Factors Determining Ionic Mobility in Ion Migration Pathways of

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C: Energy Conversion and Storage; Energy and Charge Transport

Factors Determining Ionic Mobility in Ion Migration Pathways of Polypropylene (PP) Separator for Lithium Secondary Batteries Yuria Saito, Sahori Takeda, Junichi Nakadate, Tomoya Sasaki, and Taehyung Cho J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04742 • Publication Date (Web): 26 Aug 2019 Downloaded from pubs.acs.org on August 26, 2019

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The Journal of Physical Chemistry

Factors Determining Ionic Mobility in Ion Migration Pathways of Polypropylene (PP) Separator for Lithium Secondary Batteries Yuria Saito*,† Sahori Takeda,† Junichi Nakadate,‡ Tomoya Sasaki,‡ and Taehyung Cho‡ †

National Institute of Advanced Industrial Science and Technology, 1-8-31, Midorigaoka, Ikeda,

Osaka 563-8577, Japan ‡

Sekisui Chemical Co. Ltd., Hyakuyama, Shimamoto-cho, Mishima-gun, Osaka 618-0021, Japan

ABSTRACT: To clarify the primary ion-transport factors in separator membranes, we evaluated the effects of pathway tortuosity and width on the mobilities (Dca, Dan) and microviscosities (, , and ca) of ions in a PP separator. Ionic diffusivities in different directions, along and inclined to the straight pathway composed of aligned pores, were compared in order to understand the effect of the geometrical pathway tortuosity. For cations in a specific solution moving along the straight pathway (tortuosity 1), the ca value attributable to cation–membrane interaction was around zero, which was different to the positive values of ca of cations of the same solution in random-network pathways with higher tortuosity. When cations diffuse in the direction inclined to the straight pathway, which corresponds to ion migration in a pathway of tortuosity > 1, ca was larger than both  and  attributed to the interactions between the ions and surrounding species. On the other hand,  and  were almost independent of pathway tortuosity, and depended on pathway width instead. These results suggest that reducing the geometrical pathway tortuosity of the separator,

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which assumes an ideal form with straight pathways, is key to designing separators for high ionic mobility in a high-power battery system.

INTRODUCTION The power performance of a secondary battery is mostly determined by ionic mobility in the battery system.1,2 Since the ions in a battery move between the cathode and the anode through the separator membrane during charge–discharge reactions for energy storage, controlling the ionic mobility in the separator membrane is the primary approach to developing high-power batteries. The ionic mobility is defined in the Stokes–Einstein equation using the microviscosity.3 The microviscosity can be categorized into three types that are associated with different interactions:

, which is attributed to the van der Waals interaction between the ions and surrounding species,  attributed to the Coulombic interaction between the cations and anions, and  attributed to the Coulombic interaction between the ions and the membrane in the case of an electrolyte solution in a separator.4–7 We have already evaluated the inherent diffusion coefficients of cations and anions, Dca and Dan, and the microviscosities of ions of an electrolyte solution in several types of separator by measuring the diffusion coefficients of multiple nuclear species (7Li, 19F, and 1H) and through theoretical estimations. We found that the values of  and  of the solution in a separator were generally larger than those in a free electrolyte solution, 0 and 0, owing to spatial restrictions on ionic motion in the narrow pathways. In addition, the emergence of  resulting from ionic collisions with the path walls led to enhancement of the entire microviscosity of ions with reduced ionic mobility in the pathway compared with the mobility of ions in the free electrolyte solution.


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We also confirmed that the magnitude of  attributed to ionic collisions with the pathway walls depended on the tortuosity and width of the linked-pore pathways in the separator membrane.7 The collision strength of an ion is associated with the distance between the ion and wall.8 Therefore, with decreasing the width of the pathway, the strength increases, in turn leading to an increase in

. On the other hand, tortuosity is the ratio of the mean effective migration distance of the ion path across the membrane surface to the separator membrane thickness.911 Lengthening of the ionmigration distance leads to an increase in the electrical resistance in proportion to the migration distance even if the ionic conductivity does not decrease. However, when ions migrate in a path of restricted space within a separator membrane, their mobility inevitably decreases owing to the collisions of ions with the walls of the pathway. In other words, even though the tortuosity generally represents the macroscopic and geometrical features of pathway length, it can be recognized as a dominant factor of the mobility of ions that migrate in the restricted space.11 With increasing the geometrical pathway tortuosity in a membrane, the contribution of the ionic collision with the pathway wall to ionic mobility increases owing to increase in the number of wall that the ions come across during the migration across the membrane surface. Furthermore, when the number of inflection points in a path increases due to an increase in pathway tortuosity, the frequency of ionic collision with the wall increases more than that during migration along a linear pathway because inflection points inevitably provide walls for ions advancing in the tortuous path. As a result,  becomes larger and the ionic mobility decreases with increasing pathway tortuosity. In a general separator membrane, ions migrating through paths with width of 10−210−1 m more or less collide with the walls of the paths independent of their tortuosity owing to the random walk behavior of ionic species in the restricted space.1113 This situation is ordinarily recognized by Knudsen diffusion.14 In practice, however, we discovered that   0 for a particular electrolyte


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solution in a straight pathway composed of aligned pores, while higher  was found with the same solution in a pathway with randomly arranged pores and higher pathway tortuosity.7 These results suggest that the magnitudes of  and , which are elements of ionic mobility, are dominated by pathway morphology as characterized by the tortuosity and width of the path. To systematically design separator membranes with efficient ion transport, it is therefore necessary to evaluate the correlation between the pathway morphology and the microviscosities of the ions. In practice, it is not easy to evaluate the independent effect of geometrical pathway tortuosity on ionic mobility because tortuosity is correlated with other parameters of porous membranes, such as porosity, pore size corresponding to pathway width, and membrane thickness, which are simultaneously determined during the membrane preparation process.10 In order to control tortuosity independently, we measured the diffusion coefficients of the ions in a straight alignedpore pathway by changing the diffusion direction with respect to the pathway length. In other words, the diffusivity along the pathway length was compared with the diffusivity in the direction inclined to the pathway length. The latter corresponds to diffusion in a pathway with higher tortuosity, because the direction of diffusion is more toward the wall; hence, ionic collisions with the wall make a larger contribution to the ionic mobility compared to the contribution from collisions resulting from diffusion along the pathway length. By evaluating the ionic mobility through estimating microviscosity, we determined the effect of ionic collisions; i.e., the effect of pathway tortuosity on ionic mobility in a separator membrane. The findings of this study are expected to offer guidelines for the rational design of separator membranes applicable to high-power battery systems.


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EXPERIMENTAL AND THEORETICAL METHODS Experimental Methods. Polypropylene (PP) porous membranes were prepared under dry conditions via a uniaxial stretching method; the stretching conditions such as the number of extensions, strength, and temperature were varied to control the pore size, porosity, and degree of pore alignment, producing straight aligned-pore pathways and random pathways without orientation.15,16 Seven types of aligned-pore membranes, each with a different porosity and average pore size of straight pathways across the membrane surface, were prepared for this study; two types of membrane with general random network pathways were also included for comparison. The porosities of the membranes were estimated from the ratio between the bulk density and the true density of PP.6 The respective pore sizes were determined via the mercury-penetration method with a mercury porosity meter,17 where the pore sizes were evaluated at the maximum rate of penetration of mercury into the pores. To measure the diffusion coefficients of different species in the solution through the membranes, stacked PP sheets were placed in a nuclear magnetic resonance (NMR) sample tube ( = 5 mm) so that the planes of the films were (1) vertical and (2) inclined at an angle of 53 from the longitudinal axis of the tube, as shown in Figure 1. The two film configurations permitted the diffusion measurement in different directions in the path: (1) along the length of the path for the vertical samples, and (2) at an inclination to the length of the path for the inclined samples of the aligned-pore membranes. An electrolyte solution, 1 M LiPF6 in a mixture of ethylene carbonate (EC) and diethyl carbonate (DEC) (EC/DEC = 1:1 (v/v)), was introduced into the membranes by repeated evacuation and restoration to atmospheric pressure in the presence of an excessive amount of the electrolyte solution.5


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(a)

(b)

z axis

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z axis

PP membrane sheet

Glass rod with an inclination of 37º

Diffusion measurement direction

z axis

z axis 53°

PP fibril

Pore space of pathway

37

Figure 1. Schematic illustrations showing the direction of diffusion with respect to the straight pathway of the aligned-pore membrane samples: (a) vertically stacked polypropylene (PP) membrane sheets; (b) PP membrane sheets inclined at an angle of 53 from the longitudinal axis (z axis) of the sample tube. The z axis corresponds to the direction of diffusion measurement. The enlarged illustrations represent the aligned-pore membrane with straight pathways. ; PP stem fibril,

; pore space for ion transport pathway

Images of the membrane samples were obtained with a field-emission scanning electron microscope (FE-SEM; S-4800S, Hitachi Co. Ltd., Japan) under an acceleration voltage of 1.0 kV. The diffusion coefficients of the probed nuclear species 7Li (116.8 MHz), 19F (292.7 MHz), and 1

H (300.5 MHz), labeled DLi, DF, and DH, respectively, were measured at 25 °C via pulsed-gradient

spin-echo (PGSE) NMR spectroscopy with a wide-bore spectrometer (JNM-ECP300, JEOL Co., Ltd., Japan).18 A Hahn echo pulse sequence was employed in these measurements. In order to


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determine the attenuation of the echo intensity with diffusion of the probed species, a halfsinusoidal gradient pulse was applied twice in succession after the 90° and 180° pulses.19,20 The diffusion coefficients were measured in the direction along the straight pathways for the vertically set membranes, while the measurements were inclined to the length of the straight path for the sloped samples by applying the static and gradient magnetic fields in the z direction, as shown in Figure 1. The diffusivities along the straight pathway and inclined pathway correspond to the migrations in pathways of tortuosity  1 and  1/sin 53° = 1.25, respectively, based on the general definition of tortuosity.9,10 The typical width of the gradient pulse () and the diffusion time () of the pulse sequence were 0–7 ms and 12–20 ms, respectively. The diffusion times were shorter than those generally measured for electrolyte solutions in order to prevent the effect of restricted diffusion in the presence of the separator as a barrier substrate. Typical echo attenuations are presented in Figure S1 (see Supporting Information). The ionic conductivities () of the solutions in the membranes were measured via the complex impedance method with a frequency analyzer (1250, Solartron, UK) combined with a potentiostat (1287, Solartron, UK). Conductivity cells were prepared by stacking a predetermined number (2, 4, 6, 8, or 12) of PP sheets containing the solution and sandwiching them between stainless steel electrodes, followed by laminating and sealing the device. The cell resistance across the device was plotted as a function of the number of PP membrane sheets, and the average resistance of one sheet was estimated from the slope of the plot to evaluate the ionic conductivity in the vertical direction of the membrane plane (0). A typical Cole-Cole plot of impedance data and the relationship between impedance and the number of the piled sheets are shown in Figure S2 (see Supporting Information).


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Theoretical Derivations. The diffusion coefficients of the cation, anion, and ion-pair species (Dca, Dan, and Dpair, respectively) and the microviscosities (, , and ) responsible for the magnitudes of the diffusion coefficients were estimated as described below. In general, when a lithium salt reaches dissociation equilibrium in the electrolyte solution, the dissociated cations and anions coexist with associated ion pairs. Owing to the rapid exchange between entities during the diffusion-measurement period, the detected NMR signals reflect the average conditions of the existing species.21,22 As a result, the measured diffusion coefficients, DLi, DF, and DH, which were probed by the 7Li, 19F, and 1H nuclear species, respectively, can be defined by the inherent diffusion coefficients of the entities as follows:21 𝐷Li = 𝑥𝐷ca + (1 − 𝑥 )𝐷pair , 𝐷F = 𝑥𝐷an + (1 − 𝑥)𝐷pair ,

(1)

𝐷H = 𝐷DEC = 𝐷solv,

where x is the dissociation degree of the lithium salt in the solution. Dca and Dan represent the diffusion coefficients of the two single entities (i.e., the cation and the anion) and are directly related to the cation mobility and anion mobility, respectively, according to the Einstein relation.3 Dpair represents the diffusion coefficient of the associated ion pair, LiPF6. DH was directly estimated from the peak of the neutral DEC species (DDEC) in the solvent, whose peak is denoted by Dsolv. The ionic conductivity is the sum of the cation and anion conductivities, which are functions of the net carrier concentration (xN) and the ionic-diffusion coefficient: 𝑒2

𝜎 = 𝑘𝑇 𝑥𝑁(𝐷ca + 𝐷an ),

(2)


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where e, k, T, and N represent the electric charge, Boltzmann constant, absolute temperature, and salt concentration of the solution, respectively.23 Dpair was estimated from the sizes of the ion pair (rpair) and DEC (rDEC), based on the relationship DDEC / Dpair = rpair / rDEC according to the van der Waals size and Stokes–Einstein equation.24,25 As a result, Dca, Dan, and x can be estimated simultaneously by solving eqs 1 and 2. Furthermore, the inherent Dca, Dan, and Dpair are functions of the size and microviscosity of the corresponding species, which can be obtained from the Stokes–Einstein relation as follows:3 𝑘𝑇

𝐷solv = 6𝜋𝑟 𝑘𝑇

𝐷an = 6𝜋𝑟



anion 

𝐷ca = 6𝜋𝑟

𝑘𝑇

,

DEC

,

 =  + ,

(3)

𝑟



cation 

,  =  + 𝑟 anion 𝛼 + 𝛽ca , cation

where , , and ca are the microviscosities attributed to the van der Waals interactions with the surrounding species, Coulombic interactions between the cations and anions, and Coulombic interactions between the cations and inside walls of a pathway in the membrane, respectively. Notably, when examining the interaction of the membrane with the anions, an must be included in the equation for Dan, whereas ca must be removed from the equation for Dca. If both ca and an are present in a sample, the difference between them (ca − an) can be estimated as the net effect of both terms.

RESULTS AND DISCUSSION


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Properties of Diffusion in the Direction Inclined to the Straight Pathway. Figure 2 shows SEM images of typical membranes with pathways of aligned pores and randomly arranged pores. The membrane with the aligned-pore pathways was composed of stem fibrils vertical to the membrane plane and branch fibrils parallel to the plane; the branch fibrils connected the stem fibrils together to form the membrane. The stem fibrils provided straight pathways across the membrane surface for ion transport. The branch fibrils, which were oriented along the diameter of the pathways, were too fine to disturb ion transport along the main pathways.26 Therefore, the tortuosity of this pathway is ~1. On the contrary, in the membrane with randomly arranged pores, the ions seem to change directions several times in order to traverse the membrane owing to the random network of pathways characterized by a tortuosity >1.

(a)

(b)

5.00 m

5.00 m

Figure 2. SEM images of PP membranes with (a) aligned pores and (b) randomly arranged pores.

Ions move randomly during their migration in a separator-membrane path, colliding not only with the surrounding mobile species (ions and molecules), but also with the path walls to change


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their positions along the pathway length. Depending on the frequency of ionic collision with the wall, the characteristics of ionic diffusion in a pathway reflect the barrier effect of the pathway wall.12,13 Based on the SEM image of the aligned-pore membrane shown in Figure 2, we assumed that the tortuosity effect, which is associated with the frequency of ionic collisions with the pathway wall, on ionic mobility could be systematically altered by changing the diffusion detection direction to the direction of a straight pathway in an aligned-pore membrane. For vertically stacked membranes with aligned pores, the measured diffusion direction is parallel to the direction along the length of the path, as shown in Figure 1a. The estimated diffusion coefficient would be larger than those in other directions owing to the minimal effect of the barrier wall, which is vertical to the advancing direction of the ions, on ionic diffusivity. On the contrary, the barrier wall would have the largest impact on the diffusion coefficient in the direction across the path, which has typically been characterized by restricted diffusion.8,13,27 In this scenario, the estimated diffusion coefficient would be lower than those in other directions, or the non-linear echo attenuation form of log (I/I0) versus 2 (where I/I0 is the ratio between the echo intensities after (I) and before (I0) application of the pulse sequence for diffusion measurement) can be observed owing to deviation from ideal random walk behavior.13,27 It is therefore acceptable that the estimated diffusion coefficient in the direction inclined at an angle  to the pathway length (Figure 1b) has a certain contribution from ionic collisions with the path walls. The estimated diffusion coefficient in such a case is smaller than the diffusion coefficient in the vertically stacked sample. This situation corresponds to ion migration in a pathway with tortuosity > 1, depending on , even if membranes with straight pathways are used. As explained in the Theoretical Derivations section (above), it was necessary to measure the diffusion coefficients, DLi, DF, DH, and the corresponding ionic conductivity, , in order to estimate


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Dca, Dan, , , and  using eqs 1–3. We could independently measure the diffusion coefficients in the directions parallel and inclined to the straight pathway using the method described in the Experimental Methods section. However, contrary to the conductivity parallel to the straight pathway shown in Figure 3a (0, where the superscript 0 denotes zero inclination) as explained in the Experimental Methods section, we could not directly measure the conductivity corresponding to diffusion at an inclination θ to the straight pathway shown in Figure 3b (, where the superscript θ denotes an inclination of θ) owing to the difficulty in setting up the electrodes to detect current signals in that direction. Therefore, we calculated  from 0 using the equation:

 = cos2  0,

(4)

which is based on the assumption that 0 is isotropic and  corresponds to the component of 0 at an inclination of . If the ionic collisions with the wall make larger contributions that reduce the ionic mobility, 0 would be anisotropic owing to anisotropic ionic mobility, depending on the direction of diffusion, and the actual value of  would be smaller than that obtained from eq 4; i.e.,  < cos2  0. With decreasing  in response to anisotropy of mobility, the calculated values of Dca and Dan decrease and the subsequent , , and  increase because the decreased ionic mobilities reflect enhanced interactions between the ions and the surrounding species or membrane. Therefore, , , and  obtained on the basis of the assumption of eq 4 would be the minimum expected values.


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(a)

(b) z axis

z axis

 = 37

0

(D0)



0 Along the pathway

(D)   = 37°

Figure 3. Magnified views of the direction of diffusion (z axis) in (a) vertical and (b) inclined membranes and their respective diffusion coefficients and conductivities, (D0, 0) and (D, ). The red arrow shows the diffusion direction detected in each membrane;

: stem fibrils;

: pore space for ion transport. The membranes had (a) open upper and lower ends and (b) fibril barriers along the direction of diffusion. In case of (b),  = 0cos2 is satisfied when D = D0cos2. If the effect of ionic collision with the wall on the diffusivity in the inclined direction is larger than that on D0, D < D0cos2 and the subsequent relationship  < 0cos2 are satisfied.

Estimation of Inherent Diffusion Coefficients (Dca and Dan) and Microviscosities. We evaluated the diffusion coefficients of the cation and anion (Dca and Dan) and microviscosities (,

, and ca) of the electrolyte solution in separator membranes with aligned pores and randomly arranged pores. Hereafter, we refer to Dca and Dan as “ionic mobilities” because the inherent diffusion coefficient directly corresponds with mobility through the Einstein relation.28 The values


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of Dca, Dan, , , and ca were obtained in two different directions, parallel and inclined to the straight pathway length, as functions of the normalized Gurley value (Gʹ [s(100cc)-1]) and the pathway width (2r). Gʹ was estimated by normalizing the measured Gurley permeability (G [s(100cc)-1]) with respect to the porosity (p) and width (d) of the membrane to eliminate the factor of carrier content from G and highlight the factors concerning the mobility of carriers as follows: Gʹ = G  (d0/d)  (p/p0),

(5)

where d0 and p0 are the standard width and porosity, respectively. 29,7 It is noted that the unit of G is the same as that of G, [s(100cc)-1] from eq. 5. We used d0 = 16 m and p0 = 55% in our calculations as they are the average values of d and p of the membranes used in the study. As a result, Gʹ, which reflects carrier mobility, depends on the tortuosity and width of the pathway of the porous membrane. In Figures 4 and 5, samples with Gʹ < 70 correspond to the membranes with aligned pores, and the samples with Gʹ > 100 correspond to membranes with randomly arranged pores. Furthermore, the aligned-pore membranes were separated into two groups with Gʹ  40 and Gʹ  60. Considering that the aligned-pore membranes showed almost the same straight pathways that were assumed to have a geometrical tortuosity of 1 (i.e., pathway distance  membrane thickness) from SEM measurements, the difference between the Gʹ values of the two groups can be mainly attributed to the difference in the widths of their respective pathways.7 On the other hand, Gʹ > 100 for the random-pore membranes because the tortuosities of their pathways were higher (i.e., >1) than those of pathways in the aligned-pore membranes. Figure 4 shows the estimated values of the ionic mobilities of the electrolyte solution in the vertical separator membranes (D0ca, D0an) and inclined separator membranes (Dca, Dan). The error


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bars in Figures 4 and 5 were estimated assuming that the measured values (DLi, DF, DH, and ) in equations 1 and 2 include up to 5% errors that are attributable to individual sample differences and measurement errors. In practice, we confirmed that the errors in the measured values were less than 4% through repeated measurements using two different, but similar, samples. D0ca and D0an decreased with increasing Gʹ (Figure 4a). With the exception of the membrane with the largest value of 2r, D0ca, and D0an increased with 2r for the vertical aligned-pore membranes (Figure 4c), indicating that ionic mobility depends on the magnitude of the resistance from the pathway wall even for migration along straight paths. The slight decreases in D0 ca and D0an when 2r > 1.0 m are likely caused by branch fibrils (that connect stem fibrils at longer distances), which hinder ion migration; this effect is reflected by the G values (35 s(100 mL)-1) that are close to those of the aligned-pore membrane with a much smaller 2r (0.32 m). Dca and Dan of the inclined membranes were lower than the respective D0ca and D0an of the vertically set membranes, except those with randomly arranged pores (Gʹ > 100) that showed Dca  D0ca, and Dan  D0an (Figure 4b compared with 4a). Furthermore, Dca and Dan varied differently; Dca did not show any noticeable change with either Gʹ or 2r, while Dan gradually decreased with Gʹ and increased with 2r except at 2r  1.1 m (Figures 4b and 4d), which was similar to the trends displayed by D0an (Figure 4a and 4c). These features indicate that cation mobility depends on the diffusion direction in the straight pathway; i.e., the cations are strongly affected by the collisions with the pathway walls. In order to determine the cause of these results, we estimated the microviscosities in the next stage of the study.


15


14

14

(a)

D0ca

Vertical sample

12

D0an

Dca, Dan / 110-11 m2s-1

D0ca, D0an / 110-11 m2s-1

12 10 8 6 4

aligned pore

2

40

60

80

100

(b)

Dan

10 8 6

aligned pore

0 20

120

40

60

80

100

120

-1

G' / s(100 cc)

G' / s(100 cc)

(c) Dca, Dan /110-11 m2s-1

14

12 10

D0ca D0an

8 6 4 Vertical sample

2

random pore

4

-1

14

Dca

Inclined sample

2

random pore

0 20

D0ca, D0an / 110-11 m2s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(d)

Dca

Inclined sample aligned pore membranes only

12

Dan

10 8 6 4 2

aligned pore membranes only

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.0

2r / m

0.2

0.4

0.6

0.8

1.0

1.2

2r / m

Figure 4. Estimated diffusion coefficients of cation (Dca) and anion (Dan) in (a, c) vertical membranes (identified by superscript 0) and (b, d) inclined membranes (identified by superscript

) as functions of (a, b) normalized Gurley value (Gʹ) and (c, d) pathway width (2r). (a) and (b) includes the values for the aligned-pore and random-pore membranes, and (c) and (d) includes the values for the aligned-pore membranes. The error bars were estimated assuming that the measured values (DLi, DF, DH, and ) in equations 1 and 2 include up to 5% errors that are attributable to individual sample differences and measurement errors. The extrapolated lines in (c) and (d) were drawn to show the trends in variation of Dca and Dan of the aligned-pore membranes with 2r.


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Figure 5 shows the microviscosities , , and ca as functions of Gʹ and 2r for the vertical membranes (identified by superscripts 0) and inclined membranes (identified by superscripts ). For the vertical membranes with aligned pores (G < 70) and randomly arranged pores (G > 100),

0 gradually increased with Gʹ, while 0ca was close to zero and independent of Gʹ for the alignedpore membranes, in contrast to 0ca  0 for the random-pore membranes (Figure 5a). When the results were plotted as a function of 2r to determine the effect of the pathway width of the alignedpore membranes, 0 was observed to rapidly increase with decreasing 2r below 0.3 m (Figure 5c), indicating that cation–anion Coulombic interactions are sensitive to changes in the pathway width in that range. For the inclined membranes with pathway tortuosity  1.25, it was apparent that ca was larger (Figure 5d) compared to that (0ca  0, Figure 5c) for migration along the straight pathway with tortuosity  1.0, owing to the higher frequency of ionic collision with the pathway walls. In particular, ca increased steeply with decreasing 2r below 0.3m, reflecting the dependence of the collision frequency on the width of the pathway in that range. On the other hand, we found that   0 and   0 when 2r > 0.3 m, which was different to the   0 trend observed. This means that  and  are insensitive to collision frequency in the wider pathways, contrary to our expectations because an increase in  reflects restricted ionic motion, which, in turn, causes an increase in .6 This observation is ascribable to competition between the cation– anion interaction and cationmembrane interaction, which determines the magnitudes of  and , respectively. The stronger cation–membrane interactions associated with larger  results in weaker than expected cation–anion interactions (with smaller ) in the somewhat wider space of the pathway. In practice, when the width of the pathway decreased to below the threshold value of ~3

m,  and  sharply increased, which was similar to that observed for , possibly owing to


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strong restrictions on the movements of the species with increasing interactions (both cation–anion interaction and cationmembrane interaction) in the narrower pathways. Finally, the results for the random-pore membranes, namely0  , 0  , and 0ca  ca (Figure 5a, 5b; G > 100) confirm that the random network of pathways is isotropic and that diffusivity is independent of the diffusion direction in a membrane.

12.0

0, 0, 0ca / mPa.s

10.0 8.0

12.0

0 0 0ca

Vertical sample

aligned pore

random pore

6.0 4.0

(b)



8.0 6.0 4.0

2.0

2.0

0.0 20

0.0 20

aligned pore 40

60

80

100

 ca

Inclined sample

10.0

, , ca / mPa.s

(a)

120

40

-1

random pore

60

80

100

120

-1

G' / s(100 cc)

G' / s(100 cc)

12.0

12.0

(c)

(d)

0 0ca 0

Vertical sample aligned pore membranes only

8.0 6.0 4.0 2.0 0.0 0.0

 ca

Inclined sample

10.0

, , ca / mPa.s

10.0

0, 0, 0ca /mPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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aligned pore membranes only



8.0 6.0 4.0 2.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.0

2r / m

0.2

0.4

0.6

0.8

1.0

1.2

2r / m

Figure 5. Estimated microviscosities (, , and ca) in (a, c) vertical membranes (identified by superscript 0) and (b, d) inclined membranes (identified by superscript ) as functions of (a, b) normalized Gurley value (G) and (c, d) pathway width (2r). The error bars were estimated assuming that the measured values (DLi, DF, DH, and ) in equations 1 and 2 include up to 5%


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errors that are attributable to individual sample differences and measurement errors. The extrapolated lines in (c) and (d) were drawn to show the trends in variation of the microviscosities of the aligned-pore membranes with 2r.

Therefore, the fundamental ion-transport behavior in the pathways of a polypropylene separator membrane can be summarized as follows. The main factors that dominate ionic mobility in the paths are higher cation–anion Coulombic interactions represented by  (compared with that in a free electrolyte solution) and the generation of cation–membrane interactions through ionic collisions with the interior path walls, represented by ca. A decrease in pathway tortuosity (to the ideal form of a straight pathway with the geometrical tortuosity 1), can reduce ca because of the decrease in the frequency of ions colliding with the pathway walls in the advancing direction along the path. However, the ions inevitably collide with the pathway walls owing to the isotropic random walk behavior of the species, even during migration along a straight pathway. Therefore, the narrower the path, the larger the value of ca because a shorter distance between the ions and walls leads to an increase in the interactive forces between them.7,10 Furthermore, it should be noted that, in general, the ion–membrane interaction depends on the surface condition of the pathway wall and the solvation structure of the ions associated with the surface charges on the pathway wall and carrier species, which were not evaluated in this study.5 The magnitude of  (responsible for the cation–anion interaction) is another significant iontransport parameter of a membrane pathway. In the semi-closed pathway spaces, ionic motion is restricted by the wall barriers of the paths, which leads to an increase in  from that of the free electrolyte solution. However, increases in  with changes in tortuosity and width of the path were


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gradual when compared with the increases in  ca, despite the more-constrained cationic motion resulting from the higher ca. It is generally expected that strongly restricted ionic motion leads to stronger cation-anion interaction with larger . Therefore, the weak dependence of  on tortuosity and width may be explained by competing cationanion/cationmembrane interactions, and the emergence of ca as a dominant component of Dca in the paths of the separator membranes.

CONCLUSION This study evaluated the effect of pathway tortuosity on ionic mobility in membrane pathways through estimating the microviscosities attributed to several ionic interactions. From a microscopic view point, pathway tortuosity can be evaluated by the frequency of ionic collisions with the pathway walls during ion migration. For a membrane with straight pathways across its surface, a change in the diffusion direction of the path led to changes in ionic collision contributions to ion diffusivity. A comparison of the ionic mobilities (Dca, Dan) and microviscosities (, , ca) along a straight pathway with those along an inclined pathway revealed the real effect of geometrical pathway tortuosity on Dca. This was confirmed by the strong dependence of pathway tortuosity on selective interaction between the cations and the PP membrane (represented by ca). However, the interaction between cations and anions (represented by ) was almost insensitive to tortuosity, especially in a wide pathway, which is possibly ascribable to competition between the cationmembrane interaction and cationanion interaction. Increased cation-membraned interaction would weaken the dependence of cation-anion interaction on tortuosity. This suggests that controlling pathway tortuosity is the primary approach to providing batteries with high ionic mobilities and excellent power performance.


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ASSOCIATED CONTENT Supporting Information. Brief descriptions in nonsentence format listing the contents of the files supplied as Supporting Information.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Y.S.)

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT The authors thank Sekisui Chemical Co., Ltd. for financially supporting this research.

ABBREVIATIONS DEC, diethyl carbonate; EC, ethylene carbonate; FE-SEM, field-emission scanning electron microscopy; NMR, nuclear magnetic resonance; PGSE, pulsed-gradient spin-echo; PP polypropylene; SEM, scanning electron microscopy.


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29. Ozoemena, K. I.; Chen S. in Nanomaterials in Advanced Batteries and Supercapacitors; Springer, Switzerland, 2016; p. 423.


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SYNOPSIS (Word Style “SN_Synopsis_TOC”). Dcation

D0cation



straight pathway with tortuosity = 1

tortuous pathway with tortuosity > 1

D0cation > Dcation


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Factors Determining Ionic Mobility in Ion Migration Pathways of

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