Transcript Slide 1

5. Transport in Doped Conjugated Materials
2+
+
n
3 I2
+
n
2 I 31
Nobel Prize in Chemistry 2000
“For the Discovery and Development of Conductive Polymers”
Hideki Shirakawa
University of Tsukuba
Alan Heeger
University of California
at Santa Barbara
Alan MacDiarmid
University of
Pennsylvania
2
Conducting Polymers
3
5.1. Electron-Phonon Coupling
Excitations
Charges
E
E
Lowest
excitation
state
+1
Relaxation
effects
Absorption
Emission
Relaxation
effects
GS
Ground
state
Q
Optical processes
Ionization
Q
Charge Transport
4
5.1.1. Geometry Relaxation
14
a
c
b
a
0.04
AM1(CI)
13
b
12
d
c
d
15
16
e
e
f
f
g
0.03
Change in C-C bond-length
g
 Polaron / Radical-ion
0.02
 Polaron-exciton
0.01
0.00
-0.01
-0.02
-0.03
-0.04
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28
site number
5
5.1.2. Geometrical structure vs. Doping level
Radical-cation / Polaron
+
Dication / Bipolaron
++
6
5.1.3. Geometrical Structure vs. Electronic structure
E
B
Within Koopmans approximation
A
Bond length alternation r
7
5.1.4 Electrochromism
Depending on the polymer and doping level, new optical transitions are possible
E
Neutral
Bipolaron
Polaron
Allowed
optical
transition
L
H
Spin =0
Charge = 0
Spin =1/2
Charge = +1
Infra-red
Spin =0
Charge = +2
visible
Intensity (arb. units)
100
Doubly charged
80
Neutral
60
Singly charged
40
20
0
0.0
0.5
1.0
1.5
Energy (eV)
2.0
2.5
8
salt
red
counterion
Green-blue
9
5.2. Electrochemical doping
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).10
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+ + 2eThe 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
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to oxidize Sn2+.
5.2.2. One-Electron Structure
Vacuum level =0 eV
E
EA
Conduction
Band
LUMO
IP
Forbidden
Band
Valence
Band
HOMO
H
H
C
H
C
n
H
IP=ionization potential
EA= electron affinity
12
Ionization potential vs. chain length
IP[eV]=9.8/NDB+4.2
5.4
IP [eV]
5.2
5.0
n=2
4.8
n=3
n=4
4.6
4.4
n=∞
4.2
0.00
0.02
0.04
0.06
1/NDB
0.08
0.10
n=1  monomer
n= small  oligomer
n= large  polymer
NDB = number of bonds in the conjugated pathway
 It is easier to remove an electron from a long oligomer (oxidize) than
the monomer it-self
13
W. Osikowicz et al., J. Chem. Phys., 119, 10415 (2003).
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)
14
5.2.3 Cyclic-voltammetry
A. Measure the current for a linear increase of potential
E (SHE) = -4.44 eV vs.
Vacuum level (0 eV)
15
B. In electrochemical doping, the doping charge
comes from an electrode.
Electrode
A-
+
Insertion of the anions
in the film
B+
A-
B+
B+
A-
Electron transfer= positive doping
E1
A-
B+
Migration of the cations
In the solvent
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Electrode
Polarons produced at potential E1
V
C. Measure the current for a cyclic linear increase of potential
Slope= scan speed
E2
0
E1
time
This defines the reversibility of
the electrochemical reaction
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D. Oxidation and Reduction
When 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)
reduction
e
LUMO
HOMO
Ered
oxidation
EA
IP
e
HOMO
Eox
18
A series of aromatic hydrocarbons
Electronegativity EN
is almost constant
vs. size and close to
the workfunction of
graphite (4.3 eV)
EN=½(IP+EA)
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Data taken from E. S. Chen et al, J. Chem. Phys. 110, 9310 (1999)
5.2.4 Electrochemical doping
A. Positive doping in Poly(p-phenylenevinylene) (PPV)
Radical-cation / Polaron
+
Dication / Bipolaron
++
20
+
Electrode
A-
B+
A-
B+
B+
A-
A-
Electrode
Insertion of the anions
in the film
Polarons produced at potential E1
B+
Migration of the cations
In the solvent
Electron transfer= positive doping
E1
Bipolarons produced at potential E2
A-
++
Electrode
B+
A-
A-
A-
A-
++
B+
A-
B+
A-
A-
B+
Electron transfer= positive doping
E2
Yes, but E1>E2 or E2>E1?
21
Do we form directly bipolarons or first polarons then bipolarons?
Electrode
A-
Example of polypyrrole
22
Binding energy of the polaron
23
24
25
26
27
B. Negative doping in poly(p-phenylene) (PPP)
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 In electrochemical doping, a bipolaron should be formed a lower potential
C. Prove of the bipolaron hypothesis in PPP
Negative doping of sexiphenyl
a
2-
b
3c
b
a
c
4-
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 effective
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electron transfer
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
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.
0.10
ASample - ARef
0.05
0.00
PEDOT2+PS(S-)2 + TDAE → PEDOT+TDAE+PS(S-)2
10 min TDAE exp
20 min TDAE exp
30 min TDAE exp
40 min TDAE exp
-0.05
-0.10
-0.15
400
600
800
1000 1200 1400 1600
Wavelength (nm)
bipolarons
polarons
PEDOT2+PS(S-)2 + TDAE → PEDOT+TDAE+PS(S-)2
polarons
neutral
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 l. The peak in the visible disappears.
The conductivity increases.
PEDOT-C14 + NOBF4 → [PEDOT-C14]+BF4- + NOg
neutral
polarons
[PEDOT-C14]+BF4- + NOBF4
→ [PEDOT-C14]2+(BF4-)2 + NOg
polarons
K. Jeuris et al., Synth. Met. 132 (2003) 289
F. L. E. Jakobsson et. al., Chem. Phys. Lett, 433, 110 (2006)
bipolarons
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Doping-induced change of carrier mobilities in poly(3-hexylthiophene)
films with different stacking structures.
Jiang, X et. al. Chemical Physics Letters 2002, 364, (5-6), 616.
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5.3.2 A special case for chemical doping:
protonation of polyaniline (PAni)
EB
Emeraldine base
Emeraldine salt
ES
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
33
5.3.3. Secondary doping: Morphology change
induced by an inert molecule
Example 1: polyaniline
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 Clhelps the chains to pack better,
such that the disorder is reduced.
M. Reghu et al. PRB, 1993, 47, 1758
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Example 2: Poly(3,4-Ethylenedioxythiophene) - Polystyrenesulfonate
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 threedimensional conducting network.
diethyleneglycol
O
OH
100
PSS
PEDOT
HO
10
1
Conductivity (S/cm)
0.1
0.01
PSS
0.001
0.01
0.1
%w (DEG)
1
10
AFM phase image
X. Crispin et al. Chemistry of Materials, 18, 4354 (2006)
Poly(3,4-Ethylenedioxythiophene) - Polystyrenesulfonate
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5.4. Variable range hopping conduction
The
energy
difference
between filled and empty
states is related to the
activation energy necessary
for an electron hop between
two sites
empty states
Occupied
states
Band edge
Valence Band
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.
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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:
k
ET
ij
  Eij 
 t exp

 kT 
2
  rij 

t  exp
 2r 0 
E = activation energy
t= transfer integral
N(ε)= density of states
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).
 The hopping probability from site i to site j in the transport band formed
localized states is:
 rij Eij 
P(r , T )  exp  

 r 0 kT 
(1)
37
Narrow band made of
localized states
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)]:
 N(ε 0 )2ε 0 1/ 3  0 

P( 0 , T )  exp 

r0
kT 

(4)
38
 N(ε 0 )2ε 0 
P( 0 , T )  exp 
r0

1 / 3

1) First termcoupling
<rij>= [N(εf) 2ε0]-1/3
 0 
kT 
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
1,0
P(0)=exp-(0): from <E>=0
0,8
P(0)=exp-[(0)^(-1/3)]: from <rij>
0,6
P(0)
electronic
 <rij> decreases, t increases
and kijET increases
0,4
2) Second
energy
<E>=ε0
P(0)=exp-(0^(-1/3)+0)
0,2
0,0
0
2
4
6
8
10
0
The maximum for the average hopping probability
is obtained for an optimal band width:
12
term-activation
If ε0 large, the activation
barrier is large and the charge
transfer is difficult, kijET drops
 0max   0max (T ) 
kT 3 / 4
N (
f

39
3 1/ 4
0
)r
Optimal band
(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)

 (T )   0 exp  T0 / T 
T0 

kN ( f )r03
1/ 4

Mott’s law
The numerical coefficient η is not determined in this course 40
5.4.1. Average hopping length <r>
<r> = average distance rij between states in the optimal band

 r  N ( f )

max 1/ 3
0

 r0 T0 / T

1/ 4
1,4
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.
<R> and 
1,2
1,0
Col 1 vs Col 2
0,6
0,4
0,2
=exp(-1/T )
1/4
0,0
2
However the probability ω per unit time for such
large hops is small:
1/ 4
1/4
0,8
0
  exp B / T 
<R>=(1/T)
4
6
8
10
T
B is a numerical factor related to N(εf)
 In Mott’s theory, the hopping length changes with the temperature.
That’s why this model is also called ”variable range hopping”.
41
12
5.4.2. Limits of Mott’s law
 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.

 (T )   0 exp  T0 / T 
1/ d 1

42
 When the coulomb interaction between the electron which is hopping and the hole
left behind is dominant, then the conductivity dependence is

 (T )   0 exp  T0 / T 
1/ 2

EfrosShklovskii
 In general in the semiconducting regime:

 (T )  exp  T0 / T 1 / x

ln  (T )  T 1 / x
Where x is determined by details of the phonon-assisted hopping
43
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.
Conductivity increases
5.5. Metal-Insulator transition
The resistivity ratio:
ρr= ρ(1.4K)/ ρ(300K)
ρ=1/σ
Temperature increases
Metallic regime for ρr < 3: ρ(T) approaches a finite value as T0
Critical regime for ρr= 3: ρ(T) follows power-law dependence
ρ(T)=aT-β (0.3<β<l)
44
Insulating regime ρr > 3: ρ(T) follows Mott’s law Ln ρ(T)=(T0/T)1/4
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.
Zabrodskii plot
Metallic regime: W>0
Critical regime: W(T)= constant
Insulating regime: W<0
Disorder increases
The reduced activation energy:
W= -T [dlnρ(T)/dT] = -d(lnρ)/d(lnT)
45
C.O. Yom et al. /Synthetic Metals 75 (1995) 229-239
PEDOT
PEDOT-Tos
c = 7.8 Å
e-
a = 14 Å
3.4 Å
b = 6.8 Å
e-
The arrow indicates the critical regime
At low T, metal regime occurs and
charge carriers are delocalized
46
K.E. Aasmundtveit et al. Synth. Met. 101, 561-564 (1999) Kiebooms et al. J. Phys. Chem. B 1997, 101, 11037