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Journal of Power Sources 274 (2015) 762e767

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Journal of Power Sources

journal homepage: www.elsevier .com/locate/ jpowsour

Gas transport evaluation in lithiumeair batteries withmicro/nano-structured cathodes

Xiaoning Wang a, Kechun Wen a, Yuanqiang Song a, Luhan Ye a, Kelvin H.L. Zhang b,Yu Pan a, Weiqiang Lv a, Yulong Liao c, Weidong He a, *

a School of Energy Science and Engineering, University of Electronic Science and Technology, Chengdu, Sichuan 611731, PR Chinab Department of Chemistry, Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, United Kingdomc School of Microelectronics and Solid-State Electronics, University of Electronic Science and Technology, Chengdu, Sichuan 611731, PR China

h i g h l i g h t s

* Corresponding author.E-mail address: weidong.he@uestc.edu.cn (W. He)

http://dx.doi.org/10.1016/j.jpowsour.2014.10.1170378-7753/© 2014 Published by Elsevier B.V.

g r a p h i c a l a b s t r a c t

� Designs a device to measure thecathode diffusivity in the lithiumeairbattery.

� Evaluates the performance of thelithiumeair battery with nanoscalecathodes.

� Analyze correlation between limitingcurrent density/polarization andimportant battery parameters.

a r t i c l e i n f o

Article history:Received 4 August 2014Received in revised form25 September 2014Accepted 17 October 2014Available online 23 October 2014

Keywords:Lithiumeair batteryDiffusivityConcentration polarizationLimiting current densityPorous cathode

a b s t r a c t

Inefficient gas transport in the porous cathode is disastrous for the lithiumeair battery to achieve a highelectrochemical performance. Previous evaluation of the cathode diffusivity relies on indirect calcula-tions based on multiple VeI data obtained over the intact battery system, which inevitably inducesevaluation uncertainty and material waste. In this report, an electrochemical device is designed for theout-of-cell diffusivity measurement in the lithiumeair battery with micro/nano-sized cathodes. With themeasured diffusivity, a few electrochemical parameters including the limiting current density and theconcentration polarization associated with the porous cathodes can thus be directly evaluated. The workfacilitates the development of highly-efficient cathode materials in the general field of metaleair batteryfield.

© 2014 Published by Elsevier B.V.

1. Introduction

Metaleair batteries, especially the lithiumeair battery, own anumber of attractive characteristics including high energy densityand high theoretical specific capacity [1], which together havemade such battery systems promising power-supply resources for avariety of applications, such as automotive applications, mobile

.

phone and laptop [2]. In particular, the advances in the lithiumeairbattery field have been multifold, and many high-performancematerials have been designed and realized in recent years toimprove the overall electrochemical performance of the batterysystem. For instance, alloying anode materials have been synthe-sized to enhance the capacity and the safe operation of the lith-iumeair battery [2]. In addition, endurable and highly ionic-conducting electrolyte materials such as hydrophobic room tem-perature ionic liquid electrolyte are prepared to achieve betterdischarge capacity in the battery system [3]. As for the cathode,Xiao et al. [4] have reported hierarchically porous graphene to be

X. Wang et al. / Journal of Power Sources 274 (2015) 762e767 763

employed as the cathode electrode in the battery system, Sun et al.[5] have prepared graphene nanosheets as cathode catalysts toimprove the performance of lithiumeair battery, and Li et al. [6] usenitrogen-doped carbon nanotubes as cathode to improve the spe-cific discharge capacity. With such cathode materials, high specificcapacity and long cycling life for lithiumeair battery have beenshown to be realizable. Compared to those promising advances inthe lithiumeair battery materials, much still has remained to beexplored to directly evaluate the gas transport in the porous cath-odes of the lithiumeair battery, a parameter that largely correlateswith the porosity, tortuosity and the oxygen partial pressure of thelithium-battery system [7e9]. At the cathode side, oxygen diffusesfrom the porous carbon and reacts with Li ions at the cath-odeeelectrolyte interface. Oxygen diffusion in the cathode is ofsignificant importance to the performance of the lithiumeair bat-tery since the over-potential, which is dependent on the reactionkinetics, is dominated by oxygen diffusion. A slow oxygen diffusionrate results in a large over-potential while fast oxygen diffusionleads to a small over-potential. The efficient operation of a lith-iumeair battery depends largely upon the fast diffusion of oxygen,which is then determined by the parameters including the cathodeporosity, the cathode tortuosity, the oxygen partial pressure, andthe cathode thickness [10]. There aremodels focused on the oxygendiffusion in the lithiumeair battery. For instance, Sandhu et al.proposed a limiting-diffusion model, and studied the effects ofoxygen partial pressure and current density on the specific capacityof the lithiumeair battery. The model assumes an average pore size~4 nm as the pore diameter of the cathode [11]. In this report, anelectrochemical device is designed based on a few known gastransport models for measuring, in an out-of-cell fashion, the ox-ygen diffusivity in the micro/nano-structured cathode of the lith-iumeair battery. The pore diameters used in this work range from0 to 500 nm, and cover a large range of practical values. The limitingcurrent density and the concentration polarization associated withthe lithiumeair battery are then pre-evaluated subsequently. Thework based on the quantitative analysis facilitates further devel-opment in the general field of the metaleair battery with highly-efficient micro/nano-sized electrode materials.

2. Electrochemical device

An electrochemical device is designed, as shown in Fig. 1, tomeasure the diffusivity of oxygen in the cathode of the lithiumeairbattery in the air environment. The device contains five compo-nents: a lithiumeair battery, an oxygen sensor, a current sensor, atube, and a porous cathode composed of porous carbon loadedwithcatalyst. Due to the nanoscale thickness of the cathode, a poroussupport is designed under the cathode as mechanical support, thepore size of which is large enough so that the diffusion of cathodegas is not impeded.

Fig. 1. The schematic of an electrochemical device for the out-of-cell measurement ofcathode diffusivity in the lithiumeair battery.

In the diffusivity measurement, a constant current density (i) isapplied to the lithiumeair battery. Then, there occurs the reactionO2 þ 2e� ¼ O2�

2 [12], which leads to the decrease in the partialpressure of oxygen in the tube. An oxygen flux along the oxygenconcentration gradient is then formed through the porous cathode.The Nernst potential is obtained through the oxygen sensor at afixed temperature. The correlation of the Nernst potential (E) withthe partial pressure of oxygen outside the tube (po), and the partialpressure of oxygen inside the tube (pi) is given in Eq. (1).

pi ¼ po exp��2EF

RT

�(1)

where F is the Faraday constant, R is the ideal gas constant, T is theoperating temperature, and po is the oxygen partial pressureoutside the tube, as set at 0.21 atm [13,14].

In the measurement, there is no nitrogen concentrationgradient, and nitrogen is not involved in the diffusion. The airtransport through the porous cathode can be described in Eqs.(2)e(4), where 1 and 2 represent O2 and N2, respectively, J1 is theflux of oxygen, n1 is the concentration of oxygen, X1 is the molarfraction of oxygen, J is the total flux, Deff

1 K is the effective Knudsendiffusivity of oxygen, Deff

12 is the effective binary diffusivity, p is thetotal pressure, B0 is the permeability, t is the viscosity, and D1 is thetotal effective diffusivity [13].

J1 ¼ �D1Vn1 þ X1d1J � X1r1

�nB0t

�Vp (2)

d1 ¼ Deff1 K

Deff1 K þ Deff

12

(3)

r1 ¼ 1� d1 ¼ Deff12

Deff1 K þ Deff

12

(4)

The cathode pore size is typically less than 10 times the oxygenmean free path [13]. Therefore, the Knudsen diffusivity and thebinary diffusivity are both taken into account, and the value of X1d1Jis close to zero [16]. The total pressures inside and outside the tubeare the same, and Vp ¼ 0. Based on the oxygen pressure differencebetween inside and outside of the tube, Eq. (2) can be reduced asEq. (5) [13].

J1 ¼ �D1Vn1 (5)

The correlation between the oxygen flux and the current densityis depicted in Eq. (6). Based on the ideal gas equation as depicted inEq. (7), Eq. (8) is then obtained. Integrating Eq. (8) gives rise to Eq.(9), where l is the cathode thickness [13].

J1 ¼ i2F

(6)

n1 ¼ p1kBT

(7)

i2F

¼ �D1Vp1kBT

0iNAdx2F

¼ �D1dp1kBT

(8)

pi ¼ po � iRTl2FD1

(9)

The oxygen partial pressure inside the tube is resulted from thechange in the value of current density, leading to the changes in thevalue of the Nernst potential and the value of pi based on Eq. (1). By

X. Wang et al. / Journal of Power Sources 274 (2015) 762e767764

changing the value of current density, there exists a linear correlationbetween pi and i based on Eq. (9), and then the total effective diffu-sivities can be obtained through the slope of the linear correlation.

3. Results and discussion

The correlation between the effective Knudsen diffusivity andKnudsen diffusivity is given in Eq. (10),

Deff1 K ¼ m

tD1 K (10)

where m is the cathode porosity, t is the cathode tortuosity which isdefined as the ratio of the length of the curve to the distance be-tween the ends of it [13], and

D1 K ¼ 13d

ffiffiffiffiffiffiffiffiffiffi8RTpM1

s(11)

where d is the average pore diameter of the cathode, and M1 is themolecular weight of oxygen [13]. Combing Eqs. (10) and (11), theeffective Knudsen diffusivity can be described in Eq. (12). Theeffective binary diffusivity related to the binary diffusivity (D12) isgiven in Eq. (13) and the binary diffusivity is determined by Eq. (14),where M1 and M2 represent the molecular weights of oxygen andnitrogen, respectively, p is the total pressure, s is the averagecollision diameter as set at 3.6325 (Å), andU is the collision integralset at 0.8568 [13,17].

Deff1 K ¼ 1

3d

ffiffiffiffiffiffiffiffiffiffi8RTpM1

sm

t(12)

Deff12 ¼ m

tD12 (13)

D12 ¼0:00186T

32

�1M1

þ 1M2

�12

ps212U(14)

Combining Eqs. (13) and (14), the effective binary diffusivity isshown in Eq. (15). The total effective diffusivity is a function ofKnudsen diffusivity and binary diffusivity, as described in Eq. (16).Therefore, the total effective diffusivity can be expressed in Eq. (17).

Deff12 ¼ m

t

0:00186T32

�1M1

þ 1M2

�12

ps212U(15)

D1 ¼ 1Deff1 K

þ 1Deff12

(16)

D1 ¼ Deff1 KD

eff12

Deff1 K þ Deff

12

¼ 0:00186m

t

dT32

�1M1

þ 1M2

�12 ffiffiffiffiffiffiffiffi

8RpM1

q

dps212Uffiffiffiffiffiffiffiffi8RpM1

qþ 0:00558T

�1M1

þ 1M2

�12

(17)

The effective oxygen diffusivity in the cathode correlates with thecurrent capacity of the lithiumeair battery [18]. Fig. 2 shows thecorrelation between the total effective oxygen diffusivity in the

cathode and the average pore diameter. As shown in Fig. 2, the totaleffective diffusivity increases with increasing pore diameter from10 nm to 500 nm. The rate of increase slows down with increasingpore diameter based on the slopes of plots, which suggests that thetotal effective diffusivity is more sensitive to the change of porediameter as the pore diameter is below 200 nm. The curves tend toparallel with the d-axis as the pore diameter exceeds 450 nm, avalue 10 times larger than the mean free path of oxygen [15],indicating that the effective Knudsen diffusivity is large enough andit is no longer the critical limiting factor for the total effective ox-ygen diffusion in the cathode. In Fig. 2(a), there appears a criticalpore diameter for each curve, and the critical pore diameter in-creases with increasing porosity ranging in 10%~50%, showing thatthe total effective diffusivity is more sensitive to the change of theporosities over 30%, compared with smaller porosities, and thecurves of Fig. 2(b) have the same features as the tortuosity issmaller than 2. The total effective diffusivity increases withincreasing porosity, and the difference between the adjacent curvesis approximately equal, which is ~50 � 10�4 cm2/s. Therefore, theeffective-diffusivity-versus-porosity correlation is linear, as shownin Fig. S1. In Fig. 2(b), the total effective diffusivity decreases rapidlywith increasing tortuosity. Based on the previous work, largeporosity and small tortuosity enhance the oxygen diffusion in theporous carbon cathode [19e21]. However, too large porosity hin-ders the electron transport [19]. Thus designing the porous cathodewith suitable porosity and tortuosity is desirable for not onlymaintaining a large total effective diffusivity but also ensuring theefficient electronic transport.

The limiting current density (ics) of cathode is the maximumoutput current of the lithiumeair battery limited by oxygen diffu-sion through the cathode [22]. By setting pi ¼ 0 in Eq. (9), thecathode limiting current density is then depicted in Eq. (18) [13].Combining Eqs. (17) and (18), the correlation of the limiting currentdensity with the average pore diameter is expressed in Eq. (19).

ics ¼ 2FD1poRTl

(18)

ics ¼ 0:00372dmFpotRl

T12

�1M1

þ 1M2

�12 ffiffiffiffiffiffiffiffi

8RpM1

q

dps212Uffiffiffiffiffiffiffiffi8RpM1

qþ 0:00558T

�1M1

þ 1M2

�12

(19)

Fig. 3 shows the correlation between cathode limiting currentdensity and cathode thickness, where the tortuosity, the porosity,and the pore diameter are set at 3, 30% and 100 nm because theyare close to the practical values. In Fig. 3, the limiting currentdensity decreases as the cathode thickness increases from 10 nm to800 nm, and there exists a critical cathode thickness in each curve,below which the limiting current density decreases abruptly andabove which the limiting current density decreases gradually. Thelimiting current density approaches zero as the cathode thickness islarger than 700 nm, indicating that the limiting current densitytends to be rather sensitive to the change of the cathode thicknessbelow the critical cathode thickness. The critical cathode thicknessincreases with increasing oxygen partial pressure, porosity, andtortuosity, which suggests that the limiting current density is lesssensitive to the change of the cathode thickness with increasingoxygen partial pressure, porosity, and average pore diameter.However, the critical cathode thickness decreases with increasingtortuosity ranging from 1 to 5, which is a tortuosity range selectedbased on the literature values [13,19,20]. With a certain cathodethickness, the limiting current density increases with increasingoxygen partial pressure, porosity and average pore diameter. On the

Fig. 3. Plots of cathode limiting current density versus cathode thickness at T ¼ 300 K. (a) Porosity ¼ 30%, po ¼ 0.21 atm, and d ¼ 100 nm with different tortuosities; (b)tortuosity ¼ 3, porosity ¼ 30%, and d ¼ 100 nm with different oxygen partial pressures; (c) tortuosity ¼ 3, po ¼ 0.21 atm, and d ¼ 100 nm with different porosities; (d)porosity ¼ 30%, tortuosity ¼ 3, and po ¼ 0.21 atm with different average pore diameters.

Fig. 2. Plots of total cathode effective diffusivity versus the average cathode pore diameter at T ¼ 300 K. (a) Total effective cathode diffusivity versus average cathode pore diameterwith different porosities and a tortuosity of 3; (b) total effective cathode diffusivity versus average cathode pore diameter with different tortuosities and a porosity of 30%.

X. Wang et al. / Journal of Power Sources 274 (2015) 762e767 765

contrary, the limiting current density decreases with increasingtortuosity as shown in Fig. 3(a). The results suggest that the smalltortuosity, large oxygen partial pressure, large porosity, and largepore diameter can enhance the output maximum current. Forinstance, a small cathode tortuosity results in a short diffusion pathof oxygen and a small extent of collision between oxygenmoleculesin the cathode. Such quantitative analysis provides theoretical basisfor the design of high specific capacity lithiumeair batteries [23].

Concentration polarization (CP) reflects the energy loss due toimpeded mass transport in lithiumeair batteries. In particular, largeCP decreases substantially the energy density and specific capacity oflithiumeair batteries [5,24e27,31e34]. CP arises from insufficientoxygen diffusion in the porous cathode and can be calculated throughEq. (20).

CP ¼ �RT2F

ln�1� i

ics

�(20)

where i is the operating current density [13]. Combing Eqs. (19) and(20), the detailed expression of CP is expressed in Eq. (21).

CP¼�RT2F

ln

0BBBBB@1�

itRl

dps212U

ffiffiffiffiffiffiffiffi8RpM1

qþ0:00279T

�1M1

þ 1M2

�12

!

0:00372mFpoT12

�1M1

þ 1M2

�12 ffiffiffiffiffiffiffiffi

8RpM1

q

1CCCCCA(21)

Fig. 4 shows the correlation between concentration polarizationand cathode thickness. CP increases nearly linearly as the cathodethickness increases from 10 nm to 1000 nm. In Fig. 4(a)e(c), with afixed cathode thickness, CP increases with decreasing pore diam-eter, oxygen partial pressure, and cathode porosity. Such an in-crease becomes more obvious with cathode pore size <50 nm, theoxygen partial pressure <0.15 atm and the cathode porosity <20%,evidenced by the much increased slopes of CP versus l plots. Thissuggests that larger pore diameter, oxygen partial pressure andporosity facilitate the reduction in CP. Fig. 4(d) shows the plots ofconcentration polarization as a function of cathode thickness atdifferent tortuosities. CP decreases as the tortuosity decreases with

Fig. 4. Plots of cathode concentration polarization versus cathode thickness with i ¼ 0.1 mA/cm2 and at T ¼ 300 K. (a) po ¼ 0.21 atm, porosity¼ 30%, and tortuosity¼ 3 with differentaverage pore diameters; (b) d ¼ 100 nm, porosity ¼ 30%, and tortuosity ¼ 3 with different oxygen partial pressures; (c) d ¼ 100 nm, po ¼ 0.21 atm, and tortuosity ¼ 3 with differentporosities; (d) d ¼ 100 nm, po ¼ 0.21 atm, and porosity ¼ 30% with different tortuosities.

X. Wang et al. / Journal of Power Sources 274 (2015) 762e767766

a fixed cathode thickness, indicating that reducing cathode tortu-osity improves oxygen transport and thus enhances the perfor-mance of lithiumeair batteries. The plots of concentrationpolarization versus the porosity, the oxygen partial pressure, thetortuosity, and the pore diameter are given in Fig. S2.

The correlation between the parameters associated with a bulkcathode and the performance of the lithiumeair battery has beeninvestigated recently by the authors [28]. However, there has beenrare theoretical investigation into the gas transport properties ofnano-sized cathodes. In this paper, the correlation between thenano-size cathode and the performance of the lithium air battery isanalyzed quantitatively. As noted by the data presented in thefigures, the features of the effective diffusivity and concentrationpolarization plots based on the diffusion measurement model areconsistent with the reported experimental values [29,30]. However,in an actual lithiumeair battery system, the deposition of Li2O2 andLi2O on the surface of the porous cathodes reduces the porediameter and impedes gas transport in the discharge process. Thecorrelation between the pore size and the discharge time is subjectto our future investigation.

4. Conclusion

In summary, an electrochemical device based on an oxygensensor and oxygen pump has been designed for the direct mea-surement of oxygen diffusivity in the micro/nano-structuredcathodes of the lithiumeair battery. The accurate total effectivediffusivity in the cathode of lithiumeair battery system can bemeasured via such an electrochemical device. With the measureddiffusivity, limiting current density and the concentration polari-zation can be evaluated quantitatively. The influencing factors ofgas diffusion have been taken into account and the correlations ofthese factors with the limiting current density and concentrationpolarization have been analyzed in detail. Our work implementsthe lithiumeair battery field with a state-of-the-art measurement

system and facilitates the improvement in the gas-based batterysystems for real-life applications in electric vehicles, portable de-vices and small power systems.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.jpowsour.2014.10.117.

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