Furan Substitution on Intrinsic

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Understanding the Impact of Thiophene/Furan Substitution to Intrinsic Charge-Carrier Mobility Haydar Taylan Turan, Ilhan Yavuz, and Viktorya Aviyente J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07477 • Publication Date (Web): 23 Oct 2017 Downloaded from http://pubs.acs.org on November 2, 2017

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The Journal of Physical Chemistry

Understanding the Impact of Thiophene/Furan Substitution to Intrinsic Charge-Carrier Mobility Haydar Taylan Turan, † Đlhan Yavuz, * ‡ and Viktorya Aviyente *† †

Bogazici University, Faculty of Arts and Sciences, Department of Chemistry, 34342 Bebek

Istanbul, Turkey ‡

Department of Physics, Marmara University, 34722, Ziverbey, Istanbul, Turkey.

*E-mail: [email protected] *E-mail: [email protected]

ABSTRACT One of the major challenges in rationalizing the intrinsic influences of molecular finetuning on charge-transport in organic semiconductors is due to changes in molecular packing. Thus it is, to a limited extent, desirable to elaborate materials to exhibit similar packing arrangements but slightly differ in their molecular structures. A molecular system, consisting of a heterocyclic core flanked by phthalimide end-capping units, is promising to overcome this issue. Previous XRD measurements have revealed that, when bithiophene (bi-T) core was replaced by bifuran (bi-F), the molecular packing was largely maintained while the resulting difference in charge-transport was substantial, substituting bi-T with bi-F results in more than one order of magnitude increase in hole mobility (i.e., 1.7x10-3 vs. 2.6x10-2 cm2/Vs) with a loss in electron mobility (i.e., 0.21 vs. 0.0 cm2/Vs).

The calculated hole mobilities with the MPW1K/TZ2P

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methodology are found to be lower for bi-T, as the reorganization energies of bi-T are noticeably higher than those of bi-F due to the non-planarity of bi-T. MD simulations have shown that the disordered hole mobility predictions are in good agreement with the experimental measurements, for which T->F substitution results in an increase in hole mobility. In contrast, the difference in electron mobilities with T->F substitution is predicted to be insignificant, most likely due to the lower average electronic coupling of bi-F. The discrepancy between calculated and experimental electron mobility may originate from macroscopic effects, such as the OFET device configuration which was not taken into consideration in this study. 1. INTRODUCTION Organic π-conjugated oligomers have been the subject of intense research, due to the major role they play in charge transfer in the field of organic solar cells1, organic light emitting diodes (OLED)2,3, and organic field effect transistors (OFET).4,5 Despite the low efficiencies compared to the inorganic materials, organic semiconductors are still promising due to their easy fabrication, low cost and flexibility.6,7 Convenient band gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and extended spectrum to increase the overlap are crucial features for an efficient semiconductor.8 Also, well-defined solid state packing for efficient charge drift between layers and low degradation in the presence of oxygen and moisture are other important aspects for efficient organic semiconductors.9 As a result of their unique properties, thiophene-based organic semiconductors are one of the most studied and widely used π-conjugated oligomers in organic solar cell and OFET applications.10,11 Furan, the oxygen analogue of thiophene has also received increasing interest and has shown high carrier mobility and good fluorescent property.12 Furan derivatives can be obtained


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from natural sources, polymers based on furan have been considered as a step towards renewable polymers. The optical absorption of oligofurans is somewhat blue shifted compared to oligothiophenes, but copolymers based on zinc porphyrin and furan or thiophene display similar optical band gaps.13 Although furan based conjugated polymers do provide good performance in solar cells, their efficiency is somewhat less than that for the corresponding thiophene based materials. The reduction was ascribed to the lower molecular weights that have been obtained in the polymerization reactions, replacing thiophene by furan has resulted in a reduced mobility.14 In the study of Tamura et al. the efficient photoluminescence due to molecular bending in phenylenethiophene-furan co-oligomer crystals is highlighted.15 Oniwa et al. have disclosed that a series of furan-based oligomers show distinct properties than their thiophene analogues.16 Gidron et al. have carried out a comparative study of two structural isomers highlighting the advantages of bifuran vs. bithiophene units in conjugated systems, such as higher fluorescence, solubility, and increased stability of the oxidized species.17 Charge transfer in the solid state can occur via a hopping or band mechanism depending on molecular electronic coupling.18 In many cases, π-conjugated oligomers transport their charge via hopping at high temperatures. The type of charge transfer depends on molecular packing, relative orientations and their regioregularities.19 However, correlation between the charge transfer and packing arrangement, molecular structure and natural disorder in the self-assembled crystals yet has to be fully explained.20 Despite the proposed methodologies21–24 and theoretical studies25–28 to understand structure and charge transfer behaviors, the relationship between atomistic properties and device characteristics have remain unclear.


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Scheme 1. Structures of bi-T (top) and bi-F (bottom)

Recently, Hendsbee et al.29 have synthesized alkylated phthalimide end-capped bifuran (bi-F) and bithiophene (bi-T) derivatives, as shown in Scheme 1. Although, they have different atoms on the central block of the molecule, in solid state packing, these two derivatives are quite similar to each other, with similar orientation of the neighboring molecule’s backbones to each other and the centroid to centroid distance between adjacent molecules, single-crystal X-ray measurements show that the packing motifs of bi-F and bi-T have strong similarities.30 Solely, the positions of the side chains with respect to the backbone are the only significant differences that have been observed in solid state packing.31 Their optical and thermal measurements show minimal change in electronic, optical properties. However, transistor measurements reveal that substituting bithiophene with bifuran results in more than one order of magnitude increase in hole mobility (i.e., 1.7x10-3 vs. 2.6x10-2 cm2/Vs) but, quite surprisingly, an unusual loss in electron mobility (i.e.,0.21 vs. 0.0 cm2/Vs). Nguyen et al.32 have similarly reported a decrease of electron mobility and slight increase in hole mobility when furans are substituted with thio-


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phenes. In this study, we aim to theoretically understand the influence of heteroatom substitution on structure-property relationship in bi-F and bi-T. 2. METHODOLOGY 2.1. Single molecule properties Geometries have been optimized with Density Functional Theory (DFT) by using the B3LYP33,34 functional along with the 6-311G(d,p) basis set using the Gaussian 09 software package.35 The nature of the stationary points has been characterized by calculating vibrational frequencies. For ionic states the spin-unrestricted formalism has been used.

Time-Dependent

DFT36,37 methodology has been used for excited states. The solvent effect has been taken into account with the Polarizable Continuum Model (PCM)38 methodology. Ionization potentials and electron affinities are calculated directly from the adiabatic potential energy surfaces (PESs) shown in Scheme 2 by using the ∆SCF method where Vertical Ionization Potential (VIP) is calculated as the energy difference between the neutral molecule and its cation both in the ground-state geometry of the neutral species as shown in Eq. 1.

VIP = E.∗ − E .

(1)

Adiabatic Ionization Potential (AIP) is calculated as the energy difference between the neutral and cation in their most stable geometries as in Eq. 2


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AIP = E. −E

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(2)

Vertical Electron Affinity (VEA) and Adiabatic Electron Affinity (AEA) are calculated considering the transitions from neutral to anionic state by using similar formulation. The reorganization energy of charge-transfer has two contributors; inner-sphere and outer-sphere. The inner-sphere reorganization energy arises from the geometry relaxations occurring while a charge is given or accepted by the molecule.18,39 It should be noted that, in this paper only the inner-sphere has been taken into account. The reorganization energy is calculated using Eq. 3, where 0 and + are the geometry relaxation energies upon removal (gain) of an electron for hole (electron) transfer (Scheme 2). = . = ∗ − E.∗ − E.

(3)

Scheme 2. Internal reorganization energy λ. + λ0 for hole and electron transfer.


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2.2. Bulk properties Initially supercells are constructed from the experimental X-ray crystal structures. The supercells are used first to calculate charge-transport, for the case of perfectly ordered morphologies. Further, we employ molecular dynamics (MD) simulations to introduce structural disorder, which is a more realistic situation, given the temperature effect on crystals at room temperature. All-atom MD methods are used to simulate atomistic morphologies of bi-F and bi-T. The supercells are heated from 0 to 300K and NPT equilibrated for 4 ns at 300K. A production run lasting for 20 ns is then equilibrated at constant 300K. All MD simulations are performed in AMBER12.40 Once the equilibrated morphologies are at hand we performed charge-transport simulations (see ref. [23] for details). Marcus Theory has been used to calculate the chargetransport rates of the oligomers. The rate of charge transfer in Marcus Theory41 is expressed as: =

ℏ

!" #

$%& ' ( )

*

(4)

where kij is the charge transfer rate, T is the temperature, tij is the transfer integral, λij is the reorganization energy, kB is the Boltzmann constant, ħ is the Planck’s constant (h) divided by 2π and ∆Eij (∆Eij = Ei-Ej) is the energy difference between the initial and final states; it is the site-energy difference, where Ei (Ej) is the energy difference when the charge state of molecule i (j) is changed during i->j charge-transfer. For charge-transfers between identical molecules ∆Eij=0. The calculation of ∆Eij for all of the possible charge-transfers between dimers is considerably demanding, since it requires the contributions from neighboring molecules. For this, we use polarized force-fields based on Thole model.42 Once all the ∆Eij values are calculated, we use variances in ∆Eij distributions to quantify energetic disorder.


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The transfer integral is the electronic coupling between consecutive layers; it varies with intermolecular distance and orientation

=

+ ',- ., / 0'/

(5)

In Eq. 5 t is the transfer integral, S the overlap, and ε the site energy. For perfect order morphology, the effective charge transfer integrals are calculated based on the DIPRO method via the Amsterdam Density Functional (ADF 2016) software package.43–45 The hybrid MPW1K46 functional along with the TZ2P basis set have been used in the calculations. For disordered morphologies, equilibrated at room-temperature, we use the MOO method based on semi-empirical ZINDO methodology. The main advantage of MOO/ZINDO is its fast evaluation of transfer integrals, it is many orders of magnitude faster than DFT-based methods. Therefore, in our disordered charge-transport simulations we employed MOO/ZINDO for transfer integrals.47 Charge-carrier dynamics simulations are performed through hopping-rate based kineticMonte Carlo methods for a single-charge carrier in an applied external electric field, as implemented in VOTCA.48 Hole/electron mobilities are evaluated using 1 = 2/4, where v is the velocity of the charge carrier and F is the strength of the applied field. The reported mobilities of crystalline morphologies are the averages of 10 stochastic realizations.


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3. RESULTS 3. 1. Geometrical Parameters The B3LYP/6-311G(d,p) methodology has been used to calculate the geometrical parameters of bi-F and bi-T molecules (The benchmark calculations for rubrene and pentacene are reported in the supporting information (Table S1). Table 1. summarizes the important geometric parameters of both derivatives in the ground state. Bi-F has kept its planar backbone as reported in the crystal structure,29 calculations have revealed the fact that Φ1 and Φ3 are slightly larger than the experimental ones by 4.7° and 4.8°, respectively. However, in bi-T, despite Φ2 which indicates the planarity of the central part of the molecule, Φ1 and Φ3 deviate significantly from the experimental values. Note that optimization calculations have been carried out for the monomer where the π- π stacking interactions have not been taken into account as opposed to the experimental findings: packing and stacking interactions may be more important in bi-T as compared to bi-F, the interaction between layers may force bithiophene to be planar. X-C (X=O, S) bond lengths and C-C bond distances (Table 1) as well as bond length alternation (BLA) parameters (Table S2, Table S3) of both compounds have been reported. A low BLA value is a descriptor indicating π-conjugation in a molecule. Both molecules have similar BLA values (0.06) indicating the presence of π-conjugation in both. The X-C bond lengths are coherent with the experimental results, a maximum deviation of 0.2 Å has been observed for the C6-X2 bond in bi-F and 0.34 Å for C3-X1 and X2-C8 bonds in bi-T. The C-C bridges are in agreement with experiment; bi-F has shown a better performance as compared to bi-T with a deviation of 0.19 Å and 0.49 Å respectively from experiment, the geo-


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metrical features of the monomers seem to reproduce the experimental findings even without the contribution of the closest neighbors. Table 1. Selected bond lengths (Å), dihedral angles (Φ in °) of bi-T and bi-F at B3LYP/6311G** level in CHCl3 (Φ1 = C1-C2-C3-X1, Φ2= X1-C5-C6-X2, Φ3= X2-C8-C9-C10) Experimental values are given in parenthesis.29

C2-C3 C3-X1 X1-C5 C5-C6 C6-X2 X2-C8 C8-C9 Φ1 Φ2 Φ3

bi-T 1.463 (1.512) 1.753 (1.719) 1.752 (1.720) 1.444 (1.504) 1.752 (1.720) 1.753 (1.719) 1.463 (1.512) 158.10 (175.92) 180 (180) 158.10 (172.62)

bi-F 1.450 (1.469) 1.372 (1.388) 1.365 (1.385) 1.431 (1.438) 1.365 (1.385) 1.372 (1.388) 1.450 (1.469) 179.55 (174.85) 180.00 (180) 179.65 (174.85)

Alternations of C-C bridging lengths, C-X bond lengths and dihedral angles upon the oxidation and reduction processes have been reported in Table 2. Dihedral angles of bi-F have hardly changed upon oxidation, Φ2 remained same and Φ1 and Φ3 have shown deviations of 0.4⁰, indicating that bi-F has kept its planar backbone and upon oxidation, it is expected that the latter can keep its hole mobility characteristics as well. In contrast to bi-F, dihedral changes of 11.90⁰; (Φ1 and Φ3) have been observed for bi-T upon oxidation; the latter correspond to the loss of planarity between the phthalimide moieties and the central ring. Similar findings have been observed for the reduction process as well; the changes for Φ1 and Φ3 are even more severe for bi-T in favor of intramolecular electron transfer. The C5-C6 bond between two thiophene or furan rings alters upon oxidation and reduction. Upon oxidation, bond length changes are more signifi-


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cant compared to reduction. The C5-C6 bond length is elongated by 0.038 Å and 0.035 Å, in both derivatives respectively. The potential energy surfaces around Φ2 have been reported for bi-F (Figure S1) and bi-T (Figure S2). In the case of bi-F the relative energy minimum indicates a planar backbone; in the case of bi-T the minimum is at 170⁰ and has a local maximum at 200⁰. The steric clash in bi-T may be due to the repulsion between the clouds of electron lone pairs on the S atoms. Hereby, the relative energies between the eclipsed and the staggered conformations of bi-F and bi-T are around 3 kcal/mol and 6 kcal/mol, respectively.

Table 2. Bond length (Å) and dihedral angles (Φ in °) changes of bi-T and bi-F upon oxidation and reduction at B3LYP/6-311G** level in CHCl3 (Φ1 = C1-C2-C3-C4, Φ2= X1-C5-C6-X2, Φ3= C7-C8-C9-C10).

C2-C3 C3-X1 X1-C5 C5-C6 C6-X2 X2-C8 C8-C9 Φ1 Φ2 Φ3

Oxidation bi-T bi-F 0.012 0.012 0.010 0.013 -0.005 0 0.038 0.035 -0.005 0 0.010 0.013 0.012 0.012 11.90 0.35 0 0 11.90 0.35

Reduction bi-T bi-F 0.025 0.018 -0.018 -0.008 -0.016 -0.008 0.027 0.016 -0.016 -0.008 -0.018 -0.008 0.025 0.018 19.82 0.107 0 0 19.82 0.107


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3.2. Reorganization Energies, Ionization Potentials and Electron Affinities π-conjugated molecules show thermally activated hopping-type charge transfer characteristics at high temperatures.49 Reorganization energy is an important parameter along with electronic coupling between adjacent molecules, to better analyze the charge transfer phenomena, also it provides important information to analyze the geometry relaxations that occur in a system during charge alternation and provides an important evaluation of electron-phonon coupling. High reorganization energies can be interpreted as low mobility. Computed hole reorganization energy (λHole) and electron reorganization energy (λElectron) of the bi-F are fairly similar with the values of 251 meV and 270 meV, respectively. Internal reorganization energies depend on the charge delocalization.50 The former quantities indicate that upon oxidation and reduction processes in bi-F, charge carriers are similarly localized. λHole and λElectron of bi-T have values of 370 and 337 meV, which are systematically higher than those of bi-F, in line with the higher nonplanarity of the bi-thiophenes.51 Ionization potentials (IP) and electron affinities (EA) can be used to demonstrate how easily charge replacement can occur within the molecules. VIP, AIP, VEA and AEA are displayed in Table 3. Experimental VIP and VEA values have been compared with the computed values to rationalize the accuracy of the findings. Indeed, one can see that differences with experiment are less than 0.6 eV. Furthermore, bi-F has shown 0.12 eV and 0.35 eV deviations from the experimental results for VIP and VEA, respectively. For bi-T, deviations from the experiment are higher with values of 0.57 eV for VIP and 0.43 eV for VEA. In this study, the HOMO–LUMO gap of the monomer is similar for bi-F (2.68 eV) and bi-T (2.69), however when the more realistic model of the dimer is considered, the gap between


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the frontier orbitals increases to 0.29 eV. This difference has been attributed to the high HOMO and HOMO-1 energy of bi-F as compared to bi-T; the HOMO (-5.73) and the HOMO-1 (-5.87) of bi-F are higher in energy than those of bi-T (-5.99 and -6.15 respectively) (Table S4). This latter finding is similar to one of Sharma et al.52 who claimed that due to higher HOMO energies of α-oligofurans initial doping should be easier for oligo and polyfurans than for their thiophene analogues. Table 3. Calculated (B3LYP/6-311G**) Reorganization Energies (meV), VIP, AIP, VEA and AEA (eV) in CHCl3. Experimental values are given in parenthesis.29

bi-T

λhole

λelectron VIP

AIP

VEA

AEA

370

337

6.00

-2.62

-2.76

6.09 (5.52)

bi-F

251

270

5.8 (5.68)

(-3.05) 5.68

-2.63

-2.74

(-2.98)

3.3. Frontier molecular orbitals The frontier molecular orbitals of the monomers (Figure S3A and Figure S3B) and dimers (Figure S4A and Figure S4B) have been analyzed. As seen in Figures S3A-S3B the frontier molecular orbitals of both molecules show electron density in the HOMO localized on thiophenes and furans. The LUMO in both is more delocalized with electron density extending to the phthalimide end units as reported by Hendsbee et al.29 The latter attribute the charge mobility in bi-T to the degeneracy of the LUMO and LUMO+1 orbitals (B3LYP/6-31G(d)), however the degeneracy disappears with the more elaborate basis set (B3LYP/6-311G**) employed in this


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study. The frontier molecular orbitals of the dimers of bi-F (Figure S4A) and bi-T (Figure S4B) are different from each other. While the orbitals in the HOMO of bi-F and bi-T are localized on the furans and thiophenes respectively, the LUMOs show noticeable differences. In the dimer, the LUMO of bi-F resembles the one of the monomer with slight shift of the orbitals towards the phthalimide rings. The LUMO of bi-T on the other hand is mostly located on the phthalimide rings. The latter feature of the LUMO can be attributed to the larger size of S as well as to the stacking of the layers in the dimer which facilitate charge transfer. The difference in the construct of the LUMO orbitals in the dimers may be responsible for the larger electron mobility in the case of bi-T. 3. 4. Packing and Charge Transfer Integrals. Packing in the solid state is influenced mainly by the chemical structures of the πconjugated molecules. Transfer integrals can be reliable indexes to compare charge transfer rates of the molecules. Transfer integrals can be used to understand the contribution of different dimers to the aggregated entity. In this section, the experimentally known crystal structures of bi-T and bi-F have been used to assess the charge transfer integrals between dimers.29 The solid-state packing of the derivatives are displayed in Table 4. We see that, despite the substitution of sulfur atom to oxygen on the central rings, both derivatives have similar packing motifs in the solid state; both exhibit a brick-like arrangement. The MPW1K/TZ2P calculated transfer integrals of hole (thole) and electron (telectron) and the centroid to centroid distances between adjacent molecules are reported in Table 4. Even though all plausible dimers for the hole/electron transfer have been taken into the account, only dimers 12, 13 and 14, which are closer to each other, are reported in this article. Furthermore,


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one should note that besides the distance between centroids, the orientation of the molecules plays a significant role in the charge transfer integrals. Among all, due to the close centroid to centroid distance dimer 12 has shown high charge transfer integrals with thole values of 77.8, 88.3 meV and telectron values of 19.1, 3.9 meV for bi-F and bi-T, respectively.

Table 4. Packing arrangements, transport pathways for MPW1K/TZ2P calculated transfer integrals (meV), centroid to centroid distances (r) of bi-T and bi-F. Atoms in green represent side-chains.

bi-T Dimer 12 13 14

|thole| 88.3 0.2 6.5

|telectron| 3.9 9.1 5.2

r (Å) 5.0 14.6 15.1

bi-F Dimer 12 13 14

|thole| 77.8 0.2 4.5

|telectron| 19.1 6.6 8.3

r (Å) 5.0 14.5 16.0

Molecular dynamics simulations are then performed on the perfect supercell to relax the systems at room-temperature. This process introduces an apparent structural disorder into the solids in the molecular level. Figure 1 shows a snapshot of the MD simulation. An apparent deviation from an ideal packing arrangement is visible, which breaks down the periodicity. However, the slipped packing along the π-π stacking direction and isolation of these rolled columns by side-chains still exist for both bi-T and bi-F. In order to quantify the amount of structural disorder we calculated the direction-resolved paracrystal order parameter defined as g=s/, where d is the distance between molecular pairs, is the statistical average and s is the corresponding var-


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iance. For bi-T and bi-F we find that g=2-3% for the π-π stacking direction at room temperature which is a typical value for a crystalline organic solid (Table 5). Note, for instance, that g~0 for perfectly ordered and g~10% for amorphous solids.53,54. Similar g values for both bi-T and bi-F is a consequence of similar packing arrangement. In the crystal, the distances between the molecular layers are 3.24 Å and 3.28 Å for bi-T and bi-F, respectively.

bi-F

bi-T

Figure 1. Representative MD snapshots of bi-T and bi-F morphologies equilibrated at 300K. The effect of structural disorder on the charge-transport of bi-T and bi-F can be quantified by the local and non-local intermolecular electron(hole)-phonon coupling strength as Λ=σ2/2kBT and L=Σ2/2kBT, respectively. Here σ and Σ are the energetic- and electronic-disorder, which are related to the deviations in the site-energies and electronic-couplings, respectively. Martinelli et al. have shown that Λ=λ/2 is an alternative method to calculate the total reorganization energy, including inter-molecular and intra-molecular reorganization energies.55 Λ values of electron and hole transfers of bi-T and bi-F are very similar and around 140 meV (see Table 5). This corresponds to a 280 meV of total reorganization energy, showing that the results obtained from the MD simulation are very close to the DFT results of the isolated bi-F (having 251 meV and 270


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meV for hole and electron transfer, respectively) but ~70-90 meV lower than those obtained for bi-T (i.e., having 370 meV and 337 meV for hole and electron transfer, respectively). These results suggest that the external contributions (including the suppression of torsional degrees of freedom from the neighboring molecules) to reorganization energy are small for bi-F but significant for bi-T. We suspect that the tendency of bi-T to non-planarity, again, plays a crucial role here. In order to see the influence of planarity on reorganization energy, we calculated the internal electron- transfer reorganization of bi-T using DFT but this time by freezing the dihedral angle between the thiophene rings. We find a value of 286 meV, consistent with the MD result of 264 meV. Therefore, internal structure of the bi-T and bi-F plays the central role in the local electron-phonon couplings. Non-local electron(hole)-phonon coupling strength, L, is a consequence of dynamical disorder observed at high-temperatures.56 However, since the calculation of L is relatively non-trivial and typically much lower than the local e-p coupling, it is often omitted. Table 5 shows that L of bi-F is around 5 meV and more than an order of magnitude weaker than the reorganization energies. Replacing bi-F with bi-T increases L by a factor of 3-10, making it 55 meV and 17 meV for holes and electrons, respectively. These values are consistent with higher structural disorder in bi-T compared to bi-F. On the other hand, the J/L ratio is useful to understand the charge-transport efficiency since according to band transport theory µ α J/L.57 As shown in Table 5, the J/L ratio of bi-T is lower by a factor of 3-4 than the one for bi-F for both hole and electron transport.


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Table 5. Room-temperature paracrystallinity, g, local, Λ=σ2/2kBT, and non-local L=Σ2/2kBT electron (hole)-phonon coupling strength and /L ratio. Λ and L are in units of meV.

bi-T bi-F

σ dih(0) 14 12

g(%) 2.6 2.3

Λh 139 137

Λe 132 140

Lh 55 4

Le 17 7

/Lh 1.6 4.8

/Le 2.2 8.3

The X-ray crystal structure of T->F substitution does not have a strong influence on packing arrangement but charge-transport is strongly affected by intra-molecular features. Electronic coupling is highly sensitive to relative orientations of molecular pairs. However, studies have shown that the electronic coupling is less sensitive to T->F substitutions under the same conditions, since molecular orbitals are largely localized on C=C and C-C bonds (see Figure S3 and Figure S4). Our ideal crystal results are also consistent that hole/electron transfer integrals are very similar for bi-T and bi-F. Therefore, we conclude that what could influence the bulk properties of bi-T is the relatively large amount of non-local disorder due to the non-planarity tendency of bi-T compared to bi-F. The X-ray diffraction patterns of bi-T and bi-F reported in the SI of ref. 29 have been examined to see if one can extract an experimental disorder from the Warren-Averbach graphical analysis. We noticed that the number of lines in XRD data in the SI is very limited to do so. Visual inspection of the existing peaks of the Warren-Averbach graphical analysis shows that the lines of bi-T are broader than those of bi-F, an indication of larger structural disorder in agreement with the


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paracrystallinity predictions. We could, calculate the difference between the line broadening of the strongest peak of bi-T and of bi-F from the reported XRD data in ref. 29, and thus have qualitatively figured out the amount of disorder. We found that line broadening in bi-T is ~15% larger than that of bi-F, in agreement with the predictions via paracrystallinity, i.e., ~12% larger structural disorder (g=2.6% for bi-T vs. 2.3% for bi-F). 3. 5. Hole/electron mobilities We next evaluated the hole/electron mobilities of bi-T and bi-F in order to assess their overall performances. We first assumed that the morphologies consist of almost perfectly ordered molecular packing so that g̴~0. In this case the mobility can be evaluated analytically 1=

6

0

7

∑ 9 :

(6)

assuming that occupation probabilities are the same along the jth transport direction. Here, kj is the transfer rate, Pj=kj/Σjkj is the probability of charge-transfer, dj is the distance between molecular pairs along the jth transport direction and n is the transport dimensionality. The hole/electron mobilities calculated by Eq. (6) are shown in Table 6, where the electronic couplings are predicted by MPW1K/TZ2P in all cases. The mobilities are found to be on the order of 10-2-10-1 cm2/Vs. We observe a factor of 2-3 increase in hole and electron mobilities when bi-T is replaced by bi-F. This can directly be attributed to the relatively lower reorganization energies of bi-F, since J and d values of bi-F and bi-T are practically similar. Eq. (6) is clearly inapplicable when structural disorder is introduced with MD simulations, since the occupation probabilities are no longer the same. In this case, we employed kinetic Monte Carlo simulations using the VOTCA


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package. Electronic couplings are evaluated by the ZINDO method. Hole mobility of bi-T is found to be 0.009 cm2/Vs. This low value can be attributed to significantly high Lh=55 meV value. But the hole mobility of bi-F is higher, 0.029 cm2/Vs comparing with bi-T due to decreasing Lh and λh energies. We find that the electron mobility does not change much when bi-T is replaced with bi-F. Comparing our hole/electron mobility predictions of the disordered morphologies of bi-T and bi-F with OFET measurements, we see that all of our predictions are typically within a factor of 10 for bi-T (second line, Table 6). Moreover, the increase in hole mobility by T->F substitution (µh=0.009 cm2/Vs and 0.023 cm2/Vs for bi-T and bi-F, respectively) is also consistent with the measurement (µh=0.017 cm2/Vs and 0.026 cm2/Vs for bi-T and bi-F, respectively). However, no electron mobility was measured for bi-F (.i.e. µe~0), while our theoretical prediction is µe=0.019 cm2/Vs.29 Since our result is an intrinsic value, this discrepancy should originate from the macroscopic effects, such as the OFET device configuration is somewhat preventing electron injection between source-drain electrodes.58 Interestingly, unipolar transport in, especially, bifuran containing organic materials have been observed in different studies.59,60 Nonetheless, unipolar organic materials have found a major place in organic electronics, for instance, unipolar materials became standard in solar cells such as OPVs and perovskite solar cells in which they are used as hole/electron blocking layers. 61 Huang et al have calculated the mobility and ionization potential values for 6T and 6F.62 The maximum hole-transfer mobility of 6F was found to be nearly 17 times larger than that of 6T. Their calculations have shown that nFs possess high intrinsic hole-transfer mobilities and suitable IP values for use as p-type materials. For small oligofuran molecular crystals, the hole mobility is found to be slightly larger than electron mobility in smaller oligofuran molecular crystals.63 Similarly, in this study, the hole transfer mobility of bi-F


20

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has been calculated to be almost 3 times larger than the one in bi-T (Table 6), corroborating these results. Table 6. Predicted and experimental hole and electron mobilities of bi-T and bi-F. Units are in cm2/Vs. (n.o.: not observed)

MPW1K/TZ2P (ordered) ZINDO (disordered) Experimental

bi-T hole 0.094 0.009 0.0017

electron 0.0083 0.021 0.21

bi-F hole 0.29 0.023 0.026

electron 0.016 0.019 n.o.

4. CONCLUSION The

geometrical

parameters

of

bi-F

and

bi-T

calculated

with

B3LYP/6-311G(d,p) have shown slight differences as compared with experimental data. Calculations are carried out in the gas phase for single molecules, in bi-T the rings are slightly out of plane with respect to each other, this may be due to the absence of the upper and lower layers in the calculations. Frontier orbitals for dimers have exhibited a major difference between the two species: while the HOMO orbitals in bi-F and bi-T are localized on the furan and thiophene rings respectively, the LUMOs show noticeable differences. The orbitals of the LUMO of bi-F resemble the one of the monomer with slight shift of the orbitals towards the phthalimide rings. The LUMO of the dimer of bi-T on the other hand is mostly located on the phthalimide rings. The construct of the LUMO’s in bi-T is a reminiscent of charge transfer in this molecule. Despite the substitution of sulfur to oxygen, both derivatives have similar packing motifs in the solid state; both exhibit a brick-like arrangement. The similarity has let us to understand the sole influence of atom substitution to the overall charge-transport of bi-T and bi-F. For this, we have employed MPW1K/TZ2P and calculated the hole/electron transfer integrals between the dimers of bi-T and


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bi-F and found strong similarities, as expected. The calculated hole/mobilities are found to be lower for bi-T, since both hole and electron reorganization energies of bi-T are noticeably higher than those of bi-F. We attribute the higher reorganization energy to the tendency of bi-T core to non-planarity. We have then performed MD simulations to understand the morphologies and transport properties in a less ordered environment. We have found that the paracrystallinity of molecular packing and local electron (hole)-phonon coupling of bi-T and bi-F along the π-π direction are strikingly similar but we have observed large differences in non-local (hole)-phonon coupling, i.e. those of bi-T are significantly higher than those of bi-F. This, again, can be attributed to the non-planarity in bi-T. Our disordered hole mobility predictions are in good agreement with the experimental measurements, for which T->F substitution results in an increase in hole mobility. In contrast, the difference in electron mobilities with T->F substitution is predicted to be insignificant, most likely due to the lower average electronic coupling of bi-F. On the other hand, while we have observed tangible electron mobility, the experimental measurement for bi-F turns out to be zero. The discrepancy between calculated and experimental electron mobility may originate from macroscopic effects, such as the OFET device configuration which was not taken into consideration in this study. This is particularly important due to fact that mobility calculations are based on single charge-carrier, while OFET’s operate at high charge carrier concentrations.64 One of the ultimate goals in the field of organic semiconductors is to understand the influence of molecular modifications on device features. However, the molecular modifications typically end up with drastic changes in the packing arrangements65,66 , inhibiting a clear understanding of the structure-property relationships. The structures considered in this study illustrate a very rare situ-


22

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ation where atom (S->O) substitution does not result in a dramatic change in the packing arrangement and this has excited/motivated us to understand the effect of “single-atom” substitution on the molecular, bulk and charge-transport properties of bi-T and bi-F. The hybrid computational tools utilized in this study have been successfully used to understand and elucidate the bulk/transport features upon atom substitution (S->O) except for the mobility.

ACKNOWLEDGMENT The computational resources of the High Performance Computing Center and the National Center for High Performance Computing of Turkey (UHeM) under the grant number 5003602015 are gratefully acknowledged. SUPPORTING INFORMATION The Supporting Information is available free of charge on the ACS Publications website at DOI: Benchmark test, Potential Energy Surface calculations, Bond length alternation, HOMO/LUMO orbitals of the molecules and Cartesian coordinates of optimized geometries.

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Schrader, M.; Fitzner, R.; Hein, M.; Elschner, C.; Baumeier, B.; Leo, K.; Riede, M.; Bäuerle, P.; Andrienko, D. Comparative Study of Microscopic Charge Dynamics in Crystalline Acceptor-Substituted Oligothiophenes. J. Am. Chem. Soc., 2012, 134, 6052– 6056.

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Furan Substitution on Intrinsic

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