A.C. conductivity measurements in polymeric insulator conductor systems

Synthetic Metals, 28 (1989) C83 -C88

A.C.

CONDUCTIVITY

C83

MEASUREMENTS

IN

POLYMERIC

INSULATOR

CONDUCTOR

SYSTEMS.

T.A.Ezquerra

M

, F.Kremer,

Max-Planck-Institut D-6500

Mainz,

M.Mohammadi,

J.RHhe

fHr Polymerforschung,

F.R.

and G.Wegner.

Mainz.

P.O.Box

3148,

Germany.

B.Wessling. Zipperling

Kessler

and Co.,

Ahrensburg,

F.R.Germany.

ABSTRACT Measurements types

of

between the

of

the

polymeric d.c.

general

and

a

For

frequency

region

anomalous

diffusion

conductivity as

being

every

for

in

to

the

of

found

fractal

fulfilled. has

reported

composites

frequencies

been

are

conductivity

concentration

has

dependence

due

The a.c.

= e x

frequency.

as

conductivity

insulator-conductor

9.4 GHz.

law

considered

a.c.

the

been

found

polarization

of

which

critical

additive

predictions clusters

frequencies

the

to follow a

conducting

percolating higher

than

the

has

three

frequencies

is shown

higher

where

At

for

in

can

a

been

polymeric

a for be

stronger

interpreted

matrix

between

clusters.

INTRODUCTION The

study

composite

of

experimental

work

conductivity

of

be

characterized

critical

o ~ ~-~/u

a.c.

has 1-2)

an by

concentration

concentrations like

the

materials

higher where

in

subject

According

to

of

an

insulator of

than ~ ~

the ~c

to

la

theory

conductor

is

Estructura

the

(

~c

correlation de

la

d.c.

system

conductivity the

and

transition

component

electrical

( ~ - ~c ) - u de

theoretical

multicomponent

conducting the

conductor-insulator

much

percolation

insulator-conductor

~Permanent adress: Instttuto Serrano 119. Madrid (Spain) 037%6779/89/$3.50

conductivity

been

Materia,

can at

)"

a For

behaves length CSIC,

© ElsevierSequoia/Printedin The Netherlands

C84

which can be envisioned as proportional

to the average

present clusters at a given concentration ¢ 3) the standard

theory,

"universal"

i.e.

only

the critical dependent

system 4)." However

some

theoretical

in

three

dimensional

demonstrated

on

the

non-univeral frequency

dimensionality

studies

have

p values

existence

of

of

the conductivity

system is given by the following power

The

in a

law 7)

anomalous of

the

"x"

depends

diffusion

polymeric

dependence,

in

on

between

described by

experiments where

expression

for

: (1).

mainly

the clusters

matrix

~ can

insulator-conductor

X

exponent

the

(1.5 - 2

systems

o ~ w The

that

several

composite

have been observed 5-6).

dependence

shown

of

than the universal

systems) 4)." Moreover,

the

the with

exponents ~ and v are c o n s i d e r e d

take in particular cases higher values

have

size of

In a c c o r d a n c e

two

important

and

(b)

clusters.

equation

1,

effects

polarization

In t h e

is valid

effects

first for

(a)

:

case

the

frequencies

>> w~ ~ ~-dw, where dw= 3.5 is the fractal d i m e n s i o n of a random walk

path

on

this

case

the value

the

the

exponent

are

are

considered

dependence

of

polymeric salts

of

percolating 0.6

expected

2)

In

the

network.

1) in when

the

conductivity

polypyrrole based

and Co.. The validity of eq.

exponent

is

in

Higher

studied

our

in of

the

for

two

and

effects

frequency

systems

institute

system prepared 1 has been

takes values

polarization

communication

multicomponent

prepared

composite

"x"

intercluster

present

insulator-conductor

polyaniline

The

three dimensions.

types

of

based

on

one

in Z i p p e r l i n g

type

of

Kessler

tested.

EXPERIMENTAL The

following

three different

have been prepared

polymeric

by mixing a conducting

multicomponent polymeric

systems

additive

with

an insulating polymeric matrix: (a) P o l y p y r r o l e - P o l y e t h y l e n e o x i d e (b) P o l y p y r r o l e - P o l y v i n y l c h l o r i d e

(PPy-PVC)

(c) P o l y a n i l i n e - P o l y v i n y l c h l o r i d e

(PANI-PCV)

Polypyrrole

salts

were

ammoniumperoxydisulfate cellulose composites

sulfate and

solution

of

prepared (APS)

(SCS) 6)"

electrical

described previouly a

(PPySCS-PEO)

PCV

by a)

b)

polymerization in

measurement

(case (a)) 6)." In case in

THF

(I0%)

the

without

and

of

presence SCS.

were

pyrrole of

sodium

Preparation carried

out

(b) PPy was suspended the

solvent

was

by

of as in

slowly

C85

evaporated

to give

four

configuration

probe

for

the

(0.01

highly

cm)

were

electrodes. Kessler The

ac

kHz

and

cavity

thin,

Co. S)

the

GHz

{a

by

pertubation

form =

two

technique

this

were

e")

(50

pm).

was

film

The

linear

conductivity thicker

circuit

prepared

at

(0.1

films

between

the

Z i p p e r ling.

cm

thickness).

investigated

between

impendance

analyzers

different

in case

the

case

a short

of a round

e0 ~

using

In

to a v o i d

composites

in

films

to m e a s u r e

samples.

in order

conductivity 9.4

standing employed

conducting used

PANI-PVC

and

free was

0.01 and

{a) 8)"

RESULTS AND DICUSSION The for

room

the

temperature

three

dc

conductivity

investigated

systems

data

as

a

are

shown

function

in

of

fig.

the

i

volume

concentration. 0 "

0

,1

2 -2"

0

-2

-2 .I, u t/1

-6-

,~E -6

"~ -8~ -10

~..(+-22.s ~)

,,"

-8

I0-

~-( ,I,- 23~~6

-12

c~[~.3)lts

12-

.'g. -10

0

2~) 1% ~otl

~'0

(a)

do

0

' ~0' d0'6b ~l -/o~Ot 1

(b)

Fig.

I:

The

continuous

'

(c)

D.C. conductivity as a function of the volume concentration for: a) polypyrrole SCS p o l y e t h y l e n e o x i d e b) polyaniline polyvinylchloride c) polypyrrole polyvinylchloride The solid curves represent the percolative behavior

percolation curves

2b <~1 ./. vot ]

theory

can

be

illustrated. universal average comparable

line

To

cover

agglomerate the

( a ~

(~

explained

exponents

to

shows

the are size

thickness

the

behavior

- @c )~ by

using

whole

(~

observed of

the

the

upper

"universal"

concentration

needed. as

). Only

predicted

>

2). by

sample.

the

optical This

part

of

the the

exponents

as

higher,

non

range, In

by

case

(c)

the

microscopy

is

effect

can

give

a

C86 two d i m e n s i o n a l

character

of

the

the

system,

explain

the

low

Some

the

facts

that

1)

Finite

the

of model

are:

boundaries theory.

not 2)

clusters

to

from

as

of

a

from

the

for

critical

the

anomalous

this

only

dependence. to

broader

range

observed current The

can

the

bound

of

PANI-PVC

At

frequencies

the

diffusion

over

observed. distances

is

insulating

increased,

the

1)

The and

the

between

diffusion.

polarization

That At

of

matrix

the

over

a

by

the

dependence

is

displacement

PPy-PVC

and

behavior. the

process.

to

The

lower

to

"r"

the

induces

a

a

the

charge

reflects

rise

the to

a

low

normal the

forced

size

the

through

frequency

is

carriers

effects

dependence contribution

stronger

to

and

is

fractals the

frequency

of

At a

tunneling

selfsimilar

frequencies

can give

or

type

of

are

cluster

When of

follow

carriers

hopping

are

this

dependence

the

behavior

higher

of

continuous

charge

by

clusters

= 0.6.

region

is

dependence

clusters.

displacement

conductivity

x

with

same

supposed

the

controlled

eq.1

the

additive

frequency

compared

mainly

anomalous

a

are

no

barriers mean

this

expected

in

the

frequency reflects

Here

conducting

follow

matrix.

conducting

carriers

is

lowest

to

slope

to

of

conductivity.

and

large

conductivity

reduced.

the

charge

mechanism

conductivity move

the

observed system

the

figure

the

seems

conductivity

qualitatively

of

of

in

the

this

with

value

due

the Only

conductivity

in

a" s t r o n g e r as

of

fig.2.

increased

the

due

considerations

Hz)

is

to

carriers of

line

experimental

close

shows

insulator-conductor

the

the

sample

frequencies

charge

dependence

experimentally

the

in

of

3)

theory

dependence

under

(106-108

interpreted

concentration

frequency

In

between

r e a c h e d 6)

shown

broken

= 0.6)

and

dependence

composites

the

The

concentration

high be

is

of

percolation

percolation

frequency

from

influence

standard

dependence

(x

frequencies

which

frequency

higher

The

of

model.

The

by

systems

region

the

the

the

is

strong

frequencies

make

~c

model. small

concentrations.

concentration required

slope

When

higher

considered

a

which

could

deviations

hopping

observed.

diffusion

concentration

shifts

is

expected

high

dimension This

or

9).

a

at

observed

by

the 3)

tunneling

PPySCS-PEO

frequency

frequency

represents the

the

higher

lattice

even the

assumed

randomness

The

given

effects,

matrix-matrix-interactions

above

r<<~

size

critical

the

a

produce

possibility the

system.

for values

can

negligible,

before

conductivity

the

the

~c

conductivity

the

deviations

to

lower

when of as of

an in the

dependency,

C87

0-

+ r/oVd]

PP¥

t

...............

f )SS

E

i

,/'

w

26 ,y' / ,,',8,S

._~.......,...o . ~ ¢ -2

Fig. 2 (left): a.c. conductivity of the p o l y p y r r o l e (SCS) p o l y ethyleneoxide system

/ / _.,,~ooeeeoeo

• •

e LL .e- ~e#e ~eeeo ,," +'/ o/

-4

/ ½7' -6

-1.

Log(f(Hz))

21,.5%

Fig. 3 (right): a.c. conductivity of polyaniline polyvinylchloride system

-7

.( s

Loglf{Hz)]

70%

-1

-3 57% v-mE ~J

SO%

Fig. 4 (left): a.c. conducti vity of polypyrrole polyvinylchloride system

_ _ ~

~D O

--J _?

-9

2

~

~. LogIf { Hz}]

S

6

C88 like

measured

act

as

in

our

capacitors

giving

conduetivities. behavior

This

if

the

increased. clusters

a

The

not

barriers

between

negligible

explanation

is

concentration

contribution

consistent

of

the

with

the

observed

additive

contribution

becomes

less

important

and

the

conduction

clusters

which

are

connected

by hopping

or

conductivity

tends

be

percolation

theory

tunneling.

At e v e n

intrinsic

the higher

frequencies

conductivity

of

the

the

capacitors

is

the

through

the

to

the

conducting

of

clusters

Then

essentially the

experiments.

between takes

place to

additive.

CONCLUSIONS It

has

been

universal

that

exponents

conductivity range

shown

of

data

does

of

this

concentrations.

the

exponent

the conducting

depends

stronger

dependencies.

has

observed,

been

(x = 0.6) zation

seem

exponent.

of

The

frequencies

on

every the

matrix

anomalous

and

with

follows

and

on

concentration

account

diffusion

the c o n c e n t r a t i o n

the

one.

general

The value

frequencies

region

region

diffusion the polari-

the

increase

shifts

towards

of

2)

R.B. Y.

Latbowitz

Song,

T.W.

3._00 ( 1 9 8 6 )

is increased.

Francis,

12

(1979)

S.

Lee,

6)

T.A.

Phys. G. 7)

D.J.

8)

F.

9)

B.

Noh.

S.

Lee

Introduction

and

Phys.

and

Rev.

J.R.

Lett.

Gaines,

5__~3 ( 1 9 8 4 )

Phys.

Rev.

380 B,

to Percolation

Theory

(Taylor

&

1985

J.P.

Straley,

J. Phys.

C: Solid

State

Phys.,

2151 Y. S o n g ,

Rev.

B, J.

Bergman Kremer,

Noh,

(1986)

X.

Phys.C: and

Y.

Solid Imry,

Ezquerra,

Wegner. Kunststoffe,

Chen and

J.R.

Gaines,

6719

M. M o h a m m a d i ,

T.A.

a n d G.

Wessling,

T.W.

34

Ezquerra,

Wegner,

Vilgis

Gefen,

London)

Kohut

5)

Y.

904

3) D. Stauffer,

4) P.M.

and

F.

Kremer,

State Phy.

Phys.

Rev.

Lett.

M. M o h a m m a d i ,

Solid

State 10

(1986)

Comm., 930

T.A. 21

Vilgis (1988)

39

and 7451

(1977)

W. B a u h o f e r , 66

(1988)

1222 T.A. 153

the

higher

REFERENCES 1)

o£

exhibit

frequency

anomolous

for

dc whole

concentration

a

for

At higher

can

the

lower c o n c e n t r a t i o n s

predictions

with

the

over

than a p a r t i c u l a r

frequency

Samples For

describe

systems

conductivity

fulfilled.

the

when

ac

to

composite

higher

where

to be

effect

permit

of

The

additive.

standard

not

type

law o ~ w x for f r e q u e n c i e s of

the