Structure of ionic liquids of 1-alkyl-3-methylimidazolium cations: A systematic computer simulation study Sérgio M. Urahata and Mauro C. C. Ribeiro Citation: The Journal of Chemical Physics 120, 1855 (2004); doi: 10.1063/1.1635356 View online: http://dx.doi.org/10.1063/1.1635356 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/120/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Studies of structural, dynamical, and interfacial properties of 1-alkyl-3-methylimidazolium iodide ionic liquids by molecular dynamics simulation J. Chem. Phys. 136, 124706 (2012); 10.1063/1.3696004 Liquid structure of 1-alkyl-3-methylimidazolium-hexafluorophosphates by wide angle x-ray and neutron scattering and molecular dynamics J. Chem. Phys. 134, 114521 (2011); 10.1063/1.3565458 Structure and conformation properties of 1-alkyl-3-methylimidazolium halide ionic liquids: A density-functional theory study J. Chem. Phys. 123, 174501 (2005); 10.1063/1.1979478 Dynamics in a room-temperature ionic liquid: A computer simulation study of 1,3-dimethylimidazolium chloride J. Chem. Phys. 123, 144505 (2005); 10.1063/1.2041487 Single particle dynamics in ionic liquids of 1-alkyl-3-methylimidazolium cations J. Chem. Phys. 122, 024511 (2005); 10.1063/1.1826035
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 120, NUMBER 4
22 JANUARY 2004
Structure of ionic liquids of 1-alkyl-3-methylimidazolium cations: A systematic computer simulation study Se´rgio M. Urahata and Mauro C. C. Ribeiroa) ˜ o Paulo, C.P. 26077, Laborato´rio de Espectroscopia Molecular, Instituto de Quı´mica, Universidade de Sa ˜ o Paulo, SP, Brazil CEP 05513-970, Sa
共Received 26 September 2003; accepted 28 October 2003兲 Molecular dynamics simulations of room temperature molten salts 共ionic liquids兲 containing imidazolium cations have been performed. Ten different systems were simulated at 323 K by using united atom force fields, in which the anion size (F⫺ , Cl⫺ , Br⫺ , and PF⫺ 6 ) and the length of the alkyl chain of 1-alkyl-3-methylimidazolium cations 共1-methyl-, 1-ethyl-, 1-butyl-, and 1-octyl-兲 were systematically varied. It is shown that the resulting equilibrium structures account for the observed features of experimental static structure factors when available. A detailed analysis of the simultaneous effect of changing the anion and the alkyl chain on the preferential location of nearest-neighbor anions around the cations is provided. It is shown that regions above and below the imidazolium ring are the preferential ones in case of large anions. By increasing the length of the alkyl chain, nearest-neighbor anions are pushed away from the volume occupied by the flexible alkyl chain. Partial structure factors of 1-butyl- and 1-octyl- derivatives display a peak at a wave vector smaller than the main peak, indicating the occurrence of an intermediate range order in these ionic liquids due to the presence of long alkyl chains. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1635356兴
I. INTRODUCTION
1-n-butyl-3-methylimidazolium cation in these theoretical investigations can be traced to the fact that the experimental density of this system is known,12 which one can use to address the adequacy of the potential model used in the simulation. Recently, neutron scattering investigations of 1,3-dimethylimidazolium chloride 共Ref. 13兲 and 1,3dimethylimidazolium PF6 共Ref. 14兲 have been reported, which would allow a direct comparison between the experimental and the calculated equilibrium structure of these ionic liquids. The above-mentioned simulations validated the models for those systems, where all atoms7–10 or simpler united atom7,11 models have been used. In this work, instead of focusing on a particular system, we pursue a more systematic view on the trends of the equilibrium structure of these ionic liquids when basic features are changed, namely, the anion size and the length of the alkyl chain in 1-alkyl-3methylimidazolium cations. A list of the systems simulated in this work is given in Table I. In light of the interest of this work, where ten different systems have been simulated, we used more economical models of united atoms in which the hydrogen atoms are not explicitly considered. Nevertheless, we show that equilibrium structures obtained by the present simulations are fully consistent with experimental static structure factors reported recently,13,14 and also with previous simulations.7–11 The ionic dynamics in these liquids will be discussed in a future publication. Being confident that equilibrium structures of the simulated systems are reasonable, we provided a detailed analysis of the distribution of anions around cations, and how it is dependent on the anion size and the length of the alkyl chain. This analysis was performed in real space by using partial
Since the early days of computer simulation of liquids, structure and dynamics of molten salts have been extensively investigated.1,2 The microscopic view of molten salts is worthwhile due to the technological applications of these systems in many industrial processes. Molecular dynamics 共MD兲 simulations of 共high temperature兲 molten salts have been performed mainly for systems containing simple atomic ions, alkali halides being the most investigated ones. On the other hand, when complex organic ions are involved, room temperature molten salts can be obtained, the so-called ionic liquids.3–5 One of the most common applications of ionic liquids is their use as alternative solvents in several organic chemistry syntheses. Of course, fundamental macroscopic transport coefficients, such as viscosity and conductivity, have been measured, but the increasing number of different ionic liquids demands a more detailed microscopic view on the interplay between structure and dynamics in these systems, which is still lacking.6 The experimentally most investigated ionic liquids contain imidazolium cations, in particular 1-alkyl-3methylimidazolium cations 共see Fig. 1兲, with many different anions.3–5 Computer simulations of ionic liquids have become available in the literature only recently, including 1,3dimethylimidazolium and 1-ethyl-3-methyl-imidazolium cat7 ions with chloride and hexafluorophosphate (PF⫺ 6 ) anions, 1-ethyl-3-methylimidazolium and 1-n-butyl-3-methyl⫺ 8 and BF imidazolium cations with AlCl⫺ 4 4 anions, and 1-n9–11 The predominance of butyl-3-methylimidazolium PF6 . a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2004/120(4)/1855/9/$22.00
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© 2004 American Institute of Physics
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tions. We first validate the present models by comparing the calculated total S(k) with neutron scattering data when available, and also by comparing some g ␣ (r) with previous MD simulations. In Sec. III B, a detailed analysis of equilibrium structures of the simulated systems is given, mainly by using appropriate probability density maps. In Sec. III C, further insights are gained by using partial static structure factors. Concluding remarks are given in Sec. IV. FIG. 1. Structure of 1-alkyl-3-methyl-imidazolium cations with the atom numbering. In this work, we simulated 1-methyl-, 1-ethyl-, 1-butyl-, and 1-octyl-derivatives with united atom models in which the hydrogen atoms are not explicitly considered.
radial distribution functions, g ␣ (r), together with adequate probability density maps, and also in reciprocal space by using partial static structure factors, S ␣ (k). The latter are much more appropriate for revealing any long-range spatial correlation because it appears as a peak at low wave-vector, whereas in real space it could be not discernible within the smooth asymptotic limit of g ␣ (r). In fact, it will be shown that, in the 1-butyl- and the 1-octyl-derivatives, S ␣ (k) display a peak in a wave-vector range that is smaller than the main peak, so that an intermediate range order develops in the melt. It is a direct consequence of long alkyl chains in 1-alkyl-3-methylimidazolium cations, but it also implies a corresponding intermediate range order on the anions correlation. This low wave-vector peak corresponds to the socalled first-sharp diffraction peak, a well-known and lively debated feature in glassforming liquids,15,16 and, in the authors’ knowledge, it has not been previously identified in these ionic liquids. The paper is organized as follows: Computational details are given in Sec. II. In the particular issue of partial atomic charges, we provided a comparative revision of different models available in the literature with our own models. In Sec. III, results and discussion are presented in three subsec-
TABLE I. The systems simulated in this work, densities, and intermolecular Lennard-Jones and Coulombic average potential energies.
a
1-alkyl-a
Anion
Notation
共g cm⫺3兲
V LJ 共kJ mol⫺1兲
V Coul. 共kJ mol⫺1兲
methyl methyl
F⫺ Cl⫺
metF metCl
1.30 1.21
methyl methyl
Br⫺ PF⫺ 6
metBr metPF6
1.26 1.74
ethyl ethyl butyl butyl butyl
Cl⫺ Br⫺ F⫺ Cl⫺ PF⫺ 6
etCl etBr butF butCl butPF6
octyl
Cl⫺
octCl
1.14 1.48 1.18 1.08 1.56 共1.37兲b 1.00
⫺45 ⫺22 共⫺25兲c ⫺57 ⫺59 共⫺46兲c ⫺37 ⫺32 ⫺77 ⫺54 ⫺86 共⫺89兲d ⫺35
⫺573 ⫺511 共⫺520兲c ⫺459 ⫺461 共⫺441兲c ⫺470 ⫺465 ⫺535 ⫺478 ⫺435 共⫺257兲d ⫺472
II. COMPUTATIONAL DETAILS
The MD simulations were performed with a potential energy function including intermolecular Lennard-Jones and Coulombic interactions, and intramolecular interactions including bond stretching, r, angle bending, , and torsion of dihedral angles, , V total⫽
兺 i, j i⬍ j
⫹ ⫹
再 冋冉 冊 冉 冊 册 冎
f 4⑀ij
兺
bonds
兺
ij rij
12
⫺
k b 共 r⫺r eq兲 2 ⫹
dihedrals
ij rij
兺
angles
6
⫹
q iq j rij
k 共 ⫺ eq兲 2
k 关 1⫹cos共 n ⫺ ␦ 兲兴 ,
共1兲
where r i j is the distance between atoms i and j of different ions. Equilibrium bond lengths, r eq angles, eq dihedral angles parameters, n and ␦, and the corresponding force constants, are based on the all atoms model of Ref. 10. We stress that a united atom model was used here, i.e., hydrogen atoms are not explicitly considered. We used ⑀ ii and ii LennardJones parameters of the united atom model of Ref. 11, which is based on the optimized potentials for liquid simulation 共OPLS兲 proposed by Jorgensen et al.17 For completeness, all of the potential parameters used in this work are given in Tables II and III. In line with the OPLS force field,17 intramolecular Lennard-Jones and Coulombic interactions are also considered for atoms separated by at least three bonds within a given molecule. In order to use the same set of ⑀ ii , ii , and charges, q i , these intramolecular interactions are reduced by a factor f ⫽0.5, whereas f ⫽1.0 for intermolecular interactions. The cross term parameters ⑀ i j and i j are given by usual combining rules: ⑀ i j ⫽( ⑀ ii ⑀ j j ) 1/2 and i j ⫽1/2( ii ⫹ j j ). In the literature, one finds different sets of partial atomic charges for MD simulations of ionic liquids.7–11 These partial charges have been proposed on the basis of ab initio quantum chemistry calculations, where the actual values obtained depend on the level of the theory, on the method for deriving the atomic charges, and also on the conformation of the imidazolium cation. We propose here a new set of partial charges for imidazolium cations obtained by a Mulliken analysis of ab initio calculations at the MP2 level, with the 6-311G* basis set, performed with the GAUSSIAN 98 package.18 By using the atomic coordinates given in Ref. 9 for 1-n-butyl-3-methylimidazolium, from which configurations for the others 1-alkyl-3-methylimidazolium cations
See Fig. 1. Experimental value at 303 K 共Ref. 12兲. c MD simulation at 400 K 共Ref. 7兲. d MD simulation at 298 K 共Ref. 10兲. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: b
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TABLE II. Lennard-Jones parameters and partial charges for 1-alkyl-3-methylimidazolium cations and anions. Units: ⑀ in 10⫺20 J, a in Å,a q in electrons.b 1-methyl-
⑀ N1 N2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14
0.71 0.71 0.443 0.443 0.443 0.865 0.865 ¯ ¯ ¯ ¯ ¯ ¯ ¯
1-ethyl-
q
3.25 3.25 3.88 3.88 3.88 3.775 3.775 ¯ ¯ ¯ ¯ ¯ ¯ ¯
⫺0.398 ⫺0.400 0.6053 0.2472 0.2357 0.3493 0.3613 ¯ ¯ ¯ ¯ ¯ ¯ ¯
⑀ 0.71 0.71 0.443 0.443 0.443 0.865 0.493 0.326 ¯ ¯ ¯ ¯ ¯ ¯
F⫺
a
⑀
0.72
2.73
1-butyl-
q
3.25 3.25 3.88 3.88 3.88 3.775 3.905 3.905 ¯ ¯ ¯ ¯ ¯ ¯
⫺0.401 ⫺0.395 0.6024 0.2546 0.2221 0.3457 0.2629 0.0404 ¯ ¯ ¯ ¯ ¯ ¯
⑀ 0.71 0.71 0.443 0.443 0.443 0.865 0.493 0.493 0.493 0.326 ¯ ¯ ¯ ¯
Cl⫺ q ⫺1.00
⑀
0.12
4.41
1-octyl-
q
3.25 3.25 3.88 3.88 3.88 3.775 3.905 3.905 3.905 3.905 ¯ ¯ ¯ ¯
⫺0.400 ⫺0.394 0.5999 0.2516 0.2243 0.3448 0.2671 0.0327 0.0374 0.0358 ¯ ¯ ¯ ¯
⑀ 0.71 0.71 0.443 0.443 0.443 0.865 0.493 0.493 0.493 0.493 0.493 0.493 0.493 0.326
⫺1.00
⑀
0.09
4.62
q
3.25 3.25 3.88 3.88 3.88 3.775 3.905 3.905 3.905 3.905 3.905 3.905 3.905 3.905
⫺0.427 ⫺0.410 0.6010 0.2625 0.2096 0.3681 0.2831 0.0392 0.0159 0.0188 0.0113 ⫺0.017 ⫺0.004 0.0472
PF⫺ 6
Br⫺ q
q ⫺1.00
⑀
1.67
4.72
q ⫺1.00
Reference 11. This work.
b
were generated, we performed ab initio calculations for each imidazolium cation. The partial charges used in this work are collected in Table II. It is interesting to compare the different sets of partial charges proposed in the literature for ionic liquids containing
imidazolium cations. Such a comparison is shown in Fig. 2 for 1-n-butyl-3-methylimidazolium, where the charge at each site is shown according to the atom numbering of Fig. 1. In the present work, partial negative charges are assigned to nitrogen atoms, in line with the model of Hanke et al.,7 who
TABLE III. Bond, angle and dihedral force constants.a
N1–C3 N2–C3 N1–C4 N2–C5 N1–C6 N2–C7 C4 –C5 C7–C8 Ci – Ci⫹1 (i⭓8)
kb 共kJ mol⫺1 Å⫺2兲
r eq 共Å兲
1674.7 1674.7 1674.7 1674.7 921.1 921.1 1716.6 837.4 931.6
1.34 1.34 1.38 1.38 1.47 1.48 1.36 1.53 1.53
a
eq 共deg兲
544.3 544.3 544.3 544.3 544.3 544.3 544.3 544.3 544.3 586.2 244.5
109.1 125.9 125.9 108.3 108.3 107.2 107.2 125.8 125.8 112.6 111.6
N1–C3–N2 C3–N2–C7 C5–N2–C7 C3–N2–C5 C3–N1–C4 N2–C5–C4 N1–C4 –C5 C3–N1–C6 C4 –N1–C6 N2–C7–C8 Ci – Ci⫹1 – Ci⫹2 (i⭓7)
k 共kJ mol⫺1兲 C6 –N1–C4 –C5 C7–N2–C5–C4 C7–N2–C3–N1 C6 –N1–C3–N2 C5–N2–C3–N1 N2–C3–N1–C4 N2–C5–C4 –N1 C4 –C5–N2–C3 C3–N1–C4 –C5 C3–N2–C7–C8 C5–N2–C7–C8 Ci – Ci⫹1 – Ci⫹2 – Ci⫹3 (i⭓7)
k 共kJ mol⫺1 rad⫺2兲
58.6 58.6 58.6 58.6 58.6 58.6 58.6 58.6 58.6 0.42 0.84 0.63
␦ n 1 1 1 1 2 2 2 2 2 1 1 1
共deg兲 0 0 0 0 180 180 180 180 180 180 0 0
Based on the all atoms model of Ref. 10. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.37.201.69 On: Thu, 24 Dec 2015 13:59:58
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FIG. 2. Comparison of different sets of partial atomic charges for 1-butyl3-methylimidazolium cation. See Fig. 1 for atom numbering. Note that partial charges of Ref. 7 correspond to the united atom model for 1-ethyl-3methyl-imidazolium cation.
simulated ionic liquids containing 1,3-dimethylimidazolium and 1-ethyl-3-methylimidazolium cations. It is worth mentioning that recent analyses of neutron scattering spectra carried out by Hardacre et al.13,14 were performed with the same set of partial charges of Ref. 7. Except by Hanke et al.7 and the present model, other models share the ⫹1 charge of the cation almost evenly between all of the sites. This is the reason for similar average Coulombic energies obtained in this work and in Ref. 7, but relatively different values obtained in this work and in Ref. 10 共see Table I兲. In spite of relatively different values of individual partial charges, the dipole moments obtained from these models are similar. Table IV shows the dipole moment for the particular configuration of 1-n-butyl-3-methylimidazolium with the origin at the ionic center of mass calculated with the different models, which are in reasonable agreement with the ab initio value, except by the model of Ref. 9. The MD simulations were performed in a cubic cell containing 200 cations and 200 anions at 323 K. Starting from an initial random configuration, the size of the cell was allowed to vary by using the Berendsen’s barostat19 in order to result in an average pressure of 1.0 bar. Typical equilibration runs were at least 0.5 ns long, although longer equilibration periods 共1.0 ns兲 were needed in case of 1-butyl- and 1-octylderivatives. Table I collects the equilibrium densities of all of the simulated systems, together with the notation that we will use further on. The equation of motions were integrated with the velocity Verlet algorithm,20 and the time step in the MD simulations was 3.0 fs. The production runs were typically TABLE IV. Dipole moment with the origin at the center of mass of the 1-n-butyl-3-methylimidazolium cation calculated by partial atomic charges of different models, and the ab initio result.
共Debye兲 a
This work
Ref. 8
Ref. 9
Ref. 10
Ref. 11
Ab initioa
4.30
4.27
1.74
4.49
3.90
4.32
FIG. 3. Total energy fluctuation, ⌬E(t), for the simulation of metCl. The resulting average value is 具 兩 ⌬E(t) 兩 典 ⫽0.0021.
1.5 ns long performed in a NVE ensemble. The long-range Coulombic interactions were handled with the Ewald sum method.20 In order to address the issue of energy conservation with these conditions, we used the common criterion of the total energy fluctuation, ⌬E(t)⫽ 关 E(0)⫺E(t) 兴 /E(0), where E(t) is the total energy at time t and E(0) is the initial energy.21 Figure 3 shows a representative example of the time dependence of ⌬E(t) for the particular case of metCl. Typical average value obtained in this work was 具 兩 ⌬E(t) 兩 典 ⬃0.0025, which is within the proposed acceptable numerical accuracy of 具 兩 ⌬E(t) 兩 典 ⭐0.003.21 Table I shows average intermolecular potential energies, where the energies have been split into the short-range and the electrostatic contributions. In spite of the spread of values given in Table I, one can find a clear trend at least on the dependency of Coulombic energies on anion size. Keeping the same cation, the Coulombic energy increases with increasing anion radius, due to the concomitant increase in anion–cation distances. III. RESULTS AND DISCUSSION A. Comparison with previous works
Recently, Hardacre et al.13,14 reported neutron diffraction studies on metCl and metPF6 . From the analysis of experimental static structure factors, S(k), a detailed picture of the local structure in these ionic liquids was achieved. The analysis relies on the empirical potential structure refinement process 共EPSR兲, in which liquid configurations are generated so that they are consistent with the experimental S(k). By comparing metCl and metPF6 , a clear physical picture emerged from the EPSR analysis, namely, anions around the 1,3-dimethylimidazolium cation are preferentially located above and below the ring plane in case of large anions, whereas they are close to the carbon 共3兲 atom in case of small anions 共see the atom numbering in Fig. 1兲. We can validate the present models by their ability to reproduce the observed features of the experimental S(k), at least for metCl and metPF6 . In order to extract unambiguous partial radial distribution functions from the experimental diffraction data, fully or partially deuteriated samples were
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FIG. 4. Calculated total structure factor, S(k), of metCl. The inset compares the low wave-vector range of the calculated S(k) of metCl 共full line兲 and metPF6 共dashed line兲.
investigated in Refs. 13 and 14, so that different S(k) could be obtained due to distinct neutron scattering lengths of H and D. Since the present MD simulations were performed with no explicit hydrogen atoms in the model, we calculated instead the non-neutron-weighted S(k) by computing the spatial correlation between all ␣ and  sites,22 S ␣ 共 k 兲 ⫽
1
冑N ␣ N 
冓兺 兺 N␣
N
i苸 ␣ j苸 
e
ik共 ri ⫺r j 兲
冔
.
共2兲
The calculated total S(k) of metCl is shown in Fig. 4, in which the inset compares the low wave-vector 共intermolecular兲 range of metCl and metPF6 . We stress that the relative intensity of the peaks in the calculated S(k) are not supposed to match the experimental data because the calculated S(k) is not a neutron-weighted sum of all of the partial S ␣ (k). Nevertheless, the wave-vector position of all of the observed features in the calculated S(k) nicely agree with the experimental data 共see Fig. 2 in Refs. 13 and 14兲. The assignment of the observed peaks in the total S(k) will be given below by using partial S ␣ (k). It seems from a comparison between the total S(k) of metCl and metPF6 that there is only a trivial shift to low wave vectors in the latter due to expansion of the system because of larger anions. However, detailed analysis of the equilibrium structures of the simulated systems given below indicates the same trend with anion size as suggested by the EPSR analysis of the experimental S(k). It would be also interesting to compare the liquid structures obtained in the present work with previous computer simulations of some of these ionic liquids. Thus, partial radial distribution functions, g ␣ (r), between cation–anion, cation–cation, and anion–anion of metCl and metPF6 are shown in the top and in the middle panel of Fig. 5, respectively. These results should be compared with previous MD simulations 共see Fig. 1 in Ref. 7兲, and also with the EPSR analysis of the experimental data 共Fig. 3 in Ref. 14兲. The present results are very similar to both the experimental and the theoretical works. The observed difference on the overall shape of g ␣ (r) for metCl and metPF6 obtained by the analysis of neutron scattering spectra seems more pro-
FIG. 5. Calculated radial distribution functions, g ␣ (r), of metCl, metPF6 , and butPF6 . Full line: cation–anion geometric center of the imidazolium ring; dashed line: cation–cation geometric centers of the imidazolium ring; dotted line: anion–anion.
nounced than obtained by the MD simulations of Ref. 7 and this work. Nevertheless, by integrating the calculated cation– anion g ␣ (r) up to the first minimum 共6.6 Å for metCl and 7.4 Å for metPF6 ) we found that there are on average 7.1 Cl⫺ and 7.4 PF⫺ 6 around each 1,3-dimethylimidazolium cation. The experimental g ␣ (r) were integrated up to 6.4 Å for metCl 共Ref. 13兲 and 7.5 Å for metPF6 , 14 giving the corresponding running numbers of 6.0 and 6.8, respectively. The bottom panel of Fig. 5 shows g ␣ (r) of butPF6 , which should be compared with Fig. 4 of Ref. 10 and Fig. 7 of Ref. 11. Close inspection of the butPF6 results of Refs. 10 and 11, and also the present work, reveals that the detailed shape of these g ␣ (r) are dependent on different models, although there is a reasonable agreement on the overall shape. One would expect from the larger cation size in butPF6 in comparison with metPF6 that the first peak of the cation–anion g ␣ (r) should be shifted to a larger distance in the former, but Fig. 5 shows that it is not the case. This finding is due to the fact that the preferential location of finding PF⫺ 6 anions is above or below the ring plane. In summary, the main conclusion drawn from Figs. 4 and 5 is that the present models are fully consistent with raw diffraction data and also with previous theoretical studies when available, giving us confidence on the application of the models to the other systems investigated in this work. B. Effects of anion size and alkyl chain on the liquid structure
Due to the complexity of imidazolium cations, and the corresponding large number of partial g ␣ (r) available, the analysis of all of the g ␣ (r) becomes a complex task. Using appropriate probability density maps of preferential location of nearest neighbors facilitates the analysis of the liquid
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FIG. 6. 共Color兲 Probability density maps of location of nearest-neighbor anions around the imidazolium ring in metF 共a兲, metCl 共b兲, and metBr 共c兲. In each case, the top panel shows the view above the ring plane, and the bottom panel shows the view on the ring plane. In the latter, the colored points toward the carbon atoms 共4兲 and 共5兲 were dropped in order to help visualization. Red, green, and yellow regions correspond, respectively, to high, intermediate, and low probability of finding an anion around a given cation. See text for further details.
structure of these ionic liquids. Figure 6 shows probability density maps of the location of anions around 1,3dimethylimidazolium cations in metF, metCl, and metBr. Anions were selected whenever the distance to the geometric center of the imidazolium ring was smaller than the first minimum of the corresponding g ␣ (r) 共not shown兲. Red and yellow areas in Fig. 6 indicate high and low probabilities, respectively, of finding an anion around a given cation. By high probability we mean higher than 80% of the maximum density of occurrences in these figures, and low probability means in between 40% and 60% of the maximum density of occurrences. Green color represents an intermediate probability 共between 60% and 80%兲, and probability lower than 40% of the maximum density of occurrences is not shown. For each system, the top panel in Fig. 6 shows the perspective from above the ring plane, whereas the bottom panel shows the perspective on the plane of the ring. In the latter,
we dropped the colored points toward the carbon atoms 共4兲 and 共5兲 共see the numbering in Fig. 1兲 in order to help visualization. It is clear from the top panels in Fig. 6 that the position of high probability 共red area兲 systematically changes as the anion size increases. In the case of the small F⫺ anion, the high probability region is found close to the carbon 共3兲 atom, and it shifts toward the ring for the large Br⫺ anion. The case of metPF6 共not shown兲 is very similar to metBr. This finding is in exact agreement with the conclusions drawn by Hardacre et al.13,14 on the basis of the EPSR analysis of the experimental diffraction data of metCl and metPF6 . Similar probability density maps were shown in previous MD simulations of metCl and metPF6 , 7 but the preference of large anions being directed toward above and below the ring was not clearly stated in Ref. 7. The present recourse of assign colors as a function of the density of occurrences adds further rich-
FIG. 7. 共Color兲 The same as Fig. 6, but for metCl 共a兲, etCl 共b兲, and butCl 共c兲. In case of etCl and butCl, many configurations of the alkyl chain have been superimposed.
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J. Chem. Phys., Vol. 120, No. 4, 22 January 2004
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FIG. 9. Partial radial distribution functions of butCl. Full line: anion–carbon 共6兲; dashed line: anion–carbon 共10兲.
FIG. 8. Probability density map of location of nearest-neighbor anions around the carbon atoms of the alkyl chain in butCl. The top panel shows a longitudinal cut, and the bottom panel shows a transversal view. See text for further details.
ness to the figure. Closer inspection of the bottom panels in Fig. 6 reveals four red spots of finding the small F⫺ anion close to the carbon 共3兲 atom, that shifts to two red spots in opposite sides of the ring in case of Cl⫺ , and then above and below the ring plane in case of Br⫺ . Thus, there is a clear effect of packing of anions around the cations, that is more easily satisfied for a small anion such as F⫺ . At low probability densities 共yellow spots in Fig. 6兲, one finds that there are anions directed toward every carbon atom, so that many hydrogen bonds are expected in these ionic liquids. Figure 7 shows the effect of increasing the length of the alkyl chain on the distribution of anions around the cations in metCl, etCl, and butCl. Figure 7 was drawn following the same plan as Fig. 6, and the metCl result is shown again for comparison purposes. The result for octCl 共not shown兲 is similar to butCl. One can see that the red spots of high probability are shifted from the side where the long alkyl chain is located toward the side of the smaller – CH3 group. In the bottom panels of Fig. 7, note the change of the relative location of the two red spots at opposite sides of the ring on going from metCl to etCl. Many configurations of the alkyl chain have been superimposed for etCl and butCl so that it is clear that the alkyl chain is pushing away the high probability regions of finding the anions. Focusing the attention on the yellow regions in the top panels of Fig. 7, one sees that the Cl⫺ anions hydrogen bonded to the carbon atoms 共4兲 and
共5兲 are also disturbed due to the presence of the long alkyl chain. One can also address the probability of finding anions around the imidazolium cation with respect to the carbon atoms of the alkyl chain. In case of butCl, we selected all Cl⫺ anions whose distance to the carbon atoms numbered 共8兲, 共9兲, or 共10兲, is smaller than 11.0 Å. The resulting probability density map is shown in Fig. 8, in which a longitudinal cut and a transversal view are shown. No colors were needed in these maps, so that dark and light areas mean high and low probability of occurrences, respectively. The large cut-off distance between the ions in Fig. 8 allows one to visualize at the left-hand side of the top panel, close to the imidazolium ring, a decrease in density of occurrences followed by the second neighbor shell of anions around the cation. This is also clear at the bottom panel as two concentric circles of probability of finding anions around the central cation. Interestingly, at the right-hand side of the top panel, the figure is not filled up of points despite the large distances involved 共all of the occurrences are shown in the figure兲. Instead, there is a clear depletion of anions at the side of the long alkyl chain, indicating the presence of hydrocarbonlike volumes in the liquid less favorable for the anions. The bottom panel is just the view through this region. Further evidence is provided in Fig. 9, which shows partial g ␣ (r) between anions and the carbon atom 共6兲 or 共10兲, g ⫺6 (r) and g ⫺10(r), that is, spatial correlation between Cl⫺ anions and the carbon atom of each extremity of the 1-butyl-3methylimidazolium cation. It is clear from Fig. 9 that the first peak in g ⫺10(r) is much less intense than in g ⫺6 (r), indicating that the extremity of the long alkyl chain is a much less favorable location for the anions. It will be shown in the next subsection that nontrivial correlations between anions develop at long range as the length of the alkyl chain in imidazolium cations increases. C. Partial static structure factors
Further insight on the structure at long range in these ionic liquids is gained here by computing appropriate partial S ␣ (k). Figure 10 shows partial S ␣ (k) for metCl, etCl,
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J. Chem. Phys., Vol. 120, No. 4, 22 January 2004
FIG. 10. Partial static structure factors, S ␣ (k), between atoms 共1兲–共7兲 共see atom numbering in Fig. 1兲 of metCl, etCl, butCl, and octCl, as indicated in the figure.
butCl, and octCl, in which ␣ and  correspond to atoms numbered 共1兲–共7兲 in Fig. 1. The peak at 1.1 Å⫺1, together with a similar peak in the partial anion–anion S ␣ (k) 共see Fig. 12兲, matches the corresponding feature observed in the total S(k) shown in Fig. 4. This feature is due to ionic correlations imposed by usual charge ordering effects in molten salts,1,2 i.e., it results from correlation between ionic centers of mass. In the case of butCl and octCl, the partial S ␣ (k) in Fig. 10 displays a low wave-vector peak, which is very pronounced in the latter. This low wave-vector peak indicates that a long-range order develops in the ionic liquid when the alkyl chain increases. In Fig. 11, we show partial S ␣ (k) for the carbon atoms of the alkyl chain in butCl and octCl. The sharp peak observed at 1.1 Å⫺1 in Fig. 10 is missing in Fig. 11, and the peak at k⬃0.5 Å⫺1 is very intense in the latter. In the inset of Fig. 11, the origin of the two peaked structure in S ␣ (k) of the alkyl chain atoms of butCl is further elucidated by calculating partial S ␣ (k) of the carbon atoms 共6兲 and 共10兲, S 66(k) and S 1010(k), which are at each extremity of the 1-butyl-3-methylimidazolium cation, and of carbon atom 共7兲,
S. M. Urahata and M. C. C. Ribeiro
FIG. 12. Partial anion–anion S ␣ (k) of metCl, etCl, butCl, and octCl. The inset shows anion–anion S ␣ (k) of butF, butCl, and butPF6 .
S 77(k), which is almost at the middle of the cation. In both the S 66(k) and the S 1010(k), there are short-range 共high wave-vector兲 and long-range 共low wave-vector兲 correlations due to alkyl chains or imidazolium rings in close approach or distant from each other. Thus, the imidazolium ring of two neighbor cations can point either to the same or to opposite directions. Thus, if one imagines the rotation of two neighbor molecules through its middle, the relative distance between their center 关say carbon atom 共7兲兴 remains almost unchanged, and in fact the low wave-vector peak is absent in S 77(k). The present physical picture reminds the one observed in limiting cases of crystalline phases of 关 1-alkyl-3-methylimidazolium兴PF6 with very long alkyl chains containing 12, 14, or 16 carbon atoms.23,24 In these systems, x-ray and neutron scattering investigations indicated the occurrence of liquid crystalline behavior with an arrangement of interdigitated alkyl chains separating sheets of imidazolium rings and anions 共see Fig. 7 in Ref. 23兲. A remarkable consequence of finding a low wave-vector peak in the cations partial S ␣ (k) is that this feature also extends to anion correlation. Figure 12 shows partial anion– anion S ␣ (k) for metCl, etCl, butCl, and octCl. A low wavevector peak is observed in the anions S ␣ (k) as the alkyl chain increases, so that it is absent in metCl, a clear bump in butCl, and a defined peak in octCl. Thus, in metCl, usual charge ordering effect defines a simple molten salt 共NaCllike兲 structure, whereas new features appear in the equilibrium structures of these ionic liquids by increasing the length of the alkyl chain. Furthermore, the inset in Fig. 12 shows the anions S ␣ (k) for butF, butCl, and butPF6 , where one sees that the magnitude of this low wave-vector peak is dependent on the size of the anion when keeping the same cation. Thus, as more defined is the local structure in case of a small cation such as F⫺ 共see Fig. 6兲, more pronounced is the second long-range correlation. The low wave-vector peak observed in the anions S ␣ (k) in 1-butyl- and 1-octyl-derivatives can be traced to the so-called prepeak or first-sharp diffraction peak 共FSDP兲,15,16 which is a well-known feature observed in S(k) of many glassforming molten salts, for instance, ZnCl2 共Ref. 25兲 and Ca0.4K0.6(NO3 ) 1.4 , 26 and also in organic glassform-
FIG. 11. Partial static structure factors, S ␣ (k), between carbon atoms 共8兲– 共10兲 of butCl 共full line兲, and between carbon atoms 共8兲–共14兲 of octCl 共dashed line兲. The inset shows the partial S 66(k), S 77(k), and S 1010(k), of butCl, as indicated in the figure. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
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J. Chem. Phys., Vol. 120, No. 4, 22 January 2004
ing liquids.27 The occurrence of a FSDP in S(k) indicates the presence of an intermediate range order 共IRO兲. The nature of IRO in glass forming liquids is a lively debated issue, in which voids as layers in the structure have been assigned as plausible origins for the IRO.15,16,28 In the present case, this long-range correlation results from the presence of a long alkyl chain in imidazolium cations. However, this long-range correlation seems nontrivial when one sees that it extends to the anions correlation. The wave-vector range of the FSDP, k FSDP⬃0.5 Å⫺1 , suggests that this spatial correlation is in the approximate range of 12.5 Å in real space. Such estimation is consistent with the spatial range of the nonhomogeneity of occurrences observed in the probability density map shown in Fig. 8 for butCl. IV. CONCLUDING REMARKS
Equilibrium structures of ionic liquids containing 1-alkyl-3-methylimidazolium cations have been systematically investigated by using MD simulations. The simulations were performed with united atom models, and the resulting equilibrium structures were in full agreement with neutron diffraction data and previous computer simulations when available. The experimental13,14 finding that the most favorable location of Cl⫺ anions around cations in metCl is closer to the carbon atom 共3兲, whereas for PF⫺ 6 anions in metPF6 is above and below the ring, has been corroborated by the present simulations. In fact, it has been shown that the preferential location of anions around cations systematically changes as the anion size increases. A further effect on the location of anions around cations was observed by increasing the length of the alkyl chain in 1-alkyl-3-methylimidazolium cations, so that the high probability regions of finding anions are shifted away from the side of the long alkyl chain. In case of ionic liquids based on 1-butyl-3-methylimidazolium and 1-octyl-3-methylimidazolium cations, the presence of long alkyl chains defines a long range spatial correlation, as indicated by a low wave-vector peak in partial static structure factors. This arises from the possibility that the extremities of the molecules in these relatively long cations are close to each other or far apart. Interestingly, this intermediate range order also develops in the anions correlation, as indicated by a low wave-vector peak in the corresponding partial structure factor. The probability density map of anions around the carbon atoms of the alkyl chain in fact indicates the occurrence of volumes of relatively low probability of finding anions in which entanglement of alkyl chains is expected. Thus, due to the presence of long alkyl chains in the 1-butyl- and the 1-octyl-derivatives, the anions are not evenly distributed in the simulation box, so that an additional long-range correlation is discernible in the anions partial structure factor. Although the present study was devoted to the particular series of ionic liquids based on 1-alkyl-3methyl-imidazolium cations, most probably several conclu-
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sions could be extended to other ionic liquids. For instance, if alkyl chains are introduced in the other carbon atoms of the imidazolium ring,5 one could expect similar effects on the preferential locations of anions around the cation as shown in this work. Even qualitative similarities with the present results could be also expected in case of alkylsubstituted pyridinium cations, which define other wellknown classes of ionic liquids.3,4 The systematic study of ionic dynamics in the simulated systems is now in progress. ACKNOWLEDGMENTS
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