An NMR and Ionic Conductivity Study of Ion Dynamics in Liquid Poly

Patrik Gavelin and Patric Jannasch , István Furó, Erik Pettersson, and Peter Stilbs , Daniel Topgaard and Olle Söderman. Macromolecules 2002 35 (13...
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J. Phys. Chem. B 2002, 106, 547-554

547

An NMR and Ionic Conductivity Study of Ion Dynamics in Liquid Poly(ethylene oxide)-Based Electrolytes Doped with LiN(SO2CF3)2 Kikuko Hayamizu,* Kyoko Sugimoto, and Etsuo Akiba National Institute of AdVanced Industrial Science and Technology, AIST Tsukuba Center 5, Tsukuba 305-8565, Japan

Yuichi Aihara and Toshinori Bando Yuasa Corporation, 4-5-1 Ohgi-cho, Odawara 250-0001, Japan

William S. Price Department of Chemistry, Tokyo Metropolitan UniVersity, 1-1 Minami-Ohsawa, Hachioji 192-0397, Japan ReceiVed: August 7, 2001; In Final Form: NoVember 2, 2001

NMR and ionic conduction measurements have been performed for two liquid-state high-molecular-weight comb-branched polyethers, which are macromonomers of cross-linked random copolymers, with and without LiN(SO2CF3)2 (LiTFSI) doping. The macromonomers are derivatives of glycerol bonded to (ethylene oxide)co-(propylene oxide) (m(EO-PO)) and (ethylene oxide)-co-(2-(2-methoxyethoxy)ethyl glycidyl ether) (m(EOGE)) with molecular weights of about 8 000 and 10 000, respectively. The dynamics of the lithium ion, anion, and the macromonomers were characterized by 7Li, 19F, and 1H NMR spin-lattice relaxation time (T1) and self-diffusion coefficient (D) measurements. Because the temperature dependence of the 1H and 7Li NMR T1 exhibited minima, the reorientational correlation times were able to be calculated. Above 278 K, the segmental motions in the neat liquid-state macromonomers are faster than those in the cross-linked state, and they become almost the same at lower temperatures and are slowest in m(EO-PO). When doped with LiTFSI the segmental motions in the liquid electrolytes slowed to values similar to those in the cross-linked polymer. The translational diffusion coefficients were in the order (fastest to slowest) of anions > lithium ions > macromonomers. The diffusion of the ions correlated well with the macromonomer diffusion. The ionic conductivity of doped m(EO-PO) was higher than that of doped poly(EO-PO), and comparison of the measured ionic conductivity with estimates of the ionic conductivity calculated from Danion and DLi indicates high ion dissociation in the macromonomer electrolytes. The results are consistent with a picture of the lithium ions undergoing local motions near the polymer chains, whereas the anions diffuse through a slowly fluctuating three-dimensional porous polymer matrix.

Introduction In addition to the myriad possible practical applications such as high-density solid-state batteries, capacitors, electronic devices, and sensors, solid polymer electrolytes are intrinsically scientifically interesting from the viewpoint of understanding ion dynamics in polymer networks.1 Until now, most polymer electrolytes have been based on poly(ethylene oxide) (PEO). Solid PEOs are in effect “polymer liquids” due to their flexibility and high capability for dissolving alkaline metal salts. Generally, amorphous and crystalline portions coexist, and the ratio of the crystalline portion increases with molecular weight. Since first being proposed for use as polymer electrolytes in 1986,2 there have been numerous studies of PEO-based lithium salt electrolytes mainly because of the development of rechargeable lithium batteries. In particular, those electrolytes in which the polymers have side chains are especially promising for practical applications because they have particularly high ionic conductivity over a wide temperature range.3-7 In addition to the physical and chemical properties of the solvent, which greatly * To whom correspondence should be addressed. Tel/Fax: (81-298) 61 6295. E-mail: [email protected].

affect the ion-polymer interactions, the role of the solvent in an electrolyte system varies substantially depending on the state (e.g., gel) and composition (e.g., small organic molecules, macromonomers, H2O) of the electrolyte system (e.g., see refs 8-11). The solid-state structures of the PEO-based lithium salt electrolytes have been studied by neutron diffraction12,13 and X-ray analysis.14 It has been observed that the lithium ions are located near the polymer chain and the anions exist independently. The dynamic interactions between the species in linear PEO electrolytes have been studied using NMR line width, spin-lattice relaxation, and translational self-diffusion measurements. Linear PEO chains melt at about 330 K, and fast ionic transfer occurs above the melting point. Cross-linked PEOs with side chains have the great advantage that the CH2CH2O chains do not freeze until below 273 K, and a lithium battery based on a cross-linked side chain polymer electrolyte has achieved 260 charge-discharge cycles.15 Previously, we have reported NMR and ionic conductivity measurements for the cross-linked random copolymer, poly(ethylene oxide-propylene oxide) (poly(EO-PO)), and a random ethylene oxide and 2-(2-methoxyethoxy)ethoxy ethyl

10.1021/jp013035+ CCC: $22.00 © 2002 American Chemical Society Published on Web 12/20/2001

548 J. Phys. Chem. B, Vol. 106, No. 3, 2002 glycidyl ether copolymer (poly(EO-GE)), doped with lithium bis(trifluromethanesulfonyl)imide (LiN(SO2CF3)2, LiTFSI).10,16 The NMR spin-lattice relaxation minima observed for both the polymer (1H) and the lithium (7Li) indicate that fast segmental motions occur on the time scale of 10-9 to 10-11 s in conjunction with the slightly slower correlated lithium hopping motions. Although the spin-lattice relaxation data could be analyzed as a single component for the polymer (1H), the lithium (7Li), and the anion (19F), only the spin-spin relaxation of the anion was consistent with a single component. Consequently, precise measurements of self diffusion by the pulsed-gradient spinecho (PGSE) NMR17-19 were performed for the anion. Somewhat surprisingly, when interpreted on the basis of free isotropic diffusion, the measured self-diffusion coefficient (D) of the anion decreased as the measurement time scale (∆ ≈ 100 ms) increased. Unfortunately, the anion diffusion data could not be explained by currently available “anomalous diffusion” models (e.g., see refs 20-23), although it should be noted that these models are for diffusion in (rigid) porous materials and ideal fractal networks. To clarify the origin of the time dependence of the anion diffusion, we investigated systems in which diffusion measurements of the lithium and the solvent are possible in addition to the anion. The precursor monomers of poly(EO-PO) and poly(EO-GE) were chosen because they are viscous amorphous liquids above 280 K thereby facilitating ionic conductivity and NMR measurements. These macromonomers were terminated by CH3 or H instead of the acryloyl group to prevent polymerization. The chemical structures are shown below.

Hayamizu et al. electrolyte samples with different salt concentrations were prepared: O/Li ) 10:1 (M10TF1) and 20:1 (M20TF1) for both m(EO-PO) and m(EO-GE). As a reference, samples without salt (M) were also prepared. For NMR measurements, the samples were poured into 5-mm NMR microtubes (BMS-005J, Shigemi, Tokyo) to a height of 5 mm and the tubes were flamesealed. The entire preparation procedure was performed under dry air (moisture < 10 ppm at 213 K). Ionic Conductivity Measurements. Ionic conductivities were measured using the ac impedance method on a Solartron electrochemical interface 1286 and frequency response analyzer 1255 controlled by a personal computer. A glass cell with fixed platinum electrodes was used. The cell constant was determined using 0.1 M KCl standard solution. The impedance measurements were carried out from 1 MHz to 0.1 Hz at various temperatures. The ionic conductivity was determined from the corresponding component of the electric circuit required to account for the impedance spectrum. The value of the ionic conductivity was then calculated from the cell constant and the bulk resistance. NMR Measurements. The NMR measurements were performed using a JEOL GSH-200 spectrometer with a 4.7 T widebore magnet controlled by a TecMag Galaxy system. Two different magnetic field gradient probes were used: a 1H/ broadband heteronuclear probe was used to acquire the 1H and 7Li spectra, and the 19F spectra were obtained using a 19F/1H probe. A JEOL current amplifier was used to generate the magnetic gradient pulses. The spin-lattice and spin-spin measurements were performed using the inversion recovery (i.e., 180°-τ-90°-acq) and Hahn spin-echo (i.e., 90°-τ-180°τ-acq) sequences, respectively. The PGSE self-diffusion coefficients were measured using a modified Hahn spin-echo sequence, or in the case of 7Li, because of its rapid spin-spin relaxation and its spin-lattice relaxation being longer in the current systems, a stimulated echobased sequence. When the finite length of the gradient pulse is accounted for and the effects of spin relaxation on the amplitude of the spin-echo signal are normalized out, the signal attenuation for ordinary isotropic diffusion is given by17;18;24;25

E ) exp(-γ2g2δ2D(∆ - δ/3)) On average the number of repeating units, n, are 28 and 20 for m(EO-PO) and m(EO-GE), respectively. In the present paper, the correlation times for the segmental motions of the macromonomer chains and the lithium hopping motions were obtained, and the diffusion of all of the species was measured. Time-dependent anion diffusion was observed in the macromonomer systems, but the degree was much smaller than that in the corresponding cross-linked polymer systems. Also, the lithium ions and anions diffuse faster in the liquid macromonomers than in the corresponding polymer systems. The ion dynamics are elucidated by contrasting their behavior in the macromonomer and cross-linked polymer systems. Experimental Section Sample Preparation. The macromonomers, m(EO-PO) and m(EO-GE), were obtained from Daiichi Kogyo Seiyaku, Kyoto, and LiN(CF3SO2)2 was purchased from Central Glass Co., Ltd, Tokyo. The residual water was less than 100 mg L-1 for all of the chemicals used in this study. Because the macromonomers were viscous liquids at room temperature, the samples were prepared by dissolving the salt in the macromonomers and then raising the temperature to 333 K and stirring for 48 h. Four

(1)

where γ is the gyromagnetic ratio, g is the amplitude of the (“rectangular”) gradient pulses of duration, δ, and ∆ is the separation between the leading edges of the gradient pulses. Measurements were conducted by setting g to between 4 and 9 T m-1, depending on the temperature and nucleus being studied, and measuring E as a function of δ. In all cases, free isotropic diffusion was assumed, and the data were analyzed using eq 1 to obtain an estimate of D. The absence of eddy current and gradient mismatch effects,26 which can result in an artifactual ∆ dependence of the measured diffusion coefficient, and the general reliability of the measuring procedure were verified under more severe conditions (i.e., shorter ∆ and larger g) than those used in the current work. In particular, measurements of the diffusion coefficients of pure triglyme performed at 303 K (at which convection artifacts27 can be safely neglected) were ∆-independent. To allow for structural relaxation, the samples were left at room temperature for at least one month prior to NMR measurement. Most measurements started at 353 K with at least 1 h being allowed prior to measurement to ensure that the samples had achieved thermal equilibrium. Measurements were then performed at sequentially lower temperatures. Although spin-lattice relaxation is generally insensitive to structural

NMR and Ionic Conductivity Study

J. Phys. Chem. B, Vol. 106, No. 3, 2002 549 TABLE 2: The Arrhenius Activation Energies (kJ mol-1) of the Reorientational Motions Calculated from the Temperature Dependence of the Reorientational Correlation Times (1H and 7Li) and T1 (19F) macromonomer segmental motion

sample m(EO-PO)

M

M20TF1 M10TF1 m(EO-GE) M M20TF1 M10TF1 poly(EO-PO) PL poly(EO-GE) PL a

Figure 1. Arrhenius plots of the ionic conductivities for the two electrolytes of the (a) m(EO-PO) and (b) m(EO-GE) systems.

TABLE 1: VTF Parameters Determined by Regressing the VTF Equation (i.e., eq 2) onto the Experimental Ionic Conductivity Data (see Figure 1) sample m(EO-PO) m(EO-GE)

M10TF1 M20TF1 M10TF1 M20TF1

A (S cm-1 K-1/2)

B (K)

T0 (K)

9.4 ( 2.7 3.8 ( 0.9 7.0 ( 1.2 2.8 ( 0.9

934 ( 7 878 ( 68 854 ( 42 724 ( 80

203 ( 5 192 ( 5 208 ( 3 203 ( 7

relaxation and the attainment of equilibrium conditions, the PGSE diffusion measurement is quite sensitive to sample inhomogeneity.8 Results Ionic Conductivity. Arrhenius plots of the experimentally measured ionic conductivities, σ, for the M10TF1 and M20TF1 samples of m(EO-PO) and m(EO-GE) are presented in Figure 1. The temperature dependence of the conductivity was welldescribed by the Vogel-Tamman-Fulcher (VTF) equation,

σ(T) ) AT-1/2 exp(-B/(T - T0))

(2)

where A, B, and T0 are fitting parameters. T0 is often related to the glass transition temperature, whereas B is related to the activation energy.28 The results of regressing eq 2 onto the data are summarized in Table 1. Although bordering on statistical significance, it appears that the values of B and T0 are higher for M10TF1 than those for M20TF1 for both m(EO-PO) and m(EO-GE). This implies that a higher T0, which reflects decreased mobility of the polymer chain with higher salt concentration, is correlated with a larger activation energy for the ionic conductivity. At the same salt concentration and

20.2 ( 0.4a 23.3 ( 0.3b 21.2 ( 0.2 24.3 ( 0.4 21.1 ( 0.2 20.9 ( 2.1 22.4 ( 0.5 22.2 ( 0.3 19.3 ( 0.3

lithium hopping motion

anion CF3

24.5 ( 0.9 12.6 ( 0.3 24.7 ( 0.8 10.4 ( 0.3 19.9 ( 1.7 13.4 ( 0.4 21.0 ( 0.9 10.1 ( 0.5

higher temperature range. b lower temperature range.

temperature, the ionic conductivity is higher in the m(EO-GE)based electrolytes than in those based upon m(EO-PO). NMR Spin-Lattice Relaxation Time (T1). The spin-lattice relaxations of the anion (19F), lithium (7Li), and macromonomer (1H) were single exponentials in all cases and, thus, could be characterized by a spin-lattice relaxation time (T1). As reported previously, the temperature dependence of the T1 values for the polymer chains and the lithium ions for the cross-linked polymers, poly(EO-PO) and poly(EO-GE), exhibits minima.10,16 In the present study, the T1 of the 1H, 7Li, and 19F NMR was measured from 303 to 353 K for the macromonomer electrolytes and from 253 to 353 K for the neat macromonomers of m(EOPO) and m(EO-GE). Surprisingly, the temperatures at which the T1 minima occur for the neat liquid macromonomers and the neat cross-linked solid polymers (PL) are similar (see Figure 2a). The reorientational correlation times for the dipolar interaction between the neighboring protons calculated from the measured T1 values using the Bloembergen, Purcell, and Pound (BPP) equation29 are shown in Figure 2b. A detailed description of this calculation was given in our previous paper.10 The data for cross-linked samples are also included. Except for m(EOPO), the temperature dependence of the correlation times is welldescribed by an Arrhenius relationship, and the corresponding activation energies are given in Table 2. The temperature dependence of the m(EO-PO) correlation times is not linear when plotted in Arrhenius form, but it can be divided into two Arrhenius (i.e., linear) subranges (see the dashed lines in Figure 2b) in which the slope in the lower temperature range is slightly steeper. The activation energies were calculated for each subrange separately and are given in Table 2. The results of the 1H, 7Li, and 19F NMR T1 measurements for the M10TF1 and M20TF1 samples of m(EO-PO) and m(EO-GE) are shown in Figure 3a. The 1H and 7Li T1 minima moved to higher temperature with increasing salt concentration. The correlation times were calculated from the 1H NMR T1 values using the BPP equation in the same way as for the neat samples described above. As in our previous studies,10;16 in calculating the correlation times of the lithium ions, the quadrupolar mechanism was assumed to be the dominant source of spin-lattice relaxation. The quadrupolar coupling constants used to calculate the lithium correlation times were between 40 and 55 kHz, and the validity of values in this range was discussed in our previous paper.10 The temperature dependence of the 1H and 7Li correlation times is shown in Figure 3b. The activation energies for the segmental and lithium hopping motions are given in Table 2. The activation energies increased and the motions slowed as the salt concentration increased. This implies that the salt, especially the lithium ions, intercalates

550 J. Phys. Chem. B, Vol. 106, No. 3, 2002

Figure 2. The temperature dependence of the (a) 1H NMR T1 and (b) the corresponding correlation times calculated from the T1 values by using the BPP equation for the undoped liquid macromonomers. The data for the corresponding cross-linked polymers is also included.10,16 The two subranges for the poly(EO-PO) sample are indicated by the dashed lines.

between the macromonomer side chains thereby reducing the chain flexibility. The activation energies for the CF3 group of the anion were similar to those of the corresponding cross-linked polymers10,16 and are also included in Table 2. Self-Diffusion Coefficients of Ions and Macromonomers. Above room temperature, the τ-delay dependence of the 1H, 7Li, and 19F NMR Hahn spin-echo signals of the macromonomer systems was single exponential in the present study and therefore amenable to meaningful self-diffusion measurements. This is in contrast to the cross-linked polymer systems in which the τ dependence of the signals from the cross-linked polymer (1H NMR) and the lithium (7Li NMR) was multiexponential.10,16 Multiexponential relaxation behavior implies the presence of more than one population of the target species and thus significantly complicates the analysis of the PGSE diffusion data

Hayamizu et al.

Figure 3. The temperature dependence of (a) the T1 values for the side chains (1H NMR), the anions (19F NMR), and the lithium ions (7Li NMR) and (b) the correlation times calculated from the T1 values by using the BPP equation for the side chains (1H) and the lithium ions (7Li) for the M10TF1-m(EO-PO), M20TF1-m(EO-PO), M10TF1-m(EO-GE), and M20TF1-m(EO-GE) electrolytes.

because relaxation weighting effects have to be accounted for. Because it was difficult to precisely determine the number of populations in the cases in which multiexponential behavior was observed in the previous studies, we limited our analysis to only those cases in which the relaxation is single exponential. Macromonomer Diffusion (1H NMR). The (apparent) self diffusion of neat m(EO-GE) was measured at various diffusion measuring times (∆) at 353 K. It was found that when ∆ was longer than 50 ms, semilog plots of the PGSE NMR attenuation data (i.e., ln(E) vs δ2(∆ - δ/3)) were linearsas expected for a single isotropically freely diffusing species (see eq 1). However, when ∆ was in the range of 25-50 ms, the plots were nonlinear and the deviation from linearity increased as ∆ was decreased. After excluding artifactual attenuation due to gradient mismatch (see the Experimental Section) and large scale polydispersity

NMR and Ionic Conductivity Study

J. Phys. Chem. B, Vol. 106, No. 3, 2002 551

Figure 4. The temperature dependence of the self-diffusion coefficients of the macromonomers (1H NMR) measured with ∆ ) 50 ms in the M-m(EO-PO), M-m(EO-GE), M10TF1-m(EO-PO), M20TF1m(EO-PO), M10TF1-m(EO-GE), and M20TF1-m(EO-GE) samples.

Figure 5. The ∆ dependence of the anion self-diffusion coefficients in the M10TF1-m(EO-PO) and M10TF1-m(EO-GE) electrolyte samples. The dependence is much smaller than that observed in the corresponding cross-linked polymer electrolytes.

TABLE 3: The Arrhenius Activation Energies (kJ/mol-1) for the Translational Motion Calculated from the Temperature Dependence of the Self-Diffusion Coefficients sample m(EO-PO) m(EO-GE)

M M20TF1 M10TF1 M M20TF1 M10TF1

macromonomer diffusion 23.5 ( 0.7 26.0 ( 0.8 30.4 ( 1.0 22.4 ( 1.3 25.0 ( 0.8 27.5 ( 3.0

lithium diffusion

anion diffusion

33 ( 2

35 ( 1 40 ( 1

30 ( 1

37 ( 1 46 ( 1

(see the Discussion), this would appear to indicate that the neat m(EO-GE) does not undergo normal isotropic diffusion. Thus, in all subsequent diffusion measurements of the macromonomers in both neat and doped samples, ∆ was set to 50 ms giving single-exponential PGSE data, having the same values as those observed when measured using the longer ∆. The temperature dependencies of the macromonomer diffusion coefficients in both neat and doped samples are shown in Figure 4, and the corresponding activation energies are given in Table 3. The values increased slightly with salt concentration. Anion Diffusion (19F NMR). The ∆ dependence of the (apparent) anion diffusion coefficients in the temperature range of 313-353 K are shown in Figure 5 for the M10TF1 electrolytes of m(EO-PO) and m(EO-GE). To quantitatively characterize the ∆ dependence, the ratio D(∆)20 ms)/D(∆)70 ms) was calculated. As the temperature decreased from 353 to 323 K, the ratio increased from 1.4 to 5.3 for poly(EO-PO) and from 1.9 to 7.0 for poly(EO-GE). Whereas, for the macromonomers, the ratio only increased from 1.3 to 1.7 for m(EO-PO) and from 1.1 to 1.3 for m(EO-GE). Clearly, the time dependency of the anion diffusion is much smaller in the macromonomers. Thus, phenomenologically, the anion diffusion is faster over a shorter distance and time. Interestingly, the ∆ dependence is smaller in m(EO-GE) than in m(EO-PO), which is in contrast to the larger dependence observed for cross-linked poly(EO-GE) than that for poly(EO-PO) in our previous studies.10;16

Figure 6. The temperature dependence of the anion (∆ ) 70 ms) and lithium (∆ ) 50 ms) self-diffusion coefficients in the macromonomer electrolytes.

The anion self-diffusion coefficients measured with ∆ ) 70 ms are plotted versus temperature in Figure 6, and the corresponding activation energies are given in Table 3. The anion diffusion is faster in M20TF1 than in M10TF1 and the differences between m(EO-PO) and m(EO-GE) are small at the same salt concentration. Increasing the salt concentration reduces the anion mobility. It is instructive to compare the anion diffusion in the macromonomers and the cross-linked polymers.10,16 The anion diffusion in M10TF1 and PL10TF1 (the cross-linked polymer) of the EO-PO and EO-GE systems are compared in Figure 7. Although there are only small differences in anion diffusion between the two macromonomers, crosslinking results in the anions diffusing faster in the EO-PO system but slower in PL10TF1 than in M10TF1 in the EO-

552 J. Phys. Chem. B, Vol. 106, No. 3, 2002

Hayamizu et al.

TABLE 4: The Equivalent Ionic Conductivity and the Degree of Dissociation for the m(EO-PO) Systems at 353 Ka sample

d353Kb (g cm-3)

DLi (10-12 m2 s-1)

Danion (10-12 m2 s-1)

σacc (mS cm-1)

σDd (mS cm-1)

R

M20TF1 M10TF1

1.41 1.53

4.5 1.9

22 14

0.87 0.97

0.97 0.99

0.89 0.98

a The values of ∆ used in determining D and D b Li anion were 50 and 70 ms, respectively. The specific density obtained by assuming that the expansion coefficient of the pyknometer can be neglected. This was confirmed from the linear relationship between the specific density and temperature between 293 and 253 K. c Measured directly by the ac method. d Calculated from the self-diffusion coefficients of the ions by using eq 3.

eq 3. N was determined from the specific densities of the electrolytes at various temperatures using a Hubbard-type pyknometer. The R values were determined from the ratio of the experimental to calculated (assuming complete dissociation, i.e., R ) 1) ionic conductivity values (i.e., R ) σ/σD,R)1). The calculated ionic conductivities from the ion self-diffusion coefficients and the density at 353 K and corresponding R values are given in Table 4. The R values are larger in the M10TF1 than in the M20TF1 electrolytes but are nevertheless very close to 1 in both cases, indicating that the ionic diffusion and conductivity are closely correlated in the macromonomer-based electrolytes. Further, these R values indicate that the ion dissociation is much larger in the polymer electrolytes compared to that in the liquid or gel electrolytes. Discussion

Figure 7. The temperature dependence of anion self-diffusion coefficients (∆ ) 70 ms) in the M10TF1 and the PL10TF1 electrolytes of EO-PO and EO-GE.

GE system. Clearly, the different side chain structures have a greater effect on the anion mobility in the cross-linked polymer systems. Lithium Ion Diffusion (7Li NMR). PGSE NMR diffusion measurements are inherently more difficult with 7Li than with 19F because of the much smaller γ and reduced NMR sensitivity. Also, while the anion contains six fluorine atoms, the cation is comprised of a single lithium atom. In the present 7Li NMR measurements, ∆ was set to 50 ms. The temperature dependence of the lithium self-diffusion coefficients is plotted in Figure 6, and the corresponding activation energies are given in Table 3. The lithium diffusion and its temperature dependence were reduced with increasing salt concentration. Correlation between Self Diffusion and Ionic Conductivity. In the poly(EO-PO) and poly(EO-GE) electrolytes, in which the measured lithium diffusion was much slower than the anion diffusion, the apparent long-time (i.e., long ∆) anion self-diffusion coefficient was shown to be closely related to the ionic conductivity.10 Conductivity and ionic diffusion are commonly related using the Nernst-Einstein equation (here modified to include the degree of ion dissociation, R),

σD )

Ne2 (D + Danion)R kT Li

(3)

where N is the number of the lithium ions per anion per cm3 and e is the electronic charge. To ascertain that the correlation between ionic diffusion and conductivity holds in the case of the macromonomer-based electrolytes, using the m(EO-PO) electrolytes as examples, the ionic conductivity was calculated from the anion and the lithium self-diffusion coefficients using

It is important to identity the factors that determine the flexibility of the CH2CH2O moiety of the PEO chains. As shown in Figure 2b, in the higher temperature subrange (above 277 K near the T1 minimum temperature), the segmental motions are slower in the cross-linked polymers than in the liquid macromonomers for both the EO-PO and EO-GE systems at every temperature. The speed of the segmental motions depends on the side chain (i.e., m(EO-PO), CH3 and m(EO-GE), CH2O(CH2CH2O)2CH3), and the segmental motions are faster for the shorter side chain in both macromonomers and crosslinked polymers. The segmental motions are related to the (slow) spin diffusion coefficients on the order of 10-16 m2 s-1 measured in the melt of linear PEOs by using the fringe field gradient method.30 The differences between the correlation times of the macromonomer and cross-linked polymer decrease at lower temperatures. The results clearly show that the chain segmental motions are controlled by the local specific structures (e.g., CH2CH2O) and are insensitive to the bulk liquid or solid conditions. Because the hopping motions of the lithium ions are governed by the side chain segmental motions, the speed and the activation energies of the lithium ions are similar in both the macromonomers and the corresponding cross-linked polymers. Rotation around the C3 axis is the main 19F NMR relaxation mechanism for the anion CF3 group. Because of local effects, the activation energies of this rotation are slightly larger in the macromonomers than in the corresponding cross-linked polymers.10,16 Despite its higher molecular weight, neat m(EO-GE) diffuses faster than neat m(EO-PO) (see Figure 4). Thus, the differences in shape and intermolecular interactions originating from the different length of the side chains in these two high molecular weight macromonomers confer distinct diffusional behavior. Both the magnitude and the difference in self-diffusion coefficients between these two systems decrease with increasing salt concentration and are almost the same in the M10TF1 samples of m(EO-PO) and m(EO-GE). A likely interpretation is that the intercalation of the lithium ions provides intermolecular averaging of the side chain interactions so that the macromonomer diffusion depends more on movement of the entire monomers and less on the individual nature of the side chains.

NMR and Ionic Conductivity Study

Figure 8. The self-diffusion coefficients of the lithium ions and the anions in the four electrolytes plotted versus the respective macromonomer (i.e., the solvent) self-diffusion coefficient. The linearity of the two data sets implies that the diffusive mechanisms of both the anions and lithium ions are correlated to that of the macromonomer. However, the substantially different slopes indicate that these correlations are quite different.

In the present electrolyte systems, the components diffused in the order (fastest to slowest) of anions > lithium ions > macromonomers, as shown in Figures 4 and 6. However, in liquid lithium electrolytes based on low-molecular weight organic solvents, the order of diffusion was solvent > anion > lithium ions.31 Also, the estimated degrees of ion dissociation in the organic solvents were between 0.1 and 0.65, while in the present macromonomers, they are close to 1. The differences in ordering of the self-diffusion coefficients and degree of ion dissociation demonstrate the fundamentally different nature of the ion-solvent interactions in these two types of systems. In both cases, the solvents mediate ion dissociation and in the case of low-molecular-weight solvents, solvated lithium ions move together with the solvent. However, in the high-molecularweight polyether solvents, because of the size of the solvent molecules, there is no solvation sphere; instead, the lithium ions intercalate within or between the side chains of the macromonomer, and the anions can move independently. The lithium ions jump between and modulate the interactions between the (more slowly diffusing) side chains. This model explains why the lithium ions diffuse more slowly than the anions, yet the diffusion of both ions is related to that of the solvent as shown in Figure 8. From its faster diffusion and its relaxation being uncorrelated with that of the macromonomer, it is evident that the anion diffusion, in stark contrast to the lithium ion diffusion, is little influenced by “microscopic” interactions with nearby side chains. Rather, the macromonomer in combination with the lithium ions forms a slowly fluctuating three-dimensional porous matrix through which the anions traverse. The observed multicomponent diffusion behavior of the macromonomers provides the key to understanding the origin of the apparent ∆ dependence of the anion diffusion when interpreted using the free diffusion model (eq 1). Even though polydispersity can result in nonlinear PGSE attenuation plots (e.g., see ref 32), the single

J. Phys. Chem. B, Vol. 106, No. 3, 2002 553 exponential relaxation behavior following eq 1 observed for the anions in the macromonomers in the present temperature range would indicate that the degree of polydispersity is not very large (and certainly the size of the present macromonomer should be much smaller than the mean-squared displacement of the anion during the diffusion measurement, see below); consequently, the multicomponent diffusion of the macromonomer may instead indicate that there must be structural fluctuations in the liquid on the time scale of ∆. At first sight, structural inhomogeneities seem incongruous with a pure liquid; however, such phenomena are far from uncommon, and there is evidence for structural inhomogeneities, although on different time scales, in liquids such as supercooled water and water-alcohol solutions33-35 and surfactants.36 It is to be expected that the lifetimes of such inhomogeneities would increase with molecular size and polymer structure, and indeed, the formation of hyperstructures and anomalous diffusion have recently been reported in poly(EO-PO-EO).37,38 To use M10TF1 of m(EO-PO) at 353 K as an example, the meansquared displacement during ∆ (i.e., x6D∆, where ∆ ) 50 ms) of the macromonomer is on the order of 0.5 µm, while that of the anion is significantly larger at 3.5 µm (as an aside, the mean-squared displacement of the lithium ion, 0.75 µm, is very close to that of the macromonomer). Thus, because the rate of formation and dissipation of a hyperstructure will be related to the diffusion coefficient of the macromonomers, the lifetime of such a hyperstructure will be sufficiently long to interfere with the diffusion path of the anion. Consequently, when the diffusion of the anion is measured on the time scale of ∆, it does not undergo free isotropic diffusion, but instead, its diffusion behavior will reflect a complicated time-dependent restricted diffusion process due to the presence of the structural inhomogeneities, which fluctuate on a similar time scale. Thus, the origin of this anomalous anion diffusion behavior may be fractal-like diffusion in a porous network composed of the macromonomer matrix interspersed with slowly fluctuating hyperstructures. However, as noted above, currently available anomalous diffusion models are only applicable to rigid (i.e., nonfluctuating) porous networks. At long ∆, such that the meansquared displacement of the observed species is significantly larger than the length of the individual inhomogeneous “features” in the matrix, the observed diffusion behavior reverts to that of free isotropic diffusion. Any modulation of the mechanical properties of this matrix either by cross-linking, by stiffening the matrix by salt addition, or by cooling will clearly affect the structural fluctuations, and these motional effects are reflected in the ∆ dependence of the anion diffusion. We have also noted that the ∆ dependence of the self-diffusion coefficient depends on the structure of the macromonomer (unpublished result). The effects of the structural inhomogeneities are greater at lower temperatures because of the anion taking a longer time to complete an average because of its slower diffusion. Because the electrochemical ionic conductivity measurements reflect an average over the entire sample, the estimates of the ionic conductivity calculated with the Nernst-Einstein equation by using the long ∆ diffusion values naturally agree more closely. The lithium transference numbers (i.e., DLi/(DLi + Danion)) are 0.12 and 0.17 for the M10TF1 and M20TF1 samples of m(EO-PO) at 353 K, respectively. These transference numbers are nearly 10 times larger than those for the corresponding poly(EO-PO) systems. This difference is reasonable in light of the larger lithium self-diffusion coefficients in the m(EOPO) systems.

554 J. Phys. Chem. B, Vol. 106, No. 3, 2002 Conclusions The fast segmental motions of the PEO-based CH2CH2O moiety are similar irrespective of whether in the liquid or solid state, and the motion is faster in the liquid macromonomers than in the cross-linked solid polymers. The fast lithium local motions are correlated with the chain segmental motions. The present NMR and ionic conductivity results, in conjunction with our previous studies, provide a clearer picture of the ion dynamics in polymer systems. In the present case, the macromonomer mediates the ion dissociation, and the lithium ions undergo local motions in the vicinity of the monomer side chains. The lithium ions modulate the mechanical properties of the side chains. The behavior of the anions is, however, quite distinct from that of the lithium. The anions move somewhat independently of both the polymer and lithium ions, and their translational motion is sensitive to structural homogeneities in the liquid macromonomer and the solid cross-linked polymer systems. Acknowledgment. Dr. M. Kono of Daiichi Kogyo Seiyaku is thanked for providing the macromonomers. References and Notes (1) MacFarlane, D. R.; Forsyth, M. Chem. Aust. 1996, 72-74. (2) Gorecki, W.; Andreani, R.; Berthier, C.; Armand, M.; Mali, M.; Roos, J.; Brinkmann, D. Solid State Ionics 1986, 18-19, 295-299. (3) Motogami, K.; Kono, M.; Mori, S.; Watanabe, M.; Ogata, N. Electrochim. Acta 1992, 37, 1725-1727. (4) Kono, M.; Furuta, K.; Mori, S.; Watanabe, M.; Ogata, N. Polym. AdV. Technol. 1993, 4, 85-91. (5) Nishimoto, A.; Watanabe, M.; Ikeda, Y.; Kohjiya, S. Electrochim. Acta 1998, 43, 1177-1184. (6) Zheng, Y.; Wright, P. V.; Ungar, G. Electrochim. Acta 2000, 45, 1161-1165. (7) Ikeda, Y.; Wada, Y.; Matoba, Y.; Murakami, S.; Kohjiya, S. Electrochim. Acta 2000, 45, 1167-1174. (8) Hayamizu, K.; Aihara, Y.; Arai, S.; Price, W. S. Electrochim. Acta 2000, 45, 1313-1319. (9) Aihara, Y.; Sugimoto, K.; Price, W. S.; Hayamizu, K. J. Chem. Phys. 2000, 113, 1981-1991. (10) Hayamizu, K.; Aihara, Y.; Price, W. S. J. Chem. Phys. 2000, 113, 4785-4793. (11) Saito, Y.; Kataoka, H.; Stephan, A. M. Macromolecules 2001, 34, 6955-6958.

Hayamizu et al. (12) Carlsson, P.; Swenson, J.; Bo¨rjesson, L.; McGreevy, R. L.; Jacobsson, P.; Torell, L. M.; Howells, W. S. Electrochim. Acta 2000, 45, 1449-1452. (13) Mao, G.; Saboungi, M.-L.; Price, D. L.; Armand, M. B.; Howells, W. S. Phys. ReV. Lett. 2000, 84, 5536-5539. (14) Andreev, Y. G.; Bruce, P. G. Electrochim. Acta 2000, 45, 14171423. (15) Kuratomi, J.; Iguchi, T.; Bando, T.; Aihara, Y.; Ono, T.; Kuwana, K. J. Power Sources 2001, 4215, 1-3. (16) Hayamizu, K.; Aihara, Y.; Price, W. S. Electrochim. Acta 2001, 46, 1475-1485. (17) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288-292. (18) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (19) von Meerwall, E. D. J. Non-Cryst. Solids 1991, 131-133, 735741. (20) Banavar, J. R.; Lipsicas, M.; Willemsen, J. F. Phys. ReV. 1985, B32, 6066. (21) Widom, A.; Chen, H. J. J. Phys. A: Math. Gen. 1995, 28, 12431247. (22) Ka¨rger, J.; Fleischer, G.; Roland, U. PFG NMR Studies of Anomalous Diffusion. In Diffusion in Condensed Matter; Ka¨rger, J., Heitjans, P., Haberlandt, R., Eds.; Vieweg: Braunschweig, Germany, 1998; pp 144-168. (23) Vojta, G.; Renner, U. Diffusion in Fractals. In Diffusion in Condensed Matter; Ka¨rger, J., Heitjans, P., Haberlandt, R., Eds.; Vieweg: Braunschweig, Germany, 1998; pp 306-318. (24) Price, W. S. Concepts Magn. Reson. 1997, 9, 299-336. (25) Price, W. S. Concepts Magn. Reson. 1998, 10, 197-237. (26) Price, W. S.; Hayamizu, K.; Ide, H.; Arata, Y. J. Magn. Reson. 1999, 139, 205-212. (27) Hedin, N.; Furo´, I. J. Magn. Reson. 1998, 131, 126-130. (28) Greenbaum, S. G.; Pak, Y. S.; Wintersgill, M. C.; Fontanella, J. J. Solid State Ionics 1988, 31, 241. (29) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Phys. ReV. 1948, 73, 679-712. (30) Fischer, E.; Kimmich, R.; Fatkullin, N.; Yatsenko, G. Phys. ReV. 2000, E62, 775-782. (31) Hayamizu, K.; Aihara, Y.; Arai, S.; Martinez, C. G. J. Phys. Chem. 1999, 103, 519-524. (32) Håkansson, B.; Nyde´n, M.; So¨derman, O. Colloid Polym. Sci. 2000, 278, 399-405. (33) Stillinger, F. H. Science 1980, 209, 451-457. (34) Zana, R.; Eljebari, M. J. J. Phys. Chem. 1993, 97, 11134-11136. (35) Finney, J. L.; Soper, A. K. Chem. Soc. ReV. 1994, 23, 1-10. (36) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445-482. (37) Walderhaug, H.; Nystro¨m, Bo. J. Phys. Chem. 1997, B101, 15241528. (38) Scheller, H.; Fleischer, G.; Ka¨rger, J. Colloid Polym. Sci. 1997, 275, 730-735.