Computational Materials Science 140 (2017) 344–355 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier .com/locate /commatsci Porous graphene and graphenylene nanotubes: Electronic structure and strain effects http://dx.doi.org/10.1016/j.commatsci.2017.09.009 0927-0256/� 2017 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: paupitz@rc.unesp.br (R. Paupitz). 1 Present address: Grupo de Modelagem e Simulação Molecular – DM, São Paulo State University – UNESP, Caixa Postal 473, Bauru – São Paulo, SP, Brazil. Guilherme S.L. Fabris a,1, Chad E. Junkermeier b, Ricardo Paupitz a,⇑ a São Paulo State University (UNESP), Institute of Geosciences and Exact Sciences, Rio Claro, 13506-900 SP, Brazil bResearch Corporation of the University of Hawaii‘i, Honolulu, HI 96848, United States a r t i c l e i n f o a b s t r a c t Article history: Received 9 June 2017 Received in revised form 16 August 2017 Accepted 4 September 2017 Available online 15 September 2017 Keywords: Carbon nanotubes Porous graphene Graphenylene Simulation Strain effects Porous nanotubes The unusual and unique mechanical and electronic properties of nanostructured carbon materials make them useful in the construction of nanodevices. We investigate a new class of structures, called porous nanotubes, which are constructed from two recently synthesized two-dimensional materials, namely the porous graphene (PG) and the two-dimensional carbon allotrope known as graphenylene, also known as Biphenylene Carbon (BPC). We investigate this class of quasi-one-dimensional materials using the den- sity functional tight-binding (DFTB) method to optimize geometries and to calculate electronic structure features of these systems. For each type of porous nanotube, calculations were performed on tubes with several diameters and chiralities. Our results show that the PG nanotubes have a wide band-gap, � 3:3 eV, and the graphenylene nanotubes have a semiconductor behavior with a band gap around 0.7 eV. They also show that as the diameter of a PG nanotube increases the band-gap decreases, while for the graphenylene nanotube the band gap increases. In both cases, the observed gap variation with increasing diameter is towards the value found for the respective two-dimensional membrane. Calculations on axially strained porous nanotubes show a decrease on the band gap of � 10% for some chiralities of the PG nanotube and an increase for the graphenylene nanotubes gap that can become as high as 100%. These results are in contrast with the expected behavior for carbon nanotubes, which show a linear dependence between gap opening and applied strain under similar conditions. � 2017 Elsevier B.V. All rights reserved. 1. Introduction Graphene [1,2] is a two-dimensional array of hexagonal units of sp2 bonded carbon atoms (Fig. 1) which presents unusual and interesting electronic and mechanical properties [2]. Because of these properties it may be used in diverse applications, for example electronics [3,4], water separation [5], nanomechanical resonators [6–8], chemical sensors [9], or in producing exotic materials [10– 14]. However, in its pristine form, graphene is a gapless semicon- ductor. This characteristic imposes serious limitations to its use in practical electronic applications. Many approaches have been proposed to create a gap in graphene-like materials. One of the most common strategies uses chemisorption methods, such as oxi- dation [15–17], hydrogenation [18–20], fluorination [21–24], or some other adsorbate [9,25]. Another approach is to obtain intrin- sically hydrogenated structures, such as PG (Fig. 1b), whose syn- thesis was recently achieved [26]. Other authors discussed the metallic behavior found for structures obtained by the combina- tion of biphenylenes in several configurations [27] which, despite some structural similarities, are different from the structures dis- cussed in the present work, which can present semiconducting or insulating behavior. One of these combinations is the so called gra- phenylene, which has a small band gap and delocalized frontier orbitals [28–30]. A possible route to the synthesis of graphenylene was proposed elsewhere [28] and its experimental realization, although obtained through a different route, was reported recently [31,32]. Further, Schlütter et al. reported recently that they were able to synthesize octafunctionalized biphenylene GNRs [33]. Another possibility is the combination of these geometries with functionalization [34] that can lead to interesting effects regarding gas adsorption [35]. The new generation of electronics may also be facilitated by producing any of the above structures using boron nitride (BN) or some combination of carbon, boron, and nitrogen atoms [36,37]. In this context, we consider the possibility of struc- tures based on the PG and graphenylene primitive cells and on CNT architecture, the so-called porous nanotubes (PNT). The grapheny- lene version of the PNTs was proposed recently by Koch et al. [38] http://crossmark.crossref.org/dialog/?doi=10.1016/j.commatsci.2017.09.009&domain=pdf http://dx.doi.org/10.1016/j.commatsci.2017.09.009 mailto:paupitz@rc.unesp.br http://dx.doi.org/10.1016/j.commatsci.2017.09.009 http://www.sciencedirect.com/science/journal/09270256 http://www.elsevier.com/locate/commatsci Fig. 1. Definitions of unitary vectors a1 and a2 and primitive cells for the two dimensional structures discussed throughout the text. (a) Graphene. (b) Porous Graphene. (c) Bi-Phenylene Carbon. G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 345 and, taking into account the fact that density functional theory (DFT) calculations tends to underestimate gap openings, our results are in good agreement with their findings. In the present work, we also study gap variations caused by axial strain on the proposed structures. In order to investigate structural and elec- tronic properties of this kind of material we investigate sixty-two representative one-dimensional structures. These are based on nine armchair-like, fourteen zigzag-like, and eight chiral-like PG- based PNTs with or corresponding graphenylene-based PNTs. Using DFTB we computed the electronic structure and studied the structural properties of each one of these structures. 2. Methods Geometry optimizations and electronic structure calculations of planar structures and PNTs were performed using a self- consistent-charge (SCC) version of the density functional tight- binding (DFTB) method [39–41] in the DFTB+ code [42]. This methodology can be implemented in a low computational cost code and mixes advantages of tight binding methods and of DFT precision in the description of molecular and condensed matter systems [43]. This methodology is based on a second-order expan- sion of the Kohn-Sham energy defined in DFT [40,44]. Band gap values predicted by DFTB may be underestimated, caused by the formulation being based only on valence electrons, yet it is useful in obtaining relative energy values or to explain trends in a series of large atomic structures. The particular parameterization used in the present work, pbc [45,46] Slater-Koster files, was developed for solids and surfaces and has been used in modeling systems similar to those discussed here [13]. Convergence criteria for the geometry optimization used force differences of 10�5 with a SCC tolerance of 10�4. For sampling the points in the Brillouin zone, we used a 10 � 1 � 1 Monkhorst-Pack grid [47] in which the 10 folding is in the direction related to the axis of the PNT. Also, as vacuum condi- tion, it was considered a 50Ådistance of empty space in directions perpendicular to the nanotube axis. The molecular dynamics (MD) simulations discussed in the present work were carried out using the Verlet algorithm, while temperatures were controlled through a Berendsen thermostat. Fig. 2. Geometrical definitions and chiral indices for two-dimensional structures considered in this work. The vectors a and b are the unit vectors of the PG and graphenylene sheets. The vectors A and A0 are respectively multiples of a and b used in defining the chiral vector Ch , with T being the translation vector. Shaded areas indicate the unrolled primitive cell for specific examples of chiralities. Eliptic regions delimited by dashed lines indicate the distance d. (a) PG with primitive cell of a (5,1) PNT indicated by shaded area. (b) Graphenylene sheet with primitive cell of a (5,2) PNT indicated by the shaded area. 3. Results and discussion 3.1. From membranes to tubes In order to define a systematic way for the construction of the PNTs, we took advantage of the geometrical similarities of the unit cells when comparing PG and graphenylene membranes with gra- phene. Using the well known definition of chiral indices for CNTs [48,49] we define a chiral vector for each one of our template pla- nar PG and graphenylene membranes. The construction of PNTs follow a recipe similar to that used in the case of the usual carbon nanotubes. In Fig. 2, chiral indices n and m are defined for both, PG (Fig. 2a) and graphenylene (Fig. 2b) PNTs as well as their chiral vec- tor Ch, primitive lattice vectors, translational vector T and quasi Table 1 Structural information and band gap values for primitive cell of PG-based PNTs. Columns N and Unit Cell indicate the total number of atoms and the total length for a one- dimensional unit cell respectively. D-Map and D-Calc indicate PNT diameter predicted by expression (4) and the actual value measured using DFTB+ optimized structures, respectively. Gap indicates the predicted difference between the maximum value of the valence band and the minimum of conduction band as calculated by DFTB+. DG/IG indicates if the gap is direct or indirect. (m;n) N Unit Cell (Å) D-Map (Å) D-Calc (Å) Gap (eV) DG/IG (2;2) 72 7.439 8.42 7.89 3.326 IG (3;3) 108 7.443 12.63 12.21 3.368 IG (4;4) 144 7.449 16.84 16.19 3.367 IG (5;5) 180 7.453 21.06 21.24 3.357 IG (6;6) 216 7.456 25.27 24.47 3.352 IG (7;7) 252 7.459 29.48 29.23 3.34 IG (8;8) 288 7.462 33.69 32.73 3.333 IG (9;9) 324 7.463 37.9 37.18 3.337 IG (10;10) 360 7.464 42.11 41.29 3.324 IG (2;0) 72 12.473 4.86 4.87 3.033 DG (3;0) 108 12.647 7.29 7.19 3.435 DG (4;0) 144 12.731 9.73 10.08 3.434 DG (5;0) 180 12.773 12.16 12.03 3.421 DG (6;0) 216 12.802 14.59 14.79 3.406 DG (7;0) 252 12.819 17.02 17.67 3.395 DG (8;0) 288 12.835 19.45 19.53 3.383 DG (9;0) 324 12.847 21.88 22.32 3.372 DG (10;0) 360 12.857 24.31 24.27 3.365 DG (11;0) 396 12.865 26.74 26.05 3.357 DG (12;0) 432 12.872 29.18 29.01 3.351 DG (13;0) 468 12.878 31.61 31.72 3.346 DG (14;0) 504 12.884 34.04 33.76 3.341 DG (15;0) 540 12.888 36.47 36.25 3.34 DG (2;1) 252 33.911 6.43 6.33 3.338 IG (3;1) 468 46.129 8.77 9.31 3.404 IG (4;1) 252 19.555 11.14 11.09 3.415 IG (4;2) 504 34.04 12.87 12.63 3.388 IG (5;2) 468 26.776 15.18 14.55 3.389 IG (6;2) 936 46.38 17.53 17.38 3.38 IG (8;2) 504 19.66 22.28 21.65 3.37 IG (12;2) 3096 84.5 31.89 31.49 3.34 IG Table 2 Structural information and band gap values for primitive cell of graphenylene-based PNTs. Columns N and Unit Cell indicate the total number of atoms and the total length for a one-dimensional unit cell respectively. D-Map and D-Calc indicate PNT diameter predicted by expression (4) and the actual value measured using DFTB+ optimized structures respectively. Gap indicates the predicted difference between the maximum value of the valence band and the minimum of conduction band as calculated by DFTB+. DG/IG indicates if the gap is direct or indirect. (m;n) N Unit Cell (Å) D-Map (Å) D-Calc (Å) Gap (eV) DG/IG (2;2) 48 6.777 7.39 7.56 0.494 DG (3;3) 72 6.781 11.08 11.08 0.626 DG (4;4) 96 6.782 14.77 14.86 0.675 DG (5;5) 120 6.783 18.46 18.62 0.697 DG (6;6) 144 6.783 22.16 22.38 0.709 DG (7;7) 168 6.784 25.85 26.12 0.717 DG (8;8) 192 6.784 29.54 29.87 0.721 DG (9;9) 216 6.784 33.23 33.11 0.725 DG (10;10) 240 6.784 36.93 37.34 0.727 DG (2;0) 48 11.986 4.26 4.24 0.688 DG (3;0) 72 11.856 6.4 6.46 0.443 DG (4;0) 96 11.811 8.52 8.24 0.693 DG (5;0) 120 11.789 10.66 10.79 0.709 DG (6;0) 144 11.778 12.79 12.69 0.655 DG (7;0) 168 11.771 14.92 15.11 0.719 DG (8;0) 192 11.766 17.06 17.07 0.724 DG (9;0) 216 11.763 19.19 19.43 0.699 DG (10;0) 240 11.761 21.32 21.43 0.728 DG (11;0) 264 11.759 23.45 23.75 0.729 DG (12;0) 288 11.758 25.58 25.78 0.715 DG (13;0) 312 11.757 27.71 28.07 0.731 DG (14;0) 336 11.756 29.85 30.23 0.732 DG (15;0) 360 11.756 31.98 32.26 0.723 DG (2;1) 168 31.132 5.64 5.49 0.612 IG (3;1) 312 42.485 7.69 7.6 0.691 IG (4;1) 168 17.995 9.77 9.77 0.598 IG (4;2) 336 31.105 11.28 11.22 0.708 IG (5;2) 312 24.479 13.31 13.49 0.659 IG (6;2) 624 42.39 15.37 15.67 0.72 DG (8;2) 336 17.961 19.54 20.01 0.701 DG (12;2) 2064 77.09 27.96 28.56 0.731 DG 346 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 Table 3 Comparison between CNT total energies per atom with the energies found for PG (EPG) and graphenylene (EBPC ) PNTs for various different chiralities. (m;n) ECNT (eV/atom) EPG (eV/atom) EBPC (eV/atom) (2;2) �46.288 �34.653 �46.488 (3;3) �46.869 �34.672 �46.542 (4;4) �47.087 �34.677 �46.561 (5;5) �47.185 �34.680 �46.569 (6;6) �47.238 �34.680 �46.574 (7;7) �47.269 �34.681 �46.577 (8;8) �47.290 �34.681 �46.579 (9;9) �47.304 �34.681 �46.580 (10;10) �47.314 �34.681 �46.581 (2;0) �45.430 �34.564 �46.277 (3;0) �46.112 �34.638 �46.454 (4;0) �46.588 �34.661 �46.512 (5;0) �46.846 �34.670 �46.538 (6;0) �46.997 �34.675 �46.552 (7;0) �47.097 �34.677 �46.561 (8;0) �47.158 �34.679 �46.567 (9;0) �47.198 �34.680 �46.570 (10;0) �47.230 �34.680 �46.573 (11;0) �47.252 �34.681 �46.575 (12;0) �47.268 �34.681 �46.577 (13;0) �47.282 �34.681 �46.578 (14;0) �47.292 �34.681 �46.579 (15;0) �47.299 �34.681 �46.580 (2;1) �46.155 �34.626 �46.419 (3;1) �46.382 �34.656 �46.495 (4;1) �46.747 �34.668 �46.529 (4;2) �46.900 �34.672 �46.543 (5;2) �47.024 �34.676 �46.555 (6;2) �47.114 �34.678 �46.562 (8;2) �47.204 �34.680 �46.571 (12;2) �47.283 �34.681 �46.578 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 347 one-dimensional primitive cells used in the construction of single- wall PNTs, each of which will be discussed further hereafter. The vector Ch indicates two equivalent sites on the sheet (PG or graphe- nylene) and is uniquely defined by a pair of integer numbers (m;n), Ch ¼ maþ nb; ð1Þ where vectors a and b (Fig. 2) are the lattice’s unit vectors for each case. Vector T, which indicates the axial direction of the PNT, is per- pendicular to Ch and its length is defined by the distance between the original site (the origin of Ch, for example) and its closest equiv- alent site. Rolling up the equivalent sites one over the other, forms the tube uniquely identified by the pair of integer numbers (m;n). As with CNTs, when m ¼ n the PNT is denoted as armchair-type, those with m ¼ 0 or n ¼ 0 are the so-called zig-zag tubes, while other combinations correspond to chiral tubes. In the case of CNTs, if one assumes that the known geometrical relations for two dimensional graphene membranes remain valid after wrapping, the exact number of atoms of the primitive cell of a nanotube is completely determined by its chiral indices (m;n) [48,49]. In a similar way, geometrical relations are straight- forwardly obtained for PNTs, such as the extension of a primitive cell, indicated by shaded areas in Fig. 2. It is also possible to find mathematical expressions for the number of atoms in each one of these primitive cells. In the case of PG based PNTs, the number of carbon atoms (nC), the number of hydrogen atoms (nH) and total number of atoms (nT) are nC ¼ 24 � ðn 2 þm2 þ nmÞ dR ; nH ¼ 12 � ðn 2 þm2 þ nmÞ dR ;nT ¼ nC þ nH; ð2Þ where dR is the maximum common divisor of ð2nþm;2mþ nÞ. Analogously, for graphenylene-based PNTs one can find nC ¼ 24 � ðn 2 þm2 þ nmÞ dR : ð3Þ The diameter, D, of an ideal CNT [48,49] as a function of n andm also has an analogous form for PNTs, D ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 þm2 þ nm p p a; ð4Þ where a indicates the length of the unit vectors of the two- dimensional lattice (PG or graphenylene) and its magnitude depends on the distance d between hexagons in the specific struc- ture by the relation a ¼ ffiffiffi 3 p d. Fig. 3. Geometry of representative PNTs with chirality (8,8), (8,0) a 3.2. Structural properties Before employing the rolling-up procedure discussed above we first optimized PG and graphenylene. The optimization of the membranes resulted in a unit cell with lattice parameters a and b for PG and graphenylene with values 7.61, 7.48, 6.78 and 6.78 Å, respectively. This also resulted in distances between hexa- gons of 3.87 Å and 4.41 Å for graphenylene and PG respectively. With the optimized graphenylene and PG lattice vectors computed we created PG-based and graphenylene-based PNTs. Tables 1 and 2 present the lattice parameters, number of atoms, predicted and observed diameters, and band gaps of the PG-based and graphenylene-based PNTs. Using several pairs of diametrically opposed atoms through out an optimized tube we calculated the average value for the diameter of each PNT. As expected, there are some systematic differences between the diameter values nd (8,2). (a) Porous Graphene based. (b) Graphenylene-based. Fig. 4. Charge distributions for PG and graphenylene-based PNTs, both with chiral indices (4,4). (a) and (b) Illustrate charge and charge differences for a PG based PNT, respectively. (c) and (d) Are respectively the charge distribution and charge differences found for a graphenylene-based PNT. Fig. 5. Band structure and DOS for three representative porous nanotubes. (a), (c) and (e) Show results for a (4,4), a (6,0) and a (6,2) PG-based nanotube, respectively. (b), (d) and (f) Show the corresponding DOS calculated for the same PNTs. The regions indicated by lines with double arrows highlight the maximum of the valence band and the minimum of the conduction band for each case. Whether these are vertically aligned or not defines if the gap is named as being direct or indirect respectively. 348 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 Fig. 6. Band structure and DOS for representative graphenylene nanotubes. (a), (c) and (e) Show band structure results for a (4,4), a (6,0) and a (6,2) graphenylene-based nanotube respectively. (b), (d) and (f) Show the DOS calculated for the same PNTs, namely, a (4,4), a (6,0) and a (6,2) respectively. Fig. 7. Gap values for various diameters for various PNTs based on PG membranes. The dashed line represents reference values obtained by DFTB calculations for an infinite porous graphene sheet. Blue squares, green circles and red triangles indicate armchair, zigzag and chiral architectures respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 349 predicted by Eq. (4), obtained from ideal geometries and fixed bond sizes, and the values obtained from the optimized structures. For the PNTs studied, the PG type are slightly smaller by an average percent difference of � 0:86, while the graphenylene PNTs are slightly larger than the predicted value by a percent difference of � 0:55. Table 3 provides a comparison between the energies of Fig. 8. Gap values for graphenylene-based PNTs of various chiralities. The dashed line indicates a reference value obtained by DFTB calculations for an infinite graphenylene sheet. Blue squares, green circles and red triangles indicate armchair, zigzag and chiral architectures respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 350 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 usual carbon nanotubes and the proposed PNTs of the present work. In the case of PG-based PNTs, the original hexagonal pattern is preserved with some small distortions on bond distances that became longer for inter-hexagonal bonds (typically single bonds with � 1:48 Å) if compared with the intra hexagonal bond sizes (� 1:4 Å). Representative PG-based PNTs are shown in Fig. 3. For graphenylene PNTs, bonds inside hexagons vary around two differ- ent values: � 1:46 Å and � 1:38 Å, while butadiene bonds are typ- ically close to � 1:49 Å, the last value indicating single bonds. In both cases, PG based and graphenylene based PNTs, the variation on bond distances can be interpreted as the effect of different cur- vatures on the porous nanotubes. MD simulations were used to determine if the PNTs would be stable above room temperature. Starting from the geometry deter- mined in the optimization process, MD simulations at three differ- ent temperatures, namely 300 K, 600 K and 900 K, were performed independently for at least 10 ps for each one of the PNTs. Two rep- resentative cases of simulations carried at the higher temperature (900 K) can be seen in the videos provided in the supplementary materials. These videos show nanotubes with lengths equivalent to several primitive cells of a graphenylene-based and a porous graphene-based PNT during a simulation that includes a small heating that goes from 300 K to 900 K and stabilizes at this final constant temperature of 900 K. During the MD simulations, the studied PNTs presented high structural stability with no bond breaking, despite the presence of significant deformations caused by thermal agitation. This indicates that these materials would be structurally and chemically stable even at temperatures that are much higher than those typically supported by regular elec- tronic devices. 2 For interpretation of color in Fig. 4, the reader is referred to the web version of this article. 3.3. Electronic structure Charge distributions, shown in Fig. 4, reveal important differ- ences between PG-based and graphenylene-based PNTs. In order to show representative cases, Fig. 4(a) and (c) present charge distri- butions for PG-based and BPC-based PNTs with chiral indices (4,4). The surfaces were plotted using an isosurface value of 0.01 with the VMD software [50]. The charge is nearly uniformly distributed over the C atoms in the graphenylene-based PNTs, whereas on the PG-based PNTs the charge is slightly more concentrated on the C atoms then on the H atoms. The plots in Fig. 4(b) and (d) present a comparison between the total charge density and the density that would be obtained by summing up the densities of the neutral atoms in each region of the structures. These plots characterize charge transfers between atoms in the structure. Regions in which the total electronic density is smaller than that expected for the superposition of neutral atoms are colored in red, the opposite sit- uation leads to a blue2 colored region. Fig. 4(b) shows that for the PG tubes, charge transfers from H to C atoms, while Fig. 4(d) indicates that the charge transfer is from C atoms to the region between them, due to the formation of C-C bonds. For these plots, we considered an isosurface value of 0.05. Tables 1 and 2 show that the PNTs have band gaps, DE, similar to their two dimensional counterparts, preserving the semicon- ducting and insulating characteristics of graphenylene and PG sheets respectively. For instance, values given in Table 1 indicate a DE in a range from 3.0 eV to 3.5 eV for PG-based structures while the corresponding planar sheet presented a gap of�3.27 eV. On the other hand, graphenylene PNTs present gaps in the range 0.4 eV to 0.75 eV (Table 2), while the calculated gap for their planar counter- part (graphenylene sheet) was �0.74 eV. These are also different from the results reported elsewhere indicating metallic behavior in the case of nanotubes constructed with other kind of biphenylene-based planar structures, namely those with octagonal pores [27]. Representative band structure and density of states (DOS) plots are shown in Figs. 5 and 6, each one for three different chiralities. Armchair and chiral PG-based PNTs present indirect band gaps, while zigzag PNTs show direct gaps. Whereas for graphenylene-based PNTs, zigzag and armchair PNTs present direct band gaps while chiral ones can have either a direct or an Fig. 9. Effect of axial strain in energy (relative to the zero-strain configuration) (a) PG-based PNTs. (b) Graphenylene-based PNTs. G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 351 indirect gap. These characteristics may be relevant for photoluminescence-related behavior of these structures [51]. For all PG-based PNTs we observe flat bands formed mainly by the combination of carbon’s 2p orbitals. Since the effective mass, m�, of a charge carrier (close to the top of valence band or bottom of conduction band) can be calculated by [52] m� ¼ �h2 @2E @k2 !�1 ; ð5Þ one can see that these materials present large effective masses, leading to low mobility. For this reason it is expected that PG- based PNTs will likely be insulators. In Figs. 7 and 8 the dependencies between gap values and diam- eters are shown. The trends of each chirality type of each kind of PNT are similar. As the diameter of the PG-based PNTs increases the band gap decreases towards the value found for a planar PG sheet. Such trend is only violated by the 5Ådiameter PG-type PNT. This may be interpreted as an effect due to the interaction between carbon’s 2p orbitals in the high strained structure. Con- versely, graphenylene-based PNTs gaps increase in an oscillating fashion with growing tube diameters trending towards the value of a planar graphenylene sheet. The bands formed by carbon 2p states in chiral graphenylene- based PNTs are flatter than the 2p states in armchair and zigzag graphenylene-based PNTs; see the (6,2) graphenylene-based PNT in Fig. 6(e). This is due to the higher strained configuration of these tubes if compared to zigzag and armchair ones. These flat bands result in large effective masses for the charge carriers in both, the valence band (positive carriers) and in conduction band (nega- tive carriers) indicating low carrier mobility despite the semicon- ducting band gap. Another interesting effect to study is the influence of axial stress on the electronic structure of PNTs. We considered the effect of axial strain up to e ¼ DL=L � 0:15 (L is the tube length) on gap values for the PNTs considered in the present work. In all cases, Fig. 10. Axial strain effect on gap values for PG and graphenylene-based PNTs of different chiralities, namely (4,4) representative of armchair character, (6,0) representative of zigzag and (8,2) of chiral character. (a) PG-based PNTs. (b) Graphenylene-based PNTs. 352 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 the energy increases smoothly with axial strain as shown in Fig. 9. Fig. 10(a) shows our results for PG based nanotubes where one can see that, starting with e ¼ 0, higher strain values correspond to smaller gap values with a monotonic decrease for (6,0) and (8,2) tubes. On the other hand, the (4,4) tube presents a minimum at e � 0:1 and the gap opening increases again for higher deforma- tions, although the values still smaller than 3.2 eV up to the max- imum strain considered. Fig. 10(b) shows the influence of strain in the axial direction for graphenylene-based nanotubes, which pre- sent a reversed trend if compared to that found for PG based PNTs. Gap values for graphenylene-based PNTs increase monotonically with the increasing of strain. In both cases, higher strain (e.g. DL=L � 0:2) causes plastic deformations of the PNTs, which coin- cide with abrupt changes in gap values (not shown). Earlier studies considered usual CNTs [53,54] and reported a linear dependence between the gap opening and the applied axial strain. In the present work, we found that DFTB predicts a deviation from linearity in both cases. These deviations from linearity could be due to the fact that PNTs present several bonding types (double bonds, single bonds, C-H bonds) that weakens the structure and facilitate greater atomic rearrange- ment. In this context, the effect of band gap variation observed while strain is applied can be understood as a consequence (at least partially) of electronic interactions of atomic orbitals that result in some degree of repulsion combined with orbital recom- binations that modify the band structure. In Fig. 11 it is possible to compare the projected density of states (PDOS) for represen- tative porous nanotubes investigated in the present work. In that figure, it is possible to identify that 2p states are the main con- tribution for the majority of states located close to the Fermi level (located at 0 eV in the figure). This characteristics indicates that, upon deformations, the interaction and repulsion effects Fig. 11. Effect of axial strain on PDOS for two representative porous nanotubes. In the horizontal axis, 0 eV indicates the fermi level energy. (a) Graphenylene based nanotube with chiral indexes (8,2) with no strain (e = 0%). It is important to note that the green curve (2s orbitals contribution) is close to zero, and practically coincides with the horizontal axis in black and cannot be seen clearly. (b) Porous graphene based nanotube in relaxed geometry (e ¼ 0%). (c) Graphenylene based nanotube with e ¼ 10%. Again, the green curve, that describes 2s orbitals contribution is so small that is almost coincident with the horizontal axis. (d) Porous Graphene based nanotube with e ¼ 10%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 353 between 2p states are the responsible for the gap modifications as described by Fig. 10. In order to evaluate the quality of results obtained in the DFTB approximation level, we carried some DFT calculations for repre- sentative porous nanotubes considering both types, PG and gra- phenylene based PNTs using different exchange-correlation potentials (PBE [55] and B3LYP [56,57]). Our calculations indicate that DFTB results are in relative accordance with DFT results in the sense that it predicts approximately the relative variation on gap values in both cases (PG-based and graphenylene-based). Also, DFTB predicts correctly the trends in these band gap openings, that is: an increasing gap with strain in the case of graphenylene-based tubes and decreasing gaps with strain for PG-based nanotubes. In terms of absolute values, DFTB predictions are closer to B3LYP results for the pure carbon porous nanotubes than PBE. This can be interpreted as a favorable result for DFTB if one considers calcu- lations reported elsewhere by Goddard and coworkers [58] where they conclude that B3LYP provides the best description for the gap opening of carbon nanotubes. On the other hand, for porous graphene-based nanotubes, relative variations of bandgap open- ings predicted by DFTB approximation still in accordance with B3LYP and PBE, but absolute values are closer to PBE results. 4. Conclusions We investigate the geometrical configuration and electronic structure of two new classes of nanotube architectures. The nan- otubes were built using two different repeating units, the first based on porous graphene and the second based on graphenylene structure. Band gaps vary depending on tube diameters. Porous based tubes present higher band gaps than that found for PG nanosheets, while graphenylene-based tubes present gap values smaller than their two dimensional counterpart. Variation on the diameter of these tubes revealed a variation tendency on gap val- ues of both nanotube types towards their respective planar sheets band gaps. Porous based nanotubes present a decrease in gap val- ues and graphenylene type present increase of band gap values for increasing diameters. The influence of axial strain on the band gap opening was also investigated. Our results indicate that PG-based PNTs can have their band gap decreased by � 10% in some cases. For graphenylene-based PNTs we found that strain application can induce a substantial increase on the band gap opening, that can reach up to 100% in some cases. Having these adjustable phys- ical properties make these systems good candidates for the con- struction of nano-sensors or nano-devices. 354 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 Acknowledgments Nanotube models where produced using Greenwood: A library for creating molecular models and processing molecular dynamics simulations [59]. Funding This work was supported in part by the Brazilian Agencies CNPq, CAPES, FAPESP. Ricardo Paupitz thanks the financial support of Fapesp (Grant 2014/15521-9) and CNPq (Grant 308298/2014-4). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commatsci.2017. 09.009. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (5696) (2004) 666–669. [2] A.H. CastroNeto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (1) (2009) 109–162. [3] Z. Wang, C.P. Puls, N.E. Staley, Y. Zhang, A. Todd, J. Xu, C.A. Howsare, M.J. Hollander, J.A. Robinson, Y. Liu, Technology ready use of single layer graphene as a transparent electrode for hybrid photovoltaic devices, Phys. E: Low- dimensional Syst. Nanostruct. 44 (2) (2011) 521–524, http://dx.doi.org/ 10.1016/j.physe.2011.10.003. . [4] K.E. Whitener, Reversible graphene functionalization for electronic applications: a review, in: American Chemical Society, 2014, pp. 41–54, http://dx.doi.org/10.1021/bk-2014-1183.ch003 (Chapter4) . [5] J.L. Achtyl, R.R. Unocic, L. Xu, Y. Cai, M. Raju, W. Zhang, R.L. Sacci, I.V. Vlassiouk, P.F. Fulvio, P. Ganesh, et al., Aqueous proton transfer across single-layer graphene, Nat. Commun. 6 (2015). [6] J.T. Robinson, M.K. Zalalutdinov, C.E. Junkermeier, J.C. Culbertson, T.L. Reinecke, R. Stine, P.E. Sheehan, B.H. Houston, E.S. Snow, Structural transformations in chemically modified graphene, Solid State Commun. 152 (21) (2012) 1990– 1998, http://dx.doi.org/10.1016/j.ssc.2012.04.051. . [7] M.K. Zalalutdinov, J.T. Robinson, C.E. Junkermeier, J.C. Culbertson, T.L. Reinecke, R. Stine, P.E. Sheehan, B.H. Houston, E.S. Snow, Engineering graphene mechanical systems, Nano Lett. 12 (8) (2012) 4212–4218, http://dx.doi.org/ 10.1021/nl3018059, . [8] J.T. Robinson, M.K. Zalalutdinov, C.D. Cress, J.C. Culbertson, A.L. Friedman, A. Merrill, B.J. Landi, Graphene strained by defects, ACS Nano 0 (0) (0) null, pMID: 28463478. http://dx.doi.org/10.1021/acsnano.7b00923. [9] S.C. Hernndez, C.J.C. Bennett, C.E. Junkermeier, S.D. Tsoi, F.J. Bezares, R. Stine, J. T. Robinson, E.H. Lock, D.R. Boris, B.D. Pate, J.D. Caldwell, T.L. Reinecke, P.E. Sheehan, S.G. Walton, Chemical gradients on graphene to drive droplet motion, ACS Nano 7 (6) (2013) 4746–4755, http://dx.doi.org/10.1021/nn304267b, pMID: 23659463. [10] V. Coluci, D. Galvao, A. Jorio, Geometric and electronic structure of carbon nanotube networks: ‘super’-carbon nanotubes, Nanotechnology 17 (3) (2006) 617–621. [11] V.R. Coluci, R.P.B. dos Santos, D.S. Galvao, Topologically closed macromolecules made of single walled carbon nanotubes-‘super’-fullerenes, J. Nanosci. Nanotechnol. 10 (7) (2010) 4378–4383. [12] F. Ouyang, S. Peng, Z. Liu, Z. Liu, Bandgap opening in graphene antidot lattices: the missing half, ACS Nano 5 (5) (2011) 4023–4030. [13] R. Paupitz, C.E. Junkermeier, A.C.T. van Duin, P.S. Branicio, Fullerenes generated from porous structures, PCCP 16 (46) (2014) 25515–25522, http://dx.doi.org/ 10.1039/c4cp03529a, ://WOS:000344989500039. [14] E. Perim, R. Paupitz, P.A.S. Autreto, D.S. Galvao, Inorganic graphenylene: a porous two-dimensional material with tunable band gap, J. Phys. Chem. C 118 (41) (2014) 23670–23674, http://dx.doi.org/10.1021/jp502119y, perim, E. Paupitz, R. Autreto, P.A.S. Galvao, D., ://WOS:000343333600027. [15] S. Stankovich, D.A. Dikin, R.D. Piner, K.A. Kohlhaas, A. Kleinhammes, Y. Jia, Y. Wu, S.T. Nguyen, R.S. Ruoff, Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide, Carbon 45 (7) (2007) 1558– 1565, http://dx.doi.org/10.1016/j.carbon.2007.02.034. . [16] S. Gilje, S. Han, M. Wang, K.L. Wang, R.B. Kaner, A chemical route to graphene for device applications, Nano Lett. 7 (11) (2007) 3394–3398. [17] R. Ruoff, Graphene: calling all chemists, Nat. Nanotechnol. 3 (1) (2008) 10–11. [18] J.O. Sofo, A.S. Chaudhari, G.D. Barber, Graphane: a two-dimensional hydrocarbon, Phys. Rev. B 75 (2007) 153401, http://dx.doi.org/10.1103/ PhysRevB.75.153401. . [19] S. Ryu, M.Y. Han, J. Maultzsch, T.F. Heinz, P. Kim, M.L. Steigerwald, L.E. Brus, Reversible basal plane hydrogenation of graphene, Nano Lett. 8 (12) (2008) 4597–4602. [20] D. Elias, R. Nair, T. Mohiuddin, S. Morozov, P. Blake, M. Halsall, A. Ferrari, D. Boukhvalov, M. Katsnelson, A. Geim, K. Novoselov, Control of graphene’s properties by reversible hydrogenation: evidence for graphane, Science 323 (5914) (2009) 610–613. [21] J.T. Robinson, J.S. Burgess, C.E. Junkermeier, S.C. Badescu, T.L. Reinecke, F.K. Perkins, M.K. Zalalutdniov, J.W. Baldwin, J.C. Culbertson, P.E. Sheehan, E.S. Snow, Properties of fluorinated graphene films, Nano Lett. 10 (8) (2010) 3001– 3005, http://dx.doi.org/10.1021/nl101437p, . [22] R.Paupitz, P.A.S. Autreto, S.B. Legoas, S.G. Srinivasan, T.van Duin, D.S. Galvao, Graphene to fluorographene and fluorographane: a theoretical study, Nanotechnology 24(3). http://dx.doi.org/10.1088/0957-4484/24/3/035706. [23] C.E. Junkermeier, S.C. Badescu, T.L. Reinecke, , Highly fluorinated graphene, 2014. [24] D. Solenov, C. Junkermeier, T.L. Reinecke, K.A. Velizhanin, Tunable adsorbate- adsorbate interactions on graphene, Phys. Rev. Lett. 111 (2013) 115502, http:// dx.doi.org/10.1103/PhysRevLett.111.115502. . [25] C.E. Junkermeier, D. Solenov, T.L. Reinecke, Adsorption of NH2 on graphene in the presence of defects and adsorbates, J. Phys. Chem. C 117 (0) (2013) 2793– 2798, http://dx.doi.org/10.1021/jp309419x, . [26] M. Bieri, M. Treier, J. Cai, K. Ait-Mansour, P. Ruffieux, O. Groning, P. Groning, M. Kastler, R. Rieger, X. Feng, K. Mullen, R. Fasel, Porous graphenes: two- dimensional polymer synthesis with atomic precision, Chem. Commun. (45) (2009) 6919–6921. [27] M.A. Hudspeth, B.W. Whitman, V. Barone, J.E. Peralta, Electronic properties of the biphenylene sheet and its one-dimensional derivatives, ACS Nano 4 (8) (2010) 4565–4570, http://dx.doi.org/10.1021/nn100758h, pMID: 20669980. [28] G. Brunetto, P.A.S. Autreto, L.D. Machado, B.I. Santos, R.P.B. dos Santos, D.S. Galvao, Nonzero gap two-dimensional carbon allotrope from porous graphene, J. Phys. Chem. C 116 (23) (2012) 12810–12813. [29] A.L. Enyashin, A.N. Ivanovskii, Graphene allotropes, Phys. Status Solid B-Basic Solid State Phys. 248 (8) (2011) 1879–1883. [30] E.H. Baughman, R.M. Kertesz, Structure-property predictions for new planar forms of carbon – layered phases containing sp2 and sp atoms, J. Chem. Phys. 87 (1987) 6687–6699. [31] Q.-S. Du, P.-D. Tang, H.-L. Huang, F.-L. Du, K. Huang, N.-Z. Xie, S.-Y. Long, Y.-M. Li, J.-S. Qiu, R.-B. Huang, A new type of two-dimensional carbon crystal prepared from 1,3,5-trihydroxybenzene, Sci. Rep. 7 (2017) 40796. [32] R. Totani, C. Grazioli, T. Zhang, I. Bidermane, J. Lüder, M. DeSimone, M. Coreno, B. Brena, L. Lozzi, C. Puglia, Electronic structure investigation of biphenylene films, J. Chem. Phys. 146 (5) (2017) 054705. [33] F. Schlütter, T. Nishiuchi, V. Enkelmann, K. Müllen, Octafunctionalized biphenylenes: molecular precursors for isomeric graphene nanostructures, Angew. Chem. Int. Ed. 53 (6) (2014) 1538–1542. [34] P.A. Denis, Stability and electronic properties of biphenylene based functionalized nanoribbons and sheets, J. Phys. Chem. C 118 (43) (2014) 24976–24982, http://dx.doi.org/10.1021/jp5069895. [35] P.A. Denis, F. Iribarne, Hydrogen storage in doped biphenylene based sheets, Comput. Theor. Chem. 1062 (2015) 30–35, http://dx.doi.org/10.1016/ j.comptc.2015.03.012. . [36] N. Chopra, R. Luyken, K. Cherre, V. Crespi, M. Cohen, S. Louie, A. Zettl, Boron- nitride nanotubes, Science 269 (5226) (1995) 966–967, http://dx.doi.org/ 10.1126/science.269.5226.966. [37] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (6348) (1991) 56–58. [38] A.T. Koch, A.H. Khoshaman, H.D.E. Fan, G.A. Sawatzky, A. Nojeh, Graphenylene nanotubes, J. Phys. Chem. Lett. 6 (19) (2015) 3982–3987, http://dx.doi.org/ 10.1021/acs.jpclett.5b01707, pMID: 26722903. [39] P. Koskinen, V. Mäkinen, Density-functional tight-binding for beginners, Comput. Mater. Sci. 47 (1) (2009) 237–253. [40] M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai, G. Seifert, Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties, Phys. Rev. B 58 (11) (1998) 7260–7268, http://dx.doi.org/10.1103/PhysRevB.58.7260. http://link. aps.org/doi/10.1103/PhysRevB.58.7260. [41] D. Porezag, T. Frauenheim, T. Köhler, G. Seifert, R. Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon, Phys. Rev. B 51 (19) (1995) 12947–12957, http://dx. doi.org/10.1103/PhysRevB.51.12947. [42] B. Aradi, B. Hourahine, T. Frauenheim, DFTB+, a sparse matrix-based implementation of the DFTB method, J. Phys. Chem. A 111 (26) (2007) 5678–5684. [43] H. Manzano, A.N. Enyashin, J.S. Dolado, A. Ayuela, J. Frenzel, G. Seifert, Do cement nanotubes exist?, Adv Mater. 24 (24) (2012) 3239–3245, http://dx.doi. org/10.1002/adma.201103704. http://dx.doi.org/10.1016/j.commatsci.2017.09.009 http://dx.doi.org/10.1016/j.commatsci.2017.09.009 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0005 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0005 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0005 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0010 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0010 http://dx.doi.org/10.1016/j.physe.2011.10.003 http://dx.doi.org/10.1016/j.physe.2011.10.003 http://www.sciencedirect.com/science/article/pii/S1386947711003651 http://www.sciencedirect.com/science/article/pii/S1386947711003651 http://dx.doi.org/10.1021/bk-2014-1183.ch003 http://pubs.acs.org/doi/pdf/10.1021/bk-2014-1183.ch003 http://pubs.acs.org/doi/pdf/10.1021/bk-2014-1183.ch003 http://pubs.acs.org/doi/abs/10.1021/bk-2014-1183.ch003 http://pubs.acs.org/doi/abs/10.1021/bk-2014-1183.ch003 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0025 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0025 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0025 http://dx.doi.org/10.1016/j.ssc.2012.04.051 http://www.sciencedirect.com/science/article/pii/S0038109812002578 http://www.sciencedirect.com/science/article/pii/S0038109812002578 http://dx.doi.org/10.1021/nl3018059 http://dx.doi.org/10.1021/nl3018059 http://pubs.acs.org/doi/pdf/10.1021/nl3018059 http://pubs.acs.org/doi/abs/10.1021/nl3018059 http://dx.doi.org/10.1021/acsnano.7b00923 http://dx.doi.org/10.1021/nn304267b http://refhub.elsevier.com/S0927-0256(17)30479-2/h0050 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0050 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0050 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0055 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0055 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0055 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0060 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0060 http://dx.doi.org/10.1039/c4cp03529a http://dx.doi.org/10.1039/c4cp03529a http://dx.doi.org/10.1021/jp502119y http://dx.doi.org/10.1016/j.carbon.2007.02.034 http://www.sciencedirect.com/science/article/pii/S0008622307000917 http://www.sciencedirect.com/science/article/pii/S0008622307000917 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0080 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0080 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0085 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0085 http://dx.doi.org/10.1103/PhysRevB.75.153401 http://dx.doi.org/10.1103/PhysRevB.75.153401 http://link.aps.org/doi/10.1103/PhysRevB.75.153401 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0095 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0095 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0095 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0100 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0100 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0100 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0100 http://dx.doi.org/10.1021/nl101437p http://pubs.acs.org/doi/pdf/10.1021/nl101437p http://pubs.acs.org/doi/pdf/10.1021/nl101437p http://pubs.acs.org/doi/abs/10.1021/nl101437p http://dx.doi.org/10.1088/0957-4484/24/3/035706 http://dx.doi.org/10.1103/PhysRevLett.111.115502 http://dx.doi.org/10.1103/PhysRevLett.111.115502 http://link.aps.org/doi/10.1103/PhysRevLett.111.115502 http://link.aps.org/doi/10.1103/PhysRevLett.111.115502 http://dx.doi.org/10.1021/jp309419x http://pubs.acs.org/doi/pdf/10.1021/jp309419x http://pubs.acs.org/doi/pdf/10.1021/jp309419x http://pubs.acs.org/doi/abs/10.1021/jp309419x http://refhub.elsevier.com/S0927-0256(17)30479-2/h0130 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0130 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0130 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0130 http://dx.doi.org/10.1021/nn100758h http://refhub.elsevier.com/S0927-0256(17)30479-2/h0140 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0140 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0140 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0145 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0145 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0150 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0150 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0150 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0155 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0155 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0155 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0160 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0160 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0160 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0165 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0165 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0165 http://dx.doi.org/10.1021/jp5069895 http://dx.doi.org/10.1016/j.comptc.2015.03.012 http://dx.doi.org/10.1016/j.comptc.2015.03.012 http://www.sciencedirect.com/science/article/pii/S2210271X15001188 http://www.sciencedirect.com/science/article/pii/S2210271X15001188 http://dx.doi.org/10.1126/science.269.5226.966 http://dx.doi.org/10.1126/science.269.5226.966 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0185 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0185 http://dx.doi.org/10.1021/acs.jpclett.5b01707 http://dx.doi.org/10.1021/acs.jpclett.5b01707 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0195 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0195 http://dx.doi.org/10.1103/PhysRevB.58.7260 http://link.aps.org/doi/10.1103/PhysRevB.58.7260 http://link.aps.org/doi/10.1103/PhysRevB.58.7260 http://dx.doi.org/10.1103/PhysRevB.51.12947 http://dx.doi.org/10.1103/PhysRevB.51.12947 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0210 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0210 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0210 http://dx.doi.org/10.1002/adma.201103704 http://dx.doi.org/10.1002/adma.201103704 G.S.L. Fabris et al. / Computational Materials Science 140 (2017) 344–355 355 [44] T. Kubar, Z. Bodrog, M. Gaus, C. Kohler, B. Aradi, T. Frauenheim, M. Elstner, Parametrization of the SCC-DFTB method for halogens, J. Chem. Theory Comput. 9 (7) (2013) 2939–2949, http://dx.doi.org/10.1021/ct4001922. [45] E. Rauls, J. Elsner, R. Gutierrez, T. Frauenheim, Stoichiometric and non- stoichiometric (1010) and (1120) surfaces in 2HSiC: a theoretical study, Solid State Commun. 111 (8) (1999) 459–464, http://dx.doi.org/10.1016/S0038- 1098(99)00137-4. . [46] C. Kohler, T. Frauenheim, Molecular dynamics simulations of {CFx} (x = 2, 3) molecules at Si3N4 and SiO2 surfaces, Surf. Sci. 600 (2) (2006) 453–460, http:// dx.doi.org/10.1016/j.susc.2005.10.044. . [47] H.J. Monkhorst, J.D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188–5192, http://dx.doi.org/10.1103/PhysRevB.13.5188. . [48] J.-C. Charlier, X. Blase, S. Roche, Electronic and transport properties of nanotubes, Rev. Modern Phys. 79 (2) (2007) 677–732, http://dx.doi.org/ 10.1103/RevModPhys.79.677. [49] M. Dresselhaus, G. Dresselhaus, R. Saito, Physics of carbon nanotubes, Carbon 33 (7) (1995) 883–891, http://dx.doi.org/10.1016/0008-6223(95)00017-8. [50] W. Humphrey, A. Dalke, K. Schulten, VMD – visual molecular dynamics, J. Mol. Graph. 14 (1996) 33–38. [51] H.R. Gutirrez, N. Perea-Lpez, A.L. Elas, A. Berkdemir, B. Wang, R. Lv, F. Lpez- Uras, V.H. Crespi, H. Terrones, M. Terrones, Extraordinary room-temperature photoluminescence in triangular WS2 monolayers, Nano Lett. 13 (8) (2013) 3447–3454, http://dx.doi.org/10.1021/nl3026357, pMID: 23194096. [52] S.H. Simon, The Oxford Solid State Basics, first ed., Oxford University Press, Great Clarendon Street, Oxford, Ox2 6DP, 2013. [53] K.-M. Lin, Y.-H. Huang, W. Su, T. Leung, Strain effects on the band gap and work function of zigzag single-walled carbon nanotubes and graphene: a comparative study, Comput. Phys. Commun. 185 (5) (2014) 1422–1428, http://dx.doi.org/10.1016/j.cpc.2014.02.009. . [54] J.W. Ding, X.H. Yan, J.X. Cao, D.L. Wang, Y. Tang, Q.B. Yang, Curvature and strain effects on electronic properties of single-wall carbon nanotubes, J. Phys.: Condens. Matter 15 (27) (2003) L439. . [55] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868, http://dx.doi.org/10.1103/ PhysRevLett.77.3865. . [56] A.D. Becke, Density functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (7) (1993) 5648–5652, http://dx.doi.org/ 10.1063/1.464913. [57] P. Stephens, F. Devlin, C. Chabalowski, M.J. Frisch, Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, J. Phys. Chem. 98 (45) (1994) 11623–11627. [58] Y. Matsuda, J. Tahir-Kheli, W.A. Goddard III, Definitive band gaps for single- wall carbon nanotubes, J. Phys. Chem. Lett. 1 (19) (2010) 2946–2950. [59] C.E. Junkermeier, Greenwood: A Library for Creating Molecular Models and Processing Molecular Dynamics Simulations. . http://dx.doi.org/10.1021/ct4001922 http://dx.doi.org/10.1016/S0038-1098(99)00137-4 http://dx.doi.org/10.1016/S0038-1098(99)00137-4 http://www.sciencedirect.com/science/article/pii/S0038109899001374 http://www.sciencedirect.com/science/article/pii/S0038109899001374 http://dx.doi.org/10.1016/j.susc.2005.10.044 http://dx.doi.org/10.1016/j.susc.2005.10.044 http://www.sciencedirect.com/science/article/pii/S0039602805012379 http://www.sciencedirect.com/science/article/pii/S0039602805012379 http://dx.doi.org/10.1103/PhysRevB.13.5188 http://link.aps.org/doi/10.1103/PhysRevB.13.5188 http://dx.doi.org/10.1103/RevModPhys.79.677 http://dx.doi.org/10.1103/RevModPhys.79.677 http://dx.doi.org/10.1016/0008-6223(95)00017-8 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0250 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0250 http://dx.doi.org/10.1021/nl3026357 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0260 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0260 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0260 http://dx.doi.org/10.1016/j.cpc.2014.02.009 http://www.sciencedirect.com/science/article/pii/S0010465514000411 http://www.sciencedirect.com/science/article/pii/S0010465514000411 http://stacks.iop.org/0953-8984/15/i=27/a=101 http://stacks.iop.org/0953-8984/15/i=27/a=101 http://dx.doi.org/10.1103/PhysRevLett.77.3865 http://dx.doi.org/10.1103/PhysRevLett.77.3865 https://link.aps.org/doi/10.1103/PhysRevLett.77.3865 https://link.aps.org/doi/10.1103/PhysRevLett.77.3865 http://dx.doi.org/10.1063/1.464913 http://dx.doi.org/10.1063/1.464913 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0285 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0285 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0285 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0290 http://refhub.elsevier.com/S0927-0256(17)30479-2/h0290 https://github.com/cjunkermeier/greenwood https://github.com/cjunkermeier/greenwood Porous graphene and graphenylene nanotubes: Electronic structure and strain effects 1 Introduction 2 Methods 3 Results and discussion 3.1 From membranes to tubes 3.2 Structural properties 3.3 Electronic structure 4 Conclusions Acknowledgments ack10 Funding Appendix A Supplementary material References