Considering the dispersive interactions in the COSMO-SAC model for

Considering the dispersive interactions in the COSMO-SAC model for more accurate predictions of fluid phase behavior

Chieh-Ming Hsieh,a,* Shiang-Tai Lin,b Jadran Vrabeca a

Thermodynamics and Energy Technology, University of Paderborn, Paderborn, Germany b

Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan

Abstract A term to consider the contribution of the dispersive interactions to the non-ideality of mixtures is introduced into the COSMO-SAC model on the basis of molecular simulation data from classical model force fields. This dispersion term is a one-constant Margules equation, where the constant is determined from the molecular dispersion parameter of the components. Furthermore, an atomic contribution method is proposed to calculate the dispersion parameter for a given molecule. For binary systems containing molecules consisting of C, H, N, O, F and Cl atoms, a total of 13 global parameters is introduced with the COSMO-SAC-dsp model. These parameters are obtained from regression to a large training set of binary vapor-liquid equilibrium (VLE) data from experiment. The overall deviations for VLE calculations on this training set are reduced by 25% in terms of the vapor pressure and 12% in terms of the vapor phase mole fraction. This dispersion term can provide a significant improvement for infinite dilution activity coefficient predictions, where the accuracy was increased by around 33%.

Keywords: Phase equilibria, infinite dilution activity coefficient, prediction, dispersive interaction, COSMO-SAC 1

*To whom correspondence should be addressed: Email [email protected]

Highlights 

A dispersion contribution to the activity coefficient calculation is introduced into the COSMO-SAC model



This contribution is based on molecular simulation data for classical model force fields



All parameters in the proposed term are adjustment to VLE data and the overall deviations are reduced by 25% in terms of the vapor pressure and 12% in terms of the vapor phase mole fraction



The accuracy of infinite dilution activity coefficient predictions is improved significantly, the overall deviation is reduced by about 33%

2

1. Introduction Information on the distribution of chemical species between coexisting phases is of fundamental importance in the chemical industry, environmental engineering and the pharmaceutical industry [1-5]. While such information can be obtained from experimental work, it is crucial to have reliable predictive thermodynamic models because of the significant time and cost associated with measuring experimental data. Many researchers have thus expended significant efforts in establishing methods to predict the thermodynamic properties and the phase behavior of pure fluids and mixtures [3-6]. Due to the advances in computing power, methodological efficiency and the development of accurate force fields (which describe the inter- and intramolecular interactions), numerical simulation methods (Monte Carlo or molecular dynamics) can be used to study many different problems, including the estimation of thermophysical properties and phase equilibria [6-10]. Molecular simulation methods are applicable with very few constraints, as both equilibrium or non-equilibrium conditions can be studied and both static and dynamic thermodynamic data can be sampled [11]. Furthermore, with a good description of the molecular interactions through force fields, molecular simulation can provide very accurate predictions of the thermophysical properties including phase equilibria for pure fluids and mixtures. In addition to accurate results, molecular simulation also provides an insight into the mechanisms on the microscopic level and detailed information about the effect of different interactions. However, such simulations require a large computational effort (which translates to hours for a typical vapor-liquid equilibrium state point on today’s computer equipment) to obtain results [12]. The scope of predictive thermodynamic models can range from simple cubic 3

equations of state (EOS), excess Gibbs energy (Gex) models, and their combinations through Gex-based mixing rules [3-5]. Through research over the past two decades, a new class of predictive methods has emerged that utilizes the results from computational chemistry. These COSMO-based methods (such as COSMO-RS [13-15] and its variants COSMO-SAC [16-19], COSMO-RS(Ol) [20] or COSMO-vac [21]), determine the liquid-phase non-ideality on the basis of the molecular surface charge distribution derived from first-principles solvation calculations [22,23]. This type of models does not contain any species-dependent parameters and fluid phase equilibria can be predicted with the molecular structure as the only input. Thus, COSMO-based methods do not suffer from the problem of missing parameters. With the advantage of relying only on a few global and atomic parameters, these methods have become more important and are broadly applied to the prediction of the thermophysical properties and the phase behavior of pure fluids and mixtures [1,24]. With a combination of cubic EOS and Gex-based mixing rules, the application of COSMO-based models can be extended to high pressure systems including supercritical fluids [25-30]. In preceding works, the electrostatic interactions of the COSMO-SAC model were revised to provide good predictions for phase equilibria of organic mixtures [19,31]. However, the neglect of the dispersive interactions in activity coefficient calculation for mixtures remains unsolved in the COSMO-based models. The dispersive interaction is the most general attractive intermolecular interaction in the condensed phase. It is caused by spontaneous temporary polarities in individual molecules that polarize their neighbors. The net effect of dispersive interactions is a short-range and weak attraction (compared with other molecular interactions) which, however, dominates in non-polar liquids. This interaction is expressed as a function of molecular properties (e.g., exposed surface area or surface tension) in some 4

thermodynamic models [13,32-34], whereas the composition of the solutes and solvents is taken into account in other thermodynamic models [35]. In the COSMO-based methods, the dispersive interaction is considered as the function of exposed surface area and atomic type of surface segments. Furthermore, this interaction is taken into account only for the determination of vaporization data (such as vapor pressure or enthalpy of vaporization of pure fluids) [16,17,36]. For mixtures, dispersive interaction was neglected until now in the development of the COSMO-SAC model [16]. In this study, a new dispersion term to consider the contribution of the dispersive interaction to the non-ideality of mixtures is introduced into the COSMO-SAC model on the basis of molecular simulation data from classical model force fields. It is termed COSMO-SAC-dsp model.

2. COSMO-SAC model In the original publication of the COSMO-SAC model [18], the activity coefficient of molecule i in mixture S can be determined from * chg Gi*/chg S  Gi / i

ln  i / S 

 ln  iSG /S ,

RT

(1)

where  Gi*/chg is the solvation charging Gibbs energy of molecule i in solvent j (j=i for j pure solvent i and j=S for mixture S). The Staverman-Guggenheim (SG) combinatorial term [37,38] was used to consider molecular size and shape effects

ln  iSG / S  ln

with  i 

i xi

x i qi



j

x jq j



  z qi ln i  li  i 2 i xi

, i 

x i ri



j

x j rj



, li 

j

x jl j ,

(2)

z ( ri  q i )  ( ri  1) , where z = 10 is the 2 5

coordination number, while qi and ri are the normalized surface area and volume of component i (the standard surface area and volume for normalization were 79.53 Å2 and 66.69 Å3). According to Ben-Naim’s definition [39], the solvation Gibbs energy G*sol is the Gibbs energy difference of a molecule (solute) in its ideal gas phase state and in a real solution (solvent) at the same temperature and pressure. The solvation Gibbs energy is usually determined from two contributions: cavity formation Gibbs energy G*cav and charging Gibbs energy G*chg. These are based on a hypothetical solvation process: first, a hard solute molecule is inserted into the solvent and then the interactions between solute and solvent are turned on. According to the previously developed solvation model [17,33,40-42], the charging Gibbs energy of solute i in the mixture solvent S is calculated from four Gibbs energy contributions: ideal solvation (is), charging-averaging correction (cc), restoring (rst) and dispersion (dsp)  G i*/chg   G i*is   G i* cc   G i*/rstS   G i*/dsp . S S

(3)

 G i*is accounts for the energy difference of molecule i in the ideal conductor and in the

ideal gas state.  G i* cc considers the energy shift due to the charge-averaging process for the molecule. The charge-averaging correction is required because pairwise interactions between independent segments are assumed in the COSMO-SAC model [17,18]. Since these two terms are obtained from quantum mechanical calculations considering only molecule i, they are pure component properties and cancel out in the activity coefficient calculation. Then, Eq. (1) becomes ln  i / S 

Gi*/rstS  Gi*/rsti RT



* dsp Gi*/dsp S  Gi / i

RT

dsp SG  ln  ires / S  ln  i / S  ln  i / S .

 ln  iSG /S ,

(4)

6

The residual term ln  ires/ S

mainly considers the permanent electrostatic

interactions between molecules in the mixture and is obtained by ln  ires /S 

G i*/rstS  G i*/rsti RT



Ai

nhb ,OH ,OT

a eff

  p ( t i

t

t m





) ln it/ S ( mt )  it/ i ( mt ) ,

(5)

m

where Ai is the molecular surface area and aeff is the surface area of a standard surface segment. The -profile p i ( m ) is a histogram of surface area normalized by molecular surface area with a screening charge density of  m for molecule i. In the COSMO-SAC model, for a better description of the hydrogen-bonding (hb) interactions, the molecular surface segments are categorized into three types: non-hydrogen-bonding (nhb), hydroxyl groups (OH) and other hydrogen bonding groups (OT), i.e. O, N, F and H bound to N and F. Therefore, the -profile of molecule i is the summation of these three contributions, p i ( )  p inhb ( )  p iOH ( )  p iOT ( ) [19]. The segment activity coefficient i / j ( m ) of a segment with surface charge density  m in solution S (j = S) or in its pure fluid state i (j = i) is determined by  nhb,OH,OT ln it/ j ( mt )   ln    s

 n

  W ( mt ,  ns )   p sj ( ns )is/ j ( ns ) exp   , RT  

(6)

where  W ( mt ,  ns ) describes the electrostatic interaction between surface segment of type t with screening charge density  m and surface segment of type s with screening charge density  n . It is calculated by  W ( mt ,  ns )  c ES  mt   ns   c hb ( mt ,  ns )( mt   ns ) 2 , 2

with the electrostatic interaction coefficient cES/(kcal‧mol-1‧Å4‧e-2) = 6525.69 + 1.4859∙108 /(T/K)2 and hydrogen bonding interaction coefficients

7

(7)

 4013.78  932.31 -1 4 -2 t s chb(  m ,  n )/(kcal‧mol ‧Å ‧e )   3016.43 0 

if s  t  OH and  mt   ns  0 if s  t  OT and  mt   ns  0 if s  OH , t  OT and  mt   ns  0 otherwise.

(8) The residual contribution was taken from preceding work on COSMO-SAC without modification or parameter optimization. Details can be found in Ref. [19]. In the development of the COSMO-SAC model, the dispersion contribution to the charging Gibbs energy for solute i in solvent j  G i*/dspj was estimated by using a first-order mean field approximation to consider all possible pairwise interactions between the atoms in different molecules [17]. Because the difference of this contribution in its pure fluid state (i/i) and in a mixture (i/S) is small, the dispersion contribution to the activity coefficient ln  idsp / S is also small and was assumed to be zero until now in the COSMO-SAC model. However, it is shown in the present study that this small dispersion contribution does influence the accuracy of fluid phase behavior prediction significantly. In this study, the molecular simulation tool for thermodynamic properties ms2 [12] was used to study the contribution of the dispersive interactions to the activity coefficient. The role of the dispersive interaction was quantified by a series of molecular simulations for binary mixtures composed of Lennard-Jones model fluids (summarized in Table 1). This type of model mixtures was chosen because it contains only repulsive and dispersive interactions (the residual term becomes zero). As listed in Table 1, all Lennard-Jones fluids considered in this study have the same size and shape (spheres with a constant size parameter ) in order to study the dispersion contribution in the COSMO-SAC (2010) model (the combinatorial terms become 8

zero). Different binary Lennard-Jones model mixtures, where the ratio of energy parameters 1/2 was varied from 1.2 to 1.8, were simulated to study the effect of different strengths of the dispersive interaction on the non-ideality of the mixture. The molecular simulation results for the excess Gibbs energy for binary mixtures of Lennard-Jones fluids are shown in Figure 1. These simulation results can be described by the one-constant Margules equation G ex  Ax 1 x 2 , RT

(9a)

with constant A determined from [43,44] 1  A  w    1   2    1 2  , 2 

(9b)

where w = 0.275; 1 and 2 are the interaction energy parameters of the two Lennard-Jones model components as summarized in Table 1. Since the one-constant Margules equation can describe these model systems that are dominated by dispersive interaction, it was used to consider the contribution of the dispersive interaction to the activity coefficient in the COSMO-SAC model. Only binary mixtures were regarded in this work, but it is straightforward to extend the Margules equation to multicomponent mixtures [3,5,45]. For binary mixtures containing the components 1 and 2, the activity coefficient due to the dispersion contribution for substances 1 and 2 are then ln  1dsp  Ax 22 ,

(10a)

ln  2dsp  Ax 12 ,

(10b)

where xi is the mole fraction of component i in the liquid phase and the constant A was determined from the molecular dispersion parameters 1 and 2 via Eq. (9b) with

9

- 0.275 , if (a) water  hb - only - acceptor  (b) COOH  nhb or hb - donor - acceptor  w (c) water  COOH   0.275, otherwise,

(11)

where hb-only-acceptor denotes substances that are able to form a hydrogen bond by accepting a proton from its neighbor, such as ethers, esters, ketones and nitro compounds; hb-donor-acceptor is substance that is able to form hydrogen bonds by either providing a proton or accepting a proton from its neighbors, such as alcohols and amines; COOH indicates substances with a carboxyl group, such as carboxylic acids and benzoic acids. The molecular dispersion parameter Molecule for real molecules was determined from an atomic contribution approach  Molecule 

1 N Atom

n



j

Nj ,

(12)

j 1

where j is the dispersion parameter of atom j, Nj the number of type j atoms, n the total number of atoms in the molecule and NAtom the total number of atoms for which the dispersion parameter is not zero. Currently, only hydrogen atoms were excluded in NAtom, if they are not bound to oxygen, nitrogen and fluorine atoms. This treatment is similar to the coarse-grained modeling in molecular simulations where the effect of a hydrogen atom is taken into account through other heavier atoms connected to it. The average of the atomic dispersion parameter over all atoms of a molecule, instead of the sum of it, is used to determine the molecular dispersion parameter for a molecule because we wish not to include the size effects, which has already been taken into account by the Staverman-Guggenheim combinatorial term. For example, the molecular dispersion parameter of n-hexane would be twice larger than that of n-propane when the sum of the dispersion interactions was used. This dispersion term 10

was then too large and deteriorated the prediction accuracy. Our choice of the one-constant Margules equation, which is appropriate for equally sized molecules, also helps exclude the effects from molecular size and shape differences in the dispersion term. The values of the atomic dispersion parameter j, as summarized in Table 2, were optimized here to a large set of experimental vapor-liquid equilibrium (VLE) data of binary mixtures. Detail discussion is given below.

3. Computational details and parameter optimizations The computational details and all parameter values for the residual and combinatorial contributions are the same as those for the COSMO-SAC (2010) model, details are given in Ref. [19]. The freely available cosmo-file database (VT-database) containing over 1400 compounds from Liu’s group at Virginia Tech [46,47] was used in this work. However, the cosmo-files of some compounds in the VT-database were updated by Sandler’s group at the University of Delaware and were used in this work. It should be noted that the VT-database was established using the quantum mechanical program DMol3 in Materials Studio, including the COSMO solvation calculation [22,23]. Different quantum mechanical packages provide different cosmo-files (output from COSMO calculations) and often the accuracy of the predictions may become worse when cosmo-files from other quantum mechanical packages are used [48-50]. Therefore, it is recommended that a re-optimization of the COSMO-SAC parameters may be necessary in such cases. The calculation of the dispersion contribution to the activity coefficient was as follows: First, the molecular dispersion parameter Molecule was obtained from Eq. (12). 11

Then, the activity coefficient due to the dispersion contribution was determined for both components in the binary mixture from Eqs. (9) to (11). In this study, only substances composed of carbon, hydrogen, nitrogen, oxygen, chlorine and fluorine atoms were considered. Because an atomic contribution approach was used to estimate the molecular dispersion parameter for real molecules, a total of 13 global parameters was introduced in the COSMO-SAC-dsp model. In addition, the type of hybridization was considered for carbon, nitrogen and oxygen atoms. Hydrogen atoms were taken into account only when they are bound to oxygen, nitrogen or fluorine atoms, i.e. if they are capable to form a hydrogen bond. These 13 global parameters were obtained from optimization to experimental VLE data using the following objective function  1 Obj    M

 P calc  P expt j j   P expt j 1  j  M

2

 expt   y1calc , j  y1, j  



 2    



1/ 2

,

(13)

where M is number of VLE data points, P the vapor pressure and y1 the vapor phase mole fraction of component 1 in the mixture; the superscripts calc and expt indicate the calculated results and the experimental data, respectively. All experimental VLE data were retrieved from the DECHEMA Chemistry Data Series [51-53]. The parameter optimization of these 13 global parameters was carried out as follows: First, the ten dispersion parameters for carbon, nitrogen, oxygen, chlorine and fluorine were optimized to experimental VLE data for 219 non-hydrogen-bonding (nhb) binary systems. Once these parameters were optimized, they were fixed in the subsequent optimization of the remaining parameters. Second, the dispersion parameters of H(OH) and H(NH) were optimized to experimental VLE data for 170 binary systems which contain hydrogen-bonding (hb) interactions, but no water or carboxylic acids. Finally, 52 binary VLE systems containing water and carboxylic 12

acids were used to optimize the dispersion parameters of H(water/COOH). All binary systems used in this optimization are summarized in the Supplementary Material and the values of these global atomic dispersion parameters are listed in Table 2.

4. Results and discussions In this study, VLE data and infinite dilution activity coefficient data were used to validate the COSMO-SAC-dsp model. VLE data for a total of 441 binary mixtures, containing 1308 isotherms, in the temperature range from 207.92 K to 553.15 K and pressure range from 0.084 kPa to 6.87 MPa, were considered. These data were retrieved from the DECHEMA Chemistry Data Series [51-53]. The infinite dilution activity coefficient data were taken from the literature [54-66]. They consist of 2385 data points (966 binary mixtures) in the temperature range from 238.2 K to 453.2 K. These systems can be categorized into two types: nhb and hb systems. Systems where one or both components have at least one hydroxyl (OH) group (including water and carboxylic acids) or amine (NH and NH2) group were considered as hb systems; the others are nhb systems. It should be noted that exclusively VLE data were used in the optimization of the dispersion parameters.

4.1 Vapor-liquid equilibrium results The introduced dispersion parameters were obtained from fitting to all VLE data in this study, but it is nonetheless interesting to discuss the descriptive performance of the COSMO-SAC-dsp model. Its accuracy was evaluated using the average absolute relative deviation in vapor pressure (AARD-P) and average absolute deviation in vapor phase mole fraction (AAD-y1) 13

N

AARD - P (%)   i 1

AAD - y1 (%) 

N

 i 1

calc expt  1  M 1 Pi , j  Pi , j  ,  100 %  expt  N  j 1 M P i, j  

(14a)

 M 1 calc    y1,i , j  y1expt ,i , j  100 %  ,   j 1 M 

(14b)

1 N

where M is the number of data points on an isotherm of a binary mixture; N is the number of isotherms of a binary mixture for which experimental data were considered. For some binary systems, experimental data were available for numerous isotherms in the database, such as for benzene + cyclohexane or water + methanol. Averaging over all isotherms for a binary mixture was done to avoid the overrepresentation of such systems in the overall deviation. In this work, the modified UNIFAC model [67] was used as a baseline reference. Table 3 summarizes the overall deviations with respect to VLE data from three different models. Modified UNIFAC is the most accurate, with the lowest AARD-P and AAD-y1 of 3.44% and 1.53%, but only 411 out of 441 binary VLE systems were considered because of the missing parameter issue. The overall AARD-P and AAD-y1 from the COSMO-SAC-dsp model are 5.11% and 2.12%, respectively, which are 25% and 12% lower than the overall AARD-P and AAD-y1 of the COSMO-SAC (2010) model. This significant improvement was observed for both nhb and hb systems. As listed in Table 3, the overall AARD-P and AAD-y1 for nhb systems from the COSMO-SAC-dsp model are 3.51% and 1.45%, respectively, those from the COSMO-SAC (2010) model are 4.33% and 1.56%. For hb systems, the overall AARD-P and AAD-y1 from the COSMO-SAC-dsp model are 6.68% and 2.78%, respectively, those from the COSMO-SAC (2010) model are 9.18% and 3.26%. Overall, the results from the COSMO-SAC-dsp model are significantly better than those from the COSMO-SAC (2010) model for both nhb and hb systems. Figure 2 shows VLE phase diagrams of four exemplary binary mixtures, which 14

cover a wide variety of substances: alkanes, ketones, aldehydes, acetates, aromatics and

fluoro-compounds.

In

these

cases,

the

COSMO-SAC

(2010)

model

underestimates the non-ideality of the mixtures. After considering the dispersion contribution, the COSMO-SAC-dsp model can describe these systems very well and often has a similar accuracy as the modified UNIFAC model. The COSMO-SAC-dsp model is clearly more accurate than the COSMO-SAC (2010) model, especially for systems containing fluoro-compounds. As summarized in Table 4, the overall AARD-P and AAD-y1 from the COSMO-SAC-dsp model were significantly reduced in comparison to the COSMO-SAC (2010) model. It is worth mentioning that modified UNIFAC has a severe issue of missing parameters for this type of systems (only three out of 15 binary mixtures can be described). Therefore, the COSMO-SAC-dsp model can be particularly useful for this type of mixtures. For hb systems, also a significant improvement was achieved as illustrated in Fig. 3. In analogy to the findings above, the COSMO-SAC (2010) model usually underestimates the non-ideality of mixtures which can be improved by considering the dispersive interactions in mixtures. However, it should be noted that the COSMO-SAC (2010) model sometimes overestimates the non-ideality of mixtures, especially for systems containing water or small carboxylic acids [three types of systems with w = -0.275 in Eq. (11)]. A possible explanation for this phenomenon is that the molecular structure and molecular surface screening charges from quantum mechanical and COSMO calculations cannot represent these molecules in these mixtures or under certain concentration or temperature conditions. For example, it has been experimentally shown that acetic acid forms dimers or chain fragments in the liquid phase [68,69], so using only acetic acid monomers in VLE calculations is not sufficient. Chen et al. [70] proposed a theoretically based route to better describe 15

systems containing acetic acid. In the present study, we propose an empirical way, considering dispersive interaction with w = -0.275 for these complex systems. For mixtures of acetic acid + nhb compounds, an improvement was achieved as shown in Fig. 3(c) without significantly influencing predictions for mixtures of acetic acid + hb compounds as illustrated in Fig. 3(d).

4.2 Infinite dilution activity coefficient predictions The infinite dilution activity coefficient 

∞

usually represents the highest

deviation from the ideal solution and is important for chemical processes design. This type of data is thus a good candidate to evaluate the predictive power of the COSMO-SAC-dsp model. The overall deviations of the predicted results from the experimental data were calculated as follows N

Error   i 1

1 ln  i ,calc  ln  i ,expt N

,

(15)

where N is the number of data points. The modified UNIFAC model [67] was again used as the baseline reference for comparison. As listed in Table 5, the modified UNIFAC model provides the lowest deviations for nhb systems, but the COSMO-SAC-dsp model exhibits the lowest deviations for hb systems. It has been shown in prior work [71] that the modified UNIFAC model has larger deviations for infinite dilution activity coefficients of both water in alkanes (including cyclic alkanes) and alkanes in water. Figure 4 compares the predicted

ln  

from the

COSMO-SAC-dsp model and the COSMO-SAC (2010) model. For both nhb and hb systems, the COSMO-SAC (2010) model provides good predictions, but on average it underestimates ln   , especially for higher values of ln   , cf. Fig. 4(b). The COSMO-SAC-dsp model leads to slightly higher values for ln   in case of nhb 16

systems and reduces the overall deviations by 25%. In case of hb systems, the predicted ln   from the COSMO-SAC-dsp model are shifted up if w = 0.275 in Eq. (11) or shifted down if w = -0.275. The overall deviations for hb systems were reduced by 45%. Furthermore, as listed in Table 5, a total of 1621 ln   data (861 binary mixtures) were considered as a validation dataset since these binary mixtures were not included in the training set for parameter optimization. For nhb systems, the accuracy of COSMO-SAC-dsp for the validation dataset and for the whole dataset is similar; for hb systems, the accuracy of COSMO-SAC-dsp for the validation dataset is slightly worse than that for the whole dataset. However, a significant improvement was still observed, a reduction of 26 % in overall error when comparing with that of COSMO-SAC (2010). This again supports that considering the dispersive interactions in the COSMO-SAC-dsp model can improve its predictive accuracy. It is useful to quantify the relative contribution to the activity coefficient from different terms of the COSMO-SAC-dsp model. Some examples are listed in Table 6: The experimental ln  

values included in this study range from -1.347

(methylethylketone in chloroform) to 23.384 (1-octadecanol in water) and the contribution from the dispersion term ranges from -0.876 to 0.796. For binary mixtures of alkanes + alkanes, the most important contribution is from the combinatorial term, while the dispersion term has a contribution of zero. The residual contribution dominates for most other binary mixtures, except for those having relatively small ln   values within the range of the dispersion term. This is consistent with the physics that the dispersive interaction is usually weaker than the electrostatic interaction.

17

5. Conclusions A contribution considering the dispersive interactions in mixtures was introduced into the COSMO-SAC (2010) model, denoted as COSMO-SAC-dsp model, to improve its accuracy for VLE and the infinite dilution activity coefficient. This dispersion term is based on molecular simulation data from classical model force fields for binary mixtures, where the dispersive interactions were varied. For binary mixtures, dispersion was described with the one-constant Margules equation where the constant is determined from the molecular dispersion parameter of the components. Furthermore, an atomic contribution method is proposed to calculate the dispersion parameter for a given molecule. A total of 13 global parameters was introduced into the COSMO-SAC-dsp model and all of them were obtained from regression to a large set of binary VLE data from experiments. This dispersion term significantly improves the accuracy of predictions of the infinite dilution activity coefficient for both non-hydrogen-bonding and hydrogen-bonding systems. The extension of this method to multicomponent systems is straightforward and is underway.

Acknowledgements The authors are grateful for the financial support by the Alexander von Humboldt Stiftung. We acknowledge Dr. Stanley I. Sandler at the University of Delaware for sharing the quantum mechanical and COSMO calculation results from his group. We wish to thank Frederik Zysk for his efforts on performing part of molecular simulations in this work. 18

Supplementary Material Supplementary material associated with this article can be found in the online version.

19

Tables Table 1. Summary of simulated binary mixtures of Lennard-Jones model fluids with 1/kB = 100 and 1 = 2 and the parameter A of the one-constant Margules equation

2/kB (K)

1/2

A

83.333

1.2

0.102

71.428

1.4

0.324

62.500

1.6

0.592

55.556

1.8

0.875

20

Table 2. Values of the global atomic dispersion parameters of the COSMO-SAC-dsp model

Atom /kB (K)

Atom type C (sp3)

115.7023

C (sp2)

117.4650

C (sp)

66.0691

-O-

95.6184

=O

-11.0549

N (sp3)

15.4901

N (sp2)

84.6268

N (sp)

109.6621

F

52.9318

Cl

104.2534

H (OH)

19.3477

H (NH)

141.1709

H (water/COOH)

58.3301

21

Table 3. Comparison of overall deviations of vapor–liquid equilibrium predictions from different predictive methods COSMO-SAC-dsp

COSMO-SAC (2010)



Mod. UNIFAC (1998)

Na

AARD-P (%)

AAD-y1 (%)

AARD-P (%)

AAD-y1 (%)

N a

AARD-P (%)

AAD-y1 (%)

nhb

219

3.51

1.45

4.33

1.56

197 b

2.23

0.96

hb

222

6.68

2.78

9.18

3.26

214 b

4.55

2.06

Overall

441

5.11

2.12

6.77

2.42

411 b

3.44

1.53

a. Number of binary mixtures considered in this study. It should be noted that for a given binary mixture data on several isotherms may have been used. b. Fewer binary mixtures were considered in case of modified UNIFAC due to missing parameters.

22

Table 4. Comparison of overall deviations of vapor–liquid equilibrium predictions for systems containing fluoro-compounds Na

AARD-P (%)

AAD-y1 (%)

COSMO-SAC-dsp

15

4.92

3.37

COSMO-SAC (2010)

15

9.87

3.71

Mod. UNIFAC (1998)

3b

4.57

2.03

a. Number of binary mixtures considered in this study. It should be noted that for a given binary mixture data on several isotherms may have been used. b. Fewer binary mixtures were considered in case of modified UNIFAC due to missing parameters.

23

Table 5. Comparison of overall deviations of infinite dilution activity coefficient predictions nhb

hb

Na

Error b

Na

Error b

1411 (651) c

0.199

348 (210) c

0.455

1923 (728)

0.192

462 (238)

0.336

COSMO-SAC (2010)

1923 (728)

0.255

462 (238)

0.624

Mod. UNIFAC (1998)

1923 (728)

0.104

419 (224) d

0.496

COSMO-SAC-dsp

a. Number of infinite dilution activity coefficient data points considered in this study. The number of binary mixtures is given in parentheses. b. Error was determined from Eq. (15). c. Number of infinite dilution activity coefficient data points for binary mixtures that are not included in parameter optimization. d. Fewer infinite dilution activity coefficient data were considered in case of modified UNIFAC due to missing parameters.

24

Table 6. Comparison of various contributions to ln ∞

Solute

Solvent

n-pentane n-pentane n-pentane n-pentane 1,1-dichloroethane n-pentane n-pentane benzene 1-pentene isoprene toluene chloroform acetone n-pentane benzene n-pentane 1-octadecanol n-heptane

n-heptane n-tetracosane benzene 1,2-dichloroethane 1,1,1-trichloroethane acetonitrile acetone triethylamine ethylbenzoate methylethylketone ethylacetate n-hexane 1-butanol ethanol water water water acetic acid

T (K)

ln 

 , expt i

293.15 0.000 298.15 -0.300 298.15 0.713 298.15 1.504 328.2 0.058 298.15 2.845 298.15 1.637 323.5 0.247 313.2 0.668 293.15 0.405 298.2 0.285 301 0.457 298 0.924 298 2.197 298 7.800 298.15 11.552 298.15 23.341 298 3.157

ln  i ,calc

ln  i ,calc

COSMO-SAC COSMO-SAC -dsp (2010) -0.032 -0.032 -0.611 -0.611 0.793 0.793 1.198 1.189 0.076 0.076 3.310 3.200 1.473 1.141 0.281 0.201 0.131 0.079 0.207 -0.020 0.205 -0.009 0.314 0.291 0.582 0.529 2.020 1.736 8.166 7.370 11.694 10.951 22.694 22.114 3.206 4.081

25

ln  ires

0.0001 0.0012 0.8001 1.2032 0.0787 3.3610 1.1924 0.2426 0.1426 -0.0206 -0.0185 0.3346 0.5548 1.8569 8.4222 12.3241 29.9470 4.3649

% -0.4% -0.2% 100.8% 100.4% 103.6% 101.6% 81.0% 86.3% 109.0% -9.9% -9.0% 106.7% 95.4% 91.9% 103.1% 105.4% 132.0% 136.2%

ln  icomb

-0.0317 -0.6123 -0.0075 -0.0146 -0.0032 -0.1610 -0.0513 -0.0413 -0.0632 0.0003 0.0094 -0.0434 -0.0255 -0.1214 -1.0519 -1.3733 -7.8329 -0.2835

% 100.4% 100.2% -0.9% -1.2% -4.2% -4.9% -3.5% -14.7% -48.3% 0.1% 4.6% -13.8% -4.4% -6.0% -12.9% -11.7% -34.5% -8.8%

ln  idsp

0.0000 0.0000 0.0009 0.0098 0.0004 0.1095 0.3317 0.0799 0.0514 0.2277 0.2145 0.0224 0.0525 0.2845 0.7955 0.7429 0.5793 -0.8758

% 0.0% 0.0% 0.1% 0.8% 0.5% 3.3% 22.5% 28.4% 39.3% 109.8% 104.4% 7.1% 9.0% 14.1% 9.7% 6.4% 2.6% -27.3%

Figure Caption Figure 1. Comparison of the dimensionless excess Gibbs energy from molecular simulation (◇: 1/2 = 1.2; ○: 1/2 = 1.4; ∆: 1/2 = 1.6; □: 1/2 = 1.8) and the one-constant Margules equation with a constant A as determined by Eq. (9b) (-∙∙-:

1/2 = 1.2; -∙-: 1/2 = 1.4; ---: 1/2 = 1.6; ─: 1/2 = 1.8).

Figure 2. Comparison of vapor-liquid equilibria from COSMO-SAC-dsp (─), COSMO-SAC (2010) (-∙-) and modified UNIFAC (---) for non-hydrogen-bonding systems: (a) n-butane (1) + acetone (2), (b) butanal (1) + n-heptane (2), (c) methyl acetate (1) + benzene (2) and (d) trifluoromethane (1) + isobutene (2).The results from modified UNIFAC are not shown in (d) because of the missing parameter issue.

Figure 3. Comparison of vapor-liquid equilibria from COSMO-SAC-dsp (─), COSMO-SAC (2010) (-∙-) and modified UNIFAC (---) for hydrogen-bonding systems: (a) n-hexane (1) + ethanol (2), (b) cyclohexylamine (1) + N,N-dimethylformamide (2), (c) cyclohexane (1) + acetic acid (2) and (d) ethanol (1) + acetic acid (2). The results from COSMO-SAC (2010) are not shown in (c) because it failed for this system.

Figure 4. Comparison of prediction of infinite dilution activity coefficient from COSMO-SAC-dsp (〇) and COSMO-SAC (2010) (∆) with experimental data for (a) non-hydrogen-bonding systems and (b) hydrogen-bonding systems.

26

Figures Figure 1.

ex G /RT

0.2

0.1

0.0 0.0

0.2

0.4 0.6 x1 (mol . mol-1)

27

0.8

1.0

Figure 2.

P (MPa)

0.4

343.15 K

0.2 318.15 K

0.0 0.08

P (MPa)

(a)

(b) 323.15 K

0.04 303.15 K

(c) 323.15 K

0.04 303.15 K

0.00 4

(d) 293.15 K

P (MPa)

P (MPa)

0.00 0.08

2

283.15 K

0 0.0

0.2

0.4

0.6

x1, y1 (mol . mol-1) 28

0.8

1.0

Figure 3.

473.15 K

(a)

P (MPa)

3.00 2.00 333.15 K

0.10 0.05 0.00

293.15 K

(b)

P (MPa)

0.06

393.15 K

0.04 373.15 K

0.02 0.00

P (MPa)

0.03

(c)

0.02 323.15 K

0.01 0.00

P (MPa)

0.03

(d)

0.02 0.01

313.15 K

0.00 0.0

0.2

0.4

0.6

x1, y1 (mol . mol-1) 29

0.8

1.0

Figure 4(a)

5 4 ln ∞ (cal)

3 2 1 0 -1 -1

0

1

2

3

4

5

ln ∞ (exp)

Figure 4(b)

25 20 ln ∞ (cal)

15 10 5 0 0

5

10

15

ln ∞ (exp)

30

20

25

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33

Supplementary Material to Considering the dispersive interactions in the COSMO-SAC model for more accurate predictions of fluid phase behavior

Chieh-Ming Hsieh,a,* Shiang-Tai Lin,b Jadran Vrabeca a. Thermodynamics and Energy Technology, University of Paderborn, Paderborn, Germany b. Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan

compound 1

compound 2

ethane n-pentane n-pentane n-hexane n-hexane n-hexane n-hexane n-hexane 2-methylpentane 2-methylpentane 2,2-dimethylbutane n-heptane n-heptane cyclopentane cyclopentane cyclopentane cyclohexane

benzene n-hexane benzene n-octane cyclohexane benzene carbon tetrachloride 1,2-dichloroethane n-heptane n-octane n-hexane n-octane ethylbenzene carbon tetrachloride chloroform tetrachloroethylene n-heptane

N 1 4 5 1 3 5 6 2 2 1 1 1 3 1 1 1 3

b

Tmin – Tmax (K) 298.15 298.15 289.15 328.15 298.15 293.15 293.15 298.15 318.15 328.15 298.15 328.15 298.12 298.15 298.15 298.15 298.15

-

298.15 308.7 323.15 328.15 343.15 343.15 333.15 323.15 328.15 328.15 298.15 328.15 327.76 298.15 298.15 298.15 333.15

COSMO-SAC-dsp AARD-P AAD-y1 (%) (%) 5.58 0.51 3.76 0.91 3.49 1.64 2.59 0.76 1.46 0.62 2.74 1.38 2.46 1.11 1.94 1.53 0.42 0.40 1.13 0.42 1.66 0.49 2.96 0.91 0.48 0.49 0.65 0.26 2.14 0.75 6.27 0.99 1.40 0.52

COSMO-SAC (2010)c AARD-P AAD-y1 (%) (%) 5.60 0.51 3.76 0.91 3.47 1.64 2.59 0.76 1.46 0.62 2.72 1.37 2.91 1.26 2.07 1.58 0.41 0.39 1.12 0.42 1.66 0.49 2.96 0.91 0.47 0.49 0.19 0.13 2.53 0.88 6.66 1.05 1.40 0.52

modified UNIFACd AARD-P AAD-y1 (%) (%) 20.17 0.62 3.66 0.92 2.48 1.41 3.10 0.89 0.29 0.35 0.82 0.61 0.66 0.46 1.52 1.14 0.51 0.42 1.71 0.43 1.07 0.38 2.86 0.88 2.46 0.59 1.55 0.51 0.50 0.39 12.91 1.41 0.62 0.35

cyclohexane cyclohexane cyclohexane cyclohexane cyclohexane 1-butene 1-butene 1-hexene 1-hexene 1-hexene 1-hexene 1-hexene 1-heptene 1-heptene 1,3-butadiene benzene benzene benzene benzene benzene benzene benzene toluene toluene ethylbenzene m-xylene carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride dichloromethane

2,2,4-trimethylpentane methylcyclohexane cis-decahydronaphthalene 1-octene toluene n-butane 1,3-butadiene n-hexane n-heptane n-octane benzene 1,1,2,2-tetrachloroethane n-heptane n-octane benzene n-heptane cyclohexane 1-heptene cyclohexene ethylbenzene 1,2-dichloroethane monochlorobenzene n-decane m-xylene styrene n-decane n-heptane cyclohexane benzene ethylbenzene 1,2-dichloroethane monochlorobenzene chloroform

5 1 1 1 4 7 3 2 1 1 1 1 1 1 5 17 18 1 7 4 9 5 3 3 3 3 2 4 12 7 2 6 1

308.15 308.15 298.15 313.15 298.15 310.93 310.93 328.15 313.15 328.15 298.15 333.15 328.15 328.15 298.15 293.15 283.15 328.15 273.15 453.15 283.15 298.15 373.5 373.6 323.15 373.5 298.15 283.15 283.15 293.15 303.15 293.15 318.15

-

348.15 308.15 298.15 313.15 343.15 410.93 338.71 333.15 313.15 328.15 298.15 333.15 328.15 328.15 413.15 488.15 423.15 328.15 353.15 553.15 353.15 348.15 393.7 393.7 363.15 393.7 323.15 343.15 473.15 353.15 313.15 353.15 318.15

1.33 0.26 0.79 1.29 2.00 2.91 1.13 1.00 0.94 3.60 3.65 14.98 0.05 2.84 6.37 2.87 5.02 1.49 1.18 1.43 0.59 2.42 6.68 1.52 0.90 2.57 2.19 0.85 5.39 1.74 1.90 2.12 1.84

0.44 0.15 0.13 0.26 1.62 1.31 0.65 0.46 0.48 1.05 1.02 2.74 0.15 0.68 2.19 1.75 1.87 0.62 0.62 4.10 0.28 0.66 1.45 0.84 0.76 1.73 1.13 0.34 1.96 0.37 1.26 0.75 0.34

1.33 0.26 0.79 1.28 1.99 2.91 1.13 1.01 0.94 3.60 3.66 15.44 0.05 2.83 6.37 2.85 5.00 1.50 1.18 1.43 0.76 2.44 6.67 1.52 0.90 2.56 2.66 1.13 4.63 0.98 1.84 1.67 1.83

0.44 0.15 0.13 0.26 1.61 1.31 0.65 0.46 0.48 1.05 1.02 2.84 0.13 0.69 2.19 1.74 1.87 0.63 0.62 4.10 0.36 0.66 1.44 0.84 0.76 1.73 1.27 0.44 1.73 0.24 1.24 0.61 0.34

0.78 0.17 1.03 1.35 1.32 1.82 1.81 0.26 0.95 1.96 1.63 2.46 0.81 3.98 9.16 1.02 0.38 0.82 0.60 1.17 0.40 1.60 5.49 1.68 1.05 2.13 0.78 1.05 1.14 1.64 1.35 0.61 1.00

0.30 0.14 0.13 0.34 0.88 1.24 0.67 0.15 0.20 0.65 0.50 0.21 0.26 1.01 2.50 0.78 0.25 0.40 0.32 3.98 0.10 0.57 0.75 0.86 0.74 1.59 0.43 0.41 0.71 0.42 1.13 0.26 0.13

dichloromethane chloroform chloroform chloroform chloroform chloroform 1,2-dichloroethane 1,2-dichloroethane 1,2-dichloroethane n-butane n-pentane n-pentane n-pentane n-hexane n-hexane n-hexane n-hexane n-hexane 2-methylpentane n-heptane n-heptane n-heptane n-heptane n-heptane n-heptane cyclohexane cyclohexane cyclohexane 1-pentene 1-hexene 1-hexene 1-hexene 1-hexene

1,2-dichloroethane n-hexane n-heptane benzene toluene 1,2-dichloroethane n-heptane n-octane 2,2,4-trimethylpentane acetone propanal acetone methyl acetate methyl ethyl ketone 1,4-dioxane triethylamine nitroethane 1-nitropropane nitroethane 3-pentanone n-butyl acetate ethyl n-butyrate 1,4-dioxane n-butyronitrile pyridine cyclohexanone methyl methacrylate 1,4-dioxane 1,4-dioxane methyl ethyl ketone ethyl acetate 1,4-dioxane triethylamine

4 5 1 7 2 1 3 1 1 3 1 6 1 2 2 1 2 1 1 4 2 2 1 1 2 2 3 2 1 1 3 1 1

293.15 298.15 298.15 298.2 307.95 323.15 303.15 323.15 343.15 273.15 313.15 238.15 298.15 333.15 308.15 333.15 298.15 298.15 298.15 299.15 347.85 347.85 353.15 318.15 340.95 323.15 318.12 293.15 353.15 333.15 313.15 353.15 333.15

-

323.15 328.15 298.15 333.15 318.15 323.15 343.15 323.15 343.15 313.15 313.15 422.6 298.15 338.15 353.15 333.15 318.15 298.15 298.15 368.15 373.15 373.15 353.15 318.15 353.15 348.15 348.14 308.15 353.15 333.15 333.15 353.15 333.15

1.32 3.70 4.99 1.90 3.17 2.04 1.95 1.78 4.46 2.73 1.07 2.18 3.90 1.75 5.17 2.10 14.64 5.83 12.14 5.31 2.50 1.48 3.86 9.28 3.50 9.32 3.94 7.20 11.90 5.58 2.00 7.90 1.85

1.90 1.52 0.99 1.35 1.66 0.48 0.81 0.86 1.00 1.11 0.76 2.40 2.07 0.68 2.23 0.59 2.74 1.12 1.76 1.35 0.87 1.08 1.55 2.15 2.31 1.65 1.11 3.59 3.27 2.08 0.54 2.99 0.58

1.32 4.12 5.47 1.62 2.76 1.99 2.13 1.70 4.62 10.40 8.30 8.23 2.51 5.42 5.43 1.11 9.88 6.91 6.74 6.30 4.55 2.37 4.07 10.21 3.58 11.74 1.27 7.48 12.55 9.36 5.03 8.23 0.60

1.90 1.66 1.11 1.23 1.66 0.46 0.87 0.80 1.06 2.59 2.90 2.62 1.37 2.46 2.33 0.24 1.94 1.03 1.07 2.18 1.06 1.16 1.66 2.44 2.34 2.10 0.35 3.66 3.59 3.85 1.88 3.15 0.15

1.63 0.68 0.60 1.42 3.18 1.00 0.95 2.72 2.81 1.83 3.90 1.43 2.49 4.24 2.37 0.76 5.57 4.25 0.18 4.83 3.05 2.98 0.50 3.10 1.08 5.06 1.28 4.61 5.34 0.77 1.73 1.15 0.69

1.88 0.43 0.41 1.12 1.83 0.21 0.48 1.00 0.59 0.81 1.31 1.81 0.86 1.67 1.15 0.14 1.12 1.18 0.15 0.76 0.89 1.34 0.95 0.33 1.68 0.99 0.70 3.18 3.81 0.65 0.33 1.31 0.17

benzene benzene benzene benzene benzene benzene benzene benzene benzene benzene benzene propanal butanal butanal acetone acetone acetone acetone acetone acetone acetone methyl ethyl ketone methyl ethyl ketone methyl ethyl ketone methyl ethyl ketone ethyl formate ethyl formate ethyl formate methyl acetate methyl acetate methyl acetate methyl acetate ethyl acetate

diisopropyl ether 1,4-dioxane di-n-propyl ether triethylamine nitromethane 1-nitropropane acetonitrile propionitrile N,N-dimethylaniline fluorobenzene hexafluorobenzene cyclohexane n-heptane benzene n-hexane n-heptane n-octane cyclohexane benzene carbon tetrachloride chloroform n-heptane cyclohexane benzene 1,2-dichloroethane cyclohexane benzene chloroform cyclohexane 1-hexene benzene chloroform n-heptane

3 5 3 2 2 1 4 1 1 4 5 1 2 1 9 4 1 5 7 3 13 2 1 5 1 1 1 2 2 1 3 4 2

323.15 298.15 323.15 333.15 298.15 298.15 293.15 318.15 343.15 333.15 303.15 318.15 318.15 343.15 253.15 273.15 313.15 298.15 298.15 273.15 288.15 318.15 323.15 298.15 333.15 323.15 323.15 308.15 308.15 323.15 303.15 308.15 323.15

-

343.15 333.15 343.15 353.15 318.15 298.15 343.15 318.15 343.15 353.15 343.15 318.15 343.15 343.15 338.15 338.15 313.15 328.15 328.15 423.15 433.15 323.15 323.15 333.15 333.15 323.15 323.15 318.15 313.15 323.15 323.15 328.15 343.15

3.68 6.84 0.98 3.50 2.98 11.85 1.61 5.32 4.88 1.70 14.82 1.19 0.75 0.37 1.93 2.25 3.52 1.40 2.71 2.16 1.67 3.10 2.26 2.13 0.71 3.94 0.55 2.28 3.92 1.33 1.76 4.53 2.80

0.79 2.63 0.58 1.13 0.67 1.63 0.56 1.33 0.14 0.34 5.31 0.65 0.99 0.35 1.62 1.07 0.32 0.87 0.86 2.70 1.17 1.39 0.42 0.73 0.44 2.09 0.71 0.62 2.70 0.71 0.35 1.77 1.75

3.78 7.17 0.98 1.91 7.07 13.87 3.95 6.77 4.12 2.15 7.00 5.68 4.15 3.21 8.41 8.60 10.09 9.25 9.35 5.73 1.63 7.25 6.62 5.99 2.58 2.72 5.23 0.43 3.94 6.03 7.15 2.13 1.23

0.82 2.75 0.59 0.56 2.09 1.80 1.30 1.89 0.13 0.42 2.76 2.45 1.56 1.35 2.86 2.30 1.43 2.79 3.16 2.58 0.80 2.04 2.12 2.15 1.07 0.48 2.23 0.30 0.80 2.14 2.31 1.10 0.51

1.94 3.66 1.44 0.69 0.82 9.36 0.69 1.24 2.67 1.29 0.29 0.46 0.95 0.78 1.73 1.61 2.07 3.61 1.75 2.35 0.96 3.02 0.51 1.02 1.71 1.76 1.22 0.69 2.07 1.47 0.83 1.28 0.71

0.28 1.48 0.67 0.39 0.63 1.79 0.47 0.79 0.11 0.37 0.31 0.42 1.06 0.54 1.41 1.07 0.32 0.92 0.67 2.75 0.85 2.63 0.69 0.45 0.35 0.45 0.73 0.53 0.59 0.49 0.51 0.48 0.39

ethyl acetate ethyl acetate ethyl acetate ethyl acetate ethyl acetate diethyl ether diethyl ether diisopropyl ether diisopropyl ether diisopropyl ether methyl tert-butyl ether methyl tert-butyl ether methyl tert-butyl ether methyl tert-butyl ether methyl tert-butyl ether 1,4-dioxane 1,4-dioxane 1,4-dioxane 1,4-dioxane di-n-propyl ether di-n-propyl ether di-n-propyl ether di-n-propyl ether tetrahydrofuran tetrahydrofuran tetrahydrofuran tetrahydrofuran tetrahydrofuran tetrahydrofuran carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride

cyclohexane 1-octene benzene ethylbenzene trichloroethylene carbon tetrachloride chloroform n-heptane toluene ethylbenzene n-hexane 1-hexene 1-heptene carbon tetrachloride chloroform n-octane n-nonane 1-octene toluene n-octane n-nonane toluene ethylbenzene n-hexane n-heptane cyclohexane benzene carbon tetrachloride 1,2-dichloroethane ethyl acetate 1,4-dioxane nitromethane nitroethane

5 1 4 3 3 1 2 2 3 3 1 1 3 1 1 1 1 1 2 1 1 3 3 4 1 4 4 1 4 1 6 1 1

293.15 348.15 323.15 323.15 333.15 308.15 290.15 323.15 323.15 323.15 333.15 313.15 293.15 313.15 313.15 353.15 353.15 353.15 353.15 363.15 363.15 323.15 323.15 303.15 298.15 303.15 303.15 298.15 302.15 323.14 303.15 318.15 298.15

-

345 348.15 343.15 343.15 343.15 308.15 298.15 343.15 343.15 343.15 333.15 313.15 333.15 313.15 313.15 353.15 353.15 353.15 373.15 363.15 363.15 343.15 343.15 333.15 298.15 333.15 333.15 298.15 343.15 323.14 353.15 318.15 298.15

2.14 2.27 0.46 3.31 0.69 1.25 1.41 2.58 4.67 5.76 1.76 1.53 1.64 1.77 1.74 3.13 1.96 7.25 4.21 3.52 9.79 0.97 2.12 4.71 7.02 2.85 0.76 0.26 0.96 3.69 1.17 7.42 5.57

1.52 1.79 0.33 1.96 0.87 0.30 0.91 1.46 1.11 1.28 1.04 0.43 1.12 0.67 1.03 0.87 0.80 2.24 0.69 3.38 2.75 0.93 1.50 1.47 2.14 0.77 0.33 0.31 0.37 1.32 0.44 4.13 1.89

1.89 2.68 3.75 3.84 1.73 1.40 1.39 2.53 4.79 5.87 1.69 1.61 1.71 1.93 1.62 3.32 2.25 7.51 4.58 3.52 9.73 0.99 2.21 4.78 7.13 2.93 0.92 0.32 0.97 2.18 1.13 6.73 5.25

0.74 0.29 1.23 1.10 1.06 0.35 0.89 1.45 1.12 1.28 1.01 0.45 1.10 0.73 1.00 0.93 0.70 2.35 0.77 3.37 2.74 0.92 1.47 1.49 2.17 0.79 0.34 0.31 0.37 0.66 0.44 3.86 1.82

0.74 1.62 0.71 2.52 2.21 1.10 2.44 0.42 0.82 3.14 0.16 1.83 1.47 1.35 2.11 0.64 1.56 2.06 0.83 3.48 8.80 2.48 0.87 2.04 2.93 1.06 1.06 2.55 1.62 1.10 1.01 1.49 2.06

0.42 1.56 0.28 1.62 1.16 0.66 1.28 1.16 1.72 1.57 0.55 0.51 1.17 0.51 1.60 0.92 1.33 0.85 1.10 3.21 2.55 1.58 1.85 0.50 0.95 0.37 0.60 0.71 0.98 0.32 0.79 0.93 0.80

carbon tetrachloride carbon tetrachloride carbon tetrachloride dichloromethane chloroform chloroform chloroform chloroform chloroform chloroform chloroform 1,2-dichloroethane 1,1,1-trifluoroethane triethylamine nitroethane 1-nitropropane acetonitrile acetonitrile propionitrile pyridine cyclohexane benzene carbon tetrachloride 1,2-dichloroethane 1,1-difluoroethane 1,1-difluoroethane 1,1-difluoroethane difluoromethane difluoromethane trifluoromethane pentafluoroethane 1,1,1,2,3,3,3-heptafluoropropane 1,1,1,2-tetrafluoroethane

1-nitropropane acetonitrile pyridine triethylamine methyl ethyl ketone 3-pentanone ethyl acetate 1,4-dioxane di-n-propyl ether tetrahydrofuran triethylamine 3-pentanone isobutane n-heptane n-octane monochlorobenzene n-heptane toluene n-heptane n-octane dimethyl carbonate dimethyl carbonate dimethyl carbonate dimethyl carbonate isobutane vinyl chloride 1,1-dichloroethane isobutane dichloromethane isobutane isobutane isobutane isobutane

1 1 5 1 2 4 2 1 1 4 1 4 2 2 1 2 2 2 1 2 1 4 1 3 4 2 2 2 2 2 3 3 4

298.15 318.15 313.15 283.15 318.15 313.15 313.15 323.15 333.15 298.15 283.14 323.15 323.15 333.15 308.15 348.15 293.15 321.35 318.15 353.15 298.15 298.15 298.15 298.15 303.2 303.2 303.2 301.8 303.2 283.15 293.15 303.15 293.66

-

298.15 318.15 353.15 283.15 328.15 343.15 323.15 323.15 333.15 323.15 283.14 353.15 333.15 353.15 308.15 393.15 318.15 343.15 318.15 369.75 298.15 338.15 298.15 333.15 333.2 323.2 323.2 321.8 313.2 293.15 313.15 323.15 323.2

4.76 6.97 3.18 6.16 3.01 5.22 5.81 2.86 4.90 3.56 13.57 0.89 1.15 2.93 5.49 3.88 10.65 1.94 3.57 2.38 3.78 0.96 4.33 4.07 0.46 2.20 6.28 7.21 4.39 5.15 5.19 10.36 6.90

1.11 4.05 1.35 1.01 0.77 1.81 2.15 1.06 0.69 1.08 4.20 0.46 5.50 0.86 3.16 1.28 5.87 0.95 1.32 1.19 2.20 0.43 1.51 1.28 2.09 1.20 2.58 5.74 3.50 5.02 3.12 3.09 2.37

5.00 6.32 3.01 5.80 1.63 4.19 4.38 2.84 5.05 3.46 13.39 1.96 9.05 1.57 3.86 5.25 10.56 2.77 5.21 2.47 4.12 5.92 1.76 6.28 5.94 5.40 9.73 8.52 15.79 21.59 17.86 20.65 17.89

1.13 3.85 1.29 0.97 0.44 1.53 1.80 1.05 0.73 1.05 4.16 0.74 4.32 0.56 2.23 1.78 5.46 1.61 1.91 1.21 2.43 2.31 0.84 2.16 2.26 1.80 2.11 3.87 2.77 4.56 5.80 7.72 6.88

2.13 0.53 0.89 0.73 3.54 6.55 3.10 6.17 5.34 4.45 2.85 0.75 12.13 1.01 4.74 1.64 2.69 1.44 5.28 0.74 -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a

1.02 0.82 0.30 0.13 0.94 2.23 1.37 2.39 0.87 1.38 0.85 0.56 5.43 0.46 2.52 0.61 2.76 0.89 1.81 0.95 -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a -- a

acetaldehyde acetaldehyde propanal propanal propanal acetone acetone acetone acetone acetone acetone methyl ethyl ketone methyl acetate methyl acetate ethyl acetate ethyl acetate ethyl acetate n-butyl acetate diethyl ether diethyl ether diethyl ether methyl tert-butyl ether methyl tert-butyl ether tetrahydrofuran tetrahydrofuran acetonitrile acetonitrile N,N-dimethylformamide tetrahydrofuran triethylamine dimethyl carbonate acetaldehyde cyanogen chloride

acetone methyl acetate methyl ethyl ketone methyl acetate ethyl acetate acetic anhydride methyl acetate vinyl acetate tetrahydrofuran nitromethane acetonitrile acetonitrile butanal ethyl acetate 1,4-dioxane acetonitrile furfural N,N-dimethylformamide acetone nitromethane acetonitrile methyl acetate acetonitrile ethyl acetate acetonitrile 1,4-dioxane nitromethane benzaldehyde triethylamine 1,4-dioxane diethyl carbonate 1,2-propylene oxide hydrogen cyanide

2 2 1 2 2 2 5 3 1 1 1 2 2 5 12 1 1 2 3 1 1 3 1 2 1 2 1 2 1 2 5 2 1

298.15 323.15 318.15 303.16 303.16 298.15 293.15 298.15 302.15 318.15 318.15 328.15 313.15 312.91 330.65 333.15 298.15 363.15 273.15 293.65 293.65 353.15 313.15 313.15 302.15 298.15 333.15 378.15 313.2 323.2 313.15 298.15 288.15

-

348.15 373.15 318.15 313.13 313.15 328.15 328.15 323.15 302.15 318.15 318.15 333.67 323.15 373.17 358.15 333.15 298.15 388.15 303.15 293.65 293.65 373.17 313.15 333.15 302.15 313.15 333.15 398.15 313.2 343.2 353.15 348.15 288.15

1.87 1.66 0.79 0.42 0.88 3.96 2.08 6.75 1.37 1.64 5.95 5.56 0.46 2.49 0.56 0.85 9.12 3.38 1.18 4.62 16.33 2.82 4.74 0.72 7.05 3.35 1.30 6.32 1.27 2.74 2.17 7.14 5.15

3.13 1.17 0.56 1.03 0.62 1.14 1.04 2.90 0.70 0.99 2.00 2.05 0.40 1.10 0.36 0.89 1.08 2.59 1.60 0.56 4.51 1.25 2.37 0.53 2.34 0.79 0.70 1.74 0.28 2.80 0.74 3.33 2.34

2.12 0.49 0.62 0.42 1.09 3.97 2.12 7.11 1.88 1.07 4.68 5.26 0.42 2.66 2.37 0.85 9.30 7.60 5.40 5.21 13.54 1.91 3.55 1.55 5.76 2.63 1.42 1.91 1.71 3.01 2.47 2.24 5.31

2.97 1.05 0.51 1.03 0.56 1.08 1.06 3.05 0.83 0.86 1.55 1.95 0.41 1.12 0.85 0.84 1.09 4.51 2.64 0.44 4.04 0.24 1.97 0.35 1.90 0.91 0.73 0.63 0.33 2.92 0.80 0.78 2.40

2.55 1.12 0.87 0.75 1.24 6.56 1.20 4.39 0.44 0.87 1.91 0.55 1.50 2.46 0.47 1.44 6.57 1.87 3.70 1.98 5.57 4.12 4.78 0.40 6.17 1.18 0.51 2.83 -- a -- a -- a -- a -- a

2.97 0.82 0.56 0.91 0.69 1.57 0.31 1.90 0.25 0.81 0.62 0.29 0.43 1.10 0.30 0.76 0.82 1.08 2.37 0.28 1.71 2.01 2.50 0.26 1.55 0.74 0.49 0.65 -- a -- a -- a -- a -- a

chlorodifluoromethane difluoromethane 1,1,1-trifluoroethane pentafluoroethane n-pentane n-pentane n-pentane n-hexane n-hexane n-hexane n-hexane n-hexane n-hexane 2-methylpentane 2,2-dimethylbutane 2,3-dimethylbutane n-heptane n-heptane n-heptane n-heptane n-octane cyclohexane cyclohexane cyclohexane cyclohexane cyclohexane cyclohexane 1-hexene 1-hexene benzene benzene benzene benzene

dichlorodifluoromethane 1,1-difluoroethane 1,1,1,2-tetrafluoroethane 1,1-difluoroethane 1-propanol 1-butanol 1-pentanol ethanol 1-propanol 1-butanol 2-methyl-1-propanol 2-butanol 1-pentanol 1-pentanol 1-pentanol methanol 1-butanol 2-methyl-1-propanol 2-butanol 1-pentanol phenol 1-propanol isopropanol 1-butanol 2-methyl-2-propanol 1-hexanol cyclohexanol ethanol 2-butanol 1-propanol 1-butanol 2-methyl-1-propanol 2-butanol

27 3 5 3 2 1 1 13 4 5 1 4 3 1 1 1 5 3 2 3 1 6 6 9 3 4 3 1 1 8 2 6 5

207.92 273.15 278.15 313.15 313.15 303.15 303.15 263.15 318.15 298.15 332.53 323.15 298.15 298.15 298.15 313.15 323.15 333.15 338.15 348.15 383.15 298.15 298.15 298.15 303.15 323.15 308.15 333.15 333.15 303.15 298.15 298.15 298.15

-

356.15 323.15 333.15 333.02 317.15 303.15 303.15 473.15 348.15 348.15 332.53 348.15 323.15 298.15 298.15 313.15 363.15 348.15 348.15 368.15 383.15 338.15 342.15 383.15 343.3 354.35 328.15 333.15 333.15 348.15 318.15 353.15 353.15

4.61 2.69 0.91 4.41 13.96 8.21 11.47 2.67 3.17 5.17 4.66 6.16 7.41 7.76 7.91 15.10 4.66 5.73 1.39 2.59 3.39 1.67 0.85 3.98 1.28 4.22 2.22 6.28 4.15 4.49 4.72 3.53 4.01

2.44 4.07 2.58 4.03 1.73 0.78 0.73 1.96 1.65 0.84 0.99 2.38 1.12 0.25 0.17 5.65 1.76 1.86 1.07 1.50 0.39 0.77 0.73 1.69 1.09 0.64 0.07 1.70 1.78 2.28 1.05 4.70 1.76

4.70 2.87 0.95 2.74 20.61 12.73 14.77 7.66 7.39 8.24 8.05 8.55 10.26 10.09 10.23 4.05 6.64 8.48 3.47 3.80 4.10 5.27 4.54 4.09 2.36 5.92 2.94 13.40 6.91 8.63 7.72 6.03 5.86

2.44 3.98 2.56 3.83 2.69 1.28 0.94 2.83 2.81 1.23 1.61 2.90 1.47 0.30 0.21 2.02 2.63 2.79 2.00 2.07 0.61 2.07 1.95 1.79 1.46 0.75 0.08 4.37 2.72 4.17 1.39 4.68 1.99

-- a -- a -- a -- a 6.40 1.52 2.24 2.90 2.21 1.77 2.77 5.09 1.69 0.96 1.61 2.36 3.81 1.78 0.92 0.67 0.93 1.04 1.73 3.37 1.09 1.40 1.13 2.84 1.12 1.27 1.08 2.43 2.35

-- a -- a -- a -- a 0.96 0.10 0.24 1.52 1.17 0.48 0.97 2.30 0.41 0.13 0.08 1.50 1.04 0.74 0.83 0.82 0.54 0.67 0.77 1.50 1.17 0.36 0.06 0.64 0.55 0.77 0.59 4.61 1.69

benzene toluene methanol ethanol ethanol ethanol ethanol ethanol ethanol ethanol ethanol 1-propanol 1-propanol 1-propanol 1-butanol 1-butanol 2-methyl-1-propanol 2-butanol 2-methyl-2-propanol allyl alcohol carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride carbon tetrachloride chloroform chloroform chloroform 1,2-dichloroethane 1,2-dichloroethane 1,2-dichloroethane 1,2-dichloroethane

2-methyl-2-propanol 1-butanol 1,2-dichloroethane n-heptane n-octane 2,2,4-trimethylpentane cyclohexane methylcyclohexane benzene toluene 1,2-dichloroethane n-heptane n-octane monochlorobenzene n-octane n-decane n-octane n-octane n-octane toluene ethanol 1-propanol 1-butanol 2-methyl-1-propanol 2-butanol 2-methyl-2-propanol ethanol 1-propanol isopropanol 1-propanol 1-butanol 2-methyl-1-propanol 3-methyl-1-butanol

6 5 3 5 5 4 4 6 7 9 2 3 2 1 1 3 1 1 1 1 4 5 4 3 3 7 4 1 1 4 1 4 4

298.15 333.31 313.15 303.27 318.15 273.15 283.15 273.15 293.15 308.15 313.15 298.15 358.15 368.15 373.15 358.15 373.15 358.15 343.15 363.15 298.15 293.15 308.15 338.15 338.15 288.15 308.15 328.15 323.15 323.15 323.15 323.15 323.15

-

348.15 373.15 333.15 343.17 348.15 333.15 323.15 328.15 333.15 358.15 323.15 348.15 363.15 368.15 373.15 388.15 373.15 358.15 343.15 363.15 338.15 343.15 353.15 355.15 353.15 343.15 333.15 328.15 323.15 353.15 323.15 353.15 353.15

3.97 2.83 4.92 1.48 3.06 2.24 1.86 2.08 5.19 5.52 8.36 3.93 2.41 3.30 2.15 1.87 2.17 1.96 2.39 5.12 4.39 6.82 5.03 4.85 4.00 5.50 4.61 4.41 4.97 3.25 7.22 3.02 4.73

1.94 1.56 3.36 1.49 1.49 1.46 0.73 1.61 2.59 2.25 5.30 2.84 0.98 1.81 1.31 0.59 1.12 1.11 0.95 3.12 2.08 1.47 1.24 1.48 1.25 2.91 2.41 1.56 2.32 2.80 2.82 1.11 1.08

6.19 4.87 9.42 6.34 7.10 5.96 6.44 6.32 11.53 9.99 11.86 7.61 5.76 5.01 4.64 2.15 4.08 3.88 1.38 4.08 7.45 8.31 5.72 5.54 4.68 6.13 6.77 5.50 5.96 4.83 8.58 4.25 5.00

2.81 2.16 5.48 2.38 2.11 2.42 2.85 1.89 5.25 4.02 7.05 3.58 1.93 2.59 2.28 0.62 1.68 1.31 0.39 3.02 3.49 1.88 1.39 1.64 1.50 3.16 3.50 1.92 2.78 3.52 3.27 1.54 1.22

1.77 2.49 1.71 1.30 1.47 3.55 1.14 1.44 1.48 1.78 0.81 2.01 1.61 1.54 3.13 0.71 0.70 1.68 2.69 3.91 1.34 1.21 1.14 1.46 0.84 2.20 1.97 1.12 1.55 3.83 5.46 1.87 6.24

1.56 0.62 1.32 1.35 0.69 1.75 0.65 0.80 1.39 1.00 0.99 2.53 0.42 0.74 0.65 0.38 0.50 0.77 0.56 2.15 1.06 1.04 0.59 0.92 0.67 1.67 1.04 0.73 0.84 2.30 0.70 1.28 0.62

monochlorobenzene n-hexane diethylamine diethylamine diethylamine diethylamine diethylamine n-hexane n-butylamine n-butylamine 1-hexene n-butylamine n-butylamine benzene toluene cyclohexane methylcyclohexane benzene toluene ethylbenzene styrene carbon tetrachloride monochlorobenzene cyclohexane cyclohexane benzene carbon tetrachloride benzene ethyleneimine toluene benzene n-hexane n-heptane

cyclohexanol di-n-propylamine n-hexane cyclohexane benzene toluene ethylbenzene n-butylamine n-heptane cyclohexane n-butylamine benzene toluene ethylenediamine ethylenediamine aniline aniline aniline aniline aniline aniline aniline aniline cyclohexylamine pyrrolidine N-methylformamide N-methylformamide N-methylcyclohexylamine cyclohexane o-toluidine formic acid acetic acid acetic acid

2 1 1 3 2 1 1 1 2 2 1 2 2 1 1 4 1 4 6 2 3 3 1 3 2 2 2 2 1 3 2 1 3

383.15 333.15 333.15 302.25 308.15 308.15 308.15 333.15 328.15 313.15 333.15 323.15 313.15 293.15 333.15 308.35 353.15 323.15 293.15 353.15 343.15 298.15 393.15 298.15 313.15 318.15 318.15 313.15 298.15 353.15 298.15 313.2 293.15

-

403.15 333.15 333.15 314.25 328.15 308.15 308.15 333.15 348.15 333.15 333.15 343.15 333.15 293.15 333.15 392.45 353.15 392.45 373.17 373.15 373.15 323.15 393.15 323.15 333.15 328.15 328.15 323.15 298.15 383.15 333.11 313.2 313.15

3.10 3.76 2.73 3.60 1.93 3.65 4.62 2.57 5.65 0.96 0.61 2.37 1.73 8.76 7.94 4.68 5.10 2.63 8.26 0.88 2.71 8.03 0.99 7.57 2.14 6.56 10.69 0.92 3.09 4.71 26.94 5.08 13.76

1.18 1.50 1.39 1.08 1.12 1.67 0.79 1.96 3.73 2.10 0.83 1.32 3.36 1.86 7.20 0.17 0.31 0.17 4.01 0.43 0.73 0.09 0.41 1.24 1.49 0.04 0.15 1.07 1.09 1.10 20.94 7.58 11.49

2.49 3.15 1.89 2.52 0.99 2.19 2.87 2.25 5.30 0.80 0.48 1.94 1.38 10.38 9.15 4.55 5.01 2.85 8.45 5.50 2.93 7.77 0.93 7.38 2.73 22.97 6.59 0.85 4.71 4.97 14.49 51.36 57.65

0.95 1.31 1.01 0.87 0.69 1.36 0.65 1.83 3.59 2.04 0.73 1.15 3.26 2.04 7.64 0.17 0.31 0.17 4.06 0.45 0.79 0.08 0.43 1.22 1.72 0.26 0.05 1.08 1.46 1.15 10.90 14.61 16.20

5.29 3.61 1.01 0.96 0.70 0.46 1.36 2.27 2.01 1.94 1.27 0.92 1.12 4.73 4.08 2.28 0.71 0.91 6.78 5.45 6.89 3.00 3.44 8.25 3.96 -- a -- a 5.05 11.59 2.39 -- a 7.65 3.79

1.80 1.48 0.66 0.69 0.33 0.73 0.40 0.25 0.94 1.93 0.36 0.29 3.15 0.93 2.41 0.15 0.17 0.18 3.63 1.60 2.76 0.10 1.46 1.29 1.73 -- a -- a 1.07 5.19 0.40 -- a 4.85 9.26

cyclohexane 1-hexene benzene acetic acid acetic acid acetic acid carbon tetrachloride chloroform cyclohexane acetaldehyde butanal acetone methyl ethyl ketone methyl acetate ethyl acetate tetrahydrofuran acetonitrile water water water water acetone acetone acetone methyl ethyl ketone cyclohexanone methanol methanol methanol ethanol ethanol ethanol ethanol

acetic acid acetic acid acetic acid n-octane styrene monochlorobenzene acetic acid acetic acid propionic acid water water water water water water water water 1,4-dioxane nitromethane pyridine furfural ethanol 1-propanol 1-butanol 1-butanol cyclohexanol N-methyl-2-pyrrolidone ethyl acetate diisopropyl ether methyl ethyl ketone acetylacetone methyl propionate 1,4-dioxane

1 1 5 2 1 1 2 1 1 5 5 10 5 7 3 3 3 4 5 11 4 11 3 1 1 5 1 5 2 2 1 1 1

313.2 313.2 293.15 323.15 333.15 313.15 293.15 298.15 313.2 283.15 323.15 293.15 293.15 298.15 323.15 298.15 293.15 298.15 294.15 300.2 298.15 328.15 303.15 298.15 323.15 343.15 313.15 298.15 320 298.15 298.15 298.15 308.15

-

313.2 313.2 323.14 343.15 333.15 313.15 308.15 298.15 313.2 373.15 353.15 473.15 346.75 353.15 353.15 343.15 333.15 343.15 323.15 366.35 353.15 450 313.15 298.15 323.15 383.15 313.15 333.15 330 328.15 298.15 298.15 308.15

4.96 9.62 10.39 7.30 3.28 3.41 18.98 19.75 6.82 17.03 12.43 6.23 3.57 7.56 5.99 11.87 14.75 3.37 18.14 12.28 18.07 4.55 3.09 15.82 4.36 3.63 27.94 1.42 9.50 4.11 6.49 7.88 2.42

6.87 3.43 2.45 11.17 3.96 3.80 11.91 3.57 3.80 4.49 8.89 2.32 3.53 1.72 2.82 3.35 8.56 2.81 11.39 4.06 3.15 3.82 1.25 0.58 1.74 2.24 0.43 1.10 5.22 1.85 1.40 3.49 1.98

37.94 26.85 12.80 42.58 20.82 26.41 63.77 54.67 34.02 17.24 18.71 8.45 3.47 8.03 11.95 12.01 13.31 20.99 17.76 33.78 26.95 4.52 3.37 15.78 4.44 3.62 25.95 2.74 1.17 4.22 6.89 8.04 4.80

15.44 10.52 5.24 19.23 7.32 11.40 17.16 6.42 6.97 4.51 11.85 2.74 2.23 2.08 5.82 2.53 6.75 6.48 10.24 11.31 2.96 3.82 1.35 0.64 1.82 2.22 0.40 1.48 0.88 1.89 1.51 3.56 2.80

3.62 12.38 1.78 2.65 13.16 9.63 6.17 15.21 5.59 13.85 3.91 2.71 3.38 5.68 4.18 9.50 3.78 5.19 3.99 5.65 13.49 2.00 1.42 13.32 3.88 2.62 -- a 1.59 10.29 1.64 6.57 1.09 0.78

6.84 2.77 3.20 8.33 3.69 4.35 9.64 3.15 3.75 3.99 3.24 1.12 1.53 1.55 2.35 2.87 3.29 3.18 2.30 3.59 1.77 3.41 0.63 0.52 1.20 1.60 -- a 0.80 5.42 0.40 2.67 0.65 0.44

ethanol ethanol ethanol 1-propanol isopropanol isopropanol isopropanol 1-butanol 2-methyl-1-propanol 2-butanol 2-methyl-2-propanol 2-methyl-2-propanol 2,4-xylenol 3,4-xylenol 3,5-xylenol m-cresol methyl acetate methyl acetate ethyl acetate ethyl acetate ethyl acetate n-butyl acetate methyl propionate methyl propionate diethyl ether diethyl ether diisopropyl ether 1,4-dioxane tetrahydrofuran nitromethane nitromethane acetonitrile acetonitrile

triethylamine acetonitrile dimethyl carbonate 3-pentanone nitromethane pyridine N,N-dimethylformamide n-butyl acetate pyridine pyridine acetylacetone pyridine quinoline quinoline quinoline quinoline ethanol 1-propanol ethanol 1-propanol 2-methoxyethanol phenol 1-propanol 1-butanol methanol ethanol isopropanol 2-methyl-1-propanol 1-propanol 1-butanol 1-hexanol 1-propanol 1-butanol

5 2 1 1 1 1 1 4 1 1 1 1 1 1 1 5 6 1 6 3 3 1 2 1 1 7 2 2 1 2 2 4 1

308 293.15 313.15 323.15 298.15 313.15 353.15 333.15 313.15 313.15 298.15 313.15 448.15 448.15 448.15 433.55 318.15 318.15 313.15 313.15 343.15 317.55 328.15 348.15 303.15 273.15 330 353.15 298.15 293.15 294.15 318.15 333.15

-

343.15 313.15 313.15 323.15 298.15 313.15 353.15 393.15 313.15 313.15 298.15 313.15 448.15 448.15 448.15 548.15 353.15 318.15 353.15 333.15 363.15 317.55 348.15 348.15 303.15 323.15 340 373.15 298.15 313.15 313.15 351.22 333.15

18.21 2.61 10.46 4.00 9.74 12.67 19.71 3.31 9.28 14.13 2.24 13.64 9.89 7.97 6.16 7.33 4.44 3.58 2.14 1.77 2.30 16.14 2.30 2.04 8.80 1.44 1.93 1.73 0.67 8.67 14.84 4.54 9.34

6.58 1.90 4.99 1.38 5.25 5.31 4.12 1.70 3.42 4.16 1.43 6.21 5.76 2.97 3.78 3.42 2.05 1.67 1.40 1.09 0.52 1.92 1.56 0.91 3.43 0.25 1.02 0.91 0.17 4.41 1.08 2.11 2.40

16.11 2.16 10.48 4.04 9.74 9.63 13.36 3.31 7.72 12.29 3.42 11.78 9.50 7.59 5.82 6.82 4.44 3.66 2.23 1.78 2.31 15.87 2.30 2.02 2.96 6.53 4.49 2.54 2.13 8.78 15.30 4.42 9.33

5.84 2.00 5.00 1.39 5.25 4.44 2.94 1.69 2.95 3.58 1.10 5.59 5.59 2.86 3.68 3.24 2.05 1.71 1.44 1.09 0.52 1.86 1.56 0.93 0.75 1.28 2.11 0.88 0.43 4.45 1.14 2.09 2.40

2.08 1.22 -- a 1.43 3.63 5.22 1.31 1.49 4.52 1.71 20.96 4.78 7.69 4.25 4.36 2.06 4.55 2.68 2.35 1.79 3.43 8.92 3.03 4.40 2.05 4.50 0.89 2.31 10.26 1.70 4.96 1.83 2.53

1.42 1.39 -- a 0.75 3.37 1.52 1.06 0.54 1.58 1.86 5.96 3.31 0.87 1.40 3.43 1.68 2.03 1.45 0.88 0.74 0.71 0.98 1.32 1.24 1.68 0.96 0.61 1.80 1.93 0.59 0.93 0.77 1.40

acetonitrile acetonitrile acetonitrile N,N-dimethylaniline dimethyl carbonate 1,1,2-trichlorotrifluoroethane diethylamine diethylamine diethylamine n-butylamine n-butylamine aniline N,N-dimethylaniline cyclohexylamine pyridine butanal acetone methyl ethyl ketone 3-pentanone acetic acid acetic acid ethyl acetate tetrahydrofuran methyl ethyl ketone methanol ethanol 1-propanol 2-butanol 2-methyl-2-propanol water water water water

2-methyl-1-propanol 2-butanol 2-methyl-2-propanol ethylene glycol 1-propanol methanol triethylamine acetonitrile fluorobenzene 1,4-dioxane acetonitrile nitrobenzene N-methylaniline N,N-dimethylformamide pyrrole acetic acid acetic acid acetic acid acetic acid acetic anhydride N,N-dimethylformamide acetic acid acetic acid n-butyric acid water water water water water 1-butanol 2-methyl-1-propanol 1-hexanol phenol

1 1 1 3 1 1 6 2 1 1 1 1 3 2 2 1 6 4 1 3 2 7 2 2 25 20 8 6 4 8 1 2 2

333.15 333.15 333.15 368.15 313.15 308.15 313.15 308.15 308.15 298.15 298.15 393.15 368.15 373.15 353.65 323.2 303.15 303.15 343.15 333.15 368.15 315.15 303.15 343.15 298.14 298.14 298.15 298.15 298.15 298.15 308.15 294.15 317.55

-

333.15 333.15 333.15 418.15 313.15 308.15 343.15 323.15 308.15 298.15 298.15 393.15 418.15 393.15 383.2 323.2 328.15 351.15 343.15 365.15 383.15 373.2 323.15 352.15 508.15 473.15 363.15 353.45 348.15 403.15 308.15 313.15 348.15

4.59 5.02 8.94 31.93 10.14 1.48 1.75 5.33 2.49 3.15 7.77 3.86 2.01 2.45 6.04 2.69 8.24 3.88 4.80 1.60 29.25 2.92 30.13 19.99 3.39 3.96 3.29 22.54 13.16 5.59 19.25 7.59 14.37

1.57 2.41 3.73 12.24 4.15 1.11 1.28 3.77 0.93 1.36 3.20 1.85 0.29 0.81 3.88 3.89 1.58 2.09 4.19 3.24 5.47 3.24 11.97 5.84 3.15 2.64 3.13 9.99 6.86 3.26 8.87 1.74 0.90

4.59 5.02 8.93 19.61 10.25 2.09 1.74 5.16 2.67 3.15 6.69 3.99 1.99 7.43 5.69 5.18 10.10 5.38 10.83 10.40 44.18 9.87 28.35 9.14 3.33 5.19 6.85 12.93 10.25 7.13 8.07 21.60 5.42

1.57 2.40 3.72 8.35 4.20 0.91 1.28 3.73 0.89 1.36 2.70 1.88 0.31 4.46 3.80 6.32 3.98 5.07 6.16 2.63 8.62 5.39 11.26 2.33 3.12 3.00 4.58 7.57 5.92 2.88 5.87 0.65 0.42

0.87 1.07 12.47 13.82 -- a -- a 1.22 2.47 0.48 3.76 5.17 4.03 2.76 2.56 22.68 2.05 11.35 4.56 3.34 3.38 21.44 3.61 21.81 3.00 2.17 1.65 1.75 4.84 7.37 3.73 3.42 16.41 3.66

0.67 0.92 4.66 8.27 -- a -- a 1.24 2.24 1.59 1.26 1.91 1.77 0.39 1.95 7.98 4.53 4.23 4.73 3.35 2.50 4.04 3.42 9.47 0.53 2.55 1.03 1.30 3.12 3.55 1.90 2.60 2.38 0.33

methanol ethanol 5 298.15 - 433.15 1.42 ethanol 1-propanol 5 298.15 - 353.15 3.76 ethanol 1-butanol 5 323.15 - 403.15 0.85 ethanol 2-methyl-1-propanol 4 323.15 - 353.15 6.50 ethanol 3-methyl-1-butanol 4 323.15 - 353.15 4.60 1-propanol 2-methyl-1-propanol 4 323.15 - 353.15 3.11 2-methyl-1-propanol 1-butanol 1 308.15 - 308.15 8.82 2-butanol 1-butanol 2 298.15 - 313.15 2.67 2-methyl-2-propanol 1-butanol 1 313.15 - 313.15 4.86 2-methyl-2-propanol 2-methyl-1-propanol 1 313.15 - 313.15 1.79 2-methyl-2-propanol 2-butanol 1 313.15 - 313.15 2.57 n-butylamine 1-propanol 3 318.15 - 338.15 5.52 n-butylamine 1-butanol 1 313.15 - 313.15 16.04 ethanol n-pentylamine 1 333.15 - 333.15 5.14 1-propanol n-pentylamine 1 333.15 - 333.15 4.19 aniline m-cresol 4 407.85 - 453.15 3.43 cyclohexylamine cyclohexanol 2 383.15 - 403.15 7.03 ethanol pyrrolidine 2 313.15 - 333.35 14.44 water aniline 1 373.15 - 373.15 24.19 formic acid acetic acid 3 303.15 - 343.2 7.39 acetic acid propionic acid 3 303.15 - 343.2 3.82 acetic acid n-butyric acid 1 358.2 - 358.2 10.57 ethanol acetic acid 1 323.2 - 323.2 6.36 1-propanol acetic acid 1 313.15 - 313.15 3.55 1-butanol acetic acid 1 323.2 - 323.2 3.97 acetic acid 1-pentanol 1 333.15 - 333.15 11.33 water acetic acid 21 293.15 - 502.9 11.27 acetic acid acetamide 2 358.2 - 373.2 13.96 Overall 1305 207.92 - 553.15 5.09 a. These systems cannot be described using modified UNIFAC because of missing parameter issue. b. Number of isotherms. c. J. Gmehling, J. Lohmann, A. Jakob, J. Li, R. Joh, Ind. Eng. Chem. Res. 37 (1998) 4876. d. C.-M. Hsieh, S. I. Sandler, S.-T. Lin, Fluid Phase Equilib. 297 (2010) 90.

0.83 1.12 0.72 1.14 0.65 0.58 1.08 0.68 1.83 0.66 1.26 3.18 4.06 2.83 2.66 0.85 2.33 5.10 5.17 5.46 8.51 5.93 0.75 0.98 0.84 12.65 6.22 2.43 2.12

0.82 3.94 1.21 7.17 5.95 3.21 8.82 2.67 4.86 1.79 2.57 5.48 16.95 5.24 4.37 3.66 7.47 12.93 16.75 6.42 3.98 12.14 2.55 11.04 13.95 31.67 8.16 20.11 6.77

0.75 1.17 0.83 1.36 0.92 0.59 1.08 0.68 1.83 0.66 1.26 3.06 4.41 3.14 2.73 0.89 2.44 4.75 4.04 5.62 8.62 6.39 3.15 4.73 4.30 12.79 4.97 3.95 2.42

0.83 3.89 1.12 5.48 5.05 1.41 6.78 2.39 9.19 7.79 5.83 1.79 16.54 1.48 0.98 1.69 1.35 10.73 14.10 6.47 3.81 10.43 14.11 25.12 21.13 39.76 8.37 -- a 3.44

0.78 1.16 0.78 0.82 0.75 0.73 0.94 0.70 2.96 2.54 2.37 0.85 5.42 0.71 0.53 0.57 1.13 3.31 3.63 5.70 8.49 5.90 8.04 8.88 6.94 13.10 5.07 -- a 1.53

N

AARD - P (%)   i 1

N

AAD - y1 (%)   i 1

calc expt  1  M 1 Pi , j  Pi , j   100 %   N  j 1 M Pi ,expt j 

1 N

 M 1 calc  expt    M y1,i , j  y1,i , j  100%   j 1 