Factors Controlling the Ionic Mobility of Lithium Electrolyte Solutions in

Feb 3, 2016 - Teijin Limited, 2-1, Hinode-cho, Iwakuni, Yamaguchi 740-8511, Japan. ABSTRACT: The interactions between the mobile ions and membrane ...
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Factors Controlling the Ionic Mobility of Lithium Electrolyte Solutions in Separator Membranes Yuria Saito,*,† Wataru Morimura,† Rika Kuratani,‡ and Satoshi Nishikawa‡ †

National Institute of Advanced Industrial Science and Technology 1-8-31, Midorigaoka, Ikeda, Osaka 563-8577, Japan Teijin Limited, 2-1, Hinode-cho, Iwakuni, Yamaguchi 740-8511, Japan

‡

ABSTRACT: The interactions between the mobile ions and membrane substrate were investigated for lithium electrolyte solutions confined within the separator membrane in lithium batteries through NMR and electrochemical measurements as well as theoretical analyses. Fundamental dynamic properties such as ionic mobility, dissociation degree of the salt, and microviscosities of the ion, which are responsible for ionic mobility, were different for the electrolyte confined within the membranes compared with the corresponding values for the free electrolyte. We also found that the interactions between the ion and membrane substrate depend on the type of membrane. The results of this study suggest that the ionic mobility of the electrolyte in a lithium battery can be controlled by selecting separator membranes with suitable chemical or physical properties, which would be significant for improving the performance of the battery system.

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INTRODUCTION

In secondary battery devices, the electrolyte material is held in the separator membrane and electrode sheets. Therefore, it is reasonable to assume that the ionic conditions and ion migration in the battery would, in practice, be affected by these battery components. In our previous report, we revealed via diffusion coefficient analyses of the ionic species of the electrolyte solution in the separator membrane that the separator membrane interacts with the mobile ions.4 We expect that the interactive forces exerted by the separator would depend on the morphological characteristics of the separator such as porosity and pore size as well as the chemical composition of the membrane. Ionic mobility is directly related to the power of the battery devices.5,6 High mobility of lithium ions leads to high power in lithium secondary batteries, which is important for electric vehicle applications. Furthermore, ionic mobility is indirectly related to the capacity of the battery system due to the reason as follows. During the charge-transfer reaction, the lithium ions travel from the anode through the separator to reach active sites on the cathode sheet. High ionic mobility allows the lithium ions to penetrate the electrode sheets more widely, deeply, and homogeneously, resulting in a larger amount of active sites for the charge-transfer reaction to occur. This implies that higher ionic mobility would lead to larger effective capacity. It may then be concluded that the ionic mobility within the battery

According to the Stokes−Einstein relation and Stokes’ law, the mobility of ions in an electrolyte depends on the ionic size and interactive environment with surrounding species such as counterions, solvent species, and polar groups or sites on the solvent molecules.1,2 For example, lithium ions in a lithium electrolyte solution generally have a solvated structure (e.g., Li(EC)n+). The solvation number and size of the solvated lithium ion depend on the salt concentration and the nature of the solvent. On the contrary, the interactive forces experienced by the ions can be categorized into two types, namely, van der Waals interactions that predominantly occur with the surrounding neutral species and Coulombic interactions that occur with charged species such as counterions and polar sites on the solvent molecules. These effects influence the microviscosities of the mobile species. By evaluating the diffusion coefficients of the mobile species in lithium electrolytes, we previously confirmed that the Coulombic interactions between the cation and anion are related to the solvation structure of lithium.3 We also found that the cationic and anionic mobilities in polymer gel electrolytes are controlled by the addition of acidic and basic polar sites on the polymer chains of the gel, respectively. This is based on the idea that the acidic and basic sites selectively attract the anionic and cationic species, respectively, and reduce their mobilities.2,3 These results suggest that it is possible to control the ionic mobility of electrolytes by tailoring the solvation structure of the ions as well as the structure of the polar sites in the surrounding environment. © XXXX American Chemical Society

Received: October 27, 2015 Revised: January 4, 2016

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DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Physical Properties and Solution Uptake of the Membranes

polypropylene (PP) polyethylene (PE) polyvinylidene difluoride (PVDF)

thickness (μm)

basis weight (g−2)

porosity (%)

averaged pore size (μm)

25 10.4 22

11.0 5.25

55 47 37

0.064 0.02

solution uptake (g·cm−3)

volume ratio of solution uptake/ membrane

0.724 0.757 1.723

0.553 0.578 1.315

ion migration direction in a battery system. The typical pulse width (δ) and diffusion time (Δ) for the pulse sequence were 0−7 and 50 ms, respectively, corresponding to the interval between the two gradient pulses. The ionic conductivity of the solution in the membrane was measured by the impedance method using a frequency analyzer 1250 combined with a potentiostat 1287 (Solartron). An AC potential of 50 mV was applied in the frequency range of 1 mHz to 65 kHz. The conductivity cell was prepared by sandwiching the stacked membranes containing the solution between stainless steel (SUS) electrodes (15 mm diameter) and sealing them. From the slope of the straight line (through the origin) in the plot of cell resistance versus the number of membrane sheets we estimated the ionic conductivity of the solution in the membrane. Theoretical Derivation.2,3,14 The dissolved lithium salt, LiPF6, is typically in an equilibrium state of dissociation. The reaction at equilibrium may be represented as follows (eq 1)

components would be a key factor responsible for determining the power and capacity of the battery system. This study is the first known attempt to directly estimate the interactive forces experienced by each ion in the electrolyte solution within the separator membrane based on the theoretical model originally established for polymer gel electrolytes.2,3 Through this study, we show the parameters that are suitable for evaluating the ionic situation and dynamic characteristics in the membrane. These factors have to be considered for suitably designing separator membranes for fabricating high-performance batteries.

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EXPERIMENTAL AND THEORETICAL METHODS Experimental Methods. We used three types of polymer membranes, namely, polypropylene (PP, Celgard 2500), which was purchased from Polypore, and polyethylene (PE) and polyvinylidene difluoride (PVDF), which were procured from Teijin. The fundamental properties of the membranes provided by the suppliers and partly measured by us are listed in Table 1. For measuring the diffusion coefficient of the solution within the membrane, dried and stacked membrane sheets were placed in an NMR sample tube (5 mm diameter) such that the plane of the film was perpendicular to the longitudinal direction of the sample tube. This allowed measurement of the diffusion coefficient in a direction perpendicular to the plane of the membrane. The electrolyte solution (1 M LiPF6 in 1:1 (v/v) ethylene carbonate (EC)/diethyl carbonate (DEC)) was then introduced into the membrane as follows.4 The membrane stack was compressed under vacuum with a large excess of electrolyte solution and restored to atmospheric pressure several times in the sample tube to completely fill the pore spaces within the membranes with the electrolyte solution. This treatment was performed in a dry room with a dew point of −60 °C to restrict the incorporation of water, which is a key factor causing electrolyte degradation.7 The electrolyte solution (without the membrane) was placed in a thinner 3 mm diameter NMR tube to avoid the influence of thermal convection during diffusion coefficient measurements at higher temperatures. The diffusion coefficients, DLi, DF, and DH, of the probed nuclear species 7Li (116.8 MHz), 19F (292.7 MHz), and 1H (300.5 MHz) in the membranes, respectively, were measured at 25 °C using the pulsed gradient spin−echo (PGSE) NMR technique with a JNM-ECP300W wide-bore spectrometer (JEOL).8 DH was estimated based on the attenuation of the 1 H peak assigned to DEC in the binary solvent, as the EC species predominantly solvates the lithium ions, forming solvated lithium cations.9−11 A Hahn-echo pulse sequence was used for the measurements. A half sine-shaped gradient pulse was successively applied twice after the 90 and 180° pulses to detect the attenuation of the echo intensity according to the diffusion of the probed species.12,13 The diffusion coefficients were measured in a direction perpendicular to the plane of the membranes, which corresponds to the dominant

LiPF6 + n(EC) ⇆ Li(EC)n+ + PF6−

(1)

Under these conditions, the observed diffusion coefficients, DLi, DF, and DH, could be represented in terms of the inherent diffusion coefficients of the species, Dcation, Danion, Dpair, and Dsolv, as follows DLi = xDcation + (1 − x)Dpair DF = xDanion + (1 − x)Dpair DH = DDEC = Dsolv

(2)

where Dcation, Danion, Dpair, and Dsolv are the diffusion coefficient values for Li(EC)n+, PF6−, LiPF6, and DEC, respectively. In addition, x is the degree of dissociation of the salt. In addition, the following relationship can be written based on the Stokes− Einstein equation (eq 3). rpair Dsolv = Dpair rDEC (3) where rpair and rDEC are the sizes of LiPF6 and DEC, respectively, which are estimated as 4.0 and 3.0 Å, respectively, based on the van der Waals size of the atomic species.15,16 On the contrary, the ionic conductivity σ can be expressed in terms of Dcation, Danion, and x, according to the Nernst−Einstein equation as follows (eq 4) σ=

e2 xN (Dcation + Danion) kT

(4)

where e is the proton charge, k is the Boltzmann constant, T is the absolute temperature, and N is the prepared carrier content per unit volume. In the case of separator membranes, the value of N depends on the porosity and swelling characteristics of the membrane. For example, when 1 M electrolyte solution is held in the pores of a membrane with a porosity of p (%) and no swelling, N B

DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) Arrhenius plots of Dcation and Danion and the effect of temperature on (b) Dcation, Danion, Dpair, and tLi, (c) microviscosities η and α, and (d) solvated cation size, rcation, and dissociation degree of the salt, x.

(m−3) = 6.02 × 1026 × p/100. When the membrane swelled with the solution, we measured the solution weight penetrated into the membrane, w (g), and the swollen size (volume) of the membrane after the solution insertion, V (m−3). As a result, N (m−3) = 6.02 × 1026 × w/M/V, where M (g·m−3) is the specific gravity of the 1 M electrolyte solution. By solving the simultaneous eqs 2−4, the inherent diffusion coefficients, Dcation, Danion, and Dpair, as well as the dissociation degree of the salt, x, can be estimated independently. Furthermore, the inherent diffusion values are represented by the Stokes−Einstein relationship as follows (eq 5) DDEC =

kT 6πrDECη

Danion =

kT 6πranionη′

η′ = η + α

Dcation =

kT 6πrcationη″

η″ = η +

ranion α + βcation rcation

anionic species, βanion could be included as the microviscosity of the anionic species in eq 5. Analogous to polymer gel electrolytes, βcation or βanion could be evaluated for understanding the interactions between the ionic species and the separator membrane substrate if the membrane selectively affects the ionic mobility.

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RESULTS AND DISCUSSION Dynamic Properties of the Free Electrolyte Solution. Before evaluating the ionic parameters of the electrolyte in the membrane, we first clarified the fundamental properties of the free electrolyte solution as a function of temperature. By measuring the diffusion coefficients, DLi, DF, and DH, and the ionic conductivity (σ), we estimated the inherent diffusion coefficient values (Dcation, Danion, and Dpair), dissociation degree of the salt (x), microviscosity originating from the Coulombic force (α), microviscosity related to the van der Waals force (η), and cation size (rcation) based on the approach detailed in the Theoretical Derivation section. It is noted that the term βcation was not included in the calculation of Dcation for the free electrolyte solution from eq 5 because there are no specific sites for attracting the cations and anions in the solution.17 Figure 1 shows the estimated values of the parameters as a function of temperature. Several characteristic features were observed for ionic conduction in the solution. The values of Dcation, Danion, and Dpair increased with temperature, as expected, owing to the motional activation of various species. From a microscopic point of view, this behavior may be attributed to changes in two factors, namely, ionic size and microviscosities (η and α) with temperature. Decreases in the values of η and α with temperature cause decreases in the interactive forces, owing

(5)

where η, α, and βcation are parameters representing the microviscosities on the species of the solution. The microviscosity, that the mobile species feel in migration, could be divided into two categories, van der Waals interaction and Coulombic interaction. The parameter η is a result of the van der Waals interactions from any surrounding species, ions, and the neutral species such as solvent molecules and ion pair. On the contrary, α originates from the Coulombic interactions between the cationic and anionic species. βcation arises from the Coulombic interactions between the cation and polar sites on the membrane, if there are any. When the polar sites attract C

DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C to the motional activation of the species. In particular, the change in the value of Dcation reflects not only the change in the microviscosities but also the change in rcation with temperature. Increased value of rcation at a lower temperature would cause the exchange speed of the solvating species in Li+ to decrease under the solvation equilibrium state. This would result in the formation of solvated lithium ions with a larger solvation number. In addition, with decrease in the temperature, the cation transport number (tca) decreased. This is attributed to the fact that Dcation is affected by both the increase in microviscosity as well as the increase in rcation with decrease in temperature. Solution Dynamics in the Separator Membrane. The microviscosities (η and α) of various species observed in the free electrolyte solution may be expected to increase when the solution is confined in the separator membrane, owing to the following two reasons. The first is that the ionic motion in the nearly closed pore spaces in the separator is restricted. This situation would be analogous to an increase in the collision frequency of the species of the solution, leading to increased η and α compared with the values in the free electrolyte solution.17,18 Furthermore, new components of η and α could occur, owing to the appearance of new interactions between the mobile species and the separator substrate. The new van der Waals interaction component is a result of the physical barrier effect exerted by the pore wall of the membrane, whereas the new Coulombic interaction component, characterized by βcation or βanion, results from the polar sites on the membrane surface. The latter assumes that the separator membrane containing the electrolyte is analogous to polymer gel electrolytes containing effective polar groups.2,3 Both the effects of physical barrier and polar sites would be associated with the morphological characteristics of the membrane such as the pore size, porosity, and swelling characteristics. As a result, the microviscosities for the ionic species in the separator membrane would be larger compared with those of the free electrolyte solution at the same temperature. NMR Peak Assignment of the Solution in the Membrane. In this section, we first confirm the peak assignment of the NMR spectra of the solution in the membrane by clarifying the prevailing condition of the species in the membrane. By evaluating the echo attenuation of the peak, which is assigned to identify the ions responsible for charge transport in the separator membrane, we determined the numerical values of the ionic mobility and microviscosity in the separator membranes. The number and shape of the peaks in the NMR spectra of the solution within the membranes were different from those of the free solution. This indicates that different types of species may exist depending on the prevailing location of the solution within the piled membranes in a NMR sample tube. As the 7Li spectrum of the free electrolyte solution exhibits a single peak and is much simpler compared with the 19F and 1H spectra, we discuss the peak assignments based on the 7Li spectra of the solution, with and without the membranes. Figure 2a−c represents the single pulse 7Li spectrum of the electrolyte solution without the membrane, single pulse 7Li spectrum of the solution with the separator membrane, and spin−echo pulsed 7Li spectrum of the solution with the membrane, respectively. Each of the peaks in the single pulse spectra (panels a and b) correspond to a specific chemical species, whereas the intensity of the peaks reflects the concentration of the particular species in the solution. The

Figure 2. Single pulsed 7Li spectra of (a) the solution without the membrane, (b) the solution within the separator membrane, and (c) spin−echo pulsed spectra of the solution within the separator membrane.

difference between the spectra in panels b and c is that the spectrum in panel c underwent the spin−spin relaxation process, identified by the relaxation time, T2, under the spin− echo pulse sequence. This means that the individual peak intensity in panel c changed from that of the original peak in panel b as a function of the individual T2 value. In contrast with the single peak of the free solution, panel a, the spectrum in panel b with the membrane exhibited two dominant peaks. The peak on the left side at around −2 ppm of panel b (Pe1-b) was sharp and was composed of a single component, which is similar in peak width and chemical shift position to those of spectrum a. The peak on the right side at around −3 ppm of panel b (Pe2-b) was broad and, in some cases, composed of plural peaks. It is apparent that Pe2-b appeared due to the coexistence of the solution and membrane and had a smaller T2 compared with Pe1-b due to the broadened shape. After the application of the spin−echo pulse sequence (from panels b to c), the relative intensity of Pe1/Pe2 apparently increased. This also proves that Pe2 has a smaller T2 compared with Pe1. On the basis of these features, we were able to confirm that Pe2 is associated with the lithium species that strongly interact with the surroundings and are consequently restricted in motion.19 It is probable that the lithium species responsible for Pe2 are located in almost closed pore space within the membrane, the space between the piled membranes, and the space between the inner wall of the NMR tube and membranes. On the contrary, we confirmed that Pe1 reflects the lithium species in the linkedpore space of pathway responsible for charge transport in the D

DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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E

4.56 × 10−02 2.65 × 10−02 1.88 × 10−01 10−3 10−3 10−3 10−3 × × × ×

η (Pa·s)

2.08 3.50 3.43 3.50 10−3 10−04 10−04 10−3 × × × × 2.18 2.77 8.34 5.37

α (Pa·s) x

0.710 0.318 0.294 0.632 10−10 10−10 10−10 10−10 × × × × 3.16 1.88 1.92 1.88 10−10 10−10 10−10 10−11 × × × × 2.00 2.26 2.00 9.62 10−10 10−12 10−12 10−12 × × × × 1.00 5.70 9.29 1.21 10−10 10−10 10−10 10−10 × × × × 3.50 2.08 2.12 2.08 10−10 10−10 10−10 10−10 × × × × 2.34 2.00 1.94 1.30 10−10 10−10 10−10 10−11 × × × × 1.63 1.30 1.38 7.00 1026 1026 1026 1026 × × × × 6.02 2.83 3.31 3.59 10−3 10−3 10−3 10−3 × × × × 8.00 1.30 1.27 1.38 25 25 25 25 solution only PE PP PVDF

Dpair (m2 s−1) Danion (m2 s−1) Dcation (m2 s−1) DH (m2 s−1) DF (m2 s−1) DLi (m2 s−1) N (m−3) σ (S cm−1) T (°C)

Table 2. Observed Ionic Conductivity (σ), Prepared Carrier Concentration (N), and Diffusion Coefficients (DLi, DF, and DH) and Estimated Dynamic Values (Dcation, Danion, x, and rcation)

membranes. As a result, we used the spin−echo attenuation of Pe1 for the estimation of Dcation, Danion, x, and so on. Estimation of Inherent Diffusion Coefficients and Microviscosities of the Ions in the Membrane. Table 2 shows the observed values of σ, DLi, DF, and DH used for analyses, estimated inherent diffusion coefficients (Dcation and Danion), and microviscosities (η, α, and βcation) of the solution before and after insertion into the membranes. We first estimated Dcaion, Danion, Dpair and x by solving the simultaneous eqs 2 and 4 and then estimated η, α, and βcation by solving simultaneous eq 5 using the estimated Dcation and Danion. During the process, we found that the parameter βcation is present in all membranes for the arrival at the reasonable estimated values, indicating that the lithium cation selectively interacts with the membrane substrate. Figure 3 shows a plot of the effective field of (DLi, DF) where the conditions Dcation ≥ 0, Danion ≥ 0, and 1 ≥ x ≥ 0 are satisfied for each membrane. This field was calculated using the values of σ and DH for each membrane based on eqs 2−4. The colored square region in the figure represents the effective field of (DLi, DF) where Dcation ≥ 0, Danion ≥ 0, and 1 ≥ x ≥ 0, whereas the green and red regions in the square correspond to βcation ≥ 0 and βanion ≥ 0, respectively. It is found from this Figure that the presence of βcation or βanion depends on the relative value of DLi and DF. The white dot in the green area corresponds to the observed (DLi, DF) value obtained in this study for each membrane. This result indicates that the cationic species interacted with the separator membrane substrate in this study. Comparison of the absolute values of βcation observed for the different membranes shows that the interactive force experienced by the cation is strongest in the case of the PVDF membrane. Based on the estimated values in Table 2, we here evaluate the interactive situations of the ionic species with the membrane as follows. As is expected in the section of solution dynamics in the separator membrane, the microviscosity of the van der Waals component, η, increased in the membrane compared with that of the free solution. On the contrary, the microviscosity of the Coulombic component, α, increased in the PVDF membrane and decreased in PE and PP membranes compared with that of the free solution. Considering the restricted condition for ion migration in the membrane, both η and α are expected to be larger in the membrane than those of the free solution because the restricted situation in motility corresponds to a temperature-decreased situation typically shown for η and α in Figure 1c. It is probable that the decreased α in the PP and PE membranes is associated with the larger βcation compared with that of the PVDF membrane. With increasing the attractive force originated from the particular sites on the membrane, the Coulombic interaction between the cation and anion would relatively weaken at the equilibrium state. As previously said, it is difficult to identify the polar sites on the membrane causing βcation. Considering that βcation are present in all membranes, PP, PE, and PVDF, it is not reasonable to assume that the site is a particular polar group on the polymer because there is no polar group that could attract cation species at least on the PP and PE membranes. It is rather acceptable that the site for βcation would be a kind of static electricity charged on the membrane surface. The magnitude of the electricity would depend on the chemical composition as well as the morphological features of the membrane such as the porosity and pore size because the distribution of the electronic charge depends on the physical properties of the membrane.

βcation (Pa·s)

The Journal of Physical Chemistry C

DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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AUTHOR INFORMATION

Corresponding Author

*Tel: +81-72-751-4527. Fax: +81-72-751-8564. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Bockris, J. O.; Reddy, A. K. N. In Modern Electrochemistry; Bockris, J. O., Ed.; Plenum Press: New York, 1998; pp 452−456. (2) Saito, Y.; Okano, M.; Sakai, T.; Kamada, T. Lithium Polymer Gel Electrolytes Designed to Control Ionic Mobility. J. Phys. Chem. C 2014, 118, 6064−6068. (3) Saito, Y.; Okano, M.; Kubota, K.; Sakai, T.; Fujioka, J.; Kawakami, T. Evaluation of Interactive Effects on the Ionic Conduction Properties of Polymer Gel Electrolytes. J. Phys. Chem. B 2012, 116, 10089−10097. (4) Saito, Y.; Morimura, W.; Kuratani, R.; Nishikawa, S. Ion Transport in Separator Membranes of Lithium Secondary Batteries. J. Phys. Chem. C 2015, 119, 4702−4708. (5) Jow, R. T.; Ku, K.; Borodin, O.; Ue, M. In Electrolytes for Lithium and Lithium-Ion Batteries; Springer: New York, 2014; p 5. (6) Braun, P. V.; Cho, J.; Pikul, H.; King, W. P.; Zhang, H. High Power Rechargeable Batteries. Curr. Opin. Solid State Mater. Sci. 2012, 16, 186−198. (7) Lux, S. F.; Lucas, I. T.; Pollak, E.; Passerini, S.; Winter, M.; Kostecki, R. The Mechanism of HF Formation in LiPF6 based Organic Carbonate Electrolytes. Electrochem. Commun. 2012, 14, 47−50. (8) Saito, Y.; Kataoka, H.; Capiglia, C.; Yamamoto, H. Ionic Conduction Properties of PVDF-HFP Type Gel Polymer Electrolytes with Lithium Imide Salts. J. Phys. Chem. B 2000, 104, 2189−2392. (9) Bayley, P. M.; Best, A. S.; MacFarlane, D. R.; Forsyth, M. The Effect of Coordinating and Non-Coordinating Additives on the Transport Properties in Ionic Liquid Electrolytes for Lithium Batteries. Phys. Chem. Chem. Phys. 2011, 13, 4632−4640. (10) Deshpande, A.; Kariyawasam, L.; Dutta, P.; Banerjee, S. Enhancement of lithium ion mobility in ionic liquid electrolytes in presence of additives. J. Phys. Chem. C 2013, 117, 25343−25351. (11) Lane, G. H.; Best, A. S.; MacFarlane, D. R.; Forsyth, M.; Bayley, P. M.; Hollenkamp, A. F. The Electrochemistry of Lithium in Ionic Liquid/Organic Diluent Mixtures. Electrochim. Acta 2010, 55, 8947− 8952. (12) Tanner, J. E. Use of the Stimulated Echo in NMR Diffusion Studies. J. Chem. Phys. 1970, 52, 2523−2526. (13) Price, W. S.; Kuchel, P. K. Effect of Nonrectangular Field Gradient Pulses in the Stejskal and Tanner (Diffusion) Pulse Sequence. J. Magn. Reson. 1991, 94, 133−139. (14) Kataoka, H.; Saito, Y.; Sakai, T.; Deki, S.; Ikeda, T. Ionic Mobility of Cation and Anion of Lithium Gel Electrolytes Measured by Pulsed Gradient Spin-echo NMR Technique under Direct Electric Field. J. Phys. Chem. B 2001, 105, 2546−2550. (15) Ue, M.; Murakami, A.; Nakamura, S. A Convenient Method to Estimate Ion Size for Electrolyte Material Design. J. Electrochem. Soc. 2002, 149, A1385−A1388. (16) Bondi, A. Van der Waals Volumes and Radii. J. Phys. Chem. 1964, 68, 441−451. (17) Gutmann, F.; Simmons, L. M. The Temperature Dependence of the Viscosity of Liquids. J. Appl. Phys. 1952, 23, 977−978. (18) Hsu, J.-P.; Lin, S.-H. Temperature Dependence of the Viscosity of Nonpolymeric Liquids. J. Chem. Phys. 2003, 118, 172−178. (19) Farrar, T. C.; Becker, E. D. In Pulse and Fourier Transform NMR, Introduction to Theory and Methods; Academic Press: New York, 1971; pp 46−65.

Figure 3. Effective field of (DLi, DF) for the estimated dynamic values of the solution in each membrane. The colored square region satisfies the conditions Dcation ≥ 0, Danion ≥ 0, and 1 ≥ x ≥ 0, the green area represents βcation ≥ 0, and the red area represents βanion ≥ 0. The white square mark in the effective green area represents the observed (DLi, DF) for each membrane.

From the aspect of controlling the ionic mobility systematically, it is directly effective to use the polar groups tailored on the membrane to enhance or reduce the mobility of the particular ion. Therefore, modification of the chemical composition of the membrane containing the effective polar groups would be the next target of our research for designing the separator membrane. At the same time, it is also expected that the interaction responsible for βcation (βanion) is influenced by the morphological features of the membrane. Interaction efficiency would depend on the porosity and pore size, which affect the collision frequency of the ions with the wall of the membrane in the migration pathway. Therefore, the investigation of the correlation between βcation (βanion) and morphological features of the membrane is significant to complete the designing of the separator membranes for lithium secondary batteries.

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CONCLUSIONS In conclusion, we estimated the ionic mobilities, dissociation degree of the salt in the solution within the separator membranes, as well as the microviscosities of the ionic species in the solution. We observed that the cations interact with the separator membrane substrate, which reduces the cation transport number of the solution in the separator. The degree of interaction would depend on the physical morphology and chemical features of the membrane. These results prove that it is possible to control the interaction of the ions with the separator membrane for designing a suitable combination of the electrolyte and separator, which is essential for realizing an effective battery system. F

DOI: 10.1021/acs.jpcc.5b10538 J. Phys. Chem. C XXXX, XXX, XXX−XXX