Pulse-Gradient Spin-Echo 1H, 7Li, and 19F NMR Diffusion and Ionic

Pulse-Gradient Spin-Echo 1H, 7Li, and 19F NMR Diffusion and Ionic ... E-mail: [email protected]., † ... (LiTFSI, LiN(SO2CF3)2) solvent systems wer...
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J. Phys. Chem. B 1999, 103, 519-524

519

Pulse-Gradient Spin-Echo 1H, 7Li, and 19F NMR Diffusion and Ionic Conductivity Measurements of 14 Organic Electrolytes Containing LiN(SO2CF3)2 Kikuko Hayamizu,*,† Yuichi Aihara,‡ Shigemasa Arai,‡ and Cirilo Garcia Martinez†,§ National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan, and Yuasa Corporation, 6-6 Josai-cho, Takatsuki, Osaka 569-0065, Japan ReceiVed: June 9, 1998; In Final Form: NoVember 23, 1998

The self-diffusion coefficients of the lithium ion, the anion, and the solvent in lithium bis(trifluromethanesulfonyl)imide (LiTFSI, LiN(SO2CF3)2) solvent systems were measured using the pulse-gradient spin-echo (PGSE) NMR method. Fourteen different organic solvents that are commonly used as organic solution electrolytes in lithium batteries were studied. The self-diffusion coefficients of the corresponding pure solvents were also measured. Since a good correlation between the self-diffusion coefficients of the pure solvents and the inverse of the viscosity was obtained, the results are discussed in terms of the Stokes-Einstein equation. Comparisons of the self-diffusion coefficients of the solvent, the lithium ion, and the anion (TFSI ion) illustrate the solvation behavior for each solvent. The relationship between the ionic conductivity and the sum of the diffusion coefficients of the lithium ion and the anion gives the degree of ion-pair formation and permits the roles of the solvents in the electrolytes to be clearly explained.

Introduction In functional materials, the transportation of a given component within the material is related to the specified functions. Thus, molecular motion is important in characterizing functional materials. The self-diffusion coefficient is a fundamental parameter and provides the basis for understanding the origin of such functions. Actually, many investigations of diffusion phenomena have been reported, but the methods for measuring self-diffusion coefficients have been limited and consequently diffusion data were rarely presented or discussed. Recently, the pulse-gradient spin-echo NMR (PGSE-NMR) method was shown to provide self-diffusion coefficients with good accuracy and reliability.1-5 The PGSE-NMR method is noninvasive, and it is possible to measure independently the self-diffusion coefficient of each component in the system under study, providing the components contain NMR-sensitive nuclei. Organic electrolytes are crucial elements in lithium ion batteries; however, the structures of the electrolyte solutions and the mechanisms of the ion conduction are not well-known.6 Studies of organic solution electrolytes have been conducted mainly using electrochemical techniques. To evaluate the organic solvents as electrolytes, physical parameters such as solubility, solvation, formation of ion pairs, viscosity, and mobility are important factors to consider because they govern the efficiency of the ion transportation. The ionic conductivity is strongly related to the diffusion of cations and anions. In contrast to NMR relaxation times such as T1 and T2, the PGSENMR method provides a direct measurement of the translational self-diffusion coefficient. The PGSE-NMR method has a great advantage over traditional methods for measuring diffusion * Corresponding author. Tel and Fax: +81-298-54-4525. E-mail: [email protected]. † National Institute of Materials and Chemical Research. ‡ Yuasa Corp. § Present address: Universidad Autonoma Metropolitana, Division de CBI, Area de Quimica, Av. San Pablo 180, Tamaulipas, Azcapotzalco 02200, DF, Mexico.

because it is possible to measure the self-diffusion coefficients of all the diffusing species such as the lithium ion, the anion, and the solvent by using 7Li, 19F, and 1H NMR, respectively. Since the NMR time scale is longer compared to that of most popular measuring techniques in electrochemistry, it is important to consider the exchange rate of a species. For example, in the case of a solvent molecule exchanging between the bulk solvent and the solvation shell of an ion under equilibrium conditions, if the exchange is slow, and assuming that the solvent has separate resonances for the two states, the individual diffusion coefficients for each state can be measured. In the intermediate exchange regime, the measured diffusion coefficient will be an average which depends on the relative populations and the exchange rates. In the fast exchange limit, the measured diffusion coefficient will reflect the population-weighted average value. We have applied the PGSE-NMR technique to the polymer gel electrolyte systems composed of cross-linked poly(ethylene oxide) (PEO), γ-butyrolactone, and LiBF4 and measured the self-diffusion coefficients of the polymer, the solvent, the lithium ion, and the anion. Combining the differential scanning calorimetry (DSC) and ionic conductivity data, it was possible to interpret the gel structure and the mechanism of the ion diffusion in the gel electrolytes.7 To fully understand the polymer gel electrolyte system, we found that self-diffusion coefficient data for various solution electrolytes are necessary. In the present study, we measured the diffusion of the components of the solution electrolytes composed of lithium bis(trifluromethanesulfonyl)imide (LiTFSI, LiN(SO2CF3)2) and 14 different organic solvents which are important in lithium battery systems by using PGSE-NMR. Solvents such as cyclic carbonates (ethylene carbonate (EC) or propylene carbonate (PC)) and a cyclic ester of γ-butyrolactone (GBL) are widely used as the main solvents in rechargeable lithium batteries. To improve the conductivity, additional solvents (i.e., cosolvents) such as dimethoxyethane (DME), tetrahydrofuran (THF), diethoxyethane (DEE), and

10.1021/jp9825664 CCC: $18.00 © 1999 American Chemical Society Published on Web 01/05/1999

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Hayamizu et al.

others have been used. Polymer electrolytes are also important target materials to use as the electrolytes in rechargeable lithium batteries. Poly(ethylene oxide) (PEO) is one of the most important candidates for practical usage in polymer electrolytes.8,9 In this study, we include a family of CH3O-(CH2CH2O)n-CH3 where n ) 1, 2, and 3 corresponds to DME, diglyme (DG), and triglyme (TG), respectively. To our knowledge, except for our previous paper,7 this is the first time that the self-diffusion coefficients have been measured for all the components of the solution electrolytes. In addition to those of the 14 electrolytes, the self-diffusion coefficients of the 14 pure solvents were measured. For 12 pure solvents for which reliable data of the viscosity can be found in the literature, it was found that a good correlation exists between the self-diffusion coefficient and the viscosity according to the Stokes-Einstein equation

D)

kT 6πηrS

(1)

where η is the viscosity, D is the self-diffusion coefficient, and rS is the effective hydrodynamic (or Stokes) radius. This equation provides a starting point for interpreting diffusion phenomena. From the experimental data, the validity of the equation will be discussed for the pure solvents. Using the Stokes-Einstein equation, the solvation numbers of lithium and TFSI in the electrolytes are estimated from the relative values of the diffusion coefficients of the solvent and lithium or TFSI which were measured independently. In addition to the selfdiffusion coefficients, the ionic conductivity of each sample was measured. Comparison of the ionic conductivity and the sum of the diffusion coefficients of lithium and TFSI gives a measure of the degree of dissociation of the ion pairs. Experimental Section Sample Preparation. All sample preparation was carried out in a dry air atmosphere. The lithium salt, LiTFSI, was used after drying at 60 °C under vacuum better than 0.01 Torr for 48 h. The lithium battery grade solvents were purchased from Tomiyama Pure Chemical Industries Ltd., Tokyo. The residual water was less than 20 ppm for all the solvents used in this study. The molar solvent-to-salt ratio was set as 20:1. The molar concentration was calculated using the specific density of each electrolyte measured at 30 °C. For NMR measurements, each electrolyte or pure solvent was placed into a 5 mm (o.d.) NMR microtube (BMS-005J, Shigemi, Tokyo) to a height of 5 mm. The length of the sample was intentionally made short so that it lay within the region of the constant magnetic field gradient. NMR Measurements. The PGSE-NMR measurements were made by using a JEOL GSH-200 spectrometer with a 4.7 T wide bore superconducting magnet controlled by a TecMAG Galaxy system equipped with JEOL pulse field gradient probes and a current amplifier. The self-diffusion coefficients were obtained at 30 °C except for those of EC and its electrolyte, for which the measurements were made at 40 °C. The gradient strength was calibrated as described in our previous paper7 and cross-checked using the known self-diffusion coefficient of H2O at 25 °C (2.23 × 10-9 m2 s-1).10 The measurements of the diffusion coefficients of the solvent, the anion, and the lithium ion were made by 1H, 19F, and 7Li NMR, respectively. The simple spin-echo pulse sequence was used for the diffusion measurements, and the free diffusion echo signal attenuation,

Figure 1. Self-diffusion coefficients at 30 °C versus the inverse of the viscosity at 25 °C for the pure liquids, except for ethylene carbonate, for which data were obtained at 40 °C.

E, is related to the experimental parameters by11

ln(E) ) ln(S/Sg)0) ) -γ2g2Dδ2(∆ - δ/3)

(2)

where S is the spin-echo signal intensity, δ is the duration of the field gradient with magnitude g, γ is the gyromagnetic ratio, and ∆ is the interval between the two gradient pulses. Typical acquisition parameters were ∆ ) 50-150 (1H), 50 (7Li), and 50 (19F) ms and g ) 0.80 (1H), 1.7-2.5 (7Li), and 1.0-2.2 (19F) Tm-1. The 90° pulse lengths were 9.5 (1H), 6.5 (7Li), and 9.0 (19F) µs. In all cases, a spectral width of 1000 Hz was digitized into 1K data points. Each spectrum was the average of 16-32 (1H and 19F) and 300-500 (7Li) transients for more than 12 different δ values. A recycle delay sufficient to allow for full relaxation (i.e., > 5T1) was used between each transient. All the measured signal attenuations were well described by a straight line as expected for free diffusion (see eq 2), and the standard deviations of the plots were less than 1% (1H and 19F) and 2% (7Li). The linearity of the plots was also consistent with the measured species being in the fastexchange limit on the time scale of ∆. Ionic Conductivity Measurements. The ionic conductivity measurements were performed using the ac impedance method on a Solartron 1286 electrochemical Interface and 1255 frequency response analyzer controlled by a personal computer. The measurements were carried out from 100 Hz to 1 MHz at 30 °C, except those for the EC electrolyte, which were performed at 40 °C. A glass cell with fixed platinum electrodes was used. The cell constant was determined from measuring a 0.1 N KCl (f ) 1.0056) standard solution obtained from Kanto Chemical Co., Ltd., Tokyo. Results The basic properties of the 14 pure solvents used in this study are listed in Table 1; however, no reliable viscosity data or dielectric constants could be found for EP and DEE. In Table 2, the self-diffusion coefficients of the pure solvents are listed, as well as the self-diffusion coefficients of the solvent, lithium, and TFSI of the electrolyte solutions. The ionic conductivities and the ion-pair formation parameters (degrees of dissociation) are also shown in Table 2. In Figure 1, the self-diffusion coefficients of the pure solvents are plotted versus the inverse of the viscosity, 1/η. A linear relationship was found for all 12 solvents. It is known that the viscosity of the electrolyte solutions increases with the salt concentration.12 Hence the significant decrease of the solvent self-diffusion coefficients in the elec-

Organic Electrolytes Containing LiN(SO2CF3)2

J. Phys. Chem. B, Vol. 103, No. 3, 1999 521

TABLE 1: Basic Physical Properties of the 14 Solvents name EC PC BC GBL GVL NMP TG DG DME DEE DOx THF EP DMC g

MF

ethylene carbonate propylene carbonate butylene carbonate γ-butyrolactone γ-valerolactone N-methyl-2-pyrrolidinone triglyme diglyme 1,2-dimethoxyethane 1,2-diethoxyethane 1,3-dioxolane tetrahydrofuran ethyl propionate dimethyl carbonate

C3H4O3 C4H6O3 C5H8O3 C4H6O2 C5H8O2 C5H9NO C8H18O4 C6H14O3 C4H10O2 C6H14O2 C3H6O2 C4H8O C5H10O2 C3H6O3

MW 88.1 102.1 116.1 86.1 100.1 99.1 178.2 134.2 90.1 118.2 74.08 72.11 102.1 90.1

bp (°C) 244 240 205 208 82h 216 162 85 124 78 66 99 90

ηa

a

remarks

1.85 2.51d 3.2e 1.73d 2.0e 1.67c 2.01f 1.00f 0.42f

89.6b,c 64.4c 53e 39.1c 34e 32c 7.51g 7.27g 6.99g

cyclic carbonate cyclic carbonate cyclic carbonate cyclic ester cyclic ester

0.59c 0.46c

7.1c 7.4c

0.59e

3.1e

b,c

linear ether linear ether linear ether linear ether cyclic ether cyclic ether linear ester linear carbonate

a η (viscosity, cP) and  (dielectric constant) are the data at 25 °C. b At 40 °C. c Reference 18. d Reference 15. e Reference 21. f Reference 22. Reference 23. h At 10 mmHg.

TABLE 2: Self-Diffusion Coefficients, Ionic Conductivities and Degrees of Dissociation at 30 ˚C diffusion coeff (10-10 m2 s-1)

ECa PC BC GBL GVL NMP TG DG DEE DME DOx THF EP DMC a

pure solvent (1H NMR)

solvent (1H NMR)

N(SO2CF3)2 (19F NMR)

lithium (7Li NMR)

ionic conductivity (10-3 S cm)

degree of dissociation

8.0 5.8 4.5 9.0 8.1 8.2 6.1 13 22 31.5 25.5 30 25 26

4.3 3.5 2.6 5.3 5.0 5.1 4.6 9.3 15 22 17 13 17 16

3.1 2.6 2.0 3.8 3.4 3.7 3.0 5.0 6.1 8.8 6.2 7.3 7.3 6.0

2.1 1.6 1.2 2.5 2.1 2.4 2.6 4.5 6.1 7.7 6.4 5.9 7.5 5.8

8.3 5.2 3.5 8.9 6.4 2.0 2.0 4.5 1.8 8.9 3.1 10.6 6.7 2.7

0.62 0.64 0.64 0.65 0.18 0.37 0.38 0.12 0.31 0.10 0.36 0.27 0.11

Measured at 40 °C.

Figure 2. Self-diffusion coefficients of the lithium ion and the anion (TFSI) versus the self-diffusion coefficient of the solvent. The solid circles and open squares indicate the self-diffusion coefficients of lithium and TFSI, respectively.

trolytes compared to the pure liquids in Table 2 is reasonable. The self-diffusion coefficients of lithium and TFSI are plotted versus the self-diffusion coefficient of the corresponding solvent in Figure 2. The linear relationship between the diffusion of the ions and that of the solvent indicates that the diffusion of the ions is mainly governed by the diffusion of the solvent and that the Stokes-Einstein equation is valid for the present solution electrolytes. Thus the relative ratio of the diffusion coefficients of the solvent and ions is a measure of the Stokes radius. In Figure 3, to clarify the nature of the solvents, the ratios of the solvent diffusion coefficient (Dsolvent) to the those

Figure 3. Experimental ratios of the Stokes radii of lithium, RLi, and the anion, RTFSI, relative to the solvent plotted against the self-diffusion coefficient of the solvent. The R values were calculated as the ratios of the diffusion coefficient of the solvent to those of the ions; i.e., RLi ) Dsolvent/DLi (solid circles) and RTFSI ) Dsolvent/DTFSI (open squares). The dotted lines are guides for the eyes.

of lithium (DLi) and TFSI (DTFSI), i.e., RLi ) Dsolvent/DLi and RTFSI ) Dsolvent/DTFSI, are plotted versus Dsolvent. The ionic conductivity is plotted against the sum of the diffusion coefficients of lithium and TFSI in Figure 4. At a glance, little correlation is found between the diffusion of lithium and TFSI and the ionic conductivities, including those of all the solvents. But when TG, DG, and DME, members of a glyme family, are connected, this series separates the main solvents

522 J. Phys. Chem. B, Vol. 103, No. 3, 1999

Hayamizu et al. cyclic carbonates (EC, PC, and BC), cyclic esters (GVL and GBL), cyclic ethers (DOx and THF), linear ethers (DME, DG, and TG), a linear carbonate (DMC), and NMP. This is surprising in view of the nonuniformity of compounds with respect to molecular shape and size. It has been reported that the factor 6 in eq 1 should be replaced by 4 when the boundary conditions over the surface of the sphere were changed from “stick” to “slip” in the theoretical treatment.13 Following the proposal of Collings and Mills,14 it is more realistic to rewrite eq 1 as

D)

Figure 4. Ionic conductivity versus the sum of the diffusion coefficients of lithium (DLi) and TFSI (DTFSI).

Figure 5. Degree of dissociation versus the self-diffusion coefficient of the solvent.

and the cosolvents except for THF. Within the series of the cyclic carbonates (BC, PC, and EC) and the cyclic esters (GVL and GBL), a good correlation between the diffusions of lithium and TFSI and the ionic conductivities can be observed. The linear esters and ethers, e.g., DEE, DMC, and DOx, show small ionic conductivities, although the diffusions of the solvent, lithium, and TFSI are larger. EP and THF may belong to a different solvent category. As shown in our previous paper, it is necessary to modify the Nernst-Einstein equation by introducing the degree of association, ξ, such that

σD )

Ne2 (D + D-)(1 - ξ) kT +

(3)

where N is the number of the lithium atoms per cm3. For convenience, we define the degree of dissociation R ) 1 - ξ because it is more directly related to the conductivity. The calculated values of the degree of dissociation are given in Table 2 and plotted in Figure 5 versus the diffusion coefficients of the solvents. Discussion Pure Solvents. The validity of Stokes-Einstein equation (eq 1) has been discussed for a long time. Since the experimental D values of the series of compounds are obtained in this paper, the validity of eq 1 can be examined. As shown in Figure 1, a good linear correlation between D and 1/η was found for the

kT cπηrS

(4)

where c is an arbitrary constant chosen to fit the experimental results. We stress that it is generally not possible to separate c from the calculated rS. The good linear relationship gives the value of crS ) 0.96 nm (the scatter of the plot of the data for the 12 molecules was about 4%), where T ) 303 K (30 °C) was assumed, because the diffusion coefficients were measured at 30 °C and the literature values of the viscosity are given at 25 °C and the data of EC were obtained at 40 °C. Here it is surprising that all of the organic solvents have similar values for crS. From MM2 calculations, the van der Waals radii of GBL and PC have been given as 0.268 and 0.276 nm, respectively.15 Taking the van der Waals radius as being equal to rS, the values of c are calculated to be 3.2 and 3.3 for GBL and PC, respectively. Collings and Mills proposed that the values of c are 3.61 and 3.79 for benzene and carbon tetrachloride, respectively.14 Their measurement of the self-diffusion coefficient was made by the diaphragm-cell method, and their value for benzene agrees well with our value measured by PGSENMR. The plot of benzene fits on the line in Figure 1. Their value for carbon tetrachloride deviates significantly to the lower side, and the recent value obtained by the 13C PGSE-NMR method (W. S. Price, private communication) also deviates in the same direction but to a smaller degree. This indicates that the value c for CCl4 is closer to 4. The Stokes-Einstein equation was proposed for solid spherical particles diffusing in a uniform medium, and its application to neat liquids is not physically justified; nevertheless, it is possible to relate the diffusion phenomena to the shape of a molecule or to an intermolecular interaction. The relationship between the molecular volumes and Stokes radii for many organic solvents has been discussed with regard to the shapes of the molecules;16 thus the experimental crS values are very important for describing the transport phenomena in actual systems. Until recently, reliable values of the self-diffusion coefficient were limited, and the Stokes radii have been calculated from the shapes of the molecules. Actual translational diffusion in liquids is affected by intermolecular attraction and repulsion; therefore, crS provides information on the molecular interactions. Here it is shown that the pure solvents generally used for the electrolytes in the lithium batteries have similar diffusion properties. This information is extremely important for improving the efficiency of ion transport through judicious choices of solvent combinations. Roles of the Solvents in the Diffusion of Lithium and TFSI. The self-diffusion coefficients of the solvent, the anion TFSI, and lithium shown in Table 2 indicate that the diffusion coefficient of the solvent decreases with addition of LiTFSI, although the solvent remains the fastest diffusing species. The ratio of the decrease of the diffusion coefficient of the solvent was largest in THF. From Figure 2, the diffusion coefficients of TFSI are generally larger than those of the lithium ion despite

Organic Electrolytes Containing LiN(SO2CF3)2 the smaller size of the lithium ion. Thus the solvation of the lithium ion can be assumed. From the Stokes-Einstein relationship, the ratio of the diffusion coefficient should be proportional to the reciprocal of the ratio of the radius of the species, which is shown in Figure 3. When the solvents are the cyclic carbonates and esters, RTFSI is almost 1.3. Using the van der Waals radii of TFSI (0.326 nm), GBL (0.268 nm), and PC (0.276 nm) calculated by the MM2 method,15 the ratios of the size of TFSI to those of GBL and PC are 1.22 and 1.18, respectively, which agrees with the values for RTFSI of 1.4 (GBL) and 1.3 (PC) obtained from the diffusion coefficients. The value of RTFSI indicates that TFSI is not significantly solvated and diffuses similarly to the solvent. The RLi values of lithium are between 2.1 and 2.3. Since the size of the lithium ion is about 30% of that of the solvents, RLi must be determined mainly by the size of the solvation sphere. It is likely that a lithium ion is surrounded by two solvent molecules in a sandwich type coordination, as proposed by Cazzanelli and co-workers.17 If the sandwich configuration is very stable and diffuses together with lithium, RLi should be much larger than 2. It is clear that the solvent molecules are exchanging between the coordinated sites and the bulk solvent. When the solvents are DEE, DMC, EP, and DOx, RTFSI and RLi of each electrolyte have values within the range 2.3-2.8. This indicates the strong formation of the Li and TFSI ion pairs, which are surrounded by the one or more solvent molecules. This model agrees with the small degree of dissociation shown in Figure 5. The linear ethers DME, DG, and TG, a family of glymes, show similar behavior. DME has two oxygen atoms in the ether structure, and from the large RLi value (2.8), the solvation number is larger than 2 or the anion TFSI is paired in the solvation sphere. Also, the RTFSI is large (2.4) and indicates that a 1 to 1 interaction of TFSI and solvent DME is possible. Here it is necessary to consider that the same solvent molecule enters the solvation spheres of lithium and TFSI at the same time. As discussed later, a partial ion pair is formed between lithium and TFSI in DME, where the lithium ion is surrounded by two DME molecules and one DME molecule is shared with TFSI. Since the measuring time scale of the PGSE-NMR method is of the order of ∆ (i.e., 10-2-10-3 s), the relative diffusing sizes of the ions with the solvent molecules are always well averaged. The picture of the solvation and the ion pairing in DME is that a lithium ion is coordinated by two DME molecules and forms a pair with TFSI through one solvent molecule. When the counterion is exchanged, the unit of TFSI and one molecule of DME is interchanged. Schematically, (DME-Li+-DMETFSI-) exchanges in the coordination sphere as (DME-Li+) + (DME-TFSI-). DG and TG have three and four ether oxygen atoms, respectively, in one molecule. Since there is evidence that the TFSI in DG and TG is solvated as shown in Figure 3, the solvation scheme of a lithium ion is similar to that of DME. But the stability of the solvation of DG and TG is less than that of DME because of the larger sizes of DG and TG. Diffusion and Ionic Conductivity. Since the self-diffusion coefficients measured by the PGSE-NMR method include all the species (i.e., isolated, ion-paired, and solvated states), the measured values are the population-weighted averages of the various states. On the other hand, ionic conductivity results from the charged ions (i.e., cations and anions). When the solvents are classified as shown in Figure 4, good correlations between the ionic conductivity and the sum of the diffusion coefficients can be observed. Among the cyclic carbonates and esters, the diffusions and ionic conductivities increase as the sizes of the

J. Phys. Chem. B, Vol. 103, No. 3, 1999 523 solvent molecules decrease although the carbonates and the esters belong to different series. The structural analogues of the linear ethers, TG, DG, and DME, belong to another series as shown in Figure 4. As described above, the solvation scheme is different from that of the cyclic carbonate and the esters. But the trend is much the same in that as the diffusion of the solvent increases, the ionic conductivity also increases. In DMC, DEE, and DOx, the stable ion pair is surrounded by one or more solvents on average, and as a result, the ionic conductivity is very small. When the chemical structures of DEE and DME are considered, the two terminal methyl groups in DME are replaced by ethyl groups in DEE, which gives a large difference in ion-pair formation and solvation. NMP is well-known to dissolve organic compounds well and is used in lithium battery systems.18 It is clearly shown that the lithium ion is solvated by NMP, but the ionic conductivity is very small, even compared to those of solvents of similar diffusion coefficients probably because of the small degree of dissociation. THF and EP show slightly larger ionic conductivities compared to those estimated from their diffusion behaviors. Degree of Dissociation. The Nernst-Einstein equation connecting the ionic conductivity and the diffusion of the ions was originally derived for the infinitely dilute state, and phenomenologically we applied our data to eq 3. The relationship between the degree of dissociation and the self-diffusion coefficient of the solvent in Figure 5 provides some very important information on the nature of the solution electrolytes, similar to our previous paper discussing polymer gel electrolytes.7 Principally, it must be noted that the degree of dissociation varies depending on the concentration of the salt and temperature. The dissociation factors of the cyclic carbonates and esters are between 0.6 and 0.7 and the dielectric constants of the solvent are also large as shown in Table 1. As described above, the lithium ion is solvated with two molecules on average and TFSI is isolated from the solvent, although the ion-pair formation is about 35-40%. From the self-diffusion data in Figure 3, the ion-pair formation is not clearly shown, suggesting that the lifetime of the ion-pair formation is shorter than ∆ (ms order) at 30 °C. The second group (i.e., TG, DG, THF, EP, and DME) have degrees of ion dissociation around 0.35, and the solvent dielectric constants are about 7. From the solvation scheme, in addition to the lithium, TFSI has an affinity for the solvent and the formation of ion pairs can be assumed to occur as solvated ion pairs such as “solvent-Li+-solvent-TFSI-” for TG, EG, THF, and DME. The averaged lifetime of the ion pair can be assumed to be longer than ∆ for the ion pair because its existence is estimated from the NMR diffusion measurements. The third group contains DEE, DMC, and DOx, where the degree of dissociation is about 0.1 and the dielectric constants of DMC and DOx are 3.1 and 7.1, respectively. The solvation scheme can be estimated as “solvent-Li+TFSI-” or “solvent-Li+TFSI--solvent”. The ion pair is very stable and can be observed from the diffusion measurements. Cation Transport Number. The cation transport number t+ can be calculated from the diffusion coefficient as 19;20 t+ ) DLi/(DLi + DTFSI), and the results of all the electrolytes are shown in Figure 6. The cyclic carbonates and esters have cation transport numbers between 0.38 and 0.4 because the solvated lithium ion diffuses slower than the isolated anion. The cation transport numbers in the family of glymes are ∼0.45, even if the solvent diffusion coefficients are scattered. The mechanisms of the ion diffusions in the glymes must be very similar. In the

524 J. Phys. Chem. B, Vol. 103, No. 3, 1999

Hayamizu et al. diffusion coefficients increase. The molecular weight must affect this correlation, and the degree of dissociation is about 37% for all the solvents in this family. The third solvent group includes DMC, DEE, EP, and DOx, where due to the stable ion-pair formation, the ionic conductivity is small although the solvent and the ion pair diffuse with reasonable speed corresponding to the small viscosity. Acknowledgment. C.G.M. acknowledges a ITIT and STA fellowship for a 15 month stay at NIMCR. The authors thank Dr. W. S. Price for his valuable comments. References and Notes

Figure 6. DLi/(DLi + DTFSI) versus the diffusion coefficient of the solvent.

DEE, DMC, EP, and DOx group, although the degree of dissociation is small and ion-pair formation is large, the cation transfer numbers are larger, where lithium diffuses faster together with the solvent compared to the anion diffusion. Conclusions The most commonly used organic main solvents in rechargeable lithium electrolytes form a solvation shell around the lithium ion with the average shell containing two solvent molecules while the anion TFSI is not solvated, and short-time ion-pair formation can be shown in these electrolytes. More stable ion pairs are formed in the cosolvents such as DME or the glymes where the lithium ions are surrounded by two solvent molecules, one of which is shared with TFSI. When exchange occurs between different counterions, TFSI diffuses with one solvent molecule. Other cosolvents such as DMC, DEE, or DOx form stable ion pairs without the solvents between the ions, and the solvent shells are outside the ion pairs. From the relationship between the sum of the self-diffusion coefficients of lithium and TFSI and the macroscopic ionic conductivity, the solvents can be classified into three categories. One is the cyclic carbonates and esters, which have a close correlation between the ionic conductivity and the diffusion coefficients of lithium and TFSI. The degree of dissociation of the ion pair is large and about 64%. The next category is TG, DG, and DME, which are the glyme family of CH3O-(CH2CH2O)n-CH3. As n decreases, the ionic conductivity and the

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