2212
Ind. Eng. Chem. Res. 2009, 48, 2212–2217
Group Contribution Method for Predicting Melting Points of Imidazolium and Benzimidazolium Ionic Liquids Yan Huo, Shuqian Xia,* Yan Zhang, and Peisheng Ma Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin UniVersity, Tianjin 300072, People’s Republic of China
A new model is proposed here to estimate melting points of imidazolium and benzimidazolium ionic liquids (ILs) from chemical structures by using a group contribution method, which considers the contributions of normal groups, ionic groups, and characteristic factors of molecules. The melting points of ILs are fitted by the equation presented in this study. Thirty simple groups and three characteristic factors were defined in the model based on the optimization of property values of 155 ionic liquids. The average relative deviation in this work is less than 5.86%, and calculated values of an additional 35 ILs are compared with the values in the literature. The R2 for 190 ILs is about 0.8984. The results show that melting points of ILs determined by the method are accurate and thus the new model can be applied to predict melting points of ILs. Introduction Room-temperature ionic liquids (ILs)sa class of organic molten saltssare composed entirely of anions and cations. They have attracted much attention from the scientific community, and their use as catalysts and catalytic supports has been studied extensively. ILs are considered to be “green solvents” for various separation processes,1 and are organic salts with some special characteristics that make them suitable for many applications, which have been reported in the following literature: as media for clean liquid-liquid extraction processes2-4 and for analytical and physical chemistry;5 as solvents for electrochemical applications.6,7 Primary research on the properties of pure ILs has focused on developing and understanding the relationship between the structures of the cation and anion and the physical properties. The thermodynamic property or behavior of mixtures containing ILs should be supplied to develop new processes involving ILs on an industrial scale. It is necessary to know not only a range of physical properties including viscosity, density, and interfacial tension but also the heat capacity and other thermodynamic properties, including the melting point, which is the temperature at which the substance transforms from crystal to liquid. As one of the most important physical properties, melting points of ILs have been researched with increasing interest. The applications mentioned above require knowledge of the melting points of ILs to determine the range of immiscibility in liquid-liquid equilibrium, which is related to the upper critical solution temperature in the liquid phase. The data points are so essential that many institutions have set up databases about ILs. The IUPAC Ionic Liquids Database,8 IL Thermo, is a Web research tool that allows worldwide users to access an up-to-date data collection from the publications for thermophysical properties of ILs, as well as their binary and ternary mixtures with other compounds. Also, nearly all worldwide available data points for ILs (pure component and mixture properties) can be found in the Dortmund Data Bank (DDB).9 Holbrey et al.10 made systematic studies of the influence of alkyl chains on the melting points of ILs and showed that the melting points of 1-alkyl-3-methylimidazolium tetrafluoroborates * To whom correspondence should be addressed. E-mail:
[email protected].
are related to the increment of alkyl length. Christopher et al.11 investigated the relationships between the structures of the cation and the anion and the melting point of ILs in order to discover the reason why ionic liquids have lower melting points. Brennecke et al.12 also made particular studies of the phase behavior of imidazolium ILs. Recently, a method to estimate the melting points of several imidazolium-based ILs and ionic liquid analogues was presented by Katritzky and co-workers17 using the CODESSA program in order to develop predictive tools for the determination of suitable ILs. Varnek et al.30 compared several popular machine learning methods used to predict the melting points of ILs. Group Contribution Method Joback and Reid13 defined 41 structural groups and proposed the following model equation for the freezing point: Tfp ) 122 +
∑ N ∆T k
(1)
fp
k
In eq 1, Nk is the number of times that a group appears in the molecule and ∆Tfp is the contribution to the freezing point. Constantinou and Gani14,15 proposed a complex model for the estimation of the freezing point:
[∑
Tfp ) 102.425 ln
k
1 Nk∆Tfp +W
∑ N ∆T j
j
2 fp
]
(2)
In eq 2, Nk is the number of times that a group of primary level appears in the molecule, Nj is the number of times that a group 1 2 and ∆Tfp are the of higher level appears in the molecule, ∆Tfp contributions of two levels to the freezing point, and W, which is fitted by equation, is the constant. The value of the constant is W ) 1 when two levels are considered, while W ) 0 when only the primary level is considered. The model considers the molecular structure and estimates a given property at two levels. The primary level contributes to simple groups that are useful for a wide variety of organic compounds. The higher level contains two aspects, such as polyfunctional and structural groups that provide more information about molecular fragments whose description through first-order groups is not possible. Yalkowsky et al.16 defined 61 structural groups, nine molecule corrections to the relationship between the freezing point and
10.1021/ie8011215 CCC: $40.75 2009 American Chemical Society Published on Web 01/12/2009
Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2213 Table 1. Anions abbreviation
name
formula
Cl Br I BF4 PF6 N(CN)2 NO3 NTf2 NPf2 OTf Onf TA CTf3 TSAC
chloride bromide iodide tetrafluoroborate hexafluorophosphate dicyanoamides nitrate bis((trifluoromethyl)sulfonyl)imides bis((perfluoromethyl)sulfonyl)imides trifluoromethanesulfinates perfluorobutylsulfonate trifluoroacetates tri(trifluoromethylsulfonyl)methyl 2,2,2-(trifluoromethylsulfonyl)acetamide
Cl Br I BF4 PF6 CN3 NO3 C2F6NO4S2 C4F10NO4S2 CF3SO3 C4F9SO3 C2F3O2 C4F9O6S3 C3F6NO3S
Table 2. Contributions of Simple Groups ∆Tmp
group
∆Tmp
group
Figure 1. Plot of data from literature and prediction for 190 ionic liquids.
Without Rings -CH3 -CH2>CH>C )CH2 )CH-OH -O>CdO
-0.4926 0.1324 1.470 -0.5317 2.863 -3.119 -0.1813 0.08350 -0.9594
-COO-NH2 -CN -NO2 -SO2 -F -Cl -Br
1.074 -2.106 -1.145 -2.652 -1.080 0.1022 0.5948 -1.1009
the predicting method. To the best of our knowledge, there is no group contribution method available to predict melting points of ILs. New Group Contribution Model
With Rings )CH)C
-1.497 -2.546 ∆Tmp
ionic group [)N < ] [-B][-P][-N-][-O]-
+
-N -OH
-13.85 -2.841
ionic group -
2.680 -2.261 -2.986 -0.1538 -1.305
[>C-] [Cl][Br][I]-
∆Tmp -0.6667 -3.300 -4.013 -3.396
the boiling point, and a correlated method to predict the freezing point:
∑ N ∆T k
Tfp )
fp,k
k
56.5 - 19.2 log σ + 9.2τ
(3)
In eq 3, Nk is the number of times that a group appears in the molecule, ∆Tfp,k is the contribution to the freezing point, σ is a symmetric number and is determined by the structure of the molecule, and τ is an estimated value and determined by the following equation: τ ) SP3 + 0.5(SP2) + 0.5(RING) - 1
(4)
In eq 4, SP3 is the number of non-ring, nonterminal sp3 atoms, SP2 is the number of non-ring, nonterminal sp2 atoms, and RING is the number of single rings connected to the system in the molecule. The methods mentioned above cannot be directly applied to estimate melting points of ionic liquids since there are no methods to predict melting points of ionic liquids with a consideration of the impact on electrovalent bond in the groups. Further, there are also no values of some simple groups to utilize in the model, such as [-B]-, [-P]-, and -SO2. Additionally, there are not enough experimental data in the literature to test
The factors that influence the melting points of ILs contain the charge distribution on the ions, H-bonding ability, the symmetry of the ions, and the van der Waals interactions. Sometimes precise data of ILs are difficult to measure for the phase change of ILs, which is more complex than that of normal molecule liquids. In this work, the traditional group contribution method, such as eqs 1 and 2, was eliminated because it cannot reflect the ionic character of an ionic liquid. Thus, first, ionic groups were elected independently from common groups, for there must be some groups having the function for an electrovalent bond. However, the model cannot explain complicated phenomena, including the symmetry of groups in N, N of the imidazolium ring, the substitutent of the C position, and the numbers of rings. Like eq 3, a new model contrasting the group and structure of a molecule has been carried out. The following principles are used to identify the groups and characteristic factors of a molecule: (1) The structure of a functional group should be as small as possible; for example, -CH2COC6H5 has -CH2-, >CdO, >C), and -CH) as different groups. (2) The performance of groups is independent of the molecule in which the groups occur, complying with a fundamental group contribution principle. (3) The model is constituted by considering both group contributions with additivity and characteristic factors of a molecule without additivity. In our investigations with the series of melting points of ILs, the dimension and structure of the organic anion will influence their melting points when compared with the same cation, while the cation’s symmetry can moderate the melting point if the anion is the same. Replacement of the hydrogen at the C position of the imidazolium ring by a group resulted in an increase of melting point, and so did the number of ring groups in the molecule. All of these situations are considered when the model is utilized to predict the melting points of ILs. The melting point of an ionic liquid is considered to be a function of structurally dependent parameters, which are thereby determined by summing the number frequency of each group
2214 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 3. Illustration of Calculations by the Group Contribution Method
occurring in the molecule times its contribution. As mentioned above, symmetrically substituted groups connected to N, N and the group of the C position in the imidazolium cation and the ring group in the molecule are called characteristic factors of the molecule. The contribution of an electrovalent bond presented in the model derives from the fact that ionic liquids are salts. Simple groups in the model are divided into two aspects: one is a normal group; the other is an ionic group that provides the objective possibility of forming an electrovalent bond. Property values of 155 ionic liquids were compiled from the references 10, 12, 15, 17–26, 28, 29, and 31 in order to build the model and are shown in the Supporting Information. Then thirty structural groups and three characteristic factors of the molecule were defined through the model equation for the melting temperature:
∑ N ∆T k
Tmp )
k
mp,k
+ ZH
∑ N ∆T j
mp, j
j
AH + BHσ + CHτ + DHδ
(5)
In eq 5, Nk is the number of group k in the molecule, Nj is the number of ionic group j in the molecule, and ∆Tmp,k and ∆Tmp,j are the contributions of normal group k and ionic group j to the melting temperature. σ ) 1 shows that the groups, which connect to >NH and )N- (ring of imidazolium), are the same, while σ ) 0 indicates that different groups connect to N, N in the imidazolium cation. τ is the number of ring groups in the molecule. δ ) 1 means that there is a group connect to the C position in the imidazolium cation, while δ ) 0 means that there are none. The expression of Tmp has been based on the following factors: the function has to achieve additivity in the contributions ∆Tmp,k and ∆Tmp,j, it has to illustrate the best possible fit of collected data, and it should widen the range of applicability, even in benzimidazolium. The function finds numerical values of the parameters that make the expression give a best fit to the numbers that groups occur as a function of Tmp. The parameters of the model were determined by minimizing the absolute deviation of melting points through a least-squares fit. AH, BH, CH, DH, and ZH are fitted by collected data, and the values are
Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2215
AH ) -0.4177, BH ) 0.004 665, CH ) -0.018 59, DH ) 0.005 428, and ZH ) 2.355. To demonstrate the utility of the model, melting points of four ILs were calculated and are shown in Table 3. The new model has been applied to estimate the melting points of ionic liquids and its groups contain normal groups that just work as linkages to connect to each other, and the new group contributes to electrovalent bonds of ionic liquids, including [)N< ]+, [>C-]-, [-N-]-, [-O]-, [-B]-, [-P]-, [Cl]-, [Br]-, and [I]-. To particularize the structure of anions, their names are listed in Table 1. The contributions of all groups are presented in Table 2.
rmsd )
R )
ARD )
∑ |(T
Tlit mp cal mp
× 100%
lit - Tlit mp)/Tmp |
n
(8)
1 - ( n lit 2 mp
cal 2 mp
lit mp
cal 2 mp
cal 2 mp)
]
(9) where n is the total number of values in the literature. Figure 1 depicts the plot of data from the literature and the prediction of melting points, and Table 5 gives RD, ARD, rmsd, and R2 of predicted melting points. The reliability of the model is proved by R2 ) 0.8984 and rmsd ) 28.20 K for 190 ILs mentioned in this work. Results and Discussion The estimated melting points of 35 ILs are listed in Tables 3 and 4, where predicted values are within acceptable margins of deviation. In addition, predicted values of other 155 ILs are also shown in the Supporting Information. Melting points of 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), 1-methyl-3-ethylimidazolium tri(trifluoromethylsulfonyl)methyl ([meim][CTf3]), 1-NH2-2-NH2-3-CH2COC6H4(p-OCH3)imidazolium bromide, and 2-methyl-1,3-diethylimidazolium bromide ([C2H5CH3C2H5im][Br]) are estimated as example compounds to illustrate the application of the new model proposed here. In Table 3, the calculated values are summed from each property using the values in Table 2 and compared with values in the literature. The relative deviations for these ionic liquids are 4.85%, 2.51%, 3.88%, and 7.32%, respectively.
(6)
× 100%
[ ∑ (T
2 - Tlit mp)
∑ T )( ∑ T )] 1 1 - ( ∑ T ) ][ ∑ (T ) - ( ∑ T n n lit cal mpTmp
lit 2 mp)
In each case, the accuracy of calculated data was checked from an examination of the variation of the relative deviations and average relative deviations: lit |Tcal mp - Tmp |
cal mp
[∑T
2
Reliability of the Model
RD )
1n ∑ (T
(7)
Additionally, the reliability of the model was certified by the examination of the root-mean-square deviation (rmsd) and the square of the Pearson correlation coefficient (R2):
Table 4. Melting Points of Ionic Liquids Predicted by the Model and Comparison with Literature Values ionic liquids cations no.
1-substituent
3-substituent
other substituents
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
-(CH2)3CH3 -CH2C6H5 -(CH2)9CH3 -(CH2)9CH3 -(CH2)9CH3 -(CH2)10CH3 -(CH2)11CH3 -(CH2)11CH3 -(CH2)11CH3 -(CH2)13CH3 -(CH2)13CH3 -(CH2)13CH3 -(CH2)15CH3 -(CH2)15CH3 -(CH2)17CH3 -(CH2)17CH3 -CH3 -CH3 -CH3 -CH(CH3)2 n-C4H9 -CH3 -CH)CH2 -CH)CH2 -CH3 -OCH2C6H4(p-NO2) -OCOCH(CH3)3
-(CH2)3CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3 -CH3
28 29 30 31
-CH3 -CH3 -CH2CH3 -CH3
-CH3 -CH3 -CH2CH3 -CH2COC6H4(p-NO2)
anions
lit Tmp [K]
calc Tmp [K]
Cl Br Cl PF6 BF4 BF4 Cl BF4 TfO Cl BF4 TfO Cl TfO Cl TfO Br Br Br Br Br Br Br Br Br Br Br
328.1531 399.1531 311.1731 305.1531 268.9531 294.5531 369.7831 299.5531 312.8531 292.5531 311.1531 323.1531 315.1531 331.2531 326.3531 339.1531 420.1517 474.1517 468.6517 451.1517 435.6517 383.6517 372.6517 356.1517 338.0517 441.1517 439.1517
358.95 405.37 324.63 302.22 277.32 275.13 320.24 272.93 328.91 315.86 268.55 325.56 311.47 322.21 309.28 320.53 376.86 473.69 455.96 421.93 444.98 429.80 366.08 361.69 370.00 433.69 426.55
9.39 1.56 4.33 0.96 3.11 6.59 13.40 8.89 5.13 7.97 13.69 0.75 1.17 2.73 5.23 5.49 10.30 0.10 2.71 6.48 2.14 12.03 1.76 1.56 9.45 1.69 2.87
Br Br Br Br
538.1517 548.1517 479.1517 508.6517
>596.76 534.57 477.49 543.78
10.89 2.48 0.35 6.91
RD [%]
Imidazolium Ionic Liquids
-CH2COC6H4(p-Cl) -CH3 -CH2COC6H4(m-OCH3) n-C4H9 n-C4H9 -C2H5 n-C4H9 -C2H5 -OCH2C6H4(p-NO2) -CH2COC6H4(p-Cl)
2-CH3 5-Cl 2-CH2CH(CH3)2 5-CH3
2-CH3
Benzimidazolium Ionic Liquids 2-C2H5,5-NO2 5-Cl 5-NO2
2216 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 5. Parameters Found between Estimated and Literature-Based Melting Points for All 190 Ionic Liquids
AbbreViations
parameter
value
no. of ionic liquids with RD < 5% no. of ionic liquids with RD < 10% no. of ionic liquids with RD > 10% maximum relative deviation, RD average relative deviation, ARD root-mean-square deviation, rmsd square of Pearson correlation coefficients, R2
103 159 31 32.75% 5.86% 28.20 K 0.8984
The statistical values, such as average, relative, and maximum deviations derived from comparison between predicted and literature-based melting points, and R2 and rmsd values for 190 ionic liquids, are listed in Table 5. The average relative deviation in this work is less than 5.86%, and deviations less than 10% are observed for 159 of the 190 ionic liquids, containing 106 ionic liquids whose deviations are less than 5%. Further, the randomly distributed deviations have nothing to do with the characteristics and properties of ionic liquids, evaluating each independently. For example, the maximum relative deviation is 32.75% for 1,3-dimethylimidazolium chloride, whereas the relative deviations of 1-ethyl-3-methylimidazolium chloride and 1-methyl-3-propylimidazolium chloride are 4.99% and 2.05%, respectively. Conclusion A new model has been constructed to predict melting points of imidazolium and benzimidazolium ILs. The ionic character of ionic liquids is considered in the model and thus results in the distribution of normal groups and ionic groups. Based on the fact that ionic liquids’ structure exerts a certain impact on melting points, three characteristic factors of molecule are also considered in the model. Then a least-squares fit is used to determine parameters of the model through minimization of the absolute deviations of melting points. The accuracy of the model has been checked by comparing values between predictions and the literature. The average relative deviation in this work is less than 5.86%. Additional predicted values of 35 ILs can be accepted for their average relative deviation, which is 5.16%, less than the average relative deviation of 155 ILs. Furthermore, the square analysis has been used to examine the reliability of the model. The R2 and rmsd values for all 190 ionic liquids are 0.8984 and 28.20 K, respectively. The results show that the new model can be utilized for the prediction of melting points of ILs and other applications where data are needed. Acknowledgment This research has been supported by the National Natural Scientific Foundation of China through Grant 20706040 and by 863 Project, China, through Fund No. 2006AA06Z376. Supporting Information Available: Melting points of imidazolium and benzimidazolium ILs used to build the model. This material is available free of charge via the Internet at http:// pubs.acs.org. Notation AH, BH, CH, DH, ZH ) coefficients in the model Nk, Nj ) number of times a group appears in a molecule Tmp ) melting temperature lit Tmp ) melting temperature from literature calc Tmp ) melting temperature calculated with new proposed method ∆Tmp ) contribution to melting point in the model
RD ) relative deviation ARD ) average relative deviation rmsd ) root-mean-square deviation R2 ) square of Pearson correlation coefficient Greek Symbols σ ) number of same groups which connect to >NH and )N- (ring of imidazolium) τ ) number of ring groups in the molecule δ ) number of C substitutional groups in the molecule
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ReceiVed for reView July 21, 2008 ReVised manuscript receiVed November 18, 2008 Accepted November 23, 2008 IE8011215
