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Journal of The Electrochemical Society,166 (8) A1285-A1290 (2019) A1285

Inﬂuence of the Active Material on the Electronic Conductivity of

the Positive Electrode in Lithium-Ion Batteries

Hiroki Kondo, zHiroshi Sawada, Chikaaki Okuda, and Tsuyoshi Sasaki

Toyota Central R&D Labs., Nagakute, Aichi 470-1192, Japan

Electronic conductivity is one of the critical factors that govern the performance of high-energy lithium-ion batteries. However, until

now, equations have been used to simulate electrode behavior in the absence of the necessary experimental background. In this study,

we examined whether or not two commonly used equations can be used to express the electronic conductivity of a positive electrode

fabricated with an NCA-based material. The electronic conductivity of this positive electrode was comprehensively examined, and

the experimental results were used to validate the two above-mentioned equations. It was revealed that (i) the electrode density

and weight ratio of carbon black affect electronic conductivity in different ways and (ii) electronic conductivity is inﬂuenced by

the volume fractions of both conductive carbon and active material. This deviation from classical percolation theory arises from the

electronic conductivity of the active material, which cannot be regarded as an insulator. We therefore derived an empirical equation for

a positive electrode composed of an NCA-based material. The empirical equation not only simulated the electrode more accurately,

it also provides a better understanding of the electronic-conduction mechanism and helps to facilitate better electrode and battery

design.

© The Author(s) 2019. Published by ECS. This is an open access article distributed under the terms of the Creative Commons

Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any

medium, provided the original work is properly cited. [DOI: 10.1149/2.0051906jes]

Manuscript submitted November 28, 2018; revised manuscript received February 13, 2019. Published April 18, 2019.

Lithium-ion (Li-ion) batteries are used as power sources for elec-

tric vehicles. However, to extend the cruising range of such vehicles,

the energy densities of Li-ion batteries should be improved. One sim-

ple method for obtaining high-energy batteries involves reducing the

amount of electrochemically inactive components in the battery (e.g.,

conductive carbon, binders, current collectors, electrolytes, and sep-

arators) by controlling electrode and battery design parameters (e.g.,

electrode composition, thickness, and porosity). Generally, the posi-

tive electrode comprises an active material, conductive carbon, and a

binder. For positive electrodes with layered oxides, a conductive addi-

tive is used to ensure sufﬁciently good electronic conductivity owing

to the low electronic conductivity of the active material.1However, in

high-energy batteries, the contents of conductive carbon and binder

need to be as small as possible to ensure electrode porosity. There-

fore, to optimize the design of the positive electrode for high-energy

batteries, it is important to consider the electronic conductivity of the

electrode.

Typically, carbon black (CB) is used as the conductive carbon

component in a positive electrode. Primary CB particles, which are

considerably smaller (<50 nm) than the active material particles

(<10 μm), form agglomerates referred to as “the structure.”2,3There-

fore, even with only a small amount of CB, an electrode can exhibit

high electronic conductivity resulting from size-ratio4,5and structural

effects.6–8Electronic conductivity in composites of conductive and

insulating materials has often been understood on the basis of per-

colation theory.9In such a composite electrode, CB is considered to

be a conductor, whereas the other components (i.e., the active ma-

terial, binder, and pores) are considered to be insulators. Mandal

et al.10 measured the electronic conductivities of LiMn2O4positive

electrodes with different weight fractions of active material and CB,

with the observed relationship consistent with that predicted by clas-

sical percolation theory. In addition, they found that the percolation

threshold was considerably less than that predicted for randomly dis-

tributed particles. According to percolation theory, the electronic con-

ductivity of a composite above the percolation threshold is expressed

by:10–12

σ=σc,0(v−vc)t,[1]

where σc,0is the electronic conductivity of CB, vis the volume fraction

of the conductive CB, vcis the percolation threshold, and tis the critical

exponent. That is, the electronic conductivity of the electrode depends

on the volume fraction of the CB in the electrode. The percolation

zE-mail: h-kondo@mosk.tytlabs.co.jp

threshold, vc, and the critical exponent, t,oftheLiMn

2O4electrode

were reported to 0.03 and 1.7, respectively.10

On the other hand, other equations have been used to express the

electronic conductivities of positive electrodes in mathematical sim-

ulations of Li-ion batteries.13,14 The battery-modeling technique is a

powerful tool for predicting battery performance. One of the most pop-

ular and useful Li-ion-battery models is the pseudo 2D (P2D) model,

which is based on the porous electrode theory developed by the group

of Newman.13–15 In the P2D model, most studies use a constant con-

ductivity value or the following equation to determine the electronic

conductivity of an electrode:16–18

σ=σ0εsp,[2]

where σis the electronic conductivity of the electrode, σ0is the bulk

conductivity of the composite electrode, and ɛsis the volume fraction

of the solid phase. The value of the exponent pis either 1.0 or 1.5. Ac-

cording to Eq. 2, the electronic conductivity of an electrode depends

on the volume fraction of the solid phase, which not only includes

the CB, but also includes the active material and binder, whereas that

based on percolation theory (Eq. 1) depends only on the volume frac-

tion of the CB. To design electrodes and batteries with low amounts

of conductive carbon for high-energy applications, an equation that

accurately expresses the electronic conductivity of the electrode is re-

quired; however, to the best of our knowledge, to date no studies that

validate the above-mentioned equations for positive electrodes using

layered oxide active materials in Li-ion batteries have been reported.

In this study, we focused on the electronic conductivity of a positive

electrode using a LiNi0.8Co0.15 Al0.05O2-based (NCA-based) material,

which has attracted interest for high-energy battery applications in re-

cent years because of its high capacity. We measured the electronic

conductivity of a positive electrode containing this NCA-based ma-

terial using a reliable method in order verify the above-mentioned

well-used equations (Eqs. 1and 2) and, if required, to derive a prac-

tical equation for the electronic conductivity of a positive electrode

in a Li-ion battery. In addition, the relationship between electronic

conductivity and electrode parameters is discussed.

Experimental

LiNi0.75Co0.15 Al0.05Mg0.05 O219–24 (Mg-NCA, secondary particle

size: 7 μm, Sakai Chemical Industry Co., Ltd.) was used as the ac-

tive material, CB (TB-5500, particle size: 25 nm, Tokai Carbon) was

used as the conductive additive, and polyvinylidene diﬂuoride (PVdF,

L#1120, Kureha) was used as the binder. These components were

mixed with N-methyl-2-pyrrolidone in various weight ratios, as shown

A1286 Journal of The Electrochemical Society,166 (8) A1285-A1290 (2019)

Table I. Positive electrodes for electronic conductivity measurements.

Weight ratio

AM loading on AM density Thickness on Porosity Volume fraction Volume fraction

AM∗CB PVdF one side [mg/cm2] [g/cm3] one side [μm] ɛof CB, ɛcof solid phase, ɛsp

85 1 (1.14 wt%) 1.5 6.78 2.82 24.0 0.345 0.0185 0.625

6.96 2.73 25.5 0.367 0.0178 0.605

6.89 2.46 28.0 0.430 0.0161 0.545

85 2 (2.25 wt%) 1.8 6.99 2.69 26.0 0.353 0.0352 0.613

6.91 2.49 27.8 0.401 0.0326 0.568

85 5 (5.35 wt%) 3.5 6.89 2.38 29.0 0.354 0.0777 0.589

6.92 2.16 32.0 0.412 0.0707 0.536

6.96 1.99 35.0 0.460 0.0650 0.492

85 10 (10 wt%) 5 7.00 1.97 35.5 0.379 0.1289 0.553

7.00 1.82 38.5 0.428 0.1188 0.510

6.97 1.63 42.8 0.487 0.1066 0.457

∗AM, active material.

in TableI. The electronic conductivity of a positive electrode is affected

not only by the CB weight and the electrode density, but also by the

CB structure.8,25 Therefore, in this mixing process, the viscosity of the

slurry and the mixing time were kept as constant as possible to ensure

the same degree of disintegration of the CB structure. The obtained

electrode slurry was coated on both sides of an aluminum foil so that

the loading of the active material on each side was ∼7 mg/cm2.The

electrode sheet was dried at 180°C for 8 h and compressed to control

the electrode density so that the porosity of the electrode was 0.3–

0.5. Table Ilists the ﬁnal porosity and density of the active material

for each electrode. After calendering, the electrode was vacuum-dried

again at 180°C for 8 h. Electrodes with different weight ratios of con-

ductive carbon and different active material densities were prepared

for electronic conductivity measurements (Table I).

The four-point-probe method is typically used for measuring the

electronic resistance of electrodes;10,26,27 however, this method has

several issues. Because the electrode contact point is extremely thin, it

is susceptible to the effects arising from local distribution of conductive

additives. In addition, although the macroscopic direction of electron

transfer during charge/discharge is the electrode thickness direction,

the four-point-probe method can measure the electrode resistance in

the direction parallel to the electrode sheet. Moreover, it is difﬁcult to

perform such measurements under pressure,28 and the interfacial re-

sistance between the electrode and the aluminum current collector29,30

cannot be measured. To solve these issues, Wheeler’s group proposed

a four-line-probe method,31,32 a superior approach that can measure

in-line during the electrode fabrication process. However, it is difﬁ-

cult to employ this measurement method for laboratory use because it

requires a special line probe and a simulation technique speciﬁc to the

probe. In this study, the electronic resistance in the thickness direction

of the electrode was measured using a simple two-electrode-based

method as described by Thorat et al.33 Similar measurements have

been recently reported.28,33–35 One or two electrodes were sandwiched

between two cylindrical indenters, and the direct current resistance

was measured during the application of pressure. As this approach

does not require any special probe or simulation, it avoids the above-

mentioned issues associated with the four-point-probe method.

Two electrodes were cut out into 25-mm-diameter disks with rect-

angular protrusions and sandwiched between opposite indenters, as

showninFigure1. The direct current resistance of the electrodes

was measured using an electrochemical analyzer (ALS Model 660A,

ALS Co., Ltd.). Before measuring the electronic resistance, the pres-

sure inside the wound electrode ensemble of a house-made cylindri-

cal cell was measured using a pressure measurement ﬁlm (Prescale,

Fujiﬁlm), and it was found that a pressure of 2.45 MPa was applied to

the electrode inside the wound electrode ensemble. Therefore, the ap-

plied pressure during the electronic resistance measurements was set

as 2.45 MPa. Two measurements were performed for each electrode.

The volume fraction of CB in the electrode was calculated from the

weight ratio of the electrode components, the electrode density, and

the electrode thickness using the true densities of the electrode compo-

nents (4.651, 1.80, and 1.71 g/cm3for the Mg-NCA active material,

CB, and PVdF binder, respectively). Scanning electron microscopy

(SEM; S-4300, Hitachi) was used to conﬁrm the distribution and lo-

cation of CB in the electrode.

Results and Discussion

To compare against the reported equations (Eqs. 1and 2), the log-

arithm of the measured volume conductivity was plotted against two

Indenter

V+ I+ V-I-

Stress

(2.45 MPa)

Electrochemical analyzer

Electrode

Current collector

Eliminate electrode

Electrode

Figure 1. Schematic of the setup for measuring electronic resistance of the electrode.

Journal of The Electrochemical Society,166 (8) A1285-A1290 (2019) A1287

-4

-3

-2

-1

0

1

2

0 0.2 0.4 0.6 0.8

Log σ

Volume fracon of the solid phase

10 wt%

5.35 wt%

1.14 wt%

2.25 wt%

(a- a()1-2)

(b- b()1-2)

10 wt%

5.35 wt%

1.14 wt%

2.25 wt%

0

2

4

6

8

0246810

Slope

Weight rao of CB [wt%]

-4

-3

-2

-1

0

1

2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Log σ

Volume fracon of CB

0

10

20

30

40

50

60

70

0246810

Slope

Weight rao of CB [wt%]

Figure 2. Electronic conductivity of each electrode plotted against the volume fraction of (a-1) carbon black and (b-1) the solid phase. Dotted lines show linear

ﬁts obtained using an identical intercept of logσ0=−3.1185. The slopes of the linear lines in (a-1) and (b-1) are plotted against the weight ratio of CB in (a-2)

and (b-2), respectively.

different electrode parameters. Figure 2(a-1) shows a plot of the elec-

tronic conductivity logarithm of the electronic conductivity against the

CB volume fraction in accordance with classical percolation theory

(Eq. 1). On the other hand, Figure 2(b-1) shows the logarithm of the

electronic conductivity against the volume fraction of the solid phase,

which includes the active material and CB, in accordance with Eq.

2. Here, the sum of the volume fractions of the active material and

CB is referred to as the volume fraction of the solid phase, which is

determined as (1 −ɛ−ɛb), where ɛis porosity and ɛbis the volume

fraction of the binder. Here, the sum of the volume fractions of the ac-

tive material and CB is referred to as the volume fraction of the solid

phase. The electronic conductivities of the electrodes having different

electrode densities but the same weight ratio of CB were linear in both

plots. The slopes of the straight lines differed with the weight ratio of

CB, as indicated by different colors, and with electrode densities, as

indicated by the same color, in Figures 2(a-1) and (b-1). The important

inference drawn from these results is that the electronic conductivity

depends quite differently on the electrode density and the CB weight

ratio, although both inﬂuence the volume fractions of the CB and the

solid phase.

Figure 2(a-1), which plots the electronic conductivity against the

CB volume fraction, reveals that the electronic conductivities (1.50

and 1.68 S/m) of the two electrodes with 5.35 and 10 wt% CB differ

by 12%, as indicated by the arrows, whereas the CB volume fraction

differs by 51% (0.0707 and 0.1066). The percolation theory equation

(Eq. 1), which has only one variable (i.e., the volume fraction of CB) is

unable to explain such behavior. Furthermore, the two electrodes with

1.14 and 10 wt% CB, as indicated by the arrows in Figure 2(b-1),which

plots electronic conductivity against the volume fraction of the solid

phase, exhibit approximately the same solid phase volume fraction

(0.545 and 0.553), while their electronic conductivities differ by more

than three orders of magnitude (0.0086 and 11.1 S/m). This behavior is

unable to be explained by Eq. 2, which is the most-used mathematical-

simulation equation and only relies on the volume fraction of the solid

phase as a variable.

The differences in the electrode-density and weight-ratio depen-

dences of CB are discussed here on the basis of electrode structure.

Figure 3shows SEM images of the positive electrode with a CB con-

tent of 5.25 wt% and an active material density of 2.16 g/cm3.The

positive electrode is composed of large active material secondary par-

ticles (7 μm), ﬁne CB particles (25 nm), and the PVdF binder. The

large active material secondary particles constitute the basic frame-

work of the porous electrode with the CB and binder located within

10

µ

m

Juncon

Acve material

secondary parcle

Figure 3. SEM images of an electrode with 5.35 wt% CB and an active ma-

terial density of 2.16 g/cm3.

A1288 Journal of The Electrochemical Society,166 (8) A1285-A1290 (2019)

Figure 4. Schematic cross-sections of (a) low density and (b) high density

electrode microstructures.

the pores and junctions of the active material secondary particles

(see Figure 3). Since the electrodes were fabricated by a wet pro-

cess, the large-surface-area CB and the binder are integrated together

owing to surface tension, and behavein a similar fashion to a CB/binder

conductive polymer composite. The CB/binder composite accumu-

lates in the channels of the rough surfaces of the active material sec-

ondary particles and at the junctions between the active material par-

ticles to form a conductive network in the porous electrode, as shown

in the magniﬁed image in Figure 3. Figure 4shows a cross-sectional

image of active material particles bound by the CB/binder conduc-

tive composite. The active material particles were closer together with

increasing electrode density, and only the CB/binder conductive com-

posite present at the junction was compressed. Hence, the volume

fraction of the CB/binder conductive composite at the junction as well

as its conductivity increased, although the conductivity at the active

material surface was only marginally affected (Figure 3). On the other

hand, the CB volume fraction in the entire CB/binder conductive com-

posite changed with changing CB weight ratio, irrespective of location,

and the connectiveness of the conductive network of the CB/binder

composite changed. Hence, changes in the electrode density and the

CB weight ratio affect the conductivity of the CB/binder composite

at different places. Therefore, the relationship between conductivity

and CB volume fraction changes with changing CB weight ratio and

electrode density.

In summary, the positive electrode exhibited electronic conduc-

tivity that depended differently on electrode density and CB weight

ratio. Therefore, we conclude that the two commonly used expressions

(Eqs. 1and 2) inaccurately express the electronic conductivity of a pos-

itive electrode composed of NCA-based active materials. Hence, we

chose to derive an empirical equation that better expresses the cor-

relation between the electronic conductivity and the electrode struc-

ture/composition of positive electrodes fabricated with NCA-based

materials.

Here, empirical equations for the linear relationships between

the logarithm of conductivity and the volume fractions of CB

(Figure 2a-1) and the solid phase (Figure 2b-1) were derived. Inter-

estingly, in both Figures 2(a-1) and (b-1), any linear relationship with

the weight ratio of CB could have the same intercept on the y-axis.

Therefore, the following procedure was used to develop the empiri-

cal equations. First, an individual straight line was approximated for

each weight ratio of CB using the least-squares method, and intercepts

of these straight lines were obtained. Next, the straight line for each

weight ratio of CB was approximated using the least-squares method

with the intercept ﬁxed as the average intercept (dotted lines in Fig-

ures 2a-1 and b-1). The approximated straight lines exhibited excellent

agreement with the experimental values, as seen in Figures 2(a-1) and

(b-1). The slope of each approximated straight line was plotted against

the weight ratio of CB in Figures 2(a-2) and 2(b-2). The slopes in Fig-

ure 2(a-2) show linear relationships with the CB weight ratio, whereas

the slopes in Figure 2(b-2) show logarithmic relationships with the CB

weight ratio.

AsshowninFigure2(a-1), the volume conductivity of the electrode

tended to approach the intercept value with decreasing CB weight

ratio. Therefore, the intercept could be considered to be the volume

conductivity of the electrode without the conductive additive. Hence,

electrode conductivity, σ[S/m], can be expressed by the following

empirical equations:

log σ=A1(wc)εc+log σ0[3]

σ=σ0·10(A1(wc)εc)[4]

Here, A1(wc) is the slope, which is a function of the weight ratio of

CB; wc[wt%] is the weight ratio of CB; ɛcis the volume fraction of

CB; and σ0[S/m] is the volume conductivity of the electrode without

CB. The value of σ0is 7.613 ×10−4S/m when log σ0is −3.1185.

To validate the intercept, we measured the electronic conductivity of

the electrode without CB in a similar manner; however, because the

electrode had an extremely large electronic resistance due to the large

contact resistance between particles, large and signiﬁcant variations

were observed in the results. Therefore, it was impossible to determine

the electrode conductivity without CB. A linear equation for the slope

was obtained by the least-squares method as follows (Figure 2a-2):

A1(wc)=−3.909wc+70.093 [5]

Substitution of σ0and Eq. 5into Eq. 4yields:

σ=7.613 ·10(εc(−3.909wc+70.093)−4)[6]

Thus, the electronic conductivity was obtained as a function of the

volume fraction of CB and the weight ratio of CB.

In the same manner, empirical equations for the relationship be-

tween conductivity and the volume fraction of the solid phase, as

shown in Figure 2(b-1), were obtained. The conductivity of the elec-

trode is expressed by the following equations:

log σ=A2(wc)εsp +log σ0[7]

σ=σ0·10(A2(wc)εsp)[8]

0.001

0.01

0.1

1

10

100

1000

0 0.05 0.1 0.15

Conducvity [S/m]

Volume fracon of CB

0.2

0.5

1 wt%

10 wt%

1 wt%

10 wt%

0.2

0.5

(a) (b)

8 wt%

0.001

0.01

0.1

1

10

100

1000

0.4 0.5 0.6 0.7 0.8

Conducvity [S/m]

Volume fracon of the solid phase

1 wt%

2 wt%

3 wt%

4 wt%

5 wt%

6 wt%

7 wt%

8 wt%

9 wt%

10 wt%

Figure 5. Electrode conductivities calculated using (a) Eq. 6and (b) Eq. 10. The weight fraction of conductive carbon is in the range of 1–10 wt% and the porosity

is in the range of 0.3–0.5.

Journal of The Electrochemical Society,166 (8) A1285-A1290 (2019) A1289

Here, A2(wc) is the slope, which is a function of the weight ratio of

CB, and ɛsp is the volume fraction of the solid phase. The logarithmic

equation for the slope (Figure 2(b-2)) was obtained by the least-squares

method as follows:

A2(wc)=2.6049 ln wc+1.5838 [9]

Substitution of σ0and Eq. 9into Eq. 8yields:

σ=7.613 ·10(εsp(2.6049 ln wc+1.5838)−4)[10]

Thus, the electronic conductivity was obtained as a function of the

volume fraction of the solid phase and the weight ratio of CB.

The two obtained equations for the conductivity of the electrode as

a function of the volume fraction of CB and the solid phase were val-

idated by calculating the electronic conductivity for various weight

ratios of CB and porosities (electrode densities) using Eqs. 6and

10. First, to simplify these calculations, the relationship between the

weight ratio of the binder and CB was determined. Over the entire

range of CB weight ratios investigated (Table I), a linear relationship

was obtained that connected both edges of the composition (CB:PVdF

=1:1.5 to CB:PVdF =10:5). The weight ratio of the binder is related

to that of the conductive carbon by:

wb=0.3889wc+1.1111,[11]

where wbrepresents the weight ratio of the binder in the electrode.

Figures 5a and 5b show the electronic conductivities calculated

using Eqs. 6and 10, respectively, for electrodes with 1–10 wt% CB

and porosities ranging from 0.2 to 0.5. In Figure 5a, the conductivity

initially increased with increasing CB weight ratio. However, above

a CB weight ratio of 8 wt%, the conductivity decreased as the CB

weight ratio increased. This behavior is impossible because the elec-

tronic conductivity of the electrode must increase with the amount

of conductive carbon having the same porosity. In contrast, conduc-

tivity as a function of volume fraction of the solid phase increased

continually with the weight ratio of CB (Figure 5b). From these re-

sults, we concluded that Eq. 10 was reasonable in that it expressed

the conductivity as a function of volume fraction of the solid phase.

In addition, this result indicates that the electronic conductivity of the

positive electrode was inﬂuenced not only by the conductive carbon,

but also by the active material. Thus, the conductivity could not be

explained by classical percolation theory. Moreover, Eq. 10 requires

a limitation on the range of the weight ratio of conductive carbon, wc.

When the weight ratio of the conductive carbon decreased to zero,

Eq. 10 expresses the electronic conductivity of the electrode without

the conductive carbon. Therefore, at this point, the slope should show a

positive value because the electronic conductivity of the positive elec-

trode without the conductive carbon should increase with increasing

volume fraction of the active material. However, the natural logarithm

of zero is undeﬁned and the slope expressed by Eq. 9became negative

at wc≤0.544 (Figure 2b-2). Therefore, the empirical equation ob-

tained in this study (Eq. 10) does not accurately express the electronic

conductivity for a small weight ratio of conductive carbon; i.e., less

than 0.544 wt%.

The positive electrodes with Mg-NCA did not exhibit typical per-

colation behavior (Figure 2), whereas the electrode with LiMn2O4re-

ported by Mandal et al. exhibited percolation behavior.10 One reason

for this difference in behavior involves the conductivity of the active

material. As concluded above, electronic conductivity is inﬂuenced by

the active material. The electronic conductivity of LiMn2O4is ∼1.0

×10−5S/m at room temperature.36 Unfortunately, the electronic con-

ductivity of Mg-NCA has not been reported thus far; however, the

electronic conductivity of LiNi0.8Co0.2 O2, whose composition is simi-

lar to that of Mg-NCA, was reported as 1.0 ×10−3S/m.37 Although the

electronic conductivity of solid-solution materials might vary depend-

ing on the composition, the electronic conductivity of the Ni-based

oxide is possibly greater than that of LiMn2O4. As LiMn2O4has a

much lower conductivity than that of conductive carbon, the active

material can be regarded as an insulator. In contrast, Mg-NCA elec-

trodes are considered to exhibit atypical behavior compared with that

predicted by percolation theory because the semiconducting frame-

work of Mg-NCA overlaps with the conductive network formed by

CB. The obtained empirical equation (Eq. 10) was quantitatively ap-

plicable to the speciﬁc active material and CB investigated in this work

because the intercept of the equation depends on the conductivity of

the active material, and the slope depends on the shape, structure, and

distribution of the CB. However, the basic system of this equation is

applicable to other active materials and conductive carbon. Moreover,

the empirical equation obtained for the positive electrode in this study

not only provides more-accurate simulations, but also provides a bet-

ter understanding of the electronic-conduction mechanism and helps

to facilitate better electrode and battery design.

Conclusions

In this study, we investigated the electronic conductivities of pos-

itive electrodes with various CB contents and electrode densities in

order to clarify the relationship between electronic conductivity and

various electrode parameters. It was found that the electronic conduc-

tivity depended differently on the electrode density and the CB weight

ratio. Therefore, it was concluded that the commonly used equations

based on percolation theory and used for mathematical simulations do

not adequately express the electronic conductivities of positive elec-

trodes composed of NCA-based active material because these equa-

tions rely on only one volume-fraction variable for each component,

namely the volume fractions of the CB and the solid phase.

Consequently, we successfully developed an empirical equation

that describes the relationship between electronic conductivity and

the volume fraction of the CB and the solid phase, which were found

to reasonably express conductivity as a function of volume fraction

of the solid phase. This result indicates that the active material inﬂu-

ences the electronic conductivities of positive electrodes containing

Mg-NCA; hence, the behavior of these electrodes does not obey the

classical percolation theory. The empirical equation presented herein

is expected to facilitate more accurate battery simulations and op-

timization of electrodes for high-energy batteries with low amounts

of conductive carbon. Electrode and battery designs for high-energy

applications will be optimized in our next study using this practical

equation for the electronic conductivities of positive electrodes.

ORCID

Hiroki Kondo https://orcid.org/0000-0002-2708-9039

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