Disordered distribution of defects in polythiophene

Synthetic Metals, 55-57 (1993) 4499-4506

4499

DISORDERED DISTRIBUTION OF DEFECTS IN POLYTHIOPHENE

F.C.

id~VARDA T, M.C.

DOS SANTOS $, D.S. GALVAO§ AND B. I_JkKS

Instituto de Fisica "Gleb Wataghin", Universidade Estadual de Campinas,

C.P.

8165,

13081Campinas

SP,

tDep.

de F i s i c a ,

SDep.

de Q u i m i c a F u n d a m e n t a l

§Bellcore

Brazil

UNESP-Bauru,

- Red Bank,

C.P.

473,

17033

Bauru

- UFPE, 50739 R e c i f e

NJ 07701,

SP,

PE,

Brasil

Brasil

USA

ABSTRACT In

this

work

we

study

the electronic structure associated to

a disordered distribution of bipolarons chain

is

treatment

modelled of

by

obtained

by

and

the

with

elastic

explicit

energy

of

the

interaction

The density of states of the disordered system

the use of the Negative Factor Counting technique.

show that

for the closure

coupling

Hamiltonian

The polymer

The model also includes the electrostatic

due to the counterions.

Our results

tight-binding

electron-phonon

sigma framework.

is

a

in polythiophene.

of

ion-induced conformational

disorder can account

the gap and that the states around the Fermi level

are extended. KEYWORDS:

metallic transition, bipolaron, polythiophene

INTRODUCTION Polythiophene attention

among

developed

in

common

the

order

organic

(PT)

its

conducting to

solvents

like thermochromism

and

produce and

derivatives

polymers.

New

[I]. Besides

a variety

of

studying

the

of

the obvious

physics

and

attracted

synthetic

substituted-PT's

show

offered by these soluble conjugated systems, opportunity

have

that

special

methods

are

soluble

interesting

technological

were in

phenomena advantages

they also have opened the chemistry

of

an

isolated

polymer chain.

Elsevier Sequoia

4500 While

many

different

synthetic

properties, remain

improvements

important

unsolved.

oxidizing

or

electrical doping

It

that

allow

by

excitations

are

(y)

created

in

strong

electron-phonon

systems

in order to store charges

Bipolarons optical

and

polarons created view,

are spinless,

transport

at

low

dopant

bipolarons

polarons

polymer

transferred

singly

at

charged

From

localized

in the metallic

of a common defects

metal

the

bipolaron

critical

regime,

which

due

to

lattice results

[2].

to

doping - are

levels, believed

theoretical

the

be

point

of

in PT [3].

However,

modes

lattice

with the picture array of

At

that

one

hand,

is appropriate

The

lattice

regime

of

model,

Pauli

- but fails

to reproduce

fact that the polapon bipolaron

since

material alfa-beta

lattice

could

other

-

the

hand,

could

characteristic IRAV

[5].

explain

of

intensities

is unstable against

be raised

the

polymer

and

polymerization

linkages

irregularities species

the

the

the

the

metallic

[5], besides

the distortion

the

into a

lattice.

Arguments PT

on

paramagnetism

to

for a

- the density of states vanishes at the Fermi energy

polaron

is

- have been proposed

state.

in a band structure

the

(IRAV)

based on a regular

metallic

to

in PT doped with several

vibrational

models

the

while

semiconductor

appearence

the

one-dimensional

is not consistent

lattice or polaron

transition

as a

the existence

concentration.

infrared-active

[4]. Theoretical

- bipolaron

explain

with

are found to be the most stable excitations

a

polymer moderate

properties

of

the

dopant

found

to

structure

defects

is observed

of

the

Up

strong

and bipolarons

intermediate

concentration.

after

to

doubly charged defects which dominate

chemical

persistence

PT

PT

from the dopant species.

The growing of metallic properties agents

of ordinary

of

and chemical

of

structural

increases

characteristic

properties

- paramagnetic,

of

magnitude.

is consistent

the

coupling

exposure

of

- the so-called

development

control

doping)

of physical

the

the behavior

the

orders

concentration

on

the

that

(chemical

many

the evolution

defects

made

concerning

well-known agents

of conformational These

is

reducing

of dopant

been

questions

conductivity

levels,

function

methods

have

along

should the

chains

[8]. lead

against are

not

defects Among to

material,

a

a periodic regularly cannot

other

affects

of defects

distributed

be

things,

non-uniform

which

array

avoided, those

distribution the

in

in

the

such

as

structural of

dopant

distribution

of

4501 doping-induced structure PT

defects

associated

chain

is

bipolarons

itself.

to a random

investigated.

and

is

varied

calculations

show that,

the valence

(conduction)

further

increasing

energy This

become

model

defects

extended

is also

bipolarons

used

on

in this work

of

into

thus giving

rise

random, a

chain.

In

is briefly

makes the

Our

band merges

into

concentration. around

of

the

By

Fermi

paramagnetism.

IRAV modes

possible

introduced,

dopant

ring.

to Pauli

next

long

between

the

per

states

the persistence

which

and

45Z

dopant

the

in a

interaction

the bipolaron

of dopants,

electronic

bipolarons

approximately

with

the

account

band after a critical number

work,

electrostatic

due to disorder,

states,

at

present

taken to

consistent

distribute

isolated model

the

is up

the

distribution

The

counterions

concentration

In

the

since

presence

of

section

the

theoretical

followed

by a discussion

of our results.

THEORY

AND RESULTS

The

electronic

PT chain

is obtained

H where

structure

~

:

~ electrons

by the use of a tight-binding

+

ionization

energy

to the

li>
{h

is the

hopping

associated

between

energy

sites

of

i and

of a

long

Hamiltonian:

% [i>
the atom

at site

i+I

U

and

is

i

the

~

(i) i.i is the

electrostatic

i

potential

energy

counterions.

The

energy

of

and

depend

f

the

of the atom at site last

sigma on

term

bonds.

the

bond

i due

to the

in eq.

(l)

takes

Due

the

electron-phonon

to

lengths.

We

into

interaction

used

a

account

with

the

coupling,

the

elastic ~.

l,i*l

bond-order-bond-length

i

relationship

given by:

~(R)

f(R)

= - A exp

: C ~(R)

(2)

(-R/B)

[R - R

+ B]

(S)

0

where

R is the bond

parameters

length between

to be optimized.

R

atoms

is usually 0

bond

length

but can also be optimized.

i and i+l, taken

and A, B, and C are

as the standard

2

sp -sp

2

4502 Neutral chain All

adjustable

parameters

were

ground state geometry of PT [5,7],

optimized

to

reproduce:

(i)

the

and (ii) band gaps and band widths

associated to ~ bands [H,7,8]. The resulting geometrical and electronic parameters are: Rc_ s = 1.721 A, Rc~_c ~ = 1.350 A, Rc~_c ~ = 1.441 A, and R

= 1.457 A,

for the bond

lengths

(C-S stands

for carbon-sulfur

C~-C~

bond,

Ca-C~ the ~ carbon-~ carbon bond, etc.),

for the ~-~

band gap and the bandwidth of the valence ~ band are 2.0

eV and 2.8 eV, with

and the values obtained

those

respectively.

obtained

The above

by more

results

sophisticated

are

models,

in good agreement as can

be seen

in

e n e r g y U o f atom i i s c a l c u l a t e d l i s a t t a c h e d to a c o u p l e off c o u n t e r i o n s .

by

Refs. S-8.

Bipolaron The e l e c t r o s t a t i c

potential

assuming t h a t each b i p o l a r o n the exact

geometry associated

to

the

known, we a d o p t e d t h e d i s t r i b u t i o n quaterthiophene

doped

counterions

the

at

conjugation

plane.

with

d o p a n t - c h a i n complex i s

suggested

sodium.

center

of

Civen this

The

adjacent

in Ref.7 for

proposed rings

1.62

geometrical arrangement, U

i

n o t well

the s t u d y of

geometry

and

As

places

the

A above

the

is calculated

as: U= - K ~l{Pii exp[-~ I n eq. net atom

(4) K = e2/4~¢

~ charge i

and

0

vijlxi-xj[]}/{c

[d2+ ( X l - X l ) 2 ] l / 2

= 14.4 eV, j i s t h e c o u n t e r i o n

on atom i ,

d=1.62

counterion

j

A and

projected

index,

( x f - x j)

is

in

conjugation

the

the

(4) P

distance

ti

is the between

plane.

The

constant ¢ accounts for the dielectric screening while the exponential term included in eq. c= 3.0, have

(4) describes a metallic screening [9]. The values

~=0.6 A -i and vi]=O for (xl-x j )< 5 A and ul]=1 for (x i-x ] )> 5 A

been

chosen.

Calculations

were

performed

for a 20-ring

oligomer

interacting with two acceptor species placed above the central rings. blpolaron

distortion

involving four rings:

developed

on

the

central

part

of

the

A

oligomer

the rings at the center distort symmetrically

to

the geometry having Rc_s= 1.724 A, Rc~_c#= 1.410 A, Rc~_c~= 1.377 A and the

central

Rc~_c =

1.390

valence and conduction bands the top of the valence band,

A.

Two

localized

levels

split

from

the

into the gap at O.S eV and 1.23 eV above in agreement with experimental data [I0].

4503 Disordered The

chain effects

including

up to

bipolarons chosen. matrix and

due

to

random

102 thiophene

present

rings.

on the chain,

The bonding parameters following

for

the

technique

the

of

[11]

the and

The

After

a random

values

geometry

numerical Inverse

were

establishing distribution

computed

is no

Iteration

from

5%

to

45%

distributions

of

were per

carried ring

out

The

of was

neutral

to relax.

Factor

was

chain A

Counting

used

to derive

wavefunctions.

both

concentrations regular

evolution

(y) is shown

chain

of defects

allowed

[12]

dopant

considering

bipolarons.

function of dopant content

for

a

the number

the

Negative

Method

on

to the Hamiltonlan

for

longer

techniques

the one-electron spectrum and corresponding Calculations

investigated

were then transferred

converged

bipolaron.

combination

doping

of

and

the

ranging

disordered

band

gap

as

a

in Fig. l.

0.50

0.40

0.30

k

0.20

<

,\ <

O.I0

<
0.00

' 10,0

0,0

~ 20.0

,_

' 30.0

I¸ ,

\,,

4-0.0

50.0

Y (mol~)

Figure I. Band gap (eV) as a function of y Z per ring) for ( bipolaron lattice and (---) disordered distribution of bipolarons.

In

both

remarkable, regular case eV.

cases

the

however,

distribution

a sharp

decrease

that of

gap

vanishes

at

the gap remains defects

takes

up

place

to at

high

doping

constant

y=23Z y=14%

while and

level.

at 0.48 in

the

saturates

In the low gap region of the random distribution,

It

eV for

is the

disordered around

0.04

the states around

4504 the Fermi energy are local[zed until where

they

start

wavefunctions highest

delocalize defects. ends.

for

occupied

HOMO state.

It

the

It may

be

molecular

the

noting

this

some

is just

of

and

are

molecular and

a

three

states

y=29%,

shown

orbital states

particular

those

a feature

plots

Fig. 2

the wavefunctions

containing

that

those

(HOMO)

that

level approaches

In

unoccupied

orbital

regions

appear

to obtain

delocalized.

lowest

is worth

over

However,

adopted

to

the doping

not

the

(LUMO),

just

below

necessarily

concentration

are

bound

of

the

particular

it has

not

been

at

of

chain

distribution

observed

in other

configurations.

~,

(~)

i i/l"

,hi (¢)

¢q

(d)

i!-

1

0.0

200.0

400.0

ATOM INDEX

Figure 2. Plots of the square coefficients for y=81.4% : (a) LUMO; (e) HOMO-3.

The electronic As

can

energy density states

be

seen

lies

of states become

at random

density of states for y=31.4%

all

in a

expansion wavefunct ion (c) HOMO-I; (d) HOMO-2;

of the (b) HOMO;

the

region at

the

delocalized.

band

gaps

are

of extended Fermi Due

in the gap regions

energy

already

states. does

It not

to the disorder

that correspond

is depicted closed

and

is expected change process,

much

in Fig. 3. the

Fermi

that

the

after

the

states

appear

to the parts of' the chain

4505 having

low defect

transition

to

the

concentration.

It

metallic

does

closure of the gap. dopant

but

the

On the other hand,

concentration transition

which

important not

In our calculation,

concentration

energy.

state

is

states

to

to the metallic regime

to be

that

driven

by

the the

the gap is almost closed at low

are

still

delocalization

is close

appear

to observe

that

localized

at

of states occurs

experimentally

the

Fermi

at a dopant

observed

for

the

[13].

:;I) ()

:20 I)

-E

10 0

0.0 ~10.0

-5.0

0.0 Energy

,5.0

lO.I)

(eV)

Figure 3. Histogram of the density of states bipolaron distribution (y=31.4% per ring). The Fermi energy.

for the disordered arrow indicates the

ACKNOWLEDGEMENTS This

work

has

been

supported

by

the

Brazilian

Agencies

FAPESP,

CNPq and CAPES.

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