1

5. Transport in Doped Conjugated Materials

2

Nobel Prize in Chemistry 2000

“For the Discovery and Development of Conductive Polymers”

Alan HeegerUniversity of California at Santa Barbara

Alan MacDiarmid University of Pennsylvania

Hideki Shirakawa University of Tsukuba

3

Conducting Polymers

4

5.1. Electron-Phonon Coupling

E

Q

Absorption

Relaxation effects

Emission

Ground state

Lowest excitation state

Excitations Charges

Ionization

GS

+1

E

Q

Relaxation effects

Optical processes Charge Transport

5

5.1.1. Geometry Relaxation

Polaron / Radical-ion

Polaron-exciton

AM1(CI)

141513

12 16a

a b c d e f g

b c d e f g

6

5.1.2. Geometrical structure vs. Doping level

Radical-cation / Polaron

+

Dication / Bipolaron

++

7

5.1.3. Geometrical Structure vs. Electronic structure

E

Bond length alternation r

A

B

With

in K

oopm

ans

appr

oxim

atio

n

8

Depending on the polymer and doping level, new optical transitions are possible

5.1.4 Electrochromism

Neutral

Singly charged

Doubly charged

visibleInfra-red

E

H

L

Polaron BipolaronNeutral

Spin =1/2Charge = +1

Spin =0Charge = +2

Spin =0Charge = 0

Allo

wed

op

tical

tr

ansi

tion

9

red Green-blue

salt

counterion

10

5.2.1 Prerequisite: Reduction and oxidation reactions

A reduction of a material is the gain of electrons.

M + e- M- Oxy + e- Red

An oxidation of a material is the loss of electrons.

M M+ + e- Red Oxy + e-

This system comes from the observation that materials combine with oxygen in varying amounts. For instance, an iron bar oxidizes (combines with oxygen) to become rust. We say that the iron has oxidized. The iron has gone from an oxidation state of zero to (usually) either iron II or iron III.

Someone, in a fit of perversity, decided that we needed more description

for the process. A material that becomes oxidized is a reducing agent

(Red), and a material that becomes reduced is an oxidizing agent (Oxy).

5.2. Electrochemical doping

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Redox reaction is an electron transfer reaction. Since the number of electrons is constant in a system, there is no reduction of a molecule without oxidation of another chemical species.

e.g.: 2Fe3+ + Sn2+ 2Fe2+ + Sn4+

Sometimes it is easier to see the transfer of electrons in the system if it is split into definite steps.

Sn2+ Sn4+ + 2e- (oxidation)(2+) = (4+) + (2-)

2Fe3+ + 2e- 2Fe2+ (reduction)(6+) + (2-) = (4+) (balanced for charges)

Add the two half equations: 2Fe3+ + 2e- + Sn2+ -> 2Fe2+ + Sn4+ + 2e-

The electrons cancel each other out, so equation is:

2Fe3+ + Sn2+ -> 2Fe2+ + Sn4+

Fe3+ pumps the electrons from Sn2+, Fe3+ is the oxidizing agent since it helps to oxidize Sn2+.

12

5.2.2. One-Electron Structure

E

C C

H

H

H

H

HOMO

LUMO

n

ValenceBand

ForbiddenBand

Conduction

Band

Vacuum level =0 eV

IP=ionization potentialEA= electron affinity

IP

EA

13

Ionization potential vs. chain length

5.4

5.2

5.0

4.8

4.6

4.4

4.2

IP [

eV]

0.100.080.060.040.020.001/NDB

IP[eV]=9.8/NDB+4.2

NDB = number of bonds in the conjugated pathway

n=2n=3

n=4

n=∞

W. Osikowicz et al., J. Chem. Phys., 119, 10415 (2003).

It is easier to remove an electron from a long oligomer (oxidize) than the monomer it-self

n=1 monomern= small oligomern= large polymer

14

Conjugated polymers have a conjugated π-system and π-bands:

As a result, they have a low ionization potential (usually lower than ~6eV)

And/or a high electron affinity (lower that ~2eV)

They will be easily oxidized by electron accepting molecules (I2, AsF5, SbF5,

…) and/or easily reduced by electron donors (alkali metals: Li, Na, K)

Charge transfer between the polymer chain and dopant molecules is easy

When doping neutral conjugated molecules:

A n-doping corresponds to a reduction (addition of electron)

A p-doping corresponds to an oxidation (removal of electron)

15

E (SHE) = -4.44 eV vs. Vacuum level (0 eV)

5.2.3 Cyclic-voltammetry

A. Measure the current for a linear increase of potential

16

+

Polarons produced at potential E1

A-

A-

A-

A-Ele

ctro

de

E1

Ele

ctro

de

B+

B+

B+

B+

Migration of the cationsIn the solvent

Electron transfer= positive doping

Insertion of the anions in the film

B. In electrochemical doping, the doping charge comes from an electrode.

17

time

VSlope= scan speed

E1

E2

0

C. Measure the current for a cyclic linear increase of potential

This defines the reversibility of the electrochemical reaction

18

D. Oxidation and ReductionWhen the electrode potential (V) is varied over a wide potential range, several current peak can be observed.If V> Eox, the electrode captures an electron from the organic molecule (or injection a hole). This is an oxidation or p-doping. Eox is connected to the ionization potential (IP) of the molecule. The negative counterion (anion) comes from the solution to neutralize it.If V< Ered, the electrode injects an electron. This is a reduction or n-doping. The positive counterion (cation) comes close to the negative polaron to stabilize it. Ered is related to the electron affinity (EA)

HOMO

e

LUMO

HOMO

e

reduction oxidation

EA

IP

Ered Eox

19

A series of aromatic hydrocarbons

Electronegativity ENis almost constant vs. size and close to the workfunction of graphite (4.3 eV)

EN=½(IP+EA)

Data taken from E. S. Chen et al, J. Chem. Phys. 110, 9310 (1999)

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A. Positive doping in Poly(p-phenylenevinylene) (PPV)

Radical-cation / Polaron

+

Dication / Bipolaron

++

5.2.4 Electrochemical doping

21

+

++

++

Bipolarons produced at potential E2

Polarons produced at potential E1

A-

A-

A-

A-

A-

A-

A-

A-

A-

A-A-

A-

Ele

ctro

deE

lect

rode

E2

Ele

ctro

de

E1

Ele

ctro

de

B+

B+

B+

B+

B+

B+

B+

B+

Migration of the cationsIn the solvent

Electron transfer= positive doping

Electron transfer= positive doping

Insertion of the anions in the film

A-

Yes, but E1>E2 or E2>E1? Do we form directly bipolarons or first polarons then bipolarons?

22

Example of polypyrrole

23

Binding energy of the polaron

24

25

26

27

28

B. Negative doping in poly(p-phenylene) (PPP)

In electrochemical doping, a bipolaron should be formed a lower potential

29

C. Prove of the bipolaron hypothesis in PPP

a

Negative doping of sexiphenyl

bc

4-

3-

2-a

b

c

The first step (a) is a 2electron-step, thus bipolarons are formed first.No polaron is formed. Note that peaks are purely faradic, i.e., involved in an effectiveelectron transfer

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5.3. Chemical doping

Electrochemical doping: the doping charge comes from the electrode and this is the ions of the salt included in the electrochemical bath that plays the role of the counterion (see previous section).

Chemical doping: the doping charge (electron or hole) on the conjugated molecules or polymers comes from another chemical species C (atom or molecule). The chemical species C become the counterions of the polarons created on the conjugated materials.

A strong electron donor (reducing agent) can be used to dope negatively a neutral conjugated material or to undope a positively doped material (see next slide).Example: tetrakis(dimethylamino)ethylene (TDAE), alkali metal (Li, Na, K,...)

A strong electron acceptor (oxidizing agent) can be used to dope positively a neutral conjugated material or to undope a negatively doped material. Example: NOBF4 , halogen gas (I2, ...)

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5.3.1 Examples of dedoping and doping

400 600 800 1000 1200 1400 1600-0.15

-0.10

-0.05

0.00

0.05

0.10

AS

ampl

e -

AR

ef

Wavelength (nm)

10 min TDAE exp 20 min TDAE exp 30 min TDAE exp 40 min TDAE exp

K. Jeuris et al., Synth. Met. 132 (2003) 289

PEDOT-C14 + NOBF4 → [PEDOT-C14]+BF4- + NOg

[PEDOT-C14]+BF4- + NOBF4 → [PEDOT-C14]2+(BF4

-)2 + NOg

PEDOT2+PS(S-)2 + TDAE → PEDOT+TDAE+PS(S-)2

PEDOT2+PS(S-)2 + TDAE → PEDOT+TDAE+PS(S-)2

bipolarons polarons

polarons neutral

neutral polarons

polaronsbipolarons

F. L. E. Jakobsson et. al., Chem. Phys. Lett, 433, 110 (2006)

DEDOPING: PEDOT-PSS (p-doped) is exposed to a vapor of TDAE and undergoes dedoping. Peaks in the IR dissapear, peak in the visible appears. The conductivity drops.

DOPING: PEDOT-C14 (neutral) is exposed to a NOBF4 and undergoes doping. A first Peak in the IR appear (800-1000nm=polaron), then a second broad band at higher . The peak in the visible disappears. The conductivity increases.

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Jiang, X et. al. Chemical Physics Letters 2002, 364, (5-6), 616.

Doping-induced change of carrier mobilities in poly(3-hexylthiophene) films with different stacking structures.

33

ES

EB

Emeraldine base

Emeraldine salt

The doping of PAni is done by protonation (using an acid), while with the other conjugated polymer it is achieved by electron transfer with a dopant or electrochemically

5.3.2 A special case for chemical doping:protonation of polyaniline (PAni)

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5.3.3. Secondary doping: Morphology change induced by an inert molecule

CSA-= camphor sulfonate

Cl-= Chlorine anion

The morphology of polyaniline films is modified with the chemical nature of the acid used for doping. The doping level is not changed, but this is the nature of the counterions that induces a change in morphology and packing of the conjugated chains. CSA-, more bulky than Cl- helps the chains to pack better, such that the disorder is reduced.

M. Reghu et al. PRB, 1993, 47, 1758

Example 1: polyaniline

35

PSS

PEDOT-PSS

0.01 0.1 1 10

100

10

1

0.1

0.01

0.001

Co

nd

uct

ivit

y (S

/cm

)

%w (DEG) AFM phase image

The conductivity of PEDOT-PSS increases by three orders of magnitude by using the secondary dopant diethylene glycol (DEG). This phenomena is attributed to a phase segregation of the excess PSS resulting in the formation of a three-dimensional conducting network.

Poly(3,4-Ethylenedioxythiophene) - Polystyrenesulfonate

PE

DO

T

PS

S

OHO

OH

diethyleneglycol

Example 2: Poly(3,4-Ethylenedioxythiophene) - Polystyrenesulfonate

X. Crispin et al. Chemistry of Materials, 18, 4354 (2006)

36

5.4. Variable range hopping conduction

Occupied states

The charge transport occurs in a narrow energy region around the Fermi level. The charge can hop from a localized occupied state to a localized empty state that are homogeneously distributed in space and around εf. i.e. with a constant density of states N(ε) over the range [εf – ε0, εf – ε0].

N(ε)dε= number of states per unit volume in the energy range dε.2ε0 is the width of the “band” involved in the transport. The localized character of a state is determined by the parameter r0.

empty states

The energy difference between filled and empty states is related to the activation energy necessary for an electron hop between two sites

Valence Band

Band edge

37

In the VRH model, the reorganization energy is considered to be negligible. Hence, by assuming that, the hopping rate in the VRH becomes very similar to that used in the semi-classical electron transfer theory by Marcus. The hopping rate of the charge carrier between two sites i and j is:

E = activation energy

t= transfer integral

N(ε)= density of states

kT

Etk

ijETij exp2

02exp

r

rt ij

The localization radius r0 in Mott’s theory appears to be related to the rate of fall off of t with the distance rij between the two sites i and j (see previous chapter).

kT

E

r

rTrP

ijij

0exp),(

The hopping probability from site i to site j in the transport band formed localized states is:

(1)

38

In this “band”, the average energy barrier for a charge carrier to hop from a filled to an empty state is <Eij>=ε0. (2)

The concentration C(ε0) of states in the solid characterized by the band width 2ε0 is [N(εf) 2ε0]= number of states per volume in the band.

The average distance between sites involved is <rij>= [C(ε0)]-1/3= [N(εf) 2ε0]-1/3 (3)

The average hopping probability between two states [inject (2) and (3) in (1)]:

Narrow band made of localized states

(4)

kTrTP 0

0

3/100

0

)2εN(εexp),(

39

P(0)=exp-(0^(-1/3)+0)

0

0 2 4 6 8 10 12

P(

0)

0,0

0,2

0,4

0,6

0,8

1,0

P(0)=exp-[(0)^(-1/3)]: from <rij>

P(0)=exp-(0): from <E>=0

The maximum for the average hopping probability is obtained for an optimal band width:

1) First term- electronic coupling<rij>= [N(εf) 2ε0]-1/3

If wide band, i.e. ε0 large, many states are available per volume it is easy to find a neighbor site j such that Eij<ε0

<rij> decreases, t increases and kij

ET increases

2) Second term-activation energy<E>=ε0

If ε0 large, the activation barrier is large and the charge transfer is difficult, kij

ET drops

4/13

0

4/3max0

max0

)()(

rN

kTT

f

kTrTP 0

0

3/100

0

)2εN(εexp),(

40

(i) kET or P(ε0,T) is proportional to the mobility of the charge carrier

(ii) Conductivity σ = n|e| , with n the density of charge carrier

(iii) The conductivity of the entire system is determined in order of magnitude by the optimal band (States out of the band only slightly contribute to σ).

Conductivity σ (T) ÷ P(ε0max,T)

4/100 /exp)( TTT

30

0 )( rkNT

f

The numerical coefficient η is not determined in this course

Mott’s law

Optimal band

41

5.4.1. Average hopping length <r>

<r> = average distance rij between states in the optimal band

4/1

00

3/1max0 /)( TTrNr f

In Mott’s theory, the hopping length changes with the temperature.

That’s why this model is also called ”variable range hopping”.

As T decreases, the hopping length <r> grows.

Indeed, as T decreases, the hopping probability decreases, so the volume of available site must be increased in order to maximize the chance of finding a suitable transport route.

However the probability ω per unit time for such large hops is small:

4/1/exp TB B is a numerical factor related to N(εf)

Col 1 vs Col 2 <R>=(1/T)1/4

T

0 2 4 6 8 10 12

<R

> a

nd

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

=exp(-1/T1/4)

42

1/100 /exp)( dTTT

Mott’s theory was developed for hopping transport in highly disordered system with localized states characterized by a localization length r0. Not too small values of r0 (also related to the transfer integral t) are necessary to be in the VRH regime.

If r0 is too small, i.e. if the carrier wavefunction on one site is very localized, then hopping occurs only between nearest neighbors: this is the nearest-neighbor hopping regime.

The situation of high disorder, thus the homogeneous repartition of levels in space and energy, is not strictly true for polymers with their long coherence length and aggregates. However, it has some success for an intermediate doping and conductivity.

A more general expression is given with d the dimensionality of the transport.

5.4.2. Limits of Mott’s law

43

When the coulomb interaction between the electron which is hopping and the hole left behind is dominant, then the conductivity dependence is

In general in the semiconducting regime:

2/100 /exp)( TTT

x

x

TT

TTT/1

/10

)(ln

/exp)(

Where x is determined by details of the phonon-assisted hopping

Efros-Shklovskii

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5.5. Metal-Insulator transition

The temperature dependence of the resistivity of PANI-CSA is sensitive to the sample preparation conditions that gives various resistivity ratios that are typically less than 50 for PANI-CSA.

Metallic regime for ρr < 3: ρ(T) approaches a finite value as T0Critical regime for ρr= 3: ρ(T) follows power-law dependenceInsulating regime ρr > 3: ρ(T) follows Mott’s law

ρ(T)=aT-β (0.3<β<l)Ln ρ(T)=(T0/T)1/4

ρ=1/σC

ondu

ctiv

ity in

crea

ses

Temperature increases

The resistivity ratio: ρr= ρ(1.4K)/ ρ(300K)

45

C.O. Yom et al. /Synthetic Metals 75 (1995) 229-239

Zabrodskii plot

The reduced activation energy: W= -T [dlnρ(T)/dT] = -d(lnρ)/d(lnT)

Metallic regime: W>0Critical regime: W(T)= constantInsulating regime: W<0

The systematic variation from the critical regime to the VRH regime as the value of ρr increases from 2.94 to 4.4 is shown in the W versus T plot. This is a classical demonstration of the role of disorder-induced localization in doped conducting polymers.

Dis

orde

r in

crea

ses

46

PEDOT

K.E. Aasmundtveit et al. Synth. Met. 101, 561-564 (1999)

3.4 Åa = 14 Å

c =

7.8

Å

e-

e-

b =

6.8

Å

PEDOT-Tos

The arrow indicates the critical regime

Kiebooms et al. J. Phys. Chem. B 1997, 101, 11037

At low T, metal regime occurs and charge carriers are delocalized