Ind. Eng. Chem. Res. 2008, 47, 3247-3252
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Prediction of Partition Coefficients of Benzothiophene and Benzothiophene 1,1-Dioxide in Octane/Acetonitrile System Using COSMO Theory Yusuke Shimoyama,*,† Yoshio Iwai,† Satoshi Yoda,‡ and Takeshi Furuya‡ Department of Chemical Engineering, Faculty of Engineering, Kyushu UniVersity 744 Motooka Nishi-ku, Fukuoka 819-0395, Japan, and Nanotechnology Research Institute, National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
The partition coefficients of benzothiophene (BT) and benzothiophene 1,1-dioxide (BTDO) in the octane/ acetonitrile system were predicted using the COSMO (conductor-like screening model) based activity coefficient models COSMO-SAC (segment activity coefficient) and COSMO-UNIQUAC. In COSMO-UNIQUAC, a segment activity coefficient was described in a UNIQUAC-type equation. The results with COSMO-UNIQUAC were compared with those from the COSMO-SAC model. It was found that COSMO-UNIQUAC reproduced the experimental data more accurately than COSMO-SAC. The surface charge density profiles (σ-profiles) of functional groups on BT and BTDO molecules were utilized to determine that the partition coefficients of BTDO are much lower than those of BT. A hypothetical molecule with the volume and surface area of BTDO was conducted by using the σ-profiles of functional groups on BT and BTDO. The partition coefficients of the hypothetical component were predicted by COSMO-UNIQUAC. It was revealed that the partitions of BTDO in the octane/acetonitrile system were influenced from the charge density changes by the oxidation on not only the sulfur atom but also on the carbon and hydrogen atoms. 1. Introduction Novel desulfurization processes are required to reduce the sulfur content in gasoline and diesel fuel to extremely low levels. In oxidative desulfurization, thiophene, benzothiophene, and their derivatives can be transformed into sulfones and sulfoxides. These oxidative compounds are extracted easily with polar solvents. A recent paper has stated that oxidative desulfurizations are capable of reducing the sulfur contents in fuel oil to lower levels.1 Recently, oxidative desulfurization processes with fuel oil/acetonitrile biphasic systems have been proposed.2-4 In these processes, benzothiophenes and their derivatives are extracted into the acetonitrile phase and oxidized effectively. It is very important for the oxidative desulfurization process design to recognize the liquid-liquid equilibria for fuel oil/ acetonitrile systems and the partitions of the sulfur compounds and their oxides in fuel oil/acetonitrile biphasic systems as fundamental knowledge. Furuya et al.5,6 have reported experimental data of the liquid-liquid equilibria for acetonitrile + octane, + decane, and + hexadecane systems. The partition coefficients of benzothiophene and benzothiophene 1,1-dioxide in the octane/acetonitrile system have been also measured at 298-343 K.5 In addition to these measurements, the correlations or predictions can be a highly useful tool for the design and development of oxidative desulfurization processes. Activity coefficient models, such as NRTL,7 UNIQUAC,8 ASOG,9 and UNIFAC10 models, have been utilized to correlate the liquid-liquid equilibria and the partition coefficients. However, many parameters determined by data fitting are required in these models, especially for multicomponent systems. Based on quantum calculations with the conductor-like screening model (COSMO),11 COSMO for real solvents (COSMO-RS)12 and COSMO segment activity coefficient (COSMO-SAC)13 models have been developed to predict the activity coefficients in mixtures without data fitting. These models have been utilized † ‡
Kyushu University. AIST.
to predict vapor-liquid equilibria,14-16 solubilities,17 and high pressure phase equilibria18-20 until now. From the literature, it has been verified that the COSMO-based models can be very useful to predict the thermodynamic properties of fluids and their mixtures. In this work, the partition coefficients of benzothiophene (BT) and benzothiophene 1,1-dioxide (BTDO) in the octane/acetonitrile system were predicted by using the COSMO-based models COSMO-SAC and COSMO-UNIQUAC. In COSMOUNIQUAC, the segment activity coefficients are described with the UNIQUAC equation8 as proved by Lin and Sandler.13 Furthermore, the surface charge density profile (σ-profile) on the functional groups of BT and BTDO molecules were used for the discussions about the partitions of BTDO in the octane/ acetonitrile system being much lower than those of BT. A hypothetical molecule with the volume and surface area of a BTDO molecule was constructed by using the σ-profiles on the functional groups of BT and BTDO. The predictions of partition coefficients of the hypothetical component were carried out by COSMO-UNIQUAC. These results were compared with those of BT and BTDO. 2. Definition of Partition Coefficient In this work, it was assumed that the concentrations of BT or BTDO in octane- or acetonitrile-rich phase were in infinite dilution conditions, because the experimental data5 used for the comparisons with the predictions had been obtained in very small concentrations of BT or BTDO, with 80 ppm (weight basis) as a sulfur concentration in total of those in octane- and acetonitrile-rich phases. The partition coefficient of BT or BTDO in the octane/acetonitrile system based on mole fractions Ki is given from the relationship of liquid-liquid equilibria by the following equation.
Ki ) 10.1021/ie071377h CCC: $40.75 © 2008 American Chemical Society Published on Web 04/05/2008
xIi
γIIi ) xIIi γIi
(1)
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where xi and γi are the mole fraction and activity coefficient of the component i, respectively. The superscripts “I” and “II” mean octane- and acetonitrile-rich phases, respectively. The partition coefficient based on the weight fraction Ki,w can be obtained from that based on the mole fraction as follows.
Ki,w )
(
M1xII1 Ki M1xI1
+ +
) (
M2xII2 M2xI2
)
γIIi γIi
M1xII1 M1xI1
+ +
)
M2xII2 M2xI2
(2)
where M is the molecular weight. The subscripts “1” and “2” mean octane and acetonitrile. The experimental data of the liquid-liquid equilibria in the octane/acetonitrile system5 were used for the mole fractions of octane and acetonitrile in each phase in eq 2. The activity coefficients in octane- and acetonitrile-rich phases were calculated by COSMO-SAC or COSMOUNIQUAC models as described below.
The segment activity coefficient is calculated from the σ-profile in the mixture and the exchange energy of the segment pair described as follows.
{
1n Γ(σm) ) -1n
pi(σ) )
Ai(σ) Ai
(3)
where Ai(σ) is the total surface area of the segment with charge density σ, and Ai is the surface area of molecule i. As the BT or BTDO concentrations were the infinite dilution conditions, the probability of finding σ in the mixture is obtained from the probabilities in pure octane and acetonitrile.
p(σ) )
x1A1p1(σ) + x2A2p2(σ) x1A1 + x2A2
(4)
The subscripts “1” and “2” denote octane and acetonitrile, respectively. The surface charge density σ was also used for the calculations of the segment pair energies contributed from the misfit energy Emf and the hydrogen bonding interaction Ehb given as follows.
Emf(σm,σn) )
(0.64)(0.3)a3/2 eff (σm + σn) 20
Ehb(σm,σn) ) chb max[0,σac-σhb] min[0,σdo+σhb]
(5) (6)
where aeff and 0 are the standard segment surface area and the permittivity of free space with 0 ) 5.724 × 10-8 (e2 mol J-1 Å-1), respectively. chb and σhb are the constant and the cutoff value for the hydrogen bonding interactions, respectively. σac and σdo mean the larger and smaller values of σm and σn. From these interaction energies, the exchange energy required to form the segment pair of σm and σn from a neutral pair is obtained by the following equation.
∆W(σm,σn) ) Emf(σm,σn) + Ehb(σm,σn)
(7)
n
[
]}
-∆W(σm,σn) RT
(8)
where R is the gas constant. This equation should be solved iteratively. The activity coefficient of component i in mixture γi can be obtained from the segment activity coefficient Γ.
ln γi )
Ai aeff
pi(σm)[ln Γ(σm) - ln Γi(σm)] + ln γCi ∑ σ
li )
φi
+
xi
() z
2
2
θi
qi ln
() z
(9)
m
ln γCi ) ln
3. Activity Coefficient Model 3.1. COSMO-SAC. The COSMO-SAC method13 is the method for predicting thermodynamic properties in mixtures with a statistical approach by quantum calculations, based on the COSMO model.11 In the COSMO-SAC method, the predictions of thermodynamic properties are performed by using a charge density σ of a segment in a molecular surface obtained from COSMO calculations. In this work, the COSMO calculations were carried out with Gaussian 03W software.21 The probability of finding σ in pure component i, the σ-profile pi(σ), is given by the following equation.
p(σn) Γ(σn) exp ∑ σ
(ri - qi) - (ri - 1),
φi
θi )
+ li -
φi xi
rixi
∑j xjlj
φi )
,
∑j rjxj
(10)
qixi
∑j qjxj
(11)
where z is the coordination number. r and q are the surface area and volume parameters. The superscript “C” means the combinatorial contribution from the differences of the molecular size and shapes. In eq 10, the activity coefficients were calculated in the infinite dilution condition for BT or BTDO; the mole fractions were set to zero. For the mole fractions of octane and acetonitrile, the liquid-liquid equilibrium data for the octane/acetonitrile system were used. Finally, the partition coefficient of the solute in the octane/acetonitrile system can be demonstrated from substituting eq 9 to eq 1.
1n Ki )
γIIi γIi
)
Ai
∑pi(σm)[1n ΓII(σm) - 1n ΓI(σm)] +
aeff σm
C,I (1nγC,II i - 1nγi ) (12)
3.2. COSMO-UNIQUAC. Lin and Sandler13 have explained the relationship of the segment activity coefficient from the UNIQUAC equation.8 The interaction energy between the surface charge segments σm and σn is explained with the misfit energy and hydrogen bonding interaction described by eqs 5 and 6.
U(σm,σn) ) [Emf(σm,σn) - Emf(σm,0) - Emf(σn,0)] + [Ehb(σm,σn) - Ehb(σm,0) - Ehb(σn,0)] (13) In the UNIQUAC formula, the activity coefficient of the surface charge segment in mixture can be demonstrated by the following expression.
1n Γ(σm) ) 1 - 1n
∑ σ n
[
τmn ) exp -
p(σn)τnm -
p(σn)τmn
∑ σ p(σk)τkn ∑ σ
(14)
n
k
]
U(σm,σn) - U(σn,σn) 2RT
The activity coefficients and the partition coefficients of component i are calculated from eqs 9 and 12 as in the case of the COSMO-SAC model.
Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008 3249 Table 1. Parameters in COSMO-SAC and COSMO-UNIQUAC method
chb × 10-5 aeff [Å2] σhb [e/Å2] [kJ mol-1 Å4 e-2]
ref
COSMO-SAC 13 COSMO-SAC this work COSMO-UNIQUAC this work
7.50 7.50 7.50
0.0084 0.0082 0.0082
3.581 6.268 2.501
Table 2. Deviations between Experimental and Predicted Results of Partition Coefficient of Benzothiophene (BT) and Benzothiophene 1,1-Dioxide (BTDO) in Octane/Acetonitrile System δ × 102 sulfur component
N
COSMO-SAC
COSMO-UNIQUAC
BT BTDO
6 6
1.4 0.24
1.2 0.12
w w δ ) (1/N)∑Nnd)1|Ki,exp - Ki,calc |, where N is the number of data points.
3.3. Details of Parameters in COSMO-SAC and COSMOUNIQUAC. In the COSMO-SAC and COSMO-UNIQUAC models, a standard segment surface area aeff, a constant chb, and a cutoff value σhb for the hydrogen bonding interaction are needed to calculate the exchange energy in eq 7 and the interaction energy of a segment pair in eq 13. In this work, the value of aeff given by Lin and Sandler13 was used in both COSMO-based models: aeff ) 7.50 Å2. The parameter chb was determined from fitting the experimental partition coefficient of BT in the octane/acetonitrile system at 343 K, and the value was 6.268 × 105 and 2.501 × 105 kJ mol-1 Å4 e-2 in COSMOSAC and COSMO-UNIQUAC, respectively. σhb was set to 0.0082 e Å-2 from the literature.22 Table 1 lists the values of the parameters aeff, chb, and σhb in this work and the literature by Ling and Sandler.13 The molecular volume and surface area parameters are required for the calculations of the combinatorial contributions of the activity coefficients in eqs 10 and 11. These molecular parameters are obtained from the following equation.
ri )
Vi Ai and qi ) Vst Ast
Figure 1. Partition coefficients of benzothiophene (BT) and benzothiophene 1,1-dioxide (BTDO) in octane/acetonitrile system. Experimental data:5 BT (O); BTDO (b). Predicted results: COSMO-SAC (s); COSMO-UNIQUAC (---).
Figure 2. Relationship between σ-profile of benzothiophene (BT) and segment activity coefficient difference in octane- and acetonitrile-rich phases at 298 K: σ-profile of BT (s); segment activity coefficient difference (---).
(15)
Vi and Ai are the molecular volume and surface area of molecule i resulted from COSMO calculations. Vst and Ast denote standard volume and surface area, respectively. In this work, the volume and surface area of methane molecule from COSMO calculations were applied as the standard values. These values are 37.98 Å3 and 56.04 Å2 for the volume and surface area. 4. Results and Discussion Figure 1 shows the predicted results of the partition coefficients of BT in the octane/acetonitrile system at 298-343 K. The deviations between the experimental and predicted results are listed in Table 2. The results with COSMO-SAC and COSMO-UNIQUAC for BT are in good agreement with the experimental data. The results for BTDO with COSMOUNIQUAC reproduce the experimental data more accurately than those with COSMO-SAC. These results can be explained by that the segment activity coefficients are expressed in consideration of the local area fractions of the segments in the UNIQUAC formula. As described in eq 12, the partition coefficients are calculated from a multiplication of the σ-profile of the solute and the segment activity coefficient difference in the mixture between octane- and acetonitrile-rich phases. The relationships between the σ-profile of the solute and the segment activity coefficient difference are shown for BT and BTDO in Figures 2 and 3. As
Figure 3. Relationship between σ-profile of benzothiophene 1,1-dioxide (BTDO) and segment activity coefficient difference in octane- and acetonitrile-rich phases at 298 K: σ-profile of BTDO (s); segment activity coefficient difference (---).
shown in Figures 2 and 3, the segment activity coefficient differences decrease considerably in positive and negative charge densities. The σ-profile of BT has a large peak near zero charge density. On the other hand, the profiles for BTDO indicate large values in high positive and negative charge densities. It was considered that the σ-profile for BTDO results in much lower values of the partition coefficients of BTDO than those of BT. BT and BTDO molecules were divided into the functional groups as given in Figure 4 in order to discuss the changes of these σ-profiles by the oxidation from BT to BTDO. Figure 5 shows the σ-profiles of the S group on BT and the SO2 group
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Figure 7. σ-profiles of benzothiophene (s) and hypothetical component (---).
Figure 4. Functional groups on (a) benzothiophene and (b) benzothiophene 1,1-dioxide.
Figure 8. σ-profiles of benzothiophene 1,1-dioxide (s) and hypothetical component (---).
Figure 5. σ-profiles of S group on benzothiophene (s) and SO2 group on benzothiophene 1,1-dioxide (---).
Figure 6. σ-profiles of CH groups on benzothiophene (s) and benzothiophene 1,1-dioxide (---).
on BTDO. The σ-profile of the SO2 group on BTDO shifts to the right side and has a peak higher than that of the S group on BT. It is no wonder this σ-profile changes because the SO2 group on the BTDO molecule is charged more negative due to the oxidation and the surface area increases due to the addition of two oxygen atoms. For CH groups on BT and BTDO, the σ-profiles are given in Figure 6. It is found that the σ-profile of CH groups for BTDO shifts to the negative region by the oxidation of BT. The reason is considered to be that the charged
molecule due to the oxidation is neutralized by the positive charge of the CH group. As shown in Figure 6, the surface charge densities of the CH group on BTDO are different from those on BT though the atoms of CH groups on both molecules are identical. It is considered that the differences of group properties affect the calculations of partition coefficients of BTDO. In conventional group contribution methods, ASOG9 and UNIFAC,10 the activity coefficient can be explained by contributions of groups whose properties are identical in any molecules. The effects of these differences of group properties cannot be explained by the group contribution methods. In this work, a hypothetical BTDO molecule was utilized to verify the effect of the surface charge density difference on the calculation of the partition coefficient of BTDO in the octane/acetonitrile system. The σ-profile of the hypothetical BTDO molecule was composed of those of the CH group on BT and the SO2 group on BTDO. This explanation for the hypothetical BTDO molecule is the same as the case of the conventional group contribution method. The comparisons of the partition coefficients between the hypothetical and real BTDOs are useful to verify the effect of the surface charge density difference of CH group. The volume and surface area of BTDO molecule were used as those of the hypothetical molecule. The surface charge density of the hypothetical molecule is expressed as follows. CH SO2 SO2 Ahypphyp(σm) ) ACH BT pBT (σm) + ABTDOpBTDO(σm)
(16)
where the subscript “hyp” indicates the hypothetical molecule, and the superscripts mean the functional groups on the molecule. This σ-profile is compared with those of BT and BTDO in Figures 7 and 8. As shown Figure 7, the profiles for the hypothetical molecule are almost the same as those for BT at
Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008 3251
was constructed from the σ-profiles of the CH group on the BT molecule and of the SO2 group on the BTDO molecule. The partition coefficients of the hypothetical component in the octane/acetonitrile system were predicted from COSMO-UNIQUAC. From the predicted partition coefficients of BT, BTDO, and the hypothetical component, it was revealed that the partition coefficients of BTDO are affected by the changes of the surface charge densities on CH groups by the oxidation from BT to BTDO. It is considerable that COSMO-based models can demonstrate the effect of the surface charge densities on functional groups which cannot be explained by conventional group contribution methods including the same group properties in any molecule. Figure 9. Predicted results of partition coefficients of hypothetical component, benzothiophene (BT), and benzothiophene 1,1-dioxide (BTDO) in octane/acetonitrile system with COSMO-UNIQUAC. Experimental data:5 BT (O); BTDO (b). Predicted results: hypothetical component (s); BT (‚‚‚);BTDO (---).
-0.010 to 0.007 e/Å2 contributed from the CH group. In Figure 8, the σ-profiles of the hypothetical and BTDO molecules are identical to each other at 0.005-0.015 e/Å2 contributed from the surface charge densities of SO2 groups. At the other charge densities, the σ-profile of the hypothetical molecule is more positive than that of BTDO. It corresponds to the σ-profiles of CH groups on BT and BTDO as shown in Figure 6. The partition coefficients of the hypothetical component in the octane/acetonitrile system were predicted with COSMOUNIQUAC. The predicted results are compared with those of BT and BTDO and presented in Figure 9. For the hypothetical component, the partition coefficients are 0.03-0.1 times lower than those of BT. The partition coefficients of BTDO are 0.0050.04 times lower than those of BT. These results mean that the partition coefficients of BTDO are influenced by not only the changes of the charge densities from S to SO2 groups but also the shift of the σ-profile on the CH group by the oxidation. COSMO-based models can explain these phenomena in the consideration of the charge density changes on the molecular surface by the oxidation. The COSMO-based models are superior to the conventional group contribution methods, such as ASOG9 and UNIFAC,10 in which the properties of functional groups are identical in any molecules, because the consideration of the changes of the properties of functional groups can be made in each molecule. 5. Conclusion The partition coefficients of benzothiophene (BT) and benzothiophene 1,1-dioxide (BTDO) in the octane/acetonitrile twophase system were predicted from two COSMO-based models, COSMO-SAC and COSMO-UNIQUAC. The hydrogen bonding interaction parameter in both models was determined from fitting to the experimental data of the partition coefficients of BT at 343.2 K. The predicted results for BTDO with COSMOUNIQUAC reproduce the experimental data more accurately than those with COSMO-SAC. The σ-profiles of functional groups, CH, S, and SO2, on BT and BTDO molecules were used to discuss the effect of the surface charge density changes by the oxidation on the predictions of the partition coefficients of the oxidized BTDO. The peak of the SO2 σ-profile for BTDO is at a region more positive than those of the S group on BT due to oxidation. The σ-profile for the CH group on BTDO shifts to the negative region compared with that on BT. Furthermore, a hypothetical molecule
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ReceiVed for reView October 14, 2007 ReVised manuscript receiVed January 30, 2008 Accepted February 6, 2008 IE071377H
