Solid-state order and charge mobility in [5]-[12] cycloparaphenylenes

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Solid-state order and charge mobility in [5]-[12] cycloparaphenylenes Janice B. Lin, Evan R. Darzi, Ramesh Jasti, Ilhan Yavuz, and Kendall N. Houk J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 13 Dec 2018 Downloaded from http://pubs.acs.org on December 13, 2018

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Journal of the American Chemical Society

Solid-state order and charge mobility in [5]-[12] cycloparaphenylenes Janice B. Lin,† Evan R. Darzi,‡† Ramesh Jasti,‡ Ilhan Yavuz, †§* and K. N. Houk†‖* †

Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.

§

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

‡

Department of Chemistry and Biochemistry and Materials Science Institute, University of Oregon Eugene,

Oregon, 97403-1253, USA. ‖

Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, California, 90095,

USA.

ABSTRACT We report a computational study of mesoscale morphology and charge transport properties of radially -conjugated cycloparaphenylenes [n]CPPs of various ring sizes (n = 5-12, where n is the number of repeating phenyl units). These molecules are considered as structural constituents of fullerenes and carbon nanotubes. [n]CPP molecules are nested in a unique fashion in the solid state. Molecular dynamics simulations show that while intramolecular structural stability (order) increases with system size, intermolecular structural stability reduces. Density functional calculations reveal that reorganization energy, an important parameter in charge transfer, decreases as n is increased. Intermolecular charge-transfer electronic couplings in the solid state are relatively weak (due to curved -conjugation and loose intermolecular contacts) and are on the same order of magnitude (i.e., ~10 meV) for each system. Intrinsic charge-carrier mobilities were simulated from kinetic Monte Carlo simulations; hole mobilities increased with system size and scaled as ~n4. We predict that disordered [n]CPPs exhibit hole mobilities as high as 2 cm2/Vs. A strong correlation between reorganization energy and hole mobility, i.e. ~4, was computed. Quantum mechanical calculations were performed on co-facially stacked molecular pairs for varying phenyl units and revealed that orbital delocalization is responsible for both decreasing reorganization energies and electronic couplings as n is increased.

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INTRODUCTION [n]Cycloparaphenylenes ([n]CPPs), or “nanohoops,” are composed of phenyl units linked together at the para positions in a circular fashion (Scheme 1). [n]CPPs and similar conjugated nanohoops have attracted considerable attention due to their unusual electronic and mechanical properties that arise from this radially distributed -conjugation.1,2 Unlike their linear counterparts (polyphenylenes), the HOMO-LUMO energy gaps of [n]CPPs increases as the size of the nanohoop increase.3 Since the seminal nanohoop synthesis of [9]-, [12]-, [18]CPP in 2008,4 [5]– [12]CPPs have been successfully synthesized and characterized with solid-state crystal structures.1 In general, cyclic molecules have been employed in variety of fields, such as in host-guest supramolecular chemistry (e.g., fullerene encapsulation), nanomaterials (e.g., potential building blocks of carbon nanotubes) and organic photovoltaics. 5,6,7 The structural arrangement of the CPPs allow for relatively strong non-bonded intermolecular interactions in the solid-state, where the outward-facing π-surfaces can interact with other molecules. These strong interactions can enable efficient charge migration through the material, offering promise in organic electronics. The crystal structures of [n]CPPs, where n = 5–12, have been reported by various researcher groups ([5]CPP8, [6]CPP9, [7]CPP, [8]CPP10,11, [9]CPP12, [10]CPP13,14, [11]CPP1, and [12]CPP15). These structures exhibit similar packing motifs (although multiple polymorphs have been characterized for [6]CPP16,17): herringbone-like packings, slipped with neighboring molecules in one direction and orthogonal in the other direction. While these features are strikingly similar to the ones observed in many oligomeric semiconductors,18,19 the packing of nanohoops is particularly interesting, as there are no  stacking interactions in those directions. Instead,  interactions are observed only in the lateral directions (Scheme 1). The lack of ends in the circular structures, as opposed to the linear materials, excludes structural defects that can cause charge-traps. Charge-trap are thought to be one of the major limiting factors of charge carrier mobility. Additionally, the convex interactions in the solid state are reminiscent of fullerenes and carbon nanotubes in the solid state, suggesting potential applications in organic electronics.

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Scheme 1. (top) Molecular structure and (middle and bottom) solid-state packing of [n]CPPs (nanohoops) in different crystallographic directions. The molecules exhibit herringbone type packing in one plane (middle) and slipped-layer type packing (bottom) in the other. The leftmost diagram simply demonstrates how the packing direction of nanohoop in the middle figures transform (by 90o rotation around the x-axis) into the bottom figures.

In this work, we study the effect of size scaling on structural and charge-transport properties for [n]CPPs in solid-state. The aim of this study is to establish a relationship between solid-state order and intrinsic charge-carrier mobility, which is crucial to the fundamental understanding of the electronic properties of organic materials. We use a number of parameters to characterize the packing of the molecules, including nanohoop diameters, torsional behavior of the phenyl monomers, paracrystallinity and nematic order. Charge-transport parameters were also computed, including reorganization energies, electronic couplings, energetic disorders and intrinsic mobilities. We observe that solid state structural stability scales with n. That is, packing stability decreases with increasing hoop size (due to increasing molecular strain). Hole mobility scales as n4 and is largely controlled by the reorganization energy. We also found that hole mobilities in [n]CPPs are barely susceptible to structural and energetic disorder in comparison to linear oligomers, which is attributed to the lack of end groups in these cyclic materials. To the best of our knowledge, this study is the first demonstration of a strong correlation between the molecular size and, specifically, intrinsic mobility in the field of organic semiconductors.



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II. COMPUTATIONAL METHODS Experimental crystal structures were used as starting structures for the initial supercells containing roughly 1300-1600 molecules for each [n]CPP, including the periodic boundary conditions (PBC). MD simulations in an NPT ensemble were performed on these systems at 300 K using the GPU version of Amber12.20,21 GAFF force fields were used for molecular mechanics parameters.22,23 Partial charges of ground-states were generated from B3LYP/6-311G(d,p)-optimized geometries (see S1) via the Merz-Singh-Kollman scheme24,25 using HF/6-31G(d), as implemented in Gaussian09.26 Each supercell was first heated from 0K to 300 K for 2 ns and then NPT equilibrated for another 2 ns at 300 K while restraining heavy atom positions.27 A final 20 ns production run was performed at 300 K and time-averaged pressure at 1 atm. Snapshots of the MD simulations were taken at various time points in order to obtain atomistic morphologies for subsequent charge transport calculations. Representative MD snapshots of each system equilibrated at 300 K can be found in the Supporting Information. With the MD-equilibrated morphologies in hand, charge-carrier dynamics simulations were performed to calculate charge transfer rates using Marcus theory based on incoherent hopping events, implemented in VOTCA from the Andrienko group Marcus theory relies on two assumptions: (1) charges are instantaneously localized on each site (or molecule, in the case of organic semiconductors)28 and (2) a non-adiabatic charge transfer reaction occurs through a hopping-type mechanism. Electronic coupling elements, Jij, of the charge-transfer were calculated for defined molecular pairs using the semi-empirical method ZINDO.29,30 Pairs are defined as molecules with centroid distances below 0.8 nm, each of which are added to a neighbor list, a compilation of all possible adjacent hopping sites. The reorganization energy  of each molecule was calculated using the four-point rule with B3LYP/6-311G(d,p).31 Site energies were calculated self-consistently using Thole Model, which includes contributions from electrostatic interactions due to polarization and from an external electric field (see ref. 32 for details). In accordance with the method previously described for MD simulations, partial charges of neutral and charged states were generated via Merz-Singh-Kollman scheme, using HF/6-31G(d) method based on B3LYP/6311G(d,p)-optimized geometries.24,25 Isotropic atomic polarizabilities of the neutral and charged states were re-parameterized for each species to calibrate against molecular polarizabilities obtained using B3LYP/6-311G(d,p). Energetic disorders were extracted using the Gaussian


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Disorder Model (GDM), where the histogram of site energy differences (Eij) were fitted to the following Gaussian distribution and used to extract energetic disorder (Kinetic Monte Carlo (kMC) methods were used to predict charge transport of a charge carrier in an applied external electric field, as implemented in VOTCA, and hole mobilities were obtained using velocityaveraging.32,33 III. RESULTS and DISCUSSIONS III. 1. Structural stability (order) In materials, vibrational motions caused by the thermal fluctuations result in dynamic instabilities (i.e., dynamic disorder). These motions manifest as electron-phonon coupling in charge-transport and charge-carrier mobility which can be dramatically affected by the thermal fluctuations. These structural instabilities can be translational fluctuations, intramolecular breathing, and/or intermolecular vibrations, etc. We first quantify the structural fluctuations by various parameters (vide infra). Figure 1 (a)-(d), respectively, show the stability of the molecular diameters, phenyl dihedral angles, paracrystal order and nematic order of [n]CPPs, for the MD snapshots of the morphologies equilibrated at 300 K (see S2, Table S1 and S2). Fig. 1 (a) shows the variance of diameters of the rings, which can be used to quantify the amount of intramolecular breathing of the molecules. First, the average diameters of [n]CPPs found from the MD simulations are very consistent with the experimental ones found from the X-ray measurements. The lowest of the set is [5]CPP and after MD simulations we find that it has a diameter of 6.78±0.24 Å. The diameter and its deviation increased up to 16.2±0.38 Å for [12]CPP. These MD simulations reveal that the breathing of the entire molecule amounts to a ~3% deviation for each nanohoop. An increase in instability in molecular diameter is observed with increasing n with a scaling factor of n2, as shown in Fig. 1 (a). A similar increase in instability is observed for the deviations in dihedral angles between phenyl groups, as shown in Fig. 1 (b). We attribute the increase in structural instability to decreasing rigidity of the molecules as the strain (i.e., molecular deformation away from planarity) decreases with increasing ring size. In other words, [n]CPPs with lower ns are more resistant to structural modifications. Another measure, paracrystalline order (g), is defined as the ratio between the deviations and average intermolecular distances (i.e.,

= / ̅ )34 in the lattice along a certain crystallographic



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axis (see Fig. 1 (c)). We find that paracrystallinity decreases with n, in which lower g corresponds to better intermolecular stability. However, we expect that decreasing paracrystallinity could be a result of the increasing molecular weight. Nematic order tensor is defined as >/2, where ,

= , , , and

is a units vector.35

=< 3

−

= 1 and 0 indicate perfect alignment

and isotropic alignment, respectively. We are interested in the nematic order of phenyl groups in nanohoops, so

is chosen to be a normal vector of a phenyl ring, for each case. We report the

largest value of the nematic order tensor and Q quantifies the alignment of the phenyls of a nanohoop. Fig. 1 (d) shows the nematic order distributions for each [n]CPP. The green dots in the figure correspond to the nematic order value of the respective phenyl group of the ring; the dots are connected with solid green lines solely for the purpose of clarity. For ease of representation, the phenyl groups’ positions are set to coincide with the correspond to

= 0 case; the corner of the grey lines

= 1 for each phenyl group in a certain [n]CPP. Fig 1. (d) shows interesting motifs

in Q distributions that become more exotic as n increases. We observe an overall anisotropy in Q distributions for each [n]CPP, except for [5]CPP. Quite interestingly, the Q values of the even numbered [n]CPPs have circular -symmetry, while those of odd numbered [n]CPPs have 2symmetry. This suggests that odd numbered [n]CPPs exhibits alternating packing arrangement in a certain crystallographic direction. The Q distribution of [5]CPP is close to zero, which might indicate strong misalignment of the phenyl groups. However, due to the large molecular strain of [5]CPP and dense packing in the solid state, intramolecular stability is high (see Fig. 1 (a)-(b)). Therefore, lower nematic order in [5]CPP is not due to thermal fluctuations, but rather due to the inherent relative misalignment of the neighboring phenyl groups in the solid state. For the remaining materials, the Q values are typically between 0.5–1 and are found to be somewhat larger for as n increases. This suggests that phenyl groups become more in order as n increases.


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Figure 1. Size dependence of (a) deviations in the hoop diameter, (b) in inter-phenyl dihedral for each [n]CPP (c)  stack paracrystallinity, g. (d) Nematic order, Q, results for each phenyl of each [n]CPP, where each Q of phenyls is represented by green dots (see text for details).

III. 2. Charge-transport Parameters We analyze the charge transport properties of [n]CPPs in order to understand the fundamental electronic properties of these intriguing materials. We first predict the reorganization energies, , for hole transfer, which is defined as the energetic cost for geometry modifications to undergo charge transfer from neutral ground state to the radical cation in this process. Typically, lower reorganization energies give higher mobilities and therefore better material performance. Topperforming organic materials typically have reorganization energies in the range of 100-150 meV.37 Here,  of each molecule is calculated by the isolated molecule approach using the four-point method with B3LYP/6-311G(d,p). We also perform optimizations of neutral and charged [n]CPPs with dihedral angles between the phenyl rings constrained to their XRD values, to reveal the impact of this degree of freedom. From the unconstrained optimizations, we find that the of [n]CPP is 457 meV when n = 5 and decreases to 173 meV for n = 12. As shown in Fig. 2 (a) and



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Table 1, there is a smooth decrease in as a function of n. scales almost perfectly with the hoop size as ~

. Our results are on average 20 meV different from those in ref. [36]. The reduction

in could occur from the interplay between increased charge delocalization on the larger molecule and structural rigidity. The reorganization energy of benzene is = 300 meV, while the reorganization energy per phenyl ring is predicted to be 91 meV for [5]CPP and reduces to 14 meV for [12]CPP and the remaining compounds have values within 14 - 91 meV. We calculated strain per phenyl ring from the DFT optimized ground state geometries and found that phenyl rings in [5]CPP are on average distorted by 13.6o and this value gradually reduces down to 5.3o for [12]CPP (see Table S3). This indicates that phenyl rings in an [n]CPP gain more benzene character with increasing size. The dramatic difference in reorganization energies between a single benzene (300 meV) and phenyl per ring in [12]CPP (14 meV) is, therefore, largely due to charge delocalization. From the MD equilibrated morphologies, the hole transport site-energies ( and energetic disorder of [n]CPPs were also computed. The latter is caused by the thermal fluctuations in site energies of charge transport. Similar to reorganization energy, energetic disorder enters the Marcus rate via site-energy differences. Typically, lower energetic disorder results in more efficient transport. Energetic disorder, labeled as , is often theoretically predicted from the width of the site energy difference (i-j) distributions and is typically 50 – 100 meV for organic materials.37 The average site-energies tend to shift to lower values and converge as the number of phenyl rings increase, as shown in Fig. 2 (b) and Table 1. This is consistent with the HOMO energy level variation of [n]CPPs, found from DFT calculations in ref. 3: CPPs with lower number of rings are predicted to have more quinoidal character rather than benzenoid. Even so, the variation is not smooth, e.g. as in Fig. 2 (a), due to differing packing arrangements of each organic material. Except for [5]CPP, the energetic disorder, , of [n]CPPs are relatively low and vaguely oscillate around a value of 45 meV, which makes these materials energetically less disordered. The variations in energetic disorder are directly related to structural fluctuations; there is a correlation between the nearly zero nematic order of [5]CPP and its exceptionally large energetic disorder, while there is relatively large nematic order and small energetic disorder in the remaining materials.


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Figure 2. Computed values of (a) reorganization energy, (b) average site-energy, (c) energetic disorder and (d) electronic coupling distributions of each [n]CPP. (the atomistic morphologies are equilibrated at 300 K (a representative example, [8]CPP, is shown)), (e) simulated hole mobilities of [n]CPP. (Inset: reorganization energy vs. hole mobility.)

The electronic coupling, J, distribution of each materials is shown in Fig. 2 (d). Overall, we observe similar J-distributions for CPPs; electronic coupling values are typically within 1 – 10 meV followed by a tail of weak couplings spanning over almost 0.01 meV with the weak J tail of [5]CPP being the longest. A value of 10 meV is considered moderate, given that in organic materials showing good electronic performance, electronic coupling is typically within the range of 50 – 100 meV. The reason for the moderate electronic coupling observed for [n]CPPs is due to loose intermolecular contacts arising from their circular structures, which prevents perfect  overlap. Moreover, the radial distributions of phenyl units also disrupt the conjugation in the nanohoops; as the number of phenyl rings decrease in [n]CPP, the phenyl rings are distorted away from planarity. As the size of the nanohoops increase, the molecular orbitals tend to delocalize which also prevents a better orbital overlap between individual pairs. These competing effects lead to the J-distributions observed in Fig. 2 (d). The unique circular structures of CPPs do allow for close contacts in multiple directions, similar to the situation with fullerenes. This feature substantially helps avoid charge traps in the case of the nanohoop gramework. This is in stark contrast to typical semi-conducting materials which have more charge strap sites leading to



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impaired charge transport and lowered mobilities. As shown in Fig. 2 (d), the trap density of [n]CPPs is very low and leads to improved mobility. To summarize the relationship between the materials and their transport values we reported; we found that (i) reorganization energies of hole transport decreases with the hoop size and the reduction in reorganization energy is due to the interplay of the progressive increase in charge delocalization and rigidity. (ii) Energetic disorder is relatively low and oscillates around 45 meV, expect for [5]CPP, having an energetic disorder of 66 meV. (iii) For all nanohoops, the electronic coupling values of the hole transport are typically on the order of 10 meV and the relatively low value is caused by the disrupted -conjugation due to non-planarity of the nanohoops. Overall, amongst the transport values, the reorganization energy is effected the most by the size of the nanohoop.



With computed charge-transfer rates in hand, we performed kinetic Monte Carlo simulations to obtain charge carrier mobilities for each disordered nanohoop system. The results are shown in Fig. 2 (e) and Table 1, which depicts the average mobility over multiple stochastic simulation for the direction with the largest mobility, shown in S2. The mobility of [5]CPP is predicted to be 7.2 x 10-2 cm2/Vs. The low mobility obtained for this material is due to its large reorganization energy and large energetic disorder. As the size of the [n]CPP is increased, we observe a monotonic increase in mobilities. The mobilities becomes as high as 1.83 cm2/Vs for [12]CPP. Overall, we observe that the mobilities scales as ~n4 and the mobility scaling is largely controlled by the reorganization energy, as shown in Fig 2. (e). Considering that 1 cm2/Vs is typically taken to be high mobility in disordered organic semiconductors, [n]CPPs with n > 10 are of particular interest. Finally, to understand the impact of disorder on the charge-transport, we calculate the mobilities of [n]CPPs for the case of zero structural and energetic disorder (g→0 and →0) constructed from the unit-cells and compared with the disordered cases. We found that the mobilities reduce by a factor of 2-6 with disorder. This indicates that the intrinsic mobilities in [n]CPPs are barely sensitive to charge-traps, caused by the disorder, as opposed to the linear oligomers, whose intrinsic mobility decrease typically by a factor of 20-50.37 Additionally, the ratio of the maximum mobility in one particular direction and the average mobility in all directions is roughly a factor of 2 for all nanohoop crystals. This indicates strong-enough anisotropy in the charge-carrier mobilities. The low susceptibility of [n]CPPs to disorder and isotropy can be


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attributed to the absence of the end groups observed in linear materials that usually causes trap states for charge carriers due to weak edge-to-edge intermolecular contact. Table 1. Summary of computed reorganization energies, , for unconstrained and constrained dihedral angles (unc.and c. energetic disorder, , and simulated hole mobilities of [n]CPPs.  and  are in the units of meV and  is in cm2/Vs units. [n]CPP

unc.

c.





5

457

261

66

0.072

6

391

213

49

0.056

7

304

177

48

0.28

8

260

150

45

0.24

9

240

132

49

0.48

10

211

116

42

1.12

11

196

106

52

1.07

12

173

98

45

1.83

In order to better understand the intermolecular interactions in the solid state for [n]CPPs, we cofacially pair two [n]CPPs manually with different n values at a fixed distance of 3.5Å (≅2rvdW). Note that, the CPP pairs in Fig. 3 are not the actual pairs observed in the actual unit-cells. Here, we aim to elaborate the impact of nanohoop size on charge-transport when the intermolecular contact is maximized. As shown in Fig. 3 (a), similar calculations were performed for linearparaphenylenes ([n]LPPs) to establish a link between [n]CPP and the linear planar analogs. Fig. 3 (a) shows that in the case of [n]CPP the electronic coupling reduces as the nanohoop size increases. The J values we found are, therefore, 5-7 times stronger than those we found in the solid state (see Fig. 2 (d)), since the stacking in the actual crystal structures are typically slipped cofacial. The 2J/ ratio is often used to define the dynamical origin of charge transport. For 2J/and 2J/charge transfer is governed by band-like and hopping-like transport, respectively, where the former is typically observed for very high mobility semiconductors.37,38 As shown in the inset of Fig. 3 (a), the 2J/ratio in the manually paired nanohoops monotonically evolve from



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a hopping-like transport to a band-like transport with increasing nanohoop size. Besides, as mentioned previously, electronic coupling values are typically J=1-10 meV for the MD equilibrated crystals of [n]CPPs (see Fig. 2 (d)), therefore 2J/ becomes roughly 0.01 - 0.2 for the actual nanohoop pairs, which indicates hopping-like transport for these systems.

Figure 3. Intermolecular electronic coupling, J, between (a) [n]cycloparaphenylene ([n]CPP) and (b) [n]linearparaphenylene ([n]LPP) pairs versus the number of phenyl rings of them. Two CPP and/or LPPs are cofacially paired manually with a fixed 3.5Å of intermolecular distance in each case. Dashed lines in (a)-(b) show the fit to an exponential function. Note that, J values are divided by a factor of ten in (b) for a better comparison with (a). Insets: (a) 2J/ ratio of CPPs as a function of n.  values are taken from Fig. 2 (a). (b) J/np ratio, where np is the number of phenyl-phenyl contact within 3.5Å of distance. Indeed, np=1 and np=n for [n]CPP and [n]LPP, respectively. (c) Electronic coupling between distorted phenyl dimers obtained by pulling out from the [n]CPP dimers, as shown by the diagram on the left. Missing bonds in ppositions are replaced by C-H.

A similar reduction in J is observed for [n]LPPs, as shown in Fig. 3 (b), where the J values decrease with increasing system size. However, the reduction is less dramatic than that observed in Fig 3 (a), since molecular orbitals in [n]LPPs tend to have higher density towards the central units. The


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oscillatory behavior we see in Fig. 3 (c) with varying [n]LPP is caused by the alternating orbital distribution due to even/odd number of phenyl rings.39 The electronic coupling versus the number of close phenyl-phenyl contacts, i.e. the J/np ratio, is useful to compare [n]CPP and [n]LPPs. The difference in J/np values between [n]CPPs and [n]LPPs where 5>n>8 is large, since the phenyls in [n]CPPs are highly distorted. This difference becomes smaller where 9>n>12 due to vanishing differences between the structures of [n]CPP and [n]LPP. We also calculated variations of electronic coupling due to the distortion of phenyl rings. We took various [n]CPP dimers and truncate the phenyl-phenyl contact without modifying the structure, as shown in Fig. 3, and created distorted benzene-benzene dimers. This enables us to understand the impact of the evolution from a quinoidal character (distorted) of the phenyl rings to the aromatic ones (undistorted) on electronic coupling. Fig. 3 (c) shows that the electronic coupling significantly decays with structural distortion as much as ~900 meV, which is consistent with the strong sensitivity of J to structural modifications. III. 3. [n]CPPs vs. fullerenes [n]CPPs are often envisioned as the structural units of fullerenes and/or building blocks of sidewalled (n,n) carbon nanotubes.1,4 [5]CPP has attracted considerable attention due to it is related to C60 (see Fig. 4).13,40 To compare the charge transport performance of [5]CPP against C60, we use our published charge transport calculations of C60 in ref. [41], based on the same methodology. For [n]CPPs, it is also valuable to compare C60 and [10]CPP, since [10]CPP and analogs thereof are excellent supramolecular hosts for C60, forming Saturn-like supramolecular structures.8 The solid-state mobility of C60 is predicted to be 3.1 cm2/Vs, which is in good agreement with its experimental mobility, 5.3 cm2/Vs. 42 [5]CPP has a theoretical mobility value of 0.05 cm2/Vs, two orders of magnitude lower than that of C60. The close-contact distances and average electronic coupling of [5]CPP and C60 are comparable42 (see Fig. 4), but the large deviation in mobility is due to large energetic disorder (66 meV for [5]CPP and 4 meV for C60) and, more importantly, very large reorganization energy (460 meV for [5]CPP and 135 meV for C60) of [5]CPP comparing with C60. To further probe this correlation, we constrained the dihedral angles between the phenyl rings of [5]CPP to match the experimental values during DFT optimization. Under these conditions, we obtain =261 meV, which is still significantly larger than that of C60. As mentioned



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above, the long and weak electronic coupling tail of [5]CPP is also responsible for lower mobility(Fig. 4). For comparison, the of [10]CPP is four-fold weaker and the  is a factor of ten larger than C60 with values remaining largely comparable. As a result, the mobility of [10]CPP is 17 times higher than [5]CPP and 4 times lower than that of C60 highlighting the interplay between structural elements on electronic properties.

C60

[5]CPP C60

[5]CPP

Figure 4. [5]CPP is a fragment of C60. (top-right) MD equilibrated atomic morphologies of C60 and [5]CPP, with their zoomed packing structures. (bottom-left) Electronic coupling distributions of C60, [5]CPP and [10]CPP. (bottom-right) Transport parameters of C60, [5]CPP and [10]CPP; ensemble averaged electronic coupling of close contact, energetic disorder, , reorganization energy, , and charge-carrier mobility, . Electronic coupling, energetic disorder and reorganization energy are reported in meV. Mobility is reported in cm2/Vs. The transport values of C60 are taken from ref. [42].

III. SUMMARY and CONCLUSIONS Using multilevel computational tools, including molecular dynamics and charge-transport dynamics simulations, we calculate the mesoscale solid-state morphology and intrinsic chargetransport of [n]cycloparaphenylenes (or nanohoops), where n values between 5 and 12 are considered. These molecules are of great importance; specifically, they are considered as the


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constituents of fullerenes and carbon nanotubes. Their unprecedented packing motifs, due to their cyclic structures, forms a unique transport network. Unlike the herringbone stacking observed in many organic materials is the favored direction for charge-transport due to strong  contact, the herringbone type packing adopted in [n]CPPs is disfavored; charge-transport favors lateral directions in commensurate with the outward facing -orbitals in [n]CPPs. MD simulations reveal that the intramolecular stability reduces with increasing hoop size, which is attributed to the progressive strain release. The intermolecular stability, quantified by paracrystalline order, increases with hoop size. Due to their curved -conjugation, the intermolecular contact is relatively low and results in relatively moderate electronic coupling (~10meV) comparing with high mobility organic semiconductors in the literature. From charge-transport calculations, we find that the molecular structure and packing motif in [n]CPPs lead to a nearly homogeneous transport network, which turns out to be beneficial for bypassing charge traps and/or defects. Intrinsic mobility correlates with the nanohoop size and is controlled by the reorganization energy. Finally, to provide perspective in the field of non-planar organic electronics, we compared the transport properties of C60 and [5]CPP using the same methodology and found that the electronic coupling is of the same order but the reorganization energy, energetic disorder is considerably larger for [5]CPP and thus, the intrinsic mobility is almost two orders of magnitude lower than C60. We anticipate that our study is a prototypical example of how molecular structure and bulk property is related and that nanohoops are promising and exceptional candidates for high mobility organic semiconductors. Moreover, we believe that these studies provide a road map for the design of future non-planar organic molecules for charge-transporting materials.



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ASSOCIATED CONTENT Supporting Information. Cartesian coordinates of B3LYP/6-311G(d,p) optimized ground state structures, strain per phenyl ring found from B3LYP/6-311G(d,p), representative MD snapshots equilibrated at 300K, experimental and predicted unit-cell parameters and supercell parameters of [n]CPPs can be found in the Supporting Information.

AUTHOR INFORMATION Corresponding authors e-mail: [email protected] e-mail: [email protected]

Notes The authors declare no competing financial interests. ACKNOWLEDGMENT We are grateful to the National Science Foundation (DMR-1335645) for financial support of this research. I. Y. is partially supported by BAPKO of M. U. (FEN-A-100616-0275). Calculations were performed on the Hoffman2 cluster provided by the UCLA Institute of Digital Research and Education’s Research Technology Group and SIMULAB in the Physics Dep. of MU and also on the NSF-supported Extreme Science and Engineering Discovery Environment (XSEDE)’s Gordon supercomputer (OCI-1053575) at the San Diego Supercomputing Center.


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For Table of Contents Only


Solid-state order and charge mobility in [5]-[12] cycloparaphenylenes

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