pubs.acs.org/JPCL
Unraveling Dynamical Heterogeneity in the Ionic Liquid 1-Butyl-3-methylimidazolium Chloride S ergio M. Urahata and Mauro C. C. Ribeiro* Laborat orio de Espectroscopia Molecular Instituto de Química, Universidade de S~ ao Paulo CP 26077, CEP 05513-970, S~ ao Paulo, SP, Brazil
ABSTRACT Heterogeneous dynamics within a time range of nanoseconds was investigated by molecular dynamics (MD) simulations of 1-butyl-3-methylimidazolium chloride ([bmim]Cl). After identifying groups of fast and slow ions, it was shown that the separation between the location of the center of mass and the center of charge of cations, dCMCC, is a signature of such difference in ionic mobility. The distance dCMCC can be used as a signature because it relaxes in the time window of the dynamical heterogeneity. The relationship between the parameter dCMCC and conformations of the side alkyl chain in [bmim] is discussed. Since the relatively slow relaxation of dCMCC is a consequence of coexisting polar and nonpolar domains in the bulk, the MD simulations reveal a subtle interplay between structural and dynamical heterogeneity in ionic liquids. SECTION Statistical Mechanics, Thermodynamics, Medium Effects
D
ynamical heterogeneity in supercooled liquids results from coexisting particles with mobility much above and much below the average mobility.1-3 Interest in studying dynamical heterogeneity is justified by possible connections to other well-known issues in the vast phenomenology of glass transition. For instance, decoupling between diffusion and viscosity, observed as the failure of the StokesEinstein-Debye relation, can be understood on the basis that mobile particles contribute to diffusion, whereas slow particles contribute to structural relaxation. The nonexponential decay of relaxation functions in supercooled liquids can be also the consequence of a distribution of relaxation times due to heterogeneity. Molecular dynamics (MD) simulation has become a fundamental tool to characterize dynamical heterogeneity, in particular to reveal the interplay between local equilibrium structure and dynamics. Most of the computer simulations concerned simple models such as Lennard-Jones atomic systems, and the MD simulations indicated that mobile particles might arrange in cluster whose collective motion follows a string-like pattern.1-3 The glass-forming liquids focused in this work are roomtemperature molten salts, the so-called ionic liquids.4,5 The low melting temperature of these systems results from the presence of large asymmetric organic ions that reduce the strong Coulomb interactions and also preclude packing in a crystalline array. MD simulations have been instrumental in revealing the role played by the chemical structure of ionic species on equilibrium structure and dynamics of ionic liquids. In particular, the occurrence of spatial heterogeneity in ionic liquids is now well established.6-9 Aggregation of the side alkyl chains has been found in derivatives of imidazolium cations, so that these materials are heterogeneous media on a nanometer scale, where polar domains due to the
r 2010 American Chemical Society
imidazolium ring and anions, and nonpolar domains due to the alkyl chains, coexist within the bulk of ionic liquids. The occurrence of nanoscale heterogeneity in ionic liquids based on imidazolium cations with relatively short alkyl chains has been recently corroborated by X-ray diffraction and neutron scattering spectroscopy.6-9 This structural heterogeneity implies fast conformational motions of alkyl chains within nonpolar domains of the ionic liquid. However, this is a local dynamics that might exist even with the arrest of structural relaxation, and it is not the true heterogeneous dynamics in which groups of fast and slow particles coexist. Therefore, beside the physical picture of coexisting polar/nonpolar domains in ionic liquids, it would be interesting to investigate whether there is any connection between such structural heterogeneity and the dynamical heterogeneity. Despite many MD simulations of ionic liquids reported in the literature, few works have discussed heterogeneous dynamics in ionic liquids. Del P opolo and Voth10 showed the presence of clustering of mobile and nonmobile groups of ions in 1-ethyl-3-methylimidazolium nitrate ([emim][NO3]). Habasaki and Ngai11 provided details on the mechanism involved in motions within regions of mobile particles in [emim][NO3], in particular, mutual diffusion of anions and cations at high temperatures, and the interception of paths that slows the dynamics with decreasing temperature. However, contrary to ref 10, no structural signature of dynamical heterogeneity has been given in the MD simulations of ref 11. Hu and Margulis12 showed that the local
Received Date: March 29, 2010 Accepted Date: May 13, 2010 Published on Web Date: May 18, 2010
1738
DOI: 10.1021/jz100411w |J. Phys. Chem. Lett. 2010, 1, 1738–1742
pubs.acs.org/JPCL
Figure 2. Mean square displacement of cations in [bmim]Cl simulated at different temperatures: 1000 K (red), 500 K (green), 400 K (blue), and 300 K (black). The MSDs for the 5% mobile and 5% nonmobile cations are shown by full and dashed lines, respectively, at each temperature. The inset shows the same data of the main figure for 300 K in a linear scale, together with MSD calculated considering all of [bmim] cations of the simulated system (red line).
Figure 1. Schematic structure of the 1-butyl-3-methylimidazolium cation ([bmim]). (a) The united atom model for [bmim] with the atom numbering used in the MD simulations. (b) Two different conformations resulting from turning around the N3-C7-C8-C9 dihedral angle. (c) Two different conformations resulting from turning around the C2-N3-C7-C8 dihedral angle.
order to simulate a relatively large system containing 918 cations and 918 anions, totalling 10098 atomic sites. The system was simulated at different temperatures: 300, 400, 500, 700, and 1000 K. An equilibration period of ca. 0.5 ns, allowing for average pressure of 1.0 bar, was followed by typical production runs of 9.0 ns in an NVE ensemble. The velocity Verlet algorithm was used to integrate the equation of motions with a time step of 3.0 fs.14 Instead of using the usual Ewald sum method, long-range Coulomb interactions were handled with the Wolf method,15,16 which allows for considerable saving of computer time. Further computational details can be found in our previous publication.6 The time window for heterogeneous dynamics is usually defined by the non-Gaussian parameter, R(t)=(3/5)Æ|Δr(t)|4æ/ Æ|Δr(t)|2æ - 1, where Δr(t) is the displacement of a given ion within the time interval from 0 to t.1-3,10-12 MD simulations of [emim][NO3] and [bmim][PF6] have shown that R(t) at T = 300 K reaches its maximum value at t = 1.0 ns,10-12 but a relatively high value of R(t) in [emim][NO3] is still observed after several nanoseconds of simulation. Therefore, we used here the time window of the whole MD run (9.0 ns) to identify the “fast” and the “slow” ions in [bmim]Cl on the basis of the mean-square displacement, MSD. Figure 2 shows the MSD for those 5% more mobile and 5% less mobile cations after the average mobility has been calculated by MD simulation of [bmim]Cl at each temperature. There is a clear separation of fast and slow cations as temperature decreases from 1000 to 300 K. Once the groups of fast and slow ions have been identified, partial radial distribution functions gRβ(r) indicated the occurrence of clustering of mobile and nonmobile ions (not shown), as also observed in previous MD simulations of [emim][NO3] and [bmim][PF6].10,12 Clustering of mobile cations in [bmim]Cl at 400 K is clearly observed in the top panel of Figure 3, where a snapshot of the simulation box is given with mobile cations drawn by red color. If the same
environments in 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) persist longer than the lifetime of fluorescence probes, but the mechanism by which polar/ nonpolar domains determine dynamical heterogeneity was not clear. In this work, we identify the difference in chemical structure between fast and slow cations in MD simulations of 1-butyl-3-methylimidazolium chloride ([bmim]Cl). The evidence is based on recent MD simulations performed by Spohr and Patey13 for simple models of ionic liquids. Bearing in mind the fact that charge is not located in the center of mass for typical cations of ionic liquids, different spherical models were simulated in which the positive charge is displaced from the center of mass.13 It has been found that diffusion and conductivity increases, and viscosity decreases, as the charge is put apart from the cation center of mass. If the charge is too distant from the center of mass, then the trend is reversed because strong directional ion pairing dominates. In this work, the conclusions drawn from the simple models of ref 13 have been used to characterize mobile cations in [bmim]Cl by the separation between the center of mass and the geometric center of the imidazolium ring. Therefore, the MD simulations indicate a relationship between dynamical heterogeneity and conformations of butyl chains within the nonpolar domains of ionic liquids. The MD simulations were performed with a united atom model, in which hydrogen atoms of the [bmim] cation are not explicitly considered.6 Figure 1 shows a schematic representation of the [bmim] cation with atom numbering. The potential model of [bmim] includes inter- and intramolecular contributions, whereas the chloride anion is a single LennardJonnes site with formal -1 charge. All of the potential energy function parameters can be found in our previous publication.6 We used a 35 35 200 Å3 simulation box in
r 2010 American Chemical Society
1739
DOI: 10.1021/jz100411w |J. Phys. Chem. Lett. 2010, 1, 1738–1742
pubs.acs.org/JPCL
Figure 5. Time correlation functions of dCMCC for [bmim]Cl simulated at different temperatures.
Figure 3. A snapshot of an arbitrary configuration of [bmim]Cl simulated at 400 K. The cations that have been classified as more mobile are shown by red color in the top panel. In the bottom panel, the more mobile anions are shown by green color.
distance dCMCC between the center of mass of [bmim] and the geometrical center of the imidazolium ring, which has been used as an estimate for the center of the charge of the cations. The distribution of dCMCC has been calculated for both the groups of fast and slow cations for [bmim]Cl at different temperatures. Figure 4 shows that the distributions of dCMCC for fast and slow cations are essentially the same in the high temperature limit when heterogeneous dynamics is essentially absent. However, when the temperature is reduced, the distribution of dCMCC for fast cations shifts to smaller values of dCMCC relative to slow cations. The inset of Figure 4 compares the distribution of dCMCC for fast, slow, and for a group of ca. 45 cations that were randomly picked from the simulation box. Although the difference of dCMCC distributions is small between fast and slow cations, whenever we randomly picked the cations, we obtained such distribution that is clearly distinct from the fast or slow cations distributions. Therefore, fast and slow [bmim] cations can be distinguished on the basis of the distributions shown in Figure 4, so that the distance dCMCC provides a structural signature of heterogeneous dynamics in the simulated system. Since dynamical heterogeneity in [bmim]Cl has been defined within a few nanoseconds of simulation, the relaxation of dCMCC should be comparable with such a time window if dCMCC is indeed a criteria for heterogeneous dynamics. Thus, time correlation functions CCMCC(t)=ÆdCMCC(t)dCMCC(0)æ have been calculated for [bmim]Cl simulated at each temperature. Figure 5 shows that CCMCC(t) exhibits a slow exponential stretched decay, exp[-(t/τ)β], which is the typical behavior of many time correlation functions of viscous liquids. Therefore, the relatively long-time relaxation of CCMCC(t) indicates that it is reasonable to discern nanosecond heterogeneous dynamics in [bmim]Cl on the basis of dCMCC. One expects that the distribution of dCMCC values should be related to conformations of the butyl chain. However, if the conformational motion of the butyl chain is very fast, the slow decay of CCMCC(t) shown in Figure 5 is not evident at first glance. Thus, the relative slow relaxation of dCMCC and the fast motion of the butyl chain remains to be conciliated. This apparent contradiction is eliminated by the calculation of time correlation functions of different dihedral angles associated with the [bmim] cation, Cdih(t) = Æψ(t)ψ(0)æ. Figure 6 compares Cdih(t) for the dihedral angle formed by the carbon atoms of the butyl chain (C7-C8-C9-C10; see atom numbering in
Figure 4. Distribution of the distance between the center of mass of [bmim] cation and the geometrical center of the imidazolium ring, dCMCC, obtained for [bmim]Cl simulated at different temperatures. The red and blue lines show the distributions of dCMCC for fast and slow cations, respectively. The inset in the top panel compares the distributions of fast and slow cations of the main figure with a distribution of dCMCC obtained by randomly picked cations of [bmim]Cl at 300 K (black line).
procedure of selecting fast and slow ions is performed for anions, the bottom panel of Figure 3 shows the clustering of mobile anions by green color. It is clear from Figure 3 that fast cations and anions are close together. This finding is in line with experimental evidence that ionic associations imply correlated diffusion of anions and cations, since the actual conductivity of an ionic liquid is lower than the conductivity calculated by using diffusion coefficients in the NernstEinstein equation.17 In fact, mutual diffusion of anions and cations in mobile regions has been already shown,10-12 but no clear signature of some difference in nearest neighbor anion-cation interactions is found in gRβ(r) that would indicate the enhancement of ionic mobility. The simple spherical models with different separation between the center of mass and the center of charge of cations, as depicted by Spohr and Patey13 to rationalize the interplay between structure and transport coefficients in ionic liquids, suggest a way to search for a structural difference between fast and slow cations in [bmim]Cl. We calculated the
r 2010 American Chemical Society
1740
DOI: 10.1021/jz100411w |J. Phys. Chem. Lett. 2010, 1, 1738–1742
pubs.acs.org/JPCL
(see Figure 1). Figure 7 shows maps of probability of these dihedral angles for those cations that have been previously identified as fast and slow, and for comparison purposes, the corresponding data for a randomly picked group of cations. The maps shown in Figure 7 are clearly distinct for fast and slow cations, where significant orange and red areas reveal sharper distribution of angles for slow cations, which probe larger values of the N3-C7-C8-C9 dihedral angle. However, it should be stressed that the selection of cations only on the basis of conformation does not necessarily identify fast and slow cations. We separated cations in groups with distinct range of the N3-C7-C8-C9 dihedral angle, 80 < ΨNCCC < 110 and 110< ΨNCCC
