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Electronic Structures and Optical Absorption of NType Conducting Polymers at Different Doping Levels Sarbani Ghosh, Viktor Gueskine, Magnus Berggren, and Igor V. Zozoulenko J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04634 • Publication Date (Web): 06 Jun 2019 Downloaded from http://pubs.acs.org on June 7, 2019
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The Journal of Physical Chemistry
Electronic Structures and Optical Absorption of N-type Conducting Polymers at Dierent Doping Levels Sarbani Ghosh, Viktor Gueskine, Magnus Berggren, and Igor V. Zozoulenko
∗
Department of Science and Technology, Linköping University, SE-601 74 Norrköping, Sweden
E-mail:
[email protected] Abstract
with the available experimental results.
The
electronic structure and optical absorption for Theoretical
understanding
of
the
electronic
dierent reduction levels presented here are
structure and optical transitions in n-doped
generic to a wide class of conducting poly-
conducting polymers is still controversial for
mers, which is illustrated by the corresponding
polaronic and bipolaronic states and is com-
calculations for another archetypical conduct-
pletely missing for the case of a high doping
ing polymer, poly(3,4-ethylenedioxythiophene)
level. In the present paper, the electronic struc-
(best known as PEDOT).
ture and optical properties of the archetypical
n-doped
stranded
conducting
polymer,
double-
benzimidazo-benzophenanthroline
Introduction
ladder (BBL) are studied using the density functional theory (DFT) and time-dependent
Conducting
state in the BBL chain is a spin-resolved dou-
have been extensively studied in many opto-
blet where the spin-degeneracy is lifted.
electronic applications including organic light-
The
polymers
since
2
ground state of two electrons corresponds to a
emitting diodes (OLEDs,
triplet polaron pair, which is in stark contrast
ical transistors (OECTs),
to a commonly accepted picture where two
fect
transistors
electrons are postulated to form a spinless bipo-
transistors
(OTFTs),
laron. The total spin gradually increases until
(OPVs),
sensors
the reduction level reaches
cred = 100%
7,8
bio-applications.
(i.e.
11
9
discovery
organic electrochem-
3,4
(OFETs),
6
their
1
(TD) DFT method. We nd that a polaronic
5
organic eld eforganic
organic
thin- lm
photovoltaics
and other energy
10
and
Although the conductive na-
one electron per monomer unit). With further
ture of the polymers is related to the presence
increase of the reduction level, the total spin de-
of the
backbones and
creases until it becomes 0 for the reduction level
the
chains enabling
cred = 200%.
charge motion through the material, the ma-
The calculated results reproduce
π -conjugation in their π -π stacking between the
π -conjugated
the experimentally observed spin signal without
jority of pristine (as-synthesized)
any phenomenological parameters.
polymers show either intrinsically insulating
A detailed
analysis of the evolution of the electronic struc-
nature or very low conductivity.
ture of BBL and its absorption spectra with
tivity of the conjugated polymers is drastically
increase in reduction level are presented. The
increased by means of doping
calculated UV-vis-NIR spectra are compared
dard electrochemical cyclic voltammetry or by
12
The conduc-
using the stan-
applying redox chemistry. In this way, it is pos-
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Page 2 of 19
sible to make a polymer as p-type (hole trans-
ity
port) and n-type (electron transport) material
[4',5':5,6]benzimidazo
by respectively p- and n-doping. Because of a
10,11-tetrayl)-10-carbonyl] polymer as an ideal
strong interaction between electronic and lat-
n-doped polymer. This polymer, which is com-
tice degrees of freedom, charge carriers in con-
monly known as ladder-type poly-benzimidazo-
ducting polymers are strongly localized over a
benzophenanthroline (BBL) was rst discov-
distance of several monomer units thus forming
ered in 1966
quasiparticles termed as polarons.
make
poly[(7-oxo-7,10H-benz[de]imidazo
36
[2,1-a]isoquinoline-
3,4:
in the laboratory of Van Deusen.
Two po-
BBL has an unique structural arrangement
larons can be further transformed into a single
where naphthalenic and benzoid units are con-
spinless quasiparticle, bipolaron, if the energy
densed with N-imino amide units.
gain due to the lattice re-organization exceeds
dimensional
the Coulomb repulsion energy.
This two-
polymer has an excellent ther◦ mal stability up to 600 C due to the unique
13
The p-type polymers have been widely stud-
ladder/sheet construction.
3638
However,
the
ied in the past due to their better stability com-
pristine (as-synthesized) BBL polymer is an
pared to n-type polymers.
insulator in nature with the conductivity σ ∼4×10−4 S/cm. 39 Since 1960, a number of
14
Polythiophenes,
poly(p-phenylene vinylene), poly uorene
16
15
and
their derivatives are the commonly used p-
double-stranded ladder polymers were synthe-
type polymers.
sized that exhibited excellent stability both in
Among the p-type polymers,
poly(3,4-ethylenedioxythiophene)
(PEDOT)
air and nitrogen.
36
The study of the electronic
have been extensively studied due to its high
and optical properties of this stable polymer
p-doped conductivity and high chemical sta-
were reported in eighties when BBL lms have
bility
been doped by chemical/electrochemical means
1720
(for recent reviews see e.g.,
2123
Poly-benzimidazo-benzophenanthroline
).
lad-
as the n-type and p-type materials.
3945
The
der type (BBL) and semiladder type (BBB),
doped
poly-bisindeno uorenedicyanovinylene (P-CN),
(∼2 S/cm) based on electrondonor strength
poly-naphthalene diimide (PNDI) derivatives,
polymers
(p-type)
45,46
exhibit
high
conductivities
which is attributed to the back-
poly-perylene diimide (PPDI) derivatives are
bone planarity of the polymer. It is noteworthy
the commonly used n-type polymers.
that the electron mobility of BBL matches the
2426
Note
that PEDOT is also possible to study as the
hole mobility of P3HT.
n-type material
the
20,2730
with a remarkable stabil-
performance
of
ity. Unfortunately, most of the n-type polymers
electronic devices,
have the stability issue at ambient condition.
counterpart
31
to
47
the
Hence, to enhance all-polymer
organic
BBL can act as a good
the
best
p-type
materials.
48
The negative doping of the polymer to form
N-doping of BBL using the reducing agent,
an n-type material makes them very sensitive
tetrakis(dimethylamino)ethylene (TDAE) gives
to ambient water and air which may result in
the conductivity enhancement to
unstable lms.
32
49
∼2.4
S/cm. + The ion-implanted doping of BBL lm by B , + + Ar , Kr ions gives the conductivity rise to
As a result, the performance
of n-type polymer is typically not up to the
∼200
mark as compared to their p-type counter-
S/cm without any signi cant alteration
in the structure of the pristine polymers.
parts. Hence, the need of the hour is to nd an ideal n-type polymer with high electron mobil-
50
The property that dierentiates the ladder
ity and good ambient stability to improve the
(double-stranded)
performance of the organic electronic devices.
(single-stranded) polymers is the retention of
In addition, the high electron a nity of n-type
the mechanical and structural properties upon
polymer could reduce the energy barrier of the
doping.
interface between the polymer and the cathode
7.5 Å
to have a smooth electron transfer.
that the polymeric lm made of BBL shows
34
33
2
−1
50
polymers
from
non-ladder
Two prominent peaks at 3.3 Å
and
in the X-ray diraction spectra reveal
50
The high electron mobilities (∼0.1cm V −1 35 s ), low ionization potential (4.0-4.4 eV),
formation of crystalline structure.
high structural and thermo-oxidative stabil-
doped polymers, and in particular, to BBL
Currently,
there is a strong renewed interest to the n-
ACS Paragon Plus Environment 2
Page 3 of 19
which is motivated by e.g., their utilization in
tion of two polarons leads to a spinless state as
thermoelectric applications, where both n- and
shown in Figure 1b.
p- doped materials are required for the device
ory predicts a qualitatively dierent electronic
operation.
structure for n-doped polymers. Namely, a po-
49
However, the DFT the-
laron state corresponds to the electron con gu-
7
↑ 3
0
↑↓
3
↑↓
0
-2
-2
↑
-2
1 0
Figure 1:
2 1
3
0
↑↓
7 5 3
0
b)
0
7 5
0
a)
↓
-2 c) 302
↑↓
0
d) 13 2 1
1 0
Schematic electronic structure of
gap between the valence and conduction bands as shown in Figure 1c.
5153
A bipolaron state
corresponds to a spinless electron con guration as shown in Figure 1d.
-2
ration where a spin degeneration is lifted and a single occupied molecular orbital appears in the
52
The electronic structures of n-doped conduct-
Occupied levels
↑↓
5
E(eV)
3
↑
7
5
E(eV)
5
E(eV)
↑↓
E(eV)
↑↓
bipolaron
polaron
E(eV)
bipolaron
polaron
7
Existing DFT-predictions
pre-DFT approaches
Empty levels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
ing polymers presented above have been calculated for polythiophenes (PTs) as poly(p-phenylene) (PPP).
2
53
51,52
as well
So far, DFT-
based calculations of the electronic structure
3 2
3
3
of BBL is missing.
(Note that a DFT study
polaron and bipolaron states in n-doped con-
of the optical absorption and electronic struc-
ducting polymers.
ture in undoped BBL has been recently re-
theories. tions.
13
5153
a), b) traditional pre-DFT
c), d) existing DFT-based calcula-
ported by Kim et al. tion
in
BBL
for
60
the
and optical absorp-
case
of
an
electron-
polaron have been recently reported by Wang et al.
Although electronic and optical properties of
49
). It should also be mentioned that the
the n-doped BBL polymer have been exten-
above-cited studies of n-doped PTs and PPPs
sively studied experimentally, the correspond-
were limited to the case of the relatively low
ing theoretical understanding is not satisfac-
doping levels, with the charge on the multi-
tory, with only a few theoretical studies of its
monomer chain
electronic structure based on the pre-DFT semi-
2e (bipolaron).
empirical approaches from early nighties treat-
sorption spectrometry study of multielectron
ing BBL as an in nite periodic chain.
reduction of some oligomers,
54,55
It
Q =-1e
52
(polaron)
51,52 53
and -
In this context, recently, abe.g.,
poly uo-
should be mentioned that current literature on
renes with hexyl (pF) and butyloctyl (pBuoF)
conducting polymers (both p- and n-doped) is
groups, poly(phenylene-vinylene) (PPV), and
still strongly dominated by a traditional pic-
ladder-type poly(para-phenylene) (LPPP) and
ture of the electronic structure based on the
2,7-(9,9-dihexyl uorene) were studied by Miller
pre-DFT semi-empirical approaches developed
and co-workers.
In the present study we calculate the elec-
in eighties and early nighties (for a review see e.g.,
13
61,62
tronic
). However, for p-doped polymers, there
structure
modern DFT-based picture predicting qualita-
(TD)-DFT method. A special attention is given
tively dierent electronic structure and opti-
to the evolution of the electronic structure, spin
cal transition in conducting polymer.
5153,5659
signal and optical absorption with the varia-
Much less work has so far been done on n-doped
tion of the doping level, when the charge on
polymers. The traditional picture predicts that
the chains varies from
upon doping with electrons, a pair of a spin-
sponding to the doping (reduction) level up
degenerate states appear in the gap, see Fig-
to
ure 1a,b.
For the case of an electron-polaron
unit). We also calculate the optical absorption
(one extra electron in a chain), the states are
at dierent doping levels, and relate the calcu-
lled as illustrated in Figure 1a.
lated absorption peaks in the spectrum to the
A combina-
ACS Paragon Plus Environment 3
(i.e.
and
absorption
oligomers using the DFT and time-dependent
cred = 200%
neutral
optical
pre-DFT approaches should be replaced by the
13
the
the
spectra
2
of
and
is now a growing consensus that the traditional
Q =-1e
n-doped
BBL
to -6e, corre-
2 charges per monomer
The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
transition between dierent states.
Page 4 of 19
Based on
problem inherent to many popular function-
the calculated absorption spectra we analyze
als such as B3LYP, and quantitatively repro-
the available experimental results. Finally, we
duces electronic properties of conjugated poly-
stress that the calculated results concerning
meric systems (polyenes, thiophenes and other
the character of the electronic band structure
oligomers), including the electron a nities, ion-
and optical transition at dierent doping levels
ization energies and the excitation energies.
presented in this paper are not only speci c
(Note that the charge is given in units of
to BBL, but are also generic to a wide class
Spin-restricted DFT calculations were carried
of n-doped conducting polymers. We illustrate
out for the neutral chain (Q
this by performing calculations for n-doped
case of the singlet states of the chains with
= 0)
PEDOT, whose electronic structure and the
even number of electrons (Q
absorption spectra qualitatively show the same
−6).
features as those of BBL.
the polymer, as shown in Figure 2a.
jacent fused imidazole rings is called as
B.
N
be found in Ref.
Indeed, starting from
culations result in well converged bound states is due to the limited basis set, which eectively creates a barrier for the extra electron; this is well understood in the literature.
see Figure S1,S2 in the
ions in the gas phase.
der to save computational eorts, all the results
N = 3.
solid or cluster cages.
pack-
to Zheng et al.
= 0) and n-doped single polymer chain (Q = −1, −2, −3, −4, −5, −6) were optimized 64 65 at ω B97XD /6-31+G(d) level of DFT. ω B97XD is the range-separated hybrid funcaccounts
for
22%
71
even -2.
41,70
and according
Therefore, the ex-
istence of multiply charged polymer chains is an established experimental fact. In our calculations, as it will be shown below, the higher occupied states of BBL anions do not quali-
Hartree-Fock
tatively change with increasing charge.
(HF) exchange at a short range, and 100% HF exchange at a long range.
In the case of BBL, the
per monomer is at least -1,
Neutral single polymer chain
(Q
that
69
measurements attest that an attainable charge
age without imposing any constraints on ini-
tional
In condensed mphase,
the gas phase but becomes a stable moiety in
All the geometry optimizations for this study
tial structures.
All the
the situation changes drastically. For exam− ple, it is well known that O(2 ) is unbound in
presented in this study are reported for BBL
63
67,68
above mentioned studies refer to isolated an-
Therefore, in or-
09
-1.333
as shown in Figure S3. The fact that the cal-
monomer units.
Gaussian
(i.e.
a nities turn out to be increasingly positive,
absorption spectra show the same features for
using
Q = −4,
charges per monomer) the calculated electron
to be three
We found that the electronic structure and the
performed
56
the question naturally arises if they are bound.
We
lated the properties of BBL oligomer with the
were
A detailed
When dealing with multiply charged anions,
monomer units. In this context, we also calcu-
oligomers with
and
discussion of the choice of the functional can
refer to BBL as an oligomer instead of polymer
Supplementary Information.
and for the
ω B97XD/6-31+G(d)
by applying the similar spin rule.
Here, in
and the benzene ring with two ad-
N = 6,
−5)
Vis/NIR absorption spectra
level of theory i.e.,
ring with two adjacent fused pyridine rings is
N = 6
and
were calculated by using TD-DFT at the same
this paper, the unit containing the naphthalene
as we consider its chain length
= −1, −3
paired electrons.
naphthalenic ring to form one monomer unit of
and
and
number of electrons in order to account the un-
ring is fused between one benzene ring and one
N = 3
= −2, −4
case of the triplet states of the chains with even
BBL is an unique polymer where one imidazole
longer chain length of
and for the
carried out for the chains with odd number
Model and Methods
A
|e|).
Spin-unrestricted DFT calculations were
of electrons (Q
called as
66
Thus,
extra electrons do not tend to occupy the avail-
This func-
able diuse orbitals predominantly.
tional is shown to overcome the localization
We con-
sider, therefore, that by forcing the extra elec-
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The Journal of Physical Chemistry rd
trons to stay within the molecule in our gas-
ther, an addition of 3
phase counter-ion free calculations, we actually
(i.e.,
model solid-state con ned BBL polyanions. As
tron per monomer unit,
for the gas-phase electron a nity values, these
three unpaired electrons having the total elec3 corresponding to the quartet tron spin S = 2 state (M = 4). The lling of orbitals of the
are irrelevant for the condensed-state properties, and it is not our purpose to discuss them.
Q = −3,
electron to the chain
which corresponds to one elec-
cred = 100%)
results in
BBL chain described above can be understood as a manifestation of the Hund's rule prescrib-
Results and discussion
ing a single lling of available degenerate or-
Electronic Structures
bitals to decrease the repulsion energy among the electrons. Further addition of electrons to the chain re-
First, we performed the ground state DFT cal-
sults in the reduction of the total spin.
culations of BBL oligomers by varying the reduction (doping) level
cred
in terms of number
of negative charges per chain,
Q.
Figure 2b
shows the total energy of the systems calculated for the cases of dierent spin multiplicities,
M = 2S + 1,
(where
S
increase of the reduction level of the BBL chain
is the total spin)
Q = −6 (cred = 200%) results in the singlet state (S = 0, M = 1). Apparently, the deto
and dierent doping levels. Figure 2c shows the corresponding electron spin
S
as a function of
crease of the total spin of the ground state when
Q per monomer unit. An addition of one electron to the BBL chain (Q = −1), gives rise to the doublet state (M = 2) with one unpaired 1 electron of the spin S = , see Figure 2c. This 2 state with Q = −1 is commonly known as a charge
the reduction level goes from
cred = 200%
for example, the ground state for (cred
tet states for
the DFT approaches,
56
our calculations show
, where the
0 < cred
