Donor-Acceptor Sequence Engineering in ÏâConjugated Polymers for

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C: Energy Conversion and Storage; Energy and Charge Transport

Donor-Acceptor Sequence Engineering in #–Conjugated Polymers for Enhanced Hole Transport and Photocurrent Longhua Li, Baoxin Ge, Bolin Han, and Weidong Shi J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 24, 2019

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The Journal of Physical Chemistry

Donor-Acceptor Sequence Engineering in π–Conjugated Polymers for Enhanced Hole Transport and Photocurrent Longhua Li*, Baoxin Ge, Bolin Han, Weidong Shi* School of Chemistry and Chemical Engineering, Jiangsu University, Zhenjiang 212013, P. R. China

ABSTRACT Sequence-dependent properties of synthetic polymers are of great concern. To customizing the electronic and optical properties of copolymers, it is highly desirable to realize the quantitative sequence-property relationship. The sequence-dependent carrier transport and optical properties of the donor(D)–acceptor(A) PTB7 copolymer was studied through density functional theory (DFT) calculations. The exact enumeration structures in lexicographical order with periodic boundary conditions were constructed by a high-throughput approach. The absorption coefficient, effective mass, deformation potential, and hole mobility exhibits a strong response to the sequence-patterns. Significantly, the bi/multi-block pattern [DnAn] shows much better hole mobility and short-circuit current than the well-known [(DA)n] pattern. For example, hole mobility of [DnAn] is 12%–46% larger than the [(DA)n]; and the calculated short-circuit current of [DnAn] is 1.5–2.5 times of the [(DA)n]. Our work uncovered the reason for this enhancement: the intrinsic band splittings of the additional D–D/A–A interactions could induce strong absorption coefficient and electron delocalization. The concept of additional D–D/A–A combinations may be generally applicable and could provide an additional degree of freedom for the design of donor-acceptor polymers with tunable properties.

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INTRODUCTION The physical steps in a solar cell can be simplified to the absorption of photons, exciton dissociation, and charge transport to electrodes. Thus, an organic polymer for a solar cell should have a high optical absorption coefficient, an efficient exciton separation, and large carrier mobility with minimized recombination. The morphology, backbone conformation, dopant, and side-chain were commonly known to play an important role in manipulating carrier mobility of polymers.1,

2

Recently, there is also increasing interest in precisely controlling monomers

sequence toward tuning polymers properties.3-5 The sequence engineering would expand the library of polymers to meet requirements in fields like energy, medicine, and data storage.6, 7 To date, However, only several kinds of patterns are realized in AnBm polymers due to the challenge of synthesis, for instance, alternating sequence (e.g., AB…AB), bi-/multi-block (AnBn…AnBn, n≥2), gradient distribution (AnB1An-1B2…A1Bn+1), tapered type (AmB1AnB2An1…BnA1Bm)

and position insertion (e.g., AmBAn).8-10 Indeed, the attractive differences in

properties were found within such a limited list of sequence architectures,11-15 suggesting that the fine-tuning sequence would offer an exciting opportunity for property design. Unfortunately, the available number of sequences in a copolymer chain can be varied by length. For instance, a copolymer (AnBm, n≥1, m≥1) that contains n A and m B monomers could generate permutations up to (n + m)! / (n! × m!). Though this is not exactly the case in practice because many sequence structures may be identical if applied proper symmetries, it remains true that the number of patterns would increase with chain length. Such increasing of sequence-patterns with length scales causes unprecedented difficulty in enumerating all possible sequence-solutions. While the effect of monomer ratios have commonly been addressed in previous studies,16,

17

the full

permutation of sequences attracts very little attention.18 Hutchison group19 has employed SIMILES20 notation system and Open Babel21 to construct sequence structures of oligomers for photovoltaic application. They have found sequence-dependent frontier orbital energy levels in tetramers and hexamers. However, the interrelation between sequence and carrier mobility and optical absorption in the donor-acceptor copolymers is still vague or unknown. In this work, the photovoltaic polymer that consists of benzodithiophene (BDT) and fluorothieno[3,4-b]thiophene (FTT) was studied. The BDT and FTT are the typical donor and acceptor motifs that have been broadly used in donor-acceptor (D-A) conjugated copolymers in the last decade.22 The most studied binary blend may be the poly[[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-


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b:4,5-b′]dithiophene-2,6-diyl][3-fluoro-2-[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl]] (PTB7)

and

poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b:4,5-b’]dithiophene-co-3-

fluorothieno[3,4-b]thiophene-2-carboxylate](PTB7-Th), because they exhibit superior solar energy power conversion efficiency (PCE)

of about 8–12%.23-26 The sequence-pattern

dependence of charge transport and optical properties was systematically investigated by density functional theory (DFT) calculations. All available sequence-patterns in polymers BDTnFTTn (n ≤ 6, about 80 structures) were generated by our lexicographical search method. We have set up an integrated picture of the sequence-property relationship. Our results indicate that the property of traditional D–A polymer can be further improved by sequence manipulating. For example, [DnAn] patterns show an enhanced photocurrent density of 0.75–1.1 mA/cm2, which is at least 1.6 times of the traditional [(DA)n] pattern. In addition, [D2A2], [(D2A2)2], [D3A3], and [D3A3DA] patterns exhibit higher hole mobility than the corresponding [(DA)n] pattern. We propose that the sequence-pattern may become an additional degree of freedom in customizing the D–A polymer.

METHODS AND COMPUTATIONAL DETAILS A FORTRAN code GenLS (generate lexicographical structures) was developed by implementing the lexicographical algorithm and geometry operations. Assuming there are n BDT and FTT in the periodic unit cell, the problem becomes to discover full permutations of the sequence from [DnAn] to [AnDn]. The utilization of periodic boundary conditions has been widely realized for the investigation of D-A copolymers.27-30 Mathematically, the unique ordered set with n nodes can be enumerated lexicographically.31 However, this full permutation is lack of physical meanings, i.e., it may still involve a large number of identical structures from the view of physics. We, therefore, included symmetry operations in our code. Take a general sequence [ABCDE] (in periodic boundary conditions, PBC) for instance, which should be equal to [EDCBA], [EABCD], [DEABC], [CDEAB] and [BCDEA]. In order to verify such operations, we performed calculations on the BDT2FTT2 (D2A2) polymer, which has six sequences: [DDAA], [DADA], [DAAD], [ADDA], [ADAD] and [AADD]. As expected, the total energy and frontier orbital (HOMO and LUMO) energy level of [DDAA], [DAAD], [ADDA] and [AADD] are almost same to each other; [DADA] and [ADAD] are also same (see in Figure S1, SI). Such symmetry operations, therefore, help to eliminate those sequence-patterns that defined in the same structured way. This code not only can be used to generate full permutations structures



between two moieties, but also can be used to generate general polymers in periodic or nonperiodic forms, such as (N1)n1(N2)n2(N3)n3(N4)n4… with different kinds of components (N1, N2…) and numbers (n1, n2…). And it can also be extended to generate vertical/lateral stacking structures of two-dimensional (2D) materials. There are two advantages of our developed framework: (1) it can enumerate all sequences in order without duplication or omission; (2) this code also offers a high-throughput solution for processing large amounts of structures that required in DFT calculations. The generated structures were fully optimized by the density functional theory (DFT) linear combination of atomic orbitals (LCAO) method as implemented in Atomistix ToolKit (ATK) packages.32 A double-ζ polarized (DZP) basis set was used. Core electrons were described by the Troullier−Martins norm-conserving pseudopotential with the Kleinman−Bylander nonlocal projector.33, 34 The exchange-correlation energy was treated with the Perdew−Burke−Ernzerhof (PBE) version of the generalized gradient approximation (GGA).35 A 1 × 1 × 3 Monkhorst−Pack (MP)36 k-mesh was adopted. The optimization performed until the residual forces on atoms were less than 0.01 eV/Å. After the structure optimization, the ground state was calculated with a 1 × 1 × 4 Gamma centered k-mesh. The optical absorption coefficient was evaluated through:

  2 c

12   22  1 2

(1)

Where ω and c are the wave frequency and the speed of light, respectively. The real (ε1) and imaginary (ε2) part of dielectric constant was derived from the Kubo-Greenwood formula, using a denser k-mesh of 1 × 1 × 16. We further quantify the photocurrent density by the flux of absorbed photons (Jabs), assuming every photon is converted to a unit of charge carrier. Jabs was calculated by integrating the following function from the optical gap to 280 nm (the standard maximal frequency at the reference air mass 1.5 spectra, AM1.5G):37

J abs  e  A( ) J ref ( )d 

(2)

Where A(ω) is expressed as A( )  1  exp( L) and the layer thickness L = 1 nm is using. Jref (ω) is the incident photon flux (photons/cm2·s·eV), which is obtained from the reference AM1.5G spectra.38 By multiplying the elementary charge e (1.60217662 × 10-19 coulombs), the absorbed photon flux becomes to the theoretical maximum possible photocurrent density (units of mA/cm2), that is, Jabs is the upper limit contribution to the solar cell short-circuit current.


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Charge mobility (μ) was explored by the deformation potential (DP) theory,39 assuming electron–phonon coupling is weak compared with the intermolecular electronic couplings in this system and only the lattice scattering is included. In one-dimensional (1D) systems, μ can be simply using the effective mass approximation:40

1D 

eh2C

 2 kBT 

1/2

m*me

3/2

 EDP 

2

 2 E  C   2  a0    dE EDP  edge d

(3–5)

Where ħ, kB, T, me, a0, m*, C, EDP are Plank constant, Boltzmann constant, temperature, the mass of an electron, equilibrium length of the 1D system, the effective mass of hole or electron, elastic coefficient, and deformation potential, respectively. The elastic coefficient C can be calculated by a quadratic relation between total energies (E) and strains (ε, ±3%), and the deformation potential EDP for hole/electron was evaluated by a linear fit of the highest occupied molecular orbital (HOMO)/lowest unoccupied molecular orbital (LUMO) with strains from –3% to 3%. The DP model has been widely applied in π–conjugated molecular/organometallic systems.41, 42 Thus, this model may also be reasonable for the copolymers studied in this paper. RESULTS AND DISCUSSION The moieties of the donor (BDT) and acceptor (FTT), as well as the sequence-patterns for DnAn (n = 1–5), are presented in Figure 1. Patterns of D6A6 are too many to be illustrated here, which is shown in Table S1 (SI). From the GenLS code, we found that the permutation number increases markedly with the number of donor (acceptor) in the backbone (Figure S2, SI). For example, 1, 2, 3, 8, 16, 50, 133, 440, 1387 and 4752 effective permutations are obtained in BDTnFTTn (DnAn, n = 1–10). The huge number of structures is beyond our computational power when n > 6. Therefore, lexicographical structures from [DnAn] to [(DA)n] (n = 1–6) were explored to demonstrate the effect of D–A sequence on the electronic and optical properties of conjugated polymers.



Figure 1. (a) Structures of the donor (BDT, D) and acceptor (FTT, A), the side chains are simplified to H; (b) backbone lexicographical patterns in periodic boundary conditions (PBC) for conjugated polymers BDTnFTTn; blue and orange blocks represent donor and acceptor, respectively. The total of 50 sequence-patterns of D6A6 is shown in Table S1. Sequence-pattern dependent electronic and optical properties The sequence-pattern dependence of the electronic structure is presented in Figure 2a. The [(DA)n] have similar HOMO and LUMO level (horizontal dash line), because they are the supercell of [DA]. For the [DnAn] pattern, the HOMO tends to increase with the number of donor/acceptor, but is not linearly dependent on n, wherein, the HOMO level of [D2A2] ([D4A4]) is similar to that of [D3A3] ([D5A5]). On the side of the LUMO, it decreases fast from [DA] (–3.6 eV) to [D2A2] (–3.9 eV) and then converges to about –4.0 eV in [DnAn] (n ≥ 3). In each copolymer, the traditional [(DA)n] pattern shows the lowest HOMO energy and the highest LUMO energy among all patterns; while the [DnAn] pattern often shows the highest HOMO and the lowest LUMO. By projecting the density of states (DOS) into each monomer, we found that the degenerate states in the conventional [(DA)n] sequence (Figure 2b) are split-off in [DnAn] (Figure 2c) and other sequences (Figure S3). This is due to the fact that additional D–D and A–A couplings are formed in [DnAn] and other patterns compared with the traditional [(DA)n] sequence. Such band splitting induced small band gap and multiple electronic states around the Fermi level are critical for the optical dipole transitions, which we shall discuss later. In order to understand the effect of sequence on frontier orbit energy, the HOMO and LUMO of [DnAn] are plotted as an example in Figure 2d. Generally, strong anti-bonding means high HOMO level while the enhancement of bonding strength means redshift of LUMO. According to Figure 2d, [DnAn] (n≥2) patterns exhibit stronger π‒π anti-bonding states as compared to [(DA)n],


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which are contributed not only from BDT-TT but also from TT-TT and BDT-BDT. Therefore, [DnAn] (n≥2) shows higher HOMO than the corresponding [(DA)n]. It is also noticed that the localization of HOMO density increases with the number of nodes, especially notable in BDT units. Such hole charge localization should reduce hole mobility that would be displayed later. On the side of LUMO, the σ–σ bonding strength in the [DnAn] is stronger than that in the [(DA)n] due to the σ states of the [DnAn] are not only comprised of BDT-TT but also of TT-TT and BDTBDT. Moreover, in [DnAn] (n≥3), the LUMO is similar to each other and is predominated by σ bonding states among 3 TT and 1 BDT units. Thus, the LUMO of the [(DA)n] is higher than the [DnAn], and [DnAn] (n≥3) shows a similar LUMO level.

Figure 2. (a) HOMO and LUMO energy of polymers BDTnFTTn; the horizontal dash line is the value of [(DA)n] pattern and the vertical dash line represents the [DnAn] pattern; (b) projected density of states (PDOS) of the traditional [DADADADA] sequence and (c) multi-block 𝑆 ” means bands splitting. (d) HOMO [DDDDAAAA] sequence; the Fermi level is set to zero; “□



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and LUMO for [DnAn] patterns; the isosurface value is set to 0.01 e*Bohr3; the cell boundary is not shown for clarity. The absorption coefficient is critical to the absorption of photons. Here, we take the optical absorption of D4A4 polymer as an example to illustrate the change of absorption spectra with DA pattern. It should be noticed that our GGA obtained optical gap is about 1.1 eV (Figure 2) for the normal [(DA)n] pattern, which is much smaller than the G0W043 and experimental44 value of 1.65 eV. In order to stay consistent with the previous studies, we assume that the same error is introduced by GGA functional in all patterns and a rigid shift of 0.55 eV is applied in Figure 2. Although our assumption is simple, the energy difference between them is independent of the shift. As shown in Figure 3a, p1–p8 represent the eight patterns of D4A4 polymer: [D4A4], [D3A3DA], [D3A2DA2], [D2A3D2A], [D2A2(DA)2], [D2ADA2DA], [(D2A2)2] and [(DA)4]. We found that, as compared to the traditional [(DA)4] pattern (the black line), (1) the absorption coefficient of all other patterns are enhanced in the violet, yellow and orange regions; (2) however, the absorption coefficient is significantly reduced in the blue and red regions; (3) in the green region, only the coefficients of p4 ([D2A3D2A]) and p5 ([D2A2(DA)2]) are enhanced; (4) all other patterns exhibit a much stronger optical absorption coefficient in the near-infrared region (NIR) than the traditional [(DA)4], because of the relative small band gap. In principle, the efficiency of the generation of electron-hole pairs is mainly determined by the optical absorption coefficient and absorption intensity in the visible and near-infrared regions. The absorption j

intensity is studied by integrating the area under the absorption line (αω), I    d  . The i

change of absorption intensity is evaluated relative to the [(DA)n] pattern. In the visible region (Figure S4), the [DnAn] pattern in each polymer, except the D2A2 polymer, shows the largest absorption intensity. The improvement of the absorption intensity is even more significant in NIR, see in Figure 3b. The absorption intensity of all other patterns is at least 1.5 times of the intensity of the [(DA)n] pattern; and the [DnAn] pattern in each polymer are shown the largest absorption intensity that is about 4.6–5.6 times of the [(DA)n] pattern. Such a significant enhancement of absorption intensity, especially in NIR, might result in a positive benefit for the generation of electron-hole pairs.


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In order to quantify the conversion of photons to the electric current (photocurrent density), the Jabc is calculated in Figure 3c. The [(DA)n] generate photocurrent around 0.45 mA/cm2; the photocurrent of [DnAn] patterns increase with monomer number n, from 0.75 to 1.08 mA/cm2; and other patterns generate photocurrents in the 0.6–1.0 mA/cm2 range. It is straightforward to see that all other patterns display stronger photocurrents than the traditional [(DA)n] pattern, and [DnAn] patterns present the largest photocurrent density among all patterns. The photocurrent of 1 nm thickness DnAn polymer is much smaller than that of transition metal dichalcogenides (2– 4.5 mA/cm2).37 However, we notice that there is a tendency of increasing photocurrent with increasing n, i.e., molecular weight in a unit cell. It is then expected that the photocurrent may be improved further by increasing the molecular weight (backbone length) of [DnAn] pattern. We, further, take the traditional alternating pattern [(DA)4] and multi-block [D4A4] as an example to interpret the optical property in D–D/A–A combinations. As the band structures are shown in Figure 3d, the band splittings of multi-block [D4A4] are significant, especially, the splitting between the highest (lowest) valence (conduction) band (VB1/CB1) and the second highest (lowest) valence (conduction) band (VB2/CB2). The band splittings of VB1-VB2 and CB1-CB2 reduce the band gap between VB1 and CB1, and this contributes to the absorption coefficient in NIR. Extra band splittings could result in additional subbands in the same energy range, which creates more inter-band transitions. In order to know the contribution of each bandband transition to the optical absorption coefficient, the band-resolved optical absorption is investigated by increasing VB and CB step by step. The contribution of band-pairs is clearly shown in Figure 3e and 3f. For the traditional pattern [(DA)4], the absorption spectrum is relatively simple, only three optical absorption bands are formed by the transitions between VB(1–4) and CB(1–4). The first absorption band (P1) are essentially due to the transitions of VB1–CB1, because P1 band does not change with the increase of conduction bands; the second and third absorption bands, P2 and P3, are mainly originated from VB2–CB2 and VB3(VB4)– CB3 transitions, respectively. For [D4A4], the effect of band splitting is pronounced; at least 10 optical absorption bands are associated with the eight electronic bands. The absorption bands of P1–P4 are dominated by the inter-band transitions from VB1 to CB(1–4), respectively; and the P5–P8 bands are originated from VB2 to CB(1–4), respectively; the strong peak P9 is mainly due to VB3–CB1 transitions; and the weak P10 is derived from VB4–CB2. Our results suggest that the additional D–D and A–A couplings induced band splitting is critical for the electronic and



optical properties of conjugated polymers. We believe that by further optimizing the concentration and chemical species of D–D and A–A combinations, such polymers may express greatly enhanced electronic and optical properties compared to the traditional onefold D–A couplings.

Figure 3. (a) Optical absorption of various D-A sequences in D4A4 polymer; p1–p8 represents patterns: [D4A4], [D3A3DA], [D3A2DA2], [D2A3D2A], [D2A2(DA)2], [D2ADA2DA], [(D2A2)2], [(DA)4]; the color bar from left to right represents the visible region (violet, blue, green, yellow, orange and red) and near-infrared region (NIR); a blue shift of 0.55 eV was applied for all patterns; (b) the change of the absorption intensity (as compared to the [(DA)n] pattern) in the NIR from 750 to 1500 nm; (c) the dependence of photocurrent density on D-A sequences; (d) band structures of [(DA)4] and [D4A4]; the first four valence bands (VB) and conduction bands (CB) are marked as VBn and CBn; the main inter-band transitions are presented as Pn (n = 1–10); (e) and (f) band-resolved optical absorption for [(DA)4] and [D4A4], respectively; the symbol “Pn:Vm-Ct” means that the absorption peak Pn mainly origins from the transitions between the valence band m and conduction band t.


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Sequence-pattern dependent hole transport Charge transport is a key factor in optimizing optoelectronics performance. Here, we focus on the hole mobility (μh) of studied sequences. The elastic coefficient C, which is the result of strain induced total energy shift, seems varied with D–A patterns (Figure 4a). However, the variation is slight, from the minimal 53.5 eV/Å to the maximal 55.5 eV/Å, that is, the magnitude of change in C is much less than 3.6%. Thus, the coefficient C may be regarded as a constant. The average C is 54.5 eV/Å, and the μ is simplified as:

1D 

eh2C

 2 kBT 

1/2

* 3/2

me3/2 m

 EDP 

2



431.88 m*

3/2

 EDP 

2

(6)

The difference between the result of the Eq. (3) and Eq. (6) is given in Figure 4d. The negligible difference between the Eq. (3) and Eq. (6) indicates that our assumption is reasonable. Our results suggest that the elastic coefficient is not observable dependent on the D–A sequence. A large μh could be obtained if a small mh* and EDP was achieved. The mh* is varied significantly with the D–A sequence as shown in Figure 4b. The mh* of [(DA)n] patterns (the horizontal dashed line) should be similar (0.25m0 – 0.27m0) in the studied polymers. However, the mh* of [DnAn] (n ≥ 2) patterns (the vertical dashed line) increase exponentially with n (see the insert in Figure 4b). This may be due to the Dn–An couplings (see HOMO in Figure 2d, the hole distributions become more localized with increasing n) decrease with n. The significant influence of hole localization on the reduction of hole mobility has also been discussed in other conjugated copolymers.45 It is interesting to see that mh* of all other patterns are smaller than that of the regular [(DA)n] pattern when n ≤ 4. In particularly, the [DDAA], [DDDAAA], [DDAADDAA], [DDDAADDAAA] and [DDAADDAADDAA] sequences display the smallest mh* in D2A2 (0.162m0), D3A3 (0.153m0), D4A4 (0.152m0), D5A5 (0.176m0) and D6A6 (0.164m0) copolymers, respectively. Thereby, our calculations indicate that the well-defined pattern, [(D2A2)n] (n≥1 for even D and A) or [(D3A3)(D2A2)n] (n≥0 for odd D and A), has the smallest mh* for a given copolymer with 1:1 D-A ratio. The effect of D–A sequence on DP of the hole is plotted in Figure 4c. DP can be obtained from the strain induced front molecular orbital (FMO) energy shift, which is expressed by E(FMO)=E(DP)*ε+E0, where ε is the strain on the backbone and E0 is initial energy. A high μh requires a small DP of the hole, which means that HOMO should be as insensitive as possible to the variation of the strain. All other patterns show much larger E(DP) than the [(DA)n]. Thereby,



the HOMO of the conventional pattern [(DA)n] is much rigid as compared to other patterns, indicating again the electronic states of D–D/A–A combinations are more delocalized compared to the onefold D–A couplings. Dependence of μh on D–A sequence is shown in Figure 4d. Because all other patterns show much larger E(DP) than the [(DA)n], most patterns display smaller μh than the traditional [(DA)n] polymer, ~195 cm2V-1s-1. According to the Eq. (6), the μh can be larger than that of [(DA)n] only if mh* and E(DP) satisfied the following condition:

mh*

3/2

2 * E (DP)  mh* ([D A])

3/2

2 * E (DP) ([D A])  2.16

Only [D2A2] (2.03), [D3A3] (1.55), [(D2A2)2] (1.59) and [D3A3DA] (1.98) patterns exhibit higher μh than the [(DA)n] pattern, which is mainly due to they have relative small mh*. Our DP results provide a solid support for the previous assumption18 that D–D combinations may improve charge mobility. It should be noticed that the calculated hole mobility of PTB7 ([DA] pattern) is approximately 5–6 orders of magnitude larger than the experimental value (~0.2×10-4 – 5.9×10-4 cm2V-1s-1).46 This overestimation may be ascribed to the defect-free and rigid backbones, i.e., ideal one-dimensional wires, used in the calculations. Besides, only the intrachain mobility along the backbone was evaluated in our calculations. In fact, the consequence of the “trap-free” space charge limited current (SCLC) measurement47 is not only included the intra-chain charge transport but also the inter-chain (mostly van der Waals interactions) charge transport. Intra-chain mobility is usually several orders of magnitude higher than the inter-chain mobility.48, 49 Therefore, the calculated values can be regarded as the upper limit of intra-chain mobility. The overestimations of the deformation potential model have also been reported previously in π-conjugated systems.50 Nevertheless, the deformation potential model can describe qualitative differences in the mobility of various backbone patterns.


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Figure 4. The effect of D–A sequence on (a) elastic coefficient; (b) effective hole mass; (c) deformation potential of hole; and (d) hole mobility of DnAn (n=1–6) copolymers; bar (–) represent hole mobility calculated with elastic coefficient of 54.5 eV/Å.

CONCLUSIONS In summary, we use density functional theory based electronic structure calculations to explore systematically the effect of donor–acceptor (D–A) sequence on the electronic and optical properties of conjugated polymer PTB7. A sequence search method is developed for the purpose of generating lexicographical D–A sequences. The DnAn (D: BDT; A: FTT; n ≤ 6) polymers were taken as the example to demonstrate that the electronic and optical properties fine-tuning can be achieved through programming the backbone patterns. Our results show that the welldefined pattern, [(D2A2)n] (n≥1 for even D and A) or [(D3A3)(D2A2)n] (n≥0 for odd D and A), has the smallest effective hole mass among all patterns. The [D2A2], [D3A3], [(D2A2)2] and [D3A3DA]



patterns exhibit higher hole mobility than the traditional [(DA)n] pattern. Although effective mass, deformation potential, and hole mobility are pattern-dependent, it is interesting to find that the elastic coefficient can be treated as a constant. Moreover, the photocurrents of [DnAn] patterns linearly increase with n from 0.75 to 1.08 mA/cm2, which are significantly larger than that of the traditional [(DA)n] pattern, 0.45 mA/cm2. Based on the above results, we found that the multi-block pattern [D3A3] and bi-block [(D2A2)2] may be the optimized structures to achieve high hole mobility and photocurrent density in PTB7. The enhancement of electronic and optical properties is found positively related to the subbands of D–D and A–A combinations. Note that even though the calculations are performed for PTB7, our results can be used to understand the trends in the electronic and optical properties of other DA polymers. The band splittings of D– D/A–A couplings indicate that the electronic and optical properties fine-tuning may be achieved through programming sequence and the ratio between D–A and D–D/A–A combinations. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Including: total energy and HOMO-LUMO level of D2A2; the effective permutation number of DnAn; PDOS of sequence-patterns in D4A4 polymer; the absorption intensity in the visible region; and the table of sequences of DnAn for n=1–6. CONFLICT OF INTEREST The authors declare no conflict of interest. Corresponding author [email protected]; [email protected] ACKNOWLEDGEMENTS All calculations were performed on National Supercomputing Center in Tianjin and HPC of Jiangsu University. This work was supported by National Natural Science Foundation of China (No. 11604125); Natural Science Foundation of Jiangsu Province (No. BK20160522); China Postdoctoral Science Foundation (No. 2017M611705).


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Table of Content By exploiting the lexicographical sequence-patterns of donor (D)-acceptor (A) PTB7 copolymer, the quantitative sequence-property relationship is presented. The D–D/A–A combinations exhibits enhancement of hole mobility and photocurrent compared to the traditional D–A pattern.


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