Electronic Structures and Optical Absorption of N-Type Conducting

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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-

ACS Paragon Plus Environment 1

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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), polyuorene

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-bisindenouorenedicyanovinylene (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 signicant 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 anity 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 congu-

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 conguration 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 innite periodic chain.

reduction of some oligomers,

54,55

It

Q =-1e

52

(polaron)

51,52 53

and -

In this context, recently, abe.g.,

polyuo-

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-dihexyluorene) 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 anities, ion-

and optical transition at dierent doping levels

ization energies and the excitation energies.

presented in this paper are not only specic

(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.

anities 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 conned BBL polyanions. As

tron per monomer unit,

for the gas-phase electron anity 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