THE JOURNAL OF CHEMICAL PHYSICS 124, 184902 共2006兲
Molecular dynamics simulation of polymer electrolytes based on poly„ethylene oxide… and ionic liquids. I. Structural properties Luciano T. Costa and Mauro C. C. Ribeiroa兲 Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, Codigo Postal 26077, CEP 05513-970 São Paulo, Brazil
共Received 30 January 2006; accepted 13 March 2006; published online 8 May 2006兲 Molecular dynamics 共MD兲 simulations have been performed for prototype models of polymer electrolytes in which the salt is an ionic liquid based on 1-alkyl-3-methylimidazolium cations and the polymer is poly共ethylene oxide兲, PEO. The MD simulations were performed by combining the previously proposed models for pure ionic liquids and polymer electrolytes containing simple inorganic ions. A systematic investigation of ionic liquid concentration, temperature, and the 1-alkyl- chain length, 关1 , 3-dimethylimidazolium兴PF6, and 关1-butyl-3-methylimidazolium兴PF6, effects on resulting equilibrium structure is provided. It is shown that the ionic liquid is dispersed in the polymeric matrix, but ionic pairs remain in the polymer electrolyte. Imidazolium cations are coordinated by both the anions and the oxygen atoms of PEO chains. Probability density maps of occurrences of nearest neighbors around imidazolium cations give a detailed physical picture of the environment experienced by cations. Conformational changes on PEO chains upon addition of the ionic liquid are identified. The equilibrium structure of simulated systems is also analyzed in reciprocal space by using the static structure factor, S共k兲. Calculated S共k兲 display a low wave-vector peak, indicating that spatial correlation in an extended-range order prevail in the ionic liquid polymer electrolytes. Long-range correlations are assigned to nonuniform distribution of ionic species within the simulation box. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2192777兴 I. INTRODUCTION
Poly共ethylene oxide兲, PEO, is one of the most investigated polymer for solid-state electrolytes in technology of lithium ion batteries.1,2 Ionic solid solutions can be obtained by dissolving both the polymer and the salt in a given solvent, where the polymer electrolyte is recovered after solvent evaporation. Polymer electrolytes based on PEO have been reported with many different salts, either simple inorganic salts, LiI, LiPF6, LiBF4, etc., or more complex organic salts, for instance, lithium trifluoromethanesulfonate, LiCF3SO3 共lithium triflate兲. The interesting feature of polyethers for building a polymer electrolyte is that the oxygen atoms are able to solvate ions such as Li+ cations, and simultaneously local flexibility of the polymeric chain allows for Li+ mobility and ionic conductivity. Such a microscopic picture of structure and dynamics of polymer electrolytes has become available from a combined use of several spectroscopic techniques.1–9 In addition, computer simulations play a fundamental role on our present understanding of the interplay between structure and dynamics in polymer electrolytes.10–15 Salts with very low melting points have been synthesized by combining many different asymmetric large organic ions.16–18 These species display charge delocalization and avoid efficient crystal packing, thus lowering melting or glass transition temperatures, Tm and Tg, respectively, to as low as ⬃−90 ° C. Such room temperature molten salts are a兲
Author to whom correspondence should be addressed. Electronic mail:
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now simply called ionic liquids, a denomination that has been devoted to purely ionic systems with Tm or Tg below ca. +100 ° C. Certainly the most investigated ionic liquids are based on 1,3-dialkylimidazolium cations 共the schematic structure of 1-alkyl-3-methylimidazolium cations is depicted in Fig. 1兲 with different anions, Cl−, BF−4 , PF−6 , CF3SO−3 , etc. The most important application of ionic liquids is alternative solvents in organic chemistry synthesis, where the nonvolatile characteristics make them more environmental friendly than usual organic solvents. Ionic liquids have been also proposed as electrolyte for batteries and electrodepositions.19–22 Proper to technological interest, ionic liquids have been the subject of many spectroscopic studies, for instance, by x ray,23 NMR,24 vibrational 共Raman and infrared兲,25,26 electronic,27 and neutron scattering spectroscopy.28,29 In the last five years, computer simulation is playing an important role in revealing structure and dynamics of ionic liquids.30–35 Polymer electrolytes containing ionic liquids have been synthesized and characterized mainly as concerned ionic conductivity and electrochemical stability. Adding ionic liquids changes the working temperature and enhances ionic
FIG. 1. Schematic structure of the 1-butyl-3-methylimidazolium cation with atom numbering. In this work, united atom models were used, in which hydrogen atoms are not explicitly considered.
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conductivity of polymer electrolytes.36 For instance, ionic liquids based on pyrrolidinium cations and triflate anion was added on PEO based polymer electrolytes.37 In a series of polymer electrolytes made of PEO, poly共acrylonitrile兲 共PAN兲, and poly共vinylalcohol兲 共PVA兲, with imidazolium ionic liquids, it has been reported conductivity as high as 15 mS cm−1 at room temperature, and electrochemical window of ca. 3 V.38 Improvement in conductivity of ionic liquid-polymer gels has been achieved by incorporating propylene carbonate.39 Composite of poly共acrylonitrile-cobutadiene兲 rubber with imidazolium cation ionic liquids results in transparent films, whose conductivity increases with further addition of a lithium salt.40 A very recent small angle neutron scattering investigation of PEO diluted in 关1-butyl -3-methylimidazolium兴BF4 indicated the occurrence of individual nonentangled PEO chains in random coil conformations.41 In previous publications, we reported molecular dynamics 共MD兲 simulations of polymer electrolytes based on PEO with a simple inorganic salt, namely, LiClO4,42 and pure ionic liquids based on 1-alkyl-3-methylimidazolium cations.43–45 In the case of PEO/ LiClO4, we revealed temperature and salt concentration effects on structural and dynamical properties of the polymer electrolyte.42 In the case of ionic liquids, we revealed anion size and alkyl chain length 共1-metyl-, 1-ethyl-, 1-butyl-, and 1-octyl-兲 effects on structure43 and dynamics44,45 of ionic liquids at fixed temperature. In the present study, we report MD simulations of PEO polymer electrolytes in which the salt is an ionic liquid of 1-alkyl-3-methylimidazolium cations. We already showed that the assumed united atom models, i.e., hydrogen atoms not explicitly considered, for PEO/ LiClO4 and pure ionic liquids are reasonable ones as concerned structure and dynamics of the simulated systems.42–45 Thus, the models are now combined for building a polymer electrolyte/ionic liquid prototype model. This work is a systematic study as we change salt concentration, temperature, and the alkyl chain length of the ionic liquid, that is 关1 , 3-dimethylimidazolium兴PF6 and 关1-butyl-3 -methylimidazolium兴PF6. Equilibrium structure of simulated ionic liquid polymer electrolytes is investigated in both the real space by the radial distribution function, g共r兲, and in the reciprocal space by the static structure factor, S共k兲. The analysis of dynamical properties of ionic liquid polymer electrolytes will be shown in a future publication.
II. SIMULATION DETAILS
Potential energy functions used in MD simulations of PEO and ionic liquids were already described.42,43 Briefly, the potential energy function includes intermolecular Lennard-Jones and Coulombic interactions, and intramolecular interactions including bond stretching, r, angle bending, , and torsion of dihedral angles, :
TABLE I. Lennard-Jones parameters and partial charges for 1-alkyl-3methylimidazolium cations, PEO, and PF−6 anion 共In this work, it is used a united atom model, in which hydrogen atoms are not explicitly considered.兲 Units: in 10−20 J, in angstrom, q in electrons. 1-methyl-
N1 N2 C3 C4 C5 C6 C7 C8 C9 C10
1-butyl-
q
q
0.710 0.710 0.443 0.443 0.443 0.865 0.865 ¯ ¯ ¯
3.250 3.250 3.880 3.880 3.880 3.775 3.775 ¯ ¯ ¯
−0.390 −0.390 0.605 0.241 0.241 0.355 0.355 ¯ ¯ ¯
0.710 0.710 0.443 0.443 0.443 0.865 0.493 0.493 0.326
3.250 3.250 3.880 3.880 3.880 3.775 3.905 3.905 3.905 3.905
−0.400 −0.394 0.599 0.252 0.224 0.345 0.267 0.033 0.037 0.036
PEO carbon atom CH2 CH3 q
0.138 3.620 0.174
Vtotal =
PEO oxygen atom
PF−6
0.096 3.030 −0.348
1.670 4.720 −1.000
0.173 3.700 0.000
冎 兺 再 冋冉 冊 冉 冊 册 f 4ij
i,j i⬍j
+ +
ij rij
12
−
ij rij
6
+
q iq j rij
kb共r − req兲2 + 兺 k共 − eq兲2 兺 bonds angles
兺
k关I + cos共n − ␦兲兴,
共1兲
dihedrals
where rij is the distance between atoms i and j, which carry partial charges qi and q j, req and eq are equilibrium bond length and angles, respectively. It should be noted that previous MD simulations of PEO/ LiClO4 used a Born-Mayer instead of a Lennard-Jones function for the short-range terms of the potential energy function.42 Thus, we fit the LennardJones potential to the previous Born-Mayer potential for PEO, and for completeness Table I gives the parameters of intermolecular terms of the potential energy function used in this work. We used united atom models, i.e., hydrogen atoms of the PEO chain and 1,3-dialkylimidazolium cations are not explicitly considered. We already showed43 that united atom models give anion-cation interactions similar to the ones obtained with all atom models for ionic liquids, including the directional characteristic features usually assigned to hydrogen bonding between ionic species. Thus, one expects that electrostatic interactions between oxygen atoms of PEO chains and imidazolium cations will be also reasonable reproduced with the present united atom model for ionic liquid polymer electrolytes. Anions PF−6 are also treated as a single unit carrying the full formal −1 charge. Usual combining rules, ij = 共ii jj兲1/2 and ij = 1 / 2共ii + jj兲, are employed for cross term parameters. In order to use the same set of ii, ii, and qi, for the intramolecular Lennard-Jones and Coulombic interactions between atoms separated by at least three bonds within a given molecule, interactions are reduced by a factor
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f = 0.5, whereas f = 1.0 for intermolecular interactions. All of the potential parameters for intramolecular terms can be found in previous publications.42,43 A schematic representation of the chemical structure of 1-butyl-3-methylimidazolium cation is provided in Fig. 1, with atoms numbering for further reference. For brevity of notation, the ionic liquids 关1 , 3-dimethylimidazolium兴PF6 and 关1-butyl-3-methylimidazolium兴PF6 will be designed by 关dmim兴PF6 and 关bmim兴PF6, respectively. For the PEO chains, the model contains 30 chains CH3CH2O共CH2CH2O兲25CH2CH3, that is, a molecular weight of 1174. In the case of PEO/ 关dmim兴PF6, three different concentrations were simulated, containing 100, 50, and 25 ion pairs 关dmim兴+ and PF−6 . In the case of PEO/ 关bmim兴PF6, it was simulated a single concentration containing 30 PEO chains and 100 ion pairs 关bmim兴+ and PF−6 . For brevity of notation, these mixtures will be designed by the ratio between PEO oxygen atoms to imidazolium cations. For instance, these are P共EO兲8-关dmim兴PF6, P共EO兲16 -关dmim兴PF6, and P共EO兲31-关dmim兴PF6, from the most concentrated to the most diluted one. The starting configurations of PEO/ionic liquids were generated with the help of the PACKMOL package.46 This software packs molecules in a cubic box in such a way that the closest distance between particles is greater than a chosen tolerance. After an optimization procedure, the software solves the packing problem at same time avoiding atomic overlaps that would result in excessively large potential energy. By using the PACKMOL package to generated initial configurations of ionic liquids polymer electrolytes, it was needed typically 400 ps for achieving equilibrium values of density and potential energy. We used Berendsen’s barostat and thermostat47 for keeping pressure at 1 bar and temperature at 400 K. This relatively high T was used in order to result in significant ionic displacements. At 400 K, resulting equilibrium density were 1.45, 1.41, and 1.27 gcm−3 for P共EO兲8-关dmim兴PF6, P共EO兲16-关dmim兴PF6, and P共EO兲31 -关dmim兴PF6, respectively. In the case of P共EO兲8 -关bmim兴PF6, it was 1.44 gcm−3. Furthermore, a rather large increase in temperature was performed in additional runs at 500 K, in order to make clear the temperature effect on the simulated systems. Productions runs were 2.0 ns long, performed with fixed box size according to the equilibrium density. During production runs, the Berendsen’s thermostat was kept turned on with a small system-batch coupling parameter, 0.1 ps. Equations of motions were integrated with the velocity Verlet algorithm with time step of 1.0 fs, where bond lengths were constrained with the RATTLE algorithm.48 The Ewald sum method was employed to handle the longrange Coulomb interactions.48
J. Chem. Phys. 124, 184902 共2006兲
FIG. 2. Calculated radial distribution functions, g␣共r兲, of pure 关dmim兴PF6 ionic liquid 共thin lines兲 and P共EO兲8-关dmim兴PF6 共bold lines兲 at 400 K. From top to bottom panel, it is shown the partial g␣共r兲: anion-anion, cationcation, and cation-anion, in which the imidazolium ring atom is the C3 carbon atom 共see Fig. 1兲.
of anions, and vice versa. Thus, we first address here structural changes occurring upon dilution of the ionic liquid in the polymeric matrix. Figure 2 compares anion-anion, cation-cation, and cation-anion g␣共r兲 in pure 关dmim兴PF6 共thin lines兲 and P共EO兲8-关dmim兴PF6 共bold lines兲 at 400 K. There is a remarkable increase of intensity in the first peak of partial gcat-an共r兲 when the ionic liquid is immersed in PEO. Conversely, gcat-cat共r兲 and gan-an共r兲 are smeared out, and small distance peaks in these partial g␣共r兲 in pure 关dmim兴PF6 are no long observed in the polymer electrolyte. The most important conclusion drawn from Fig. 2 is that the ionic liquid was in fact dissolved in the polymeric matrix, as same charged species were put apart in the polymer electrolyte. Simultaneously, ionic pair formation is enhanced in P共EO兲8 -关dmim兴PF6 in comparison with pure 关dmim兴PF6. In line with MD simulations of pure ionic liquids,31–36,43 the closest contact between cations and anions take place by the C3 carbon atom of the imidazolium ring 共see Fig. 1 for atom numbering兲. This is corroborated by partial g␣共r兲 shown in Fig. 3, which also highlights differences between P共EO兲8-关dmim兴PF6 and P共EO兲8-关bmim兴PF6. The 1-butylchain in 关bmim兴+ cations evidently disrupt the symmetry of each side of the imidazolium ring, so that occurrence of anions on the side of the long 1-butyl- chain is less favored, as it is particularly clear in the inset of the bottom panel of
III. RESULTS AND DISCUSSION
Equilibrium structure of ionic liquids containing 1,3dialkylimidazolium cations have been revealed by neutron scattering spectroscopy28,29 and MD simulations.31–36,43 As expected in a molten salt, partial radial distribution functions, g␣共r兲, indicate charge ordering in ionic liquids, i.e., the first neighbor shell around imidazolium cations is made
FIG. 3. Calculated partial g␣共r兲 between anions and carbon atoms of the imidazolium ring 共see atom numbering in Fig. 1兲 in P共EO兲8-关dmim兴PF6 共top panel兲 and P共EO兲8-关bmim兴PF6 共bottom panel兲 at 400 K.
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FIG. 4. Partial g␣共r兲 between the C3 共top panel兲 or C6 共bottom panel兲 carbon atoms of the imidazolium ring with oxygen 共bold lines兲 or carbon 共thin lines兲 atoms of PEO chains in P共EO兲8-关dmim兴PF6 at 400 K.
Fig. 3. In fact, previous MD simulations indicated that ionic liquids containing long alkyl chains, namely, 1-butyl-3methylimidazolium or 1-octyl-3-methylimidazolium cations, develop hydrocarbonlike regions in the bulk of the liquid, where depletion of occurrences of anions is observed.43 The local environment of PEO chains around imidazolium cations in P共EO兲8-关dmim兴PF6 is revealed by partial g␣共r兲 shown in Fig. 4. It is clear that the closest approach between 关dmim兴+ and polymer take place by the oxygen atoms of PEO chains. This finding is analogous with the wellknown ability for ionic solvation provided by oxygen atoms of polyethers in simpler polymer electrolytes that have been intensively investigated by MD simulations.10–15,42 Comparison of top and bottom panels of Fig. 4 indicates that the first peak is much more intense for partial g␣共r兲 including the C6 than the C3 carbon atom of 关dmim兴+ cations. This is exactly the opposite as concern the solvation of 关dmim兴+ cations by anions discussed above 共see Fig. 3兲. Furthermore, when one compares Figs. 3 and 4, first neighbor distance between oxygen atoms of PEO chains and 关dmim兴+ is smaller than corresponding distance between anions and 关dmim兴+. The same is true for 关bmim兴+, as shown in Fig. 5 for P共EO兲8 -关bmim兴PF6. This preferred solvation of cations by oxygen atoms of PEO chains, instead of anions, is consistent with the larger distance shift of gcat-an共r兲 in the polymer electrolyte with respect to the pure ionic liquid result 共see the bottom panel of Fig. 2兲. The top panel of Fig. 5 further illustrates
FIG. 5. The same as Fig. 4, but for P共EO兲8-关bmim兴PF6 at 400 K. The inset shows corresponding partial g␣共r兲 between oxygen 共bold lines兲 or carbon 共thin lines兲 atoms of PEO chains with carbon atoms of the 1-butyl-chain of the 关bmim兴+ cation 共C7 to C10 atoms of Fig. 1兲.
J. Chem. Phys. 124, 184902 共2006兲
FIG. 6. Probability density maps of location of nearest-neighbor anions around the 关dmim兴+ cation in P共EO兲8-关dmim兴PF6. The right panel shows the view above the ring plane, and the left panel shows the view almost on the ring plane. Darker areas indicate regions of high probability of finding an anion around a given cation. See text for further details.
that preferential solvation of 关bmim兴+ by PEO chains occurs by the imidazolium ring, as the inset shows that partial g␣共r兲 between PEO and carbon atoms of the 1-butyl- chain peaks at slight larger distance. Using probability density maps of preferential location of nearest neighbors helps visualizing the local environment around imidazolium cations in the polymer electrolytes. We generated probability density maps of location of both PF−6 anions and oxygen atoms from PEO chains around imidazolium cations. A given pair is considered as nearest neighbor whenever its distance is smaller than the first minimum of the corresponding g␣共r兲. We then assigned high probability when occurrence is higher than 80% of the maximum density of occurrences, low probability when it is smaller than 40% of the maximum, and intermediate probability in between 40% and 80%. Figure 6 shows probability density maps of PF−6 anions around the 关dmim兴+ cation in P共EO兲8-关dmim兴PF6. It is clear that higher probabilities of occurrences for anions are above or below the imidazolium ring plane, and that it is displaced toward the C3 carbon atom. This finding is consistent with positions of the first peak of partial g␣共r兲 shown in top panel of Fig. 3, and it is analogous with previous one obtained by MD simulations of pure ionic liquids.43 Figure 7 shows corresponding maps for location of oxygen atoms of PEO chains around 关dmim兴+ cations. A remarkable characteristic feature of maps shown in Figs. 6 and 7 is that one can discern mutual exclusion of preferred location for anions and oxygen atoms around cations. It is particularly clear from the top view in the right of both the figures that preferential location for anions around 关dmim兴+ is not occupied by oxygen atoms, and vice versa. The physical picture that arises is that ionic pairs are maintained upon dissolution of the ionic liquid into the polymeric matrix, and PEO chains solvate
FIG. 7. The same as Fig. 6, but for oxygen atoms of the PEO chains.
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TABLE II. Population 共%兲 of dihedral angles in gauche conformation 共0 ⬍ = ⬍ = 120° 兲 in ionic liquid polymer electrolytes 共In pure PEO at 400 K, the calculated population of dihedral angles in gauche conformation is 81% and 7% for OCCO and COCC, respectively兲. OCCO
FIG. 8. The same as Fig. 6, but for nearest-neighbor anions around the 关bmim兴+ cation in P共EO兲8-关bmim兴PF6.
cations in remaining sites as to involve the 关dmim兴+ cation. This picture is even more evident in corresponding probability density maps for P共EO兲8-关bmim兴PF6 shown in Figs. 8 and 9. In the case of the 关bmim兴+ cation, the preferential location of anions is displaced towards the C3 carbon atom of the imidazolium ring, and there is a clear depletion of anions within the region occupied by the flexible 1-butylchain 共see Fig. 8兲. This finding was already observed in pure ionic liquids.43 Conversely, Fig. 9 shows a discernable population of oxygen atoms around the 1-butyl- chain of the 关bmim兴+ cation. Thus, the region just around the long alkyl chain of a given 关bmim兴+ cation that is not allowed for anions, is, however, solvated by PEO chains. Most probably, the elevated number of van der Waals interactions is responsible for the observed occurrence of PEO chains around the region occupied by the 1-butyl- chain of the 关bmim兴+ cation. In the case of polymer electrolytes containing PEO and simple inorganic salts, it has been shown that local changes of polymeric chains are needed in order to allow for cation solvation.10–15,42 For instance, MD simulations of PEO/ LiClO4 at 373 K indicated that population of COCC dihedral angles in gauche conformation increases from 14% to 23% when LiClO4 concentration increases from P共EO兲31 -LiClO4 to P共EO兲8-LiClO4.42 This segmental modification occurs because typically five oxygen atoms of PEO chains embrace the relatively small Li+ cation 共for instance, see the snapshot of a MD simulation of PEO/LiI in Fig. 1 of Ref. 50兲. In PEO/ LiClO4 polymer electrolyte, we found on average three oxygen atoms of a PEO chain and two oxygen atoms of ClO−4 anions around a given Li+ cation 共see Fig. 7 in Ref. 42兲. In this work, we use the same definitions for gauche and trans-conformations of dihedral angles , that is, 0 ⬍ = ⬍ = 120° and 120° ⬍ ⬍ = 180°, respectively.42 Table II gives the calculated population of dihedral angles in gauche conformation as a function of ionic liquid concentration and temperature. Concentration effect on the population of OCCO dihedral angles in PEO/ 关dmim兴PF6 is similar to
FIG. 9. The same as Fig. 8, but for oxygen atoms of the PEO chains.
P共EO兲31-关dmim兴PF6 P共EO兲16-关dmim兴PF6 P共EO兲8-关dmim兴PF6 P共EO兲8-关bmim兴PF6
COCC
400 K
500 K
400 K
500 K
83 85 86 83
84 84 84 82
6 7 6 7
8 8 7 7
PEO/ LiClO4 共see Table II in Ref. 42兲. However, in contrast to PEO/ LiClO4, changing ionic liquid concentration has only marginal effect on the population of COCC dihedral angles. Furthermore, the population of COCC dihedral angles in gauche conformation in ionic liquid polymer electrolyte is smaller than previous finding in PEO/ LiClO4. This difference is understood on the basis of a common model for the local structure in polymer electrolytes.1,49 When the PEO chain solvates the small Li+ cation, the nearest neighbor shell around Li+ comprises a sequence of oxygen atoms along the chain.50 The local environment provided by a PEO chain and two anions around a 关bmim兴+ cation is illustrated in Fig. 10 for an arbitrary configuration of the simulated system. In the case of ionic liquid polymer electrolyte, segments COCC are allowed to acquire a more extended trans-conformation because the polymeric chain is embracing a much larger species. The chain dimension of PEO as a whole changes on going from pure PEO to ionic liquid polymer electrolytes. We used two criteria to quantify dimension of PEO chains, the radius of gyration, 具s2典, and the end-to-end distance, 具r2典, 具s2典 =
冓兺 1 N
兩ri − rcm兩2
i
冔
共2兲
and 具r2典 = 具兩rn − ro兩2典,
共3兲
where rcm is the coordinate of the center of mass of a given PEO chain, N is the number of atoms in a chain, ro and rn are the coordinates of the first and the last atoms of the chain, respectively. Table III gives concentration and temperature
FIG. 10. Snapshot of an arbitrary configuration of simulated P共EO兲8 -关bmim兴PF6 showing a PEO chain around a 关bmim兴+ cation. Location of two nearest-neighbor anions is indicated by the large circles. The right panel shows the view above the ring plane, and the left panel shows the view almost on the ring plane.
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TABLE III. Average end-to-end distance, 具r2典1/2, and radius of gyration, 具s2典1/2, in ionic liquid polymer electrolytes at 400 K 共In pure PEO at 400 K, calculated 具r2典1/2 and 具s2典1/2 are, respectively, 25 and 12 Å兲. Corresponding values at 500 K are given in parentheses.
P共EO兲31-关dmim兴PF6 P共EO兲16-关dmim兴PF6 P共EO兲8-关dmim兴PF6 P共EO兲8-关bmim兴PF6
具r2典1/2 共Å兲
具s2典1/2 共Å兲
25.2 共22.2兲 22.8 23.4 共24.2兲 27.1 共31.2兲
9.2 共13.1兲 8.7 8.6 共8.8兲 9.4 共14.2兲
FIG. 12. Total static structure factor, S共k兲, of P共EO兲8-关dmim兴PF6 共bold line兲 and P共EO兲8-关bmim兴PF6 共thin line兲 at 400 K. Inset shows S共k兲 of pure PEO.
limit of g共r兲 at large distance. For instance, in the case of ionic liquids based on 1-alkyl-3-methylimidazolium cations, we found the so-called prepeak in S共k兲, i.e., a peak at k ⬃ 0.5 Å−1, whose intensity increases with increasing length of the 1-alkyl- chain.43 This is the typical manifestation of an intermediate-range order, IRO, which was assigned to the fact that in the bulk of the ionic liquid hydrocarbonlike regions develop, where anions are barely observed. In the case of PEO/ LiClO4 polymer electrolytes, the IRO was interpreted as a nonuniform distribution of ions in the simulation box.42 The Fourier transform relates S共k兲 and g共r兲, but in order to avoid numerical artifacts, we calculated partial S␣共k兲 directly by its definition53
effects on calculated 具s2典1/2 and 具r2典1/2 in ionic liquid polymer electrolytes. Concentration effect seems to superimpose on temperature effect in PEO/ 关dmim兴PF6, as even a rather large increase from 400 to 500 K do not change significantly both the 具s2典1/2 and the 具r2典1/2 in the limit of elevated concentration. At fixed T = 400 K, 具s2典1/2 is only marginally affected by increasing 关dmim兴PF6 concentration in comparison with PEO/ LiClO4 that displayed a more significant variation of 具s2典1/2 with LiClO4 concentration at 373 K.42 We assigned this difference between PEO/ LiClO4 and PEO/ 关dmim兴PF6 polymer electrolytes to the large difference between cationic radius of each system. In fact, keeping concentration and temperature fixed, Fig. 11 compares the distribution of 具r2典1/2 共top panel兲 and 具s2典1/2 共bottom panel兲 in P共EO兲8 -关dmim兴PF6 and P共EO兲8-关bmim兴PF6. It is clear from Fig. 11 that PEO chains are more extended in P共EO兲8-关bmim兴PF6 than in P共EO兲8-关dmim兴PF6. Furthermore, Fig. 11 indicates that calculated distributions of 具s2典1/2 and 具r2典1/2 are nearly Gaussian as one expects for homopolymers.51,52 The radial distribution functions and the probability density maps shown in Figs. 2–9 are appropriate tools for revealing local short-range equilibrium structures of the simulated systems. On the other hand, we showed that PEO/ LiClO4 and pure ionic liquids display structural order in an extended spatial range.42,43 This is more easily investigated by calculating the static structure factor, S共k兲, because any long-range correlation manifest as a low-k peak in S共k兲, whereas it would be only an ill-defined oscillation on the asymptotic
where ␣ and  stand for different species. Figure 12 shows total S共k兲 for P共EO兲8-关dmim兴PF6 and P共EO兲8-关bmim兴PF6 at 400 K. Interesting k range is below k ⬃ 3.0 Å−1, because at larger k one is simply probing very short-range 共intramolecular兲 correlations. It is clear from Fig. 12 that a prepeak at k ⬃ 1.0 Å−1 is observed in calculated S共k兲 of ionic liquid polymer electrolytes, but it is absent in S共k兲 of pure PEO shown in the inset. The prepeak is more intense in P共EO兲8 -关bmim兴PF6 than P共EO兲8-关dmim兴PF6. Aiming to identify the nature of density fluctuations responsible for the IRO, further characterization of atomic correlations is provided by partial S␣共k兲. Figure 13 shows partial cations, Scations共k兲, partial anions, Sanions共k兲, and partial PEO, SCO共k兲, for P共EO兲8
FIG. 11. Calculated distribution of end-to-end distance, 具r2典1/2 共top panel兲, and radius of gyration, 具s2典1/2 共bottom panel兲 in P共EO兲8-关dmim兴PF6 共bold lines兲 and P共EO兲8-关bmim兴PF6 共thin lines兲 at 400 K.
FIG. 13. Partial S␣共k兲 of P共EO兲8-关dmim兴PF6 共top panel兲 and P共EO兲8 -关bmim兴PF6 共bottom panel兲 at 400 K. In each panel, it is shown the partial S␣共k兲: cations 共dashed lines兲, anions 共thin lines兲, and PEO chains 共bold lines兲. The inset shows partial cations S␣共k兲 including only atoms from the imidazolium ring 共bold line兲 or from the 1-butyl-chain 共thin line兲.
S␣共k兲 =
1
冑N ␣ N 
冓
N␣ N
兺 兺 eik共r −r 兲 i
i苸␣ j苸
j
冔
,
共4兲
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J. Chem. Phys. 124, 184902 共2006兲
Simulation of polymer electrolytes
-关dmim兴PF6 共top panel兲 and P共EO兲8-关bmim兴PF6 共bottom panel兲 at 400 K. One sees from Fig. 13 that correlation between PEO chains mainly determine the main peak in S共k兲 at k ⬃ 1.8 Å−1, whereas the main contribution to the prepeak at k ⬃ 1.0 Å−1 comes from ionic correlations, in particular, cations correlations. As anions follows cations in their firstneighbor shell, small prepeak in Sanions共k兲 is also observed. The inset in the bottom panel of Fig. 13 further splits Scations共k兲 into contributions from atoms of the imidazolium ring 共atoms 1–5 in Fig. 1兲 and atoms from the 1-butyl-chain 共atoms 7–10 in Fig. 1兲, where one sees that the imidazolium ring contributes more to the low-k peak than the 1-butylchain. Thus, in line with MD simulations of polymer electrolytes containing relatively small ionic species,42 ionic liquid polymer electrolytes containing large imidazolium cations also display extended-range spatial correlations arising from nonhomogeneous distribution of ionic species within the simulation box.
IV. CONCLUDING REMARKS
The present MD simulations of ionic liquid polymer electrolytes were performed with representative models, as PEO is one of the most investigated systems for polymer electrolytes with simple inorganic ions, and the majority of proposed ionic liquids contain 1-alkyl-3-methylimidazolium cations. In the polymeric matrix, we found ionic pairs whose local structure resembles known pattern in pure ionic liquids.28,29,31–36,43 The distance between oxygen atoms of PEO chains to cations is slightly smaller than anion-cation distance, so that imidazolium cations should be thought as solvated by both the anions and the polymeric chains. The local environment experienced by cations is well defined, where there is a mutual exclusion of the preferred location for anion and oxygen atom around imidazolium cations. It is well known that conformational changes of PEO chains occur on formation of polymer electrolytes with simple inorganic salts, such as alkali halides, LiClO4, etc.31–36,42 This finding was also obtained in the present case where much larger cations were added within the polymeric matrix. However, PEO is able to solvate the large imidazolium cation with less stringent local modification in comparison with the need when embracing small ions such as Li+ cations. Besides this short-range order, the simulated ionic liquid polymer electrolytes also display an intermediate-range order that is revealed by a low-k peak in calculated S共k兲. It is worth mentioning that IRO was already observed in MD investigations of pure ionic liquids43 and PEO/ LiClO4 polymer electrolytes.42 In the case of ionic liquid polymer electrolytes, the origin of IRO was assigned to spatial correlation between the ionic species. Previous MD simulations showed the remarkable interplay between structure and dynamics in pure ionic liquids and polymer electrolytes based on PEO and inorganic salts.10–15,31–36,44,45 The investigation of dynamical properties of ionic liquid polymer electrolytes is now in progress.
ACKNOWLEDGMENTS
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