Thermal Diffusivity Electrodes 2

8/3/2019 Thermal Diffusivity Electrodes 2

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Elecwochin rica Acta, Vol. 39. No. 4. pp. 511-526, 1994copyrightQ 1994 Elsevie .kience Ltd.Printed in Great Britaia All ii&s rcsed

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THERMAL ANALYSIS OF LITHIUM POLYMERELECTROLYTE BATTERIES BY A TWO DIMENSIONAL

MODEL-THERMAL BEHAVIOUR AND DESIGNOPTIMIZATIONYUFEIC.&EN* and JAMESW. EVANS?

Materials Science Division, Lawrence Berkeley Laboratory/Department of Materials Science andMineral Engineering, University of California, Berkeley, CA 94720, U.S.A.(Received 15 July 1993; in revisedform 27 September 1993)

Ahstrati-Thermal analysis of lithium polymer electrolyte batteries is carried out to examine therelationship between battery thermal behaviour and design parameters. By studying the effect of stacksize and cooling/insulating conditions on battery temperature under diRerent discharge rates, informationis obtained as to how to maintain operating temperature by designing proper cell stacks and choosingproper cooling/insulating systems. Moreover, temperature distributions within cell stacks for different celldesigns, including different thickness of cell components and different current collector materials, arecalculated so as to carry out cell structure optimization from a heat transfer point of view. Finally,thermal characteristics of lithium polymer electrolyte batteries based on different positive electrodes (esV,O,, , TiS, and redox polymer) are discussed.Key words: mathematical model, heat transfer, polymer electrolyte, lithium batteries, design optimization.

NOMENCLATURE

average specific heat of battery/J kg- K- specific heat of layer i/J kg- K- open-circuit voltage of one cell/Vcut-off voltage of one cell/Vconvective heat transfer coefficient/Wme2K-superficial current density/Arm-a~ermag;K hermal conductivity of battery/thermal conductivity of layer i/W m - K - tthermal conductivity of insulating material/Wm-K-aWerma_gf;h_e:mal onductivity in X direction/average thermal conductivity in Y direction/Wm-K-heat conduction distance/cmthickness of insulating material/cmthickness of one cell/cmthickness of layer i/cmthickness of cell stack/cmheight of cell stack/cmwidth of cell stack/cmcell number in a stackrate of heat generation per unit volume/Wmm3temperature of battery/Ktemperature of cell/Kinitial temperature of cell/Kambient temperature/Ktime/s

l Visiting scholar.t Author to whom correspondence should be addressed.

V cell voltage/VAx step length in X coordinateAY step length in Y coordinateGreek symbols%UY

PPi

= kJpC, average thermal diffusivity in Xdirection/m? s - = k,/pC, average thermal diffusivity in Ydirection/m s- average density of battery, kgmw3density of layer i/kg m- 3

INTRODUCTIONDevelopment of advanced rechargeable batteriesfor electric propulsion applications has been thesubject of intensive study worldwide due to the bene-ficial impact[l] of battery-powered electric vehicleson atmospheric air quality. However, the main prob-lems associated with battery-powered electric vehi-cles, eg the limited vehicle range and speed, wouldlead such vehicles to be less competitive as comparedwith those with internal combustion engines.Lithium batteries, which may have high specificenergy and specific power, because of the lightnessand high electropositivity of lithium, may providesolutions to the limitations of the current batterytechnology. In addition, polymer electrolyte based,all solid state lithium batteries have a number ofother attractive features[2] which may also makethis kind of battery suitable for electric vehicle appli-cations. Accordingly, the lithium/polymer electrolytebattery has been considered to be one of the mostpromising long-term advanced battery technologiesby the U.S. Advanced Battery Consortium[3].

517


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518 , Y. CHEN and J. W. EVANSTo date, polymeric electrolyte based lithium bat-teries with either intercalation compound (eg V,O,,or TiS,)[4, 51 or redox polymer[6] as the activematerial of the positive electrode have been shown toexhibit attractive performance at a laboratory scale.Also, battery prototypes containing cells scaled-upby a factor of 1000 have been tested[7-91 and no

evidence of degradation has been observed. It seemsthat lithium/polymer electrolyte batteries for electricvehicle applications may be close to reality in a fewyears. However, much work still remains to be donefor large scale applications, among which is batterythermal management. This is because the low ionicconductivity of the polymer electrolyte has limitedthe application of the battery to elevated tem-perature (eg 80-14OC), and the operating tem-perature range should be maintained so as toachieve optimum performance. Mathematical simu-lation of heat transport within large batteries is aneffective tool to obtain knowledge about whetherexcessive heat generated during the battery discharge/recharge process can be removed, and how operatingtemperature can be controlled. Previous exampleshave been given by Choi and Yao[ 10, 1 ] for lead-acid batteries, Lee et aI.[12] for lead-acid andnickel/iron batteries, Parnell and Szpak[ 131 forLi/SOCl, batteries, and White and coworkers[14-163 for Li/SOCl, cells and nickel-hydrogen bat-teries. In the previous paper by the present authors,basic heat transfer phenomena in lithium/polymerelectrolyte batteries for electric vehicle applicationshave been presented[17]. In the present work,further studies of the effect of battery design param-eters on battery thermal behaviour have been con-ducted by a modified model, with emphasis on theeffect of insulation, thicknesses of cell components,and different current collector materials on tem-perature distribution, so as to obtain fundamantalideas concerning the optimization of cell structurefrom the viewpoint of heat transfer. Furthermore, theheat transport phenomena in lithium/polymer elec-trolyte batteries with different positive electrodes arecompared.

Mathematical ModelAs shown in Fig. 1, a battery is composed of oneor more multi-cell stacks, and a cell stack is com-posed of many series-connected bipolar units con-nected in parallel[18]. The cell number in a stack isdetermined by the desired battery capacity andvoltage. This design is considered to be suitable for

traction battery applications and is expected toexhibit high specific energy.Because a thin-film cell design is adopted, thegreatly differing thermal properties of different layersmay have significant influence on heat transferbehaviour within a battery. In our previouswork[17], heat transfer equations in cell stacks withheterogeneous thermal-physical properties of differ-ent layers were solved and the results indicated thatthe temperature within one cell is invariant across itsthickness, and is close to that computed using thethermal properties of the polymer. Nevertheless, itappeared to be impractical, because of the long com-putation time, to calculate temperature profiles in acell stack with practical thickness by the mathemati-cal model for stacks with heterogeneous thermalproperties. Therefore, thermal behaviour was conser-vatively predicted by treating the battery as consist-ing of a homogeneous isotropic medium with thethermal properties of the polymer (which had thepoorest thermal transport properties in this system).This treatment is a sutlicient approximation foranalysis when the maximum temperature in thebattery is of concern. However, it may be arguedthat thermal conductivity is relatively large along theheight (Y) direction. To take this feature into con-sideration, in the present paper, a modified twodimensional model in which the cell stack is assumedto be of orthotropic thermal properties, that is, thethermal conductivity in thickness (X) direction is dif-ferent from that in height (Y) direction, is applied tofurther investigate the thermal performance of thebatteries. More importantly, this improved modelcan be applied to analyze the effect of different cellcomponent thicknesses and of using different

Currentcollector fNcgh%electrode -t-Polymer -I--electrolyte &Positive 4electrodeBipolarconnr.ctor

Cell Extents1 lnsuhtion Coolinn Cellstack rurhx channel, suck/

----t -

Fig. 1. Two-dimensional model of bipolar connected cell stack.


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Two dimensional analysis of lithium polymer batteries 519materials for the positive electrode and for the cooling law is appliedcurrent collector. Because there is a significant short- tions :age of experimental data for the thermal-physicalproperties of cell components in the literature, quan- at x = 0 or LX, any y:titative results cannot be obtained even by a threedimensional model. Therefore, for simplicity, only -k_ El

to obtain boundary condi-

= MTx=oor~xT,) (6)Xeat transfer in the X and Y direction is consideredat this stage of modeling (see discussion in the fol-lowing section). Under the above assumption, thefollowing two-dimensional transient heat transportequation is obtained:

pC,~==k,~+k,~+qw (1)where the thermal conductivities in X direction k,and in Y direction k, are estimated in a similar wayto determining the equivalent electric resistances inan electric circuit consisting of series- or parallel-connected electric resistances, respectively, that is

(2)and

The average volumetric heat capacity PC, is givenby

The average thermal diffusivity in X direction (a3or in Y direction (a,,) is the ratio of the correspond-ing average thermal conductivity (k, or k,) toaverage heat capacity.The average thermal diffusivities thus obtained areindependent of the arrangement of cell components.However, preliminary calculations indicate that agood approximation to the temperature profiles cal-culated from the model for stacks with heter-ogeneous properties of different layers[17] has beenachieved for the investigated multi-layer, thin-filmconfigured stack design.q in equation (1) is the heat generation rate whichis assumed to be uniform throughout the battery. Interms of the general expression of heat generation forbattery systems derived by Bernardi et aI.[19], underthe assumption that no phase change is involved andonly electrochemical/intercalation reactions exist forthe solid state lithium cells of the present investiga-tion, q can be written as

N

4=where temperature T is supposed to be the averagebattery temperature which will change during thebattery discharge process.It is further assumed that forced convection isapplied to the external surfaces (Y = 0 and Y = LY)and the cooling channels (X = 0, and X = LX), andthat the air temperature and heat transfer coefficientare uniform around the stack surface. Newtons

aty=OorLY,anyx:-k,Eay=oorr,r = h(Ty=oorLr - T,)- (7)

If the battery temperature drops below its oper-ational temperature during a low rate discharge, itmight be expected that the cooling systems would beturned off and insulation material used to maintainbattery temperature. In that case, heat will be con-ducted through the insulation material and then dis-sipated to the surroundings by natural air flow.Supposing that the temperature increase in insula-tion material is negligible (i e that the insulation is ata thermal quasi-steady state), and that the insulationmaterial is treated as the boundary of the cell stack(as in Lees two-region model[12]), the followingboundary conditions are obtained

(8)and

where the term on the right hand side is obtained byequating the heat fluxes at the inside and outsidesurfaces of the insulation material.The battery is initially heated to operational tem-perature T,, , thus the initial condition isT=T,,,att=O,anyxandanyy. (10)

The implicit alternating-direction technique[20] isapplied to cast equation (1) associated with theboundary conditions, into finite difference formswhich are then solved by the Gaussian eliminationmethod. The solutions are unconditionally stable,and converge on the solutions of the original partialdifferential equation as At + 0, Ay + 0 and Ax + 0.Table 1 lists the parameters used in the presentcalculations. Most of the thermal-physical param-eters for positive electrodes (V,O,, , TiS, and redoxpolymer) are not available in the literature. In orderto conduct the mathematical simulation, certainassumptions for choosing the values of modelparameters are needed. The density and specilic heatfor V,0,3 are assumed to be approximated by thoseof V,O,[21], while its thermal conductivity value ischosen from within the parameter value range ofmetals and their oxides[21]. The specific heat andthermal conductivity of titanium oxi& are used forTiS,. Thermal parameters adopted for polymer arethose of redox polymer and metallixed plasticcurrent collector. The effective average density and


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520 Y. CHEN and J. W. EVANSTable 1. Parameter values for model calculation

Thermal-physical properties

Parameter Li [21] PolymerVJA, TiS, Redox polymercomposite composite compositeelectrode electrode electrode Ni [21] Al [21]

P Wgme3) 534.0C, (JKgK-) 3514.6K (Wm-K-l) 81.8

1200.0 [22] 2208.0* 2490.07 2285.03 1540.05 8900.0 2700.02050.0 [23] 1148.5 1054.62 884.6 1916.2 471.0 908.00.16 [23] 5.77 7.18 5.71 2.03 82.7 200.8

Inout and initial dataSystemOpen-circuit voltage of one cell E, (V)Cut-off voltage of one cell E,,, (V)Temperature coefficient of E,, , dE,/dT (V K-l)Current density i (mA cm -)Initial cell temperature qeO (K)Ambient temperature T, (K)

f-i/v@,B3.21.752.20 x lo-4

0.10-5.0373

Li/TiS, Li/Xl 113.0 3.01.40 1.02.20 x lo-4 2.20 x lo-40.5-2.0 0.5-4.0373 35729850-1006.0Thickness of cell components LX, (pm)Convention coefficient h (W m-K-l)Insulating material ki, (w m - 1K - ) 0.03* composition[4]: 45% v/o V6013; 5% v/o carbon; 50% v/o PEO-LiX.t composition[25] : 75.4% w/o V,O, 3 5% w/o carbon; 19.6% w/o PEO-LiX.$composition[S]: 50% v/o TiS,; 10% v/o acetylene black; 40% v/o PEO-LiX.Ejcompositionr241: 45% w/o Xl ; 10% w/o carbon; 45% w/o PEO-LiX.11 l :himerca$todithiazole polymer.specific heat for composite positive electrode are cal-culated as linear combinations of those (within thebattery operation temperature range) of its consis-tent components. Calculated results indicate that thethermal behaviour of lithium/solid polymer electro-lyte battery is mainly determined by the low thermalconductivity of the polymer. Therefore, it is con-sidered that no significant error will be caused bychoosing these values for model parameters. Dis-charge curves of lithium polymer electrolyte cellswith V,O,,, TiS, and redox polymer as compositepositive electrodes reported by Hooper andcoworkers[2, 43, by Gauthier et aI.[S] and by Liu etaI.[6], respectively, are used in the present calcu-lations. For most battery systems, the temperaturecoefficients of open-circuit voltage are the valuesof a magnitude of 10e4V K- . In this paper,2.2 x 10 -4 V K- is arbitrarily chosen, and prelimi-nary calculations suggest that any likely discrepancyfrom the real value will not result in remarkable dif-ferences in temperature distribution.It seems that most experimental cells are of athickness of about 4OOpm, though optimum cellthickness may be expected to be typically in therange from 150 to 2OOpm[26]. Except where other-wise indicated, results presented in this paper are forcell stacks consisting of cells with a thickness of4OOpm (the difference in the thermal behaviourbetween 400 and 2OOym cells is discussed in the fol-lowing section).

RESULTS AND DISCUSSIONTemperatu re profiles in cell st acks

In order to design a battery with desired capacityand voltage, many cells are stacked together. Forexample, in the Harwell prototype, 30 bipolar-connected-20-cell units are connected in parallel[7],

which results in a cell stack thickness of about 6cm.It is necessary to study the influence of variousdesign parameters and operating conditions onbattery thermal behaviour so as to demonstratewhether battery prototypes can be successfullyscaled-up. Munshi and Owens[25] assessed theoptimum cell area to be between 400 and 2500cm2from the point of view of achieving high specificenergy and specific power. Therefore, LY = 20cmcan be reasonably chosen as the height of a cell so asto study the effect of stack thickness (LX) on thermalbehaviour. Figures 2 and 3 show temperature pro-files in the center of a 10cm thick cell in the X direc-tion (at y = LY/2) and in the Y direction (atx = Z,X/2), respectively (unless otherwise stated,results are for the Li/V,013 system). The flat tem-perature distributions in Y direction indicate that itis relatively easy to conduct heat in the Y direction400 r c/o.3_

shY 60 t340

tCl8

/-_c-----

--w320 i0 2 4 6 8 10

X/cmFig. 2. Temperature distributions in X direction (y = LY/2) in a 1Ocm thick cell stack at the end of discharge for rate

C/O.3 and C/8.


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Two dimensional analysis of lithium polymer batteries 521400 - c/o.3

0 5 10 15 20Y/cm

Fig. 3. Temperature distributions in Y direction (x = LX /2) in a 10cm thick cell stack at the end of discharge for rateC/O.3and C/g.as compared with that in X direction. It can be seenthat under low discharge rate, the temperature in thestack will decrease. However, under high dischargerate, temperature in the cell stack will increase sig-nificantly. This is because, on the one hand, the lowthermal conductivity of the polymer will limit heatconduction in the X direction, and on the otherhand, the relatively large dimension of the stackheight will result in a long relaxation time for heatconduction @/a), even in the Y direction.Because steep temperature distributions exist inthe X direction, the following results are intended toexamine the effect of stack thickness and insulationon thermal behaviour.Effect of stack siz e and insulation on maximumtemperature

Figure 4 depicts the effect of stack thickness onmaximum temperature in cell stacks for different dis-charge rates. The results are in good agreement withthe observation that the major thermal managementproblem at low discharge rates is more likely to bethe maintenance of operating temperature[2].Because battery temperature will decrease duringthe process of low rate discharge, insulating

0 2 4 6 8 10.LX/cm

Fig. 4. Effect of stack size on maximum temperature in cellstacks for different discharge rate.

390r i

___ ,i x0.8cm

340 I II I I I0 0.5 1.0 1.5 2.0 2.5L&m

Fig. 5. Effect of thickness of insulation material on tem-perature in cell stack at the end of discharge of rate C/4(LX = 10.0~~1, LY = 2O.Ocm, T,, = 373K,0.03 Wm-K-l). K,, =

materials are needed. Figure 5 shows the variation ofthe temperature in a cell stack at the end of dis-charge with the thickness of insulation under theassumption that the thermal conductivity of thematerial is 0.03 W m-l K-i (the thermal conductivi-ty for typical insulating materials is from 0.03 toO.l7Wm-K-[27]). It is predicted that a 0.8cmthick layer of such an insulating material will be suit-able to maintain the temperature around the initialtemperature of the cell. This is probably one advan-tage of lithium polymer electrolyte batteries for elec-tric vehicle applications because conventionalinsulation materials with a suitable thickness will besufficient to maintain the temperature within theoperating range.From Fig. 4, it can also be seen that if a stackthickness is larger than a certain value, the tem-perature will increase under high discharge rate (egC/0.3). Figure 6 illustrates the effect of the convectiveheat transfer coefficient on temperature profile in a5cm thick stack. Obviously, the improvement incooling conditions is not an effective means ofreducing the temperature increase in the center of alarge stack. Instead, it may cause steep temperatureprofiles. In order to prevent the battery temperature

400 r

T 13:: -/ \

-.-./ h-25 W III-~ K- \- - - h-15 W ,-2 K-360 -- h-6 W m-2 K-

35050 1 2 3 4 5X/cmFig. 6. Effect of heat transfer coetE&nt on temperatureprofile in thickness direction (Y = LY/2) at the end of dis-charge (LX = KOcm , LY = 20.0 cm, C/0.3).


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Y. CHEN and J. W. EVANS

380Siwy 370

F-*- LY=SOcm- LY-2Ocm

360t

-- LY=IOcm

350 1 I I I I I0 1 2 3 4 5X/cm

Fig. 7. Effect of stack height on temperature profile in Xdirection (Y = LY/2) at the end of discharge of rate C/O.3

(LX = 5.0cn-1, l&O = 373 K).

from increasing significantly under a high dischargerate, a suitable stack thickness should be designed.For example, from Fig. 4, it can be seen that underthe discharge rate of C/0.3, operational temperaturecan be approximately maintained if a stack is of asmall thickness (around l.Ocm).In Figs 7 and 8, the effect of stack height (or planearea in three dimensions) on temperature profile andon maximum temperature in cell stacks, respectively,is shown. It is demonstrated that the increase instack height within the range from 10 to 50cm willnot significantly influence the temperature distribu-tions in cell stacks. Therefore, it is considered thatbattery thermal behaviour will not be remarkablyaffected if the cell area is of a value within such arange from 400 to 2500cmz[25].Effect of thickness of cell components on thermalbehaviour

Optimum design of cell structure is important inorder to obtain high specific power and specific

400 c/o.3

380

g 360?ha 340

320 C/8

-300 _U 10 20 30 40 50

LYlcmFig 8. Effect of stack height on maximum temperature at Fig. 10. Effect of thickness of different layer on averagethe end of discharge of rate C/O.3 and C/8 (LX = S.Ocm, thermal diffusivity of cell stack in Y direction (basic cell: Li

qeo = 373 K). (114pm), PEO (2Opm), VO, (lOOpm), Al (15pm)).

10r

20 40 60 80 100 120LX+m

Fig. 9. Effect of thickness of different layer on averagethermal diffusivity of cell stack in X direction (basic cell: Li(114pm),PEO(20prn),VO,(1OOpm),Al(15~m)).

energy. Munshi and Owens[ZS, 281 discussed thedependence of specific energy and specific power oncell design. Based on their cell configuration (ie Li:3 x cath. capacity; electrolyte: 0.2 x thickness ofcathode; Ni: 25 pm as current collector; Al: 15 pm asbipolar connector), the effect of thicknesses of cellcomponents on temperature profiles in cell stacks isinvestigated in the present work.Figures 9 and 10 show the effect of the thicknessof lithium negative electrode, polymer electrolytefilm and vanadium oxide composite positive elec-trode on average stack thermal diffusivity. It can beseen that thermal diffusivity increases with lithiumthickness, and decreases with increasing thickness ofthe polymer electrolyte if the thicknesses of othercomponents are kept constant. Also, the thermal dif-fusivity in the X direction has a very small valuebecause the contribution to average thermal diffusi-vity in X direction mainly comes from that ofpolymer electrolyte, while the average thermal diffu-sivity in Y direction, is of the order of the magnitude

I I I I I I0 20 40 60 80 100 120

LX&m


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Two dimensional analysis of lithium polymer batteries 5231. Li(2Spm ). PE O@pm ),

WJ5orSn). Ni(lpm)2. LW 14j1m).PEO(2O(un),

VO,(lOOW. Al(lSW

h- 3. Li(l14pm). PEO(4Opm),J O,(l~W, Al(lSW

380 4. Li(57pm). PEO(2Opm).VO,(lOOW. Al(lSpm)

370 I0 1 2 3 4 5X/cm

Fig. 11. Effect of th ickness of different cell component ontem per at ur e p rofile in a cell sta ck (Y = LY/2) (LX =

5.0cm, LY = 20.0011, xeo = 373K, C/0.3).

of those of its metal components (Li: 4.36 x10-sm2s-1 andNi: 1.97 x 10-sm2s-1).The effect of different design on the temperatureprofile is shown in Fig. 11, which is obtained underthe assumption that the heat generation rate is thesame within stacks with same thickness (this assump-tion is adopted so as to study the effect of thermaldiffusivity on heat conduction). Contrary to whatmight be expected, an increase in lithium thicknessdoes not cause a decrease in temperature, instead itresults in a small increase in battery temperature.This is because, if stacks have close values of thermaldiffusivities (lines 2 and 4 in Fig. 11, correspondingto 114 and 57 pm thick lithium negative electrode,respectively), the temperature increase in stacks withlarger heat capacity will be lower (see Fig. 12, whereit is shown that heat capacity decreases with increas-ing lithium electrode thickness). In Fig. 11, it appearsthat there is no dramatic difference in temperaturedistributions in the stack center for different celldesign. This is probably because the variation of thethickness of different cell components, within acertain range, will not cause significant change in

2.5 -

2.4 -;t i:E 2.3 -29; 2.2 -rp= 2.1-

./ 90,

2.0 I I I I I I0 20 40 60 80 100 120LX/pm

Fig. 12. Effect of thickness of &&rent layers on averageheat capacity of cell stack (basic cell: Li (114&, PEOW/WI VO, (toorunh Al W/J&).

thermal conductivity. However, it is considered, froma heat transport point of view, that there exist somebetter designs, for which temperature gradient withina cell stack may be minimized. Also, for differentdesigns, the large temperature gradients in the Xdirection may again suggest that the low thermalconductivity in X direction will limit heat removalrate, and therefore, the heat transport behaviour inthe battery through the thickness direction is mainlycharacterized by the low thermal conductivity of thepolymer.E$iect of bipolar connector material on temperatureprofile

In order to reduce the cost and weight associatedwith the nickel current collector, and thus to increasethe specific energy and specific power of a battery, alow density metal (eg aluminum) and metallizedplastic current collector (eg 1000 A Ni on each sideof a plastic sheet[25]) have been suggested for use inlithium/polymer electrolyte batteries. It is interestingto calculate what kind of current collector is prefer-able. Figure 13 shows the effect of different bipolarconnector materials on temperature profiles in a cellstack. The results indicate clearly that no markeddifference in temperature profile will result fromchoosing different current collectors. Therefore, ametallized plastic current collector, the thermal con-ductivity of which is lower than those of Al and Ni,can be applied in the battery from a heat transferpoint of view.Temperature profiles in lithium polymer electroly tebatt eries wit h redox polym er or TiSZ as positiveelectrode

In addition to vanadium oxide positive electrodebased lithium polymer electrolyte batteries, signifi-cant advances have been achieved in the study ofbatteries with redox polymer[6] and TiS,[S] aspositive electrodes. In relation to heat generationand heat transport in batteries, the most importantcharacteristics distinguishing lithium/solid polymerelectrolyte batteries from other batteries are the low

2 390 i. Al(lS~)2. MeUized phr tic

380

I--

(15~ plastic + 2xl000ANi )3. Ni(lSpm)

370 0 1 2 3 4 5X/cm

Fig. 13. Effect of bipolar current collector material on tem-perature profile in a cell stack (Y = LY/ Z) (C/0.3,Lx = 5.Ocm. LY = 2O.Ocm, T, = 373 K) (ceil componen t:Li (114&, PEO(20~), VO, (KJOkm))).


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524 Y. CHENand J. W. EVANS370 r

ia2.OmA cm-z

340

t330 w0 1 2 3' 4 5

X/cmFig. 14. Temperature profiles in a cell stack (Y = LY/2)under different discharge current density (Li/PEO-LiX/Xl,theoretical cell capacity: OS83mAhcn-*[6]) (LX =S.Ocm, LY = 2O.Ocm,Lx, = 0.04, T,, = 357K).

current density of the cell, and the low thermal con-ductivity of the polymer. Therefore, it would beexpected that these two effects might cancel and thatsimilar thermal behaviour will be exhibited inlithium polymer electrolyte batteries with differentmaterials for positive electrodes. This can be seenfrom Figs 14 and 15, which show the calculated tem-perature profiles in the redox polymer (Xl: dimer-capto dithiazole polymer) and in TiS, basedbatteries, respectively. It is found that thermal char-acteristics similar to those in V,O,, system exist inTiS, and the redox polymer systems, that is, underlow discharge rate, insulating materials are needed tomaintain battery operational temperature, whiletemperature will rise in large stacks during high ratedischarge.In most experimental cells, the cell thickness isabout 4OOpm. However, this kind of design is not anoptimum design. To obtain high specific power, athin positive electrode film is needed[28]. Also, thethickness of the polymer electrolyte must be reduced

390 -

i=Z.OmA cm-

:a-----

hY

350 10 1 2 3 4 5X/cm

Fig. 15. Temperature distributions in a cell stack (Y LY/2) at the end of discharge under different discharge currentdensity (Li/PEO-LiX/TiS, , theoretical cell capacity:0.868mAhcm-2[5]) (LX = 5.0cm, Y = 2O.Ocm, LX, =O.O4cm, q=,, = 373 K).

to increase current density (if the path lengthbetween the electrodes is lOO/lm, a limiting currentdensity is estimated to be 4mAcm-[29]). Finally, itis considered that there is a large excess of lithiumwith 1OOpm thick lithium metal foil and efforts mustbe made to reduce lithium thickness to 30-40 pm percell[26]. Hence, thin-film configured cells, eg with athickness around 2OOpm, should be adopted. If totalheat generation in one cell is assumed to be the samein the 4OOpm thick experimental cell as that in the2OOpm cell (this assumption is a good approx-imation if the contribution to the electrode polariza-tion mainly comes from charge transfer), themaximum temperatures within a stack of the samethickness consisting of 400 and 2OOpm cells, respec-tively, are estimated as a function of current densityand are shown in Fig. 16. As would be expected, themaximum temperature in 2OOpm cell stack is higherthan that in 4OOcm cell stack. However, even in the200/1m cell stack, it appears that the temperatureincrease under high discharge rate will not result in athermal runaway problem, for instance, themaximum temperature in the cell stack is expectedto be lower than the melting point of lithium.Effect of heat transport in width direction on resultsfrom two dimensional model

In most batteries with a rectangular geometry,gradients are predominantly in the cell thicknessdirection, such as the temperature gradients in the Xdirection encountered in the present analysis. This isbecause there are usually substantial differencesbetween material properties encountered in thatdirection and, as in the present case, heat transportin that direction is typically governed by onematerial of low conductivity. Consequently, in twodimensional modeling of batteries, the usual choiceof the two dimensions is one in the thickness direc-tion and one of the two orthogonal directions.It is thought that practical thin lilm lithiumpolymer electrolyte batteries for electric vehicles arelikely to consist of cells of from 400 to 2500 cm2 area.The corresponding height and width would be from20 to 50cm. Comparing the thermal diffusivities inFigs 9 and 10, the diffusivities in the X direction are400

r / _--Mm.

z 380Ih 370

360One cell thickness

- 0.04cm- - 0.02cm

350 d0 0.5 1.0 1.5 2.0ilmA cm-

Fig. 16. Effect of discharge current density on maximumtemperature in a cell stack (Li/PE&LiX/TiS, ,LX = KOcm, Y = 2O.Ocm, Te,, = 373 K).


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Two dimensional analysis of lithium polymer batteries 525

, 380

Kz;,0 10 20 30 40 50

LZlcmFig. 17. Effect of stack width (LZ) on maximum tem-perature in cell stacks for discharge rate C/O.3 (LY =20.0cm, qeO = 373 K) *T,,,ur,iw: maximum temperature ifcell stacks are insulated.two orders of magnitude less than those in the Ydirection. For LX greater than, say, 5 cm, heat trans-port in the X direction becomes less than that in theY and 2 directions. For such thick stacks, it is thenplausible to use a second two-dimensional modelwhere the chosen dimensions are the Y and Z direc-tions.In that case, k, replaces k , in the equations aboveand, because k, equals k,, the model becomes ahomogeneous one. Figure 17 shows the effect of thewidth of the battery on the maximum temperature inthe battery. It can be seen that if the width is muchlarger than the battery height, the maximum tem-perature, in the stack will be very close to that whenthe stack is insulated. This implies that the twodimensional (X-Y) model, which has been used togenerate the results of prior figures in this paper, willbe satisfactory except for batteries where the heightand width are comparable. For this last case, thealternative model described in this paragraph shouldbe used, in the case of thick stacks, or, in the case ofthin stacks, a full three-dimensional model (whichthe authors hope to present in a future publication)should be employed.

CONCLUSIONSThermal analysis of lithium solid polymer electro-lyte batteries has been conducted to obtain informa-tion about how to maintain operating temperatureby designing a proper battery structure and choosinga suitable cooling/insulating scheme. It is demon-strated that under high discharge rate, in order toprevent battery temperature from increasing signifi-cantly and to minimize temperature gradients acrossthe battery, cell stack8 with small thickness may be

preferable. However, under low discharge rate, thethermal management problem is how to maintainbattery operational temperature, which can be rea-lized by choosing conventional insulating materials.The effect of thickness of cell components on thetemperature profile has been investigated. Also, theeffect of different bipolar connector materials ontemperature distribution has been examined. The

results indicate that the change in thicknesses of cellcomponents within a certain range, and the adoptionof different current collector materials may not resultin significant differences in battery thermal per-formance from the viewpoint of heat transfer, thoughthere may exist some better designs for which tem-perature gradients along the thickness direction maybe minimized.The thermal characteristics of the batteries withdifferent positive electrodes, including V,O,s , TiSland redox polymer, have been compared, and thiscomparison suggests that this kind of battery hassimilar thermal behaviour because of the lowthermal conductivity of the polymer and the smallcurrent density of the cell.Acknowledgements--We would like to thank Professor L.C. De Jonghe of University of California at Berkeley forproviding us experimental data. Our thanks also go to DrFrank R. MacLamon, Lawrence Berkeley Laboratory forhelpful comments on this work. The Li Foundation Inc.,NY, is acknowledged for awarding Y. Chen a postdoctoralfellowship at Berkeley. Finally, we appreciate the commentsfrom the reviewers of this paper.

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Thermal Diffusivity Electrodes 2

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