Chem. Mater. 2005, 17, 3673-3680
3673
Conduction Mechanisms in Crystalline LiPF6‚PEO6 Doped with SiF62- and SF6 D. Brandell,† A. Liivat,†,‡ A. Aabloo,§ and J. O. Thomas*,† Department of Materials Chemistry, Ångstro¨m Laboratory, Uppsala UniVersity, Box 538, SE-751 21 Uppsala, Sweden, Institute of Materials Science, Department of Physics, Tartu UniVersity, Ta¨he 4, 51010 Tartu, Estonia, and Institute of Technology, Tartu UniVersity, Ta¨he 4, 51010 Tartu, Estonia. ReceiVed March 10, 2005. ReVised Manuscript ReceiVed May 16, 2005
Molecular dynamics (MD) simulations have been made under imposed electric fields for crystalline LiPF6‚PEO6, (LiPF6)1-x(Li2SiF6)x‚PEO6, and (LiPF6)1-x(SF6)x‚PEO6 for x ) 0.01 under standard pressure and temperature conditions with the aim of identifying the conduction mechanisms in the systems. Contrary to the results of earlier experimental investigations where only cation mobility was observed, ionic transport is here found to occur in regions between the polymer hemi-helices, with a high transference number (0.9-1.0) for the PF6- anions.
1. Introduction The rechargeable lithium-ion polymer battery is characterized by high energy density, reliability, and safety. The battery consists of a graphite anode and a lithium-containing transition-metal oxide (LiMOx) cathode which can reversibly intercalate and release lithium ions, separated by a polymer electrolyte.1-4 The most suitable solid electrolytes are formed by dissolving a lithium salt into poly(ethylene oxide) (PEO); -(CH2-CH2-O)n-. However, these electrolytes show acceptable ionic conductivity (σ > 10-4 S‚cm-1) only at temperatures above 70 °C, where the polymer has become amorphous.5 Much attention has therefore been devoted to the task of increasing the amorphous content of the PEOsalt systems at ambient temperatures; either by using large anions,6,7 adding liquid plasticizers or ceramic fillers to the polymer,8,9 or by modifying the PEO with side-chains and/ or cross-linkages.10,11 Recently, incorporation of ionic liquids into polymer electrolytes has been shown to be a promising strategy for raising the conductivity.12,13 * To whom correspondence should be
[email protected]. † Uppsala University. ‡ Institute of Materials Science, Tartu University. § Institute of Technology, Tartu University.
addressed.
E-mail:
(1) Tarascon, J. M.; Armand, M. Nature 2001, 414, 359. (2) Winter, M.; Besenhard, J. O.; Spahar, M. E.; Nova´k, P. AdV. Mater. 1998, 10, 725. (3) Bruce, P. G. Solid State Electrolytes; Cambridge University Press: Cambridge, 1995. (4) van Schalwijk, W. A.; Scrosati, B. AdVances in Lithium-Ion Batteries; Kluwer Academic/Plenum Publishers: New York, 2002. (5) Gray, F. M. Polymer Electrolytes; The Royal Society of Chemistry: Cambridge, 1997. (6) Benrabah, D.; Sanchez, J-Y.; Armand, M. Solid State Ionics 1993, 60, 87. (7) Benrabah, D.; Sanchez, J-Y.; Deroo, D.; Armand, M. Solid State Ionics 1994, 70/71, 157. (8) Chintapalli, C.; Frech, R. Solid State Ionics 1996, 86-88, 341. (9) Croce, F.; Appetecchi, G. B.; Persi, L.; Scrosati, B. Nature 1998, 394, 456. (10) Reiche, A.; Weinkauf, A.; Sandner, B.; Rittig, F.; Fleischer, G. Electrochim. Acta 2000, 45, 1327. (11) Aihara, Y.; Arai, S.; Hayamizu, K. Electrochim. Acta 2000, 45, 1321.
This whole picture has recently been brought into question, however, through the work of Gadjourova et al.,14 which has shown 1 order of magnitude higher conductivities (ca. 10-8 S‚cm-1 at 293 K) in the crystalline system LiSbF6‚PEO6 compared to values in the corresponding amorphous phase at the same temperature. The isostructural compounds LiPF6‚PEO6 and LiAsF6‚PEO6 display the same kind of behavior.15 This result is believed to originate in the specific structures of the materials. Bruce and co-workers have shown by neutron and X-ray diffraction that the crystal structures are composed of coaxial hemi-helices of PEO, which pairwise form cylindrical channels containing the lithium ions coordinated to ether oxygens;16,17 the anions lie outside the hemihelical pair channels, with no direct contact to the lithium ions; see Figure 1. Despite the fact that the anions are more mobile than the cations in amorphous electrolytes, NMR studies of the transference number in LiSbF6‚PEO614 show the Li+ ions alone to be the charge carriers. Although these values are far lower than those for highly conductive amorphous PEO salts such as LiTFSI‚PEO6,18 it has been shown that the conductivity can be increased by 1-2 orders of magnitude by replacing AsF6- by 5 mol % isovalent N(SO2CF3)2- (TFSI),19 or by 2 orders of magnitude through (12) Shin, J.-H.; Henderson, W. A.; Passerini, S. Electrochem. Commun. 2003, 5, 1016. (13) Shin, J.-H.; Henderson, W. A.; Passerini, S. Electrochem. Solid State Lett. 2005, 8, A125. (14) Gadjourova, Z.; Andreev, Y. G.; Tunstall, D. P.; Bruce, P. G. Nature 2001, 412, 520. (15) Stoeva, Z.; Martin-Litas, I.; Staunton, E.; Andreev, Y. G.; Bruce, P. G. J. Am. Chem. Soc. 2003, 125, 4619. (16) MacGlashan, G. S.; Andreev, Y. G.; Bruce, P. G. Nature 1999, 398, 792. (17) Gadjourova, Z.; Martı´n y Marero, D.; Andersen, K. H.; Andreev, Y. G.; Bruce, P. G. Chem. Mater. 2001, 13, 1282. (18) Armand, M.; Gorecki, W.; Andreani, R. In The Second International Symposium on Polymer Electrolytes; Scrosati, B., Ed.; Elsevier: London, 1990. (19) Christie, A. M.; Lilley, S. J.; Staunton, E.; Andreev, Y. G.; Bruce, P. G. Nature 2005, 433, 50.
10.1021/cm0505401 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/16/2005
3674 Chem. Mater., Vol. 17, No. 14, 2005
Figure 1. Structure of the simulated crystalline polymer electrolyte system LiPF6‚PEO6 viewed along the polymer axes, showing columns of Li+ and PF6- ions between the polymer hemi-helices.
aliovalent substitution by 1 mol % SiF62-.20 In the latter case, charge compensation is provided by extra Li+. Higher doping rates result in phase separation. In an earlier study,21 we have attempted to model LiPF6‚ PEO6 using molecular dynamics (MD) techniques. The hemihelical structure and anion-cation separation were retained at equilibrium, although somewhat different polymerbackbone configurations and coordination numbers were found than those suggested by the experimental studies. However, apart from anion rotation, there was very little dynamics in the system at 293 K and 1 bar pressure; therefore no conclusions could be drawn about the conduction mechanism. Our goal here is therefore to probe the mechanisms related to the observed comparatively high conduction in the crystalline phase, and the enhancement caused by doping. To this end, we have applied a series of external electric fields and substituted 1% of the PF6- anions by aliovalent SiF62- ions and SF6 molecules. These systems allow either an extra Li+ to be inserted into the system, or the creation of a Li+-ion vacancy, although gaseous SF6 can be difficult to introduce in stoichiometric amounts into the material. 2. MD Simulations In an MD simulation, atomic motion in a chemical system is modeled in classical mechanics terms by solving Newton’s equations of motion simultaneously for all particles in an appropriately chosen periodic simulation box. This set of equations is solved by a computational algorithm and the result depends implicitly on the description of the forces acting between the particles. The intramolecular potentials for PEO, describing bending and torsional motion in the polymer chain, are taken from Neyertz et al.22 This set of potentials, developed originally by Gejji et al.23 (20) Bruce, P. G. The 12th International Meeting on Lithium Batteries (IMBL-12); Nara, Japan, June 27-July 2, 2004. (21) Brandell, D.; Liivat, A.; Kasema¨gi, H.; Aabloo, A.; Thomas, J. O. J. Mater. Chem. 2005, 15, 1422. (22) Neyertz, S.; Brown, D.; Thomas, J. O. J. Chem. Phys. 1994, 101, 10064. (23) Gejji, S. P.; Tegenfeldt, J.; Lindgren, J. Chem. Phys. Lett. 1994, 226, 427.
Brandell et al. from MP2/6-311++G**//HF/3-21G energy minimization of the diglyme system and validated for crystalline PEO, has been used extensively and appears to reproduce the polymer-chain conformation satisfactorily. We have also used these potentials to model several PEO-salt systems.24-33 The intermolecular potentials are described by a combination of Buckingham (B) or Lennard-Jones (L-J) potentials: U(r) ) A exp(-r/B) - C/r6 - D/r4 + q1q2/4π0r or U(r) ) A/r12 - C/r6 + q1q2/4π0r, respectively, where A, B, C, and D are constants depending on the interacting atom-types. The values of the constants for different interactions within PEO were taken from Neyertz et al.,22 while the intermolecular potentials involving LiPF6 have been developed by Borodin et al.34-36 These potentials take into account the contribution of polarization to the total energy, and have been scaled for condensed-phase systems. The potentials involving SiF62- have been taken from Liivat et al.;37 the potentials for SF6 were developed from a model of Kinney et al.,38 originally optimized for neutral clusters in a condensed phase. To verify the force field for interactions involving ionic species, the potential energy surface (PES) for the SF6/Li+ system was mapped in C2-, C3-, and C4-symmetry conformations using Gaussian 98 software39 at the MP2/6-311+(2df) level, with SF6 treated as a rigid octahedron with an S-F distance of 1.565 Å. The SF6/Li+ force-field parameters were then fitted to the PES data points. All van der Waals parameters except D could be obtained using standard Lorentz-Berthelot combination rules; the values of D were obtained from the fitting procedure. The resulting parameters are listed in Table 1. The MD simulations use periodic boundary conditions and an Ewald summation routine, which treats the long-range electrostatic forces. The short-range cutoff used is 16 Å and the Verlet sphere used in the construction of the Verlet neighbor-list has a 0.5 Å radius. An NVT Nose-Hoover thermostat has been used consistently. A multiple time-step technique was used, with a longer time(24) Neyertz, S.; Brown, D.; Thomas, J. O. Electrochim. Acta 1995, 40, 2063. (25) Neyertz, S.; Thomas, J. O. Comput. Polym. Sci. 1995, 5, 107. (26) Neyertz, S.; Brown, D. J. Chem. Phys. 1996, 104, 3797. (27) Brandell, D.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. Int. J. Quantum Chem. 2000, 80, 799. (28) Brandell, D.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. J. Mater. Chem. 2002, 12, 565. (29) Brandell, D.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. Macromol. Symp. 2002, 18, 51. (30) Kasema¨gi, H.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. J. Mater. Chem. 2001, 11, 3191. (31) Kasema¨gi, H.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. Solid State Ionics 2002, 147, 367. (32) Kasema¨gi, H.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. Electrochim. Acta 2003, 48, 2273. (33) Hektor, A.; Klintenberg, M.; Aabloo, A.; Thomas, J. O. J. Mater. Chem. 2003, 13, 214. (34) Borodin, O.; Smith, G. D.; Jaffe, R. L. J. Comput. Chem. 2001, 22, 641. (35) Borodin, O.; Smith, G. D. Macromolecules 1998, 31, 8396. (36) Borodin, O.; Smith, G. D. Macromolecules 2000, 33, 2273. (37) Liivat, A.; Aabloo, A.; Thomas, J. O. J. Comput. Chem. 2005, 26, 716. (38) Kinney, K. E.; Xu, S.; Bartell, L. S. J. Phys. Chem. 1996, 100, 6935. (39) Gaussian 98, Revision A.11, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kuden, K. N.; Strain, M. C.; Farkas, O.; Tomas, J.; Barone, V.; Cossi, M.; Cammi, R.; Menucci, B.; Romelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, G.; Kormaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian Inc., Pittsburgh, PA, 2001.
Conduction Mechanisms in Crystalline LiPF6‚PEO6
Chem. Mater., Vol. 17, No. 14, 2005 3675
Table 1. SF6/LiPF6·PEO6 Force-Field Parametersa atom pair
A
B
C
D
potential type
S-S S-Li S-FPF S-FSF S-P S-C S-O S-H FSF -FSFb FSF-Li FSF -P FSF-FPF FSF-C FSF-O FSF-H
2921452 6238 692098 87979 2493160 1694060 771936 213901 87979 1356 388235 112189 303082 132992 33662
0 3.767798 0 0 0 0 0 0 0 3.681153 0 0 0 0 0
1875 80 849 135 3889 1097 644 314 135 20 990 221 299 172 80
0 60 0 0 0 0 0 0 0 85 0 0 0 0 0
L-J B L-J L-J L-J L-J L-J L-J L-J B L-J L-J L-J L-J L-J
a
Energy in units of kcal/mol. b FPF and FSF refer to fluorine atoms in PF6- and SF6, respectively.
Figure 3. Snapshot from the MD simulation of a typical Li+-SiF62- ionpair formed in (LiPF6)0.99(Li2SiF6)0.01‚PEO6.
ion was placed (in two separate series of simulations) both close to and far away from the SiF62- ion in the box. These systems were first relaxed for 300 ps; external fields from 1 to 5 × 106 V/m were then applied along the direction of the hemi-helices for another 300 ps; (iii) a PF6- ion was replaced by a neutral SF6 molecule, and a corresponding Li+ ion was withdrawn from the MD box to create a vacancy in one hemi-helical pair; see Figure 2b. This (LiPF6)0.99(SF6)0.01‚PEO6 system was first relaxed for 300 ps; external fields between 1 and 5 × 106 V/m were then applied along the direction of the hemi-helices for another 300 ps.
3. Results and Discussion
Figure 2. Regions of the SiF62-- and SF6-doped structures prior to simulation: (a) (LiPF6)0.99(Li2SiF6)0.01‚PEO6 and (b) (LiPF6)0.99(SF6)0.01‚ PEO6, showing the aliovalent anions and extra/vacant Li-sites, respectively. The extra Li+ ion is orange, Si is dark blue, and S is light blue; other colors are as in Figure 1. Hydrogens are omitted for clarity.
step of 1 fs for longer distances, and a shorter time-step of 0.2 fs inside a sphere of radius 6 Å. The simulations made under an imposed external electric field were treated with shorter timesteps: 0.5 and 0.1 fs, respectively. Simulations were performed under ambient conditions: 293 K and a pressure of 1 bar. The polymer MD simulation program DL_POLY40 was used. The starting structure for the MD simulation box contained 3 × 2 × 4 unit cells of crystalline LiPF6‚PEO6 with dimensions a ) 35.169 Å, b ) 34.750 Å, c ) 34.768 Å, β ) 107.8°, involving 32 PEO hemi-helices each with 18 EO units, along with 96 LiPF6 units. The start structure used was that given by Gadjourova et al.,17 with no internal symmetry conditions imposed within the periodic simulation box. This structure was simulated for 1 ns, i.e., 106 time-steps. It was found to retain structural stability.21 Three different systems were studied, as follows: (i) a series of external fields ranging from 1 to 7 × 106 V/m was applied along the x-direction (parallel to the hemi-helices) in the LiPF6‚PEO6 box; each was simulated for a further 300 ps; (ii) one PF6- ion was replaced by an SiF62- ion and an extra compensating Li+-ion was inserted at the metastable 4-coordinated position within one helix; see Figure 2a. This system is equivalent to (LiPF6)0.99(Li2SiF6)0.01‚ PEO6 and corresponds to a dopant concentration of ∼1% (that shown experimentally to give the highest conductivity20). The Li+ (40) The DL_POLY Project. Smith, W.; Forester, T. TCS Division, Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, UK.
3.1 Effect of Dopant on Local Structure. Inserting the divalent SiF62- anion or neutral SF6 (with appropriate Li+ compensation) is seen to destabilize the local environment near the dopant. The more highly charged SiF62- anion also repels the neighboring PF6- ions; an effect which is compensated by the extraction of a Li+ ion from within the polymer hemi-helices, to form an Li+-SiF62- ion-pair with a net charge of -1. Such an ion-pair can be seen in Figure 3. This occurs in both simulated (LiPF6)0.99(Li2SiF6)0.01‚PEO6 systems. This implies that, when Li+ is inserted far away from an SiF62- dopant, ion-pair formation creates a vacancy in an adjacent polymer helix. Columns containing 5 or 7 Li+ ions differ slightly from those containing 6 Li+ ions; repulsion between the Li+ ions is obviously strong, forcing the Li+ ions into an equi-spaced arrangement. This can be seen in the radial distribution functions plotted in Figure 4 (poor statistics mean that the plots for the 5- and 7-Li+ ion cases are less smooth). The Li-Li distance is ∼6 Å for 6 Li+ ions within the helices; while a broader distribution extending to larger distances is seen in the presence of a Li+ vacancy, as in the situation of SF6 doping or when SiF62- extracts a Li+ ion from a helix. For helices with 7 Li+ ions, on the other hand, this Li-Li distance is shorter: 4.0 and 5.5 Å for the two types of site. These changes in lithium distance also influence polymer geometry around the cations; the hemi-helical structure is retained, but the dihedral-angle conformation changes from ttctgjggtgjttctggjgjtc to ttctgjcgtcttctggjgjtc for hemi-helices with 5 lithium ions, while it is retained for the columns containing 7 lithium ions. This effect is illustrated in the plot of the dihedral-angle distribution along the original crystallographic asymmetric unit sampled every thousand time-steps (Figure 5). Poor statistics for helices containing 5 or 7 Li+ ions again give the plots a more irregular form. These differences are relatively small, especially considering that the coordination
3676 Chem. Mater., Vol. 17, No. 14, 2005
Brandell et al.
Figure 4. Radial distribution functions for Li-Li contacts within PEO hemi-helical channels in (LiPF6)0.99(Li2SiF6)0.01‚PEO6 (7-Li+ and 6-Li+) and (LiPF6)0.99(SF6)0.01‚PEO6 (6-Li+ and 5-Li+) at 293 K in the absence of an external electric field: thin solid line, 7 Li+ hemi-helices; dashed line, 6 Li+ hemi-helices; and thick solid line, 5 Li+ hemi-helices.
Figure 5. Distribution of dihedral angles for hemi-helical PEO in (LiPF6)0.99(Li2SiF6)0.01‚PEO6 (7-Li+ and 6-Li+) and (LiPF6)0.99(SF6)0.01‚PEO6 (6-Li+ and 5-Li+) at 293 K. The boxes show sequentially each individual polymer bond-angle in the crystallographic asymmetric unit. Blue lines, 7-Li+ hemi-helices; black lines, 6-Li+ hemi-helices; and red lines, 5-Li+ hemi-helices.
numbers (see below) and Li+-Li+ distances vary quite significantly. The equidistant spacing of the cations must cause relaxation of the polymer backbone, but the polymer is evidently sufficiently rigidly to maintain its general conformation, although slight shifts in atomic position occur. The difference compared to the “normal” 6-Li+ helix is smallest for the 7-Li+ case, where the polymer geometry only changes near the regions of lower Li+-Oet coordination number. In 5-Li+ helices, the occurrence of double peaks (Figure 5) indicates that the space-group is broken when the chain conformation changes. Changes in polymer structure and Li-Li distance are also reflected in the lithium to ether-oxygen coordination number. In helices containing 7 Li+ ions, the average coordination number is 5.1 (compared to 6.0 for a “normal” helix); 4 of the lithiums coordinate 6 ether oxygens; the remaining 3
Figure 6. Hemi-helical PEO pair containing 5 equi-spaced Li+ ions in (LiPF6)0.99(SF6)0.01‚PEO6 after 300 ps in the absence of an imposed external field. Labels are as in Figure 1; hydrogens are omitted.
lithiums each coordinate only 4 oxygens. In helices containing vacancies, all 5 lithiums coordinate to 6 oxygens. This leaves 6 ether oxygens at longer distances (>2.8 Å) from the lithiums; these are evenly distributed along the helix (Figure 6). 3.2 Ion Conductivity. All systems investigated exhibit ionic conductivity above a certain field strength; the threshold values are listed in Table 2. The conductivity is seen as anion
Conduction Mechanisms in Crystalline LiPF6‚PEO6
Chem. Mater., Vol. 17, No. 14, 2005 3677
Table 2. Threshold Values for the Applied Electric Fields (in 106 V/m) for Ion Migration and Hemi-Helical Breakdown in the Systems Simulated
LiPF6‚PEO6
SiF62doped (distant from extra Li+)
SiF62doped (close to extra Li+)
SF6 doped
ion migration
5.0
4.0
4.75
4.0
onset of helical breakdown
5.25
4.5
5.0
5.0
Table 3. Ion-Jump Frequencies for Different Systems (in Jumps/ns)
system LiPF6‚PEO6 SiF62-doped (distant from extra Li+) SiF62-doped (close to extra Li+) SF6 doped SF6 doped
external field/ 106 V/m
PF6jump frequency
Li+ jump frequency
5.0 4.0
120 140
0 3
4.75
130
27
4.0 4.5
150 300
0 25
jumps parallel to the hemi-helical axes. A typical plot of anion movement along the column is shown in Figure 7; the two (of 16) columns where mobile anions occur are illustrated. The equivalent plot for Li+ motion in the opposite direction is included. Conductivity can, in principle, be calculated using the Nernst-Einstein equation and the diffusion coefficient extracted from the mean-square displacement of the ions in the simulation box. Such values are most unreliable, however, in view of the poor statistics of the simulations and the nonrandomicity of the ionic motion under the influence of an imposed electric field. Ion-jump frequencies can nevertheless be used for comparison purposes; jump frequencies are listed for structurally stable conducting systems in Table 3. NMR studies of the LiXF6‚PEO6 (X ) Sb,P) systems have suggested that the conductivity is dominated by the movement of lithium ions, i.e., the lithium transport number (t+) is 1.0.14 In contrast to this, our MD result (Table 2) suggests that it is anions (and Li+-SiF62- clusters) which dominate the ionic motion, with t- close to 1.0. This is also clear from inspection of the MD simulated structure: the cations coordinate strongly to the two hemi-helical polymer chains, thereby holding them together. The average lithium coordination number is close to 6, and the Li+-Oet distance is ca. 2.0 Å;21 in reasonable agreement with the experimentally determined structure.17 In our previous MD simulation of the LiPF6‚PEO6 structure, it was clear that the anions were free to rotate about two different axes, suggesting a weak interaction with the polymer, while the cations were quite immobile. The different simulated systems display somewhat different threshold values of the applied external field for the onset of the conduction processes (Table 2). It is clear from the comparatively low field strengths at which ion-hopping begins that aliovalent (SiF62-) doping has an enhancing effect on ion conduction in the system. On the other hand, it is difficult to quantify the effectsthreshold values for the electric field are not directly related to the jump frequencies.
3.3 Structural Sensitivity to an External Electric Field. Up to a certain field strength, the hemi-helical polymer structure and the ion-coordination do not change significantly. At the onset of ion conduction, Li+ ions tend to migrate out of the helices, forming neutral ion-pairs with the PF6- ions. These are generally stable and immobile, thereby hindering the movement of the rest of the anions in the column. Occasionally, a Li+ ion which has left the polymer helix but is still coordinated to PEO oxygens, migrates back into the helix. The vacancies left by the migrating Li+ ions otherwise destabilize the polymer helices, and can lead to its ultimate break-up. The three systems (four if the two (LiPF6)0.99(Li2SiF6)0.01‚ PEO6 systems are considered separately) display different field threshold values (Table 2). When this applied field is too high, the hemi-helices break up and the whole system becomes amorphous. The situation is very sensitive: field strengths 0.25‚106 V/m greater or less than the threshold value can correspond either to break-up of the helix, or to minimal ionic conductivity. This has also been monitored via the mean-square-displacements (MSD) of the polymer atoms. When the helical structure is retained, the MSDs are typically up to 1 Å2; these values increase abruptly when the system becomes amorphous. There is also a general trend (seen in Table 2) that the systems most stable to the applied field are those which display the lowest ion conductivity. Doping would also seem to lower the stability of the system. Helical break-up is also clearly correlated to the extraction of Li+ ions from the helices (Figure 8). This is probably due to the destabilization which the polymer chain experiences when lithium is withdrawn from the helical structure, and shows clearly how the structure is determined by Li-Oet coordination within the helix. The structural stability induced by Li-Oet coordination can also be related to the high anion transference number. While some local cation structures destabilize the helices and result in chain entanglement and amorphicity, no analogous effect appears to exist for the anions. It is also interesting to note the dramatic decrease in ion transport when the system becomes amorphous. The ionhopping exemplified in Figure 7 is replaced by a slow drift of the entire system in the direction of the applied electric field. When chain entanglement disrupts the anion channels, ion-hopping is severely hindered. This is consistent with the lower conductivity observed experimentally in the amorphous system, and illustrates well how structural order facilitates ion conductivity. 3.4 Conduction Mechanisms. Inspection of ion-hopping sequences gives information on the mechanisms of ion conduction. The displacement of lithium and the anions in the yz-plane, i.e., perpendicular to the helical axis, is plotted for a sequence of anion-jumps in Figure 9: anions are seen to approach the polymer helix, while Li+ ions move out toward the anion column. Li+ ions thus create an available site for the anions close to the polymer. The coordination of an anion to Li+ also releases one ether oxygen atom from the Li+-coordination sphere, causing a small twist to occur in the polymer chain. This pattern of coupled Li+ and PF6displacements in the yz-plane, as illustrated in Figure 10, is
3678 Chem. Mater., Vol. 17, No. 14, 2005
Brandell et al.
Figure 7. The x-coordinate (along the polymer chains) for 16 P(F6-) atoms and one Li+ ion in different ion columns plotted over 100 ps for (LiPF6)0.99(SF6)0.01‚PEO6 at E ) 4.5 × 106 V/m. Mobile anions are plotted as thick lines; the Li+ ion is plotted as open circles.
surprising, however, since these calculations were based on the crystallographically determined structure, which is somewhat different from our MD simulated structure. Interestingly, the energy barrier for lithium migration out from the polymer helices is no lower than that for Li+ movement along the helix. This barrier varies greatly depending on the direction of migration from the helix, but is never found to be less than 300 kJ/mol for 6-coordinated lithium sites. This means that the relaxation of the polymer chain must play a crucial role in lowering the barrier for lithium migration out from the helices. Li+
Figure 8. Correlation plot between the number of ions extracted from the helices and PEO break-up in the simulation of LiPF6‚PEO6 doped with Li2SiF6 under an imposed electric field of 5 × 106 V/m.
common to all anion jumps, although displacement alone is not always sufficient to induce ion-hopping. The mechanism for the less frequent Li+-ion jumps along the polymer-channels is shown in Figure 11. Here, the ions jump a shorter distance (generally ∼3 Å) compared to the PF6- jumps of ∼6 Å. The Li+ ions generally move from 6- to 5-fold coordinated positions, followed by a small twist of the polymer chain to reestablish the 6-fold coordination. This process does not require a Li+ vacancy; it can also occur within 6-Li+ helices. As seen from Table 3, Li+ ions jump far less frequently than the anions. In fact, there is a greater tendency for the cations to migrate out of their double hemi-helices into the inter-helical anionic column than there is for them to move in the direction of the field within the helices. Outside, the Li+ ions form stable ion-pairs with PF6- ions which, in turn, do not move along the helical axes. The fact that Li+ ions prefer to leave the helices rather than migrate along them is, however, inconsistent with our estimate of the energy barrier for lithium migration. From the force field used, this is calculated to ca. 240 kJ/mol for moving six Li+ ions simultaneously along a double hemi-helix. This figure compares rather badly with the barrier height of 95 kJ/mol estimated from quantum chemical calculations.41 This is not
This mechanism, involving predominantly anionic charge transport, also helps explain the lower conductivity found experimentally in the crystalline phase of LiClO4‚PEO6 compared to that in its amorphous counterpart.42 Diffraction shows that this compound is isostructural with LiPF6‚PEO6. However, if the charge distribution of the anion and its chemical interaction with the polymer chain is crucial for the conduction mechanism, exchanging PF6- for ClO4- can significantly influence the transport process. ClO4- can be expected to coordinate more strongly with Li+, thereby more readily creating ion-pairs which then hinder ion motion in the anion columns. 3.5 Effect of Aliovalent Doping. We see from Table 2 that aliovalent doping clearly has some effect on ionic conductivity in the systems studied; in good agreement with experiment. It would not appear that this is a result of Li+-ion migration across a vacancy inside the polymer channels, or of an extra Li+-ion being pushed along the double hemi-helix. It follows rather from a destabilization induced by the dopant in the arrangement of anions and cations in the yz-plane. This is analogous to the experimental study of the effect of 5 mol % substitution of isovalent bis(trifluoromethane-sulfonyl)imide (TFSI) for PF6-, which shows conductivity enhancement by 1-2 orders of magnitudespresumably also without introducing Li+ vacancies or interstitials into the helices. This substitution merely perturbs (41) Johansson, P.; Jacobsson, P. Electrochim. Acta 2003, 48, 2279. (42) Henderson, W. A.; Passerini, S. Electrochem. Commun. 2003, 5, 575.
Conduction Mechanisms in Crystalline LiPF6‚PEO6
Chem. Mater., Vol. 17, No. 14, 2005 3679
Figure 9. Displacement of the lithium (dashed line) and anions (alternating thick and thin solid lines) from the helical axis in the yz-plane in LiPF6‚PEO6 under an imposed external electric field of 5.0 × 106 V/m.
Figure 10. Successive steps in the PF6- ion-hopping mechanism through a Li+-coordinated site close to the polymer chain in LiPF6‚PEO6 under an imposed electric field of 5.0 × 106 V/m: (i) Li+ and PF6- approach one another through displacements in the yz-plane (A); Li+ coordination number to oxygens is reduced (B); (ii) a second anion approaches the Li+coordination site (C), while the anions jump (D); (iii) the first Li+coordinated anion is released (E).
the crystal field experienced by Li+ ions in the regions of the TFSI anion, and can thus be related to the two cases of doping (with SF6 and SiF62-) simulated here. In the case of SF6-doping, the vacancy introduced is not filled by jumping Li+-ions but, nonetheless, the dopants seems to enhance the conductivity. The effect is rather a result of a perturbation in the local crystal field, leading to anion shifts, which, in turn, facilitate the conduction mechanism described above. In the case of SiF62- doping with the “extra” lithium located
Figure 11. Mechanism for Li+ movement along the x-direction of a polymer helix in (LiPF6)0.99(Li2SiF6)0.01‚PEO6 under an imposed electric field of 4.75 × 106 V/m: (i) a Li+ ion releases two ether oxygens (A) while moving into a 5-coordinated site (B); (ii) the lithium ion becomes 6-coordinated through motion of the polymer (C); (iii) this motion induces shifts along the chain (D).
within a helix distant from the dopant anion, the enhancement mechanism is similar: the lithium redistribution within the hemi-helix leads to shifts in the yz-plane for the anions close to this helix, thus giving rise to the hopping mechanism for PF6-. It is vital to bear in mind, however, that the actual materials studied experimentally differ in one very important way from the MD-simulated models: most of the experimental work has been performed on low Mw, methoxy end-capped PEO. Such a short-chain system obviously contains a high concentration of polymer end-group “defects”. How these behave structurally and how they influence ion mobility has not been addressed either in the crystallographic studies or
3680 Chem. Mater., Vol. 17, No. 14, 2005
in our MD simulations. It is likely that the methoxy endgroups contribute significantly to ion-hopping mechanisms, but it is futile to speculate further on the precise mechanism; this is being explored in extensive ongoing MD simulation studies of conduction mechanisms in related short-chain systems.
Brandell et al.
On the other hand, the structures derived both from diffraction17 and from our MD studies (both of which neglect polymer end-groups) suggest strong lithium coordination to the polymer helices. Anion conduction also gives a rational explanation for the observed increase in conductivity following aliovalent doping. The results of our current shortchain simulations can be decisive in resolving this situation.
4. Conclusions Clearly, there is qualitative disagreement between this simulation study and the result of the experimental NMR study: the transference number is found to be 1.0 for Li+ions from NMR but is here found to be close to 1.0 for the PF6- anions. This can result from our use of an infinitechain instead of short-chain PEO model in the simulations.
Acknowledgment. This work has been supported by grants from The Swedish Research Council (VR). The excellent service provided by The Stockholm Parallel Computer Center (PDC) is also gratefully acknowledged, as is a stipend to A.L. from The Archimedes Foundation (T.05-04/08). CM0505401
