Ind. Eng. Chem. Res. 1991,30,889-897 Am. Chem. SOC. 1970,92,6451-6454. Szalewicz, K.; Cole, S. J.; Kolos, W.; Bartlett, R. J. A Theoretical Study of the Water Dimer Interaction. J. Chem. Phys. 1988,89, 3662-3674. Szczesniak, M. M.; Scheiner, S. Correction of the Basis Set Superposition Error in SCF and MP2 Interaction Energies. The Water Dimer. J. Chem. Phys. 1986,84,6328-6335. Wells, B. H.; Wilson, S. Van der Waals Interaction Potentials.
889
Many-body Effects in Ne,. Mol. Phys. 1989, 66 (2), 457-464. Wu, H. S.; Sandler, S. I. Proximity Effects on the Prediction of the UNIFAC model-I. Ethers. AIChE J. 1989, 35 (l), 168-172. Zerner, M. Private communication, 1990. Received for review June 8, 1990 Revised manuscript received January 3, 1991 Accepted January 22,1991
Use of ab Initio Quantum Mechanics Calculations in Group Contribution Methods. 2. Test of New Groups in UNIFAC Huey S. Wu and Stanley I. Sandler* Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
In this paper we show that functional groups identified previously from ab initio molecular orbital calculations lead t o better UNIFAC predictions of vapor-liquid equilibrium, especially for mixtures involving molecules in which proximity effects are important. We also find that, for the functional groups we have defined, in many cases it is generally not necessary to distinguish between subgroups. This reduces the total number of main groups and subgroups that must be considered. For some hydrogen-bonding mixtures, neither the new nor the old functional groups lead to satisfactory excess Gibbs free energy predictions. This is in agreement with our previously reported supermolecule calculations which showed that hydrogen-bonding energies did not satisfy group additivity and therefore could not be accounted in group contribution methods.
Introduction In a previous paper (Wu and Sandler, 1991) we showed that ab initio molecular orbital calculations could be used to compute the charge on atoms and on groups of atoms in molecules. Then, on the basis of the principles of unchanging geometry and approximate group electroneutrality, we were able to identify functional groups for use in group contribution methods. Some of the groups we identified were the same as are currently used in UNIFAC (Fredenslund et al., 1975; Reid et al., 1987);however, some were different. Further, on the basis of suppermolecule calculations of several hydrogen-bonding systems, we also surmised that because of intramolecular interferences in some mixtures in which hydrogen bonding occurs, it may not be possible to achieve accurate predictions for such mixtures with current group contribution models. Complete testing of any proposed new groups, or other modifications of the UNIFAC method, can only be done within the context of a refitting of all model parameters using an enormous collection of experimental vapol-liquid equilibrium data such as that collected in numerous volumes of the Chemistry Data Series (Gmehling et al., 1977). Such an analysis is beyond the scope of the authors, though we hope this paper and the preceding one will encourage such an activity. Our goal here is more modest in that we will test the use of some of the newly proposed groups, assuming that the surface area, volume, and interaction parameters for the other groups are unchanged from the currently accepted values. The typical test is as follows. We will look at a number of mixtures containing the same functional groups in which only one is different between the currently used and the proposed functional groups. We fit the interaction parameters for both the current and the proposed functional groups to vapor-liquid equilibrium (VLE)data for one mixture, and compare the predictions with experimental VLE data for other mixtures containing the same functional groups. We will see that in some cases the use of the newly defined functional groups leads to large improvements in 0888-5885/91/2630-0889$02.50/0
the UNIFAC predictions, while in other cases there is little improvement. In no case do the newly defined functional groups we propose lead to predictions that are worse than the groups currently in use.
Main Groups and Subgroups In the framework of the UNIFAC model a family of similar groups is referred to as a main group and may be separated into subgroups. For example, the main group of primary amines consists of the three different subgroups CH3NH2,CH2NH2,and CHNH,. The interaction parameter for any of the subgroups of the same main group with other groups is the same; the different subgroups do, however, have different surface areas and volumes. In the UNIFAC method, the surface areas and volumes of groups have been computed by the method of Bondi (Bondi, 1968) relative to unit values for a methylene group. However, in some cases the surface areas and volumes (R and Q parameters) are completely empirical; for example, the parameters for the OH group and the tetrahydrofuran group have been made larger merely to obtain better fits of the data. More recently, in the modified UNIFAC model (Weidlich and Gmehling, 1987), all the R and Q parameters are treated as adjustable parameters obtained by correlating experimental VLE data. The question of surface areas and volumes of subgroups arises in the work here since some of the functional groups we have defined based on the requirement of electroneutrality contain more atoms than previously defined groups, and different parts of the group may have different chemical functionality. We expect that the addition or removal of a hydrogen atom away from a heteroatom in a group, such as in CH,COCH, and CH,COCH2, would have little effect on the group properties. However, in the UNIFAC model, the change may affect the surface area by 10 or 15% and may result in large effects on the configurational and residual contributions to the free energy. We believe the UNIFAC model overemphasizes such changes in surface area and volumes. 0 1991 American Chemical Society
890 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991
As part of the work here we also consider several alternatives or simplificationsof the UNIFAC model. In the first we neglect the differences in surface areas and volumes of subgroups within the same main group when these result only from differences in numbers of hydrogens away from the dominant heteroatom. This has the effect of reducing the number of different subgroups that must be considered. We also consider another approach in which we distinguish between functional subgroups by their mean square atomic charge Z defined as
\
, \
/
I
\ \
V
C
1000
vi
n
where N is the number of atoms and I k is the net atomic charge of atom i determined from the results of the ab initio molecular orbital calculations reported earlier (Wu and Sandler, 1991). The basis for this is that the interactions between functional groups may be approximately related to the distribution of atomic charges on each. Therefore, if two subgroups have the same mean square atomic charge, we can treat them as being identical (ignoring the surface area and/or volume differences between them). However, if the mean square atomic charges of two subgroups are different, the ratio of their R parameters and of their Q parameters is taken to be the same as the ratio of the mean square atomic charge. We recognize that this is a purely empirical modification. For comparison, we also consider the case in which the Bondi surface area and volume method is used to account for the hydrogen atom difference as is traditionally done in the UNIFAC method.
Test of Some of t h e Newly Defined Functional Groups
I. Non-Hydrogen-Bonding Mixtures. Mixtures of Cyclic Ethers and Hydrocarbons. We start with a study of the cyclic ethers and hydrocarbons since this is one of the cases in which there is a significant improvement in group contribution predictions by using the newly defined functional groups. In this study vapor-liquid equilibrium data for binary mixtures of tetrahydrofuran with cyclohexane and 1,3-dioxolanewith cyclohexane both at 313.15 K (Wu and Sandler, 1988,1989) were used to test the accuracy of the UNIFAC model with the new cyclic ether group cCH,OCH, and the empirically defined FCH,O group. Thus tetrahydrofuran is considered to contain one cyclic cCH20CH2group and two CH, groups in the new description, and one FCH,O group and three CH2groups in the old description. Similarly, 1,3-dioxolane is considered to have two cyclic C C H ~ O [ C H groups ~ ] ~ / ~in the new description, and two FCH,O groups and one CH2 group in the old description. Here the CH2 located between two oxygens in 1,3-dioxolane has been divided in ~ / ~ satisfies the half so that the cyclic C C H , O [ C H ~ ]group electroneutrality criterion and has an electronic charge distribution equivalent to that of the cyclic cCH20CH2 group in tetrahydrofuran. The only difference between these two groups is in their surface areas and volumes since half of a methylene group is involved. Thus, in the context of the UNIFAC model, these two groups belong to the same main group (cyclic ether: cCH,OCH,), but are two different subgroups. The functional group volumes and surface areas used here, except for the newly defined group, are the same as those in the original UNIFAC model. The van der Waals volumes (R)and surface areas (Q)obtained from the work of Bondi (Bondi, 1968) were used to compute the volume and surface area for the cCH,OCH,
9
W
111
500
u x
w
0
0.0 0 . 1
0.4 0 . 5 0.8 0.7 0.8 0.9 1.0 Mole Fraction of Ether Compounds
0.2 0.3
Figure 1. Comparison of excess Gibbs free energy data derived from experiment for the tetrahydrofuran + cyclohexane ( 0 )and the 1,3dioxolane + cyclohexane (A)systems at 313.15 K with UNIFAC group contribution calculations. Interaction parameters for the cyclic ether-CH2 groups were found by correlating the data for the THF mixture, and then used to predict the properties for the 1,3dioxolane mixture. The dashed lines result from using the empirically defined cyclic ether group, and the solid lines result from the quantum mechanically defined group.
subgroups. These values and those of the optimal interaction parameters A - determined below are listed in Table I, as are the values ofthe parameters for the other mixtures considered in this paper. In correlating the data we treat the two interaction parameters of the cCH,OCH, group with the CH, group (new description) and the FCH,O group with the CH, group (old description) as the adjustable parameters. To compare the predictions of the UNIFAC model using the cyclic cCH,OCH, and the FCH,O groups, the optimal interaction parameters were determined from vapor-liquid equilibrium measurements for the cyclohexane tetrahydrofuran mixture. Having determined the interaction parameters for cCH,OCH, with CH, and for FCH,O with CH,, predictions were then made for the vapor-liquid equilibrium of the 1,3-dioxolane + cyclohexane mixture. The molar excess Gibbs free energies for these two mixtures for the two ways of defining groups are compared in Figure 1. In this figure the points are obtained from the experimental measurements, the dashed lines are from the UNIFAC model with FCH,O group, and the solid line is from the UNIFAC model using the cCH,OCH, group. The figure shows that for the mixture of 1,3-dioxolane + cyclohexane the prediction using the theoretically based cCH,OCH, is much better. The P-T-x-y diagram for the 1,3-dioxolane + cyclohexane mixture is plotted in Figure 2, where again the dashed line results from the UNIFAC model using the FCH,O group and the solid line from using the cCH,OCH, group. This figure shows that the UNIFAC model with the FCH,O group is so seriously in error as to predict liquid-liquid equilibrium, while the prediction made by the UNIFAC model using the cCH,OCH, group is in excellent agreement with experimental measurements. The average error in pressures and vapor compositions for this comparison, and others to be done later, are reported in Table 11.
+
1 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 891
1500
+0
EXPI Erpi (1) (3) Acetone 2-Penlanone
-.$ 1250 9 '=.
0
R
-
-
Old C H X V (1) Old CH3CO (3) New CH3COCH3 ( I ) Old & New (2) New CH3COCHZ ( 3 )
( 1 ) Acetone
+ n-Hcxme
1000
E!
E"
Y
e
!i
750
F. m
n
n
,
30
500
) n-Heptane
+
.?-Pentanon
v1
U u wX
250
0.0
0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of the first component
1.0
Figure 3. Excess Gibbs free energies derived from experiment for the acetone + n-hexane (+) at 328.15 K, n-hexane 2-butanone (0) at 333.15 K, and n-heptane 2-pentanone ( 0 )at 363.15 K mixtures. The dashed lines result from UNIFAC using the empirical CH,CO group, while the solid lines result from using the new CH3COCH, group as described in the text.
+
+
This is a rather dramatic example of how a small change in the choice of groups in the existing UNIFAC model can lead to a significant improvement. In most other cases the improvements are more modest. Mixtures of Ketones and Hydrocarbons. Measured vapor-liquid equilibrium data for the binary mixtures acetone + n-hexane at 328.15 K (Kudryavtseva and Susarev, 1963), 2-butanone n-hexane at 333.15 K (Hanson and Van Winkle, 1967), and 2-pentanone + n-heptane at 363.15 K (Scheller and Rao, 1973) are used to compare the accuracy of predictions of the UNIFAC model with the new ketone group CH,COCH, and with the previously defined CH,CO group. Here acetone, 2-butanone, and 2-pentanone are all considered to contain one CH,COCH, group. We will consider two possibilities. First, we will make no distinction between the CH3COCH3of acetone and the CH3COCH2of 2-butanone and 2-pentanone, as the mean square atomic charges of CH3COCH3(I= 0.317) and the CH3COCH2group (I= 0.318) are similar and only a secondary hydrogen is different in the two cases. For comparison we consider the groups to have (1)the same van der Waals volumes, surface areas, and interactions; (2) different volumes and surface areas based on I; and (3) surface areas and volumes computed by the Bondi method. To compare the predictions of the UNIFAC method with the CH,COCH, and CH,CO groups, the optimal interaction parameters were first determined by using the vapor-liquid equilibrium measurements of the hexane + 2-butanone mixture. In this way, the interaction parameters for CH,COCH, with CH, and for CH,CO with CH, were found. Next, the predictions for the vapor-liquid equilibrium of mixtures containing acetone + n-hexane and 2-pentanone + n-heptane were made using the UNIFAC model with the two choices for the ketone groups. The excess Gibbs free energies for these three mixtures are compared in Figure 3; the points are obtained from the experimental measurements, the dashed lines are from the UNIFAC model with the CH,CO group, and the solid line results from the UNIFAC model with the CH,COCH,
140
-0-
---
-
+
Expt Lquld ErpI Vapor Old C H X O Lquid Old CH3M Vepor New CH3COCHZ Lquid New CHSCOCHZ Vapor
120
a
B \
100
L
80
0.0 0.1
0.2 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Mole fraction of acetone
Figure 4. P-T-2-y predictions for the acetone + n-hexane system at 328.15 K using the CH3C0 (- - -) and CH3COCHl (-1 functional groups compared with experimental data.
group (assuming both subgroups have the same R and Q parameters). This figure shows that for the mixture of 2-pentanone + n-heptane both predictions are equally good, while for the mixture of acetone + n-hexane the prediction for the excess Gibbs free energy using the CH,COCH, group is slightly better. The P-T-x-y diagram for acetone + n-hexane at 318.15 K is shown in Figure 4 where the dashed line results from the UNIFAC model with the CH&O group, the solid line results from using the CH3COCH2group, and the points are the experimental data. Here we can see the predictions of the
892 Ind. Eng. Chem. Res., Vol. 30,No. 5, 1991 Table I. Group Constant and Interaction Parameters
A;; group CH, FCHI,O
Q
CH2
FCHzO
0.6744 0.9183
0.5400 1.1000
0.00 83.36
251.50 0.00
R
Q
0.6744 1.5927 1.2555
0.5400 1.3200 1.0500
group CH2 cCH20CH2 ~CHZO[CHZII/Z
R
group
R
Q
CH3 CHZ CH&O
0.9011 0.6744 1.6724
0.8480 0.5400 1.4880
group CH3 CHZ CH3COCHz CH3COCH3
R
Q
0.9011 0.6744 2.3468 2.3394
0.8480 0.5400 2.0280 2.0220
CH2 0.00 -15.00 -15.00
CH3 0.00 0.00 23.23
CH3 0.00
CH2
Aij cCHZOCHZ
cCHzO[CHzI,/z
250.00 0.00 0.00
250.00 0.00 0.00
Aij CH2
CHSCO
0.00 0.00 23.23
422.00 422.00 0.00
Ail CH3COCHp 301.20 301.20 0.00 0.00
0.00 0.00 -32.21 -32.21
0.00 -32.21 -32.21
group
R
Q
CH3
A;; CHZ
CH3 CHZ CHO
0.9011 0.6744 0.9981
0.8480 0.5400 0.9480
0.00 0.00 2925.00
0.00 0.00 2925.00
CH3COCH3 301.20 301.20 0.00 0.00
CHO 634.90 634.90 0.00
Ail group
R
Q
CH3
CH2
CHzCHO
CHCHO
CH3 CHZ CHpCHO CHCHO
0.9011 0.6744 1.6725 1.6670
0.8480 0.5400 1.4880 1.4830
0.00
0.00 0.00 20.70 20.70
369.60 369.60 0.00 0.00
369.60 369.60 0.00 0.00
0.00 20.70 20.70
group
R
Q
CH3
At1 CHZ
HCOO
CH3 CHZ HCOO
0.9011 0.6744 1.2420
0.8480 0.5400 1.1880
0.00 0.00 84.82
0.00 0.00 84.82
575.20 575.20 0.00
group CH? CH; HCOOCHZ HCOOCH,
R
Q
CH3
CHZ
A, HCOOCHp
HCOOCH,
0.9011 0.6744 1.9164 1.7870
0.8480 0.5400 1.7280 1.6120
0.00 0.00 5.247 5.247
0.00 0.00 5.247 5.247
352.7 352.7 0.00 0.00
352.7 352.7 0.00 0.00
0.9011 0.6744 0.9183 1.2070
0.8480 0.5400 1.1000 1.4040
0.00 0.00 83.36 65.33
0.00 0.00 83.36 65.33
251.5 251.5 0.00 589.80
255.70 255.70 -2 14.40 0.00
group
R
Q
CH2
HZO
A;; cCHZOCH~
cCHZNHCHZ
CH3 CHZ CCHZOCHZ cCH~NHCHZ
0.6744 0.6744 1.5930 1.8814
0.5400 0.5400 1.3200 1.9926
0.00 0.00 -15.0 -19.07
0.00 0.00 -15.0 -19.07
250.00 250.00 0.00 480.20
139.80 139.80 -259.10 0.00
group CH3
2
R
Q
0.9011 0.6744
0.8480 0.5400 1.2000
1.Oooo
Aij CHZ
CH3 0.00 0.00
0.00 0.00
170.70
170.70
OH 990.10 990.10 0.00
Aij ErOUD
R
Q
CH.
CH,
CHqOH
CHQOH
CH3 CH2 CH,OH CH3OH
0.9011 0.6744 1.2044 1.0840
0.8480 0.5400 1.1240 1.0120
0.00 0.00 90.68 90.68
0.00 0.00
1112.0 1112.0 0.0 0.0
1112.0 1112.0 0.0 0.0
90.68 90.68
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 893 Table I (Continued) 4 j
8
R
group
CHS
CHZ
CHSOH
CHZOH Aij
group CH3 CHZ OH HzO
R
8
0.9011 0.6744
0.8480 0.5400 1.2000 1.4000
1 .oooo
0.9200
CH, 0.00 0.00 170.70 300.00
CHZ
OH
H20
0.00 0.00 170.70 300.00
990.10 990.10 0.00 -160.70
1318.00 1318.00 222.90 0.00
Atj
group CH3 CHZ CHZOH CH30H
HzO
R
8
CH3
CH2
CHzOH
CHSOH
H20
0.9011 0.6744 1.2044 1.0840 0.9200
0.8480 0.5400 1.1240 1.0120 1.4000
0.00 0.00 90.68 90.68 300.00
0.00 0.00 90.68 90.68 300.00
1112.0 1112.0 0.00 0.00 -83.88
1112.0 1112.0 0.00 0.00 -83.88
1318.00 1318.00 93.97 93.97 0.00
Aij
R
8
FCHZO
0.6744 0.9200 0.9183
0.5400 1.4000 1.1000
group
R
8
CH2
HzO
0.6744 0.9200 1.593 1.2555
0.5400 1.4000 1.320 1.050
0.00 300.00 -15.0 -15.0
1318.0 0.00 479.6 479.6
group CH2
HZO
CH2 0.00 300.0 83.36
H20
FCHzO
1318.0 0.00 323.1
251.5 -238.9 0.00
Aij
CHZ H20 cCHzOCHz c~~z~[CHzI1/2
UNIFAC model using the CH3COCH2group are closer to the experimental measurements than when using the CH,CO. The functional group volumes and surface areas used in these calculations and the optimal interaction parameters Aij for different choices of functional groups are listed in Table I. In this table we see that using either the same R and Q parameters or parameters based on the mean square atomic charge leads to better predictions than using parameters calculated from the Bondi method. For simplicity then, it is easiest to use the same R and Q parameters for these two subgroups. Mixtures of Aldehydes and Hydrocarbons. Vaporliquid equilibrium data for binary mixtures of n-pentane + n-propionaldehyde at 313.15 K, n-heptane + n-butyraldehyde at 318.15 K, and n-heptane + 2-butyraldehyde at 318.15 K (Eng and Sandler, 1984) are used to test the accuracy of the UNIFAC model with both the CH,CHO and the CHO aldehyde groups. Here there is little difference in the mean square atomic charges of the CH2CH0 group (I = 0.304) of n-propionaldehyde and n-butyraldehyde and the CHCHO group (I= 0.303) of 2-butyraldehyde. We again consider the cases in which CH2CH0 and CHCHO are considered to have the same and different R and Q parameters. To compare the predictions of the UNIFAC model using the CH,CHO and CHO groups, the optimal interaction parameters for CH,CHO with CH, and for CHO with CH, were first determined with the vapor-liquid equilibrium measurements for the n-heptane + n-butyraldehyde mixture. The predictions for the vapor-liquid equilibrium of the n-propionaldehyde + n-pentane and 2-butyraldehyde + n-heptane mixtures were then made with the UNIIFAC model. The excess Gibbs free energies for these three mixtures are compared in Figure 5 where the points are obtained from experimental measurements, the dashed lines are from the UNIFAC model with the CHO group, and the solid lines are from the UNIFAC model using the CH,CHO group without subgroup distinctions. The figure shows that, for the mixture of n-pentane + n-propion-
0
--
CCH~OCH, 250.0 -284.5 0.00 0.00
cCHzO[CH211/2 250.0 -284.5 0.00 0.00
Expermen1 (ZJ ErperrmenI (3) OJd New New
- New
CHO
(I)
CHZCHO fJJ CHZCHO fZJ CHZCHO f3J
( 1 ) n-Propionaldehyde
(3) ]so-Butylaldehyd
Mole fraction of t h e f i r s t component
Figure 5. Comparison of excess Gibbs free energies derived from experiment for the n-pentane + n-propionaldehyde (+) at 313.15 K, n-heptane + n-butyraldehyde (0)at 318.15 K, and n-heptane 2-butyraldehyde at 318.15 K mixtures with UNIFAC predictions using the CHO (- - -) and CHzCHO (-4 groups as described in the text.
+
aldehyde, the prediction based on the CH,CHO and CHO groups are equally good, while for the mixture of 2butyraldehyde + n-heptane the prediction using the theoretically based CH,CHO group is slightly better. Also, in predictions for the molar excess Gibbs free energies based on the CHO group, the UNIFAC model does not predict the differences between the butyraldehyde + nheptane and 2-butyraldehyde + n-heptane mixtures found experimentally. The P-T-x-y diagram for the 2-butyraldehyde + n-heptane mixture at 328.15 K is plotted in
894 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 Table 11. Comparison between Original and Newly Defined Functional Groups in UNIFAC
0
--
Ap: kPa AYb 1,3-Dioxolane + Cyclohexane original 9.25 0.1140 new 0.29 0.0058 original nevf newd newC
Acetone + n-Hexane 2.43 1.30 1.43 7.69
0.0136 0.0060 0.0059 0.0215
original newd
n-Heptane + 2-Pentanone 2.23 2.25
0.0100 0.0099
60
, -
Expf b q w d Expl vapor Old CHO &quad Old CHO Vapor New CHZCHO L p u i d N e w CHZCHO Vapor
I
2-Butyraldehyde + n-Heptane 1.12 0.0074 original new 0.48 0.0064 newd 0.53 0.0045 ne@ 2.08 0.0230 n-Pentane original ne&
+ Propionaldehyde 2.14 2.38
0.0107 0.0112 0.0
+
Methvl Formate n-Hexane 7.03 12.01 original 4.88 8.21 nevf newd 3.59 4.73 6.31 ne@ 13.99 original new
Morpholine + n-Octane 2.76 0.45 n-Hexane
original new n-Hexane originalf nevf
+ 1-Propanol
0.3 0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 6. P-T-x-y predictions for the n-heptane + 2-butyraldehyde system at 318.15 K using the CHO (- --) and CHICHO (3 functional groups compared with experimental data (0,0).
8
0.0141 0.0077
+ Methanol 2.88 2.38
0.0234 0.0199
original new
1-Propanol Water 1.53 1.48
originalf nevf
Methanol Water 0.32 0.98
0.0091 0.0053
original new
1,3-Dioxolane + Water 22.09 17.43
0.1589 0.1109
+
0.2
Mole fraction of iso-butylaldehyde
0.0451 0.0144
2.57 0.79
+
0.1
0.0308 0.0290
u
I
.-3 .->
A?,% for methyl formate t n-hexane. * Ayz% for methyl formate n-hexane. ' R and Q parameters for subgroups as reported in Table I, computed by using ratio of mean square atomic charge. dNo distinction between R and Q parameters of different subgroups belonging to same main group. e R and Q parameters for subgroups computed by using method of Bondi. fMethanol is considered as a separate main group from OH group.
$ 4
2
+
Figure 6, where the dashed line is from the UNIFAC model using the CHO group and the solid line results from using the CH,CHO group. Clearly, there is only a very small improvement when the new group definition is used in this case. Also, in Table I1 we show the differences that result between using the same and different R and Q parameters for CH2CH0and CHCHO. Again we find using the same parameters for both is best, which obviates the need for two subgroups. Mixtures of Esters and Hydrocarbons. Binary vapopliquid equilibrium data for mixtures of methyl formate + n-hexane at 760 mmHg (1.013bar) (Ogorodnikov et al., 1961) and ethyl formate + cyclohexane at 500 mmHg (0.667 bar) (Ohta and Nagata, 1980) were used to test the accuracy of the UNIFAC model with both the HCOOCH, formate group and the HCOO formate group. Here methyl
0.0
0.1
0.2 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Mole fraction of first c o m p o n e n t
Figure 7. Activity coefficients derived from experimental data for the ethyl formate + cyclohexane (0) at 500 mmHg and methyl formate + n-hexane).( at 760 mmHg mixtures compared with UNIFAC calculations using the HCOO (- - -) and HCOOCH2 (-) groups.
formate and ethyl formate are considered to have one HCOOCH, group or one HCOO group and again we consider the cases in which there is, and there is not, a subgroup distinction between the HCOOCH, group (I= 0.377) of methyl formate and the HCOOCH2 group (I = 0.404) of ethyl formate. To compare the predictions of the UNIFAC model using the HCOOCH, and HCOO groups, the optimal interaction parameters were determined using the measured vaporliquid equilibrium data for the cyclohexane + ethyl formate mixture. In this way, the interaction parameters for HCOOCH, with CH, and for HCOO with CH, were determined, so that the predictions for the vapor-liquid
Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 895
I 5 O0i
0
--
40 Experfmen& ffCH20. cCHZh'Hj (cCHZOCH2. cCH2NHCHZ)
35
m 30
n
Y \
n
25
zc I
0.0 0.1
I
I
I
0.2 0.3 0.4 0.5 0.6 0.7 0.8 Mole Fraction of Morpholine
I
0.9
1.0
Figure 8. Comparison of excess Gibbs free energy data derived from experiment for the morpholine + n-octane system ( 0 )at 353.15 K with UNIFAC predictions using the current FCH20 (- - -) and the quantum mechanically derived cCHzOCH2(-) functional groups.
+
equilibrium of mixtures containing methyl formate nhexane could be made by use of the UNIFAC model. Here, because the vapol-liquid equilibrium data are isobaric, the activity coefficients for these two mixtures are compared in Figure 7. In this figure the points are obtained from the expeirmental measurements, the dashed lines are from the UNIFAC model using the HCOO group, and the solid line is from the UNIFAC model using the HCOOCH, group without subgroup distinction. This figure shows that for the mixture of methyl formate n-hexane the prediction based on the newly defined HCOOCH, group is slightly better. Table 11, containing the summary data for this system, again shows that there is only a small advantage to making a subgroup distinction between the HCOOCH, groups based on the mean square atomic charge and a disadvantage to using the Bondi method. On the basis of simplicity, then, we propose that a subgroup distinction not be made. 11. Hydrogen-Bonding Mixtures. Mixtures of Cyclic Amines and Hydrocarbons. In this study vapor-liquid equilibrium data for binary mixtures of tetrahydrofuran with cyclohexane, pyrrolidine with cyclohexane, and tetrahydrofuran with pyrrolidine all at 333.15 K, and morpholine with n-octane at 353.15 K (Wu and Sandler, 1988,1989; Wu et al., 1990,1991) were used to test the accuracy of the UNIFAC model with the new cyclic amine group cCH,NHCH, and the empirically defined cCH,NH group. Thus, pyrrolidine is considered to contain one cyclic cCH2NHCH2group and two CH2groups in one description, and one cCH,NH group and three CH2 groups in the other. Similarly, morpholine is considered to have one cyclic cCH2NHCH2and one &H20CH2 group in the new description, and one FCH,O, one cCH2NH,and two CH2groups in the old description. Note that, in order to distinguish cyclic and noncyclic amine, the surface areas (Qparameters) are used differently. To compare the predictions of the UNIFAC model using the cyclic cCH,OCH, and the cCH,NH groups, the optimal interaction parameters were determined from vapor-liquid equilibrium measurements for the pyrrolidine
+
0.0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 Mole Fraction of Morpholine
0.9
1.0
Figure 9. Comparison of P-T-x-y experimental data for the morpholine + n-octane system at 353.15 K with UNIFAC predictions using the FCHzO (- - -) and cCH20CH2(-) groups.
+
cyclohexane and pyrrolidine + tetrahydrofuran mixtures. Having determined the interaction parameters for cCH,NHCH, with CH, and with cCH,OCH,, and for cCH,NH with CH, and with FCH,O, predictions for the vapor-liquid equilibrium of the morpholine + n-octane mixture were made. The molar excess Gibbs free energies for these two mixtures for the two ways of defining groups are compared in Figure 8. In this figure the points are obtained from the experimental measurements, the dashed lines are from the UNIFAC model with cCH,NH group, and the solid line is from the UNIFAC model using the cCH,NHCH, group. The figure shows that for the mixture of morpholine + n-octane the prediction using the theoretically based cCH,NHCH, is much better. The P-T-x-y diagram for the morpholine + n-octane mixture is plotted in Figure 9, where again the dashed line results from the UNIFAc model using the &H,NH group and the solid line from using the cCH,NHCH, group. This figure shows that the UNIFAC model with the cCH,NH group is less accurate than the prediction made by the UNIFAC model using the new cCH,NHCH, group. Mixtures of Alcohols and Hydrocarbons. Vaporliquid equilibrium data for binary mixtures of n-hexane separately with methanol (as reported in Gmehling et al. (1977)), with ethanol (Kudryavtseva and Susarev, 1963), and with l-propanol (Brown et al., 1969),all at 318.15 K, are used to test the accuracy of predictions of the UNIFAC model with both the CH,OH and OH alcohol groups. Unlike when the current UNIFAC alcohol groups are used, here methanol, ethanol, and l-propanol are all considered to contain the same CH,OH main group. We consider the possibility of a distinction between the CH30H group of methanol and the CHzOH of ethanol and of l-propanol as a result of the slightly different electronic charge distributions of CH30H (I = 0.310) and of CH20H (I = 0.342) which, based on the previously reported supermolecule calculations (Wu and Sandler, 1991), is considered to be significant in hydrogen-bonding mixtures. Thus CHSOH will be taken to have the same interaction parametes as CH20H but different volumes and surface areas; on the basis of our discussion above, we computed the surface area
896 Ind. Eng. Chem. Res., Vol. 30, No. 5, 1991 2000
2500 Expl (IJ Ue(hMO1
1 2000
4
: -:
0
0 Expl (ZJ m b a n d A Expt (3) I-Propanol - Old & New (2) Old OH (3) New CH3OH IIJ New CHZOH 131
Expl I J Expl ZJ W p l 3) Old OH
-_ - Old
--
- New
Elbenol I-Propanol (I)
OH (3J CH3OH f l J
New I Old CHZOH (2) New CHZOH f3J
n-Herme + ! & m a d
(1)
Melhanol
I-Propanol
f
Water
c7
Q
1500
&.
E
w
0
L
IO00
a P, 0
vi
0
w
500
0
I
0.0
0.1
I
I
I
I
I
I
I
0.2 0.3 0.4 0.5 0.6 0.7 0.8 Mole Fraction of Hexane
I 0.9
1
Figure 10. Excess Gibba free energies derived from experiment for mixtures of n-hexane with methanol (a),ethanol (o),and 1-propanol (A)all at 318.15 K compared with UNIFAC predictions as described in the text.
and volume of the CHzOH group based on the work of Bondi and then obtained the values for the CH,OH group from the ratio of the mean square atomic charges of the two subgroups. To compare the predictions of the UNIFAC model with CH,OH and OH alcohol groups, the optimal interaction parameters for CH,OH with CH, and for OH with CH, were first determined with the use of the vapor-liquid equilibrium data for the n-hexane + ethanol mixture. Predictions for the vapor-liquid equilibrium of the methanol + n-hexane and n-hexane + l-propanol mixtures were made with the use of the UNIFAC model. The excess Gibbs free energies for these three mixtures are shown in Figure 10. The points were obtained from the experimental measurements, the dashed lines are from the UNIFAC model using the OH group, and the solid line results are from using the UNIFAC model with the CH,OH group. The figure shows that the UNIFAC predictions for the n-hexane + l-propanol and the methanol n-hexane mixtures using the CH,OH group are quite satisfactory. Thus, for these alcohol + hydrocarbon mixtures, the single theoretically based CH,OH group works as well as the currently used two empirical OH (with artificially chosen R and Q parameters) and methanol groups. Consequently, as would be expected from our molecular orbital calculations, it appears to be unnecessary to define two alcohol main groups, one for methanol and another for the alcohol group in higher alcohols. Mixtures of Alcohols and Water. Vapor-liquid equilibrium data for the binary mixtures methanol + water at 333.15 K (Broul et al., 1969), ethanol + water at 328.15 K (Mertl, 1972), and l-propanol + water at 333.15 K (as reported in Gmehling et al. (1977)) were used to test the accuracy of the UNIFAC model with the CH,OH and OH alcohol groups. To compare the predictions of the UNIFAC model with CH,OH and OH alcohol groups, the optimal interaction parameters for CH,OH with CH, and for OH with CH, were first determined by using the vaporliquid equilibrium measurements for the ethanol + water mixture. The vapor-liquid equilibrium for the methanol
+
0.0
0.1
0.2 0.3 0.4
0.5
0.6
0.7
0.8
0.9
1.0
Mole Fractlon of Alcohol
Figure 11. Excess Gibbs free energis derived from experiment for at 318.15 K, and water with methanol (A)at 333.15 K, ethanol (0) l-propanol ( 0 )at 333.15 K compared with UNIFAC predictions as described in text. The important observation is that only a single alcohol main group is needed in the new description.
+ water and l-propanol + water mixtures were then made by use of the UNIFAC model. The excess Gibbs free energies for these three mixtures are compared in Figure 11. Again, the points are obtained from the experimental measurements, the dashed lines result from the UNIFAC model using the OH group, and the solid lines result from using the CH,OH group in the UNIFAC model. The figure shows that for the water + l-propanol mixture predictions based on the OH and CH,OH alcohol groups are similar, while for the methanol + water mixture the prediction based on the CH,OH is better than the case when methanol is considered to contain one CH3group and one OH group. Thus again there is evidence that it is unnecessary to consider methanol to be different from the alcohol group in higher alcohols. Mixtures of Cyclic Ethers with Water. Vapor-liquid equilibrium data for the binary mixtures of tetrahydrofuran (THF) + water at 343.15 K (Matous et al., 1972) and 1,3-dioxolane+ water at 343.15 K (Wu and Sandler, 1989) were used to test the accuracy of the UNIFAC model with the newly defined cyclic ether group cCH,OCH, and with the currently used FCH20group. The choice of functional groups for these two ether compounds are the same as discussed earlier. To compare the predictions of the UNIFAC model with CH,OCH, and FCH20 groups, interaction parameters of ether group + water were first determined by using the vapor-liquid equilibrium measurements for the THF + water mixture, and then predictions for the vapor-liquid equilibrium for the 1,3-dioxolane + water mixture were made with the UNIFAC model. The excess Gibbs free energies for the mixtures are compared in Figure 12 where the points are obtained from the experimental measurements, the dashed lines are from the UNIFAC model using the FCH20group, and the solid line results from using the UNIFAC model with the CH,OCH, group. The figure shows that while the predictions using the theoretically based CH,OCH, are somewhat closer to experimental data, both predictions are unsatisfactory. This was to be anticipated on the basis
Ind. Eng. Chem. Res., Vol. 30, No. 5,1991 897 2500
previously provide an explanation of the failure of functional group contribution modeling for such complex multiple hydrogen-bonding mixtures. Consequently, such quantum mechanical calculations also provide a way of predicting when group contribution methods may fail.
2 2000
s >-
Acknowledgment This work was supported, in part, by Grant No. CTS89914299 from the National Science Foundation and Grant No. DE-FG02-85ER13436 from the United States Department of Energy to the University of Delaware. Financial support of Union Carbide and Du Pont is also gratefully acknowledged.
V h 1500
F
8
u V
r:
1000
P
cV
Literature Cited
n
u Y
500
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction of the Ether Compounds
Figure 12. Excess Gibbs free energies derived from experiment for mixtures of water with tetrahydrofuran (0)and 1,3-dioxolane(+) all at 343.15 K compared with UNIFAC predictions as described in the text. As a result of hydrogen-bonding interference with the two ether groups, neither the old (- - -) nor the new (-) cyclic ether functional groups give a satisfactory prediction for the water + 1,3-dioxolane system.
of the differences in hydrogen-bonding energies found in our ab inito supermolecule calculations discussed earlier (Wu and Sandler, 1991). In particular we found that the differences in water hydrogen-bonding energies with the various cyclic ethers were large and of the same magnitude as the excess Gibbs free energies of mixing. Since these hydrogen-bonding interference effects are not included in current group contribution models, we can understand why UNIFAC is not satisfactory for these mixtures. Conclusions The accuracy of predictions of the UNIFAC model with both empirically chosen functional groups and those we have identified using ab initio molecular orbital calculations are compared. For the cases considered, the results based on the theoretically chosen functional groups and the procedures we proposed here are generally found to be better, and never any worse, than the current choice of functional groups in the UNIFAC model. This is encouraging because the new functional groups were determined based only on quantum mechanical calculations. In general, when proximity effects, that is the interaction between neighboring groups of the same molecules, are important, the newly defined functional groups are clearly superior to the groups currently used. Also, we find that when the only difference between main group members is in the number of hydrogens at least two carbons removed from a heteroatom, there is no need to make a distinction between subgroups based on surface areas and volumes. This reduces the number of functional subgroups that need to be considered. Finally, for hydrogen-bonding mixtures, such as 1,3dioxolane + water, both theoretically and empirically chosen functional groups are unable to give a satisfactory prediction in the UNIFAC model. The quantum mechanical ab initio supermolecule calculations discussed
Bondi, A. Physical Properties of Molecular Liquids, Crystals, and Glasses; Wiley: New York, 1968; pp 1-120. Broul, M.; Hlavaty, K.; Linek, J. Liquid-vapor equilibrium in systems of electrolytic components. V. The system CH30H-H20LiCl at 60°. Collect. Czech. Chem. Commun. 1969,34,3428-3432. Brown, I.; Fock, W.; Smith, F. Design of a mass spectrometer ion source based on computed ion trajectories. J.Chem. Thermodyn. 1969,1, 273-291. Eng, R.; Sandler, S. I. Vapor-Liquid Equilibria for Three Aldehyde/Hydrocarbon Mixtures. J. Chem. Eng. Data 1984, 29, 156-161. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AZChE J. 1975,21, 1086-1099. Gmehling, J.; Onken, U.; Arlt, W. Vapor-LiquidEquilibrium Data Collection, DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1977; Vol. I (12 parts), I(2a), p 252. Hanson, D. 0.;Van Winkle, M. J. Alteration of the relative volatility of hexane-1-hexene by oxygenated and chlorinated solvents. J. Chem. Eng. Data 1967,12,319-325. Kudryavtaeva, L. S.; Susarev, M. P. Liquid-vapor equilibrium in the systems acetone-hexane and hexane-EtOH. Zh. Prikl. Khim. 1963,36,1471-1473. Matous, J.; Novak, J. P.; Sobr, J.; Pick, J. Phase equilibrium in the system tetrahydrofuran(l)-water(2). Collect. Czech. Chem. Commun. 1972,37, 2653-2655. Mertl, I. Liquid-vapor equilibrium. 11. Phase equilibrium in the ternary system ethyl acetate-ethanol-water. Collect. Czech. Chem. Commun. 1972,37, 366-369. Ohta, T.; Nagata, I. Thermodynamic Properties of Four EsterHydrocarbon Mixtures. J. Chem. Eng. Data 1980,25,283-286. Ogorodnikov, S. K.; Kogan, V. B.; Nemtsov, M. S. Separation of C6 hydrocarbons by azeotropic and extractive rectification (IV) Liquid-vapor equilibrium in systems of hydrocarbons and methyl formate. Zh.Prikl. Khim. 1961,34, 581-586. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987; pp 314-332. Scheller, W. A.; Rao, S. V. N. Isothermal vapor-liquid equilibrium data for system heptane-2-pentanone at 90°. J. Chem. Eng. Data 1973,18, 223-225. Weidlich, U.; Gemhling, J. The Modified UNIFAC Model: -ym, h", and VLE. Ind. Eng. Chem. Res. 1987,26, 1372-1381. Wu, H. S.; Sandler, S. I. Vapor-Liquid Equilibrium of Tetrahydrofuran Systems. J. Chem. Eng. Data 1988,33,157-165. Wu, H. S.; Sandler, S. I. Vapor-Liquid Equilibrium of 1,3-Dioxolane Systems. J. Chem. Eng. Data 1989, 34, 209-213. Wu, H. S.; Sandler, S. I. The Use of ab Initio Quantum Mechanics Calculations in Group Contribution Methods. 1. Theory and Basis for Group Identification. Ind. Eng. Chem. Res. 1991, preceding paper in this issue. Wu, H. S.; Locke, W. E., 111; Sandler, S. I. Isothermal Vapor-Liquid Equilibrium of Binary Mixtures Containing Pyrrolidine. J. Chem. Eng. Data 1990,35, 169-172. Wu, H. S.; Locke, W. E., III; Sandler, S. I. Isothermal Vapor-Liquid Equilibrium of Binary Mixtures Containing Morpholine. J. Chem. Eng. Data 1991,36, 127-130.
Received for review June 8, 1990 Revised manuscript received January 3, 1991 Accepted January 22, 1991
