Kinetics of staging transition in H2SO4-graphite intercalation compounds

Synthetic Metals, 34 (1989) 315-321

315

K I N E T I C S OF STAGING T R A N S I T I O N IN H 2 S O 4 - G R A P H I T E INTERCALATION COMPOUNDS

R. NISHITANI,

Y. SASAKI and Y. N I S H I N A

Institute for Materials Research,

T o h o k u University, Katahira,

Sendai 980

(Japan)

ABSTRACT The growth pattern of staging t r a n s i t i o n in graphite intercalation compounds

(GICs) has been a n a l y z e d by time- and s p a c e - r e s o l v e d Raman scattering

m e a s u r e m e n t s of the e l e c t r o c h e m i c a l

intercalation process in H2SO4-GICs.

The

staging kinetics can be c o n t r o l l e d by changing the overpotential or electric current in two d i f f e r e n t m o d e s of e l e c t r o c h e m i c a l current and o v e r p o t e n t i a l

intercalation.

The choice of

for a given mode can cause a variety of domain distri-

bution of stages i, 2, 3 and higher. The experimental results can be explained s e m i q u a n t i t a t i v e l y in terms of o n e - d i m e n s i o n a l d i f f u s i o n in a m u l t i p h a s e system with m o v i n g phase boundaries. The m e c h a n i s m for staging kinetics for the case of a p p l y i n g high o v e r p o t e n t i a l or high current density is found as diffusion-limited. On the other hand, the rate of the chemical reaction at the interface plays a key role in the staging kinetics for low o v e r p o t e n t i a l or low current density.

INTRODUCTION The i n t e r c a l a t i o n into graphite crystal is a unique form of crystal growth in view of the presence of the stage structures[l,2].

The D a u m a s - H 6 r o l d domains

a s s o c i a t e d with the stage structures plays a key role in staging transition[l,2]. The formation process of the D a u m a s - H e r o l d domains with various stage indices has been simulated in terms of the m i c r o s c o p i c model by Kirczenow[2,3].

The

kinetics of the change in the stage d i s t r i b u t i o n in a m a c r o s c o p i c scale, however, has not been s a t i s f a c t o r i l y clarified. The i n t e r c a l a t i o n process on a m a c r o s c o p i c scale can be regarded as a consecutive reaction which includes some elemental processes such as interface reaction and d i f f u s i o n of the intercalant substances[4]. limiting factors,

Therefore,

among these rate-

the slowest one d e t e r m i n e s the staging kinetics of the motion

of the phase b o u n d a r i e s b e t w e e n the domains of n e i g h b o r i n g stage indices and their stage distribution.

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316 In this paper, we report that the staging kinetics in electrochemically intercalated graphite i.e. H2SO4-GICs can

be controlled experimentally by

changing the overpotential or the electric current in two different modes of electrochemical reaction. The choice of initial current and/or overpotential can cause a variety of domain distribution of stages i, 2, 3 and higher. In addition, we report that the stage distribution in the intercalation process can be semiquantitatively explained in terms of one-dimensional diffusion in a multiphase system with moving phase boundaries. A part of the present study has been already published elsewhere[5,6]. EXPERIMENTAL TECHNIQUE The intercalation of H2SO 4 to a thin rectangular piece of H O P G ( ~ 1 2 x 4 x 0 . 1 m m ) is carried out by means of electrochemical reaction[5-8].

In the present method,

only a short edge of the sample is in contact with the surface of liquid H2SO 4 so that the intercalation reaction takes place only through the interface in contact with the liquid surface. The electrochemical intercalation was made in two different modes, i.e. the constant potential mode and the constant current mode.

The time dependence of the stage distribution during intercalation was

measured as a parameter of intercalation speed or degree of overpotential by choosing initial current or overpotential for a given mode. The time dependence of domain distribution of different stage indices during staging transition has been obtained by means of time- and space-resolved Raman scattering measurements of H2SO4-GICs [5-7]. The Raman scattering spectrum due to the graphite intralayer mode('~1600cm -I) is monitored to probe the stage structure. The laser beam of 488nm in wavelength is focused on the sample with a cylindrical lens. The Raman scattered light from the c-face of GICs has

been

analyzed using the optical multichannel analyzer(OMA) system(Spex-Triplemate) combined with a two-dimensional detector of a vidicon with silicon intensified target(SIT). This method enables us to obtain in a real time position-dependent Raman spectra in the Raman-shift range from 1350 to 1750cm -I. RESULTS Topographic view of stagin ~ transition We have obtained simultaneously a set of Raman spectra at four different positions separated from each other by 0.33mm on the c-face of the sample. By changing the irradiated position of laser beam, a large number of a set of four Raman spectra is measured.

The stage index is determined from the Raman frequency

and the relative intensities of the doublet component(E2g 2 modes) of the spectra. From this topographic study, the overall intercalation process is summarized as follows:[5] (1)The staging transition from stage n to n-I begins at the interface between the intercalant reservoir and the a-face of the GIC sample.

(2)The

d o m a i n s of different stage indices are separated macroscopically by the phase

317 boundary,

and the boundary moves toward the lnterlor of the c-plane during th(:

intercalation.

Current densit~ d e p e n d e n c e of stage d i s t r i b u t i o n In order to study the effect of reaction speed on the staging kinetics,

the

time variation of the stage d i s t r i b u t i o n has been measured with the current density(defined chemlcal

as current per graphite mass)

intercalation reaction.

function of electrochemical to It/M(I is the current,

as a parameter in the electro-

Figure 1 shows the results by solid lit.as as

charge(Q)

per initial graphite mass(M) which is equal

and t is the tlme elapsed after the onset of reaction].

The o r d i n a t e represents the d i s t a n c e from the short edge of the sample ~:hich Ls in contact with liquid H2SO 4. The intercalation

is completed almost at electro

chemical charge Q / M : 3 0 0 which is independent of the current density. The stage d i s t r i b u t i o n during intercalation, current density. electrochemical

however,

shows wide v&riatior~ depending on the

The amount of the phase boundary movement for a given number of charge is larger for the case of the low current density that for

the high current density.

In a high current density of 40~A/mg,

for example, more

than two phases appear always through the intercalation reaction, region occupies a rather small area of the GIC sample.

,"

(b)

~1:< h'/~

/'

e / / / ~. 6k/ /

t-

stage2 -

21-_.

¢-

//

'

~."~

(b)

,.u.." 1.0

....

(d)

""

h.s.

2o°k<'

/,"

/sta(

~

-(c) col0

"

/i

o

higher s t a.g ~j.

0

//,

0.6

//

l J

,

L~04

¢ / 0

i

i

I

:

t

o

i

r o

o

1

4 2

I

I

• stage I o stage 2

05

C3

and the stage 2

In a low current density

L I00

I ~ 2O0

Q/M

d

l

I

I00

200

(coul/g)

°

°

•

;

5 O.3o2

Fig.l 01

Fig.l The stage d i s t r i b u t i o n along the c-face of H 2 S O 4 - G I C s as a function of electrochemical charge at various current densities given in the corner right below of each figure. The dashed lines are the results of simulation.

o ° o

DI :lY-,4 D2 : I 73 D3 :0.09 mm~'sec

~/

Decree

of

0.5 ]o overpotential

Fig.2

Fig.2 (a) C o e f f i c i e n t of the motion of the stage boundaries. (b) The ratio of the w i d t h of the stage-2 region to that of the stage-l. Solid lines are the c a l c u l a t e d results.

318 of 5H/mg, for example, on the other hand, the stage-2 region occupies almost all of the sample at the staging transition from stage 2 to i. It seems for the case of much lower current density that the amount of the phase boundary movement for a given number of electrochemical

charge is very large, and only two

stages coexist always during the staging transition from stage n+2 through stage n+l to stage n. Overpotential dependence of the phase boundary motion[6] The boundary motion has been determined as a function of the degree of overpotential(DOP) electrochemical

of the stage-I phase, ~ H / H I = ( H - HI)/HI , where HI is the

potential at staging transition from stage 2 to 1 in an equi-

librium phase diagram, and H is the electrochemical potential of the intercalant reservoir(H2SO 4 liquid) with respect to the reference electrode of graphite. The sample before intercalation is a piece of HOPG.

The time dependence of boundary

motion is measured after the electrochemical potential is set at H in a stable region of the stage i.

The results of the boundary motion are plotted in Fig.2(a)

as a dimensionless parameter(Yi=~i/2 ~ ) DOP. The filled(open)

of the boundary motion as a function of

circles show a DOP dependence of the boundary motion, ~i =

~i/2 D~it(y2=~2/2 D / ~ 2 t) between stages 1(2) and 2(3).Here ~i(~2 ) is the location of the phase boundary between stages 1(2) and 2(3) measured from the edge of the sample at time t after the initiation of intercalation reaction. Di(i=l , 2) is the diffusion constant of intercalants in a stage-i phase. Figure 2(b) shows the ratio of the width of the stage-2 region to that of the stage-i region along the c-face, (~2 - ~I)/~i ' as a function of DOP. ANALYSIS Model of the boundary motion[6] In order to describe the stage distribution or the phase boundary motion shown in

Figs. 2 and 3, we present a model of one-dimensional diffusion in a

system consisting of three phases with two moving boundaries. model of staging transition.

Figure 3 shows the

Figure 3(a) shows the concentration C(x,t) of

intercalants before the onset of intercalation reaction, and Fig.3(b)

shows that

after the onset of the phase separation into three phases due to intercalation reaction.

Here the phases i, 2 and 3 correspond to stage i, stage 2 and higher

stages, respectively.

We assume that the intercalant reservoir is placed at

x<0 and is in contact with the a-face of the sample at x=0.

We now have the

three diffusion equations for the respective phases: ~c --=

2 a c D

(i) i

~t (i=l for O
2 ~x i=2 for ~l
conserved at the phase boundary so that

319

(C

- C

12

21

)d+

1

= I-D1 I~-C]

Jl-D

(~C) ~dt 2\~)x ~,.0J

Sx/~,'0

(2)

at x=61, and -

(C23

C32)d62

-m2

at x=62. Above condition constant.

SC

D3

Jl-

Z. 0

(3)

can be satisfied for all values of t, if 6i/t I/2 is

Thus we assume the relation 6i=2Yi(Dt)i/2.

from eqs.(2)

In order to determine

condition.

If we determine Y1 and ~2

and (3), then we obtain the location of phase boundaries yi s and to

The conditions

corresponding

common to all experiments

for x>0 and t=0,

to each experimemtal

are

(4)

C=C12 for x=61-0 ,

(5)

C=C21 for x=61+0 ,

(6)

C=C23 for x=~2-0 ,

(7)

C=C32 for x=62+0.

(8)

These quantities 0.417,

C12 , C21 , C23 and C32 for the H2SO 4 have been evaluated as 0.714,

0.333 and 0.246, respectively. J7,8] The concentration

composition

61 and 62.

solve the above diffusion equation as functions

of x and t, we need the boundary conditions

C=C 0

dt

~÷0

of C20HSO4-(H2S04)2.5

which corresponds

is normalized

at the

to the saturated stage 1

[7,8]. C0=0 for the initial piece of graphite.

C(x t)

(a)

6.7 mA/g

(b)

C(x t)

30 mA 4

C 2

t<0

t>O 50000 I

I

I

I

I I r L I

I

6000

3

Co

I~,~e°3 0

~,

~z

i

X

i

i

i

i

4000 s~llstage2 Fig. 3 +.~

Fig.3 A model of staging transition by diffusion in a three-phase system with two moving boundaries. Concentration of intercalants (a) before and (b) after the intercalation reaction. Fig.4 The calculated time-dependence of the concentration profiles for the stages I, 2 and higher at the current density of (a)6.7mA/g and (b)30mA/g.

I

i

I

°

I

J

i

l

l

l

l

22

r.-

I

I

I

I

I

l

Time 26000 se ~'stage 1 stage: I

I

I

I

l

l

l

Time 2000sec

i

0 Distance

l

from

120 sample

Fig. 4

edge(mm)

12

32O Analysis for the constant current mode The intercalant flow J across the interface should be constant for the constant current mode in the e l e c t r o c h e m i c a l reaction. conditions,

Then,

in addition to the above

the following condition is assumed.

J = -D

constant.

(9)

1 Using a solution of eq.(1), this relation results in the time d e p e n d e n t surface c o n c e n t r a t i o n Cs(t)= C12 + (zt/DI)I/2 J erf(Yl).

Here err is the error function.

On the basis of the above model with the b o u n d a r y conditions,

~i and ~2 can

be d e t e r m i n e d for various current d e n s i t y as a function of time. The results of the b o u n d a r y motion during i n t e r c a l a t i o n reaction are shown in Fig. 1 by dashed lines for various current density.

Here the following diffusion constants are

used: D l = l . 4 4 D 2 = l . 7 3 D 3 = 0 . 0 3 6 m m 2 / s .

A rather good agreement between experimental

results can be o b t a i n e d a l t h o u g h some d i s a g r e e m e n t s in details still exist.

The

v a r i a t i o n in stage d i s t r i b u t i o n is well d e s c r i b e d in terms of the current density. The d e n s i t y profiles for two cases of current density are displayed in Fig. 4 as a function of time. We can see that the surface c o n c e n t r a t i o n at x=0 increases with an increase in time.

Analysis for the c o n s t a n t potential mode Here we give an a p p r o x i m a t i o n that a surface c o n c e n t r a t i o n is linearly related to the e l e c t r o c h e m i c a l potential.

T h e r e f o r e the b o u n d a r y condition for the

constant potential mode means a t i m e - i n d e p e n d e n t C=Cs(cOnstant)

surface concentration,

i.e.

for x=0 and t>0.

Thus the e l e c t r o c h e m i c a l potential gives the c o n c e n t r a t i o n at the interface, Cs, as a parameter.

The above model allows us to find Y1 and Y2 for various

values of C s.

Figures 2(a) and (b) gives y s and ($2-~i)/~i , respectively, by l the solid lines as a function of DOP. The d i f f u s i o n constant D 1 is estimated as 0 . 0 9 m m 2 / s e c from curve fitting of Y1 and Y2 to the experimental results.

DISCUSSION

AND SUMMARY

We have shown that the stage d i s t r i b u t i o n over the c-face the initial current and/or o v e r p o t e n t i a l

in e l e c t r o c h e m i c a l

of GICs

depends on

intercalation. The

b o u n d a r y motion for a given amount of e l e c t r o c h e m i c a l charge is faster in slow i n t e r c a l a t i o n reaction than in rapid reaction. The diffusion in the sample in such a case is fast compared to the other reaction process such as interface reaction. Namely,

the i n t e r c a l a n t should d i s t r i b u t e uniformly within the sample.

Then, in the staging transition a high stage should appear initially, and the successive staging transitions occur toward d e c r e a s i n g stage indices. high reaction rate of intercalation,

In the

the diffusion limits the staging kinetics.

Then the intercalant can not d i s t r i b u t e

uniformly within the sample. In this case

32] we expect

to o b s e r v e

the c o e x i s t e n c e

Figure

4 represents

these

rizing

experimental

results,

of o v e r p o t e n t i a l the reaction

or h i g h

The e x p e r i m e n t a l kinetics

results

for two d i f f e r e n t

different

One m a y note,

modes

on the b o u n d a r y

for c o n s t a n t

potential

Possible

reasons

boundary

motion

the c u r r e n t exactly

the cross

of Yi

The third p o s s i b i l i t y concentration

on the basis

of a m u l i p h a s e

current m o d e

across

which

is more

analysis

of a m u l t i p h a s e besides

system.

electrochemical

model

current

sensitive

flows.

can be useful

It can be applied

in our model

Secondly,

we ignore

current

mode.

and the surface In spite of

for d e s c r i b i n g

the growth

types of intercala

one if we know the c o n c e n t r a t i o n s

as well as the d i f f u s i o n

to

to define

mode.

to other

the

difficult

for the constant

potential

from

mode.

First of all,

between overpotential

for the c o n s t a n t

phase

deduced

Dl=0.09mm2/sec

for c o n s t a n t

the current

in the present

the p r e s e n t

tion[9]

would

constants

are considered.

is that the r e l a t i o n

pattern

Authors

system with m o v i n g

that the d i f f u s i o n

and D l = 0 . 0 3 6 m m 2 / s e c

is i n a p p r o p r i a t e

crude a p p r o x i m a t i o n

boundaries

the staging

than the value of DI, but it is rather

section

for a low

intercalation

do not agree w i t h each other;

for the c o n s t a n t

the time d e p e n d e n c e

kinetics

can elucidate

for such d i s c r e p a n c i e s

density

in the staging

of high degree

On the other hand,

motions

model

mode,

limited.

In summa-

of e l e c t r o c h e m i c a l

however,

of e x p e r i m e n t

mode.

on the c o n d i t i o n

is d i f f u s i o n

a key role

at any one time.

current

density.

modes

of o n e - d i m e n s i o n a l d i f f u s i o n boundaries.

kinetics

density

plays

or a low current

than two phases

for the constant

the staging

current

at the i n t e r f a c e

overpotential

of m o r e

situations

at the stage

constants.

like to a c k n o w l e d g e

Dr. A.W. Moore

of Union Carbide

for supplying

HOPG crystals.

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Safran,

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and S.A.

Physics,

New York),

Solin,

3 G. Kirczenow,

Phys.

Rev.

Axdal

and D.D.L.

(1987)

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Intercalation

4 S.H.

Anderson

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(1985)

Chung,

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Compounds

Turnbull

and H.

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New York,

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and Y. Nishina,

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D.

Eklund,

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C.H.

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F.J.

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Holler,

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