Electronic and Mechanical Properties of Partially Saturated Carbon

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C: Physical Processes in Nanomaterials and Nanostructures

Electronic and Mechanical Properties of Partially Saturated Carbon and Carbon Nitride Nanothreads Pedro Demingos, and Andre Rodrigues Muniz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11329 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 29, 2019

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The Journal of Physical Chemistry

Electronic and Mechanical Properties of Partially Saturated Carbon and Carbon Nitride Nanothreads Pedro G. Demingos and Andre R. Muniz∗ Department of Chemical Engineering, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil E-mail: [email protected]

Abstract Carbon nanothreads (NTs) are ultrathin materials synthesized by solid-state reaction of crystalline benzene or pyridine under high pressure. Recent experimental studies show that the sp2 -sp3 conversion in C-C or C-N bonds toward NT formation is not always complete, typically resulting in samples constituted by a mixture of both partially and fully saturated structures. The objective of this study is to use Density Functional Theory calculations to compute the mechanical and electronic properties of partially saturated carbon and carbon nitride nanothreads, and analyze how they differ from those of conventional fully saturated NTs. The results show that partially saturated NTs have lower ideal strengths and stiffness compared to their fully saturated versions, but they are still remarkably strong. The electronic behavior vary from semi-conducting to insulating, with band gaps in the range of ∼ 1.8-4.0 eV, while fully saturated NTs usually have wider gaps (> 4.0 eV). These results show that partially saturated nanothreads can be used for the same applications previously suggested for

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fully saturated NTs based on their outstanding mechanical strength, and novel applications may be envisioned due to their wider range of possible band gaps.

Introduction Carbon nanothreads or diamond nanothreads (C-NTs or DNTs) are ultrathin threads of sp3 -hybridized carbon atoms with hydrogenated surfaces, obtained by high-pressure solidstate reaction of crystalline benzene. 1–3 These one-dimensional nanostructures exhibit outstanding mechanical properties, 4–6 and many potential technological applications have been suggested for them. 7–10 The use of other aromatic molecules as precursors for nanothreads (NTs) has been proposed in theoretical/computational studies, such as benzene derivatives (aniline, phenol, toluene, etc.) and heterocyclic aromatic compounds (pyridine), 11 as well as polycyclic aromatic hydrocarbons (such as naphthalene, coronene, and many others). 12,13 Experimental studies have demonstrated the feasibility of nitrogenated carbon nanothreads from both aniline 14 and pyridine 15 crystals, stimulating the search for novel nanomaterials using this process. These nanostructures are formed when the creation of sp3 covalent bonds between stacked benzene molecules is induced under high pressures. A complete sp2 -sp3 conversion of the C-C bonds may lead to 1D materials with a significant variety of atomic structures, depending on the relative stacking of molecules and C-C bonding patterns. 16 An investigation of mechanisms for the benzene-NT transformation using Density Functional Theory (DFT) calculations 17 has shown that possible pathways include the formation of partially saturated configurations either as intermediates or final products, characterized by the coexistence of sp3 and sp2 C-C bonds (i.e., not all C sites on a benzene molecule react with the neighboring rings). Detailed characterization of nanothread samples obtained from both benzene 18,19 and pyridine 15 shows that these are usually composed of a mixture of fully saturated nanothreads with varied atomic structures and partially saturated nanothreads with varied degree

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of saturation (DS, defined as the number of sp3 bonds formed for each benzene or pyridine molecule, ranging from 1 to 6). Considering that the relative stability of several of these fully and partially saturated nanothreads are similar, 16,17 the precise atomic structure of the material obtained in the process is very likely to depend on kinetics, and mixtures of nanothread with varied atomic configurations are expected to be found at the end of the process under normal conditions. Considering that partially saturated nanothreads are natural products of the synthesis process, and that their properties have not been properly investigated so far, the objective of this study is to use DFT calculations to evaluate how the electronic and mechanical properties of partially saturated nanothreads differ with respect to those typical of fully saturated nanothreads. 4,20,21 We show that the mechanical strength in tensile strain tests decreases with respect to fully saturated C-NTs, but the ultimate strength and Young’s modulus are remarkable as well, making these materials suitable for the same applications previously suggested for fully saturated sp3 nanothreads. The electronic behavior of the partially saturated nanothreads is found to range from semiconducting to insulating, with a band gap dependent on details of the atomic structure (mainly the distribution of remaining double bonds along the threads) and on the presence of N atoms and nature of C-N bonds.

Computational methods The atomic and electronic structure of the carbon nanothreads were computed by DFT calculations, as implemented in the QUANTUM ESPRESSO package. 22 These calculations were carried out within the Generalized Gradient Approximation (GGA/PBE), using Grimme’s D2 semi-empirical correction to describe vdW interactions. Valence and core electrons were treated using PAW pseudopotentials. Plane waves were employed for the expansion of the Kohn-Sham orbitals, using a cutoff energy of 45 Ry. The first Brillouin zone was sampled with a uniform 1 x 1 x 9 Monkhorst-Pack mesh. A vacuum of ∼16 angstroms in the super-

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cell directions perpendicular to the main axis was used to avoid interactions between images. These parameters were selected from a preliminary convergence study (see Supporting Information). The atomic structures are relaxed with respect to internal atomic positions and the axial dimension of the supercell. The electronic band structure, electronic density of states (DOS), and projected density of states (PDOS) were then computed for the optimized configurations. Mechanical properties under uniaxial tensile strain were also computed, by generating stress-strain curves according to the same methodology described in previous studies. 4,11–13 The Young’s modulus is computed from the slope of the curve at the linear regime, and the ultimate strength and fracture strain are taken at the maximum of the curve. Results are expressed in terms of 1D stress (force units) to avoid introducing arbitrary definitions for nanothread diameter in the calculation of atomic volume, and allow a consistent comparison between results for different 1D configurations; 4,11–13 in this case, the ideal strength correspond to the force required to break a single nanothread.

Results and discussion Atomic structure and relative stability As discussed before, experimental characterization of carbon nanothread samples 18,19 have pointed out the coexistence of fully saturated C-NTs (DS = 6) and C-NTs with varied degrees of saturation (DS = 2 or 4), i.e., containing unsaturated C=C double bonds. There is a significant variety of possible atomic configurations for these partially saturated NTs, differing with respect to the relative orientation between stacked benzene rings and to the C atoms which are involved in the sp3 bonds. A theoretical analysis has systematically enumerated a series of such configurations based on different stacking patterns between benzene molecules and plausible reaction pathways connecting the precursor molecules to the fully saturated NTs. 17 4


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Some of these proposed configurations with DS = 4 were observed in real samples in a recent study, 19 using a combination of experimental and computational techniques. These were chosen to carry out the present analysis, and are illustrated in Figure 1. Each one is labeled consistently to the original reference 17 (namely IV-6, IV-7, IV-8, with IV denoting DS=4), and are named respectively as syn, anti, and syn-anti isomers. These have been shown to be formed through a pathway involving [4+2] cycloadditions of stacked benzene molecules toward saturated 1D structures. 17 These three partially saturated configurations (Fig. 1(a,b,d)) differ with respect to the relative alignment between the remaining C=C double bonds in the structure. Two successive C=C double bonds can be either on the same side of the nanothread (syn) or on opposite sides (anti ); the third possibility (syn-anti ) results from an alternation of these two patterns along the chain. The syn configuration can further react to form a fully saturated nanothread (syn-sat, Fig. 1(c)), also referred as Square Polymer 19 (or [146532] C-NT according to the notation introduced by Xu et al. 16 to enumerate all possible C-NT configurations). The anti isomer cannot increase its DS because the remaining double bonds are in opposite sides of the chain. Interestingly, the syn-anti (IV-8) configuration can also be further saturated, leading to a C-NT structure (syn-anti -sat) which has not been reported to our knowledge, presented in Fig. 1(e). The IV-8 configuration has been considered as a natural end point in a possible pathway involving [4s+2s] cycloadditions. 17 The aforementioned experimental/theoretical study 19 showed that the combination of partially saturated anti (IV-7) and syn-anti (IV-8), and the fully saturated Square Polymer and Stiff-chiral-3 structures in the sample provides the best fit to measured NMR data. The IV-6 configuration was not observed because it was likely fully converted to the most stable Square Polymer structure (the relative stability of these configurations is discussed later in the text). We also extended our investigation to carbon nitride (CN-)NTs, considering that partially saturated configurations have also been observed in samples of nanothreads obtained by compression of pyridine 15 as mentioned before. NMR spectra of these samples suggested

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Figure 1: Atomic structure of fully and partially saturated (a-e) C-NTs and (f-j) CN-NTs. Grey and magenta sites correspond to sp3 and sp2 hybridized C atoms, respectively, and blue and white to N and H atoms. Dashed boxes depict the unit cell for each configuration. Orange arrows indicates related structures with increasing degree of saturation. Each one is labeled according to the notation introduced in the text and/or in previous studies. 16,17

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the presence of imine N=C bonds on some nanothreads, and the configuration anti -N22 (equivalent to IV-7, Fig. 1(f)) was considered a possible candidate for the DS = 4 structure. We studied nitrogenated versions of the aforementioned configurations (also depicted in Fig. 1), considering that the benzene molecule (C6 H6 ) is structurally similar to a pyridine molecule (C5 H5 N, in which one CH group within the benzene ring is replaced by a N atom). Therefore, we investigated anti -N and syn-N unsaturated configurations (differing by the relative positions of either N=C or C=C unsaturated bonds), as well as their fully saturated counterparts, as illustrated in Figs. 1(f-j). The reduced symmetry of pyridine molecules compared to benzene leads to a more significant variety of possible NT configurations, due to variations in the relative position of the N sites along the thread as shown in a previous study. 11 We limited our investigation to configurations with supercells defined by two rings. Therefore, there are two N atoms in the unit cell, and they can be either sp3 (within the main chain) or sp2 (in a C=N bond appended to the chain), as observed in Fig. 1. We then augmented the label used to designate each investigated structure by including two numbers according to the hybridization of N atoms, namely -N22 (both sp2 ), -N33 (both sp3 ) and -N23 (one of each). Fig 1 shows some examples of partially saturated CN-NTs, as well as their fully saturated analogues. Fully saturated configurations were labeled accordingly to their partially saturated version (e.g., name-Nxx -sat, where name = anti or syn, and x = 2 or 3) despite having only sp3 bonds, in order to stress the relationship between them. Examples of other investigated CN-NT configurations are illustrated in the Supporting Material. To analyze the relative stability between the investigated configurations, we computed the binding energy (Eb ), defined as the difference between the energy of the NT after structural optimization (normalized by number of equivalent precursor molecules) and the energy of the molecule from which it derives (isolated benzene or pyridine molecule in the vacuum). When comparing isomers, the lower the Eb , the most stable the structure. Table 1 shows the binding energy computed for the C-NTs and CN-NTs depicted in Fig. 1. Fig. 2 provides the Eb of several other possible CN-NT structures as described above. In general, fully saturated

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NTs are more stable than their partially saturated counterparts, in agreement with previous theoretical studies. 17 The preference for fully saturated configurations is also suggested by experiments, 19 as discussed in the previous section, which indicates the presence of the fully saturated Square Polymer and not its precursor syn IV-6 in a C-NT sample. However, the same study suggests the presence of partially saturated syn-anti IV-8 and not of its fully saturated version presented here (Fig. 1(e)). The computed Eb for these two structures show that the fully saturated syn-anti -sat configuration is the most stable of the two, suggesting that kinetic effects might be important, hindering the transformation of IV-8 to syn-anti -sat in this case. Among the partially saturated configurations, anti and syn-anti are more stable than the syn isomers. These differences in relative stability can be attributed to the presence of van der Waals interactions/repulsions between the appended unsaturated pairs of atoms typical of syn configurations. Interestingly, the anti -N22 nanothread (shown in Fig. 1(f)) is even more stable than any saturated CN-NT, but the same does not happen for C-NTs. Among the CN-NTs, the most stable configurations for a given arrangement (either syn or anti ) are the ones which have remaining C=N double bonds appended to the chain instead of C=C, i.e., partially saturated configurations on which N is bonded to sp3 C atoms within the main chain are disfavored. This observation is corroborated by experiments; as mentioned before, characterization of pyridine-based CN-NTs indicates the presence of imine C=N bonds in the material. 15

Electronic structure The electronic band structure of the partially and fully saturated configurations described in the previous section were also computed. Previous studies 11,16,20,21 have shown that carbon nanothreads are insulators with gaps larger than 3.5 eV according to GGA/PBE DFT calculations, as expected due to their intrinsic C-C sp3 bonding (similarly to diamond). The use of the HSE hybrid exchange-correlation functional in the DFT calculations, which provides 8


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Table 1: Computed properties of all C-NTs and the main CN-NTs studied.a Nanothread Eb (eV) Eg (eV) Ym (nN) anti 0.006 3.96 60.9 syn 0.567 1.84 82.2 syn-sat -0.465 4.25 103.2 syn-anti 0.018 3.46 40.0 syn-anti -sat -0.495 4.45 55.4 anti -N22 -0.177 3.82 60.1 syn-N22 0.025 3.08 86.7 syn-N22-sat -0.069 3.48 111.2 syn-N33 1.144 1.92 83.2 syn-N33-sat -0.105 3.09 118.0 a Eb is the relative binding energy, Eg the electronic bang gap, and Ym the 1D Young’s modulus.

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syn−N22 . syn−N23 syn−N33 syn−N22−sat syn−N23−sat syn−N33−sat anti−N22 anti−N23 anti−N33

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more reliable estimates for band gaps compared to GGA (which usually underestimates the gap), show that these gaps are even larger (by ∼ 1.0 eV). 21 Calculations also show that the presence of N within fully saturated NTs reduce the band gap, due to the introduction of midgap states. 11 Table 1 shows the computed band gaps for selected configurations, and Fig. 3 provides some representative band dispersion curves, as well as DOS and PDOS plots. Figure 2 reports the band gaps along with the binding energy for several CN-NTs configurations. All Cand anti -N- nanothreads have a direct band gap, while syn-N and syn-N-sat exhibit indirect ones (as exemplified in Fig. 2). The investigated fully saturated C-NTs are insulators with wide gaps (> 4.2 eV) as expected, 11,16,20,21 while the partially saturated ones present lower values (∼ 1.8 to 4.0 eV). The syn configuration is the one with the narrowest band gap (1.84 versus 4.25 eV for its fully saturated counterpart). The smaller band gaps observed for the partially saturated NTs are related to the presence of double C=C bonds in the structure; the pz orbitals of these C sites introduce energy states near the gap, as observed when comparing the DOS/PDOS plots of the saturated and partially saturated C-NT configurations in Fig. 3(a-d). When these orbitals are closer to each other (as in syn or syn-anti ), the energy differences between the valence band maximum (VBM) and conduction band minimum (CBM) decreases, likely due to the interaction between these orbitals. The application of uniaxial strain did not affected significantly the band gaps for the investigated structures (see Supporting Information). Figures 2 and 3 show that nitrogenated fully saturated structures have narrower band gaps compared to the equivalent C-NT (2.80-3.50 eV versus 4.25 eV), a result of additional states near the gap introduced by the N atoms, as seen when comparing Figs. 3(d) and 3(h). A similar effect has been observed before for another fully saturated NT (the well-known Tube(3,0) nanothread). 11 Band gaps for partially saturated C-NTs range from 1.5-4.0 eV depending on the nature of the appended double bonds (either C=C or C=N) and their spatial disposition along the chain. Anti configurations have larger gaps than syn ones as

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Figure 3: Electronic band structure and total/projected density of states (on the left and right side of each frame, respectively) for partially and fully saturated (a-d) C-NTs and (e-h) CN-NTs. Green arrows indicate the indirect gaps. The color scheme used for the total and projected DOS for the orbitals of sp2 or sp3 -hybridized C or N atoms is shown in the right (a color version of this figure is available in the online version). The Fermi level (Ef = 0) was taken as the maximum of the VBM.

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discussed for C-NTs, and N22 CN-NTs (with two C=N bonds per unit cell) have larger gaps than N33 ones (with two C=C bonds per unit cell). In all cases (Fig. 3(e-g)), the pz orbitals of the atoms involved in the unsaturated sp2 bonds are responsible for additional energy levels within the gap compared to the fully saturated cases, analogously to the C-NTs as discussed before. The band gap is smaller when only pairs of C=C bonds are present on the structure, and increases as sp2 C atoms are swapped by sp2 N (leading to C=N/C=C and C=N/C=N pairs). Figure 4 shows differences in the integrated local density of states (ILDOS) for syn and syn-N22, computed within energy ranges comprising the VBM and CBM. The higher electronegativity of N atoms leads to more localized states in the C=N bonds, compared to the C=C ones (as also seen in the flat bands in Fig.3(e)). (b) syn-N22 CN-NT

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Figure 4: Isosurfaces of Integrated Local Density of States (ILDOS) computed within energy ranges close to the valence band maximum (VBM) and conduction band minimum (CBM) for partially saturated (a) syn and (b) syn-N22 configurations.

Mechanical properties In a previous study, 4 DFT calculations showed that fully saturated NTs are characterized by high ideal strength and Young’s modulus (for the configurations investigated in Ref., 4 within 9.7-15.7 nN and 64-168 nN, respectively, or analogously 67-101 GPa and 440-1080 GPa in 3D 12


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stress, estimated using a conventional definition for atomic volume). Some NTs are softer than others, but quite flexible before rupture (reaching fracture strains of ∼ 0.23), due to a particular deformation mechanism which occurs in certain corrugated structures. 4,13 The presence of functional groups attached to the surface or heteroatoms within the sp3 chain does not significantly affect the mechanical properties, oppositely to what is usually observed for functionalized carbon nanostructures. 11 Stress-strain curves for a variety of C-NTs and some CN-NTs are depicted in Figure 5 (results for the fully saturated Polymer-I nanothread 4 are also shown for comparison, due to their structural similarity). Figure 6 shows images depicting the structural evolution of selected NTs upon application of tensile strain. The initial and final (right before onset of fracture) states are shown for each presented case, illustrating the typical deformation mechanisms of partially saturated NTs. Partially saturated NTs exhibit brittle behavior, as observed for conventional C-NTs without defects. 4–6 The Young’s modulus of the NTs depicted in Fig. 1 are given in Table 1. In general, the ideal strength and stiffness of partially saturated nanothreads are in the same order of magnitude of those exhibited by fully saturated ones; when compared to their saturated versions, partially saturated nanothreads are softer (82 versus 103 nN for syn and 40 versus 55 nN for syn-anti, a relative decrease of 20-27 %) and have lower ideal strengths (10.0 versus 12.8 nN for syn and 7.7 versus 10.7 nN for syn-anti, a relative decrease of 22-28 %). The stress-strain curves in Figure 5 also shows that the presence of N atoms in NTs does not affect significantly the properties compared to the pure carbon equivalent structures, as observed before for other fully saturated NTs. 11 The syn-sat configuration was the strongest among the investigated cases, with an ideal strength and Young’s modulus close to that of the equally fully saturated Polymer-I (both undergo fracture in the cross-section with the smallest number of bonds, i.e., two 4 ). The anti and syn-anti configurations are the softest ones but reach the highest fracture strains (as high as 0.24), due to their corrugated chain; the alternation of bonding patterns for every pair of rings confers the structure a larger flexibility, which was not observed for the syn

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configurations. The structure is initially straightened upon tensile straining (mostly through angular deformation) as illustrated in Figure 6, and only at higher deformations the C-C bonds get more significantly strained, eventually inducing the fracture. The structure of syn configurations deforms evenly upon straining (as depicted in Fig. 6), and the fracture strain is close to values typically exhibited by fully saturated C-NTs with similar mechanical response. 4,11,12 The corrugated surface of anti and syn-anti NTs is expected to improve interfacial load-transfer in composites, as previously suggested for fully saturated NTs with similar structural features. 9,10 The high flexibility exhibited by these NTs could confer the composite an interesting combination of strength and elasticity, a subject that could be better explored in future studies. The corrugated chain characteristic of syn-anti might also help understanding why this structure is present at experimental samples of C-NTs, despite being less stable than its fully saturated counterpart, as discussed in Sec. 3.1., due to changes in the interatomic distances between the appended C=C pairs upon straining or compression (see Supporting Information). 15

1D Stress (nN)

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Figure 6: Atomic structures of several C-/CN-NTs at low and high strains (on the left and right side of each given pair, respectively), depicting the structural transformations undergone before rupture.

Conclusions We have presented a comprehensive computational study of structural, electronic and mechanical properties of partially saturated carbon and carbon nitride nanothreads. Representative atomic structures of partially saturated NTs as reported in experimental observations 15,18,19 and theoretical studies of NT formation pathways 17 were selected for this investigation. These partially saturated NTs are weaker and softer that their fully saturated counterparts (with a relative reduction of ∼ 20-28 % in the computed properties), but exhibit remarkable strength and stiffness as well, being able to be used in the same applications previously proposed for conventional NTs. The significant flexibility of some NT configurations and their intrinsic corrugated surfaces may be properly explored in future studies on the application of these materials as fillers in reinforced composites. The presence of unsaturated double C=C and C=N bonds leads to a reduction on the electronic band gap compared to fully sp3 NTs. The presence and disposition of N atoms along the structure leads to significant variations on the same property. Band gaps varies from 1.8-4.0 eV in the pure Cand CN-nanothreads investigated, lower than those exhibited by conventional NTs, a feature that may be explored towards new applications for these materials. Partially saturated NTs 15



are natural by-products of the high pressure process, and the present study brings a more comprehensive understanding on their properties and mechanical and electronic behavior; these nanostructures are equally suitable for most of the previously proposed applications for conventional fully saturated NTs, and certainly will enable new possibilities.

Acknowledgement The authors acknowledge the National Laboratory for Scientific Computing (SDumont supercomputer, LNCC/MCTI, Brazil) and the Centro Nacional de Supercomputacao (CESUP/UFRGS, Brazil) for providing computational resources for the calculations reported in this paper. P.G.D. acknowledges a BIC scholarship from BIC/UFRGS program.

Supporting Information Available Additional results and discussion. This material is available free of charge via the Internet at http://pubs.acs.org/.

References 1. Fitzgibbons, T. C.; Guthrie, M.; Xu, E.-s.; Crespi, V. H.; Davidowski, S. K.; Cody, G. D.; Alem, N.; Badding, J. V. Benzene-derived carbon nanothreads. Nature materials 2015, 14, 43. 2. Li, X.; Baldini, M.; Wang, T.; Chen, B.; Xu, E.-s.; Vermilyea, B.; Crespi, V. H.; Hoffmann, R.; Molaison, J. J.; Tulk, C. A. Mechanochemical synthesis of carbon nanothread single crystals. Journal of the American Chemical Society 2017, 139, 16343–16349. 3. Cai, W.; Dunuwille, M.; He, J.; Taylor, T. V.; Hinton, J. K.; MacLean, M. C.; Molaison, J. J.; Dos Santos, A. M.; Sinogeikin, S.; Deemyad, S. Deuterium isotope effects in

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Graphical TOC Entry

sp3 / sp2

sp3

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Electronic and Mechanical Properties of Partially Saturated Carbon

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