High-θ polyacetylene: DC conductivity between 14 mK and 300 K

Sy~ztheticMetals. 28 (1989) D11 D18

HIGH-~ POLYACETYLENE:

TH. SCHIMMEL,

I311

DC C O N D U C T I V I T Y BETWEEN 14 mK AND 300 K

G. DENNINGER,

W.RIESS,

J . V O I T and M . S C H W O E R E R

P h y s i k a l i s c h e s I n s t i t u t and BIMF, U n i v e r s i t ~ t Bayreuth,

D-8580 Bayreuth, W . - G e r m a n y

W. S C H O E P E U n i v e r s i t a t Regensburg,

W.-Germany

H. N A A R M A N N BASF Ludwigshafen,

W.-Germany

ABSTRACT Highly stretch-oriented polyacetylene vities

a of

typically

20

000

-

(6.5:1)

000

room tempe-

14 mK,

~ d e c r e a s e s m o n o t o n i c a l l y by about a factor of 5 for fresh

samples

is

within

a

400

fitted

SHENG

formula

model

On

dicular

to

(a~)

the the

conductivities stretching

anisotropy A=~i/a~

mechanism

temperature

the

of

by

the

phenomenological

measurements

dent

mK

Between

at

when highly

Above

iodine.

y i e l d s conducti-

~-icm-i

rature

samples.

d o p e d with

i00

for both,

cally changes a(T)

~!

axis

of about and

~.

T = 300 K and T =

dependence and

can

be

fresh

samples,

parallel

(~i)

show

for

interpreted MONTGOMERY and

a temperature

25 i n d i c a t i n g Deliberate

perpenindepen-

a common

oxygen

fresh

limiting

ageing

drasti-

and results in a t e m p e r a t u r e d e p e n d e n c e of A.

INTRODUCTION Very lene

recently,

with

interest

300 K of fresh the

data,

[4].

however,

showed

an

well

[1-4].

of h i g h l y

above A

20

study

almost

models A

good

is

the

are fit

to

SHENG

temperature

A=al/~ , indicating

not

a common

able the

to

Q - i c m -I

has

between

iodine

showed the

precision

(equ.

independent

polyacety-

a(T)

explain

high

formula

conducting

000 of

samples h i g h l y doped w i t h

standard

dependence

synthesis

conductivities

considerable

of

the

i).

K

and

that most

temperature experimental

Fresh

conductivity

limiting mechanism

aroused 3

samples

anisotropy

for both,

a! and

a~ [4]. The e x p e r i m e n t s f o l l o w i n g questions: 0379-6779/89/$3.50

presented does the

below SHENG

are d i r e c t e d towards the formula d e s c r i b e ~(T) at

© Elsevier Sequoia/Printed in The Netherlands

DI2 temperatures

below

3

K?

Can

we

fit

to

data

correlation

between

the

samples

its

temperature

effect

and

from

the

microscopic

room

of a g e i n g

extract the

a

consistent

SHENG

temperature

formula?

dependence

value?

on the c o n d u c t i v i t y

And

of

a

finally:

anisotropy

set

Is

of

there of

a

fresh

what

is the

A?

EXPERIMENTAL (CH)x

was

obtained

by

the

elsewhere

[i]. We u s e d

films

propylene

as

and

ching.

The

in d r i e d films, setup

resulting for the

a

from

as

300

several

as 3 K.

50

data

The

SEM

3He/4He an

18

by

dilution Hz

the

ac

cryostat,

with

four-probe

and M O N T G O M E R Y

All e x p e r i m e n t s

EXPERIMENTAL

fresh

la

of

sample

to

2.8

a i by and

measured

[6,7],

about a

thickness.

4.2

we

K

was 3

used

measured

K,

we

a

via

performed

all

of

both,

leading

which

standard

to c o n s i s t e n t

four-probe

the ohmic

is

to about

technique.

regime.

Dependence the

of

temperature

fresh

depending a i of

20

000

decreasing

fresh

of

14 mK.

conductivity

a

fresh

at -

room i00

from

300

a I and

~-icm-l. The

K to

Fig.

sample

within

the

vary a

range

a

from

decreases

reduction

the

for

absolute

3 K varies

2 shows

decreasing

a~

The

temperature

000

sample.

is still

of

technique.

temperature.

samples

on the

dependence

dependence

via M O N T G O M E R Y

samples

between

with

cooling

The

was

sample

We u s e d

the s t a n d a r d within

obtained

a(T)

samples,

~-icm-l.

techniques

as d e t e r m i n e d

at

4,

Above

different

> 20 000

were performed

sample

monotonically of

K)

-

conductivity

method.

15

3 K, we a p p l i e d

shows

sample

values

the

the

mK

tempe-

we

is l i m i t e d

of

14

of

The

[4,5],

RESULTS

a) T e m p e r a t u r e Fig.

and

than

of a(300

Below

from

bridge

more

had v a l u e s

results.

determination range

resistance

measurements

accuracy value

Q.

single

curve

of

temperature

one

Each

relative

0.5

elsewhere

points.

factor

1.5

on the

range,

of the a b s o l u t e

low

iodine

pressed

this

; the a c c u r a c y

the

for

stret-

of

typically

described hours

on poly-

mechanical solution

mechanically of

described

grown

Within

0.01%

For

6.5-fold

3 K,

to

cycle.

technique

saturated

resistances

above

thousand

temperature

a

were

long K

by

in

contacts

contact

times

sweep

typically

in

aligned

doped

experiments

sweep

rature

were

CCl 4. P l a t i n u m

allowed

as

substrate

samples

polymerization

of i - 5 ~ m t h i c k n e s s

factor between

temperature from

monotonically

4 K to down to

DI3 14 mK by about the

total

varies

from

3.7

correlation, values

a factor

reduction

of

to

the samples ~5 "T

5.4

however,

~(300

K)

of 1.34

factor for

could and

the

in this t e m p e r a t u r e

of ~I by cooling these be

highly

observed

reduction

I

F

range.

Thus,

300 K to

14 mK

conducting between

factor,

samples.

the

No

individual

respectively,

for

examined.

'

o C~ ~

from

I

0%'

f O%

b ~3

f

O

o --2

[(CH)(J3)0.065 ]x MONTGOMERY M E T H O D

(:1 I

I

100

200

300 0

I

I

100

200

T/K

300

T/K

Fig. i: al (T) and ~ ( T ) of s t r e t c h - a l i g n e d (6.5:1) [(CH) (J3)0.065] x (one t e m p e r a t u r e cycle), a) fresh sample; b) the same sample after 02-ageing. I

1

I

O01A

'EE 8.1

~

,

01

1

T/K

390

E

7"~

,o

o

c~

".- 7.s:

I0-0385 0

//

/

55 380

o 6.1 0.014

I

I

I

1

2

3

I

-190

T/K

-060

070

i0g TI K

Fig. 2: at(T ) b e t w e e n 14 mK and 4 K in two d i f f e r e n t plots. The dotted line in a) is the SHENG fit, the dotted line in b) the fit to a power law.

DI4

TIK 100

50

10

I

I

I

i

E tO

42

I

I

o

cn o

~3a

34

30

a-el

26

oxygen ageing increasing

0.3

04

_k.....__

22

os 0.6 T-~/z./K -1/4

a ~oo

Fig. 3: ~i(T) for d i f f e r e n t stages of a g e i n g of by 1 at 02 (standard four-probe measurement), a) b) after 2 hours at 260 K, c) after a d d i t i o n a l 1 d) after a d d i t i o n a l 1 hour at 320 K and e) after hours at 320 K [4].

200

300 T/ K

the same sample fresh sample, h o u r at 260 K, additional 2

Fig. 4: T e m p e r a t u r e d e p e n d e n c e of the c o n d u c t i v i t y a n i s o t r o p y A = ~i/~ for the data of Fig. la (fresh sample, curve a) and Fig. ib (same sample after ageing, curve b).

b) A n i s o t r o p y and A g e i n g Deliberate drastic

ageing

of

the

samples

change of the t e m p e r a t u r e

with

oxygen

dependence

results

of both,

~i

in

a

and ~ ,

leading to a r e d u c t i o n of the c o n d u c t i v i t i e s m a i n l y at low temperatures.

Fig.

250 K for a

3 shows fresh

log(~l(T))

sample

a g e i n g of the same sample rature

value

conductivity nitude.

Only

(curve a)

by

3 K is d i m i n i s h e d

strongly

and

(curves b-e)

of a i is reduced at

versus

aged

T -0-25

for d i f f e r e n t

8 K

degrees

and of

[4]. W h i l e the room tempe-

less

than

by more

samples

between

a

factor

than

exhibit

an

of

i0,

the

5 orders

of mag-

almost

constant

factor of r e d u c t i o n of the c o n d u c t i v i t y on further a g e i n g d-e).

(curves

D15

For

fresh

dependence:

samples,

~i and ~

show almost

the a n i s o t r o p y A(T)

the

has v a l u e s of 20 - 26 and changes

by only about 2 - i0 % from 300 K to 3 K. Fig. the sample

of Fig.

same t e m p e r a t u r e

4a shows A(T)

la. A g e i n g the sample of Fig.

for

la for one week

at room t e m p e r a t u r e by 100% oxygen at ambient p r e s s u r e leads to a r e d u c t i o n of ~(300 K) by a factor of 6 and a change rature

dependence,

which

is

shown

in

Fig.

~(300 K)/~(3 K) = 2.8

for the fresh sample of Fig.

to

Fig.

more

than

anisotropy rature. fresh

in

increases

Its

sample,

changes

increase

increase

of

lb.

only

temperature

pronounced This

I00

During

slightly

this

by

dependence,

about

the

60

%

anisotropy

about

8%

(Fig.

While

it amounts

process,

at

as

towards

is

lb.

la,

ageing

however,

significantly

of

in the tempe-

room

tempe-

compared 4

b)

lower

perfectly

the

to

the

showing

a

temperatures.

reproduced

with

d i f f e r e n t samples.

DISCUSSION Different the

room

for

the

samples

Q - I c m -I, even

no

the

creasing not

fresh high-~

temperature with

~(300

of K).

contribute

This

scattering carbon higher

should

significantly (see

not

of

larger the

c o n s t a n t v a l u e ~o

and play

and who

that

below),

conductivities

did

indicate

could

not

that

the

HEEGER an

phonon

copper. than

the

This

(see Fig.

also

height

conductivity la).

ideal

of

in

with

at

that

indoes room

phonon

one-dimensional

value

of ~ to be

that

potential

asymptotically Thus,

i00 000

of PIETRONERO

explains the

Even

scattering

argued,

role

the

5 in

observed;

resistance

who

important

estimated

of be

decrease

sample

[9],

of

investigated.

dependence

curves

to

by a factor

been

is c o n s i s t e n t with c o n s i d e r a t i o n s

~ polymers, than

s(T)

This may

KIEVELSON

of

have

highest

significantly

[8]

differing

temperature

the

temperature. and

the

"metallic"

slope

samples

conductivity

for

barriers

approaches

i/~ o could be

kT

a

interpreted

as the r e s i s t a n c e d e t e r m i n e d by defect scattering. A good

fit of the t e m p e r a t u r e

dependence

is o b t a i n e d w i t h the SHENG formula

~(T)

= ~o" exp[- TI/(T + To) ]

Equ.

1 fits

the

experimental

in the

temperature).

fresh sample

[10,]2].

(i) data

rature range from 0.4 K to 300 K magnitude

for the

(Figs.

(i.e.

The

la,

2a)

in the

tempe-

for almost three orders of

parameters

~o,

T 1 and T o are

D16

given

in T a b l e

differ

from

for fresh which

sample

we

Fig

la,

dependence,

2

the

was

the

is

a

[4],

sample

400

mK.

For

Tloc,

aged

more

the the

than

factor

width.

is about which

Tlo c

the

shallow

3%.

for

3 K and

For

most

1.5,

K of

temperature deviations

fresh

is m u c h

of

300

sample

Severe

the

of

dependence

fit b e t w e e n

the

samples

a

of T 1 and T o

temperature

line

with

deviation

temperature

i. The v a l u e s

not

graphical

the average

below

by

sample,

recently

within

which

sample

For the

published

perfect

Fig.

to

samples.

was

arise

1 for the data of Fig.

sample

higher,

up

of to

50 K. sample

Go / Q-icm-i

II

fresh

w /

112

9.6

14.7

2180

71

113

9.7

15.8

12900

50

240

21

32.6

519

55

274

24

31.7

II

Table I: P a r a m e t e r s of equ.

The

SHENG

different

barriers

model

groups

assuming

has in

highly

1 and 2 (~E = k.Tl).

been

the

applied

past

conducting

doped

regions

barriers,

SHENG

derived

introduced amount

of

a parabolic

where

E

is

the

image

dielectric

A

describes by

potential

transfer

is caused For para-

The

applicability

of

is not quite obvious

correction, is given

by

constant

of

by

~(T)

fluctuations.

A in his theory,

force

barrier.

i.

however,

a parameter

gives

equ.

polyacetylene

It

separated

e n h a n c e d by thermal v o l t a g e

SHENG model to polyacetylene,

for the

to

[4,12-16].

of w i d t h w and height V o. The charge

by tunneling,

SHENG

~E / m e V

76

(Y..u

bolic

T1 / K

53500

~

aged

TO / K

which

the

[17]:

is a measure

and which,

for

A=0.07

l=0.795-e2/(16~coWVo) the

barrier

[12].

The

v a l u e s of w and V o r e s u l t i n g from our e x p e r i m e n t a l data of T o and T 1 (see Table theory. However, data

i),

in the

approaches temperature thermally

are

not

in a p h e n o m e n o l o g i c a l

is possible,

model:

however,

a

low

consistent

model,

independent

of the

temperature

limit

finite

value

~(T=0)

=

conductivity

A

in SHENG's

an i n t e r p r e t a t i o n of the

applicability of

equ.

i,

the

~o'exp(-Tl/To);

limit T >> To, G(T) b e c o m e s activated

with

of

the

SHENG

conductivity in

the

high

a = a o - e x p ( - T l / T ) being a

with

an

activation

energy

DI7 A E = k T I. Thus,

the SHENG

a formula w h i c h limits

and

as

correctly

which,

interpolates

formula

in

between

a tunneling

(equ.

describes

the high

accordance

these

i) may be r e g a r d e d just as

with

limits.

The

yields

the

conductivity

and

the

low t e m p e r a t u r e

experimental

interpretation width

w

of

of the

data, a(T=0)

potential

barriers:

(2)

TI/T O = v ~ m V ~ - ~ . w . 2 / h (rectangular barriers). data of Fig.

The values of bE and w r e s u l t i n g

1 are shown in Table I. Thus,

from the

reasonable microscopic

p a r a m e t e r s of the b a r r i e r s can be derived. For v e r y low t e m p e r a t u r e s temperature

dependence

the d o m i n a t i n g on

less

fitted

~(T)

=

a

+

higher

of

the

aged

temperatures

expected, and bE.

ageing

g.

in

this

see Fig.

ageing

[18],

~(T)

temperature

only

be

for T

> 50

K

(e.g.

in

Fig.

cannot range,

be but

6 = 0.0247),

2b.

can

leads to an increase

For strong

a change

(~ = 6716 Q-Icm-IK-B,

samples (e.

indicates

samples

b-T 0"5

= ~-T s,

log(~(T))~log(T)+const., ~(T)

which

m u c h steeper

C o n t r a r y to other experiments

polyacetylene

obeys a p o w e r law ~(T) i.e.

observed,

t r a n s p o r t mechanism.

conducting with

is

(T<0.4 K), a different,

fitted

to

in Fig.

equ.

ib).

1 for

As

to be

in the a v e r a g e values 3, curves d-e),

no such

of w fit

is possible.

CONCLUSIONS For fresh samples of high-~ p o l y a c e t y l e n e we c o n c l u d e from our experiments, <

300

K

regions.

that the t e m p e r a t u r e

is

determined

For

becomes

much

causing

an

T

<

Tlo c

stronger, additional

by =

dependence

barriers 400

mK,

of ~ for 400 mK < T

between the

w h i c h may be due resistivity.

highly

conducting

temperature

dependence

to l o c a l i z a t i o n For

aged

effects,

samples,

Tlo c

i n c r e a s e s w i t h i n c r e a s i n g degree of ageing.

ACKNOWLEDGEMENTS We doping

thank and

discussions. ELP

03

E.

Schliebitz

sample

preparation

This w o r k was

C214-I.

for

sample and

supported

synthesis,

E.

Dormann

J.

for

by B A S F / B M F T

Gmeiner

for

many

helpful

within

Project

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