Solvation Structure of Li+ in Concentrated LiPF6−Propylene

6104

2007, 111, 6104-6109 Published on Web 05/12/2007

Solvation Structure of Li+ in Concentrated LiPF6-Propylene Carbonate Solutions Yasuo Kameda,† Yasuhiro Umebayashi,*,‡ Munetaka Takeuchi,‡,§ Mohanmmad Abdul Wahab,‡ Shuhei Fukuda,‡ Shin-ichi Ishiguro,‡ Motoya Sasaki,† Yuko Amo,† and Takeshi Usuki† Department of Material and Biological Chemistry, Faculty of Science, Yamagata UniVersity, Kojirakawa-machi 1-4-12, Yamagata 990-8560, Japan, Department of Chemistry, Faculty of Science, Kyushu UniVersity, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan, and Fujitsu Limited, Nakase 1-9-3, Mihama-ku, Chiba 261-8588, Japan ReceiVed: April 3, 2007; In Final Form: April 17, 2007

Time-of-flight neutron diffraction measurements were carried out for 6Li/7Li isotopically substituted 10 mol % LiPF6-propylene carbonate-d6 (PC-d6) solutions, in order to obtain structural information on the first solvation shell of Li+. Structural parameters concerning the nearest neighbor Li+‚‚‚PC and Li+‚‚‚PF6interactions were determined through least-squares fitting analysis of the observed difference function, ∆Li(Q). It has been revealed that the first solvation shell of Li+ consists in average of 4.5(1) PC molecules with an intermolecular Li+‚‚‚O(PC) distance of 2.04(1) Å. The ∠Li+‚‚‚OdC bond angle has been determined to be 138(2)°.

Introduction In recent years, electrolyte solutions of carbonate solvents have been the subject of an increasing interest due to their important role in electrochemical devices such as high performance electric double layer capacitors and lithium ion secondary batteries. Propylene carbonate (PC, Chart 1) is the most widely used solvent constituting the electrolyte because of its chemical and electrochemical stability, wide liquid range, and relatively low toxicity. Since PC has a large dielectric constant (64.92), it can dissolve a variety of lithium salts. Most of the lithium ion secondary batteries have used LiPF6 as solute because in practice LiPF6 solutions exhibit the highest conductivity. The solvation structure of the Li+ ion and the ion association with various counter anions in nonaqueous solvent solutions including PC have been studied in terms of conductivity,1 viscosity,1,2 and self-diffusion coefficient by the pulsed-gradient spin echo (PGSE) NMR.3 According to the Stokes-Einstein formula, the number of solvent molecules surrounding the Li+ ion can be estimated from the ratio of the solvent-to-ion self-diffusion coefficients. The PGSE NMR self-diffusion study suggested that the lithium ion is surrounded by 2.2 PC molecules in LiBF4-PC and LiTFSI (bis-(trifluoromethanesulfonyl) imide)PC solutions.3 However, it is well-known that a great care may be needed because of the validity of employed assumptions, when the hydrodynamically and/or electrochemically estimated ion solvation structure is interpreted.4 Therefore, it is indispensable to elucidate the solvation structure of the Li+ ion and the ion association in nonaqueous solutions including PC at the molecular level. * To whom correspondence should be addressed. E-mail: yumescc@ mbox.nc.kyushu-u.ac.jp. Fax.: +81-92-642-2582. † Yamagata University. ‡ Kyushu University. § Fujitsu Limited.

10.1021/jp072597b CCC: $37.00

CHART 1: Schematic Illustrations of Propylene Carbonate (PC) and Ethylene Carbonate (EC)

Structural properties of Li+ in PC have been investigated by density functional theory and ab initio molecular orbital calculations, which revealed that there is a strong interaction between the Li+ ion and the carbonyl oxygen atom of the PC5 and ethylene carbonate (EC)6 molecules, which has a structure closely related to the PC molecule. The result of the electrospray ionization mass spectroscopic study has indicated that Li+(PC)2 and Li+(PC)3 complexes are the main cationic species,7 which implies that the smaller coordination number, nLiO, less than four is more favorable. On the other hand, molecular dynamics simulations by Soetens et al. have suggested that the first solvation shell of the Li+ ion involves four PC molecules in the Li+BF4- + 214 PC system.8 However, Tasaki demonstrated that the weak ion pair formation between Li+ and PF6- ions by molecular dynamics (MD) simulations for the system containing 11 LiPF6 salt and 98 PC (ca. 1 mol dm-3 LiPF6).9 A four-coordinated Li+ ion has also been reported by MD simulations for single Li+ ion6 and LiTFSI10 solutions in EC. Although a number of Raman and IR spectroscopic studies have been reported, there seems to be also some controversies on the Li+ solvation structure and the ion association in carbonate solvents.11-19 The Li+ ion solvation structure, even the solvation number, and the ion association in PC solutions have not yet been clearly understood. Direct experimental information concerning the solvation structure of the Li+ ion in the concentrated © 2007 American Chemical Society

Letters

J. Phys. Chem. B, Vol. 111, No. 22, 2007 6105

TABLE 1: Isotopic Composition and Average Scattering Length, bLi, Scattering and Absorption Cross Sections, σs and σa, and Number Density of the Stoichiometric Unit, (*LiPF6)x(PC-d6)1-x, G, Used in This Study sample I (6LiPF6)0.1(PC-d6)0.9 II (natLiPF6)0.1(PC-d6)0.9 a

6

Li/%

95.5 7.5

Li/%

bLi/10-12 cm

σs/barns

σa/barnsa

F/Å-3

4.5 92.5

0.1810 -0.1904

50.159 50.197

59.281 13.277

0.007299

7

For incident neutron wavelength of λ ) 1.0 Å.

PC solution is therefore necessary. Neutron diffraction with the 6Li/7Li isotopic substitution is one of the most suitable experimental methods. Although a number of studies on the hydration structure of the Li+ ion in aqueous solutions have been published,20 limited information is obtained on the solvation structure of the Li+ ion in nonaqueous solutions20d,l,21,22 and that in polymers.23-25 In order to obtain detailed information concerning the local structure around the Li+ ion in the propylene carbonate solution, knowledge of the microscopic structure in the partial structure function level is indispensable. In the present letter, we describe the results of time-of-flight (TOF) neutron diffraction measurements on 10 mol % LiPF6 solutions in deuterated propylene carbonate in which the 6Li/7Li isotopic ratio has been changed. Experimental Section Materials. 6Li-enriched 6Li2CO3 (95.5% 6Li, Tomiyama Chemical Co. Ltd.) and natural natLi2CO3 (92.5% 7Li, natural abundance) were first converted to 6LiCl and natLiCl, respectively, by reacting with HCl in the aqueous solution. The product solution was dehydrated in vacuum to obtain anhydrous *LiCl (*Li: 6Li and 7Li). Enriched *LiCl was reacted with AgPF6 in the acetonirile solution. After filtering the precipitated AgCl, the filtrate was evaporated to dryness under reduced pressure to obtain anhydrous *LiPF6. Required amounts of anhydrous 6LiPF6 and natLiPF6 were then dissolved into fully deuterated propylene carbonate-d6 (98% D, Cambridge Isotope Laboratories, Inc.) in a high performance glovebox, in which the water content was kept less than 1 ppm, to prepare two 10 mol % *LiPF6-PC-d6 solutions with different 6Li/7Li isotopic compositions. Each sample solution was sealed in a cylindrical Ti-Zr null alloy cell (8.0 mm in inner diameter and 0.3 mm in thickness) and was used for the neutron diffraction measurements. Sample parameters are listed in Table 1. Neutron Diffraction Measurements. TOF neutron diffraction measurements were carried out at 25 °C using the HIT-II spectrometer26 installed at the spallation neutron source (KENS) in the High Energy Accelerator Organization (KEK), Tsukuba, Japan. Scattered neutrons were detected by 104 3He counters covering the scattering angles of 10 e 2θ e 157°. The data accumulation time was 20 and 13 h for 6Li enriched samples I and II, respectively. Measurements of an empty cell, background, and vanadium rod of 8 mmφ, were made in advance. Observed scattering intensities for the sample were corrected for instrumental background, absorption of sample and cell,27 and multiple28 and incoherent scatterings. The coherent scattering lengths as well as the scattering and absorption cross sections for the constituent nuclei were referred to those tabulated by Sears.29 The wavelength dependence of the total cross sections for H and D nuclei was estimated from the observed total cross sections for liquid H2O and D2O, respectively.30 The corrected intensities were converted to the absolute scale using the corrected scattering intensities from the vanadium rod.

Figure 1. Total interference term observed for 6LiPF6- and nat LiPF6-PC solutions (dots). The best-fit of the calculated iintra(Q) is shown by solid lines. The residual functions, δ(Q), are indicated below.

Results and Discussion As the preliminary analysis, the reliability of the observed scattering cross section for sample solutions, particularly for the 6LiPF6 sample with a large absorption coefficient from 6Li, was checked by the following procedures. (1) The total interference term, i(Q), for samples I and II was obtained from scattering intensities for low-angle detectors located at 10 e 2θ e 51° by applying the inelasticity correction using the observed scattering cross section for the null water.31 The corrected scattering intensities from each detector were combined in the Q interval of 0.1 Å-1 to obtain the total i(Q) in the range of 0.1 e Q e 26 Å-1, which is indicated in Figure 1. (2) Since the contribution from the intermolecular interference term involved in the total i(Q) is negligibly small in the sufficiently high-Q region (typically, Q > 10 Å-1), the normalization constant, χ, can be determined by comparing the oscillational amplitude for the calculated intramolecular interference term, iintra(Q), and that for observed i(Q) in the high-Q region. In the present analysis, the intramolecular interference term was evaluated by the following equation,

iintra(Q) ) (1 - x)iintra(Q) (for PC) + xiintra(Q) (for PF6-) (1)

6106 J. Phys. Chem. B, Vol. 111, No. 22, 2007

Letters

TABLE 2: Values of the Coefficients in Eq 4 A/barns

B/barns

C/barns

D/barns

E/barns

F/barns

0.1164

0.2592

0.1772

0.0252

0.0038

-0.0003

The intramolecular contribution from the PC and PF6- was estimated by

iintra(Q) (for PC or PF6-) ) ΣΣbibj exp(-lij2Q2/2) sin(Qrij)/(Qrij)

(2)

i*j

where, bi is the coherent scattering length of the ith atom within the molecule. Parameters lij and rij denote the root mean square (rms) displacement and internuclear distance of the i-j pair, respectively. Values of rij and lij were taken from the literature determined by the ab initio molecular orbital (MO) calculation and X-ray diffraction studies for PC32 and by single-crystal X-ray diffraction works for PF6-.33,34 (3) The normalization constant, χ, defined below, was determined through the least-squares fitting procedure in the range of 12 e Q e 26 Å-1, where contribution from intermolecular interference is negligible.

i(Q) ) χ × iintra(Q)

(3)

Prior to the fitting analysis, the correction for the lowfrequency systematic errors35 was adopted to the observed i(Q). The values of χ determined were 1.019(1) and 1.023(1) for 6LiPF and natLiPF solutions, respectively. The fact that they 6 6 are very close to unity indicates that the present data correction and normalization procedures were adequately carried out. The overall normalization error in the observed scattering cross section is roughly estimated to be within approximately 2%. The difference in the normalization constant between samples I and II can be evaluated to approximately 0.4%. The first-order difference function,36 ∆Li(Q), was derived from the numerical difference between scattering cross sections observed for samples I and II. In the present ∆Li(Q), the inelasticity effect mainly arising from the self-scattering term of H and D nuclei is expected to be cancelled out by taking the difference between two samples in which identical inelasticity distortion should be involved.36 The ∆Li(Q) scaled at the stoichiometric unit, (*LiPF6)x(PC-d6)1-x, can be written as a linear combination of partial structure factors, aLij(Q), involving contribution from the Li‚‚‚j pair:

∆Li(Q) ) A[aLiO(Q) - 1] + B[aLiD(Q) - 1] + C[aLiC(Q) - 1] + D[aLiF(Q) -1] + E[aLiP(Q) - 1] + F[aLiLi(Q) - 1] (4) where,

A ) 6x(1 - x)∆bLibO

B ) 12x(1 - x)∆bLibD

C ) 8x(1 - x)∆bLibC E ) 2x2∆bLibP

D ) 12x2∆bLibF F ) x2(b6Li2 - bnatLi2)

and ∆bLi ) b6Li - bnatLi. Since the observed ∆Li(Q) from 64 sets of forward angle detectors at 10 e 2θ e 51° agree well within the statistical uncertainties, they were combined at the Q interval of 0.1 Å-1 and used for the subsequent analysis. Coefficients A-F in eq 4 are numerically listed in Table 2.

Figure 2. (a) ∆Li(Q) observed for 10 mol % LiPF6 solutions in propylene carbonate-d6 (dots), and the best-fit of the calculated ∆Limodel(Q) (solid line). (b) Residual functions (dots).

The distribution function, GLi(r), around the lithium ion was obtained by the Fourier transform of the observed ∆Li(Q),

GLi(r) ) 1 + (A + B + C + D + E + F)-1(2π2Fr)-1

∫0Q

max

Q∆Li(Q) sin(Qr) dQ

) [AgLiO(r) + BgLiD(r) + CgLiC(r) + DgLiF(r) + EgLiP(r) + FgLiLi(r)] × (A + B + C + D + E + F)-1 (5) The upper limit of the integral, Qmax, was set to be 20 Å-1 in the present study. Since the magnitudes of coefficients A, B, and C are much larger than that of D and E in the present experimental condition, GLi(r) is dominated by the contribution from Li+‚‚‚PC interaction. The difference function, ∆Li(Q), observed for 10 mol % LiPF6-PC solution is shown in Figure 2a. Diffraction peaks located at Q ) 1.6 and 2.6 Å-1 are obviously identified. The oscillational feature of ∆Li(Q) extends to the higher Q region. The observed distribution function, GLi(r), is represented in Figure 3. A dominant first peak at r ) 2.0 Å and the second peak appearing at r ≈ 3 Å in the present GLi(r), clearly indicate the existence of a well-defined first solvation shell around the Li+ ion. The first peak at r ) 2.0 Å is attributable to the nearest neighbor Li+‚‚‚O(PC) interaction from the electrostatic point of view. If we assume this first peak as the Li+‚‚‚O interaction, the number of oxygen atoms around Li+ can be estimated to be approximately 4.5 from the integration of the present GLi(r) in the range of 1.70 e r e 2.36 Å. The second peak appearing at r ≈ 3 Å and broadened third peak at r ≈ 5 Å are considered to involve both interactions between Li+ and PC and between Li+ and PF6-. Structural parameters concerning the first solvation shell of the Li+ ion were determined through the least-squares fitting procedure for the observed ∆Li(Q), employing the model function ∆Limodel(Q) involving both the short- and long-range contributions:37-39

∆Limodel(Q) )

∑R 2xnLiR∆bLibR exp(-lLiR2Q2/2)

sin(QrLiR)/(QrLiR) + 4πF(A + B + C + D + E + F) exp(-lLiR2Q2/2) × [Qr0 cos(Qr0) - sin(Qr0)]Q-3 (6) where, nLiR denotes the coordination number of R atom around

Letters

J. Phys. Chem. B, Vol. 111, No. 22, 2007 6107 TABLE 3: Results of the Least-Squares Fitting Analysis of the Observed ∆Li(Q)a interaction

i‚‚‚j

short-range Li+‚‚‚O(PC)

rij/Å

lij/Å

l*/Åb

nij

2.04(1) 0.10(1) 0.16(1) 4.5(1) R ) 138(2)c β ) 57(2)d

Li+‚‚‚F(PF6-) 2.98(1) γ ) 124(2)e long-range Li+‚‚‚PC 8.27(1) r0/Å 6.32(1) Li+‚‚‚Xg

0.23(1) 0.26(1) 7.0(1) δ ) 0(10)f 1.72(1) 23(1) l0/Å 0.90(1)

a

Figure 3. Distribution function around Li+, GLi(r), observed for 10 mol % LiPF6 solutions in propylene carbonate-d6 (solid line). Fourier transform of the calculated ∆Limodel(Q) is shown by a thick broken line. The short-range Li+‚‚‚PC and Li+‚‚‚PF6- contributions are denoted by thin dotted and thin dashed-dot lines, respectively. Contribution from the long-range interaction is shown by thin-broken line.

the Li+ ion. Parameters, lLiR and rLiR, correspond to the rms displacement and internuclear distance for the Li+‚‚‚R pair, respectively. The long-range parameter, r0, means the distance beyond which the continuous distribution of atoms around the Li+ ion can be assumed. The parameter, l0, describes the sharpness of the boundary at r0. Structural parameters, nLiR, lLiR, rLiR, l0, and r0, were determined from the least-squares fit to the observed ∆Li(Q). The fitting procedure was performed in the range of 0.1 e Q e 20 Å-1 with the SALS program,40 assuming that the statistical uncertainties distribute uniformly. Prior to the fitting analysis, correction for the low-frequency systematic errors involved in the ∆Li(Q) was adopted.35 The model function, ∆Limodel(Q), in eq 6, was evaluated on the basis of the following assumptions. (a) For the nearest neighbor interaction between the Li+ ion and the PC molecule, structural parameters, rLiO, lLiO, nLiO, the bond angle, R () ∠Li+‚‚‚OdC), and the dihedral angle β between the plane involving atoms, Li+‚‚‚OdC, and the plane involving OdCO2 atoms within the PC molecule were treated as independent parameters. The molecular geometry of the PC molecule was fixed to those determined from ab initio calculations for an isolated PC molecule and from X-ray diffraction measurements for pure liquid PC.32 The rms displacements for nonbonding interactions between the Li+‚‚‚PC molecule except for the first neatest neighbor Li+‚‚‚O(carbonyl) pair, lLij, were approximated through the following equation:37

lLij ) (lLiO + l*) × (rLij/rLiO)1/2

(7)

In the present analysis, the modification factor for the rms displacement, l*, was introduced to take into account for the geometrical fluctuation of the Li+‚‚‚PC interaction within the first solvation shell of the Li+ ion. (b) Structural parameters for the nearest neighbor Li+‚‚‚PF6- interaction, rLiF, lLiF, nLiF, the bond angle, γ (∠Li+‚‚‚F-P), and the dihedral angle δ between the plane involving Li+‚‚‚F-P atoms and the plane involving F-PF3 atoms within the PF6- were refined independently. The molecular geometry of PF6- was fixed to those determined from the single-crystal X-ray diffraction studies.33,34 (c) Structural parameters for the long-range random distribution of atoms, r0 and l0, were treated as independent parameters. In the preliminary analysis of ∆Li(Q), it was found that a significant

Estimated errors are given in parentheses. b Modification factor of the rms displacements for nonbonding interactions. c Bond angle ∠Li+‚‚‚OdC. d Dihedral angle between the plane involving atoms Li+‚‚‚OdC and the plane involving OdCO2 atoms within the PC molecule. e Bond angle ∠Li+‚‚‚FsP. f Dihedral angle between the plane involving atoms Li+‚‚‚FsP and the plane involving FsPF3 atoms within PF6-. g X: O, C, D, F, P, and Li.

improvement of the fit in the low-Q region was obtained by introducing an additional intermolecular interaction at r ≈ 8 Å. Then, this additional interaction was involved in the longrange contribution in the present analysis. In evaluating this interaction, the coherent scattering length, bR, in eq 6 was tentatively assumed as the sum of coherent scattering lengths of constituent atoms within a PC molecule; 6bD + 4bC + 3bO. The best-fit result is compared with the observed ∆Li(Q) in Figure 1a. A satisfactory agreement is obtained between observed and calculated ∆Li(Q) in the whole Q range. The Fourier transform of the calculated ∆Limodel(Q) was also in good agreement with the observed GLi(r) as depicted in Figure 3. Final values of all independent parameters are summarized in Table 3. Before a more detailed discussion, we briefly survey the previous results for the Li+ ion in nonaqueous and polymer solution by neutron diffraction technique. Cartailler et al. has reported that the first coordination shell of the Li+ ion in the 3.1 mol % LiBr-CD3CN solution involves three CD3CN molecules and one Br-.20d We reported that the first coordination shell of Li+ ion is found to consist of three and two CD3OD molecules respectively in highly concentrated 25 mol % LiBr and 33 mol % LiI solutions in methanol.20l,21 The fourfold structure around Li+, Li+(CD3OD)3Br-, and Li+(CD3OD)2(I-)2 was suggested, considering the observed nearest neighbor Li+‚‚‚O(methanol) distances (rLiO ) 1.97(5) Å for LiBr and rLiO ) 1.93(5) Å for LiI solutions).20l) Structural information concerning the interaction between the Li+ ion and the carbonyl oxygen atom has been reported for the 6 mol % LiBr-acetone solutions.22 The first coordination shell of the Li+ ion has been found to involve 3.2(1) carbonyl oxygen atoms of the acetone molecule and 0.8(1) bromide ion with intermolecular distances of rLiO ) 2.24(1) Å and rLiBr ) 2.86(2) Å, respectively.22 The nearest neighbor Li+‚‚‚O(ether) distance and coordination number has been obtained for concentrated poly(ethylene oxide) solutions involving LiI (rLiO ) 2.10(4) Å, nLiO ) 4.2(5)),23 LiN(SO2CF3)2 (rLiO ) 2.10(4) Å, nLiO ) 4.9(5)),24 and LiClO4 (rLiO ) 2.07(4) Å, nLiO ) 4.2(6)).25 The present value of the nearest neighbor Li+‚‚‚O(PC) distance 2.04(1) Å with the coordination number 4.5(1) is in good agreement with those reported for concentrated Li-salt solutions of poly(ethylene oxide),23-25 in which the Li+ ion coordination number is found to be 3.5∼4.9. In addition, in the crystals of coordination compounds including the Li+ ion,41 the average Li+-O distances of the tetrahedrally four-coordinated Li+ ion are 1.944, 1.962, 1.923, and 1.957 Å for water, ethers, amides, and carboxylates, respectively, and those of the square

6108 J. Phys. Chem. B, Vol. 111, No. 22, 2007 pyramidal (SP) and the trigonal bipyramidal (TBP) fivecoordinated structure are 2.032 and 2.099 Å for ethers, 2.035 Å (SP) for amides, and 2.057 (SP) and 2.071 Å (TBP) for carboxylates. According to Shannon, the ionic radii of the Li+ ion of the four- and fivefold coordination are 0.59 and 0.73 Å, respectively.42 By employing 1.50 Å as the van der Waals radius of the carbonyl oxygen atom in PC,43 the atomic distances between Li+‚‚‚O(PC) are thus 2.09 Å for the fourfold coordination and 2.23 Å for the fivefold coordination, respectively. The present value of 2.04 Å is close to the former, implying that tetrahedrally four-coordinated Li+ ion is predominant in the present PC solution. On the other hand, the number of PC molecules bound to the Li+ ion recently reported from Raman spectra of the concentrated LiPF6 and LiBF4 PC solution is considerably smaller than that determined by the present work. Sano et al. recorded Raman spectra of LiPF6 and LiBF4 in PC solutions. They evaluated the apparent solvation number of the Li+ ion in PC to be 2.5-3 for LiPF6 solutions, whereas 1.2-1.6 for LiBF4.2 They ascribed the difference to the extent of the ion association of LiPF6 and LiBF4 and finally proposed that the PC solvation number of the Li+ ion is 4, though their determined solvation number in LiPF6 solutions was smaller, as will be discussed in detail below. As mentioned in Introduction, there have been some controversies on the solvation number of the Li+ ion in carbonate solutions investigated by means of Raman and IR spectroscopy in connection with the ion association. The early studies by means of Raman/IR spectroscopy have been mainly focused on LiClO4 salt solutions. The pioneering works have been made by Hyodo and Okabayashi.11 They revealed that the apparent solvation number of the Li+ ion in 0.1-1.0 mol dm-3 LiClO4 salt solution of EC decreased with the increase of the salt concentration, while the ion pairing corrected solvation numbers of the free Li+ ion were 4.0-4.9. They also found that no preferential solvation between EC and PC occurs in the mixed solvent system, indicating that the solvation number of the Li+ ion in PC is similar to that in EC.11 Aroca et al. showed that Li+ and ClO4- ions form the spectroscopically defined contact ion pair with bidentate ClO4coordination from Raman/IR spectra and higher level ab initio calculations.12 On the other hand, Cazzanelli et al. proposed that the Li+ ion was solvated less than four solvent molecules in the concentrated LiClO4 solution of the mixed solvent; that is, Li+ ion was “sandwiched” between two rings of the solvent molecules.13 Barthel et al. recorded IR spectra of PC containing 0.12-1.29 mol dm-3 LiClO4 and evaluated the apparent solvation number of the Li+ ion to be 2.3-1.7.14 They ascribed the smaller solvation number less than 4 to the steric hindrance of relatively bulky PC molecule and the contact ion pair formation. According to recent attentuated total reflection (ATR)-IR study by Brooksby and Fawcett,15 it turned out that the contact ion pair formation occurs in PC even in relatively low concentration, and the PC solvation number of the Li+ ion is 3 rather than 4. With regard to the LiPF6 salt solution, Morita et al. reported Raman spectra of 0.5, 1.0, and 1.5 mol dm-3 LiPF6 in EC and dimethyl carbonate (DMC) mixed solvents and determined the individual solvation numbers for the respective solvent components.16 The total solvation numbers, which are given as the sum of the individual solvation numbers, of the Li+ ion were 4.4, 4.1, and 3.9 for 0.5, 1.0, and 1.5 mol dm-3 LiPF6, solutions, respectively, suggesting that the Li+ ion is fully coordinated by four solvent molecules in the examined concentration range. On the other hand, Aroca et al. pointed out the possibility of

Letters the Li+-PF6- contact ion-pair formation by Raman/IR spectra of the EC-DMC mixed solvent and quantum mechanical calculations.17 Doucey et al. studied the LiAsF6 solution of DMC-PC solvent, which is closely related to LiPF6.18 They revealed that the solvation number of free Li+ ion corrected on the basis of the contact ion pairing in even in a relatively low dielectric constant solvent DMC was approximately 4 and independent from the salt concentration. Burba and Frech clearly demonstrated that Li+ and PF6- ions exist predominantly as free ions in a 5 mol % LiPF6 solution of PC by IR spectroscopic measurement, while significant ion association was found in the same salt concentration solution of DMC.19 The small values obtained from the recent Raman study on the LiBF4 and LiPF6 in PC2 were estimated without taking the Raman scattering coefficients into consideration. It is wellknown that the Raman scattering coefficient (or scattering cross section) depends on the polarizability of the scattering molecule. Therefore, one can easily expect that the Raman scattering cross section of the solvent bound to the metal ion may vary from that of the bulk solvent molecules upon solvation. Moreover, the situation of the solvent molecules bound to relatively small and hard Li+ ion can be serious. Apart from the problem of ignoring the Raman scattering cross section, the ion pair formation was not considered during the course of Raman spectra analyses in the literature, as the authors recognized. Judging from the above two problems, the solvation number 2.5-3 and 1.2-1.5 is considered to be too small. In fact, Hyodo and Okabayashi have reported the solvation number of the free Li+ ion in a closely related LiClO4 salt solution of EC to be 4.0-4.9 in consideration of the Raman scattering coefficient and the ion pair formation.11 It is worth mentioning the structural parameters obtained from molecular orbital calculations5,6 and molecular dynamics simulations.5a,6,8-10 According to MO calculations, the Li+‚‚‚O intermolecular distances within the isolated Li+(PC)n clusters in gas phase are 1.741 and 1.783 Å at the B3LYP/6-31G(d,p) level of theory5a and 1.769 and 1.811 Å at the B3PW91/ 6-31G(d)5b for n ) 1 and 2, respectively. For more larger clusters, the values of 1.893 and 1.968 Å for n ) 3 and 4 were obtained at the same level of theory.5b It is easily expected that the isolated Li+(PC)4 cluster in gas phase gives a slightly shorter Li+‚‚‚O(PC) distance because of none of the surrounding solvents. According to Probst et al.,6 the Li+‚‚‚O distances are 1.760, 1.800, 1.871, and 1.947 Å for the isolated Li+(EC)n clusters (n ) 1-4) at the MP2/6-31G level of theory. With regard to the ∠Li+-O-C(EC) angle, the value of approximately 145° was predicted by MO calculation for the Li+(EC)4 cluster,6 which is in good agreement with that obtained in the present work (138°). The Li+‚‚‚O distance, slightly less than 1.78 Å, reported by Soetens et al.,8 who performed MD simulations of the system containing 1 Li+BF4- and 214 PC molecules at 298 and 323 K, is much smaller, and the ∠Li+-O-C(PC) angle 160° at 348 K is larger than those obtained in the present work. The situation seems to be similar to those predicted by MD simulations for the system consisting of 1 Li+ ion and 214 EC molecules.6 On the other hand, the Li+‚‚‚O distances reported to be 2.05 and 2.06 Å for PC and EC, respectively, from MD simulations by Tasaki9 and approximately 1.95 Å for EC by Borodin et al.10a agree with the present one. Moreover, the ∠Li+-O-C(EC) angle 142° are also in good agreement with the present value.10a The present value of the nearest neighbor Li+‚‚‚F(PF6-) distance, rLiF ) 2.98(1) Å, is much larger than the sum of ionic

Letters radius of the Li+ ion42 and van der Waals radius of the F atom43 (0.59 + 1.47 ) 2.06 Å). This suggests that the Li+‚‚‚PF6contact ion pair is little formed in the present solution, though the formation of the Li+‚‚‚PF6- ion pair in PC was proposed from electrochemical measurements1 and MD simulations.9 It should be noted that there are nine solvent PC molecules per one Li+ ion and one PF6- ion in the concentrated 10 mol % LiPF6 solution of PC. Therefore, most of the ions may exist as at least the solVent shared and solVent separated ion pairs in such a concentrated solution. Evidently, the present study revealed that the PF6- ion dominantly exists in the second or higher solvation sphere of the Li+ ion. The concentration dependence of the conductivity of the highly concentrated LiPF6-PC system indicated that the maximum of the conductivity occurs in a 5∼9 mol % LiPF6 composition.2 A significant decrease in the conductivity observed for more concentrated solutions above approximately 13 mol % LiPF6 is considered to be closely related to the formation of the Li+‚‚‚PF6- contact ion pair which may be formed in more concentrated LiPF6PC solutions. It is of considerable interest to investigate the structure of the Li+‚‚‚PF6- contact ion pair formed in highly concentrated LiPF6-PC solutions, which requires additional Raman/IR measurements and neutron diffraction ones on 6Li/7Li and H/D isotopic substituted samples. This will be a future project. Acknowledgment. The authors thank Professor Toshiharu Fukunaga (Kyoto Univrtsity) and Dr. Keiji Itoh (Kyoto University) for their help during the neutron diffraction measurements. All calculations were carried out at the Yamagata University Networking and Computing Service Center. This work was partially supported by Grant-in-Aid for Scientific Research (C) (Nos. 16550049, 17350037, and 19350033) and Creative Scientific Research (No. 16GS0417), from the Ministry of Education, Culture, Sports, Science, and Technology. References and Notes (1) (a) Ue, M. J. Electrochem. Soc. 1994, 141, 3336. (b) Ue, M.; Mori, S. J. Electrochem. Soc. 1995, 142, 2577. (2) (a) Kondo, K.; Sano, M.; Hiwara, A.; Omi, T.; Fujita, M.; Kuwae, A.; Iida, M.; Mogi, K.; Yokoyama, H. J. Phys. Chem. B 2000, 104, 5040. (b) Tsunekawa, H.; Narumi, A.; Sano, M.; Hiwara, A.; Fujita, M.; Yokoyama, H. J. Phys. Chem. B 2003, 107, 10962. (3) (a) Hayamizu, K.; Aihara, Y.; Arai, S.; Martinez, C. G. J. Phys. Chem. B 1999, 103, 519. (b) Aihara, Y.; Sugimoto, K.; Price, W. S.; Hayamizu, K. J. Chem. Phys. 2000, 113, 1981. (4) (a) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93, 1157. (b) Ohtaki, H. Monatsh. Chem. 2001, 132, 1237. (5) (a) Li, T.; Balbuena, P. B. J. Electrochem. Soc. 1999, 146, 3613. (b) Wang, Y.; Balbuena, P. B. J. Phys. Chem. B 2002, 106, 4486. (6) Masia, M.; Probst, M.; Rey, R. J. Phys. Chem. B 2004, 108, 2016. (7) Fukushima, T.; Matsuda, Y.; Hashimoto, H.; Arakawa, R. Electrochem. Solid-State Lett. 2001, 4, A127. (8) Soetens, J.-C.; Millot, C.; Maigret, B. J. Phys. Chem. A 1998, 102, 1055. (9) Tasaki, K. J. Electrochem. Soc. 2002, 149, A419. (10) (a) Borodin, O.; Smith, G. D. J. Phys. Chem. B 2006, 110, 4971. (b) Borodin, O.; Smith, G. D. J. Phys. Chem. B 2006, 110, 6293. (11) (a) Hyodo, S.; Okabayashi, K. Electrochim. Acta 1989, 34, 1551. (b) Hyodo, S.; Okabayashi, K. Electrochim. Acta 1989, 34, 1557. (12) (a) Battisti, D.; Nazri, G. A.; Klassen, B.; Aroca, R. J. Phys. Chem. 1993, 97, 5826. (b) Klassen, B.; Aroca, R.; Nazri, G. A. J. Phys. Chem. 1996, 100, 9334.

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