- Email: [email protected]
Why are aromatic compounds more soluble than aliphatic compounds in dimethylimidazolium ionic liquids? A simulation study
Chemical Physics Letters 374 (2003) 85–90 www.elsevier.com/locate/cplett
Why are aromatic compounds more soluble than aliphatic compounds in dimethylimidazolium ionic liquids? A simulation study C.G. Hanke a, A. Johansson a, J.B. Harper b, R.M. Lynden-Bell a
a,*
Atomistic Simulation Group, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK b School of Chemical Sciences, University of New South Wales, Sydney, NSW 2052, Australia Received 21 March 2003; in final form 24 April 2003
Abstract Molecular dynamics simulations of solutions of benzene in dimethylimidazolium chloride and dimethylimidazolium hexafluorophosphate have been performed with a view to answering the question posed in the title. The difference between the chemical potential of a normal model of benzene and one with no charges was found to depend on the solvent but is at least 4 kB T . This difference is sufficient to account for the observed solubility differences. There are substantial changes in the local structure around benzene with and without charges. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction The alkylimidazolium liquids have been proposed as potential green solvents for a variety of industrial organic reactions. As they have vanishingly small vapour pressure, these solvents have the advantage that there is no pollution from their vapours and, provided that they can be satisfactorily recycled and the products easily extracted, there is little problem with waste. Moreover they are desirable solvents for a number of reactions,often either enhancing rates or improving selectivities [1–3]. Atomistic simulation has been *
Corresponding author. Fax: +442890241958. E-mail address: [email protected] (R.M. LyndenBell).
used to aid our understanding of solvation and allows one to interpret changes in solvation thermodynamics in terms of the local structure around the solute and solute–solvent and solvent–solvent interactions [4,5]. One general observation about solubilities in ionic liquids is that aromatic compounds are more soluble than aliphatic compounds of a similar size [6,7]. The existence of p electrons in orbitals above and below an aromatic ring results in a much stronger electrostatic field around an aromatic molecule compared to a saturated aliphatic molecule. In general, alkanes and alkyl side chains give very small electrostatic fields. Benzene, on the other hand, has a significant quadrupole moment of about an order of magnitude greater than that for cyclohexane [8]. Another difference is that benzene is more polarisable than cyclohexane.
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00703-6
86
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
Both these differences lead to an enhanced stabilisation of the aromatic solute in an ionic liquid. In this Letter, we show that the difference in the average electrostatic fields is sufficient to explain the difference in solubility of aromatic and aliphatic compounds; any effects of the fluctuations in the electronic structure of the aromatic system due to local fields will just exacerbate the difference. In simulations one can use models which do not correspond to a real physical situation but which allow one to isolate a particular part of an interaction in an unambiguous way. Thus, in order to isolate the electrostatic contribution to the different behaviour of aromatic and aliphatic compounds we calculate the difference in chemical potentials between a model of benzene with partial charges on the carbon and hydrogen sites which reproduces the experimental quadrupole moment and a model of Ôuncharged-benzeneÕ that has no charges on the atomic sites, but is otherwise identical to the charged model. The latter model can be said to approximate the electrostatics of an aliphatic compound of the same size as benzene. We find that the effect of turning off the charges increases the chemical potential in solution by an amount which is quite sufficient to explain the differences in solubility. We have also investigated the local liquid structure around both normal and uncharged benzene and find that the charges on the benzene induce strong local charge ordering which is propagated some distance into the liquid.
2. Technical details The models for the molecules of the ionic liquid þ were described in our earlier work [9], the ½dmim cation being treated as a rigid ten-site body with united methyl groups. The intermolecular potential consists of Buckingham-type interactions between atomic sites and Coulomb interactions between the partial charges on these sites. Likewise, the Cl ion has a single site and a charge of e and the ½PF6 anion is modelled as a rigid body with seven sites each containing partial charges and short-range Buckingham potentials. In a few calculations the methyl groups were modelled with four sites, so that explicit effects of
the methyl hydrogen atoms were included. The site–site Buckingham terms have the form Vij ¼ ðAii Ajj Þ1=2 expððBii þ Bjj Þrij =2Þ ðCii Cjj Þ
1=2
=rij6 ;
ð1Þ
and values of the parameters are given in Table 1. Benzene was modelled with the 12-site model proposed by Williams and Starr [10] which was recommended in a review of models by Smith and Jaffe [11]. The parameters are given in Table 1. The quadrupole moment of this model is )9 DA (30 1040 cm2 ), which compares with experimental and calculated values ranging from )8.7 to [8]. The hexadecapole moment is 1:8 )9.9 DA 1058 cm4 , which has the correct sign, but is lower than the calculated value [8] (2:5 1058 cm4 ). Classical molecular dynamics simulations were performed with a modified version of the program DL_POLY [12] in a NVT-ensemble at 400 K (127 °C) using a Berendsen thermostat and cubic periodic boundary conditions. The simulation box contained 191 formula units of [dmim]Cl or [dmim]½PF6 together with one solute molecule. The long range electrostatic interactions were computed by the Ewald summation. The timestep used was 2 fs. Calculations were performed for four types of system, benzene in [dmim]Cl, benzene in [dmim]½PF6 and uncharged benzene in the two types of ionic liquid. Three-dimensional probability distribution functions for the cations and anions relative to a benzene molecule were constructed by averaging over configurations from the simulation. These were expressed as a sum over products of spherical harmonic functions YLM and functions of distance gLM ðrÞ. As benzene is nearly cylindrically symmetrical, two-dimensional plots of the functions with M ¼ 0 were plotted as a function of axes in the plane of the benzene ring and perpendicular to it. In the figures displayed in this Letter, the expansion was carried out to L ¼ 8. The difference in chemical potential of charged and uncharged benzene in solution was measured using thermodynamic integration over a number of intermediate states with scaled charges. If q is the final charge on each proton with q on the carbon sites, then the integration path is over
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
87
Table 1 Intermolecular Buckingham site–site parameters Aii (kJ/mol)
B1 ii ) (A
Cii 6 mol1 ) (kJ A
q/e
Benzene C H
367 496 11684.9
0.27778 0.26738
2415.8 136.1
)0.15 +0.15
½dmimþ N C2 C4 ,C5 H2 H4 ,H5 Me(united) C(Me) H(Me)
254 525 369 737 369 737 11 971 11 971 241 473 369 737 11 971
0.264550 0.277778 0.277778 0.267380 0.267380 0.344520 0.277778 0.267380
1378.4 2439.8 2439.8 136.4 136.4 10 303 2439.8 136.4
)0.267 0.407 0.105 0.097 0.094 0.316 0.124 0.064
Cl and ½PF6 Cl P F
924 653 0.0 363 725
0.284900 – 0.240385
7740.3 3255.0 844.
1.0 0.74 )0.29
Atom
solute molecules with site charges kq and kq, respectively. The rate of change of the free energy difference with k is given by [13,14] oF oH ¼ : ð2Þ ok ok k This derivative is just proportional to the Coulomb part of the solute–solvent interaction energy EC in a simulation with a fixed value of k, oF hEC ik ¼ : ð3Þ ok k This quantity was evaluated in separate 90 ps simulations with partial charges scaled by k ¼ 0:25, 0.5, 0.75 and 1.0. The derivative at k ¼ 0 is taken to be zero as the Coulomb energy is expected to decrease for both positive and negative charges and hence to have zero slope at the origin (k ¼ 0). The free energy change, which is equal to the difference in chemical potentials of the two solutes, was determined from the values of oF =ok by integration using SimpsonÕs rule. 3. Local structure and energetics There is a good deal of local order of the ionic liquid around the benzene molecule. This is
shown in Fig. 1, which is a cross-section of the probability distribution around a benzene molecule in dilute solution in dimethylimidazolium chloride. Regions with an excess of cations are shown in shades of orange, while regions with an excess of anions are shown in shades of blue. The most prominent features in the immediate vicinity of the benzene are an excess of cations in the polar regions above and below the ring and an excess of anions around the equator of the benzene. The interaction energies shown in the first line of Table 2 demonstrate that the solute– solvent interaction with the chloride ion is much stronger than that with the [dmim] cation and that this interaction is dominated by the electrostatic terms. The electron distribution in the benzene molecule gives a net positive charge around its equator and a region of negative charge above and below the molecule. Thus the anions favour the equatorial region where they experience a strong attractive Coulomb force. Although the net interaction of the cations with the benzene molecule is favourable, it is small and the Coulomb contribution to the interaction is repulsive. We interpret the preference of the cations for the polar regions as due to their interaction with the anions in the equatorial plane
88
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
Fig. 1. Cross-section of the three-dimensional probability distributions around benzene in [dmim][Cl]. The axis of the benzene molecule lies in the vertical direction and the plane of the molecule lies in the horizontal direction, perpendicular to the field of view. The difference in distributions of the cations and anions is shown; regions in shades of blue are more likely to contain anions, while regions in shades of orange tend to contain cations. The scale is in multiples of the average concentration of cations (or anions) in the solution.
Fig. 2. Cross-section of the three-dimensional probability distributions around uncharged ÔbenzeneÕ in [dmim][Cl]. The difference in distributions of the cations and anions is shown; regions in shades of blue are more likely to contain anions, while regions in shades of orange tend to contain cations. The orientation and scales are the same as in the figure. Note that the differences are much less than in the simulations of benzene (Fig. 1).
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
89
Table 2 Solute–solvent interaction energies in kJ per mole of solute Solvent
Solute
Cation E
NC
Anion E
C
E
tot
ENC
EC
Etot
[u-dmim][Cl]
Benzene Uncharged benzene
)49 )51
+41 0
)8 )51
)6 )11
)67 0
)73 )11
[u-dmim]½PF6
Benzene Uncharged benzene
)35 )34
+17 0
)18 )34
)14 )18
)43 0
)56 )18
[e-dmim]½PF6
Benzene Uncharged benzene
)37 )38
+20 0
)17 )38
)18 )34
)41 0
)59 )34
The dimethylimidazolium cations are modelled with either united methyl groups ([u–dmim]) or explicit methyl groups [e-dmim]. The total interaction energy Etot is divided into contributions from the non-Coulombic part ENC and the Coulombic energy EC .
rather than to their direct interaction with the benzene molecule. The pattern of probabilities further from the benzene shows alternation of cation and anion preferences, and hence a charge oscillation which persists to quite a long distance in the axial direction perpendicular to the plane of the benzene. The importance of the electrostatic interaction between the benzene and the solvent is reinforced by calculations of a hypothetical Ôuncharged benzeneÕ. Fig. 2 shows that there is much less perturbation of the distribution of solvent species around the molecule. What effects there are, are largely geometrical in origin and lead to a much lower degree of charge alternation along the axial direction. The contributions to the solvent–solute interactions are shown in the second line of Table 2, whence it can be seen that the non-Coulombic interactions are similar for both charged and uncharged solutes. However the Coulomb contributions to the energies are large and differ in sign between anions and cations. It is this difference which accounts for the difference in behaviour of the charged and uncharged solutes. The pattern of energies and three-dimensional distributions are qualitatively similar when the chloride ion is replaced by ½PF6 . This is shown in Table 2 which also gives the results from simulaþ tions of a more sophisticated model of ½dmim with the protons on the methyl groups included explicitly. The 2–3 kJ/mol differences between this model and the cheaper model with united methyl groups are similar to the uncertainty in the energies.
4. Free energy differences between charged and uncharged models The differences of standard chemical potentials of normal and uncharged benzene in the two ionic liquids were found to be loq loq¼0 ¼ 22 2 kJ=mol in ½dmim½Cl;
ð4Þ
loq loq¼0 ¼ 12 2 kJ=mol in ½dmim½PF6 :
ð5Þ
At 400 K the value of kT is 3.6 kJ/mol, so that the stabilisation of normal benzene compared to the uncharged benzene is high in both cases. For example the ratio of the vapour pressures in dilute solutions at the same concentration is given by pq¼0 =pq ¼ expð½lq¼0 lq =kT Þ, which gives a difference of a factor of 30 for uncharged and normal benzene dissolved in [dmim]½PF6 and a factor of 450 for uncharged and normal benzene dissolved in [dmim][Cl]. It should be noted that, as these calculations do not give the absolute values of the chemical potentials, it is not possible to estimate the relative solubility of benzene in [dmim]½PF6 and [dmim] [Cl]. Although the direct interaction of benzene and [dmim][Cl] is more negative than for [dmim]½PF6 , the solvent vaporisation energy is also greater in the former case, so that the solvent rearrangement energy is likely to be greater. Experimentally it is found that benzene is much less soluble in [dmim][Cl] than in [dmim]½PF6 [15] suggesting that the solvation energy is more negative in the latter case.
90
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
5. Discussion and conclusions We conclude that local electrostatic interactions between solutes and the ionic species of the solvent are very important in determining both solute chemical potentials and local liquid structure in ionic liquids. These calculations provide at least a partial answer to the question posed in the title. Alkanes, with their saturated carbon–carbon and carbon–hydrogen bonds, give rise to very small electrostatic fields, which are normally taken to be zero. Thus the uncharged model of benzene is essentially a model for a generic aliphatic solute. Aromatic compounds with electron density above and below the plane of the ring give quadrupole and higher electrostatic multipole moments. This is modelled by partial charges in the Ônormal modelÕ of benzene. The large decrease in the chemical potential when the charges are turned on shows that the increased solubility of aromatic compounds compared to aliphatic compounds can be explained by the local electrostatic solute–solvent interactions. The models used do not allow for fluctuations in the solute electrostatics. As fluctuations only occur if the result is a lowering of the free energy of the system, inclusion of fluctuations would result in increased stabilisation of benzene in ionic liquids. As aliphatic molecules are less polarisable, the effect of fluctuations would be less. Thus fluctuations enhance the relative stabilisation of aromatic compounds as compared to aliphatic compounds. The local structure shown in the three-dimensional probability functions confirms the importance of the electrostatic interactions between both the solute and solvent and between the ionic species in the solvent. The solute perturbs the local structure in its immediate vicinity, but the ion–ion interactions propagate this disturbance to greater distances. The importance of local electrostatic interactions also explains one of the apparent anomalies
of the solubility of gases in ionic liquids. Carbon monoxide is much less soluble than carbon dioxide in ionic liquids [16]. This can readily be explained in terms of the small dipole and quadrupole moments of CO and the larger quadrupole moment of CO2 . Acknowledgements We are grateful to EPSRC for funding through Grant GR/M/72401, IASTE for a summer studentship (A.J.) and the School of Chemical Sciences, UNSW for travel funds (J.B.H.). References [1] P. Wasserscheid, W. Keim, Angew. Chem. 39 (2000) 3772. [2] P. Wasserscheid, T. Welton (Eds.), Ionic Liquids in Synthesis, Wiley–VCH, New York, 2003. [3] T. Welton, Chem. Rev. 99 (1999) 2071. [4] C.G. Hanke, N.A. Atamas, R.M. Lynden-Bell, Green Chem. 4 (2002) 107. [5] R.M. Lynden-Bell, N.A. Atamas, A. Vasilyuk, C.G. Hanke, Mol. Phys. 100 (2002) 3225. [6] K.R. Seddon, A. Stark, M.J. Torres, Pure Appl. Chem. 72 (2000) 2275. [7] L.A. Blanchard, J. Brennecke, J. Ind. Eng. Chem. Res. 40 (2001) 287. [8] C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids I, Clarendon Press, Oxford, 1984. [9] C.G. Hanke, S.L. Price, R.M. Lynden-Bell, Mol. Phys. 99 (2001) 801. [10] D.E. Williams, T.L. Starr, Comput. Chem. 1 (1977) 173. [11] D.S. Smith, R.L. Jaffe, J. Phys. Chem. 100 (1996) 9624. [12] W. Smith et al., Available from
Why are aromatic compounds more soluble than aliphatic compounds in dimethylimidazolium ionic liquids? A simulation study C.G. Hanke a, A. Johansson a, J.B. Harper b, R.M. Lynden-Bell a
a,*
Atomistic Simulation Group, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK b School of Chemical Sciences, University of New South Wales, Sydney, NSW 2052, Australia Received 21 March 2003; in final form 24 April 2003
Abstract Molecular dynamics simulations of solutions of benzene in dimethylimidazolium chloride and dimethylimidazolium hexafluorophosphate have been performed with a view to answering the question posed in the title. The difference between the chemical potential of a normal model of benzene and one with no charges was found to depend on the solvent but is at least 4 kB T . This difference is sufficient to account for the observed solubility differences. There are substantial changes in the local structure around benzene with and without charges. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction The alkylimidazolium liquids have been proposed as potential green solvents for a variety of industrial organic reactions. As they have vanishingly small vapour pressure, these solvents have the advantage that there is no pollution from their vapours and, provided that they can be satisfactorily recycled and the products easily extracted, there is little problem with waste. Moreover they are desirable solvents for a number of reactions,often either enhancing rates or improving selectivities [1–3]. Atomistic simulation has been *
Corresponding author. Fax: +442890241958. E-mail address: [email protected] (R.M. LyndenBell).
used to aid our understanding of solvation and allows one to interpret changes in solvation thermodynamics in terms of the local structure around the solute and solute–solvent and solvent–solvent interactions [4,5]. One general observation about solubilities in ionic liquids is that aromatic compounds are more soluble than aliphatic compounds of a similar size [6,7]. The existence of p electrons in orbitals above and below an aromatic ring results in a much stronger electrostatic field around an aromatic molecule compared to a saturated aliphatic molecule. In general, alkanes and alkyl side chains give very small electrostatic fields. Benzene, on the other hand, has a significant quadrupole moment of about an order of magnitude greater than that for cyclohexane [8]. Another difference is that benzene is more polarisable than cyclohexane.
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00703-6
86
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
Both these differences lead to an enhanced stabilisation of the aromatic solute in an ionic liquid. In this Letter, we show that the difference in the average electrostatic fields is sufficient to explain the difference in solubility of aromatic and aliphatic compounds; any effects of the fluctuations in the electronic structure of the aromatic system due to local fields will just exacerbate the difference. In simulations one can use models which do not correspond to a real physical situation but which allow one to isolate a particular part of an interaction in an unambiguous way. Thus, in order to isolate the electrostatic contribution to the different behaviour of aromatic and aliphatic compounds we calculate the difference in chemical potentials between a model of benzene with partial charges on the carbon and hydrogen sites which reproduces the experimental quadrupole moment and a model of Ôuncharged-benzeneÕ that has no charges on the atomic sites, but is otherwise identical to the charged model. The latter model can be said to approximate the electrostatics of an aliphatic compound of the same size as benzene. We find that the effect of turning off the charges increases the chemical potential in solution by an amount which is quite sufficient to explain the differences in solubility. We have also investigated the local liquid structure around both normal and uncharged benzene and find that the charges on the benzene induce strong local charge ordering which is propagated some distance into the liquid.
2. Technical details The models for the molecules of the ionic liquid þ were described in our earlier work [9], the ½dmim cation being treated as a rigid ten-site body with united methyl groups. The intermolecular potential consists of Buckingham-type interactions between atomic sites and Coulomb interactions between the partial charges on these sites. Likewise, the Cl ion has a single site and a charge of e and the ½PF6 anion is modelled as a rigid body with seven sites each containing partial charges and short-range Buckingham potentials. In a few calculations the methyl groups were modelled with four sites, so that explicit effects of
the methyl hydrogen atoms were included. The site–site Buckingham terms have the form Vij ¼ ðAii Ajj Þ1=2 expððBii þ Bjj Þrij =2Þ ðCii Cjj Þ
1=2
=rij6 ;
ð1Þ
and values of the parameters are given in Table 1. Benzene was modelled with the 12-site model proposed by Williams and Starr [10] which was recommended in a review of models by Smith and Jaffe [11]. The parameters are given in Table 1. The quadrupole moment of this model is )9 DA (30 1040 cm2 ), which compares with experimental and calculated values ranging from )8.7 to [8]. The hexadecapole moment is 1:8 )9.9 DA 1058 cm4 , which has the correct sign, but is lower than the calculated value [8] (2:5 1058 cm4 ). Classical molecular dynamics simulations were performed with a modified version of the program DL_POLY [12] in a NVT-ensemble at 400 K (127 °C) using a Berendsen thermostat and cubic periodic boundary conditions. The simulation box contained 191 formula units of [dmim]Cl or [dmim]½PF6 together with one solute molecule. The long range electrostatic interactions were computed by the Ewald summation. The timestep used was 2 fs. Calculations were performed for four types of system, benzene in [dmim]Cl, benzene in [dmim]½PF6 and uncharged benzene in the two types of ionic liquid. Three-dimensional probability distribution functions for the cations and anions relative to a benzene molecule were constructed by averaging over configurations from the simulation. These were expressed as a sum over products of spherical harmonic functions YLM and functions of distance gLM ðrÞ. As benzene is nearly cylindrically symmetrical, two-dimensional plots of the functions with M ¼ 0 were plotted as a function of axes in the plane of the benzene ring and perpendicular to it. In the figures displayed in this Letter, the expansion was carried out to L ¼ 8. The difference in chemical potential of charged and uncharged benzene in solution was measured using thermodynamic integration over a number of intermediate states with scaled charges. If q is the final charge on each proton with q on the carbon sites, then the integration path is over
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
87
Table 1 Intermolecular Buckingham site–site parameters Aii (kJ/mol)
B1 ii ) (A
Cii 6 mol1 ) (kJ A
q/e
Benzene C H
367 496 11684.9
0.27778 0.26738
2415.8 136.1
)0.15 +0.15
½dmimþ N C2 C4 ,C5 H2 H4 ,H5 Me(united) C(Me) H(Me)
254 525 369 737 369 737 11 971 11 971 241 473 369 737 11 971
0.264550 0.277778 0.277778 0.267380 0.267380 0.344520 0.277778 0.267380
1378.4 2439.8 2439.8 136.4 136.4 10 303 2439.8 136.4
)0.267 0.407 0.105 0.097 0.094 0.316 0.124 0.064
Cl and ½PF6 Cl P F
924 653 0.0 363 725
0.284900 – 0.240385
7740.3 3255.0 844.
1.0 0.74 )0.29
Atom
solute molecules with site charges kq and kq, respectively. The rate of change of the free energy difference with k is given by [13,14] oF oH ¼ : ð2Þ ok ok k This derivative is just proportional to the Coulomb part of the solute–solvent interaction energy EC in a simulation with a fixed value of k, oF hEC ik ¼ : ð3Þ ok k This quantity was evaluated in separate 90 ps simulations with partial charges scaled by k ¼ 0:25, 0.5, 0.75 and 1.0. The derivative at k ¼ 0 is taken to be zero as the Coulomb energy is expected to decrease for both positive and negative charges and hence to have zero slope at the origin (k ¼ 0). The free energy change, which is equal to the difference in chemical potentials of the two solutes, was determined from the values of oF =ok by integration using SimpsonÕs rule. 3. Local structure and energetics There is a good deal of local order of the ionic liquid around the benzene molecule. This is
shown in Fig. 1, which is a cross-section of the probability distribution around a benzene molecule in dilute solution in dimethylimidazolium chloride. Regions with an excess of cations are shown in shades of orange, while regions with an excess of anions are shown in shades of blue. The most prominent features in the immediate vicinity of the benzene are an excess of cations in the polar regions above and below the ring and an excess of anions around the equator of the benzene. The interaction energies shown in the first line of Table 2 demonstrate that the solute– solvent interaction with the chloride ion is much stronger than that with the [dmim] cation and that this interaction is dominated by the electrostatic terms. The electron distribution in the benzene molecule gives a net positive charge around its equator and a region of negative charge above and below the molecule. Thus the anions favour the equatorial region where they experience a strong attractive Coulomb force. Although the net interaction of the cations with the benzene molecule is favourable, it is small and the Coulomb contribution to the interaction is repulsive. We interpret the preference of the cations for the polar regions as due to their interaction with the anions in the equatorial plane
88
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
Fig. 1. Cross-section of the three-dimensional probability distributions around benzene in [dmim][Cl]. The axis of the benzene molecule lies in the vertical direction and the plane of the molecule lies in the horizontal direction, perpendicular to the field of view. The difference in distributions of the cations and anions is shown; regions in shades of blue are more likely to contain anions, while regions in shades of orange tend to contain cations. The scale is in multiples of the average concentration of cations (or anions) in the solution.
Fig. 2. Cross-section of the three-dimensional probability distributions around uncharged ÔbenzeneÕ in [dmim][Cl]. The difference in distributions of the cations and anions is shown; regions in shades of blue are more likely to contain anions, while regions in shades of orange tend to contain cations. The orientation and scales are the same as in the figure. Note that the differences are much less than in the simulations of benzene (Fig. 1).
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
89
Table 2 Solute–solvent interaction energies in kJ per mole of solute Solvent
Solute
Cation E
NC
Anion E
C
E
tot
ENC
EC
Etot
[u-dmim][Cl]
Benzene Uncharged benzene
)49 )51
+41 0
)8 )51
)6 )11
)67 0
)73 )11
[u-dmim]½PF6
Benzene Uncharged benzene
)35 )34
+17 0
)18 )34
)14 )18
)43 0
)56 )18
[e-dmim]½PF6
Benzene Uncharged benzene
)37 )38
+20 0
)17 )38
)18 )34
)41 0
)59 )34
The dimethylimidazolium cations are modelled with either united methyl groups ([u–dmim]) or explicit methyl groups [e-dmim]. The total interaction energy Etot is divided into contributions from the non-Coulombic part ENC and the Coulombic energy EC .
rather than to their direct interaction with the benzene molecule. The pattern of probabilities further from the benzene shows alternation of cation and anion preferences, and hence a charge oscillation which persists to quite a long distance in the axial direction perpendicular to the plane of the benzene. The importance of the electrostatic interaction between the benzene and the solvent is reinforced by calculations of a hypothetical Ôuncharged benzeneÕ. Fig. 2 shows that there is much less perturbation of the distribution of solvent species around the molecule. What effects there are, are largely geometrical in origin and lead to a much lower degree of charge alternation along the axial direction. The contributions to the solvent–solute interactions are shown in the second line of Table 2, whence it can be seen that the non-Coulombic interactions are similar for both charged and uncharged solutes. However the Coulomb contributions to the energies are large and differ in sign between anions and cations. It is this difference which accounts for the difference in behaviour of the charged and uncharged solutes. The pattern of energies and three-dimensional distributions are qualitatively similar when the chloride ion is replaced by ½PF6 . This is shown in Table 2 which also gives the results from simulaþ tions of a more sophisticated model of ½dmim with the protons on the methyl groups included explicitly. The 2–3 kJ/mol differences between this model and the cheaper model with united methyl groups are similar to the uncertainty in the energies.
4. Free energy differences between charged and uncharged models The differences of standard chemical potentials of normal and uncharged benzene in the two ionic liquids were found to be loq loq¼0 ¼ 22 2 kJ=mol in ½dmim½Cl;
ð4Þ
loq loq¼0 ¼ 12 2 kJ=mol in ½dmim½PF6 :
ð5Þ
At 400 K the value of kT is 3.6 kJ/mol, so that the stabilisation of normal benzene compared to the uncharged benzene is high in both cases. For example the ratio of the vapour pressures in dilute solutions at the same concentration is given by pq¼0 =pq ¼ expð½lq¼0 lq =kT Þ, which gives a difference of a factor of 30 for uncharged and normal benzene dissolved in [dmim]½PF6 and a factor of 450 for uncharged and normal benzene dissolved in [dmim][Cl]. It should be noted that, as these calculations do not give the absolute values of the chemical potentials, it is not possible to estimate the relative solubility of benzene in [dmim]½PF6 and [dmim] [Cl]. Although the direct interaction of benzene and [dmim][Cl] is more negative than for [dmim]½PF6 , the solvent vaporisation energy is also greater in the former case, so that the solvent rearrangement energy is likely to be greater. Experimentally it is found that benzene is much less soluble in [dmim][Cl] than in [dmim]½PF6 [15] suggesting that the solvation energy is more negative in the latter case.
90
C.G. Hanke et al. / Chemical Physics Letters 374 (2003) 85–90
5. Discussion and conclusions We conclude that local electrostatic interactions between solutes and the ionic species of the solvent are very important in determining both solute chemical potentials and local liquid structure in ionic liquids. These calculations provide at least a partial answer to the question posed in the title. Alkanes, with their saturated carbon–carbon and carbon–hydrogen bonds, give rise to very small electrostatic fields, which are normally taken to be zero. Thus the uncharged model of benzene is essentially a model for a generic aliphatic solute. Aromatic compounds with electron density above and below the plane of the ring give quadrupole and higher electrostatic multipole moments. This is modelled by partial charges in the Ônormal modelÕ of benzene. The large decrease in the chemical potential when the charges are turned on shows that the increased solubility of aromatic compounds compared to aliphatic compounds can be explained by the local electrostatic solute–solvent interactions. The models used do not allow for fluctuations in the solute electrostatics. As fluctuations only occur if the result is a lowering of the free energy of the system, inclusion of fluctuations would result in increased stabilisation of benzene in ionic liquids. As aliphatic molecules are less polarisable, the effect of fluctuations would be less. Thus fluctuations enhance the relative stabilisation of aromatic compounds as compared to aliphatic compounds. The local structure shown in the three-dimensional probability functions confirms the importance of the electrostatic interactions between both the solute and solvent and between the ionic species in the solvent. The solute perturbs the local structure in its immediate vicinity, but the ion–ion interactions propagate this disturbance to greater distances. The importance of local electrostatic interactions also explains one of the apparent anomalies
of the solubility of gases in ionic liquids. Carbon monoxide is much less soluble than carbon dioxide in ionic liquids [16]. This can readily be explained in terms of the small dipole and quadrupole moments of CO and the larger quadrupole moment of CO2 . Acknowledgements We are grateful to EPSRC for funding through Grant GR/M/72401, IASTE for a summer studentship (A.J.) and the School of Chemical Sciences, UNSW for travel funds (J.B.H.). References [1] P. Wasserscheid, W. Keim, Angew. Chem. 39 (2000) 3772. [2] P. Wasserscheid, T. Welton (Eds.), Ionic Liquids in Synthesis, Wiley–VCH, New York, 2003. [3] T. Welton, Chem. Rev. 99 (1999) 2071. [4] C.G. Hanke, N.A. Atamas, R.M. Lynden-Bell, Green Chem. 4 (2002) 107. [5] R.M. Lynden-Bell, N.A. Atamas, A. Vasilyuk, C.G. Hanke, Mol. Phys. 100 (2002) 3225. [6] K.R. Seddon, A. Stark, M.J. Torres, Pure Appl. Chem. 72 (2000) 2275. [7] L.A. Blanchard, J. Brennecke, J. Ind. Eng. Chem. Res. 40 (2001) 287. [8] C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids I, Clarendon Press, Oxford, 1984. [9] C.G. Hanke, S.L. Price, R.M. Lynden-Bell, Mol. Phys. 99 (2001) 801. [10] D.E. Williams, T.L. Starr, Comput. Chem. 1 (1977) 173. [11] D.S. Smith, R.L. Jaffe, J. Phys. Chem. 100 (1996) 9624. [12] W. Smith et al., Available from