Influence of the Morphological Characteristics of Separator

Yuria Saito,a* Wataru Morimura,a Sadamu Kuse,a. Rika Kuratani,b Satoshi Nishikawab. aNational Institute of Advanced Industrial Science and Technology...
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Influence of the Morphological Characteristics of Separator Membranes on Ionic Mobility in Lithium Secondary Batteries Yuria Saito,*,† Wataru Morimura,† Sadamu Kuse,† 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: Microviscosity components influencing the ionic mobility of lithium electrolyte solution in separator membranes were evaluated and the ionic mobility was correlated with membrane morphology. The microviscosity component responsible for the anion−cation Coulombic interactions (α) was anomalously large in low porosity membranes compared to that in the free electrolyte solution, owing to restricted ionic motion in the narrow pore spaces within the membrane. With increase in the membrane porosity, α diminished owing to the enlarged space and motional freedom for the ionic species, whereas βcation, which is responsible for the cation/membrane interactions, appeared. This behavior may be due to the specific charge on the walls of the pore spaces and the increased collision frequency for the ions. Consequently, the cationic mobility (Dcation) selectively decreased, whereas the anionic mobility (Danion) increased in high porosity membranes. Despite the positive correlation between the diffusion coefficient distribution width (σ) and averaged diffusion value for the anion and solvent species, a clear correlation between σ and Dcation was not observed, which is attributed to the fact that the cation is specifically affected by the membrane, perhaps via Coulombic interactions, as evidenced by the appearance of βcation. Controlling the microviscosities of the ions in the electrolyte by controlling the porous morphology of the separator membrane is significant for designing high-performing battery systems.

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INTRODUCTION An important role of separator membranes in battery systems is as a medium for ion transport from one electrode to the other. The ionic mobility of the electrolyte within the separator governs the high-rate charge−discharge characteristics of the battery system.1,2 The ion transport mechanism within the porous separator membranes is similar to ion migration in the electrodes. The ions on an electrode surface migrate in the pathways within the electrode pore spaces to reach active sites, where they undergo charge transfer. Therefore, controlling the ion transport mechanism in the separator membrane is important for controlling the battery performance. The predominant factors that govern the ionic mobility in separator membranes include (1) ionic structure (solvation structure) and properties of the solvent in the electrolyte, (2) porous structure of the separator membrane, and (3) interactions between the ions and membrane. In terms of membrane structure, pore size, porosity, tortuosity, and chemical composition are all factors that affect the mobility of the ions located in the pathways containing linked pores. In practice, it is difficult to control these factors individually during the conventional preparation process of the separator membranes. However, systematic evaluation of the effects of these factors is indispensable for designing separator membranes for battery systems with reliable performance. © XXXX American Chemical Society

We previously presented a novel approach for evaluating the factors that determine the ionic mobilities and microviscosity components responsible for interactions of the ionic species in the separator membranes by measuring and analyzing the dynamic properties of the mobile species.3,4 In these studies, we found that a specific interaction occurs between the lithium cation and separator membrane, in addition to the conventional interactions between the cation/anion and ion/solvent in the free electrolyte. It is reasonable to think that the interactions between the ions and separator depend on the structure of the separator membrane. The structural characteristics of the membrane may be categorized into two types, namely morphological features and chemical characteristics. A typical example of a membrane in which the chemical characteristics influence the ionic mobility is membranes with polar groups or sites. In this case, the polar groups or sites attract specific ions through Coulombic interactions, thereby affecting the ionic mobility. This is analogous to the behavior of polymer gel electrolytes containing polar sites on polymer chains.5,6 The magnitude of the Coulombic force and the resultant mobility of the attracted Received: October 19, 2016 Revised: December 27, 2016 Published: January 24, 2017 A

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Fundamental Properties of the PE Porous Membranes

a

sample no.

weight/g·m−2

thickness/μm

gurley/s·(100 cm3)−1

porosity/%

average pore size/μm

PE-1 PE-2 PE-3 PE-4 PE-5 PE-6 PE-7 PE-8 PE-9 PE-10 PE-11 C2500a

5.25 5.66 5.37 6.07 11.09 5.40 5.15 3.69 3.43 3.47 3.16 11.0

10 13 12 33 79 10 9 5.8 5.5 5.7 5.8 25

185 112 79 9 1 150 329 129 137 148 90 200

47 54 52 80 85 41 41 33.7 34.6 35.9 42.7 55

0.043 0.063 0.134 1.456 8.448 0.075 0.039 0.092 0.095 0.089 0.086 0.098

C2500, polypropylene (PP) membrane of Celgard 2500 for reference.

v) ethylene carbonate (EC)/diethyl carbonate (DEC), Kishida Chemical Co. Ltd.) was then introduced into the membrane as follows.3,4 The membrane stack was compressed under vacuum with an excess of electrolyte solution (200%, 400% and 800 of the total pore volume of the membranes in the sample tube) and restored to atmospheric pressure several times in the sample tube, in order to completely fill the pore spaces within the membranes with the electrolyte solution. In the case of the nonporous PET membrane, two samples with 0.278 mL, which corresponds to the amount of the 800% in the porous membrane samples, and 0.128 mL of solution in each tube were prepared using the same deaeration treatment. This treatment was performed in a dry chamber with a dew point of −60 °C, in order to restrict the incorporation of water, which is a key factor that causes electrolyte degradation.12 Samples prepared with 400% solution were used for the diffusion measurement analyses. 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), respectively, were measured at 25 °C using the pulsed gradient spin−echo (PGSE) NMR technique with a JNM-ECP300W wide-bore spectrometer (JEOL Co. Ltd.).13 The value of DH was estimated based on the attenuation of the 1 H peak assigned to DEC in the binary solvent, as the EC species predominantly solvate the lithium ions forming solvated lithium cations, unlike the isolated condition of the DEC species. A Hahn−echo pulse sequence was used for the measurements. A half sine-shaped gradient pulse was applied twice in succession after the 90° and 180° pulses, in order to determine the attenuation of the echo intensity with the diffusion of the probed species.14,15 The diffusion coefficients were measured in a direction perpendicular to the plane of the membranes, which is the dominant ion migration direction in a battery system. The typical pulse width (δ) and diffusion time (Δ) for the pulse sequence were 0−7 and 20 ms, respectively. This diffusion time was fairly short compared to those determined from measurements of the conventional electrolyte solutions and gel electrolytes because the relaxation time of the target species was fairly short, as explained in detail below. The ionic conductivity of the solution in the membrane was measured by the impedance method using a frequency analyzer (model 1250) combined with a potentiostat (model 1287, Solartron). An ac voltage of 50 mV was applied in the frequency range of 1 mHz to 65 kHz. The conductivity cell was prepared by stacking a prescribed number of sheets (2−12) containing the solution and sandwiching them between SUS

ionic species depend on the Lewis acid/base strength of the polar sites and their concentration in the membrane. Another effect that induces Coulombic force in the membrane would be surface charge such as that induced by the diffusion layer, which would be characterized by the ζ potential at the particle surface in a medium.7 In pores filled with an electrolyte solution, a charged layer is assumed to be present at the interface between the solution and membrane substrate. On the other hand, the morphological or physical factors of the membrane such as pore size and porosity also influence the ionic mobility because these factors determine the width and tortuosity of the pore-linked pathways through which ions migrate in the separator membranes. In this study, we examine the correlation between the morphological features of polyethylene (PE) fine porous membranes and ion dynamic parameters such as ionic mobilities and interactive forces on each ion. On the basis of this information, we would like to shed light on the ion migration mechanism in the separator membrane at the nanoscale, which is indispensable not only for designing an ideal battery system but also for controlling the transport system of the species in catalytic and separation materials for gases and liquids.

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EXPERIMENTAL AND THEORETICAL METHODS Experimental Methods. We used 11 PE membranes with different porosities and pore sizes as shown in Table 1. All the membranes were prepared based on the following wet process.8,9 PE powder and liquid paraffin were mixed and heated to promote dissolution. Subsequently, the solution was pushed and cooled to form a base tape of PE. The tape was extended in the vertical and horizontal directions and then immersed in methylene chloride to extract liquid paraffin for forming the porous PE membranes. The porosity of the membrane was estimated from the ratio of bulk density to true density whereas the pore size was determined using the specific surface area measured by the BET method, assuming that the pores were columnar in structure.10,11 For measuring the NMR spectra and diffusion coefficients of the species in the solution within the membrane, dried and stacked membrane sheets (5 mm in diameter and ∼5 mm in height) were placed in an NMR sample tube (5 mm ϕ), such that the plane of the films 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/ B

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. 7Li single pulsed NMR spectra of the electrolyte solution in (a) nonporous PET, (b) Celgard 2500, and (c) PE membranes with 200%, 400%, and 800% solution in the sample tube. Red lines represent the spectra of the solution in the sample tube containing the membrane and black lines represent the free electrolyte solution. The blue-capped peaks correspond to Pe1, which is contributed by the solution outside the membranes, whereas the red-capped peaks correspond to Pe2, which is contributed by the solution within the pore spaces of the membranes.

electrodes with a diameter of 15 mm. The sandwich was finally laminated and sealed. The cell resistance was plotted as a function of the number of membrane sheets and the plot was found to be linear. From the slope of the straight line (passing through the origin), we estimated the ionic conductivity of the solution in the membrane. Outline of the Theoretical Derivation. The main idea behind the evaluation of microviscosity originating from the interactions between the mobile species in the solution or between the mobile species and the membrane substrate has already been explained in detail in our previous paper.4 Therefore, we only briefly present the key aspects of the derivation here. Under equilibrium lithium salt dissociation conditions in the lithium electrolyte solution, dissociated cations and anions, as well as associated ion pairs coexist. However, they are not detected individually on the NMR experimental time scale, which probes an average environment due to rapid exchange between entities. As a result, the measured diffusion coefficients, DLi, DF, and DH probed by the 7Li, 19F, and 1H nuclear species, respectively, can be defined with the inherent diffusion coefficients of the entities, Dcation, Danion, and Dpair as shown in eq 1,

σ=

(2)

where N is the salt concentration in the solution. As DH directly reflects the diffusion coefficient of the DEC species (Dsolv) the diffusion coefficient of the neutral ion pair (Dpair) is estimated using the sizes of the ion pair (rpair) and DEC (rDEC) based on the relationship, Dsolv/Dpair = rpair/rDEC according to the van der Waals size and the Stokes−Einstein equation.17,18 As a result, Dcation, Danion, and the dissociation degree of the salt, x, can be determined by solving the simultaneous equations eqs 1 and 2. Each of the inherent diffusion coefficient values, Dcation, Danion, and Dsolv are functions of size and microviscosity of the corresponding species according to the Stokes−Einstein relation as follows eq 3. Dsolv =

kT 6πrDECη

Danion =

kT η′ = η + α 6πranionη′

Dcation =

r kT η″ = η + anion α + βcation rcation 6πrcationη″

(3)

where η, α, and βcation are the microviscosities attributed to the van der Waals interactions with the surrounding species, Coulombic interactions between the cation and anion species, and Coulombic interactions between the cation and attractive sites on the membrane, respectively. When the attractive sites interact with the anion, βanion has to be included in the equation for Danion, whereas βcation has to be removed from the equation for Dcation eq 3. Using eq 3, the microviscosities are estimated using the following procedure. η is first estimated from the relation involving Dsolv. Following this, α is estimated from the equation for Danion using the estimated η value. Finally, βcation is derived from Dcation using the estimated η and α values. If the calculated βcation value is less than 0, which implies that the sites on the membrane attract the anion species and not the cation

DLi = xDcation + (1 − x)Dpair DF = xDanion + (1 − x)Dpair DH = DDEC = Dsolv

e2 xN (Dcation + Danion) kT

(1)

where x is the dissociation degree of the lithium salt in the solution. Dcation and Danion, which represent diffusion values of single entity cation and anion, are directly related to the cation and anion mobilities, respectively, according to the Einstein relation.16 On the other hand, ionic conductivity is the summation of the cation and anion conductivities, which are functions of the carrier concentration, xN, and ionic diffusion coefficient as shown in eq 2. C

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. Comparison of the single pulsed (top) and spin−echo pulsed (bottom) 7Li spectra with Δ = 50 ms for (a) PET, (b) Celgard 2500, and (c) PE-8 membranes containing electrolyte solution inside and outside the membranes. Red lines represent the spectra of the solution in the sample tube containing the membrane and black lines represent the free electrolyte solution.

applying the spin−echo pulse sequence including the field gradient pulses for diffusion coefficient measurements.14,15 The main difference between the two types of spectra is that the spin−echo pulsed spectra undergo a spin−spin relaxation process characterized by the relaxation time, T2. In the case of the PET membrane, both the spectra are identical in shape, indicating that all the peaks originate from the species at the same location with the same relaxation time, outside the membranes. On the contrary, the relative intensity of the peaks (Pe2/Pe1) decreases in the spin−echo pulsed spectra compared with that in the single pulsed spectra for the porous C2500 and PE-8 membranes. This indicates that the relaxation time for Pe2 is fairly short and the species responsible for Pe2 tends to be influenced by the environment. On the basis of Figures 1 and 2, we confirm that Pe2 predominantly originates from the lithium species in the solution within the pore space, whereas Pe1, which originates from the PET membrane, is attributed to species outside the membrane. The shorter relaxation time of Pe2 suggests that the species in the pore spaces are likely to interact with the walls of the membrane pathway. Considering the fact that the peaks of PET occur in the chemical shift range of Pe2, some of the peaks in the vicinity of Pe2 such as the peak at 0.3 ppm in the Celgard spectra, may correspond to species present outside the membrane. NMR Echo Attenuation Characteristics in the Separator Membrane. Diffusion coefficient is measured from the slope of the decay plot, log M vs δ2Δ, where M is the NMR echo intensity. While the echo attenuation in the NMR spectra of the free electrolyte solution changes in a linear fashion, the decay plot for the solution in the porous membrane assumes a curved form projected upward.4,19 This is attributed to the distribution of diffusion coefficients in the sample, which is caused by the pore size and length distributions as well as tortuosity distribution in the linked pore pathway. The diffusion coefficient distribution may be represented by the average diffusion coefficient, D0 and associated standard deviation, σ, as shown in eq 4.4,18

species, βanion has to be included in the calculation of Danion and βcation has to be removed from the calculation of Dcation with eq 3. In this case, α is first estimated from the equation for Dcation which includes contributions from η and α. Finally, βanion is estimated from the equation for Danion, which includes contributions from η, α, and βanion. In this approach, either βcation or βanion could be estimated if there is a microviscosity component other than η and α, owing to the numerical limitations on the fitting parameters and observed values. In the case of the free electrolyte solution, β does not appear in the equations of both Dcation and Danion.

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RESULTS AND DISCUSSION Peak Assignment for the NMR Spectra of the Solution in the Porous Membranes. In our previous paper, we discussed the peak assignments for the NMR spectra of the electrolyte solution in the separator membrane.4 In this section, we reconsider the previous peak assignments by comparing the spectra of samples with different solution contents and of the porous and nonporous membranes. Figure 1 shows the 7Li NMR spectra of the solution in nonporous PET, porous Celgard 2500 (polypropylene, PP), and PE, as a function of solution content in the sample tube. The spectral shape of the porous membranes is found to gradually change as a function of solution amount, in contrast with the PET membrane, where the spectral shape is independent of the solution content. All the peaks in the NMR spectra of the nonporous PET membrane may reasonably be attributed to the solution outside the membrane, such as that in the spaces between the membranes in the stack and between the membrane and wall of the sample tube. In the case of porous membranes, a broad peak (Pe2) appears initially at a smaller solution content, whereas the peak on the left side (Pe1) appears later. The intensity of Pe1 increases with increase in the amount of solution incorporated in the sample tube. The Pe1 peaks of PE and Celgard membranes are identical to the peak around 0.7 ppm for the PET membrane, owing to the consistent chemical shift and peak width. These results suggest that the initial Pe2 peaks for the porous membranes correspond to the lithium species in the solution present in the pore space of the porous membranes. Figure 2 compares the single pulsed spectra (top) and spin− echo pulsed spectra (bottom) of the solution within each membrane. The spin−echo pulsed spectra were obtained after

M = M0

∫ f (D) exp[−γ 2g 2δ 2D(4Δ − δ)π −2] dD

f (D) = D

⎡ (D − D )2 ⎤ 1 0 ⎥ ⎢− exp 2πσ 2 2σ 2 ⎦ ⎣

(4)

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Here γ is the gyromagnetic constant, g is the strength of the field gradient pulse, δ is the width of the field gradient pulse, and Δ is the diffusion time. In this study, we estimate the diffusion coefficients, DLi, DF, and DH, which are the starting values for the analyses, from the averaged diffusion coefficient values by fitting the original echo decay of each nuclear species to eq 4. Inherent Diffusion Coefficients and Microviscosities of the Ions in the PE Separator Membrane as a Function of Porosity of the Membrane. As mentioned previously, the fundamental morphological parameters of the porous membranes include pore size, porosity, and tortuosity of the porelinked pathways. Each of these parameters affects the mobility of the species that migrate in the pore-linked pathways. In practice, however, it is difficult to control these factors individually during the membrane preparation process. In particular, it may be reasonably suggested that the tortuosity can be evaluated once the porous morphology is determined by characteristics such as pore size and porosity and cannot be intentionally controlled at will. Figure 3 shows the correlation between pore size and porosity of the membranes used in this study. The pore size

Parts b and c of Figure 4 show the microviscosites on the species of the solution in the membrane as the result of the interaction with the surrounding species and membrane. η, which originates from the van der Waals interactions with the surrounding species, and α, which is related to the Coulombic interactions between the cation and anion, monotonically decrease with increase in porosity as expected, owing to the increased degree of freedom of the species when the space available for migration is widened (Figure 4b). In particular, it is noted that α is over four times as large as η in membranes with low porosity. Furthermore, the interactions between the membrane and ionic species are detected by the presence of βcation and βanion, as shown in Figure 4c. βanion is dominant in membranes of lower porosity, whereas βcation appears and increases with increase in the membrane porosity. This indicates that the dominant ion/membrane interactions depend on the porosity of the membrane. In order to recognize the changes in βcation and βanion with porosity, we consider the causes of interactions between the ionic species and membrane in the pore space of the membrane in detail. The interactions are attributed to the physical and chemical properties of the membrane substrate. The chemical properties may originate from the polar groups and surface charge on the membrane, which induce Coulombic interactions with the charged species. On the other hand, tortuosity of the ion migration pathways composed of linked pores is a physical property associated with the porosity of the membrane. In membranes with high porosity, the linked pores form a dense three-dimensional network. In this case, the tortuosity of the pathway for ion migration could be low in many routes through the membrane. On the contrary, because there are only a few courses in the linked pores in membranes with low porosity, the ions cannot but move in the limited courses with high tortuosity. In other words, membranes with high porosity could provide ion migration pathways with low tortuosity, whereas membranes with low porosity have limited pathways with high tortuosity. On the basis of this assumption, we could interpret the ion/ membrane interactions observed in Figure 4c using the diagram shown in Figure 5. Ion/membrane interactions may be considered in two parts, namely a physical factor represented by the tortuosity of the ion transport pathway and a chemical factor represented by Coulombic interactions, as indicated by the two arrows at the bottom of Figure 5. Increases in the tortuosity of the pathway and the Coulombic effect of the membrane lead to decrease in the ionic mobility. The two factors depend on the porosity of the membrane, as indicated by the center arrow in Figure 5. As discussed in the preceding section, a decrease in the porosity of the membrane results in an increase in the tortuosity of the pathway as shown by the blue arrow on the left side. This tendency is assumed to be correlated to the change in βanion as shown in Figure 4c. Increase in βanion with decrease in porosity would be due to increase in the tortuosity of the pathway. It is probable that a smaller anion would be more sensitive to changes in the tortuosity of the pathway compared to the solvated cation, allowing the former to be easily trapped in corners in the pathway. On the contrary, βcation increases with increase in the porosity. However, anomalously, membrane/cation interactions are enhanced even though the free space and freedom of motion of the ions increase with increase in porosity. This can be explained by considering the individual interactive effects on the cation species. As shown in Figure 4b, the cation/anion

Figure 3. Correlation between the porosity and pore size of the PE membranes: (■) PE membranes; (red ▲) Celgard 2500 membrane.

roughly increases with increase in the porosity. However, for membranes with porosity less than 60%, there is no apparent correlation between the two parameters. Therefore, we first reviewed the dynamic values such as Dcation, Danion, x, η, α, and βcation as functions of porosity and pore size of the membrane. The estimated values are clearly correlated with porosity and the effect of change in membrane morphology on the dynamic values may be understood as follows. Figure 4 presents the estimated Dcation, Danion, η, α, and β values as functions of porosity. The numerical data is also summarized in Table 2. The values of Dcation and Danion exhibit different behaviors with porosity changes (Figure 4(a)). Unlike the monotonous increase in Danion with increase in porosity approaching the value in the free electrolyte solution at 100% porosity, the value of Dcation initially increases in the low porosity range, whereas it decreases at porosities over ∼50%. The absolute values of Dcation and Danion are almost identical at porosities less than 50%, whereas they diverge above 50% porosity. This difference in behavior between Dcation and Danion could be attributed to the differences in the interactions of the cation and anion species in the membrane. E

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 4. Estimated dynamic values: (a) Dcation, Danion, (b) η, α, (c) βcation, βanion, and (d) dissociation degree of the salt, x of the electrolyte solution in the separator membranes as a function of porosity of the membrane. Solid marks represent the PE membranes, hollow marks at 55% represent the PP membrane, and hollow squares at 100% represent the free electrolyte solution.

to the interactions between the cation and membranes, as characterized by βcation. The cation/membrane interactions could possibly change the solvation structure of the cation, leading to a decrease in the solvation number as well as the dissociation degree of the salt, x. The ion dynamic results in the membrane may be summarized as follows. In the restricted space available in membranes with low porosity, a high degree of Coulombic interactions (α) predominantly occur between the cation and anion species, leading to smaller Dcation and Danion values compared to those in the free electrolyte solution. This is attributed to the fact that the cation and anion mutually control the movement of each other in the narrow spaces. Furthermore, the anion is selectively restricted in motion due to the high tortuosity associated with low porosity, as confirmed by the presence of βanion. Further, owing to the high α values of the ionic species in the membrane with low porosity, the cation/ membrane interactions (βcation) would become negligible if βcation is present, because α and βcation exert competing forces on the cation. With increase in the membrane porosity and freedom of motion of the species in wide pore spaces, interactions between the cation and anion are reduced, approaching the levels in the free electrolyte solution. Instead, interactions between the cation and membrane substrate become significant. Large βcation value in membranes of high porosity and reduced α suggest that the lithium cation is

Coulombic interactions as well as the van der Waals interactions originating from the electrolyte solution itself decrease with increase in porosity. This implies that the motional freedom of the individual ions increase as the mobile space is widened. This also leads to enhanced collision frequency of the ions with the pore walls. In cases where the pore walls of the membrane carry a specific electric charge due to the presence of polar groups or surface charge, which causes ζ potential to develop on the membrane, cation or anion species could be attracted selectively by the membrane with βcation or βanion, respectively. Therefore, increase in the estimated value of βcation with increasing porosity reveals that the walls of the pore space are negatively charged, thereby attracting cations and selectively restricting the cation mobility, as shown in Figure 4a. This situation is represented by the red arrow on the right-side in Figure 5. In other words, the ionic mobility is controlled by a balance of interactions represented by η, α, and β. When η and α decrease, the Coulombic effect of the membrane becomes clear, leading to an increase in βcation in the PE membranes. Figure 4d presents the effect of porosity on the dissociation degree of the salt, x. The value of x is found to decrease with increase in the porosity. Considering that the ionic environment in the wide spaces in the membrane resembles that in the free electrolyte solution in infinite space, an anomalous low value of x in membranes with high porosity may be attributed F

DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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1.65 × 10−02

1.23 × 10−02 8.41 × 10−03

9.78 × 10−03

6.27 × 10−03 2.52 × 10−03 2.98 × 10−03

10−04 10−03 10−02 10−01 × × × × 6.46 1.93 2.66 1.15

x βan/Pa·s βca/Pa·s

8.31 × 10−03

10−03 10−03 10−03 10−04 10−03 10−03 10−03 10−02 10−02 10−02 10−02 10−03 × × × × × × × × × × × ×

α/Pa·s

5.95 7.81 7.82 9.75 3.12 4.37 8.99 2.13 2.18 1.49 1.18 7.19 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−03 × × × × × × × × × × × × 3.10 2.78 5.51 3.11 2.80 5.27 4.92 4.23 4.55 4.28 3.64 3.67 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 × × × × × × × × × × × × 2.12 2.37 1.19 2.11 2.35 1.25 1.34 1.55 1.45 1.54 1.81 1.79 × × × × × × × × × × × ×

10−03 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−03

1.02 8.75 5.17 1.02 1.20 6.21 5.66 4.49 2.81 5.16 6.13 6.64

× × × × × × × × × × × ×

10−10 10−11 10−11 10−10 10−10 10−11 10−11 10−11 10−11 10−11 10−11 10−11

9.75 1.14 7.83 2.10 1.90 7.10 6.94 4.91 4.52 4.87 6.00 1.11

× × × × × × × × × × × ×

10−11 10−10 10−11 10−10 10−10 10−11 10−11 10−11 10−11 10−11 10−11 10−10

2.35 2.62 1.32 2.34 2.60 1.38 1.48 1.72 1.60 1.70 2.00 1.98

× × × × × × × × × × × ×

10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10 10−10

5.55 4.68 2.80 9.34 2.37 4.18 3.56 2.50 1.30 3.06 3.74 1.25

× × × × × × × × × × × ×

10−11 10−11 10−11 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−11

4.91 8.05 6.39 2.09 1.44 5.36 5.19 2.99 3.24 2.71 3.58 7.84

× × × × × × × × × × × ×

10−11 10−11 10−11 10−10 10−10 10−11 10−11 10−11 10−11 10−11 10−11 10−11

selectively attracted by the Coulombic effect of the PE membranes owing to increased motional freedom and collision frequency of the ionic species. The cation/membrane interactions appear to affect the dissociation degree of the lithium salt in the membrane. This may be attributed to the change in the solvated lithium structure at dissociation equilibrium of the lithium salt in the pore spaces of the membrane. Evaluation of the Diffusion Coefficient Distribution. As mentioned above, the diffusion coefficient distribution of the species in the membrane is attributed to the morphological features of the membrane such as the distributions of pore size and tortuosity of the migration pathway. In addition, the results described in the previous section suggest that the interactions between the ions and membrane could contribute to the distributed diffusion coefficient of the ions because the diffusion coefficient distribution would be associated with the tortuosity of the pathway in the membrane. We elucidate the correlation between the distribution width (standard deviation, σ) calculated from the decays for DLi, DF, and DH, and the inherent diffusion coefficients Dcation, Danion, and Dpair, estimated from the analyses. It should be noted that the echo decays for DLi and DF have contributions from the ion and neutral ion pair as shown in eq 1 and do not reflect the single inherent diffusion coefficients of the ions (Dcation or Danion). At present, however, our selection of correlation parameters is ideal to examine the morphological effect on the diffusion behavior. Figure 6 shows plots of σ(Li) versus Dcation, σ(F) versus Danion, and σ(H) versus Dpair for all the PE membranes. We find that σ(F) and σ(H) monotonously increase with increase in Danion and Dpair, respectively. This suggests that the higher the averaged diffusion value, the wider would be the width of the diffusion coefficient distribution. This result may be interpreted as follows. Danion and Dpair roughly increase with increase in the porosity of the membrane, as shown in Table 2. Therefore,

1.30 2.03 1.33 3.55 2.31 1.11 1.06 5.89 5.23 6.45 9.77 1.27

η/Pa·s

Figure 5. Schematic diagram illustrating the interactive situation in the separator membrane on the ionic species. Yellow arrows at the bottom represent the physical and chemical factors, associated with the tortuosity and Coulombic effect, respectively, in the ion/membrane interactions. The blue arrow on the left represents the correlation between the tortuosity of the pathway and porosity of the membrane, which causes βanion to appear, whereas the red arrow on the right represents the correlation between the selective Coulombic effect and porosity of the membrane, which causes the appearance of βcation. This diagram suggests that the porosity of the separator membrane should be low to enhance the cationic mobility and reduce the anionic mobility in the cell only from the point of view of interactions between the ions and membrane.

PE-1 PE-2 PE-3 PE-4 PE-5 PE-6 PE-7 PE-8 PE-9 PE-10 PE-11 C2500

Dpair/m2s−1 Danion/m2s−1 Dcation/m2s−1 DH/m2s−1 DF/m2s−1 DLi/m2s−1 σ/S·m−1

Table 2. Observed Ionic Conductivity (σ), Diffusion Coefficients (DLi, DF, and DH), and Estimated Dynamic Values (Dcation, Danion, x, rcation, η, α, βcation, and βanion)

0.704 0.786 0.74 0.542 0.494 0.755 0.786 0.847 0.886 0.829 0.833 0.676

The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.6b10543 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 6. Correlation between the standard deviation, σ, of the diffusion coefficient distribution and inherent diffusion coefficients: (a) σ(Li) vs Dcation, (b) σ(F) vs Danion, and (c) σ(H) vs Dpair. σ(Li), σ(F), and σ(H) were estimated from the echo attenuations observed for 7Li, 19F, and 1H nuclear species, respectively, according to eq 4.

increases in σ(F) and σ(H) would be associated with increase in the membrane porosity. Expansion of the pathway network with increase in porosity allows the mobile species to migrate faster, owing to increase in alternative transport pathways and the possibility of selecting pathways with lower tortuosity. At the same time, with increase in the number of pathways in a sample, there is a wider mobility distribution in the pathways due to increased number of pathways with different width, length, and tortuosity. On the other hand, there is no clear correlation between σ(Li) and Dcation. Thus, this result indicates the existence of a specific factor besides the morphological features of the anion and solvent species that influences the diffusion coefficient dispersion for the cation. We hypothesize that the selective interactions between the membrane substrate and cation, which are thought to be Coulombic interactions, are related to this anomalous σ(Li) result.

the separator membrane by controlling the porous morphology of the membrane is important for designing high-performing battery systems.

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AUTHOR INFORMATION

Corresponding Author

*(Y.S.) Telephone: +81-72-751-4527. Fax: +81-72-751-8564. E-mail: [email protected]. ORCID

Yuria Saito: 0000-0002-9616-6309 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors appreciate Teijin Limited for the financial support for this research.

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CONCLUSIONS In conclusion, the ionic mobility and microviscosity, which is responsible for the mobility of the ions, were estimated for the electrolyte solution within the separator membrane. The microviscosity, α, which is attributed to the Coulombic interactions between the cation and anion, exhibited a large value in low porosity membranes owing to restricted motion of the species in narrow pore spaces. With increase in the porosity of the membrane, α decreased and a new microviscosity component, βcation, which may be attributed to the cation/ membrane Coulombic interactions, appeared. Controlling the microviscosities of the ions of the electrolyte solution within

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