ARTICLE pubs.acs.org/IECR
Volumetric Connectivity Index: A New Approach for Estimation of Density of Ionic Liquids Yan Xiong, Jing Ding, Dahong Yu, Changjun Peng,* Honglai Liu, and Ying Hu State Key Laboratory of Chemical Engineering and Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China
bS Supporting Information ABSTRACT: A new approach named volumetric connectivity index (VCI) based on the physical observable volumes of groups and the concept of molecular connectivity index is proposed for the prediction of the density of ionic liquids (ILs). The capability of VCI in the prediction by combination of group (formula units) volumes for a new and as yet not prepared modification can provide an estimate of the density of that compound. In this work, the densities at room temperature of 142 pure ILs including imidazolium, pyridinium, pyrrolidinium, piperidinium, quaternary ammonium, and quaternary phosphonium are estimated by this new model, and the results are compared with the experimental data collected from the most commonly used literatures. The average deviation for the prediction of all the 142 ILs is only 0.63%, and R2 and rmsd are 0.9971 and 0.01214 g 3 cm3, respectively. Combined with a model called mass connectivity index (MCI), the new model can also be used to predict the densities of ILs at different temperatures accurately with the room temperature density obtained input in MCI.
1. INTRODUCTION Ionic liquids (ILs) are molten salts of great industrial interest and are now attracting a large number of researchers because of their unique characteristics, that is, wide liquid range, thermal stability, negligible vapor pressure, tunable physicochemical properties, and many others.1,2 Thousands of ILs have been designed and synthesized for specific applications in different fields in both academic and industrial studies in the past decades. Physical properties of pure ILs, such as melting points, densities, gas solubilities, viscosities, conductivities, and thermal properties are required in practical applications. Although a large amount of experimental data have been measured and reported, the number of potential ILs is so enormous, some say3 as many as 1012 to 1018, that it is impossible to determine all these data by laboratory methods which are complicated, time-consuming, and sometimes are even hard to develop.4 In recent years, many attempts have succeeded in developing methods to estimate the physical properties of unknown ILs to facilitate the design of new modifications and reduce the expenses in experimental work. In this work, attention is paid to the density of ILs, an important physical property required in industrial design and in almost all thermodynamic calculations. In industrial applications, the density decides the size of equipments, it is also necessary in the design of the process of vaporliquid or liquidliquid separations and the material and energy balances. In thermodynamic calculations, the density is often used as a basic characteristic data in the simulation of phase behavior and the correlation of other thermodynamic properties. The close relationship between the density and some useful properties of ILs has been recently reported in a great number of papers. For example, Valderrama and Zarricueta5 reported a simple and generalized relationship among the density, critical temperature, critical volume, normal boiling temperature, and molecular mass of ILs. Singh and Singh6 explained the correlation between the ultrasonic velocity, viscosity, surface tension, r 2011 American Chemical Society
and density of ILs. More properties such as the isothermal compressibility,7 refractive index,8 ionic conductivity and self-diffusion,9 and so forth are all found closely related to the density. Thus accurate values of the density have been in urgent need no matter whether obtained experimentally or by prediction model. For estimating densities of ILs, there have been at least five kinds of predicting methods adapted from literatures: equation of states (EOS) method,1013 group-contribution (GC) method,1416 quantitative structure property relationship (QSPR) method,17 COSMO-RS method18 and generalized correlations,5 those based on characteristic properties of the substances, such as critical properties. Extensive experience is needed to decide the adjustable parameters and necessary experimental data sets, as well as the time-consuming computational methods. All of them restrict the application of these methods for predicting the properties of unknown ILs. In recent years, some volume-based approaches have been developed to estimate the densities of ILs. For instance, Gardas et al.19 extended the Ye and Shreeve group contribution method20 for density estimation of ILs in a wide range of temperatures and pressures by the following equation F¼
W NV0 ða þ bT þ cPÞ
ð1Þ
where F is the density, W is the molar weight, N is the Avogadro constant, and V0 is the molecular volume at the reference temperature (T0) and pressure (P0), whereas the coefficients a, b, and c are all regression constants. Slattery et al.21 provided another way to predict the density of ILs based on the molecular volume using Received: August 10, 2011 Accepted: October 31, 2011 Revised: October 18, 2011 Published: October 31, 2011 14155
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the following equation: F ¼ Mr gVmh
ð2Þ
where Mr is the molar mass, Vm is the molecular volume, g and h are empirical constants of best fit. Both eq 1 and eq 2 have shown the crucial relation between the molecular volume Vm and the density of an IL, where Vm is calculated in the same way by a simple model for IL molecular volume prediction proposed by Jenkins et al:22 þ
Vm ¼ Vion ðA Þ þ Vion ðX Þ
ions (or formula-units) Vion/nm3 ions (or formula-units) Vion/nm3
ð3Þ
where the molecular volume of a given ionic liquid is considered as the sum of the effective molecular volumes occupied by the corresponding cation and anion. The ionic volume is a measure of the size of an ion, similar to the traditional ionic radius. Moreover, it is possible to assess ionic volume on the basis of extrapolation of available data or simple quantum chemical calculations. Thus, the volume parameters can be established for unknown ILs with certain accuracy prior to synthesis.23 However, the molecular volume of a designated group varies in a certain range when it is involved in different molecules or connected to different other groups. The sum of the assumed permanent volumes of the cation and the anion of ILs can not reflect the variation of volumes or distinguish the different connecting styles of groups. As a reasonable alternative, the molecular connectivity index is then considered. The index proposes an algorithm to encode bond contributions to a molecule based on the geometric and topological properties of bonds in the molecule. The first step in obtaining the characteristic index for a certain kind of molecular fragment is to generate the hydrogen-suppressed graph of the fragment. In this graph, any atom in the fragment is represented with a dot (called vertex), and connections between those vertexes are shown as lines (called edges). The first calculation carried out refers to the Vertex Valence for atoms, which take into account the electronic differences between the elements in the periodic table.24 This concept can be considered as an encoding of the structure in a nonempirical way since it can at least partially quantify the extent of branching in a molecule, especially for ILs. The combination of the concepts of the molecular volume and the connectivity index seems to be an effective approach to avoid the traditional drawbacks. A similar concept named mass connectivity index (MCI) with the molecular mass instead of the Vertex Valence for atoms was proposed by Valderrama and Rojas in 2010.25 In the model, MCI is defined as: ! 1 λ¼ ð4Þ pffiffiffiffiffiffiffiffiffi mi mj
∑
ij
In this equation, mi and mj are the masses of neighboring groups i and j in a molecule. In summing up the connections, mimj is different from mjmi. Then they proposed an equation to calculate the density of ILs as following: F ¼ F0 þ aλðT T0 Þ
Table 1. Physical Volume Values of Some Selected Basic Ions (or Formula-Units)22,23
ð5Þ
Here F0 is the density at T0 = 298.15 K and constant a is determined by regression analysis of 479 data points for 106 ILs obtained from available experimental data in the literatures. The average absolute derivation within 0.3% supported the conclusion that the value of density can be estimated with good accuracy at other temperatures, which shows that the method can be considered
CH3
0.033
NO3
0.064
CH2 B3+
0.023 0.013
NO2 OH
0.055 0.032
F
0.015
O2
0.043
5+
P
0.019
CO2
0.039
CN
0.044
CF3+
0.060
SO32
0.071
CF2+
0.045
SO42
0.091
Cl
0.047
SO22
0.048
ClO4
0.082
to be predictive. However, the size of the groups forming the molecule (the volume parameter) as an embodiment of the molecular structure is not considered in the estimation. In this work, a new approach to estimate the density of ILs called the volumetric connectivity index (VCI) is established in which the molecular mass is substituted for the group volume. The new model is anticipated to develop a series of independent parameters combining the advantages of both volume-based efforts and connectivity index. In this Article, the concept of VCI will be explained in detail first, then the densities at room temperature of some pure ILs are estimated, and the results are compared with the experimental data collected from the most commonly used literatures. Finally, combined with MCI, the new model is used to predict the densities of ILs at different temperatures.
2. VOLUMETRIC CONNECTIVITY INDEX (VCI) The volumetric connectivity index (VCI), denoted by σ, is defined as the sum of the inverse of the group volumetric connectivity interactions, calculated as the square root of the product of the volumetric connectivity interaction parameters of groups immediately connected in a molecule: ! 1 ð6Þ σ ¼ ∑ pffiffiffiffiffiffiffiffiffiffi fVi fVj ij
where fVi and fVj are the volumetric connectivity interaction parameters of neighboring groups i and j in a molecule. In summing up the connections, different from MCI, fVifVj is equal to fVjfVi. On the other hand, the whole molecule is divided into less but larger group-units than in MCI. In general, the entire anion and the ring structure in a cation such as imidazolium ring are regarded as one group in VCI model. Distinguished from the physical observable volume of groups, fVi and fVj are defined as dimensionless parameters depended on the object to be estimated. As in the estimation of density, considering the well-known relationship between the density and volume as F = m/v, the dimensionless volumetric connectivity interaction parameter is empirically defined as the reciprocal of the corresponding volume of groups as: fVi ¼ 1=ðVgi =nm3 Þ
ð7Þ
Vgi is the volume of group i. However, group volumes are poorly defined and not physically meaningful for nonsymmetrical ions such as those found in many ILs. In contrast, ionic (or formula-unit) volumes are well-defined and equally valid for symmetrical and 14156
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Table 2. Physical Volume and the Volumetric Connection Interaction Parameters of Groups in ILs groups
Vgi/nm3
fV i
groups
Vgi/nm3
fV i
CH3
0.033
30.303030
[CF3BF3]
0.118
8.4745763
CH2
0.023
43.478261
[C2F5BF3]
0.163
6.1349693
[Cl]
0.04722,23
21.276596
[n-C3F7BF3]
0.208
4.8076923
[BF4]
0.07319,21,22
13.698630
[L-lactate]
0.117
8.5470085
[PF6]
0.10919,21,22
9.1743119
[DL-lactate]
0.234
4.2735043
[TfO]
0.13121
7.6335878
[N]+
0.03419
29.133940
[NTf2]/[TFSI]
0.23219,21
4.3103448
—PO3—
0.06722,23
14.925373
22,23
[AlCl4] [P]+
0.156 0.03721
6.4102564 27.154800
—O— [PP]+
0.04322,23 0.09921
23.255814 10.019380
[Im]+
0.06121
16.393443
[PY]+
0.09621
10.382610
nonsymmetrical ions.21 So the group volume Vg here is calculated as the sum of volumes of the ions (or formula-units, Vion) involved in a group. For example, the volume of group [CF3BF3]— is the sum of the volumes of CF3+, B3+, and three F, equal to 0.118 nm3. The volumes of some selected basic ions (or formula-units) studied in this work are listed in Table 1, and the resulting volume values of groups along with all the volumetric connectivity interaction parameters of groups in ILs are shown in Table 2. For some commonly used group volumes that have been defined before such as [BF4]— and [PF6]—, the calculated volumes conform with those in literatures. On the other hand, the difference between the physical volume values of groups is slight even in nm3, and the calculation of reciprocal and square root reduces the difference further; adequate significant digits are absolutely necessary to distinguish different groups. The VCI σ can be determined by summing up the connections in the molecule according to the eq 6. For instance, the calculation of VCI σ of a typical IL, 1-[2-(2-Methoxyethoxy)ethyl]-3-methylimidazolium trifluoromethyltrifluoroborate ([CH3(OCH2CH2)2MIm][CF3BF3]), is as follows: In this case, five kinds of groups are invovled in the IL, group CH3 is designted by 1, O by 2, CH2 by 3, imidazolium ring by 4, and [CF3BF3]— by 5, the molecular volumetric connectivity interaction parameters listed in Table 2 tell that fV1 = 30.303030, fV2 = 23.255814, fV3 = 43.478261, fV4 = 16.393443, and fV5 = 8.4745763, respectively. By using eq 6, the VCI σ for [CH3(OCH2CH2)2MIm][CF3BF3] is 1 σ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 30:303030 23:255814 3 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 23:255814 43:478261 2 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 43:478261 43:478261 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16:393443 43:478261 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16:393443 30:303030 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16:393443 8:4745763 ¼ 0:345178 Values of VCI(σ) for some selected ILs are shown in Table 3.
3. RESULTS AND DISCUSSION 3.1. Estimation of the Density of ILs at Room Temperature by VCI. The relationship between VCI and the density (F0) of ILs at
room temperature is shown in Figure 1 indicating that VCI is almost linearly correlated with F0 for ILs with the same anion. The slope of the line is only decided by the kind of anion in ILs. On the other hand, the intercept of the line is not only concerned with the kind of anion but also that relevant to the substituent groups connected to the cation. This evidence leads to the conclusion that the main influential factor for the density of ILs is the anion. Enlightened by Figure 1, the density of ILs at room temperature (298.15 K) can be estimated by the equation below F0 ¼ aσ þ b þ c
ð8Þ
where F0 represents the density of ILs at room temperature (T0 = 298.15 K) and σ is the value of VCI calculated by eq 6. a, b, and c are all constants with units the same as F0, that is, g 3 cm3. Here, b represents the fundamental contribution to the density for a category of ILs with a same anion. The term aσ is a correction originated from the volumetric connection interaction between groups. The constant a is a negative value dependent on the anion. The larger volumetric connection interaction parameters fVi, the stronger the volumetric interactions, the smaller distances between groups, the smaller VCI σ will be. As the value of a is negative, less correction from b will be conducted. As for the constant c, it is a structure factor which embodies an effect of the substituent groups connected to the cation to densities. All these constants can be determined by regression analysis of a few accurate experimental data points of densities. In this work, the experimental densities at 298.15 K for 142 pure ILs including imidazolium, pyridinium, pyrrolidinium, piperidinium, quaternary ammonium, and quaternary phosphonium are collected for the correlation.2645 However, differences in density data between different literature sources can be as high as 10 to 15%; sufficient care has been taken in our selection of the data to guarantee that the results are accordant or almost the same in two or more literatures. In the collection, 62 data points of typical pure ILs are picked out to determine the constants in the model and all the resulting parameters are listed in Table 4 and Table 5. The remaining 80 data points are used to check the predictive capabilities of the model. Once the values of VCI in Table 3 and the constants a, b, and c listed in Table 4 and Table 5 are all identified, densities of different ILs at 298.15 K can be calculated by eq 8. For example, the estimation of the density at room temperature of the same ILs mentioned above ([CH3(OCH2CH2)2MIm][CF3BF3], σ = 0.345178), in this case, anion [CF3BF3] means 14157
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Table 3. Comparison of Density Predicted by VCI with Experimental Results for the Selected ILs σ
3 Fcal 0 /g 3 cm
3 Flit 0 /g 3 cm
RD (%)a
[C4MIm][BF4]
0.222604
1.2078
1.208026
0.0166
[C6MIm][BF4]
0.268604
1.1614
1.160027
0.1207
[C8MIm][BF4]
0.314604
1.1150
1.110026
0.4504
[C10MIm][BF4]
0.360604
1.0687
1.072026
0.3078
[PY1,1O2][BF4]
0.279409
1.2395
1.235431
0.3319
[C4MIm][PF6]
0.237414
1.3688
1.368033
0.0585
[C6MIm][PF6]
0.283414
1.2960
1.292834
0.2475
[C7MIm][PF6] [C8MIm][PF6]
0.306414 0.329414
1.2596 1.2233
1.262033 1.220035
0.1902 0.2705
[C4MIm][NTf2]
0.274835
1.4371
1.436033
0.0766
[C6MIm][NTf2]
0.320835
1.3798
1.378037
0.1306
[C10MIm][NTf2]
0.412835
1.2651
1.271033
0.4642
[N112,1O2][NTf2]
0.332408
1.4543
1.450032
0.2965
[P222,1O1][NTf2]
0.549044
1.4192
1.420041
0.0563
[P222,2O1][NTf2]
0.383609
1.3905
1.390041
0.0360
[CH3O(CH2)2MIm][NTf2] [P13][TFSI]
0.293403 0.303476
1.5030 1.4014
1.496043 1.400038
0.4679 0.1000
[PP1,1O2][TFSI]
0.349585
1.4329
1.435531
0.1811
[N1113][TFSI]
0.268852
1.4446
1.440044
0.3194
[N6222][TFSI]
0.403825
1.2763
1.270039
0.4961
[P1116][TFSI]
0.345665
1.3488
1.340040
0.6567
[DEIM][TfO]
0.219406
1.3371
1.330026
0.5338
[C4MIm]Cl
0.209417
1.0784
1.080035
0.1481
[C8MIm]Cl [C3MIm][CF3BF3]
0.301417 0.217714
0.9961 1.3117
1.000035 1.310028
0.3900 0.1298
[C3MIm][C2F5BF3]
0.232588
1.3811
1.380028
0.0797
[C3MIm][n-C3F7BF3]
0.245514
1.4373
1.440028
0.1875
[CH3(OCH2CH2)2MIm][C2F5BF3]
0.360052
1.3629
1.370028
0.5182
[CH3(OCH2CH2)2MIm][CF3BF3]
0.345178
1.3078
1.310028
0.1679
[P14][CF3BF3]
0.283600
1.2192
1.213531
0.4697
[PY1,1O1][C2F5BF3]
0.297855
1.3712
1.377631
0.4646
[N112,1O2][C2F5BF3] [C6Im][L-lactate]
0.317970 0.241488
1.3407 1.0367
1.340045 1.038342
0.0522 0.1541
[C9Im][L-lactate]
0.310488
0.9990
0.999642
0.0600
[C12Im][L-lactate]
0.379488
0.9614
0.962642
0.1247
[C5OCIm][L-lactate]
0.281384
1.0529
1.053042
0.0095
[C10OCIm][L-lactate]
0.396384
0.9902
0.991042
0.0807
[C6Im][DL-lactate]
0.276481
1.0350
1.037442
0.2313
[C9Im][DL-lactate]
0.345481
0.9946
0.990842
0.3835
[C12Im][DL-lactate] [C5OCIm][DL-lactate]
0.414481 0.316377
0.9542 1.0497
0.959142 1.049042
0.5109 0.0667
[C10OCIm][DL-lactate]
0.431377
0.9823
0.986142
0.3853
ILs
a
lit lit cal lit RD(%) = ((|Fcal 0 F0 |)/(F0 )) 100, where F0 and F0 represent the calculated result of density at room temperature obtained by the VCI model and
corresponding experimental value, respectively.
a = 1.4037 g 3 cm3 and b = 1.6173 g 3 cm3, the substituent group connected to the cation —(OCH2CH2)n— gives c = 0.1750 g 3 cm3, so the predicted value is F0 ¼ 1:4037 0:345178 þ 1:1673 þ 0:1750 ¼ 1:3078
ðg 3 cm3 Þ
The corresponding experimental value28 is 1.3100 g 3 cm3, the relative deviation (RD) of the calculated value is only 0.17%. Some
other predicted results of densities of selected ILs are listed in Table 3. To validate the estimation method and illustrate the efficiency of correlation, some statistical parameters including the relative deviation (RD), the average relative deviation (ARD), the rootmean-square deviation (rmsd), and the correlation coefficient square (R2) are calculated too. Table 6 summarizes the results, showing the values of all the statistical parameters that describe the accuracy of the proposed model. It is found that the overall 14158
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Table 6. Checking Results of Density of 142 ILs Predicted in This Studya parameter
value
maximum relative deviation, RDmax
3.98%
average relative deviation, ARD root-mean-square deviation, rmsd
0.63% 0.01214 g 3 cm3
correlation coefficient square R2
0.9971
cal lit lit m ARD(%) = [(1/Nm)(∑N i = 1 |(F0 F0 )/(F0 )|i))] 100; rmsd = [(1/ Nm cal lit 2 1/2 Nm)∑i = 1(F0 F0 )i ] ; Nm is the total number of data points. a
Figure 1. Relationship between VCI and density of ILs (]:[CxMim][NTf2]; 2: [CxMim][PF6]; Δ: [CxMim][CF3BF3];[: [CxMim][BF4]; 3: [CxMim][DL-lactate];b: [CxMim] [L-lactate];g: [CxOCim][DL-lactate];f: [CxOCim] [L-lactate]).
Table 4. Values of the Constant a and b in the Equation 7 a/g 3 cm3
b/g 3 cm3
[BF4]
1.0078
1.4321
[PF6]
1.582
1.7444
[TfO]
1.9131
1.7569
[NTf2]/[TFSI]
1.2468
1.7798
[Cl] [CF3BF3]
0.8943 1.4037
1.2657 1.6173
[C2F5BF3]
1.5155
1.7336
[n-C3F7BF3]
2.5409
2.0611
[L-lactate]
0.5458
1.1685
[DL-lactate]
0.5855
1.1969
[AlCl4]
1.1717
1.5371
anions
Table 5. Values of the Constant c in the Equation 7 substituent groups
c/g 3 cm3
CH3/CH2
0
—(OCH2CH2)n—
0.1750
CH3O(CH2)2—
0.0890
—PO3—
0.2828
—CH2O(CH2)n—
0.0380
average relative deviation in calculated densities using the proposed correlation is only 0.63% and the correlation coefficient square result is R2 = 0.9971. The maximum relative deviation: RDmax= 3.98% results from the estimation of quaternary ammonium ILs just like the same phenomena that occurred in the molecular volume-based prediction provided by Slattery et al.21 Predictions with higher deviations are likely attributed to the two factors: (i) the nitrile-functionalization significantly changes the intergroup interactions in the ILs, and this strongly affects the density changes; (ii) the inaccuracies of the volume-based approach inherited in the high complexity of some specific ILs. Except that, the relative deviation of the estimation of other kinds of ILs selected is mostly less than 1% just as
Figure 2. Comparison of densities of 142 ILs predicted by the VCI with experimental results.
shown in Table 3. The detailed comparison of density predicted by VCI with experimental results for 142 ILs can be found in the Supporting Information materials. A comparison of densities of 142 ILs predicted by the VCI with experimental results is shown in Figure 2; it is found that abundant spots lie near the diagonal line. All the statistical parameters and the intuitive conclusion generalized from Figure 2 support the conclusion that the densities at room temperature can be estimated with good accuracy by the proposed VCI model. 3.2. Estimation of Densities of ILs at Different Temperatures. As mentioned above, the MCI method can be considered to be predictive in the sense that the density can be estimated with good accuracy at other temperatures under the condition that the value of the property at the reference temperature is available. Considering eq 5 of MCI, eq 8 can be extended as follows F ¼ aσ þ b þ c þ dλðT T0 Þ
ð9Þ
where F represents the density of ILs at the temperature T(K). d is the constant determined by regression analysis, equal to 3.119 103 according to ref 25. To test the accuracy of predicted densities at other temperatures given by eq 9 when the VCI model is combined with the MCI model, several density data points at the temperatures ranging from 298.15 K to 338.15 K of some commonly used ILs were selected to be calculated. The results shown in Figure 3 tell that the reliability of the two models has become integrated, and their application range is greatly enhanced. 14159
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’ NOTATION fVi/fVj = volumetric connectivity interaction parameters of group mi/mj = molar mass of group Vg = physical volume of group Vion = physical volume of basic ion or forluma-unit T0 = room temperature, 298.15 K W = molar weight N = Avogadro constant a,b,c,d = constants determined by regression analysis Greek Letters
Figure 3. Comparison of densities at temperatures (298.15 K to 338.15 K) of some selected ILs predicted by this study with experimental values (The dotted lines represent the values predicted by the model in this study and the solid icons represent experimental data points, including f, [C4MIm][BF4];8b, [C3MIm][NTf2];469, [C4MIm][NTf2];472, [C4MIm][PF6];8(, [C4MIm][TFO]8).
4. CONCLUSIONS A new approach named volume connectivity index (VCI) model is proposed for the prediction of the density of ILs, which is found almost linearly correlated with the density at room temperature (F0) when the same anions are involved in ILs. The simple linear relationship indicates the great store of opportunity that properties of the whole series of ILs may be predicted rapidly and accurately if only a few data of ILs with similar molecular structure in the series are available. The density at room temperature of 142 pure ILs including imidazolium, pyridinium, pyrrolidinium, piperidinium, quaternary ammonium, and quaternary phosphonium are estimated by the new model, and the results are compared with the experimental data points collected from the most commonly used literature values. The average deviation for the prediction of all the 142 ILs is only 0.63%, and R2 and rmsd are 0.9971 and 0.01214 g 3 cm3, respectively. Combined with the MCI model, the new model can also be used to predict the densities of ILs at different temperatures accurately. ’ ASSOCIATED CONTENT
bS
Supporting Information. The comparison of density predicted by VCI with experimental results for 142 ILs. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Phone: 86-21-6425 2767. Fax: 86-21-6425 2767. E-mail: cjpeng@ ecust.edu.cn.
’ ACKNOWLEDGMENT The authors appreciate the financial support by the National Natural Science Foundation of China (Nos. 20876041 and 20736002), the National Basic Research Program of China (2009CB219902) and the 111 Project of China (No. B08021).
σ = value of volumetric connectivity index λ = value of mass connectivity index F0 = density at room temperature F = density Fcal 0 = calculated result of density at room temperature Flit 0 = experimental value of density at room temperature collected from literatures Abbreviations
ILs = ionic liquids Eq = equation VCI = volumetric connectivity index MCI = mass connectivity index RD = relative deviation ARD = average relative deviation rmsd = root-mean-square deviation R2 = correlation coefficient square(r square) [Im] = imidazolium [PP] = piperidinium [PY] = pyrrolidinium
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