Delimited Polyacenes: Edge Topology as a Tool To Modulate Carbon

Article Cite This: Chem. Mater. 2018, 30, 947−957

pubs.acs.org/cm

Delimited Polyacenes: Edge Topology as a Tool To Modulate Carbon Nanoribbon Structure, Conjugation, and Mobility Qianxiang Ai, Karol Jarolimek, Samuel Mazza, John E. Anthony, and Chad Risko* Department of Chemistry & Center for Applied Energy Research, University of Kentucky, Lexington, Kentucky 40506-0055, United States S Supporting Information *

ABSTRACT: Carbon nanoribbons offer the potential of semiconducting materials that maintain the large charge-carrier mobilities of graphene. Here, starting with polyacene as a reference, we present a theoretical investigation as to how polycyclic aromatic hydrocarbons inserted into the polymer structure modulate the edge topology of the zigzag polyacene. The variations in edge topology, in turn, produce nanoribbon structures that have electronic properties that span insulators to narrow-gap semiconductors. Clear connections are made among foundational models in aromatic chemistry, namely, descriptions in terms of Clar formulas and bond-length alternation patterns, and the nanoribbon electronic, phonon, and charge-carrier mobility characteristics. These relationships, for systems that are synthetically feasible from bottom-up, solution-based approaches, offer a priori and rational design paradigms for the creation of new nanoribbon architectures.

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INTRODUCTION Graphene is of immense academic, industrial, and popular interest, given that its intriguing electronic characteristics could impact a wide range of (opto)electronics applications, from traditional semiconductors to advanced nanoscale technologies. Large charge-carrier mobilities, which range in experimental measurements from 105 to 106 cm2 V−1 s−1,1−3 make graphene, for instance, an ideal component for next-generation transistors, although the gapless nature of the graphene electronic structure4 prohibits such applications given the need for controllable device turn-off. A promising strategy to bypass this limitation is to reduce the graphene dimensionality by creating one-dimensional (1D) graphene-like polymers, often referred to as graphene nanoribbons (GNR), that possess finite electronic gaps. Such a strategy, verified by simulations that consider electron correlation5,6 and experiment,7−10 has been successfully applied to transistors that demonstrate promising performance metrics.11−13 Synthetic approaches to GNR are generally classified as either (i) top-down, where a precursor, typically graphite, is chemically or physically broken into irregular fragments, or (ii) bottom-up, which relies on traditional organic synthetic techniques. Although top-down methods have the advantage of offering high-throughput production, GNR with well-defined structure and chemical accuracy are only obtained through bottom-up approaches.14−18 Concerning bottom-up approaches, GNR fabrication with atomic precision has been realized by the polymerization of small molecular precursors both on metal surfaces9,19−21 and in more traditional, solutionbased polymerization reactions.10,22,23 Unfortunately, on-surface synthetic approaches are hindered by strong interactions between the GNR and metal substrate, often in the form of © 2018 American Chemical Society

metal−carbon covalent bonds that prevent GNR exfoliation. This constraint, in turn, leaves solution-based polymerizations as the main routes to realize free-standing GNR that are suitable for device applications.24 Regardless of the synthetic protocol, a key handle to synthetically control GNR electronic characteristics is to direct the topology of the GNR edges, as both theory25−31 and experiment32−35 demonstrate the critical role that the edge topology plays in narrow-width GNR. Although the complex structure−property relationships are still not fully understood, the design principle to control edge topology has been showcased as a practical route to construct GNR targets with customizable electronic properties.36−39 From the perspective of chemical structure manipulation, it is reasonable to contemplate polyacene (PA, Figure 1) as the conceptually smallest zigzag graphene nanoribbon (ZGNR). Although the synthesis of PA remains a challenge, because of its inherent instability,40 PA is an intriguing theoretical model as its electronic structurea gapless electronic band structure with a Dirac coneallows it to be considered a one-dimensional (1D) analogue of graphene.41 The existence of the PA Dirac cone is preserved in GW calculations,42 whereas for wider ZGNRs, the band gap is opened when electronic correlations are included. Kivelson and Chapman, making use of a tight-binding model,43 showed that, instead of being protected by lattice symmetry, as is well-known in the case of graphene, the band crossing in PA is an accidental degeneracy that is produced by certain constraints on the hopping integrals. Furthermore, unlike the Received: November 9, 2017 Revised: January 16, 2018 Published: January 17, 2018 947

DOI: 10.1021/acs.chemmater.7b04715 Chem. Mater. 2018, 30, 947−957

Chemistry of Materials

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COMPUTATION DETAILS

Geometric and Electronic Characteristics. For all 1D DPA polymers, density functional theory (DFT) calculations were carried out with the Perdew, Burke, and Ernzerhof (PBE) exchangecorrelation functional56 with electron−ion interactions described by the projector augmented-wave method57 and full periodic boundary conditions using the Vienna Ab-initio Simulation Package.58 In order to obtain accurate energy-volume relations, the fast Fourier transformation mesh was manually set to 150 × 150 × 150 for all unit cells. The kinetic energy cutoff for the plane-wave basis set was 520 eV, and Gaussian smearing with a width of 0.05 eV was employed. The total energy convergence criterion was set to 0.01 meV in all self-consistent field iterations, and the maximum force allowed on each atom was 0.01 eV/Å. The Brillouin zone, unless specified otherwise, was sampled with a (300/a) × 1 × 1 Γ-centered grid, where a is the lattice constant of the DPA polymer (in Ångströms). Note that a vacuum is inserted into the respective unit cells in order to treat each structure as a noninteracting, 1D polymer; enough vacuum is inserted such that the shortest distance between two 1D polymers is >10 Å. For isolated, gas-phase molecules, the ground-state geometries and electronic structures were obtained via DFT calculations using the PBE exchange-correlation functional and 6-31G(d,p) basis set.59 Molecular calculations were carried out with the Gaussian 09 (Revision E.01) software suite.60 Estimates of the Charge-Carrier Mobility. For GNRs with welldefined structure, scattering in low-field carrier transport can be mainly attributed to the presence of acoustic phonons with longitudinal acoustic (LA) modes.61,62 By using the deformation potential theory for a 1D system,63 the mobility can be expressed as shown in eq 1: Figure 1. Chemical structure of polyacene, with its corresponding [bottom left] electronic band structure and [bottom right] density of states (DOS). In the band-structure diagram, the valence and conduction bands are represented by the color red. Although widely reported in the literature,41,44 the PA electronic characteristics and DOS are reproduced here as reference for the remainder of the discussion.

μ=

eℏ2C 2πkBT |m*|3/2 E12

eτ = m*

(1)

where e represents the elementary charge, τ the relaxation time, m* the effective mass, C the elastic constant, and E1 the deformation potential constant. The value of m* was determined using the finite difference method code that was developed by Fonari and Sutton.64 C and E1 were obtained by using the following expressions:

C = l0

graphene density of states (DOS), the PA DOS is nonzero at the Fermi level,44 revealing its metallic nature. Building off of the PA structure as a subset of ZGNR, we are interested in understanding how to dictate GNR electronic characteristics by controlling the edge topology. In particular, we aim to develop design guidelines for GNR that maintain large charge-carrier mobilities with finite electronic gaps. Here, we consider the insertion of polycyclic aromatic hydrocarbons (PAH) of varying structure and symmetry within the PA backbone to create so-called delimited polyacenes (DPA). Such chemical modifications have been invoked in bottom-up, solution-phase syntheses of extended acenes, producing molecular structures with high numbers of consecutive, fused aromatic rings.45−55 However, particularly in the case of the numerous aza-acene examples of this approach, the actual “acene” character of the resulting materials does not appear to materialize. The PAH delimiters and subsequent DPA topology considered are depicted in Figure 2. Note that the distance between the delimiters, or number of benzene rings in the acene segment (denoted by a lowercase, italicized p in Figure 2), is varied to tune the electronic characteristics. The results presented here showcase a great diversity in terms of the available DPA electronic characteristics, including the ability to completely break the π conjugation, and shed further light on underlying structure−function relationships that can be used to fine-tune narrow carbon nanoribbon design.

∂ 2E ∂l 2

l = l0

(2)

and E1 = l0

∂ε ∂l

l = l0

(3)

where E is the total energy, ε is the energy at the conduction band minimum (CBM) or valence band maximum (VBM), l is the lattice constant, and l0 is the equilibrium lattice constant.

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RESULTS AND DISCUSSION We begin by considering how the delimiter structure and distance between said delimiters, which when combined, define the carbon nanoribbon edge topology, impact the DPA geometric and electronic structure. Estimates of the chargecarrier mobility are then presented to demonstrate how these changes in edge topology impact this essential material characteristic. Here, given the periodic boundary condition calculations, the DPA are being described as three-dimensional (3D) crystals with sufficient vacuum space in the unit cells to eliminate interactions among 1D DPA polymers. Four DPA classes are considered, as represented in Figure 2, where the delimiters are either pyrene (P; D2h), perylene (PER; D2h), or rubicene (R; C2h). The pyrene delimiter is evaluated in two orientations: vertical (v) and oblique (o). In the text, the DPA are labeled based on the delimiter, delimiter orientation, and length of oligoacene unit (p) separating the delimiters in 948


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Figure 2. Chemical structures of the [top] delimiters and [bottom] delimited polyacenes (DPA) considered. The lowercase, italicized p in the nomenclature, also represented diagrammatically, denotes the number of benzene rings that comprise the acene segment between each delimiter.

BLA, starting from the middle, in oligoacenes as their lengths increase (see Figure 3 (top right), as well as Figure S1 in the Supporting Information).16−18,70 It is within this framework that we will understand the impact of the delimiters on the geometric properties of the DPA. In the figures that follow, each bond is colored such that the color linearly changes from blue (long, 1.46 Å) to red (short, 1.35 Å); within this color scheme, the midpoint bond length (1.405 Å) in PA is colored white. A second approach to understand bond length equivalence in PA stems from the Clar formula of PA. Clar proposed that the chemical structure with a maximum number of sextets best represents the behavior of π-electrons.71 We note that approaches involving Clar aromaticity have been developed and used to investigate relationships among the geometric and electronic structures of wider GNR.27−31,35 Within this framework, for oligoacenes of arbitrary length, only one sextet can be drawn from its Kekulé formula, which is a consequence of the open boundary conditions. The Clar formula for PA, which can be considered as an infinitely long acene, returns zero sextets and is identical to the Kekulé formula. This result indicates an ideal (complete) delocalization of π-electrons, and a zero BLA along the edges. Representative BLA patterns and corresponding Clar formulas for the DPAs (p = 5) are illustrated in Figure 3. A definitive BLA pattern is evident in all DPA considered in this study, with symmetry that follows the underlying DPA structure. For the vP-p-DPA, there is a reflection symmetry

the monomeric unit. The DPA monomer symmetries, assuming symmetric addition of the oligoacene units to either side of the delimiter are as follows: vP-p-DPA, D2h; oP-p-DPA, C2h; PERp-DPA, C2h; and R-p-DPA, C2h. While the vP-p-DPA and R-pDPA symmetries correspond to the symmetry of the delimiter, there is a reduction in the symmetry of the oP and PER delimiters when coupled to the oligoacenes. We note that the vP-p-DPA systems are the smallest analogues of the so-called coved GNR (CGNR).38 DPA Geometric Structure: Bond-Length Alternation and Clar Formulas. When considering the geometry of PA, a natural comparison is to polyacetylene (Pa), the prototypical conducting polymer,65 because PA can be considered as two σlinked trans-Pa chains related by reflection symmetry. In Pa, if all of the bond lengths are equal (i.e., there is no bond-length alternation (BLA)), then a metallic (gapless) state is expected. However, in accord with Peierls theorem for 1D metals,66 there is a strong electron−phonon (vibronic) coupling that reduces the geometric symmetry and removes the degeneracy of the highest occupied and lowest unoccupied levels, making Pa a semiconductor.67 In the case of PA, the existence of BLA remains a topic of wide interest.68,69 It has been argued that such a Peierls distortion is disfavored in PA, partially because of the quadratic form of electronic energy as a function of distortion that is guaranteed by the mirror symmetry in PA.43 This concept is displayed in Figure 3 (top left), which shows the lack of BLA for the trans-Pa segments of PA from the present calculations. This is also consistent with the vanishing 949


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nanoribbons that span insulators to narrow-gap semiconductors. DPA Electronic Band Structures. As a reminder, the reference electronic structure for the impact of the delimiters is that of PA, whose band structure and DOS are given in Figure 1. Starting with vP-p-DPA (Figure 4), the introduction of the vertically oriented pyrene delimiter opens a finite gap between the valence and conduction bands (VB and CB, respectively) in the PA band structure. Increasing the spacing between the delimiters by increasing the value of p results in a rather dramatic decrease in the gapfrom 2.35 eV when p = 1 to 0.34 eV when p = 5 (see Table 1, presented later in this work). Such a large change in the electronic band gap suggests the potential for exquisite control of the conducting properties of vP-p-DPA. However, the VB of the vP-p-DPA systems are flat when p > 1, and the CB becomes increasingly flat as p increases; this trend is counter to the presence of the dispersive VB and CB found for all other DPAs. Such flat CB and VB lead to quite large electron effective masses and infinite hole effective masses. vP-1-DPA differs slightly, because, at the Γpoint, the VB-1 is flat and the VB is dispersive, although midway along the Γ → X trajectory these bands cross. Such flat bands have previously been observed in the band structures of ZGNR, and were attributed to the localization of edge states,25 and, notably, polyparaphenylene.72 Similar localization arguments are valid for vP-p-DPA, as the charge densities of flat bands are localized on the acene segments (see Figure S2 in the Supporting Information). Notably, the acene-localized charge densities strongly resemble the highest-occupied (lowest-unoccupied) molecular orbitals [HOMO (LUMO)] of the isolated acene moieties. This implies that the vertically oriented pyrene delimiter breaks the conjugation across the PA-like backbone in vP-p-DPA, with the oligoacene segments electronically isolated from each other quite an interesting electronic character for a system that is built completely from aromatic units. Hence, it is expected that these DPA will have insulator-like electronic properties. To provide a deeper understanding to the origin of these flat bands, we examined the frontier molecular orbitals (MO) of fragments that could be considered to comprise vP-2-DPA: pyrene and 1,2-benzodiene, and the subsequent dibenzo(de,uv)tetracene. The HOMO (LUMO) of the pyrene and 1,2-benzodiene moieties possess symmetries that, unfortunately for these structures, limit the degree of wave function overlap when they are combined to form dibenzo(de,uv)tetracene (Figure 5), as evidenced by the lack of wave function delocalization across the full dibenzo(de,uv)tetracene structure. Hence, when a second 1,2-benzodiene is appended on the other side of the pyrene, there will be limited to no electronic coupling between the naphthalene-like units. While the analysis of the segment MO is related to the flat bands observed in the vP-p-DPA, we emphasize that this is merely an intuitive abstraction of intercell electronic coupling, because the dibenzo(de,uv)tetracene unit does not fully represent the vPp-DPA unit cell. To show the generality of the relationship between the MO symmetry of the corresponding units that comprise the DPA and the potential for flat bands in the polymer electronic structure, we consider the structure DBC-p-DPA, where the PA is delimited by dibenzo(bc,kl)coronene (DBC; see Figure 6). Importantly, the DBC HOMO and LUMO symmetries are the same as those for pyrene, and the symmetry of the 1,2benzodiene connectivity onto DBC is also the same as pyrene.

Figure 3. [Top] Bond length alternation (BLA) in PA and oligoacenes, where the color changes linearly, with respect to bond length, from blue (1.46 Å) to white (1.405 Å) and then red (1.35 Å). [Bottom] BLA patterns, using the same color scheme, and Clar formulas for all DPA with p = 5. The purple rectangles indicate the corresponding 1D unit cells, and the black rectangles with double dashed lines mark acene segments within the DPA.

of the BLA in the acene segments, similar to that illustrated for the unsubstituted oligoacenes. For all other DPA considered, the BLA in the acene segments is centrosymmetric. In the vP-pDPA, PER-p-DPA, and R-p-DPA BLA patterns, short bonds in the phenyl rings peripheral to the PA backbones indicate localized states, which are corroborated by sextet formation in the context of the Clar formulas. The Clar formulas for both vP-p-DPA and PER-p-DPA can be regarded as concatenations of the Clar formulas for the delimiter and oligoacenes, whereas, for oP-p-DPA and R-p-DPA, the Clar formulas are unique to the combined structures. Notably, the BLA pattern in the acene segments of the R-p-DPA represents an asymmetric distortion that breaks the reflection symmetry. Hence, clear patterns, from both analysis of the BLA and the Clar formulas, emerge with regard to the connections between the delimiter structure and the edge topology. The delimiter variations produce distinct patterns in the edge bond lengths, which are expected to foreshadow diverse electronic characteristics. We now turn to the electronic structures and showcase how the edge topology modifications can lead to carbon 950


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Figure 4. DPA electronic band structures. The valence band and conduction bands (CB and VB, respectively) are denoted by the red color.

variations in the MO distributions between these structures as a function of the bonding symmetry of the acene to pyrene. In the case of the PER-p-DPA, a relatively large band gap is obtained that decreases as p increases. No peaks nor valleys are present in the band structures, and the effective masses are insensitive to p. However, as we will discuss later, the mobility is dependent on p due to electron−phonon scattering. For R-p-DPAs, a small but finite gap is present in all structures, which can be correlated with small geometric distortions (see the DPA Geometric Structure: Bond-Length Alternation and Clar Formulas section). If an in silico PA model is generated where the same geometric distortions as observed in R-5-DPA are applied, a finite gap can be opened at the Dirac point and the resulting band structure approaches that of R-5-DPA. Interestingly, the band gap in R-5-DPA is slightly larger than that in such a distorted PA (Figure 8). Thus, while the BLA and Clar formulas indicate localized charge densities in the peripheral phenyl rings of R-p-DPA, the impact of these phenyl rings on the electronic structure of R-p-DPA cannot be neglected. This is also in agreement with the finite coupling between the PA-like backbone and peripheral phenyl rings of R-5-DPA, as shown in Figure 9. Although the dispersion relations are quadratic at the band extrema, very small effective masses (∼0.01 m0) for both carriers are obtained. As with the edge topology, the variation in the delimiter is shown to have a dramatic effect on the electronic band structure. There is indeed great tunability of the electronic band gapover a few eValthough some of the tunability, as in the case of vP-p-DPA, is for VB and CB that are flat, which is a

Taking DBC-4-DPA as an example, the electronic structure reveals flat VB and CB, acene-like charge densities that are localized between the DBC delimiters, and a BLA within the acene segment that is similar to that of an isolated tetracene. Hence, as one may expect, there is an explicit need to take into account the MO symmetry of the delimiter with respect to the coupling acene unit when constructing DPA. These results suggest that a deeper analysis of the impact of delimiters on extended acene-like structures recently reported in the literature is needed.45−55 For the oP-p-DPAs, which possess distinct chirality, the band gap is inversely correlated with p when p < 5; the band gap of oP-5-DPA is slightly larger than that of oP-4-DPA. Interestingly, the effective masses are also inversely correlated with p. While both the VB and CB show parabolic character at the zone edge for p < 4, a relatively flat region appears in the VB and CB from k = 0.41 to k = 0.5 (k = 0 to k = 0.16) when p = 4 (p = 5). The flat region contains a weakly pronounced peak (valley) in the VB (CB) in the reduced first Brillion zone (FBZ). Figure 7 illustrates the charge densities of two VB states, denoted A and B, near the peak in the reduced FBZ of oP-5-DPA. While the charge density tends toward zero in the acene segment of state A, the charge density remains notably larger for state B. This situation is similar to the symmetry change in states around the band crossing of PA,42 which indicates the possibility for recovering a PA-like electronic structure at large p-values in oP-p-DPAs. For reference, a molecular orbital (MO) analysis for the oP-p-DPA structures, as discussed above for vP-p-DPA, is presented in Figure S4 in the Supporting Information, which showcases important 951


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Figure 6. (a) Frontier molecular orbitals of dibenzo(bc,kl)coronene. (b) VB and CB charge densities of DBC-4-DPA, the isovalue is set to 0.03 e/Å3. (c) Band structure of DBC-4-DPA. (d) Bond length alternation (BLA) in DBC-4-DPA.

Figure 5. [First two rows] HOMO and LUMO charge densities in naphthalene and VB and CP charge densities in vP-2-DPA; the isovalue is set to 0.03 e/Å3. [Last two rows] Frontier MO of pyrene (left), 1,2-benzodiene (middle), and dibenzo(de,uv)tetracene (right), with the respective MO symmetries provided for reference. The isovalue is set to 0.05 e/Å3.

result of localized charge densities that can be attributed to the delimiter structure and acene bonding position. For the other delimiters considered, the electronic band structures meet characteristics consistent with narrow-gap semiconductors. With this information in hand, we now consider models of charge-carrier mobility and demonstrate the impact that longitudinal acoustic (LA) phonons have on the expected charge-carrier characteristics. Charge-Carrier Mobility. Equation 1 and information pertaining to the electronic band structures were used to evaluate the charge-carrier mobilities of different DPA structures (Table 1). Given the similar structural width, all DPA considered here have similar C (the elastic constant), which is a result consistent with previous theoretical studies of GNR that reveal that the chirality does not significantly affect the mechanical behavior.73 On the other hand, E1 (the deformation potential constant) adopts varying values across the DPA. Under the assumptions described in the Computation Details section, the scattering probability between charge carriers and LA phonons is inversely correlated with E1. This is also reflected in eq 1, where the mobility is inversely proportional to E1. Previous studies38,74 on charge-carrier scattering induced by acoustic phonons revealed an empirical rule that states that crystal orbitals running perpendicular (parallel) to the stretching direction of the phonons have a tendency to induce large (small) E1. This empirical rule will be used as a basis for the evaluation of the E1 for the DPA.

Figure 7. Symmetry changes in the charge density around the VB peak in oP-5-DPA. The charge densities reside in the plane 0.7 Å away from the polymer plane. The charge densities range from 0 to 0.03 e/Å3. An alternative plot of the charge density distribution is shown in Figure S3 in the Supporting Information.

Because of the flat valence bands in vP-p-DPA, infinite hole effective masses result when p > 1, which leads to zero chargecarrier mobility. vP-1-DPA does have a finite mobility since the VBM is curved. While the CB are not completely flat, the electrons are still “heavy” for all cases, because of small CBM 952


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Figure 8. Band structures of undistorted (black dashed) and asymmetrically distorted (red solid) PA and R-5-DPA (blue solid). The Brillouin zone is sampled with a 200 × 1 × 1 Γ-centered grid.

Figure 9. VBM and CBM charge densities for select DPA: oP-4-DPA, oP-3-DPA, PER-1-DPA, PER-2-DPA, and R-5-DPA. The DPA chemical structures are provided for reference. The isovalue is set to 0.01 e/Å3 for all isosurfaces.

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Table 1. Band Gap (Egap), Hole Effective Mass (mh*), Electron Effective Mass (me*), Elastic Constant (C), Valence Band Deformation Constant (E1h), Conduction Band Deformation Constant (E1e), Hole Mobility (μh), and Electron Mobility (μe) of DPA DPA

Egap (eV)

PA vP-1-DPA vP-2-DPA vP-3-DPA vP-4-DPA vP-5-DPA oP-1-DPA oP-2-DPA oP-3-DPA oP-4-DPA oP-5-DPA PER-1-DPA PER-2-DPA PER-3-DPA PER-4-DPA PER-5-DPA R-1-DPA R-2-DPA R-3-DPA R-4-DPA R-5-DPA

0 2.35 1.99 1.46 1.06 0.77 0.443 0.232 0.096 0.085 0.100 1.22 1.19 0.99 0.75 0.53 0.027 0.031 0.037 0.044 0.053

m*h (0.01m0)

m*e (0.01m0)

C (eV /Å)

10.8

137.3 86.9 94.1 125.1 174.3 14.3 12.6 11.2 10.0 5.6 20.4 20.4 22.1 22.0 20.3 0.9 0.9 1.4 1.1 1.4

49.41 49.98 49.54 49.95 48.58 49.68 47.22 44.24 44.89 42.01 43.18 48.36 48.36 48.49 48.85 48.68 50.58 48.60 49.58 56.73 44.13

15.1 13.4 11.9 10.5 5.8 18.7 17.9 19.0 19.9 19.6 0.9 0.9 1.4 1.1 1.4

E1h (eV)

E1e (eV)

4.79

2.65 3.91 4.71 5.31 5.78 7.26 7.13 7.17 3.23 3.77 4.37 6.37 7.23 7.37 7.29 4.70 4.82 5.02 5.04 5.08

2.28 2.45 2.54 6.38 6.31 3.99 4.02 3.93 4.04 4.09 4.71 4.92 5.13 5.46 5.63

μh (× 102 cm2 V−1 s−1) 4.88

12.32 11.96 13.49 2.41 6.18 2.99 3.14 3.01 2.68 2.66 212.55 187.17 90.52 131.29 66.90

μe (× 102 cm2 V−1 s−1) 0.35 0.31 0.19 0.09 0.05 1.31 1.54 1.85 10.13 18.24 2.18 1.02 0.71 0.69 0.79 213.46 195.02 94.53 154.08 82.17

higher than other DPA investigated here, the largest mobility, which is theoretically determined for R-1-DPA to be 2.1 × 104 cm2 V−1 s−1, is smaller than that of graphene (∼105−106 cm2 V−1 s−1, determined by both theory75 and experiment1−3). This may be attributed to a more pronounced electron−phonon scattering in narrow ribbons, as the carriers in R-p-DPAs are almost massless.

curvatures. Interestingly, this is the only DPA construct with broken electron−hole symmetry. For oP-p-DPA, there is a sudden increase (decrease) of E1h (E1e) when p varies from 3 to 4, which leads to a drastic change in hole (electron) mobility. This can be explained by the already-mentioned empirical phonon rule and the VBM and CBM charge densities shown in Figure 9. For oP-4-DPA, the VBM (CBM) charge density in the pyrene unit runs perpendicular (parallel) to the stretching direction of the LA phonons, which is opposite to the scenario in oP-3-DPA. The reversal in the band extrema charge densities then leads to a reversal in E1 values, as well as that in mobilities. This reversal also coincides with a shift of band extrema as p changes: in oPp-DPA with p < 4, the band extrema are found at the boundaries of FBZ, and, starting from p = 4, the band extrema reside within FBZ. On the other hand, the effective masses are almost halved upon going from p = 4 to p = 5, which, in turn, leads to a significant increase in mobilities of both carriers. Similarly, there is a large difference between the hole and electron mobilities in PER-p-DPA when p > 1. Again, this trend can be understood within the context of the empirical phonon rule. In PER-1-DPA, the VB charge densities in the acene segments run perpendicular to the ribbon, while charge densities of the CBM run perpendicular to the ribbon in the perylene unit. This combination leads to small differences between E1h and E1e. However, in the VBM of PER-2-DPA, the charge densities of all segments are aligned parallel with the ribbon, while the CBM charge densities in the perylene moieties are perpendicular to the ribbon. Such differences in the VBM and CBM charge density distributions in PER-2-DPA, and the other PER-p-DPA when p > 1, leads to different mobilities for different carriers. For R-p-DPA, a small difference between E1h and E1e is observed, which is expected since both the VBM and CBM charge densities extend in a parallel alignment with respect to the LA phonons. While the mobilities of the R-p-DPA are

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CONCLUSIONS

In this study, we explored how PAH of different symmetry, when inserted into the PA framework, act as delimiters to modulate nanoribbon edge topologies, electronic structures, and charge-carrier mobilities. Appropriate choice of the delimiter, with an emphasis on the delimiter molecular symmetry and connectivity within the ribbon, provides the ability to exquisitely control nanoribbon electronic characteristics, creating semiconductor materials that could have chargecarrier mobilities that approach that of graphene. Conversely, we have also demonstrated how certain PAH delimiters can lead to nanoribbons with (almost) flat VB and CB, limiting their usefulness in semiconductor applications, although they could be of interest as tunnel junctions. Moreover, the work has further demonstrated how concepts established in the chemistry of aromatic compoundsnamely, the Clar formulas of aromatic hydrocarbons and BLA patternscan be used to understand the resulting impact of the nanoribbon architecture on the electronic properties.27,35 Such foundations offer clear a priori, rational design principles to build, from the bottom up, nanoribbons with distinctive edge toplogies for future semiconductor applications. Importantly, the potential combinatorial chemistry to organize acene and PAH delimiters and chemical substitutions within these units is vast, opening new avenues to create materials with well-controlled electronic properties for advanced electronic technologies. 954


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b04715. Bond length alternation of extended oligoacenes; integrated charge densities of the flat valence bands in the vP-p-DPA; integrated charge densities of the valence band in oP-5-DPA (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

John E. Anthony: 0000-0002-8972-1888 Chad Risko: 0000-0001-9838-5233 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work at the University of Kentucky was supported in part by start-up funds provided to C.R. by the University of Kentucky Vice President for Research. J.E.A. acknowledges support from the Department of the Navy, Office of Naval Research (ONR), under Award No. N00014-16-1-2390. Supercomputing resources on the Lipscomb High Performance Computing Cluster were provided by the University of Kentucky Information Technology Department and Center for Computational Sciences (CCS).

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