Composite electrodes

Solid State lonics 5 (1981) 343-346 North-Holland Publishing Company

COMPOSITE ELECTRODES

J.R. Owen, J. Drennan, G.E. Lagos, P.C. Spurdens and B.C.H. Steele

Wolfson Unit for Solid State Ionics Department of Metallurgy and Materials Science Imperial College, London, SW7 2BP, U.K. A model is developed to describe the performance of composite electrodes - i.e. polycrystalline insertion electrodes bound with a solid electrolyte - in solid state batteries. By solving the Nernst-Planck equation in terms of the ionic conductivities of the electrode and electrolyte together with the Faradaic capacity of the electrode, the composite is represented by a network of electrical components. A.c. and d.c. experiments are presented to illustrate the influence of grain size, relative conductivities and other parameters of the materials with particular reference to the electrodes V O and the electrolyte polyethylene oxide lithium trifluoromethane sulphona~el3, Linl

i.

INTRODUCTION

The term "composite electrode" is used here to describe an agglomeration of small grains of an insertion electrode material bound together by another phase, usually but not necessarily a soft solid electrolyte, and may therefore be applied to all situations where an insertion electrode is used in polycrystalline form. In the simplest treatment, electronic conduction is assumed to be unrestricted even at interparticle contacts so that ionic conduction through the intergrain phase will play the major role in ensuring continuity of the mass transport route.

teries is distributed between studies of transport in electrolytes, electrodes and their interfaces, and in order to be able to judge how much emphasis should be placed on each aspect, the rate limiting steps should be clearly identified. An unfortunate complication of many transport calculations is the formulation of equations simultaneously involving F i c k ' s l a w and Ohm's law with the result that the overall situation is difficult to visualize. A simplification is achieved below by obtaining the ionic conductivity of the insertion electrode from its diffusion coefficient thereby expressing Fick's law in a more useful form. 2.

The composite electrode is thus the solid state analogue of the porous electrode used in liquid electrolyte batteries, however, here are four important differences in the electrochemical analysis: (a) The insertion electrode material itself may, in some cases, transport the electroactive ions as effectively as the electrolyte, which is generally a poorer conductor than its liquid counterpart. (b) The composition of the insertion electrode varies within the grains and the consequent variation of the surface redox potential is a major contribution to the cell overpotential. (c) The composition of the electrolyte is generally regarded as constant, in which case there is no concentration overpotential in the electrolyte. (d) The activation barrier against the ion passing between two phases is of a different nature to that encountered in interfaces where a new phase is grown, and the impedance arising from the barrier may be less important in the former case. Current research on materials for advanced bat-

THE E L E C T R O C H E M I C A L MODEL OF THE DIFFUSION PROCESS

The properties of an insertion electrode are usually described in terms of the chemical diffusion coefficient, D, thermodynamic factor, d~na/d~nc, and the open circuit electrode potential, E, as a function of the guest ion concentration, c (mole cm-3):

d~na d~(M+) . 1 where ~(M+)is the chemical d--~nc = ~ R-T potential of t ~ neutralized -zFc.dE inserted ion,M RT dc The Nernst-Einstein equation (i) relates the self-diffusion coefficient, D, to the ionic conductivity, writing this in molar units we have: cDz2F 2 ,and since th~ chemical diffusion RT coefficient,D, is usually equal to D.d~n a/d~n c we obtain,

k is the electrolytic capacitance per unit volume whose inverse is demonstrated by the rate of change of electrode potential with applied ionic current (balanced by an equal electronic current preserving bulk charge neutrality): for a small volume, ~V, Faraday'S law gives:

0 1 6 7 - 2 7 3 8 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © North-Holland Publishing Company

J.R. Owen ut al. / ('ompo~it<' uh'<'trode.~

344

= I (M +) = zF~V

I (e-)

=

dc/dt

zFdV

(]E/dc) -I

dE dt

impedance :

= -klIV d E / d t (Since c/k = - D and o k = ~zF(dE/dc) -2 , <~ and k m a y be e a s i l y found e x p e r i m e n t a l l y e.g. by coulo m e t r i c titration), R a t h e r than a p p l y i n g F i c k ' s law to the t r a n s p o r t of ions in the e l e c t r o d e , the ionic c u r r e n t density, J ( M +) m a y be seen as the r e s p o n s e to the e l e c t r o c h e m i c a l p o t e n t i a l gradient, a c c o r d i n g to the N e r n s t - P l a n c k equation:

J ( M +)

=

-0(M+).dE(M

where

E ( M +)

)/dy

is the

of M + e x p r e s s e d and

similarly,

J(e

) =-@(e

electrochemical ~ ( M +) =

)/dy

-

+ = /I ( M )

= k~V

. . . . k'~V d / d t

{EI',M+)

.£J(e

+ E

) =

~J(M +)

:

(e-)-i

+

-k
) +

i.

or

~',e-))/'~t...

<<

where it is realized that the electrode pot~.ntial, E, i s t h e n e g a t i v e sum o f the_ i o n i c and electronic electrochemical potentials. The equations (1) t o (%) a r e i l l u s t r a t e d by t h e n e t work of fig. ]. and an analysis similar to that of de Levie (2) g i v e s : o 2 d ~ E / d y - { (M +) + i (e-)}j~kE = O where = i/: (j,k is the ad~.littance per unit \,olsme g i v e n by the e l e c t r o l y t i c c a p a c i t a n c e at a n g u l a r f r e q u e n cy, ~0. A l t h o u g h the e q u a t i o n is e q u i v a l e n t to F i c k ' s law it m a y be a p p l i e d to some c~ses of pseudo-diffusional b e h a v i o u r in w h i c h d i f f u s i o n c o e f f i c i e n t s are not n o r m a l l y defined. Solutions to the e q u a t i o n w i l l be p u b l i s h e d elsew h e r e (3) hut some i m p o r t a n t r e s u l t s are g i v e n here.

dy/oe-

d,stance,

y

Relationships between electrochemical and p a r t i a l c u r r e n t s in a m i x e d con-

Insertion particle

]

_1 2.

th( J i:

}~~--

t:; fb~

The

APPLICATION

insertion

reaction

TO C O M P O S I T E

ELECTRODES

T h e colrp]ete d e s c r i p t i o n ot the inter ~ction between in irlsertion e l e c t r o d e p a r t i c l e and th<' ~]<~ctrolyce matrix is a p p r o x i m a t e d by discrete c o m p o n e n t s in fig. 3 A c c o r d i n g to the r e l a t i v e ionic coi]ductivJties of the e l e c t r o d e and e l e c t r o l y t e the m o d e l s i m p l i f i e s as in th~ following <.xamples. In e a c h ease the i m p e d a n c e Z( -n ) g i v e s rise to a time d o m l i n r e s p o n s e to a g a ] v a n o s t ~ t i c step of v(tzb. , eLectrolyte

insertian e l e c t r o d e ' , . ,~ parhde 'e[ecrrolyre

:

Figure

3.].

a

~

3.

~ ~ i~t erfac~at r esJstar,~e

~

k

A

,

A M+

io~c reslgan~e

Interaction electrode

o electrolyte size.

e-

2

l

between an insertion and the electrolyte. >

electrode:

large

graJr

In this
2. i.

(4)

le-

g..

F i g u r e i. potentials ductor.

_.~--= .... ; " =

F Figure

.... (2)

-,

Boukdmp

(a)

dE/dr

_

[ "]

potential

The e l e c t r o l y t i c c a p a c i t a n c e per unit volume, k is seen as a c o n t i n u o u s source or sink for ionic an<] e l e c t r o n i c c u r r e n t accord] ng to
ef

wh£~reas f o r a ] i r c J e p e n e t r a t i o n w( o b t l i n equival(nt ot a resistance ~il~ c a p a c i t ~ n c < series (fig. 2{b}) - i ~ -f ZA = {j.kL} + L/~:,M }

'i~(M+)/zF

for e l e c t r o n s , ).dE(e

~,]-j)

.... (I)

in volts,

l (j,.k (M ~)- ~ ,u -b -<, (2D) (dE/]c)~ "

ZA :

of ions

into

an e l e c t r o d e

R e f e r r i n g to fig. 2 (a) the a s s u m p t i o n of infinite e l e c t r o n i c c o n d u c t i v i t y leads to the f o l l o w i n g e x p r e s s i o n of the i m p e d a n c e at angular f r e q u e n c y ~) + -½ ZA = { (M +) ,I coth (L/>,) w h e r e ) : (jek¢ (M)) . . . (4) For a small p e n e t r a t i o n d e p t h (}.) of the elect r o c h e m i c a l d i s t u r b a n c e we o b t a i n the W a r b u r g

< electrolyte

> < e l e c t r o d e : small

grairl

size. The ~ b e h a v i o u r above d e g e n e r a t e s into .'-!~ as the p e n e t r a t i o n d e p t h into the g r a i n a p p r o a c h e s the g r a i n size. The g r a i n is then a simple capa c i t a n c e w h i c h m a y be a d d e d to a s i g n i f i c a n t interfacial (e.g. d o u b l e layer _ i} or adsorption) capa c i t a n c e (fig. 4 (b)). The ~, behaviour appears as a d i f f u s i o n a ] process, a l t h o u q h the o r i g i n of the " d i f f u s i o n c o e f f i c i e n t " is not di ffusJona] .

J.R. Owen et al. / Composite electrodes

3.3.

J electrode

> ~ electrolyte

E l e c t r o l y t e is added to the i n s e r t i o n e l e c t r o d e compact, if at all, to fill in voids b e t w e e n particles. The l i m i t i n g r e s i s t a n c e is at the g r a i n b g u n d a r i e s as in fig. 4(e). A g a i n we obtain ~- m b e h a v i o u r w h i c h is not c o r r e c t l y interp r e t e d by a simple d i f f u s i o n c o e f f i c i e n t . electrode par t icleNs

345

site/(PEO) s L i C F 3 S O 3 were m e a s u r e d using a sinusoidal V o l t a g e signal s u p e r i m p o s e d on a d.c. bias equal to the cell e.m.f. In this way the cells were not c h a r g e d or d i s c h a r g e d d u r i n g measurement. S t r a i g h t line p l o t s are shown in fig. 6 c o r r e s p o n d i n g to the e x p e c t e d Z = k(j~J) -I/n behaviour.

ele/ct rode I particles

5.2.

i_k]i±}

il i r:l ~{:RCT

electrolyte resistance

electrolyte resistance

Galvanostatic

step technique.

C o n s t a n t c u r r e n t s were a p p l i e d to L i / P E O / V O13 c o m p o s i t e and L i A I / P E O / V 6 0 c o m p o s i t e cel~s at 120 o C . The v o l t a g e / t l.m e b e1l a v l o u r s h o w e d an initial r e s i s t i v e drop f o l l o w e d hy a p p r o x i m a t e ly t ~ b e h a v i o u r then a fast p o l a r i z a t i o n region {e.g. fig. 6). C u r r e n t i n t e r r u p t i o n (not shown)

¢ledr~e i par t,ck,~

Figure

4.

4

Representations trodes.

of c o m p o s i t e

PREPARATION AND MICROSTRUCTURAL OF C O M P O S I T E E L E C T R O D E S .

elec-

EXAMINATION

P o l y c r y s t a l l i n e V 6 0 1 3 + x was p r e p a r e d as desc r i b e d in the c o m p a n i o n p a p e r (5). V60~3 was m i x e d w i _ h a s o ] u t l o n of (polyethylene OXl~e) 5 Li C F 3 S O 3 in a c e t o n i t i l e and the s o l v e n t was a l l o w e d to e v a p o r a t e leaving a tacky powder. The p o w d e r was then p r e s s e d at i O , O O O psi. In this way c o m p o s i t e e l e c t r o d e s w i t h p o l y m e r volume f r a c t i o n s b e t w e e n zero and 50% were made in the form of ]OO m i c r o n thick discs, w h i c h were then d r i e d in vacuo at 150°C. Density measure~]ents i n d i c a t e d that in each case the V O occ6 13 L1pied only half the total volume so that the p o l y m e r only p a r t i a l l y filled the void space between the e l e c t r o d e p a r t i c l e s . 2-point e l e c t r o nic c o n d u c t i v i t y m e a s u r e m e n t s gave v a l u e s of the o r d e r of i O - 3 S c m -I.~ The e l e c t r o n m i c r o g r a p h s shown in fig. 5 show the V O13 p a r t i c ] e s as a g g l o m e r a t e s of c r y s t a l l i t e s a ~ o u t iOOO~ across by a b o u t iOO~ thick; the surface area e n h a n c e m e n t was very large. A h i g h e r degree of p r e f e r r e d o r i e n t a t i o n was o b t a i n e d at the low p o l y m e r volume fractions. LiAI p o w d e r of about 50 m i c r o n size was obtained from Foote M i n e r a l Co. and p r e p a r e d into comp o s i t e e l e c t r o d e s as abcve inside an argon filled olove box. 5.

5.1.

ELECTROCHEMICAL ELECTRODES.

A.C.

Impedance

MEASUREMENTS

50i

ON COMPOSITE

technique

The A.C. i m p e d a n c e s p e c t r a of the cells Li/ ( P E O ) s L i C F 3 S O 3 / V 6 O I 3 c o m p o s i t e and LiAI c o m p o -

Figure

5.

S.E.M.

and T.E.M.

of V6013.

PEO

(10%)

J.R. Owen et al. / Composite electrodes

346

c a u s e d a l m o s t i m m e d i a t e r e l a x a t i o n to the voltage shown by c o n t i n u a t i o n of the t ~ b e h a v i o u r . 6.

(2)

R. De Levie, Adv. E l e c t r o c h e m and E l e c t r o c h e m Eng. 6, 329, (1967). J.R. Owen, work to be p u b l i s h e d . B.A. Boukamp, J.D. R a i s t r i c k and R.A. Huggins, "Fast Ion T r a n s p o r t irl Solids" (Vashishta, M u n d y and S h e n o y eds] N o r t h H o l l a n d (1979). P.C. S p u r d e n s et al., these p r o c e e d i n g s . J. Ross Macdonald, J. Chem. Phys. 54, 2026 (1971].

(3) (4)

DISCUSSION

The t h e o r e t i c a l a n a l y s i s above was d e v e l o p e d for an ideal s y s t e m in w h i c h b o t h the i n s e r t i o n electrode and the e l e c t r o l y t e are single phase materials with constant conductivities. F r o m this p o i n t of view the t e c h n o l o g i c a l l y i n s p i r e d choice of m a t e r i a l s was u n f o r t u n a t e in the sense that b o t h e l e c t r o d e s and the e l e c t r o l y t e are k n o w n to e x i s t in m a n y p h a s e s d e p e n d i n g on their composition. Thus, at this stage there is a c o n f l i c t of i n t e r e s t b e t w e e n the study of the f u n d a m e n t a l p r o c e s s e s and the d e m o n s t r a t i o n of the v i a b i l i t y of the b a t t e r y s y s t e m - w h i c h will be r e q u i r e d in order to j u s t i f y a more r e a l i s t i c model i n v o l v i n g c o n c e n t r a t i o n d e p e n d e n t p a r a meters. The i m p e d a n c e m e a s u r e m e n t s showed n = 4 b e h a v iour of the LiAI c o m p o s i t e anode, i n d i c a t i v e of case 3.1. above. I m p r o v e m e n t of the anode may t h e r e f o r e be e x p e c t e d b o t h by i n c r e a s i n g the e l e c t r o l y t e c o n d u c t i v i t y and d e c r e a s i n g the particle size. The W a r b u r g i m p e d a n c e o b s e r v e d w i t h the L i / P E O / V 6 0 1 3 c o m p o s i t e cells is more d i f f i cult to assign. The cases 3.2. and 3.3. above both p r e d i c t W a r b u r g b e h a v i o u r and since few data on the a n i o n i c t r a n s p o r t n u m b e r s of p o l y m e r i c e l e c t r o l y t e s are available, the o r i g i n of the W a r b u r g i m p e d a n c e in the e l e c t r o l y t e (6) can not be r u l e d out. A s s u m i n g that case 3.2. applies, k n o w n v a l u e s of k (V 0 3 ) give an effective ionic c o n d u c t i v i t y of 6 1 10_ 5 to i O - 6 S c m -I which, c o n s i d e r i n g the m i c r o s t r u c t u r e , w o u l d be s i g n i f i c a n t l y i m p r o v e d by a more c o n t i n u o u s polymer matrix.

(5) (6)

ACKNOWLEDGEMENTS J. Owen a c k n o w l e d g e s s u p p o r t from E.E.C. (D.G.12) and all a u t h o r s e x p r e s s t h a n k s to their c o l l e a g u e s at the W o l f s o n Unit, p a r t f c H l arlv N. Bonanos, T. G o l d r i c k dnd D. Waters.

lO:Hz-- o

° ~IO-.

o°

~H~.~,°~H~

i

~-

o

~ o _ _ ~

n ~ N

~

hAl anode


-

cathode

V~01~cathod e "~.~..~.~

W. W e p p n e r and R. H u g g i n s , A n n . Sci. 8, 269, (1978).

o

log f/Hz

6(b) Log Z " / l o g f p l o t s L i A I . P E O at 170°C.

for the above,

also

Oo D O

Ooo

0 ]mAcro

O O

O

O

REFERENCES (i)

IYax~s d~sp{aceme~t!

o

O

In c o n c l u s i o n , we m a y e x p e c t that a p o l y m e r e l e c t r o l y t e is in g e n e r a l e f f e c t i v e in e n h a n c ing the t r a n s p o r t w i t h i n p o l y c r y s t a l l i n e electrodes, Fast ion t r a n s p o r t i~ the i n s e r t i o n electrode, will not always be necessary, w h e r e as the c o n d u c t i v i t i e s of all m o b i l e c h a r g e s in the e l e c t r o l y t e and their d e p e n d e n c e on compos i t i o n will d e t e r m i n e the success of the solid state battery.

,

500 ~C,02 ZA[ncm~i 6(a) Complex impedance plots on Li/PEO/V6013 (upper points) and V 6 O I 3 . P E O ( 3 0 % ) (lower points) cells at 120°C.

"~<~<~

The g a l v a n o s t a t i c e x p e r i m e n t s were i n t e n d e d to e v a l u a t e the rate c a p a b i l i t y of a solid state cell thus the large v o l t a g e range p r e c l u d e d analysis by the simple model. However, an important feature c o m m o n to all e x p e r i m e n t s was the p o i n t of i n f l e x i o n f o l l o w e d by fast p o l a r i z a tion w i t h the c h a r a c t e r i s t i c s of a r a p i d l y increasing resistance. As well as the p a r t i n g of the l i t h i u m / e l e c t r o l y t e i n t e r f a c e p o s s i b l e exp l a n a t i o n s are loss of e l e c t r o n i c c o n d u c t i v i t y in V6013 and " s a l t i n g out" of the e l e c t r o l y t e at the anode.

~z

i

Rev. Mater.

TIMEIsis]

6 (c) G a l v a n o s t a t i c e x p e r i m e n t on L i / P E O / V L i / P E O / V 6 O I 3 . P E O at 120°C.

~-or