Constraining Carbon Nanothread Structures by Experimental and

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Constraining Carbon Nanothread Structures by Experimental and Calculated Nuclear Magnetic Resonance Spectra Tao Wang, Pu Duan, En-shi Xu, Brian Vermilyea, Bo Chen, Xiang Li, John V. Badding, Klaus Schmidt-Rohr, and Vincent H. Crespi Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01736 • Publication Date (Web): 28 Jun 2018 Downloaded from http://pubs.acs.org on June 29, 2018

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Constraining Carbon Nanothread Structures by Experimental and Calculated Nuclear Magnetic Resonance Spectra Tao Wang,1,2Pu Duan,3 En-Shi Xu,1,2Brian Vermilyea,1Bo Chen,4 Xiang Li,2,5John V. Badding,1,2,5,6Klaus SchmidtRohr3 and Vincent H. Crespi* 1,2,5,6 1

Department of Physics, Pennsylvania State University, University Park, PA 16802, USA 2

Materials Research Institute, Pennsylvania State University, University Park,

Pennsylvania 16802, USA 3

Department of Chemistry, Brandeis University, Waltham, MA 02453, USA

4

Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, New York 148531301, United States 5

Department of Chemistry, Pennsylvania State University, University Park, PA 16802, USA

6

Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA

Email: [email protected]

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Abstract

A one-dimensional sp3 carbon nanomaterial with high lateral packing order, known as carbon nanothreads, has recently been synthesized by slowly compressing and decompressing crystalline solid benzene at high pressure. The atomic structure of an individual nanothread has not yet been determined experimentally. We have calculated the 13C NMR chemical shifts, chemical shielding tensors and anisotropies of several axially ordered and disordered partially saturated and fully saturated nanothreads within density functional theory and systematically compared the results with experimental solid-state NMR data to assist in identifying the structures of the synthesized nanothreads. In the fully saturated threads, every carbon atom in each progenitor benzene molecule has bonded to a neighboring molecule (i.e. six bonds per molecule, a so-called “degree-6” nanothread) while the partially saturated threads examined retain one double bond per benzene ring (“degree-4”). The most parsimonious theoretical fit to the experimental one-dimensional solid-state NMR spectrum, constrained by the measured chemical shift anisotropies and key features of the two-dimensional NMR spectra, suggests a certain combination of degree-4 and degree6 nanothreads as plausible components of this one-dimensional sp3 carbon nanomaterial, with intriguing hints of a [4+2] cycloaddition pathway towards nanothread formation from benzene columns in the progenitor molecular crystal, based on the presence of nanothreads IV-7, IV-8 and square polymer in the minimal fit.

Keywords: Nanothreads, NMR, Structure Identification, Linear Regression, DFT

1 INTRODUCTION


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The family of sp3-hybridized carbon systems includes zero-dimensional diamondoid molecules,1 twodimensional graphanes,2,3and three-dimensional diamond. For the largely unexplored case of onedimensional (1-D) sp3 carbon materials, theorists have predicted possible structures from several different perspectives. Stojkovic et al.4 generated the first predicted sp3 thread-like structure by analogy to an sp2 (3,0) nanotube; Wen et al.5 obtained the so-called “polymer I” structure by computational compression of crystalline benzene that collapses along a barrierless reaction pathway at high pressure; Barua et al.6 constructed a 1-D system they called “polytwistane” by linearly extending a hydrocarbon molecule, twistane. Recently, Fitzgibbons et al.7 successfully synthesized a well-ordered 1-D sp3 carbon product – carbon nanothreads – by slowly compressing solid benzene to 20 GPa, followed by slow decompression. Xu et al.8 then systematically enumerated 50 topologically distinct, fully-saturated nanothread structures with a naming convention based on the connectivity between adjacent progenitor benzene rings and performed detailed property calculations for the fifteen energetically most stable structures, which include the predicted tube (3,0) (123456 in the nomenclature of Xu et al.8, also explained in the Supporting Information Figure S1), polymer I (135462) and polytwistane (143652). Chen et al.9 investigated possible reaction pathways from benzene to fully-saturated (i.e. degree 6) nanothreads, and enumerated all partially-saturated (CH)6 stacks with constraints of unit cell size. 13C magic angle spinning (MAS) solid state NMR spectra of 13C-enriched samples have revealed

% sp3 carbon content, with the remainder

being sp2 carbon7,10 and the 1-D NMR response of a limited set of high-symmetry nanothread structures has been calculated.11 Isolated double bonds as well as aromatic rings have been identified by twodimensional NMR, and the length of pure sp3-hybridized segments with multiple nonequivalent sites, which account for 25 -50% of the nanothreads, has been estimated at > 2.5 nm based on 13C NMR with spin diffusion.10 Further experimental12 and theoretical13-15 work has explored more deeply the composition and properties of these fascinating nanothread geometries.


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To help guide the extraction of atomic-level structural information from NMR spectra, we report here the calculated solid-state NMR spectra for several different axially ordered and disordered degree-4 and degree-6 nanothreads. By synthesizing experimental constraints arising from measured chemical shifts, chemical shift anisotropy (CSA) parameters, and 2-D NMR of sp2-sp3 bonded carbon sites, we produce a theoretical fit with a minimal number of nanothread structures to the experimental 1-D NMR spectrum, yielding a small subset of most plausible structural candidates. We also investigated whether this subset is mostly limited to degree-4 and -6 threads that are plausible products of a specific reaction pathway, e.g. [4+2] cycloaddition, and whether any member of the fitted subset has a more complex structure that may be an indirect signal of on-thread structural disorder in the experimentally synthesized nanothread sample. The remaining member of the fitted subset has more complex structure, and its presence in the fit may be an indirect signal of on-thread structural disorder in the experimentally synthesized nanothread sample. 2 COMPUTATIONAL AND EXPERIMENTAL DETAILS All density functional theory (DFT) calculations were performed within the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) density functional16 implemented in Quantum ESPRESSO.17 The NMR parameters were calculated using the gauge-including projector augmented wave (GIPAW) approach as implemented in Quantum EXPRESSO, introduced by Pickard and Mauri et al.18 (later enhanced19-21). This plane-wave pseudopotential approach facilitates the calculation of accurate and reliable NMR parameters (chemical shielding and electric field gradient tensors) for periodic systems.22-24 PBE Trouillier-Martins norm-conserving pseudopotentials with GIPAW reconstruction of D. Ceresoli25 were used, with an energy cutoff for the plane wave basis set (100 Ry) and k-point spacing ( 70 ppm. Nonpolar tertiary carbons (sp3 CH bonded to three other carbons)

typically have a relatively small

δ aniso ≈ 11 ppm. This suggests that the chemical-shift anisotropy may

serve as a measure of the deviation from tetrahedral bonding symmetry around C-H carbons in nanothreads (Figure S6). The CSA leads to characteristic line broadening, known as a powder pattern, which can be determined most directly by taking the spectra without sample spinning.28 In molecules with many chemically inequivalent sites, overlap of several powder patterns makes it difficult to discern the contributions of the CSA and of the different isotropic chemical shifts. Fortunately, this is a minor concern in carbon nanothreads with a single band near 40 ppm. However, in 13C-enriched samples, broadening due to 13C-13C dipolar couplings will also contribute to the line width in static spectra. For three dipolar couplings of 3 kHz,


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a broadening by ~ 3 × 3 kHz = 5 kHz = 50 ppm is expected, and long-range couplings will further increase this width. This problem can be resolved by homonuclear decoupling, for instance in the evolution period of a 2-D experiment (see SI for details). This approach with MREV-8 decoupling yielded the bold-line spectrum in Figure S7 (a), covering a spectral range corresponding to δaniso ≈ 24 ppm – 42 ppm = –18 ppm. The sign of the asymmetry of the spectrum shows that δ aniso is predominantly negative. For reference, we compare with corresponding spectra of polystyrene 20% 13C-labeled in the backbone CH position, see Figure S7 (b). The broadening is smaller and consistent with δaniso ≈ 29 ppm – 40 ppm = – 11 ppm. The comparison of the widths of the spectra in Figure S7 (c) directly shows that the anisotropy of the CH group is larger in carbon nanothreads than in polystyrene. The line shape does not match single-site powder patterns, indicating that multiple sites with different CSAs are present in the carbon nanothreads. Shift anisotropy could also arise from couplings of the carbon spins to unpaired electrons. This source of anisotropy can be excluded in carbon nanothreads by analyzing T1H and T1C relaxation.10 In the static spectrum, the broadening due to the CSA is convoluted with the distribution of isotropic chemical shifts. This can be avoided by magic-angle spinning, which separates isotropic and anisotropic chemical-shift effects. The dephasing of the sharp peaks can be observed under MAS by the recoupled chemical shift anisotropy, with the recoupling achieved by three π-pulses in a constant-time dephasing period that precedes signal detection. 31,32 Since MAS refocuses the 13C-13C dipolar coupling and π-pulses leave the dipolar coupling unaffected, this also provides a simple alternative solution to problems due to 13C-13C dipolar couplings. This analysis is confirmed by the experimental CSA dephasing of CH peaks in uniformly 13

C-enriched valine: In spite of the strong 13C-13C dipolar couplings, both the NCH and side group CH

dephase slowly, see Figure 2, similarly as in unlabeled valine as well as polystyrene and consistent with literature values of δ aniso ≈ 11 ppm.30 The dephasing of the 41-ppm CH signal in the carbon nanothreads is


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faster, indicating a relatively large chemical-shift anisotropy of δ aniso ≈ 20 ppm, which agrees with the static spectra and suggests significant distortions from tetrahedral bonding symmetry.

Figure 2. Normalized 13C NMR signal intensities of CH sites after 5-pulse chemical-shift anisotropy dephasing. A fast decay indicates a greater chemical shift anisotropy and a greater deviation from tetrahedral bonding symmetry. Filled red hexagons: Overall sp3-hybridized nanothread signal (with peak maximum at 41 ppm); open hexagons: nanothread signal at 30 ppm; open rotated hexagons (lower): signal at 50 ppm; crosses: signal at 130 ppm (sp2-hybridized C). Filled blue squares/diamonds: uniformly 13Cenriched valine; open squares/diamonds: unlabeled valine; squares: valine sidegroup CH; diamonds: valine NCH; filled green circles: polystyrene alkyl CH.

Within the inhomogeneously broadened main MAS peak of carbon nanothreads, signals at different isotropic chemical shifts show significantly different CSA dephasing. The curves for 30 and 50 ppm signals


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in Figure 2 show that the larger the isotropic chemical shift value, the larger the CSA. The same trend is observed in the calculated chemical-shift data in Table S1 and Figure S8. Comparison of the measured CSA of ~ –20 ppm with calculated CSAs can be used, in addition to the isotropic chemical shift comparison, to exclude a dominant contribution by certain types of nanothreads, and to favor others. For instance, the –10 ppm CSA of polytwistane is much smaller than observed experimentally, ruling out this structure as a major constituent of the experimental sample. Similarly, stiffchiral-2 thread cannot be the main component since they have predominantly positive δ values around +25 ppm, incompatible with the measured –20 ppm. For the 5-8 polymer (see Figure S5), the averaged CSA is around –28 ppm, which is too large in magnitude. Polymer I’, zipper polymer and stiffchiral-4 cannot be primary components since the magnitudes of their CSA are too large (Figure S9). Degree-6 square polymer (Figure S5) is acceptable with only slightly too negative CSAs. On the other hand, stiffchiral-3 with its predominantly negative δ aniso and average magnitude δ aniso ≈ 21 ppm is in good agreement with experiment (SI Table S1 and Figure S9). Tube (3,0) and polymer I could not be ruled out only based on their CSAs that are predominantly negative with average magnitudes in a range of 20–24 ppm. The average magnitude of CSA for IV-2 is around 21 ppm; however, the CSAs are predominantly positive, which does not agree with experiment. The average magnitudes of the CSA for IV-7, IV-8, IV-11, IV-13 and IV-14 are in a range of 15–25 ppm and the CSAs are also predominantly negative (SI Table S1 and Figure S10), so these could account for the sp2 component of the synthesized material. The other degree-4 structures can be ruled out on the basis of a much larger or smaller magnitude of CSA (SI Figure S10). With the constraints from 13C isotropic chemical shift and CSA, the most plausible structures are square polymer and stiffchiral-3 as degree-6 threads, and IV-7, IV-8, IV-11, IV-13 and IV-14 as degree-4 threads. Structural Information from 2-D NMR Spectra. After considering the constraints imposed by the experimental 1-D NMR spectrum and CSA, most nanothread structural candidates can be excluded as dominant contributors to the sample. To further constrain the plausible degree-4 candidates, we compare 13 ACS Paragon Plus Environment

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the calculated isotropic chemical shifts for bonded sp2 and sp3 carbon sites in degree-4 threads (Table S2) with the measured 2-D NMR spectrum.10 This comparison reveals that among the remaining degree-4 candidates, IV-14 is least plausible since its signals deviate far from the center. Next, IV-11 and IV-13 are acceptable, IV-8 is better, and IV-7 agrees best with the experiment (see Figure S11 for a detailed comparison between calculation and experiment). Minimal Fit to 1-D NMR Spectrum. Armed with this guidance as to the most plausible thread candidates, we next employed multi-linear regression using the calculated chemical shifts with Gaussian broadening, attempting to find a minimal set of thread candidates that can successfully reproduce the overall shape of

Figure 3: Fit of the experimental data with 2 degree-4 and 2 degree-6 nanothreads by multi-linear regression. The simulated spectrum was broadened by convolution with a Gaussian with σ = 2.5 ppm.

the experimental 1-D solid state NMR spectra. A linear regression with two degree-4 threads: IV-7 and IV-8, and two degree-6 threads: square polymer and stiffchiral-3, outperforms other attempted fits with fewer or more candidates. The fits with fewer candidates cannot reproduce the observed peak shapes, while adding IV-11, IV-13 or both yields a near-zero weight for the added threads and no improvement in fit


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quality (A quantitative analysis of the fitting quality for different combinations of candidates is discussed in the SI with coefficients of determination (R2) for each fit shown in Table S4. The best fits for alternative numbers and types of threads are shown in Figure S12; these generally have worse performance in terms of matching the experimental spectrum). Figure 3 shows the resulting best fit with 18% IV-7, 25% IV-8, 36% square polymer, and 21% stiffchiral-3 at a Gaussian broadening of σ = 2.5 ppm with a multi-linear regression fitting algorithm implemented in MATLAB. The overall peak shapes and positions are wellreproduced; the discrepancies around 120 ppm and in the “tails” of the sp3 peak are likely associated with disorder, as discussed below. Without significant change of the coefficient of determination and reasonable reproduction of the main peaks of the experimental spectrum, the relative fraction can vary from 30 to 41% for square polymer and 13 to 30% for stiffchiral-3 (Table S7). While the changes in the contributions of square polymer and stiffchiral-3 are relatively independent, those for IV-7 and IV-8 are strongly anticorrelated, with the total fraction of degree-4 (i.e. the sum of IV-7 and IV-8) remaining within ±6 % of 43% while the contribution of either IV-7 or IV-8 individually can go as low as 4–8%. We note an interesting pattern in the fitted threads: degree-4 threads IV-6, IV-7, and IV-8 can all form by [4s+2s] cycloaddition, with small unit cells, as shown in Figure S2. Whereas IV-7 and IV-8 cannot easily continue to degree-6 because of an anti configuration of the remaining double bonds (i.e. successive double bonds are on opposite sides of the thread), thread IV-6 can continue to full saturation, and doing so yields square polymer, which is one of the two degree-6 polymers in the fitted set. In addition, square polymer has 4-fold rings and the distance between the diagonal carbons reproduces a shoulder at 2.2 Å in the measured pair distribution function.7 Thus, three of the four thread structures in the most plausible fit are natural endpoints to polymerization that begins with a [4s+2s] cycloaddition. The remaining thread in the fitted subset, stiffchiral-3, has a much more complex structure that can be traced back to a degree-4 polymer formed by a combination of [4+2]-cycloadditions and radical polymerizations. Alternatively (or in addition), the presence of stiffchiral-3 in the fitted subset may actually reflect the presence of some


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measure of disorder in the experimental thread sample; i.e. stiffchiral-3, with its complex unit cell and local carbon environments, may be a proxy for some admixture of disordered local environments – the resolution of this question awaits further investigation. NMR Response of Axially-disordered Nanothreads. Although the main features of the experimental spectrum can be fitted reasonably well with the four axially-ordered degree-4 and degree-6 threads

Figure 4: DFT-optimized structures of axially disordered nanothreads without (left three) and with (right three) the constraint of [4+2] (including [4s+2s] and [4a+2a]) cycloaddition, generated by randomization of the bonding patterns between progenitor benzene rings.

included in Figure 3, the shoulder near 120–125 ppm to the right of the sp2 peak and the “tails” of the sp3 peak around 60 and 20 ppm are not well reproduced. A small amount of polymer I might contribute to the tail around 60 ppm (since it has a chemical shift signal around 57 ppm), however, no axially ordered threads that we calculated could reproduce the shoulder near 120–125 ppm and the tail around 20 ppm, since none of them have chemical shift signals in that range. Thus we also consider the NMR response of nanothreads with on-thread disorder. Although the most probable reality for disorder is some combination of domain boundaries and point defects, simulating such a situation encounters a forbidding combinatorial complexity when the ordered component of thread structure remains only partially constrained. Instead,


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we examine a well-defined “end-state” on the order-disorder continuum: maximally disordered threads. These exploratory maximal-disorder calculations are intended as a means to determine which features in the NMR spectrum may be associated with on-thread disorder, not as an assertion that the actual thread is so comprehensively disordered. To this end, we created a long supercell stack of interlinked six-fold rings in either class 2 or class 3 bonding patterns8 (i.e. successive rings sharing either 3,3,3… or 2,4,2,4… bonds with each other, also illustrated in Figure S1 ) and then progressively disordered only the inter-ring bonding patterns until all memory of the initial inter-ring bonding pattern is lost. Two such ensembles were created, one of which was additionally constrained to only those configurations derivable from [4s+2s] or [4a+2a] cycloadditions (depicted in Figure S2), see Figure 4 for structures and Supplementary Information for details on the disorder generation.


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Figure 5: (a) Calculated NMR chemical shift distributions of fully axial disordered (left) and [4+2]constrained disordered (right) nanothreads. Top: degree-6 with class 2 bonding pattern; middle: degree-6 with class 3 bonding pattern; and bottom: degree-4. The experimental spectrum is shown for comparison. (b) Fits of the experimental data with fully and [4+2]-constrained disordered degree-6 and degree-4 nanothreads by multi-linear regression using MATLAB. The chemical shifts are broadened using Gaussian convolution with σ = 2.5 ppm.

As expected, these highly disordered threads have a multitude of distinct carbon sites and thus a broad range of chemical shifts, as shown in Figure 5 (a). The class-2 disordered spectra (with alternating 2 and 4 bonds between adjacent progenitor benzene rings) for both the unconstrained and [4+2]-constrained ensembles tend to over-weigh the region around 50–60 ppm, while the disordered degree-4 without the [4+2] constraint fails to cover the shoulder around 120ppm. The CSAs of the class-3 disordered threads are


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in better agreement with experiment (predominately negative and around –20 ppm) than those for class 2 (generally larger in magnitude) (Table S3). Furthermore, only the [4+2]-constrained degree-4 threads have significant weight in the shoulder region around 120 ppm. These observations favor the presence of class-3 threads and those with the [4+2] constraint, as will also be reflected by the explicit spectrum fit described below. These observations based on the chemical shift peak distributions can be confirmed by an explicit spectrum fit including an empirical broadening, as shown in Figure 5 (b). The fit to the unconstrained ensemble has nearly equal weights of degree-4 (51%) and degree-6 class 3 (49%) and a negligible fraction of class 2 (less than 5%, and excluding it entirely does not degrade the quality of the fit, see Table S5). The fit to the [4+2]-constrained ensemble yields an overall higher-quality fit in terms of reproducing the shape of the spectrum but with almost the same coefficient of determination (R2) compared with the fit to the fully axially disordered threads with 36% degree-6 class-2, 24% degree-6 class-3, and 40% degree-4 thread, again reasonably consistent with experiment in the degree-4/6 ratio. Fits with fewer [4+2]-constrained types of threads cannot yield comparable performance (see Table S6 for details). The sensitivity of the fit quality to variations in the fraction of each thread in unconstrained and [4+2]-constrained ensembles are characterized and discussed in the Supporting Information, Tables S8,9. Recall that both degree-6 class 2 (square polymer) and degree-6 class 3 (stiffchiral-3) participate in the fit with ordered threads (Figure 3), and the degree-6 class-2 thread can be derived from a [4+2] degree-4 polymer (i.e. IV-6). The relative weights of degree-6 class 2 and degree-6 class 3 in the [4+2]-constrained fit are actually similar to the relative weights of class-2 square polymer and class-3 stiffchiral-3 in the ordered fit. As anticipated, only the [4+2]-constrained ensemble captures the shoulder around 120 ppm. We examined the bond angles and bond lengths for the carbon sites that contribute to this shoulder but could not identify any distinguishing characteristics that position them in this range. The “tail” around 60 ppm can also be captured by either the fully disordered or [4+2]-constrained disordered ensembles; the small feature at 20


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ppm remains unexplained. Overall the examination of maximally disordered threads provides some additional, if tentative, support for the [4+2] reaction pathway towards thread formation, and suggests a significant role for on-thread disorder in current nanothread samples, the precise character of which requires further experimental investigation. We do not anticipate that carbon nanothreads actually suffer from maximal disorder, as that conclusion would be inconsistent with axial beading observed in highresolution transmission electron microscropy.33 Moreover, we do not interpret the relative fractions in the fitting results, especially for fully disordered threads, to predict the actual portions of different types of threads as synthesized; instead, these results suggest a significant structural role for intermittent localized disorder such as domain boundaries between threads of different types and/or point defects.

4 CONCLUSIONS The NMR chemical shifts for a variety of possible fully saturated (degree-6) and partially saturated (degree4) nanothreads were calculated with the GIPAW approach in density functional theory. Constraining the fit of the 1D NMR spectrum to a minimal number of thread structures, all of which are consistent with additional NMR constraints (chemical shift anisotropy and 2-D NMR), yielded a minimal set of mostplausible structural candidates that include two degree-4 threads that are natural termination points to polymerization, plus one degree-6 thread, all of which follow from [4+2] cycloadditions. A significant role is also played by disorder, evinced in several ways: (1) the need to incorporate significant disorder broadening in the fits, (2) the appearance of a long, complex unit-cell candidate in the minimal ordered fit, and (3) the presence of an otherwise-unexplained shoulder around 120 ppm. Current experimental data, combined with computational results, are highly informative, but cannot yet fully elucidate the nanothreads’ atomic structure. However, the reaction products could be tuned by changing the synthesis conditions, and the analysis of the experimental and calculated solid-state NMR spectrum could facilitate the identification of different components in the samples and provide feedbacks for guiding synthesis.


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Author Contributions

TW performed the NMR calculations and interpretation. PD and KSR performed the NMR measurements. BV generated disordered thread coordinates. EX and BC assisted in thread classification. XL and JB assisted in data interpretation. VHC provided guidance in fitting strategies. All authors have given approval to the final version of the manuscript. Supporting Information Methods for generating axially disordered carbon nanothreads, the naming convention for degree-6 threads (Figure S1), a scheme for [4s+2s] cycloaddition and [4a+2a] polymerization (Figure S2), solid state NMR pulse sequences (Figure S4) and static spectra (Figure S7), details of calculated (Table S1-3, Figures S3, S6, and S8-10)) and measured (Figure 11) NMR parameters, and structures of degree-4 and degree-6 threads (Figure S2 and S5) (PDF) Structures of the fully axially disordered and [4+2] constrained axially disordered threads (CIF)

Acknowledgement This work was supported as part of the Energy Frontier Research in Extreme Environments (EFree) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science under Award Number DE-SC0001057. The authors thank Dr. Roald Hoffmann for stimulating discussions and comments. The authors declare no competing financial interest.

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Duan, P.; Li, X.; Wang, T.; Chen, B.; Juhl, S. J.; Koeplinger, D.; Crespi, V. H.; Badding, J. V.; Schmidt-

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P.; Wentzcovitch, R. M. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21 (39), 395502–395520. (18) Pickard, C. J.; Mauri, F. All-electron magnetic response with pseudopotentials: NMR chemical shifts. Phys. Rev. B 2001, 63 (24), 245101–245113. (19) Yates, J. R.; Pickard, C. J.; Mauri, F. Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials. Phys. Rev. B 2007, 76 (2), 024401–024411. (20) Joyce, S. A.; Yates, J. R.; Pickard, C. J.; Mauri, F. A first principles theory of nuclear magnetic resonance J-coupling in solid-state systems. J. Chem. Phys. 2007, 127 (20), 204107–204110. (21) Green, T. F. G.; Yates, J. R. Relativistic nuclear magnetic resonance J-coupling with ultrasoft pseudopotentials and the zeroth-order regular approximation. J. Chem. Phys. 2014, 140 (23), 234106– 234117. (22) Ashbrook, S. E.; Berry, A. J.; Frost, D. J.; Gregorovic, A.; Pickard, C. J.; Readman, J. E.; Wimperis, S. 17

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TOC Graphic


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aPage 27 of 32 Intensity(AU)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Nano Letters Alkene and nearby alkyl CH CH-only

sp3

sp2

160

140

120 13

Intensity(AU)

b

80

60

40

20

C Chemical Shift (ppm) Stiffchiral

Achiral tube (3,0)

polytwistane

5-8 polymer zipper polymer polymer I’

square polymer

stiffchiral-4

stiffchiral-3

polymer I

70

60 13

stiffchiral-2

50

40

30

20 70

C Chemical Shift (ppm)

60 13

50

40

30

20


Intensity(AU)

Intensity(AU)

Intensity(AU)

c

100

150

100 13

ACS Paragon 50 Plus Environment 150


13

100

50


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

ACS Paragon Plus Environment

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deg-6_class2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

deg-6_class3

deg-4

[4+2]_deg-6_class2

Nano Letters


[4+2]_deg-6_class3

[4+2]_deg-4

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160

Intensity(AU) Intensity(AU)

disordered-degree-6-class3

disordered-degree-4

140

120 13

b

Nano Letters

disordered-degree6-class2

Intensity(AU)

Intensity(AU) Intensity(AU)

100

80

60

40

160 20 160

[4+2]-disordered-degree6-class2 disordered-degree6-class2

[4+2]-disordered-degree-6-class3 disordered-degree-6-class3

[4+2]-disordered-degree-4 disordered-degree-4

140 140


Full axial disorder

100 80 60 100 80 60 Chemical Shift (ppm) C Chemical Shift (ppm)

13 13 C

40 40

20 20

[4+2]-constrained disorder

Intensity(AU)

linear regression experiment 160

120 120

Intensity(AU)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

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120 13

100

linear regression

ACS Paragon Plus Environment 80

60


40

20

160

140

experiment 120 13

100

80

60


40

20

Intensity(AU)

experiment Nano Letters linear regression

1 2 3 4 5 6 7 160 8

36%

21%

18%

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linear regression experiment Plus Environment ACS Paragon 140

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Constraining Carbon Nanothread Structures by Experimental and

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