroscopical property is decided by substance structure and reciprocity of molecules, and the intermolecular force can be denoted by five molecular descriptors of the LFERs theory. Therefore, the five molecular descriptors of the LFERs can express the reciprocity of molecules, and as a result Tc can be expressed as a function of five molecular descriptors

0.9572 0.8944 0.9628 0.9580 0.9697 0.5565 0.9211 0.9736 0.9127 0.9363 0.9467 0.7733 0.5169 0.5410 0.9485 0.9156

Article



Article

In the study, the equations for estimating Tc of pure substances procured good effect. The R2 of 11 fitting equations are more than 0.95, and the R2 of 4 equations are about 0.92, indicating that these equations are generally fine. The performances of these equations were tested through crossvalidation by the LOO, and Tropsha et al.104 pointed out that a high value of this statistical characteristic (Q2 > 0.5) was considered as a proof of the high predictive ability of the model. As shown in Table 1, most of the Q2 for cross-validation are greater than 0.90, and for the types of aniline, amide, and hydroxybenzene, the cross-validation coefficients are 0.5169, 0.5410, and 0.5565, respectively, indicating that the predictabilities of their equations are inferior. Therefore, these equations have favorable estimation stability and predictive ability as a whole. Otherwise, the relative mean error of 16 types of substances are from 0.01% to 2.73%, and most of them are smaller than 2%, showing that our method has advantages in prediction accuracy. It is undeniable that our equations have no remarkable increase in precision and even decrease a little for some equations and substances. The reason may be the defection and the insufficiency of molecular descriptors. Among five molecular descriptors, V is the characteristic volume of molecule, and for the isomers they have identical V values. However, their space structures are different to each other, bringing on the unlikeness of the surface area of the isomers. The difference of the space structures induced dissimilar intermolecular effective contact. Thus, the intermolecular interactions are unlike, and consequently, these isomers possess different macroscopically physical and chemical properties. The presenters of V neglect the diversities of actual volumes for the isomers. So the descriptions of molecular characteristic volume are crude in some sort, and the imperfection of V makes for some errors in calculating the various physical properties. Again, because of the multiplicity of the molecular structure and complexities of intermolecular interaction, it is very difficult to describe accurately the intermolecular interaction and the chemical environment a molecule is situated in. Although the five molecular descriptors express the molecular structure and the interaction, they cannot completely include all of the factors that affect the physical properties of a molecule. Therefore, for some substances the error of predicting Tc is great. These aspects may be the deficiencies of our method. In order to preferably express the prediction effect of Tc by the fitting equations obtained by our method, three types of compounds were randomly selected to illustrate the data, as shown in Figure 1−3, which exhibit the fitting effects intuitively. The practical fitting data will be listed in the Supporting Information for the sake of conciseness.

Figure 1. Comparison of experimental and calculated Tc values for 40 arenes, MD = 0.98%.

Figure 2. Comparison of experimental and calculated Tc values for 59 halohydrocarhons, MD = 1.78%.

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APPLICATIONS OF THE FITTING EQUATIONS This paper developed a new method for calculating Tc of pure substance, which is based on the thermodynamics theory and is combined with the LFERs model. The obtained equations not only describe the Tc quantificationally and correctly but also expand the applicability of LFERs. In addition, we can estimate conveniently the molecular descriptors of other compounds through a large number of experimental data of Tc and the determinate equations, providing another approach of obtaining molecular descriptors besides gas chromatography and ADME software.105 In order to verify the applicability of our equation, 9 types of 43 compounds that were absent from regression were selected

Figure 3. Comparison of experimental and calculated Tc values for 30 amines, MD = 2.73%.

to predict their Tc. The comparison of predictive Tc with experimental values is tabulated in Table 2. As seen from Table D



Article

Table 2. Comparison of Experimental and Calculated Tc Values for Various Compounds no.

formulas

name

Tc(exp)/K

Tc(cal)/K

error/%

halide

CH3Cl CHBr3 CHI3 C2H2Br4 C2H3Cl C2H4I2 C3H6Br2 C3H6Cl2 C5H11Cl C7H15Br C3H8 C4H10 C4H10 C5H12 C3H4 C3H6 C4H6 C4H6 C4H8 C4H8 C4H8 C4H8 C2H2 C3H4 CH2O2 C4H6O2 C3H5NO C5H11NO C3H4O2 C3H6O2 C4H6O2 C6H10O4 C9H18O2 C13H26O2 C3H2N2 C4H5N C8H15N C2H6O C3H6O C4H6O C6H14O C7H8O C8H18O

methyl chloride tribromomethane triiodomethane 1,1,2,2-tetrabromoethane chloroethene 1,2-diiodoethane 1,2-dibromopropane 1,1-dichloropropane 2-chloro-2-methylbutane 1-bromoheptane propane 2-methylpropane n-butane 2,2-dimethyl propane propadiene 1-propylene buta-1,3-diene buta-1,2-diene isobutene 1-butene trans-2-butene cis-2-butene ethyne (acetylene) methylacetylene formic acid trans-crotonic acid acrylamide tert-butylformamide vinyl formate methyl acetate vinyl acetate diethyl oxalate n-octyl formate methyl dodecanoate malononitrile methacrylonitrile 1-cyanoheptane dimethyl ether methyl vinyl ether divinyl ether di-i-propylether anisole dibutyl ether

416.25 696 794.55 824 432 749.91 634.11 560 548.97 651 369.82 408.14 425.18 433.78 393.15 364.76 425.37 444 417.9 419.59 428.63 435.58 308.32 402.39 580 666 710 692 498 506.8 524 646 645 712 715 554 674.45 400.1 437 463 500.05 641.65 581

461.60 657.93 874.26 746.23 475.34 828.40 569.72 589.61 534.85 634.72 459.52 480.65 480.65 501.76 471.23 440.41 491.11 496.84 461.41 461.44 468.36 468.36 454.37 463.06 632.17 632.54 768.56 730.91 538.62 532.86 549.23 601.86 602.80 657.82 667.41 619.36 618.44 434.17 471.86 503.09 524.81 612.70 556.05

−10.90 5.47 −10.03 9.44 −10.03 −10.47 10.15 −5.29 2.57 2.50 −24.26 −17.77 −13.05 −15.67 −19.86 −20.74 −15.45 −11.90 −10.41 −9.97 −9.27 −7.53 −47.37 −15.08 −9.00 5.02 −8.25 −5.62 −8.16 −5.14 −4.81 6.83 6.54 7.61 6.66 −11.80 8.31 −8.51 −7.98 −8.66 −4.95 4.51 4.29

alkane

alkene

alkyne acid amide ester

nitrile

aether

thousand compounds in the descriptor database,79 and many of them can be consulted in published papers49−94 or can be estimated based on existing methods.50,53,87 Also, we can obtain molecular descriptors by ADME software.105

2, most of the results have good accuracy in that their relative errors are smaller than 10% and some of them are about 10%. However, there is serious departure for some compounds. For example, the error of the type of alkyne is large obviously. The reason may be that the equation of alkyne contains only one independent variable, which cannot fully describe all impacts influencing Tc. The error of alkane in Table 2 is also large relatively, and it may be owing to the insufficiency of variable and imperfection of descriptors because most of the descriptors are zero for substances being tested. For other cases of great error, incomplete picture of the molecular structure and chemical conditions may be the main reason. As a whole, the calculated Tc values are in accordance with the experimental counterpoint. Despite some errors, our method has other advantages of simple form and easy calculation. Molecular descriptors are available for several

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CONCLUSION In this study, based on the LFERs theory and thermodynamics formulas, a new method is proposed for the first time to predict Tc of pure fluids. Correlation equations for estimation of Tc using molecular descriptors are obtained according to the regression analysis of 16 homologues of 616 substances. The MD of the 16 equations are from 0.01% to 2.73%, and most of them are under 2%. In summary, the new method presented in this paper for calculating the Tc of pure fluids investigated the contributions of intermolecular interaction and molecular structure on Tc. It E



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successfully combines macroscopic physical properties with microstructure, possessing important theory meaning for setting up a bridge between macroscopic properties and microstructures. Additionally, our method has a sound theoretical basis for the combining basic thermodynamics formulas with LFERs theory. The equations of this paper bear the advantages of simple form, distinct meaning, convenient and rapid calculation, higher prediction accuracy, and strong currency, being applicable to engineering design. Finally, the substances studied in this article are abundant and belong to broad types. The method breaks through the experimental or theoretical application scope, perfecting calculation of Tc for pure fluids. However, it must be noted that this method has some shortcomings. As everyone knows, the molecular structure and the intermolecular interaction are very complex, and it is very difficult to describe accurately the intermolecular interaction and the chemical environment of a system. Therefore, the five molecular descriptors cannot completely include all of the factors that affect the physical properties of a molecule. In addition, the molecular descriptor itself has defection, for instance, the isomers have identical V values, which is always non-conformable with the real case. All of these factors lead to an incomplete picture of the molecular structure and its chemical condition and further cause errors in predicting physical properties. These aspects may be the main deficiencies of our method.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00454.

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Tc and molecular descriptors of compounds (XLSX)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhiwei Li: 0000-0002-7962-7636 Funding

This work is supported by the Natural Science Foundation of Guangdong Province, China (No. 2015A030313705) and Zhaoqing University Innovation and Strong School Project (No. CQKYPT201605). Notes

The authors declare no competing financial interest.

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REFERENCES

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(49) Abraham, M. H. Scales of Solute Hydrogen-bonding: Their Construction and Application to PhysicochemicaI and BiochemicaI Processes. Chem. Soc. Rev. 1993, 22, 73−83. (50) Abraham, M. H.; Ibrahim, A.; Zissimos, A. M. Determination of Sets of Solute Descriptors from Chromatographic Measurements. J. Chromatogr. A 2004, 1037, 29−47. (51) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. Hydrogen Bonding. Part 14. The Characterisation of Some NSubstituted Amides as Solvents: Comparison with Gas-Liquid Chromatography Stationary Phases. J. Chem. Soc., Perkin Trans. 2 1990, 1851−1857. (52) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. Hydrogen Bonding Part 13. A new Method for the Characterization of GLC Stationary Phases-The Laffort Data Set. J. Chem. Soc., Perkin Trans. 2 1990, 1451−1460. (53) Abraham, M. H.; Andonian-Haftvan, J.; Whiting, G. S.; Leo, A.; Taft, R. S. Hydrogen Bonding. Part 34. The Factors that Influence the Solubility of Gases and Vapours in Water at 298 K, and a New Method for its Determination. J. Chem. Soc., Perkin Trans. 2 1994, 1777−1791. (54) Abraham, M. H.; Chadha, H. S.; Whiting, G. S.; Mitchell, R. C. Hydrogen Bonding. 32. An Analysis of Water-Octanol and WaterAlkane Partitioning and the Delta Log P Parameter of Seiler. J. Pharm. Sci. 1994, 83, 1085−1100. (55) Abraham, M. H.; Treiner, C.; Roses, M.; Rafols, C.; Ishihama, Y. Linear free energy relationship analysis of microemulsion electrokinetic chromatographic determination of lipophilicity. J. Chromatogr. A 1996, 752, 243−249. (56) Abraham, M. H.; Chadha, H. S.; Leitao, R. A. E.; Mitchell, R. C.; Lambert, W. J.; Kaliszan, R.; Nasal, A.; Haber, P. Determination of solute lipophilicity, as log P(octanol) and log P(alkane) using poly(styrene−divinylbenzene) and immobilised artificial membrane stationary phases in reversed-phase high-performance liquid chromatography. J. Chromatogr. A 1997, 766, 35−47. (57) Abraham, M. H.; Ibrahim, A.; Acree, W. E., Jr Partition of compounds from gas to water and from gas to physiological saline at 310 K: Linear free energy relationships. Fluid Phase Equilib. 2007, 251, 93−109. (58) Holley, K.; Acree, W. E., Jr.; Abraham, M. H. Determination of Abraham model solute descriptors for 2-ethylanthraquinone based on measured solubility ratios. Phys. Chem. Liq. 2011, 49, 355−365. (59) Abraham, M. H.; Acree, W. E., Jr. Linear free-energy relationships for water/hexadec-1-ene and water/deca-1, 9-diene partitions, and for permeation through lipid bilayers; comparison of permeation systems. New J. Chem. 2012, 36, 1798−1806. (60) Zissimos, A. M.; Abraham, M. H.; Du, C. M.; Valko, K.; Bevan, C.; Reynolds, D.; Wood, J.; Tam, K. Y. Calculation of Abraham descriptors from experimental data from seven HPLC systems; evaluation of five different methods of calculation. J. Chem. Soc. Perkin Trans. 2 2002, 2001−2010. (61) Abraham, M. H.; Acree, W. E., Jr. Comparative analysis of solvation and selectivity in room temperature ionic liquids using the Abraham linear free energy relationship. Green Chem. 2006, 8, 906− 915. (62) Zissimos, A. M.; Abraham, M. H.; Barker, M. C.; Box, K. J.; Tam, K. Y. Calculation of Abraham descriptors from solvent−water partition coefficients in four different systems; evaluation of different methods of calculation. J. Chem. Soc., Perkin Trans. 2 2002, 470−477. (63) Abraham, M. H.; Acree, W. E., Jr. Correlation and prediction of partition coefficients between the gas phase and water, and the solvents dodecane and undecane. New J. Chem. 2004, 28, 1538−1543. (64) Abraham, M. H.; Zissimos, A. M.; Acree, W. E., Jr. Partition of solutes into wet and dry ethers; an LFER analysis. New J. Chem. 2003, 27, 1041−1044. (65) Abraham, M. H.; Whiting, G. S.; Carr, P. W.; Ouyang, H. Hydrogen bonding. Part 45. The solubility of gases and vapours in methanol at 298 K: an LFER analysis. J. Chem. Soc., Perkin Trans. 2 1998, 1385−1390. (66) Abraham, M. H.; Chadha, H. S.; Dixon, J. P.; Rafols, C.; Treiner, C. Hydrogen bonding. Part 41. Factors that influence the distribution

(27) Mohammadi, A. H.; Afzal, W.; Richon, D. Determination of Critical Properties and Acentric Factors of Petroleum Fractions Using Artificial Neural Networks. Ind. Eng. Chem. Res. 2008, 47, 3225−3232. (28) Kung, G.; Zhao, S. Y.; Zhao, Z. S.; Wang, L. E. Prediction of Critical Properties for Organic Compound by Group-Contribution Artificial Neural Network Method. Comput. Appl. Chem. 2001, 18, 396−399. (29) Lymperiadis, A.; Adjiman, C. S.; Jackson, G.; Galindo, A. A generalisation of the SAFT-gamma group contribution method for groups comprising multiple spherical segments. Fluid Phase Equilib. 2008, 274, 85−104. (30) Gharagheizi, F.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. Determination of critical properties and acentric factors of pure compounds using the artificial neural network group contribution algorithm. J. Chem. Eng. Data 2011, 56, 2460−2476. (31) Gharagheizi, F.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. Determination of parachor of various compounds using artificial neural network-group contribution approach. Ind. Eng. Chem. Res. 2011, 50, 5815−5823. (32) Spencer, C. F.; Danner, R. P. Improved equation for predictions of saturated liquid density. J. Chem. Eng. Data 1972, 17, 236−241. (33) Zhang, H. Y.; Ma, P. S. Calculation of critical parameters by Raekett equation. Comput. Appl. Chem. 1997, 14 (s1), 319−322. (34) Klincewicz, K. M.; Reid, R. C. Estimation of Critical Properties with Group Contribution Method. AIChE J. 1984, 30, 137−142. (35) Lu, Y. P.; Xu, X.; Peng, B.; Liang, Y. Estimation of critical constants with co-relation equation. Comput. Appl. Chem. 2003, 20, 709−712. (36) Wang, X. H.; Jia, Q.; Gao, J.; Xia, S. Q.; Ma, P. S. Calculation of Critical Properties of Pure Substances from Their Simple Properties. Petro Chem. Technol. 2005, 34, 254−257. (37) Vejahati, F.; Nikoo, M. B.; et al. Simple correlation estimates critical properties of alkanes. Pet. Sci. Technol. 2007, 25, 1115−1123. (38) Hsieh, C. M.; Lin, S. T. Determination of cubic equation of state parameters for pure fluids from first principle solvation calculation. AIChE J. 2008, 54, 2174−2181. (39) Twu, C. H. A novel theory for predicting critical constants and the function for pure polymers. Ind. Eng. Chem. Res. 2010, 49, 11801− 11808. (40) Zang, L. Y.; Zhu, Q. L.; Yun, Z. Critical properties prediction based on a quartic equation of state. Can. J. Chem. Eng. 2010, 88, 1003−1009. (41) Wakeham, W. A.; Cholakov, G.; Stateva, R. P. Liquid Density and Critical Properties of Hydrocarbons Estimated from Molecular Structure. J. Chem. Eng. Data 2002, 47, 559−570. (42) Tahery, R.; Satherley, J.; Schiffrin, D. J. Dependence of the Critical Temperature on Molecular Parameters. J. Phys. Chem. B 2007, 111, 5941−5945. (43) Ghatee, M. H.; Moosavi, F.; Zolghadr, A. R.; Jahromi, R. Critical-Point Temperature of Ionic Liquids from Surface Tension at Liquid-Vapor Equilibrium and the Correlation with the Interaction Energy. Ind. Eng. Chem. Res. 2010, 49, 12696−12701. (44) Nezbeda, I.; Smith, W. R. On the calculation of the critical temperature from the second virial coefficient. Fluid Phase Equilib. 2004, 216, 183−186. (45) Krejčí, J.; Nezbeda, I. The critical temperature and properties of real gas from low order perturbed virial expansions. Fluid Phase Equilib. 2012, 314, 156−160. (46) Wescott, J. T.; Kung, P.; Nath, S. K. Vapour-liquid coexistence properties and critical points of two branched alkanes series. Fluid Phase Equilib. 2003, 208, 123−139. (47) Desgranges, C.; Ngale, K. N.; Delhommelle, J. Prediction of critical properties for Naphthacene, Triphenylene and Chrysene by Wang-Landau simulations. Fluid Phase Equilib. 2012, 322−323, 92− 96. (48) Zheng, L.-Y.; Chiu, Y.-N.; Lai, S. T. Calculation of critical temperature Tc in high temperature superconductivity using grand canonical ensemble. J. Mol. Struct.: THEOCHEM 2004, 680, 37−39. G



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of solutes between water and hexadecylpyridinium chloride micelles. J. Chem. Soc., Perkin Trans. 2 1997, 19−24. (67) Abraham, M. H.; Rafols, C. Factors that influence tadpole narcosis. An LFER analysis. J. Chem. Soc., Perkin Trans. 2 1995, 1843− 1851. (68) Hills, E. E.; Abraham, M. H.; Hersey, A.; Bevan, C. D. Diffusion coefficients in ethanol and in water at 298 K: Linear free energy relationships. Fluid Phase Equilib. 2011, 303, 45−55. (69) Mintz, C.; Clark, M.; Burton, K.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of Solvation Correlations for Gaseous Solutes Dissolved in Toluene and Carbon Tetrachloride Based on the Abraham Model. J. Solution Chem. 2007, 36, 947−966. (70) Sprunger, L. M.; Proctor, A.; Acree, W. E., Jr.; Abraham, M. H.; Benjelloun-Dakhama, N. Correlation and prediction of partition coefficient between the gas phase and water, and the solvents dry methyl acetate, dry and wet ethyl acetate, and dry and wet butyl acetate. Fluid Phase Equilib. 2008, 270, 30−44. (71) Abraham, M. H.; Gola, J. R. M.; Gil-Lostes, J.; Acree, W. E., Jr.; Cometto-Mũniz, J. E. Determination of solvation descriptors for terpene hydrocarbons from chromatographic measurements. J. Chromatogr. A 2013, 1293, 133−141. (72) Mintz, C.; Burton, K.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of solvation correlations for gaseous solutes dissolved in chloroform and 1,2-dichloroethane based on the Abraham model. Fluid Phase Equilib. 2007, 258, 191−198. (73) Abraham, M. H.; Poole, C. F.; Poole, S. K. Solute effects on reversed-phase thin-layer chromatography A linear free energy relationship analysis. J. Chromatogr. A 1996, 749, 201−209. (74) Stephens, T. W.; De La Rosa, N. E.; Saifullah, M.; Ye, S.; Chou, V.; Quay, A. N.; Acree, W. E., Jr.; Abraham, M. H. Abraham model correlations for solute partitioning into o-xylene, m-xylene and pxylene from both water and the gas phase. Fluid Phase Equilib. 2011, 308, 64−71. (75) Abraham, M. H.; Acree, W. E., Jr. Prediction of gas to water partition coefficients from 273 to 373K using predicted enthalpies and heat capacities of hydration. Fluid Phase Equilib. 2007, 262, 97−110. (76) Sprunger, L. M.; Gibbs, J.; Acree, W. E., Jr.; Abraham, M. H. Correlation and prediction of partition coefficients for solute transfer to 1, 2-dichloroethane from both water and from the gas phase. Fluid Phase Equilib. 2008, 273, 78−86. (77) Stephens, T. W.; De La Rosa, N. E.; Saifullah, M.; Ye, S.; Chou, V.; Quay, A. N.; Acree, W. E., Jr.; Abraham, M. H. Abraham model correlations for transfer of neutral molecules and ions to sulfolane. Fluid Phase Equilib. 2011, 309, 30−35. (78) Mintz, C.; Burton, K.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of solvation correlations for gaseous solutes dissolved in dimethyl sulfoxide and propylene carbonate based on the Abraham model. Thermochim. Acta 2007, 459, 17−25. (79) Stephens, T. W.; Chou, V.; Quay, A. N.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of solvation correlations for organic solutes and gases dissolved in 1-propanol and tetrahydrofuran. Thermochim. Acta 2011, 519, 103−113. (80) Mintz, C.; Burton, K.; Ladlie, T.; Clark, M.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of solvation correlations for organic solutes and gases dissolved in N,N-dimethylformamide and tert-butanol. J. Mol. Liq. 2009, 144, 23−31. (81) Sprunger, L. M.; Achi, S. S.; Pointer, R.; Blake-Taylor, B. H.; Acree, W. E., Jr.; Abraham, M. H. Development of Abraham model correlations for salvation characteristics of linear alcohols. Fluid Phase Equilib. 2009, 286, 170−174. (82) Sprunger, L. M.; Achi, S. S.; Pointer, R.; Acree, W. E., Jr.; Abraham, M. H. Development of Abraham model correlations for solvation characteristics of secondary and branched alcohols. Fluid Phase Equilib. 2010, 288, 121−127. (83) Sprunger, L. M.; Achi, S. S.; Acree, W. E., Jr.; Abraham, M. H. Development of correlations for describing solute transfer into acyclic alcohol solvents based on the Abraham model and fragment-specific equation coefficients. Fluid Phase Equilib. 2010, 288, 139−144.

(84) Sprunger, L. M.; Achi, S. S.; Acree, W. E., Jr.; Abraham, M. H. Linear Free Energy Relationship Correlations for Enthalpies of Solvation of Organic Solutes into Room-Temperature Ionic Liquids Based on the Abraham Model with Ion-Specific Equation Coefficients. Ind. Eng. Chem. Res. 2009, 48, 8704−8709. (85) Abraham, M. H.; Nasezadeh, A.; Acree, W. E., Jr. Correlation and Prediction of Partition Coefficients From the Gas Phase and from Water to Alkan-1-ols. Ind. Eng. Chem. Res. 2008, 47, 3990−3995. (86) Zissimos, A. M.; Abraham, M. H.; Klamt, A.; Eckert, F.; Wood, J. A Comparison between the Two General Sets of Linear Free Energy Descriptors of Abraham and Klamt. J. Chem. Inf. Comput. Sci. 2002, 42, 1320−1331. (87) Platts, J. A.; Abraham, M. H.; Butina, D.; Hersey, A. Estimation of Molecular Linear Free Energy Relationship Descriptors by a Group Contribution Approach. 2. Prediction of Partition Coefficients. J. Chem. Inf. Comput. Sci. 2000, 40, 71−80. (88) Abraham, M. H.; Acree, W. E., Jr. Solute Descriptors for Phenoxide Anions and Their Use To Establish Correlations of Rates of Reaction of Anions with Iodomethane. J. Org. Chem. 2010, 75, 3021− 3026. (89) Hoover, K. R.; Acree, W. E., Jr.; Abraham, M. H. Chemical Toxicity Correlations for Several Fish Species Based on the Abraham Solvation Parameter Model. Chem. Res. Toxicol. 2005, 18, 1497−1505. (90) Abraham, M. H.; Ibrahim, A.; Acree, W. E., Jr. Air to Blood Distribution of Volatile Organic Compounds: A Linear Free Energy Analysis. Chem. Res. Toxicol. 2005, 18, 904−911. (91) Sprunger, L.; Acree, W. E., Jr.; Abraham, M. H. Comment on “Systematic Investigation of the Sorption Properties of Polyurethane Foams for Organic Vapors. Anal. Chem. 2007, 79, 6891−6893. (92) Sprunger, L.; Acree, W. E., Jr.; Abraham, M. H. Linear Free Energy Relationship Correlation of the Distribution of Solutes between Water and Sodium Dodecyl Sulfate (SDS) Micelles and between Gas and SDS Micelles. J. Chem. Inf. Model. 2007, 47, 1808− 1817. (93) Mintz, C.; Clark, M.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of Solvation Correlations for Gaseous Solutes Dissolved in Water and in 1-Octanol Based on the Abraham Model. J. Chem. Inf. Model. 2007, 47, 115−121. (94) Zhao, Y. H.; Abraham, M. H.; Ibrahim, A.; Fish, P. V.; Cole, S.; Lewis, M. L.; de Groot, M. J.; Reynolds, D. P. Predicting Penetration Across the Blood-Brain Barrier from Simple Descriptors and Fragmentation Schemes. J. Chem. Inf. Model. 2007, 47, 170−175. (95) Berthod, A.; Mitchell, C. R.; Armstrong, D. W. Could linear solvation energy relationships give insights into chiral recognition mechanisms? 1. π−π and charge interaction in the reversed versus the normal phase mode. J. Chromatogr. A 2007, 1166, 61−69. (96) Bui, H.; Masquelin, T.; Perun, T.; Castle, T.; Dage, J.; Kuo, M.S. Investigation of retention behavior of drug molecules in supercritical fluid chromatography using linear solvation energy relationships. J. Chromatogr. A 2008, 1206, 186−195. (97) Endo, S.; Brown, T. N.; Goss, K.-U. General Model for Estimating Partition Coefficients to Organisms and Their Tissues Using the Biological Compositions and Polyparameter Linear Free Energy Relationships. Environ. Sci. Technol. 2013, 47, 6630−6639. (98) Horn, M.; Matyjaszewski, K. Solvent Effects on the Activation Rate Constant in Atom Transfer Radical Polymerization. Macromolecules 2013, 46, 3350−3357. (99) Uslu, H. Extraction of Gibberellic Acid from Aqueous Solution by Amberlite LA-2 in Different Diluents. J. Chem. Eng. Data 2012, 57, 3685−3689. (100) Hofmann, K.; Spange, S. Influence of the Boron Atom on the Solvatochromic Properties of 4-Nitroaniline-Functionalized Boronate Esters. J. Org. Chem. 2012, 77, 5049−5055. (101) Dean, J. A. Lange’s Handbook of Chemistry, 15th ed.; McGraw Hill: New York, 1999. (102) Lide, D. R. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press/Taylor and Francis: Boca Raton, FL, 2004. (103) Yaws, C. L. Chemical Properties Handbook, McGraw-Hill: New York, 1998. H



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