DFT study of electronic band structure of alternating triphenylamine-fluorene copolymers

Polymer 54 (2013) 2535e2543

Contents lists available at SciVerse ScienceDirect

Polymer journal homepage: www.elsevier.com/locate/polymer

DFT study of electronic band structure of alternating triphenylamine-fluorene copolymers Lin Ling, Jolanta B. Lagowski* Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, NL, Canada A1B 3X7

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 January 2013 Received in revised form 22 February 2013 Accepted 9 March 2013 Available online 16 March 2013

Triphenylamine-fluorene alternating copolymers TPAFn (n ¼ 1e3) can be employed as hole transport layer and blue light-emitting materials of the (multilayer) polymeric light-emitting diodes. In this work we investigate their electronic band structures using the solid state density functional theory (DFT) approach. All polymers are treated as one-dimensional infinite conjugated chains generated by applying periodic boundary condition to their repeat units. We consider six DFT approximations (PBE1PBE, B3LYP, O3LYP, OB95, PBEPBE, and TPSSTPSS) in this study. 6-31G(d) basis set and 32 k points are employed in all calculations. We compare the electronic band gaps (Egap’s), and highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) energy levels with experimental data. In all DFT calculations for TPAFn’s, the best agreement with experiment is obtained with hybrid DFT functionals for band gaps and ionization potentials (IP’s). For electron affinities (EA’s), the gradient-corrected functionals perform better. Based on the computational results, TPAF1 would be predicted to be the best material for the electron-blocking/hole transport layer. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Conjugated copolymers DFT solid state calculations Hole transport layer

1. Introduction Fluorene-based polymers have been used in various devices [1]. They are especially known for their excellent chemical stability and high photoluminescence (PL) efficiency both in solution and solid films, with emitted wavelengths primarily in the blue spectra region [2]. However, pure homopolymers such as polyfluorenes (PF’s) display poor performance [1] in many commercial applications. For organic conjugated polymer such as PF’s, charge transport is the key property that determines the efficiency of the devices. It has been found that devices [3] with multilayer heterogeneous structures, such as multilayer organic light-emitting diodes (OLED’s), bulkheterojunction organic photovoltaic cells (OPVC’s) or multilayer heterojunction organic field effect transistors (OFET’s), give improved performance due to a more balanced charge carrier transport. Typically, copolymers (instead of homopolymers) such as alternating triphenylamine-fluorene copolymers (TPAFn, n ¼ 2, 3 [4] see Fig. 1) and similar others such as triphenylamine-fluorene copolymers (TPAF1, see Fig. 1) with aldehyde, monocyano and dicyano pendant acceptor groups [5] or poly(9,9-dioctylfluorene-co-N(4-butylphenyl)-diphenylamine) (TFB) [6e9] are employed in these multilayer/heterogeneous OPVC’s [5,6], OFET’s [7] or OLED’s [4,8,9]. * Corresponding author. E-mail addresses: [email protected] (L. Ling), [email protected] (J.B. Lagowski). 0032-3861/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2013.03.021

In all of the multilayer/heterostructure devices mentioned above, alternating triphenylamine-fluorenes based polymers act primarily as hole transport layers (HTL’s) maximizing the hole injection from the anode and blocking the electron leakage [4e9]. Most multilayer devices such as diodes are fabricated using solution processing. This may lead to complications when two successive layers are placed on top of each other since the first layer may dissolve while the second layer is deposited. One way to resolve this problem is to make the first layer insoluble by using cross-linking. Cross-linking can also stabilize the morphology of the layer(s) [10]. For example, in a multilayer polymer light-emitting diode (PLED), the (first) layer consisting of polymers such as TPAF2 or TPAF3 (which were synthesized with hydroxyl groups on side chains) was thermally cross-linked with the use of a cross-linker, tris(4-dihydroxyboranylphenyl) amine [4]. This process produced TPAF films with very good solvent resistance. It was found that the thermal cross-linking of these HTL polymers containing TPAF can slightly improve their PL quantum efficiency but it did not change their electrochemical properties [4]. Hence, cross-linking is considered to have negligible effect on the electronic structure of the polymers studied and is not taken into account in this work. As an example, we consider the operation of a typical multilayer PLED [4] containing TPAFn’s. In this case electrons are injected from the cathode metal (Mg/Ag or Ca) into the conduction band of the electron transport layer (ETL) consisting of copolymers such as

2536

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

Fig. 1. Chemical composition of TPAFn (n ¼ 1,2,3) (typically R is an alkyl chain, e.g. R ¼ C8H17). The dihedral angle (1,2,3,4) is denoted as f1in the text. Similarly torsional angles between the fluorene units are designated as f2 and f3 in TPAF2 and TPAF3.

fluorine-oxadiazole copolymers (OxFn, n ¼ 2, 3) where they combine radiatively and non-radiatively with the holes generated in the HTL (TPAFn, n ¼ 2, 3) which may be in contact with tin-doped indium oxide (ITO) anode. The recombination of electrons and holes produces electroluminescence (EL) in the emissive layer which, in this case, is the same as the ETL. As stated above, the introduction of triphenylamine group in the fluorene-based polymers such as TPAF2 and TPAF3 increases their hole transport and electron-blocking capabilities and hence significantly enhances the luminescence of diodes [4]. It is shown [4] that the multilayer PLED with TPAF2 and OxF3 employed as ETL and HTL respectively gives the best performance. In general, it is believed that a balanced charge transport in devices such as organic diodes can be obtained by matching the top energy levels of HTL and ETL with the work functions of the cathode and the anode respectively. That is, the transport of electrons in PLED can be increased by matching the energy level of the lowest unoccupied molecular orbital (LUMO) of the ETL polymers (such as OxFn’s) with the work function of the cathode metal (Mg/Ag (3.7 eV) or Ca (2.9 eV)) and the transport of the holes can be enhanced by the matching the energy level of the highest occupied molecular orbital (HOMO) of the HTL polymers (such as TPAFn’s) with the work function of the anode (ITO (4.8 eV)) [4]. We equate the negative of the HOMO and LUMO eigenvalues with the polymer ionization potential (IP) and electron affinity (EA) energies respectively. Experimentally, a technique of cyclic voltammetry (CV) [11] was used to determine the energy levels of organic conjugated polymers such as OxFn’s and TPAFn’s. These known CV results can be used to determine which one of the density functional theory (DFT) exchange-correlation functionals is best suited for estimating top energy levels for conjugated organic polymers with large (containing 30 or more atoms) unit cells. In the previous work [12], we computed the energy levels of ETL polymers such OxFn’s (n ¼ 1e3) with the use of one-dimensional (1D) DFT band structure calculations. In this work, we complete this investigation and determine the energy levels of HTL polymers such as TPAFn’s (n ¼ 1e3), again using the same hybrid and the gradient-corrected functionals as for OxFn’s (n ¼ 1e3) in the 1D band structure calculations. This way a complete DFT band structure of these PLED systems can be compared with the experimental (CV) data and appropriate conclusions can be made about their charge transport behaviors. 2. Computational details All calculations in this work have been performed with Gaussian 03 [13]. We have performed 1D DFT solid state calculations [14] for TPAFn (n ¼ 1e3) copolymers (also referred to as PBC calculations where PBC stands for the periodic boundary condition). As mentioned above, the conjugated polymers studied in this work have large multi-atom unit cells. Previous (OxFn’s) band structure

calculations [12] showed that the sufficient number of k points to sample the first Brillouin zone is 32 for polymers with large unit cells. Since TPAFn’s are characterized by as large or even larger multi-atom unit cells relative to OxFn’s, we also employed 32 k points in the TPAFn’s band structure calculations. Similarly [12], for the purpose of displaying the top occupied and unoccupied bands in the first Brillouin zone, we used the keyword, IOp(5/103 ¼ 1), to output five sets of top occupied and unoccupied eigenvalues (each set contains 32 values corresponding to the 32 k points) which were then plotted as functions of k points. As shown in Fig. 2, in all TPAFn’s (n ¼ 1e3), the long side-chains (typically C8H17) denoted by R in Fig. 1 have been replaced with short ethyl groups (C2H5) in order to reduce the computation time. This replacement does not significantly change the geometry or the energies of fluorene-based polymers [15]. In fact recent work indicates that the length of sidechains is known to have a small effect (less than 0.02 eV) on the electronic band gaps (Egap’s) and (HOMO and LUMO) energy levels in 1D solid state computations [16]. It should be noted that in this work, we calculate the fundamental electronic (not optical) band gaps. That is, Egap is defined as the minimal energy difference between HOMO and LUMO bands which corresponds to the energy difference between the top of the valence band and the bottom of the conduction band. Egap is the minimum energy required to create unbound electronehole pairs that can then participate in the charge transport (hence this band gap is sometimes also referred to as a transport gap). In all DFT calculations the polarized split-valence (double-zeta) basis set 6-31G(d) was employed. We tested the influence of a larger basis set on the energies and the structures of TPAFn (n ¼ 1e3) polymers by employing (higher) triple-zeta basis set (6-311G(d,p)) in 1D 32 k-point PBC/DFT/B3LYP calculations (see Table 1). Similar to what has been observed in previous study [16], the comparison in Table 1 shows that both the IP and EA values have increased (and, hence, the corresponding HOMO and LUMO eigenvalues have been lowered) by approximately the same amount (very close to 0.25 eV). These upward shifts in the IP and EA values cancel out when the differences (Egap’s) were calculated, leaving the band gaps essentially unchanged (they were lowered by 0.02 eV or less). Also, in each case, the optimized structures (with double- and triple-zeta basis sets) have shown to have nearly the same geometrical parameters (the translational vectors (Tv’s) and the dihedral angles between fluorene and triphenylamine (f1) are shown for comparison in Table 1 as an example). Since the structures and the band gaps are virtually the same for both basis sets and the IP and EA values are both increased by nearly the same amount (z0.25 eV) it can be concluded that 6-31G(d) basis set is adequate for the work presented in this paper. It should be noted that the PBC/DFT calculations carried out in this work also ignore other contributions that may affect the electronic energies (IP’s, EA’s, band gaps etc). In particular we ignore the effect of temperature since all DFT computations are performed for ground states (T ¼ 0 K) of the polymer systems. At room

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

2537

Fig. 2. Molecular (optimized) structure of repeat unit of (a) TPAF1, (b) TPAF2, (c) TPAF3.

temperature, kT (k is a Boltzmann constant) is approximately equal to 0.026 eV which is very small relative to IP, EA and Egap values. Hence it is expected that, at least near room temperature, these energy values would not be significantly affected by this contribution since its main effect would be to cause random thermal Table 1 Comparison of IP’s, EA’s, band gaps, max-gap values, translational vectors (Tv’s) and dihedral angles (f1’s) of TPAFn (n ¼ 1e3) as obtained from 32 k points 1D solid state DFT/B3LYP calculations using 6-31G(d) and 6-311G(d,p) Basis sets. All energies are in eV’s, Tv’s are in Å’s and f1’s are in degrees. DE stands for energy difference. Method TPAF1 B3LYP/6-31G(d) B3LYP/6-311G(d,p) DE TPAF2 B3LYP/6-31G(d) B3LYP/6-311G(d,p) DE TPAF3 B3LYP/6-31G(d) B3LYP/6-311G(d,p) DE

IP

EA

Egap

Max-gap

Tv

f1

4.76 5.00 0.24

1.28 1.54 0.26

3.48 3.46 0.02

3.83 3.81 0.02

17.3 17.3

47.9 49.4

4.83 5.08 0.25

1.45 1.72 0.27

3.38 3.37 0.01

3.53 3.51 0.02

25.6 25.6

28.3 28.4

4.79 5.03 0.24

1.48 1.73 0.25

3.31 3.30 0.01

3.41 3.40 0.01

33.0 32.9

31.8 33.5

motion of ions which, in turn, would be averaged out producing equilibrium structures close to the ones obtained with the (groundstate) DFT calculations. Furthermore, our calculations are carried out at reduced dimensionality (1D instead of 3D). That is, we ignore the intermolecular, van der Waals interactions between chains due to attractive and repulsive non-bonded electrostatic, induction (also called polarization) and dispersion (London) forces. Since the polymer chains are neutral (and carry small dipoles), it is expected that of the three contributions to the van der Waals forces, the dispersion forces will dominate the non-polar intermolecular interactions between chains in the systems studied. From our previous study [16], we note that the effect of the (dispersive) intermolecular interactions for the organic conjugated polymers is that in ideal crystalline solids they tend to organize into lamellar 3D structures [16] that are largely stabilized by p-p stacking of the polymer backbones. In this p stacking process the backbones become more planar and band gaps decrease (since IP’s decrease and EA’s increase and Egap ¼ IP-EA). We performed two types of molecular calculations (using DFT/ B3LYP/6-31G(d)) to assess the effect of increased planarity on the electronic energies of the TPAF polymers. One type of the

2538

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

calculation involves a full geometry optimization of the repeat units of TPAFn (n ¼ 1e3) and another is a partially constrained optimization where the torsional angles between triphenylamine and fluorene (f1, see Fig. 1) and between fluorenes (f2 and f3 when present) are reduced to zero while all the other parameters are allowed to relax. While these molecular calculations are not PBC types, the main focus are the energy difference between planar and non-planar structures, hence we believe that it is a valid comparison for polymers. It should be noted that in the fully optimized molecular calculations, f1 was reduced from 48 (1D PBC) to 35 in TPAF1(chain became more planar) whereas f1and f2 in TPAF2and f1, f2and f3 in TPAF3 all became nearly the same (close to 37 ) which is similar to the average values of 35 and 39 as obtained in the respective (optimized) 1D PBC calculations. The results of these molecular calculations show (see Table 2) that energy differences are decreased by the amount between 0.15 and 0.25 eV (IP’s decrease by less than 0.1 eV and EA increase by approximately 0.2 eV). Based on these results, it is expected that the band-gap decreases due to the enhanced planarity would be largely due to the increases in EA’s (or the lowerings of the LUMO eigenvalues) for the systems studied in this work. The relatively small changes in IP’s can be understood in terms of the molecular orbital analysis given in Section 3.4. All HOMO’s are primarily localized on the nitrogen containing triphenylamine group and planarization of the backbones may not have a large effect on this group. In real systems the polymers are not fully planar even in ideal crystals (see for example reference 16 where it was shown that the torsional angles in similar organic conjugated polymers were reduced from approximately 50 to approximately 20 , not 0 ). Hence, we estimate that in bulk solid state TPAF systems, the band gaps will be reduced by less than 0.2 eV due to increased planarity. It is expected that other intermolecular interactions will have the net effect of further reducing the band gaps. Hence, we estimate that the net effect would be to decrease the 1D band gaps by approximately 0.2 eV (probably closer to 0.1 eV for TPAF1) in comparison to the corresponding bulk 3D values. We also ignore the disorder effect. It is expected that in multilayer devices, the polymer films are either amorphous (fully disordered) or polycrystalline (partially disordered). The disorder will have the effect of increasing the distances between polymers and hence decreasing the intermolecular (van der Waals) interactions. In the presence of disorder, polymer chains may ‘relax’ and their backbones may acquire geometry that is closer to that of a single (isolated) chain than the one observed in ordered crystals. This would mean that 1D PBC calculations may be a good approximation for determining the electronic properties of disordered bulk systems. 1D PBC would still only be an approximation since

Table 2 Comparison of the HOMO and LUMO eigenvalues (εHOMO’s and εLUMO’s) and their differences (Egap’s) of TPAFn (n ¼ 1e3) repeat units as obtained from the molecular DFT/B3LYP/6-31G(d) fully and partially geometry optimized calculations. All energies are in eV’s. DFT/B3LYP/6-31G(d) TPAF1 Full optimized Planar Difference TPAF2 Fully optimized Planar Difference TPAF3 Fully optimized Planar Difference

εHOMO

εLUMO

Egap

4.87 4.83 0.04

1.07 1.19 0.12

3.80 3.64 0.16

4.86 4.80 0.06

1.30 1.48 0.18

3.56 3.32 0.24

4.86 4.79 0.07

1.43 1.62 0.19

3.43 3.17 0.26

even in disordered systems intermolecular interactions are present which will (typically) decrease the band gaps relative to the isolated single chains. All 1D DFT/PBC calculations were geometry optimized, that is, all nuclear positions and the unit cell repeat lengths were allowed to relax in order to find the lowest energy state for the ground states of the polymers. The convergence criteria of the selfconsistent field (SCF) computations were kept the same as in the previous work [12]. All polymers were treated as closed-shell neutral molecular systems. As in our previous study [12], we tested six DFT functionals: PBE1PBE [13,17] (PBE1), B3LYP [18], O3LYP [19], OB9519,20, PBEPBE [17](PBE), and TPSSTPSS [21] (TPSS). PBE1, B3LYP, O3LYP are examples of typical one- (PBE1) and threeparameter (B3LYP, O3LYP) hybrid exchange-correlation functionals, and OB95, PBE, and TPSS belong to the gradient-corrected (generalized gradient approximation (GGA) (OB95, PBE) or meta-GGA (TPSS)) class of functionals. A more detailed description of these energy functionals can be found in our previous work [12]. Again a main motivation for choosing the above exchange-correlation DFT functionals was to test the claim that they can describe the properties of the p-conjugated systems better than other functionals [17e21]. GaussView visualization software [22] was used to display the optimized geometries (Fig. 2) and orbitals (Fig. 4) of the polymers studied. The analysis of the generated band structures focuses on the determination of the electronic band gaps, band widths (Ewidth’s) and top energy levels (corresponding to HOMO’s and LUMO’s) of the polymer systems. As indicated above, the (fundamental) electronic band gap is related to the energy barrier for the electron transport. The Ewidth is defined as the energy difference between the minimum and the maximum energies for a particular band, its width indicates the degree of charge delocalization in the band. Typically wider bands mean larger charge delocalization and vice versa. The maximum energy gap (referred to as max-gap) is also computed. 3. Results and discussion As stated in the introduction the main role of the various transport layers in PLED is to better match the HOMO and LUMO energies of these polymers with the anode and cathode work functions respectively in order to reduce the barriers to charge injection and hence to improve their overall PL and EL efficiencies. In this section we present and discuss the results of 1D DFT band structure computations for TPAFn (n ¼ 1e3) polymers and compare them to the experimental data that were mainly determined with the use of CV. CV [11] is one of the experimental methods that can be used to determine the top energy levels of the organic polymers such as TPAFn’s as well as of cathode and anode materials [4]. In some cases (TPAFn n ¼ 2, 3), as discussed above, we used the experimental energy levels and gaps that were obtained for the cross-linked TPAFn (designated by X-TPAFn [4]) for our comparisons. It was shown in reference 4 that the cyclic voltammograms of pristine and cross-linked TPAFn (n ¼ 2, 3) gave very similar results for the top energy levels, hence we conclude that their cross-linked results can be used to estimate the energy levels and gaps of pure bulk TPAFn’s. More importantly, since all polymers are treated as (pseudo) 1D conjugated chains in the gas phase, their interchain interactions are neglected. As discussed in Section 2, these intermolecular effects, which tend to bring chains closer to each other and in the process make their backbones more planar, are known to reduce the 1D infinite polymer chain band gaps by 0.1e0.2 eV in most conjugated polymers with large unit cells [16,23,24]. Appropriate adjustments should be made to the theoretical 1D band gaps when comparing

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

2539

Fig. 3. The DFT/B3LYP 1D band structure of (a) TPAF1, (b) TPAF2, (c) TPAF3 obtained using 6-31G(d) basis set and 32 k points. (In these figures, C in HOCO, LUCO etc stand for crystal, they have the same meaning as HOMO, LUMO etc in this work.)

with the 3D empirical data. In this work (see discussion above) we reduce the 1D Egap’s by 0.2 eV when comparing them with experimental 3D Egap’s. It should be noted that most of the band-gap decreases appear to originate from the lowering (by 0.2 eV in TPAFn (n ¼ 2, 3) and 0.1 eV in TPAF1) of the LUMO eigenvalues. 3.1. TPAF1 e 1D PBC-DFT band structure We begin the investigation of TPAFn’s with the simplest compound, TPAF1 (see Fig. 2(a)). In order to further insure that 32 k points is sufficient for our 1D solid state computations TPAF1 we performed 12 and 32 k points (B3LYP, O3LYP and OB95) DFT (with 6-31G(d) basis set) calculations. We have found that these two (12 and 32 k points) computations gave very similar results for the geometry parameters and energies (most IP’s, EA’s and Egap’s

were identical to two decimal places). Hence we performed 32 k point 1D solid state calculations for all the remaining DFT approximations. TPAF1 unit cell consists of one fluorene and one triphenylamine compound, hence the content of the triphenylamine (hence nitrogen) is highest in this polymer compared to, say, TPAF2 or TPAF3. There is a torsional angle (f1) of the order of 50 between the fluorene and the triphenylamine (see Table 3 where f1 for all six functions is given), hence (single, isolated) TPAF1chain is not planar. Table 3 shows that f1 is largest for OB95 (52 ), followed by O3LYP (51 ) with remaining functionals giving a similar result of 48 . TPAF1 has a finite dipole moment along the chain backbone which is of the order of 0.6 debye. Table 4 shows the energy results of TPAF1 for the various DFT approximations. Egap ranges from 2.18 to 3.79eV. The experimental value for Egap for TPAF1 is taken as 3.0 eV which is actually obtained

2540

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

Fig. 4. Six top molecular orbitals for (a) TPAF1, (b) TPAF2 and (c) TPAF3: HOMO, HOMO-1 and HOMO-2 on the left and LUMO, LUMOþ1 and LUMOþ2 on the right.

for TFB [6,9], a polymer very similar to TPAF1 with the additional alkyl chain on the phenyl group that is not part of the chain backbone. Since it is known that the side chains have little effect on the electronic energy levels of the polymers, it is believed that the TFB values for EA, IP and Egap can be used to estimate corresponding values for TPAF1. The 3D bulk effect corrected Egap’s of TPAF1 (by subtracting 0.2 eV (or 0.1eV) from the computational data as given in Table 4) for hybrid functionals O3LYP and B3LYP are 2.8 and 3.3 eV (or 2.9 and 3.4 eV) respectively and compare well with the (approximate) experimental value of 3.0 eV with O3LYP underestimating and B3LYP overestimating this value. PBE1 overestimates the experimental value by more than 0.5 eV. The functionals OB95, PBE and TPSS all underestimate the experimental Egap by nearly 1 eV. The IP (related to the negative of the HOMO eigenvalue) is very important for the energy level matching with the ITO work function. It can be seen that the experimental value of 5.30 eV is best Table 3 Torsional angles between triphenylamine (T) and fluorene (F) (f1) and fluorenes (f2andf3) are listed for TPAFn (n ¼ 1e3) for all six DFT functionals. All angles are in degrees. Molecule

Functional

TPAF1 PBE1 B3LYP O3LYP TPSS OB95 PBE TPAF2 PBE1 B3LYP O3LYP TPSS OB95 PBE TPAF3 PBE1 B3LYP O3LYP TPSS OB95 PBE

f1 T-F1 48.6 47.9 50.6 48.3 52.1 47.8 T-F1 28.7 28.3 28.4 26.3 30.2 26.9 T-F1 31.7 31.8 37.9 26.5 33.6 27.0

f2

reproduced by the hybrid functional PBE1 followed by B3LYP and O3LYP with the corresponding differences of 0.3, 0.5 and 0.9 eV respectively. Non-hybrid functionals give values that differ by more than 1 eV. EA (related to the negative of the LUMO eigenvalue) is also important in enhancing the hole transport of HTL since its relatively small value can block the electron transport and hence can increase the probability of a holeeelectron recombination in the emissive layer. Table 4 shows that the experimental EA (2.3 eV) is best reproduced by the GGA and meta-GGA functionals, i.e. PBE is followed by OB95 and TPSS with respective differences of 0.3, 0.4 and 0.5 eV. These differences can be reduced by the intermolecular interactions by approximately 0.1 eV. The hybrid functional EA’s differ from the experimental value by approximately 1 eV. These results indicate that while the best agreement for IP is obtained using Table 4 IP, EA, band gap, and max-gap values of TPAFn (n ¼ 1e3) as obtained from 32 k points 6-31G(d) 1D solid state DFT calculations. All energies are in eV’s. Molecule

Method

IP

EA

Egap

Max-gap

TPAF1

PBE1 B3LYP O3LYP TPSS OB95 PBE Expa PBE1 B3LYP O3LYP TPSS OB95 PBE Expb,c PBE1 B3LYP O3LYP TPSS OB95 PBE Expb,c

5.00 4.76 4.44 4.12 4.09 4.15 5.3 5.07 4.83 4.55 4.16 4.13 4.19 5.16 5.02 4.79 4.49 4.16 4.14 4.19 5.21

1.21 1.28 1.44 1.84 1.87 1.97 2.3 1.39 1.45 1.71 2.01 2.05 2.13 2.27 1.42 1.48 1.60 2.04 2.03 2.15 2.32

3.79 3.48 3.01 2.28 2.23 2.18 3.0 3.67 3.38 2.84 2.15 2.08 2.06 2.89 3.61 3.31 2.89 2.12 2.11 2.03 2.89

4.15 3.83 3.34 2.59 2.52 2.49

f3

TPAF2

F1-F2 41.2 42.0 41.0 39.5 39.8 39.7 F1-F2 39.3 38.9 43.0 38.8 43.4 38.6

TPAF3

F2-F3 45.1 45.0 49.0 42.5 47.1 42.5

a b c

Refs. [6,9]. Reference [4]. Cross-linked.

3.83 3.53 3.00 2.31 2.25 2.22 3.71 3.41 2.98 2.21 2.20 2.12

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

hybrid PBE1, the best agreement for EA is obtained using its nonhybrid counterpart PBE. In both cases the disagreement is in the range 0.2e0.3 eV. In general, fluorene-based polymers are known to present flat energy band structure due to their large unit cells. This is clearly illustrated in Fig. 3 where a typical (B3LYP) band structure of top ten bands (corresponding to five occupied, HOMO, HOMO-1, .,HOMO-4 and five unoccupied, LUMO, LUMOþ1,.,LUMOþ4 orbitals) is shown for all three compounds. We use these band structures to estimate the widths of the top bands since their widths are typically associated with charge delocalization along the chain backbone. Fig. 3 shows that the max-gap values are approximately equal to the sum of the HOMO and the LUMO band widths plus the band gap. This indicates that in the case of TPAF1 (see Fig. 3(a)) the Ewidth’s of the top levels are less than 0.2 eV which is quite narrow suggesting that charge mobility in TPAF1 is relatively low. In fact, Fig. 3(a) shows that all ten of the top bands of TPAF1 are generally quite flat and are almost parallel to each other. Another interesting feature of the TPAF1 band structure is that three of the bands, HOMO-1, HOMO and LUMO are separated from the rest of the respective bands (and from each other in the case of the HOMO-1 and HOMO bands) by energy gaps in the range of 0.5e1 eV which are larger than their widths by more than a factor of two. 3.2. TPAF2 e 1D PBC-DFT band structure The molecular structure of TPAF2 unit cell is shown in Fig. 2(b). Compared with TPAF1, TPAF2 has one more fluorene group which should, in principle, improve its hole transport efficiency due to a longer conjugation length along fluorenes in the unit cell. However, the polymer is still highly nonplanar, the dihedral angle between fluorene and triphenylamine (f1) is reduced to approximately 30 from the close to 50 in TPAF1 and the torsional angle between fluorene units (f2) is of order of 40 (see Table 3) which means that p orbital overlap is not optimal, affecting negatively the charge transport along the (single) chain backbone. Table 3 shows that f1 ranges between 26e29 and f2 between 40e42 illustrating that all DFT functionals predict very a similar structure for TPAF2. The dipole moment along the chain backbone is similar to the one obtained for TPAF1 and is close to 0.6 debye. Experimentally, Egap of TPAF2 is approximately 0.1 eV smaller than that of TPAF1 (see Table 4). This lowering of the band gap for TPAF2 relative to TPAF1 is relatively well reproduced by most functionals (with the exception of O3LYP and OB95 which give values closer to 0.2 eV). As far as the magnitude is concerned, once again, O3LYP and B3LYP give values that are closest to the observed value for the band gap of TPAF2. O3LYP’s gives a value of 2.6 eV for the bulk-state corrected Egap while B3LYP predicts 3.2 eV which are respectively 0.3 eV smaller and larger than the experimental value of 2.9 eV. Again PBE1 overestimates Egap the most by approximately 0.6 eV. TPSS, OB95 and PBE underestimate Egap by approximately 1 eV. The trends for the comparison of the TPAF2’s experimental IP and EA values to the calculated ones are similar to TPAF1’s. B3LYP and O3LYP consistently give reasonably good agreement with the observed IP (5.16 eV), however PBE1 gives the best agreement (0.1 eV difference in comparison to 0.4e0.6 eV for these other hybrid functions). TPSS, OB95 and PBE underestimate the IP value by approximately1 eV. This trend reverses when the EA values of TPAF2 are compared. PBE, OB95, and TPSS give better agreement (0.1e0.3 eV differences, which could be reduced even further to approximately 0.1 eV when intermolecular interactions are taken into account) with the experimental EA value of 2.3 eV while O3LYP, B3LYP and PBE1 give the differences in the range of 0.6e0.9 eV (which again could be reduced by as much as 0.2 eV when

2541

dispersion correction effects are included). The IP and EA results for TPAF2, similar to TPAF1, indicate that the best agreement for IP is obtained using the hybrid PBE1 and the best agreement for EA is obtained using its non-hybrid counterpart PBE. In both cases the disagreement is of the order of 0.1 eV (or less when the dispersion correction effect is taken into account). The top bands for TPAF2 are shown in Fig. 3(b). The Ewidth’s of TPAF2 top (HOMO and LUMO) bands are somewhat smaller than those of TPAF1 and are less than 0.1 eV. Again all five of the top bands for TPAF2 are quite flat. Also similar to TPAF1 band structure, there are now five bands (corresponding to HOMO-2, HOMO-1, HOMO, LUMO, LUMOþ1) that are separated from the respective remaining bands. The energy separations are smaller (closer to 0.5 eV). 3.3. TPAF3 e 1D PBC-DFT band structure The molecular structure of TPAF3 unit cell is shown in Fig. 2(c). The results of TPAF3 are similar to those of TPAF1 and TPAF2. The unit cell consisting of triphenylamine and three fluorene groups is also quite nonplanar, the torsional angles are approximately 30 between triphenylamine and fluorene, 40 between the two middle fluorenes and closer to 45 between the two end fluorenes (see Table 3). The range of the various dihedral angles (f1, f2, f3) are bit broader for TPAF3 than for TPAF1 and TPAF2 for the five DFT functionals (f1 ranges between 27e38 , f2 between 39e43 and f3 between 43e49 ). This shows that isolated TPAF3 and TPAF2 (see Section 3.2) are somewhat more planar than TPAF1 chains. The dipole moment for TPAF3 is closer to 1 debye, a bit larger than for TPAF1 and TPAF2. The B3LYP and O3LYP approximations give the best agreement with the observed value (2.9 eV) for the band gap of TPAF3, their bulk-state corrected Egap’s are respectively 2.7 and 3.1 eV which is respectively 0.2 eV smaller and larger than the experimental value. PBE1 overestimates the experimental Egap (by approximately 0.5 eV) and OB95, TPSS and PBE underestimate it, again by approximately 1 eV. With respect to experimental IP (5.21 eV) and EA (2.32 eV) values, both B3LYP and O3LYP IP’s give reasonably good agreement with the observed IP (with differences 0.4e0.7 eV), however PBE1 again gives the best agreement with the observed IP (with difference less than 0.2 eV). Similarly, TPSS, OB95 and PBE underestimate the IP by approximately 1 eV. For the EA, PBE, OB95, and TPSS all give better agreement with the experimental EA value (with the maximal difference of 0.3 eV) than B3LYP, O3LYP or PBE1 (with differences in the range of 0.7e0.9 eV). Once again, these differences most likely will be reduced by 0.2 eV when EA’s are corrected for the intermolecular interactions. Hence, similar to TPAF1 and TPAF2, PBE1 gives the best prediction for the IP and PBE for the EA of TPAF3. The Ewidth’s of the ten TPAF3 bands are quite flat and are smaller than those of TPAF2 (and TPAF1) as is shown in Fig. 3(c). Also, the top valance and conduction bands of TPAF3 are more or less evenly separated from each other in their respective regions. 3.4. Molecular orbital analysis of TPAF1, TPAF2 and TPAF3 All the molecular systems studied in this work are in their ground states. We plot the six top molecular orbitals (MO’s) for the TPAF1(see Fig. 4(a)), TPAF2 (see Fig. 4(b)) and TPAF3 (see Fig. 4(c)) unit cells. That is, Fig. 4 shows the adjacent top MO’s: HOMO, HOMO-1 and HOMO-2 and LUMO, LUMOþ1 and LUMOþ2. The HOMO and LUMO of TPAF1 have the expected p and p* delocalized structures that are often observed in the organic conjugated systems and the nonplanarity of this molecular system is clearly illustrated. Fig. 4(b) shows that as the unit cell gets larger (as in TPAF2), the HOMO of TPAF2 tends to be more localized on the triphenylamine unit, its HOMO-1 on the two fluorenes and HOMO-2

2542

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543

is delocalized over the whole repeat unit, whereas the LUMO of TPAF2 is more extended over the two fluorenes and its LUMOþ2 is more localized on the triphenylamine unit. The top orbitals for TPAF3 are similar to those of TPAF2’s (see Fig. 4(c)). Once again the HOMO of TPAF3 tends to be more localized on the triphenylamine unit and its HOMO-1 delocalized over the whole repeat unit, whereas LUMO and LUMOþ1 of TPAF3 are more extended over the whole repeat unit. The MO analysis suggests that the HOMO valance bands of TPAFn’s can be attributed mainly to the triphenylamine (nitrogen) MO’s and the HOMO-1 band to the (extended) conjugated (p) MO’s of the fluorenes. The LUMO conduction band, on the other hand, is primarily due to (p*) MO’s of the fluorenes. 4. Conclusions TPAFn (n ¼ 2, 3) polymer layers are used to improve the hole transport of PLED by better matching their energy levels to anode (ITO) work function [4]. In this work we also studied the electronic properties of TPAF1. It has also been found that all TPAFn’s (n ¼ 1e3) have direct band gaps and their band structures are closely related to their geometries. Structurally single TPAF1 polymer chain is highly nonplanar, TPAF2 and TPAF3 chains are similarly distorted (but a bit less than TPAF1). These nonplanarities tend to decrease the effective conjugation length and, hence, charge mobility in these polymers. It is expected that in their solid (bulk) state these nonplanarities can be reduced somewhat. Experimentally it was observed [4]that TPAF2 reduces the energy barrier with the cathode more than TPAF3, that is, the IP of TPAF2 is closer to the work function of ITO (4.8 eV) than TPAF3. DFT calculations, for any functional, show that the smallest IP (hence closest to ITO work function) is produced by TPAF1, followed by TPAF3 which is either slightly smaller (by 0.05 eV) than or the same as that for TPAF2. Hence our calculations suggest that from the hole transport point of view, TPAF1 and TPAF3 (not TPAF2) are slightly better materials for matching the ITO work function. As shown in Table 2, the dispersion correction effect on IP would be small but comparable to 0.05 eV and for these systems may be significant. When the dispersion corrections are taken into account and are applied to, say, B3LYP values, we obtain 4.72, 4.77 and 4.72 eV for the IP for TPAF1, TPAF2 and TPAF3 respectively. Once again, this comparison shows that IP’s of TPAF1 and TPAF3 are smaller than the IP of TPAF2. This, of course, does not agree with experimental data which indicates that TPAF2 is best suited for hole transport since it has the smallest IP (the highest HOMO eigenvalue) relative to those of TPAF3 and TPAF1. From the point of view of electron blocking property the HTL material should have relatively small EA (corresponding to high LUMO). Experimental data shows that the smallest EA is obtained for TPAF2 followed by TPAF1 and TPAF3. DFT computations predict that the smallest EA (even after the dispersion corrections as given in Table 2 are applied) is obtained with TPAF1, followed by TPAF2 and then TPAF3 (which is in partial agreement with the observed data) again showing TPAF1 would be preferable, at least as far as its electron blocking property is concerned. It should be pointed out that the experimental results for TPAF1 have an uncertainty associated with them because we used data of a closely related compound (TFB) for them. Focusing on the comparison of TPAF2 and TPAF3, the DFT results predict that TPAF3 would be slightly better than TPAF2 for the hole transport but TPAF2 has a slightly better electron blocking property than TPAF3. Considering that such small energy differences (in most cases less than 0.05 eV) are involved in these comparisons, it can be speculated that from the point of view of charge mobility, for nearly the same HOMO levels (IP’s) (due to mostly the presence of the nitrogen in these larger unit cells), it is the electron blocking property

that determines which material will have better quantum efficiency in the various devices. Based on this TPAF2 should display slightly better performance (which it does in some OLED application [4]). As far as the use of the various functionals in these 1D band structure calculations are concerned, the general trend is that the gradient-corrected (non-hybrid) functionals such as PBE, TPSS, and OB95 match the experimental EA’s better while the hybrid functionals such as PBE1, O3LYP, and B3LYP match the experimental IP’s better. Hybrid functionals give better predictions for Egap’s, the main reason for this is the fact the discrepancies between their HOMO and LUMO eigenvalues (eεHOMO and eεLUMO) and the respective experimental IP’s and EA’s are of similar order of magnitude for these functionals whereas the gradient-corrected functions give improved agreement for EA but much less so for IP (i.e. the two top eigenvalues are not shifted upward roughly by the same amount in the case of gradient-corrected functionals). In particular, in this study, in all three cases, the best agreement with experimental data was obtained with PBE1 for IP, PBE for EA, and O3LYP and B3LYP for band gaps. This is in agreement with our previous study [12] that indicated that for unit cell consisting of many atoms (as in OxFn (n ¼ 1e3)) similar conclusions for IP’s, EA’s and band gaps were obtained. Finally, the molecular orbital analysis indicates that TPAF1 behaves somewhat differently than TPAF2 and TPAF3. In particular as the number of fluorenes in the unit cell increases, on going from TPAF1 to TPAF3, the HOMO tends to be more localized on the triphenylamine whereas the LUMO extends more over the fluorenes rather than triphenylamine. It is expected that as the number of fluorenes increases even further the effect of triphenylamine unit (nitrogen) will decrease and the HOMO will include larger charge delocalization over fluorenes and the polymer will behave more like pure polyfluorene (with IP of the order of 5.8 eV, EA of 2.12 eV and Egap (CV) of 3.68 eV [1]) which means that, eventually, the material will become less optimal for the efficient hole transport. It is clear from this MO analysis that the smaller band gap in TPAF’s (as compared to pure polyfluorene) is largely due to the presence of the nitrogen containing group along the chain backbones. Acknowledgments This work was, in part, supported by the Natural Sciences and Engineering Council of Canada (NSERC). Also we would like to thank the Atlantic Computational Excellence Network (ACEnet), the Western Canada Research Grid (WestGrid) and Compute/Calcul Canada, and Memorial University of Newfoundland (St. John’s, NL, Canada) for the use of their computing resources. ACEnet is the regional high performance computing (HPC) consortium for universities in Atlantic Canada that includes the provinces of Newfoundland and Labrador, Nova Scotia, and New Brunswick. WestGrid is the HPC consortium that encompasses 14 partner institutions across provinces of British Columbia, Alberta, Saskatchewan and Manitoba in western Canada. References [1] Chen S-A, Lu H-H, Huang C-W. Polyfluorenes -Advances in polymer Science 212 (Polyfluorenes for device applications). Berlin/Heidelberg: Springer-Verlag; 2008. 49-84. [2] Skotheim TA, Elsenbaumer RL, Reynolds JR, editors. Handbook of conducting polymers. New York: Marcel Dekker Inc.; 1998. [3] Bradley DDC. Synth Met 1993;54:401e15. [4] Lu J, Jin Y, Ding J, Tao Y, Day M. J Mater Chem 2006;16:593e601. [5] Zhang Z-G, Zhang K-L, Liu G, Zhu C-X, Neoh K-G, Kang E-T. Macromolecules 2009;42:3104e11. [6] Hains AW, Liu J, Martinson ABF, Irwin MD, Marks TJ. Adv Funct Mater 2010;20:595e606.

L. Ling, J.B. Lagowski / Polymer 54 (2013) 2535e2543 [7] Liu C, Sirringhaus H. Org Electronics 2010;11:558e63. [8] Choulis SA, Choong V-E, Patwardhan A, Mathai MK, So F. Adv Funct Mater 2006;16:1075e80; Hwang J, Kim E-G, Liu J, Bredas J-L, Duggal A, Kahn A. J Phys Chem C 2007;111: 1378e84. [9] Yan H, Lee P, Armstrong NR, Graham A, Evmenenko GA, Dutta P, et al. J Am Chem Soc 2005;127:3172e83. [10] Zuniga CA, Barlow S, Marder SR. Chem Mater 2011;23:658e81. [11] Bard AJ, Faulkner LR. Electrochemical methods: fundamentals and applications. 2nd ed. Wiley, ISBN 0471043729; 2000. [12] Ling L, Lagowski JB. J Mol Struct Theochem 2010;944:146e55. [13] Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, et al. Gaussian 03, Revision B.05. Pittsburgh PA: Gaussian, Inc; 2003. [14] Kudin KN, Scuseria GE. Chem Phys Lett 1998;289:611e6; Kudin KN, Scuseria GE. Chem Phys Lett 1998;283:61e8; Kudin KN, Scuseria GE. Phys Rev B 2000;61:16440e52; Yazyev OV, Kudin KN, Scuseria GE. Phys Rev B 2002;65:205117-1e205117-8. [15] Belletete M, Beaupre S, Bouchard J, Blondin P, Leclerc M, Durocher G. J Phys Chem B 2000;104:9118e25. [16] Eslamibidgoli MJ, Lagowski JB. J Phys Chem A 2012;116:10597e606. [17] Perdew JP, Burke K, Ernzerhof M. Phys Rev Lett 1996;77:3865e8; Perdew JP, Burke K, Ernzerhof M. Phys Rev Lett 1997;78:1396.

2543

[18] Becke AD. J Chem Phys 1993;98:5648e52; Becke AD. Phys Rev A 1988;38:3098e100; Vosko SH, Wilk L, Nusair M. Can J Phys 1980;58:1200e11; Lee C, Yang W, Parr RG. Phys Rev B 1988;37:785e9; Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ. J Phys Chem 1994;98: 11623e7. [19] Handy NC, Cohen AJ. Mol Phys 2001;99:403e12; Hoe W-M, Cohen AJ, Handy NC. Chem Phys Lett 2001;341:319e28; Baker J, Pulay P. J Chem Phys 2002;117:1441e9; Guner VA, Khuong KS, Houk KN, Chuma A, Pulay P. J Phys Chem A 2004;108: 2959e65. [20] Becke AD. J Chem Phys 1996;104:1040e6; Sancho-Garcia JC, Cornil J. J Chem Phys 2004;121:3096e101. [21] Tao J, Perdew JP, Staroverov VN, Scuseria GE. Phys Rev Lett 2003;91: 146401-1e146401-4; Staroverov VN, Scuseria GE, Tao J, Perdew JP. J Chem Phys 2003;119: 12129e37. [22] GaussView visualization software, version 4.1.2. Shawnee Mission, KS: Semichem Inc; 2000e2006. [23] Gierschner J, Cornil J, Egelhaaf H-J. Adv Mater 2007;19:173e91. [24] Salzner U, Pickup PG, Poirier RA, Lagowski JB. J Phys Chem A 1998;102: 2572e8.