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Ind. Eng. Chem. Res. 2009, 48, 2290–2296
CORRELATIONS In Silico Prediction of Molecular Volumes, Heat Capacities, and Temperature-Dependent Densities of Ionic Liquids Ulrich P. R. M. Preiss,† John M. Slattery,‡ and Ingo Krossing*,† Institut fu¨r Anorganische and Analytische Chemie, UniVersita¨t Freiburg, Albertstrasse 21, D-79104 Freiburg, and Department of Chemistry, UniVersity of York, Heslington, York, YO10 5DD, U.K.
We present a fast and reliable general estimation of the heat capacity, Cp, and temperature-dependent density, F, of ionic liquids, based on a new in silico method to calculate the molecular volume, Vm. The knowledge of Vm allows the prediction of many physical properties of hitherto unknown ionic liquids as well as the prediction of lattice energies and entropies of salts. 1. Introduction Ionic liquids (ILs) are often regarded as being potentially tuneable materials, which could be designed specifically for particular applications like solvents, lubricants, pump oils, phase change media, and many others.1-4 The large number of salts that have the potential to form ILs and the resulting range of physical properties support this idea.5 However, to fully utilize the designer potential of ILs, simple methods to predict their properties are needed.6-14 One physical observable value that describes properties of ILs is the molecular volume Vm. Hitherto, Vm has been used in volume-based thermodynamics (VBT) to calculate the lattice energy and the entropy of solids.15-18 Recent studies connected quantities like viscosity, density, electric conductivity, and melting point of ILs to Vm (see Figure 1).19-22 These relationships may be the basis for simple tools to predict physical properties of yet unknown ILs prior to their synthesis. By definition, the molecular volume Vm refers to the solid state. For a 1:1 salt [A]+[X]- it is defined as the sum of the ionic volumes Vion([A]+) and Vion([X]-). From the experimental unit cell dimensions of X-ray crystal structures, Vm and the ionic volumes are calculated by Vm ) Vion([A]+) + Vion([X]-) )
Vcell(A+X-) Z
of thermal expansion. Indeed, typical error bars for ionic volumes are in the order of 0.005-0.02 nm3. Despite this deficiency, the tabulated X-ray volumes in the solid state proved to be very valuable as an ordering principle for physical properties of liquid ILs, as well as for the prediction of lattice energies of solids as needed in extended Born-Haber cycles.21,22 Rebelo et al. used a combination of van-der-Waals (vdW) volumes, density measurements and group contribution methods to obtain the molar volume Vmolar of ILs in the liquid state (which is related to Vm).23-25 This is an a posteriori approach depending on experimental measurements, though. A priori (as necessary for the prediction of physical IL properties preceding synthesis), Vm can be approximated by several methods that we found to be lacking in one way or another. Atomic and/or group contribution methods have been widely used, but they are almost always restricted in their choice of possible molecules.26-29 In addition, tabulated volumes of ions in solution are dependent on solvent and concentration (which may be idealized as infinite dilution).30,31 For this work, we chose Hofmann’s atomic volumes26 for comparison; however, we have already shown22
(I)
Vcell is the volume of the unit cell of the crystal and Z is the number of formula units in the cell. If the ionic volume of one of the ions is accurately known (e.g., halide anions or alkaline metal cations), it may be used as a reference ion to determine the ionic volume of the other ion in the structure.18,20 This procedure was previously used to derive the experimental ionic volumes for a number of anions and cations commonly used in ILs. Thus, in order to obtain Vm of the ionic liquid in question from experimental studies, suitable crystal structure data is needed.16 At this point, it should be noted that the temperature of the X-ray measurement is not considered in any of the currently tabulated18-20 Vm and Vion values and, since typical X-ray data collections are performed at temperatures between 90 and 298 K, a small scattering is expected due to the neglect * To whom correspondence should be addressed. E-mail:
[email protected]. † Universita¨t Freiburg. ‡ University of York.
Figure 1. The central role of Vm for the prediction of physical properties of ionic liquids. A and B are empirical constants of best fit which differ between the properties. M is the molecular mass.
10.1021/ie801268a CCC: $40.75 2009 American Chemical Society Published on Web 01/05/2009
Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2291 3 a
Table 1. Ions, Their X-ray Volumes, and Assigned Errors (in nm ) cation [N2H5]+ [HPy]+ [C(N2H3)3]+ [N1,1,1,1]+ [P1,1,1,1]+ [C2MIM]+ [C2(CN)MIM]+ [S2,2,2]+ [C4MIM]+ [N1,1,1,4]+ [N2,2,2,2]+ [C5MIM]+ [C4(CN)MIM]+ [C4C1MIM]+ [C5MPyr]+ [C6MIM]+ [N2,2,2,5]+ [S1,φ,φ]+ [C8MIM]+ [N4,4,4,4]+
Vion error reference 0.030 0.095 0.105 0.113 0.133 0.156 0.167 0.177 0.196 0.198 0.199 0.219 0.222 0.229 0.238 0.242 0.268 0.268 0.288 0.383
-/-/-/0.013 -/0.018 0.013 0.017 0.021 0.013 0.016 0.015 0.013 0.012 0.018 0.015 0.016 0.015 0.015 0.008
20 20 20 18 20 22 19 19 22 19 18 22 19 22 22 19 22 19 19 22
anion [CN][OCN][NO2][N3][SCN][ClO4][FSO3][Dca][C1SO3][PF6][Tfa][AsF6][BiF6][OTf][Tcm][AlCl4][AlBr4][Sb2F11][NTf2][Al(hfip)4]-b
Vion error reference 0.050 0.054 0.055 0.060 0.071 0.082 0.088 0.089 0.099 0.107 0.108 0.110 0.124 0.129 0.130 0.161 0.198 0.227 0.232 0.585
0.006 0.002 0.007 -/0.003 0.013 0.004 0.010 -/-/-/0.007 0.014 0.007 0.006 0.004 0.005 0.020 0.015 0.009
18 18 18 20 18 18 18 19 20 20 20 18 18 33 36, 37, 38 39 18 18 22 40, 41
a Please also consider the supplementary information of the given references, since in some cases the volumes were only established there. b hfip ) -OC(CF3)2H. Other abbreviations are common in IL chemistry; a full list is given in the appendix.
that the volumes obtained by this approach are less correlated with the physicochemical properties than Vm obtained by X-ray analysis. Gavezzotti integrated the space occupied by the molecule, bounded by vdW radii.32 Dixon et al. report on a quantum chemical approach to assess ionic volumes.33 A B3LYP calculation with double-ζ basis sets was used and Vm was assessed by calculating the volume enclosed within the charge density boundaries up to a limiting value of one electron per nm3; this method is computationally rather expensive and lacks the desired simplicity necessary for predictions.34 Furthermore, this arbitrary approach disregards the fact that different atoms have different electronegativities and polarizabilities, suggesting that there is no universal cutoff of the electron density. Markedly, none of the aforementioned methods takes charge into account; however, cations of the same summary formula are always smaller than anions. For example, the experimental ionic volumes of [NO2]+ and [NO2]-, as given in ref 18, are 0.022 and 0.055 nm3, respectively. Consequently, Wherland et al. used a charge-dependent fit for the volumes calculated with a method similar to Gavezzotti’s.35 In the current contribution, we wanted to systematically combine these ideas and improve on them to calculate ionic volumes that quantitatively agree with the solid state X-ray volumes. An emphasis was put on those ions relevant to ionic liquids. Thus, our methodology gives values that may directly be used for the prediction of properties that depend on Vm (see Figure 1).
Table 2. Correlation Parameters for the 20 Experimental Cationic Volumes from Table 1 vs Their Calculated Counterparts (Vc) method
a
b [nm3]
r2
errø (%)
Hofmann0 Hofmann PM3+G PM6+G BP86/SV(P)+G BP86/TZVP+G PM3+C PM6+C BP86/SV(P)+C BP86/TZVP+C
1.000 0.964 1.458 1.437 1.420 1.411 1.070 1.062 1.063 1.080
0.000 -0.007 -0.019 -0.016 -0.013 -0.013 -0.017 -0.017 -0.018 -0.019
0.9865 0.9865 0.9918 0.9897 0.9823 0.9855 0.9905 0.9899 0.9925 0.9925
10.8 5.4 3.8 4.4 5.3 5.9 3.7 3.8 3.4 3.3
a cavity based on optimized radii, which, for most elements, are the van der Waals (vdW) radii multiplied by 1.17; the volume of this cavity then is an estimation of the ionic volume Vion.49-51 In each case, all sets of calculated volumes, Vc, were found to correlate linearly with the experimental ion volumes listed in Table 1 according to Vion ) aVc + b
with different parameters a and b for cations and anions and for each of the methods. Solvation models like the isodensity surface polarized continuum model (IPCM) and the self-consistent isodensity surface polarized continuum model (SCI-PCM) provide an isodensity surface of the ion in question which may be integrated to give the enclosed volume and thus also would have been interesting to study Vion.52 However, these methods are tuneable with many variables and each parameter also influences the output volume, which is why we found their exploration to be beyond the scope of the present study. Computational Details. Gas-phase PM3 optimizations have been done with ChemBioOffice 2008, 1986-2007 CambridgeSoft. PM3 optimizations with COSMO as well as all PM6 optimizations have been done with MOPAC2007.53 The calculations of Gavezzotti’s volumes have been accomplished using the freeware program steric.54 All DFT optimizations have been carried out with the TURBOMOLE55 program package (version 5.10) using the Resolution of Identity56 (RI) approximation. For BP86/SV(P) geometries, vibrational frequencies were calculated with AOFORCE for each molecule to make sure they represent a true minimum.57,58 These geometries were then used for further optimization with the TZVP basis set. The implementations of COSMO are the ones used in the respective programs. All geometries have been calculated in the highest possible point group, except for COSMO calculations with TURBOMOLE, which were always done in C1. The mean error (errø), used throughout the paper, is defined as
2. Theoretical Basis As a basis to estimate ionic volumes Vion, we selected 20 cations and 20 anions with experimentally well-established X-ray structures that were taken from the literature (see Table 1). The following calculations were performed on each ion: (1) Hofmann’s simple incremental method.26 (2) Gas phase structure optimizations with PM3,42 PM6,43 BP86/SV(P),44-46 and BP86/ TZVP,47 each followed by applying Gavezzotti’s method.32 (3) The same optimizations as above, but with COSMO applied.48 For the DFT calculations, the dielectric constant, r, was set to ∞; for PM3 and PM6, it was set to 999.0, the maximum value possible within this specific implementation. COSMO constructs
(II)
∑ | y - 1| xi
i
i
× 100% (III) N where y denotes the independent observable and x denotes the calculated value. errø: )
3. Results and Discussion Calculated vs Experimental Ion Volumes Vion. The results are collected in Tables 2 and 3; +G stands for “Gavezzotti’s method applied”, +C for “COSMO applied”. The experimental errø of the volumes obtained by X-ray analysis is 7.3% for the 16 cations and 5.6% for the 16 anions from our list where an
2292 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 3. Correlation Parameters for the 20 Experimental Anionic Volumes from Table 1 vs Their Calculated Counterparts (Vc) method
a
b [nm3]
r2
errø (%)
Hofmann0 Hofmann PM3+G PM6+G BP86/SV(P)+G BP86/TZVP+G PM3+C PM6+C BP86/SV(P)+C BP86/TZVP+C
1.000 0.946 1.423 1.427 1.457 1.377 0.966 0.964 1.051 1.031
0.000 0.027 0.010 0.011 0.008 0.013 0.020 0.020 0.002 0.004
0.9864 0.9864 0.9918 0.9923 0.9910 0.9913 0.9831 0.9826 0.9969 0.9967
21.2 7.8 5.6 5.1 5.7 5.9 14.0 13.9 4.4 4.3
error was defined. For comparison, we also give the unscaled (i.e., a ) 1 and b ) 0) Hofmann values, as he intended them in the original publication (designated Hofmann0). The need for a charge-dependent linear fit is obvious: The unscaled Hofmann0 volumes give a remarkably larger errø than the scaled Hofmann ones.59 The difference in electron count leads to a negative y-intercept (b-value) for the cations and a positive value for the anions. The higher slopes (a-values) for Gavezzotti’s method are caused by the aforementioned fact that it uses nonscaled vdW radii, while COSMO uses scaled ones. The fit also has the advantage that values for Vion, either experimentally determined or calculated with any method, can be arbitrarily combined to give Vm. Overall, for every method, the correlation between Vc and Vion is very high, with a correlation coefficient (r2) > 0.98. Hofmann’s volumes, either with or without a fit, are the worst methods. The semiempirical models PM3 and PM6 perform well for the cations (errø: 3.7-4.4%); however, especially the errors of the anion volumes using PM3 or PM6 together with COSMO (errø: 13.9-14.0%) are very large and thus these models are not as well suited as others. For BP86/SV(P) or BP86/TZVP with COSMO, and for almost all cases with Gavezzotti’s method applied, the errø values of Vion (3.8-5.9%), regardless of charge, are smaller than the experimental error of the volumes obtained by X-ray analysis. In general, predictions of anionic volumes are less reliable than those for cations. Intrinsic to the experimental data, percentual errors tend to be higher for smaller ions (highest in [N2H5]+ and [ClO4]-), and diminish with size. Overall, we think that the calculated volumes using the best methods from Tables 2 and 3 are more internally consistent than Vion determined by X-ray analysis, since the latter ones are not corrected for thermal expansion and the calculated volumes always refer to one point of reference (the converged structure optimization) independent of temperature or counterion. With these results in mind, ionic and molecular volumes obtained with the best method for both anionic and cationic volumes, BP86/TZVP + COSMO, were used for all the following calculations and predictions. Assessment of Temperature Dependent Densities of ILs. The densities of ionic liquids were determined by many different experimentators in the past, and temperature-dependent rules have been set up. Recently, Coutinho found an equation for the estimation of densities for arbitrary pressures and temperatures.60 However, he took X-ray volumes as the basis and derived other molecular volumes by group contributions as needed. For testing our best computational method (BP86/ TZVP + COSMO) against these results, we chose another, more varied set, including functionalized ILs, and made a different, more precise deduction of the temperature dependency. The cubic isobaric thermal expansion coefficient Rp, is defined as
Rp ) -
1 ∂F F ∂T
( )
p
(IV)
and so the density F at a given temperature T can be expressed as: ln(F ⁄ F0) ) -RpT + β
(V)
-1
with F0 ) 1 g cm . Both Rp and β are dependent on the nature of the IL in question. Building on the impressive corpus of experimental work accomplished by other authors, we compared the quality of eq V for a representative selection (26 different ionic liquids in 12 references) of test series. Correlation coefficients were always >0.999. We hold the minimum temperature range for the validity of this equation to be 298-323 K, the intersection of all test series. The maximum temperature range is 273-415 K. For the data of ref 61, analyzing ILs from different manufactures, we took the average densities at the given temperatures. In our quest for a universal rule, we found the following Vmbased relationships for Rp and β, which are independent from the nature of the IL in question: Rp ) c ln(Vm ⁄ V0) + d
(VI)
with c ) 0.0001747 K-1, d ) 0.0008028 K-1, V0 ) 1 nm3, and
( )
β ) e ln
MV0 +f M0Vm
(VII)
with e ) 1.158, f ) -7.413, M ) molar mass, M0 ) 1 g mol-1, V0 ) 1 nm3. Written out, the temperature-dependent, empirical expression for the density F of all hitherto investigated ILs is F(T) ) (V0 ⁄ Vm)cT+e(M ⁄ M0)e exp(-dT + f)
(VIII)
with coefficients c-f and M0 and V0 as above. Equation VIII expands and replaces our old expression for the calculation of IL densities which was valid only at 294 K (F ) gM(Vm)-h, with g, h constants).19 Densities were calculated according to eq VIII; then, errø was independently calculated for each test series over the entire given temperature range. [P6,6,6,14][NTf2] and [N1,8,8,8][NTf2] were excluded,61,67 as they pose exceptions to eq VI (but not to eq VII), maybe because of the formation of liquid crystals.62 The average error values of all test series for each IL can be found in Table 4. They are comparable with Coutinho’s values and rarely exceed 1%. The largest errors occur in the case of watersaturated ILs, functionalized cations or cations with long alkyl chains, which also may form liquid crystal phases. For eq VI, the correlation coefficient (r2) of calculated and experimental data is most excellent (0.9933); for eq VI, it is less satisfactory (0.6095), but, even so, the calculated densities are in very good agreement with the experimental ones. It is reasonable to assume that Rp contains information about intermolecular interactions. Since all coefficients c-f are independent of the specific nature of the IL and, thus, F only depends on the molar mass M and calculated volumes Vm, eq VIII shows the potential for the in silico prediction of densities of hitherto unknown ILs. From eq VIII, a simple expression for isobaric expansion at T2 ) T1 + ∆T follows, given that the density at any temperature T1 is known: F(T2) ) (V0 ⁄ Vm)c∆T exp(-d∆T) F(T1)
(IX)
with V0 ) 1 nm and temperatures in K. Assessment of the Integrated Heat Capacity, Cp. Because heat capacity is dependent on entropy, which, in turn, is related 3
Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2293 Table 4. errø in % for eq V and Molecular Volumes in nm (BP86/TZVP + COSMO), Calculated for Different Test Series 3
IL
a
Vm
errø
reference
[C4MIM][PF6]
0.307
[C2MIM][NTf2]
0.382
0.82 0.83 0.80 0.80 2.08a 0.62 0.74 1.12 0.86 0.75 0.92 2.24a
61 69 63 64 64 65 66 67 61 68 64 64
[C4MIM][BF4]
0.276
[C8MIM][PF6] [C8MIM][BF4] [C4Py][BF4] [C4MPyr][Fap] [C4Py][Fap] [C4MIM][OTf] [C1MIM][SCN] [C6MIM]Cl [C4MIM][C8SO4]
0.402 0.371 0.270 0.547 0.526 0.323 0.201 0.285 0.465
0.40 0.46 0.42 0.18 0.36 0.14 0.25 0.69 1.63 1.16 1.81 0.72
61 69 64 67 67 67 61 61 61 61 73 68
IL
Vm
errø
reference
[C4MIM][NTf2]
0.430
0.09 0.09 0.07 0.09 0.27 0.06 1.18*
61 68 69 70 63 64 64
[C2MIM][C2SO4]
0.282
[N1,1,1,4][NTf2]
0.416
[C6MIM][NTf2] [C8MIM][NTf2] [C1MIM][C1SO4] [C6MIM][Fap] [C1(CN)Py][NTf2] [C1(CN)MPyr][NTf2] [C10MIM][NTf2] [C8MIM]Cl [C6MIM][PF6]
0.477 0.525 0.237 0.578 0.381 0.406 0.564 0.333 0.354
0.55 0.63 0.86 0.80 0.40 0.63 0.79 1.40a 0.21 1.11 1.40 0.41 3.63 3.63 1.54 2.71 0.05
61 68 69 64 71 68 64 64 61 61 72 61 61 61 61 73 70
) water-saturated.
to the molecular volume,16,17 we also explored the possibility of a direct correlation between Vm and Cp. Heat capacity data of ILs measured at different temperatures are available, but the functional for their temperature dependency contains up to six coefficients.74,75 Also, data for the same IL but from different test series tends to possess very dissimilar temperature behavior, mostly caused by varying water content.76,77 Accordingly, Kabo’s correlation scheme shows quite limited applicability.74 So we refrained from seeking a general rule as for densities and restricted ourselves to two distinct temperatures (298 and 323 K). We calculated Vm of 34 ionic liquids for which the integrated heat capacities were taken from the NIST IL database.78 For many of these compounds, there are too few, if any, crystal structures to gain a meaningful experimental Vm, so we calculated them using our most reliable method (BP86/ TZVP + COSMO). We divided the ionic liquids into two groups, depending on moisture. For set 1 with low (5%; especially at 323 K, they are remarkably larger than the errors for the BP86/TZVP + COSMO volumes. 4. Conclusion For the calculation of Vm, a geometry optimization with the BP86 functional and either TZVP or SV(P) basis set followed by a COSMO calculation and a charge-dependent fit will give the results with the highest agreement with X-ray data. Secondbest, PM3 or PM6 with Gavezzotti’s method can give very fast approximations. If only rough estimates are needed, scaled Hofmann volumes might give a good starting point as well. The solid state volume Vm as an in silico measure is, as
2294 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 6. The Additional ILs of Set 2 with Vm [nm3] (BP86/TZVP + COSMO), Experimental and Calculated Cp [J mol-1 K-1] at 298 and 323 Ka Cp298 IL
Vm
[perfluoro-C6MIM][NTf2] [(C2)2Nic][C2SO4] [C3C1MIM][NTf2] [C6C1MIM][NTf2] [C8MIM]Br [C4MIM]Cl ECOENG 41M [C6MIM]Br [C8MIM][BF4] [C4MIM][Dca] [N4,4,4,4][Docusate] [C4MIM][PF6] [C6MIM][BF4] [C8MIM][NTf2] [C4C1MIM][PF6] [C4MIM][OTf] [C2MIM][C2SO4] a
exptl
Cp323
calcd
exptl
calcd reference
0.553 725 693 752 718 0.363 513 472 530 493 0.430 554.5 550 558.7 572 0.498 686 629 705 653 0.339 392 443 408 464 0.238 322.7 325 333.7 344 0.423 643 542 652 564 0.291 344 387 357 407 0.371 506 480 526 501 0.286 364.6 381 370 400 0.953 1325 1161 1385 1194 0.307 402.6 406 413.5 426 0.322 416 424 433 444 0.525 654 661 677 685 0.329 433.6 431 449.1 452 0.323 417.2 424 423.1 445 0.282 378 377 383.9 396
80 80 79 80 80 79 80 80 80 79 80 63,79 80 80 79 79 84
Table 8. Legend for Substituted Pyridinium Cations cation
R1
R2
R3
R4
R5
[HPy]+ [C1(CN)Py]+ [C6Py]+ [C6DMAPy]+ [C2C1Py]+ [(C2)2Nic]+ [C4C1Py]+ [(C4)2Nic]+ [C6C1Py]+ [C6(C1)2Py]+ [C6C1DMAPy]+ [C6C3(C2)2Py]+
H N≡CCH2 C6H13 C6H13 C2H5 C2H5 C4H9 C4H9 C6H13 C6H13 C6H13 C6H13
H H H H H H H H H H H C3H7
H H H H CH3 C2H5OC(O) CH3 C4H9OC(O) CH3 CH3 CH3 C2H5
H H H N(CH3)2 H H H H H H N(CH3)2 H
H H H H H H H H H CH3 H C2H5
Regarding anions, [Tfa]- ) [CF3CO2]-, [Dca]- ) [N(CN)2]-, [Tcm]- ) [C(CN)3]-, [OTf]- ) [CF3SO3]-, [NTf2]- ) [(CF3SO2)2N]-, [Fap]- ) [PF3(C2F5)3]-, [C1SO3]- ) [CH3SO3]-, [C1SO4]- ) [CH3SO4]-, [C2SO4]) [C2H5SO4]-, [C8SO4]- ) [C8H17SO4]-, [Docusate]- ) [R-CH2-CH(SO3)-R]- (with R- ) -C(O)O-CH2-CH(C2H5)(C4H9)). Abbreviated compounds: ECOENG 41M ) [C4MIM][CH3O-C2H4O-C2H4SO4], ECOENG 500 ) [N(CH3)(C2H4O-C2H4OH)2(C13H27)] [C1SO4].
References are given for the experimental values.
Table 7. Correlation Constants i [in J mol-1 K-1 nm-3] and j [in J mol-1 K-1] in eq X) for the Dependency of Cp from Vm (BP86/ TZVP + COSMO) data set
T [K]
i
j
r2
errø (%)
errø (%)a
1 1 2 2
298 323 298 323
1169 1189 1169 1189
47.0 61.0 47.0 61.0
0.9693 0.9765 0.9682 0.9703
3.9 3.2 4.8 4.6
5.5 5.9 6.0 6.8
a
Using scaled Hofmann volumes. The best-fit coefficients i and j to calculate this error are derived from the data set with low water content and are 1244 and 27.8 at 298 K and 1226 and 42.8 at 323 K, with units as above.
properties of yet unknown ionic liquids, Vm and its dependent properties should be calculated using our methodology. Acknowledgment This work was supported by the Albert-Ludwigs-Universita¨t Freiburg and the DFG priority program SPP 1191. We thank the referees for elaborate and useful comments. Supporting Information Available: Tables containing calculated and experimental ionic volumes, experimental and calculated viscosities and densities as well as calculated geometries for all compounds. This material is available free of charge via the Internet at http://pubs.acs.org. Appendix Nomenclature of ILs
Figure 2. The relationship of experimental and calculated Cp at 298 K for set 2. [N4,4,4,4][Docusate] was left out due to its extraordinarily high Cp (exptl: 1325 J mol-1 K-1).
Ammonium, phosphonium, and sulfonium cations [X#,#,#(,#)]+ (X ) N, P, S): the comma-separated indices show the number of C-atoms the n-alkyl ligands possess; φ means phenyl. Figure 3 shows the substitution patterns we used for other compounds. 3-Methylimidazolium cations: For [C#MIM]+/[perfluoroC6MIM]+/[C#(CN)MIM]+ R1 ) n-alkyl/3,4,5,6-perfluorohexyl/ omega-cyano-n-alkyl, R2 ) H; for [C#C1MIM]+, R1 ) n-alkyl, R2 ) methyl. 1-Methylpyrrolidinium cations: For [C#MPyr]+/ [C1(CN)MPyr]+, R1 ) n-alkyl/cyanomethyl. Pyridinium cations are described in Table 8. Literature Cited
Figure 3. Substitution patterns for IL cations used in this work.
demonstrated here for the first time, well-correlated to heat capacity and temperature-dependent density of ionic liquids and allows an approximation of physical properties of ILs prior to synthesis. Thus, we propose that for the prediction of physical
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ReceiVed for reView August 19, 2008 ReVised manuscript receiVed November 4, 2008 Accepted November 10, 2008 IE801268A
