Mesoscale charge transport in polyaniline

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Mesoscale charge transport in polyaniline

R. Pelster, G. Nimtz, B. Weßling

To cite this version:

R. Pelster, G. Nimtz, B. Weßling. Mesoscale charge transport in polyaniline. Journal de Physique II,

EDP Sciences, 1994, 4 (4), pp.549-553. �10.1051/jp2:1994145�. �jpa-00247979�

Classification Physics Abstracts

71.55J 72.15 81.35

Short Communication

Mesoscale charge _transport in polyaniline

R. Pelster

(~),

^{G. Nimtz}

(~)

and B.

Weflling

(~)

(~ II.Physikalisches Institut der Universitit _2u K61n, Zfilpicher Strafle 77, 50937 K61n, Germany (~) Zipperling Kessler & Co, Komkarnp 50, 22926 Ahrensburg, Germany

(Received

15 February 1994, accepted 22 February

1994)

Abstract. Froln broad-band temperature dependent transport studies _on PAni-blends _we

can now conclude that the electric conductivity of PAni is governed by charge hopping _on aInesoscopic scale between metallic crystalline regions (8

nm)

separated by thin amorphous barriers.

The

conductivity

of

polyIners

has attracted much attention for both their basic under-

standing

and their

promising

device

potential iii. Fully protonated polynaniline (PAni-ES)

represents an

intrinsically

conductive

polymer

^with a

thermally

activated

conductivity

_[2]

a = aoexp

(-@@)

_{which has been} related _{to an} electronic

hopping

between localiza-

tion centers. However,

origin

and size of the localization centers have not yet ^been identified.

Up

to _now different transport mechanisms _{on a} molecular level have been

discussed,

_as I-D intermolecular

hopping

in the

amorphous

parts ^{of the material} _[2] of 3-D

hopping

between

single quasimetallic

molecular strands [3].

Samples

_were

prepared

from

fully doped polyaniline (VERSICON powder; doping

level _y

=

0.5 and

protonated

with _an

organic

acid

H+X~) dispersed

in _an

insulating

^PETG

copolyester

based _on

polyethylene terephtalate (KODAR

PETG

copolyester,

Eastman

Chemical).

The

samples

_are

placed

ⁱⁿ a shielded

parallel-plate

condenser and the transmission coefficient is measured with network

analyzers (HP

35778 and HP

85108).

A novel calibration

technique

[4] allows to determine the

complex conductivity

_or dielectric function in _a broad range of both

frequency

and temperature

(5

Hz to 2

GHz;

100 K to 300

K).

Below _a critical volume

filling

factor

fc

=

VpAn;/l~ampi~x

^100% ₌ ^8.4% the conductive PAni is well

dispersed

in the

insulating

matrix and there _{are no}

conducting paths (see Fig.

la,

sample

with

f

₌

8.I%). Figure

16 shows the

conductivity

at 5 Hz

increasing

_up to 12 orders of

magnitude

_near

fc

due _to the formation of _a closed network of PAni. Above

fc

the blends exhibit _a

dc-conductivity equal

to the constant

low-frequency

data

(Fig.

la,

samples

with 12.4$lo

550 JOURNAL DE PHYSIQUE II N°4

I ₂

_~

_~

'~ 4

CS

~ ^{28 OX t}

~i

~ ~

i

I -2 ^~

ti

° -4

124% _~

~ ^-

~

_-8

o o

-6 _{8 IX} 3°

-12 o

~ 0 lo 20 30 40

f

[Xl

0 2 3 4 5 6 7 8 9

b)

log~~( u

[Hz]

a)

Fig. I. a) Real part ^{of the} conductivity _{al vs.} frequency at T

= 24 °C for three samples with different PAni content,

b)

_al at 5 Hz

vs. filling factor. In the _range of the solid line _al

= ado holds.

and 28.0%

PAni).

At the

highest frequencies

measured _{occurs a}

dispersion

due to a conduction current relaxation

(conducting paths

which _are not

parallel

to the electric

field)

_(5].

In order to determine the size of the

crystalline

metallic

regions

in PAni _we consider the interfacial

polarization

of free

charge

carriers in

samples

with

f

<

fc,

which

yields

_an enhanced dielectric

polarization.

The

experimental

data do not show _any loss due to free carriers

(only

the so-called

p-relaxation

of _pure PETG is

observed;

details will be

published

elsewhere

[6]).

Therefore,

the relaxation

frequency

of the interfacial

polarization

lies above _our measurement range as

expected

from the

high conductivity

of PAni (ur~jax « apAn; Cf 2000

S/m

at room

temperature

[7]).

With

increasing filling

factor the measured effective

high frequency

^values

of the

DF,

_ccc, increase

(the

low

frequency

values _are

given by

_ccc + A~ where A~ is the relaxation

strength

of the above mentioned

p-relaxation).

The

dispersed polarized

PAni acts like _a dielectric material with _a

quasistatic

dielectric _constant ES. ^{The dielectric mixture}

formula of

Looyenga

_[8]

(which

works well without

dissipation) yields

for the PAni component

(see Fig. 2)

ES =

f~~ (e)~ ^{(l f) )@~~)~}

m 400

(epETG

"

3)

with _an

uncertainty

of about 20.

Nonprotonated insulating

PAni exhibits _[9]

ec ci 4-10, I.e. the enhancement due to the quasistatic interfacial

polarization

is obvious.

The enhancement is correlated with the size of the

conducting regions

_[10]. For _a metallic cube of side

length

L with infinite

potential

walls

(standing

electron

waves)

holds [10] e~ =

ec + G

n~/~

L~

(G

= 6.I _x 10~

m~~;

_{ec: core}

polarization;

_n:

charge

carrier

density).

Therefore,

the

larger crystalline

metallic

regions

with

higher conductivity

will _govern the total

conductivity.

With _n <

I/(Vdimer

+ Vcounter;on) > 4 _x 10~~

m~~,

_{ec ct} 4-10 _we estimate

L / 6.3 _nm

Up

to _now we have not discussed the transport

mechanism, however,

_we have confirmed the

soo

E)

_soo

~oo o-

°

~-

300

200

oo

0

2 5 30 35 40 4 5 50 5 5

f [Sl)

Fig. 2. Quasistatic dielectric _constant of the dispersed PAni according to _an effective medium

analysis with Looyenga's formula [8].

T ~~~

[K

~~~]

0 04 0 05 0 06 0 07 0 08 0 09 0 lo

Q ^{-0 6}

7 K

I -0 8

I fl -10

~

j~ -12

-1.4

-1.6 o

_i~ ^a

-20

0 004 0 006 0 008 0 0 lo 0 012

1/T[K

_~]

Fig. 3. Thermal activation of the dc-conductivity of _a PAni blend with f ₌ 18.5%.

morphological picture

of

mesoscopic

metallic islands embedded in

amorphous

material _pre- sented

previously

_[2].

The size of the localization _centers between which

hopping

occurs can be determined from their

corresponding charging

_energy. ^Above

fc

there _are

conducting paths

of _pure PAni

(see Fig. 1).

^The

dc-conductivity

of the blends is

thermally

activated _as shown in

figure

3 for

a

sample

with

f

₌ 18.5%. Between 200 and 300 K it

obeys

_an Arrhenius behaviour _a

=

al

exp(-W/kBT)

with _an activation energy in the order of

magnitude

of the thermal _energy

(see

lower

z-axis).

For W _> kBT the

conductivity

follows _a

=

aoexp(-@@) _(see

upper z-

axis),

characteristic for I-D _or 3-D

(with

a

density

of states

proportional

to the

temperature

_[3]

552 JOURNAL DE PHYSIQUE II N°4

Table I.

Analysis

of the size of

regions

between which

hopping

occurs via their

charging

energy

(see text).

At

higher filling

factors

f

> 14% _{ccc cannot} be determined because of the

huge conductivity

of the

samples

f[%

_ccc W

[mev] dT (nm]

10.0 6.5 20.8 10.6

11.2 10 21.2 6.8

12.4 10.5 17.5 7.8

13.8 II-s 18.2 6.9

a)

f

b)

C)

~

8nm 1.6nm

Fig. 4. Schematic view of a) electronic wave-functions

((:

localization

length), b)

potential, and c) morphology of crystalline metallic regions and aInorphous barriers.

hopping.

Above

fc

the ratio of

hopping

distance to localization

length

is

R/(

=

3/8. @@

_ci I

at 100 K in agreement with measurements _on pure PAni [7]

(compressed Versicon). Thus,

_we conclude that the

dispersion

of PAni in PETG results in _a lower effective

conductivity

but does not

change

^barrier widths and transport mechanism because the

paths

consists of _pure PAni.

The activation energy W is, given

by

the

charging

_energy of the localization centers for both intermolecular

hopping

_{[3] or}

hopping

between metallic

grains ill],

I-e- W

=

II (4xeo) e~/dT (I loco

I

le~ (dTi

3-D

averaged

diameter of the

region

to be

charged).

Since each localization

center is surrounded

by

an effective

medium,

_{we can use} the measured low and

high frequency

values of the blends

(lle~

<

llecc).

The result is given in table I. The _mean diameter of the

regions

between which

hopping

_occurs is

dT

t 8 _nm

in agreement ^{with the value obtained in the first}

approach.

30% of the PAni

(Versicon powder)

are

crystalline,

I-e- 0.3 ₌

(x/6) (dT Id) (with

_{a mean} distance of localization _centers

d). Thus,

for the barrier width in the

paths

of _pure PAni holds _s

= d dT

=

dT(d/dT I)

_ci 1.6 _nm.

Up

to _some GHz the transport ^{mechanism of} pure PAni is determined

by hopping

between

mesoscopic

^metallic

regions (dT

ct 8

nm), amorphous

PAni forms the much smaller barriers.

The electronic transport scenario is illustrated in the sketch

diplayed

in

figure

4. The metallic

crystalline regions

with

amorphous

shell

(ci

10

nm) correspond

to the sc-called

primary parti-

cles, I-e- the smallest units observed

by morphological

studies

(STM

_[12], membrane filtration

or PCS of

liquid

PAni

dispersions

_[13,

14]).

The

conductivity

of

fully protonated polyaniline

is limited

by interparticle hopping

and not

by

the

conductivity

of the metallic

regions.

Further

investigations

have to prove whether this process ^at a

mesoscopic

scale _may also be relevant for other conductive

polymers.

References

ill

Gustafsson G., Car Y., Treacy G. M., Klavetter F., Colaneri N. and Heeger A. J., Nature 357

(1992)

477-479.

[2] Wang Z. H., Scherr E. M., MacDiarmid A. G. and Epstein A. J., Phys. Rev. B 45

(1992)

4190- 4202.

[3] ^Li Q., Cruz L. and Phillips P., Phys. Rev. B 47 1840-1845.

[4] ^Pelster R., PhD Thesis, K61n

(1993)

and application for _a patent

PCT/EP 92/02711.

[5] Yamamoto K. and Narnikawa H., Jpn. J. Appl. Phys. 28

(1989)

2523-2527.

[6] ^Pelster R., Nimtz G. and Weflling B., Phys. Rev. B to be published.

[7] Subrarnaniam C. K., Kaiser A. B., Gilberd P. W. and Weflling B., J. Polyrr. Sci. B 31

(1993)

1425.

[8] ^St61zle S., ^Enders A. and Nimtz G., J. Phys. I France, 2

(1992)

765-1777.

[9] ^Zuo F.,

Angelopoulos

M., MacDiarmid A. G. and Epstein A. J., Phys. Rev. B 39

(1989)

3570- 3578.

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[III

Adkins C. J., J. Phys. C: Solid State Phys. 15

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