Structural and Thermal Stability of Graphyne and Graphdiyne

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Structural and Thermal Stability of Graphyne and Graphdiyne Nanoscroll Structures Daniel A. Solis,†,‡ Daiane D. Borges,† Cristiano F. Woellner,† and Douglas S. Galvão*,† †

Applied Physics Department and Center for Computational Engineering & Sciences, University of Campinas-UNICAMP, Campinas, SP 13083-959, Brazil ‡ Grenoble INP, Université Grenoble Alpes, CEA, CNRS, INAC-SPINTEC, F-38000 Grenoble, France

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S Supporting Information *

ABSTRACT: Graphynes and graphdiynes are generic names for families of twodimensional carbon allotropes, where acetylenic groups connect benzenoid-like hexagonal rings, with the coexistence of sp and sp2 hybridized carbon atoms. The main differences between graphynes and graphdiynes are the number of acetylenic groups (one and two for graphynes and graphdiynes, respectively). Similarly to graphene nanoscrolls, graphyne and graphdiynes nanoscrolls are nanosized membranes rolled into papyrus-like structures. In this work we studied through molecular dynamics simulations, using reactive potentials, the structural and thermal (up to 1000 K) stability of α,β,γ-graphyne and α,β,γ-graphdiyne scrolls. Our results demonstrate that stable nanoscrolls can be created for all the structures studied here, although they are less stable than corresponding graphene scrolls. This can be elucidated as a result of the higher graphyne/graphdiyne structural porosity in relation to graphene, and as a consequence, the π−π stacking interactions decrease. KEYWORDS: carbon, nanoscrolls, graphyne, graphdiyne, molecular dynamics simulations

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INTRODUCTION Graphene synthesis has created a genuine material science revolution, and as consequence several other two-dimensional (2D) materials have been studied, such as the carbon allotropes graphynes and graphdiynes.1−5 These materials were predicted for the first time in 1987.1 Graphynes and graphdiynes are generic names for families of 2D carbon allotropes, where acetylenic groups connect benzenoid-like hexagonal rings (see figures below), with the coexistence of sp and sp2 hybridized carbon atoms. Graphynes and graphdiynes have different numbers of acetylenic groups (one and two for graphynes and graphdiynes, respectively). In principle, it is possible to create an almost infinite number of related structures, just increasing the number of acetylenic groups.1−5 So far, most of the reported investigations have been focused on graphynes and graphdiynes.6,7 Recent important advances have been possible due to the novel synthesis methodologies, which include metalcatalyzed cross-coupling reactions,8−10 template synthesis,11 alkyne metasynthesis,12 and explosion approach.13,14 Nanoscroll structures can be produced by rolling nanosheets into a papyrus-like topology15 (Figure 1). In principle, any layered structure can be rolled up into scrolled ones, provided the necessary conditions for an energy-assisted process and structural stability. In fact, many scrolls of different materials have already been obtained, such as graphene,16,17 V2O5,18 alkyne metathesis,19 and 2D-hBN.20 The scrolling process is a competition between elastic bending and van der Waals (vdW) interactions. As the planar configurations are very stable, to curl it is necessary to provide © XXXX American Chemical Society

external energy to induce the bending. The scroll formation can be a favorable process after a critical overlapping area is reached, depending on the surface area and the initial shape of the nanosheet21 (for a better visualization of the process, see Video 1 in the Supporting Information, which contains four videos and a pdf file with three figures described in the manuscript). The nanoscrolls are structures morphologically similar to multiwalled nanotubes but with open ends.22 Different techniques can be used to produce nanoscrolls. For example, graphite can be mixed with potassium oxide, separated with ethanol, and then sonicated,16 which results in good-quality carbon nanoscrolls. Another method involves the use of graphene sheets within a solution of isopropyl alcohol, which spontaneously scroll.22 Recently, other experimental methods are being tried to produce scrolls of high quality and in large quantities.22 The scrolled arrangement can be more stable than the planar configuration, as the increased vdW interactions due to the scrolled process can be larger than the cost of the bending elastic energy to scroll it. The scroll topology for having ends open can be exploited in many applications, such as electroactuators (structures with mechanical charge-dependent response), electronic or photoelectronic devices, as gas storage,21 etc. As graphyne Special Issue: Graphdiyne Materials: Preparation, Structure, and Function Received: March 1, 2018 Accepted: June 7, 2018

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DOI: 10.1021/acsami.8b03481 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Figure 1. (a) Planar configuration of a sheet of width W and length L; (b) formed nanoscroll of length L formed from rolled up planar configuration displayed in (a); (c) top (cross-section view) of the nanoscroll displaying its inner radius, which is defined as the distance between the nanoscroll main axis and the closest line of atoms. For all structures the dangling bonds were not passivated.

and graphdiyne sheets have been already experimentally realized19 their scrolled configurations are feasible to obtain with our present-day technologies. In this work we investigated the structural and thermal (up to 1000 K) stability of graphyne and graphdiyne nanoscrolls through molecular dynamics (MD) simulations. We considered α, β, and γ-type topologies (see Figures 2 and 5).

were generated, the sheets were rolled up using the Sculptor plugin implemented in the VMD software.25 Because of the finite size of the sheets, to achieve a realistic and appropriate spiral shape, static calculations were initially performed to obtain the energy profiles as a function of the number of turns and sheet dimensions (these calculations were performed at room temperature, T = 300 K). For the dynamical analyses of the graphyne and graphdiyne nanoscrolls, we considered the parent planar structures sheets with width W ≈ 200 Å and length L ≈ 100 Å and two turns; this is θ = 4π. These sheet dimensions are large enough to allow many scrolled turns. A systematic study of the stability of nanoscrolls was performed using a Nosé−Hoover thermostat and a canonical ensemble (NVT).26,27 For different temperatures in a range from 100 to 1000 K, the systems were thermalized until achieving equilibrium using a time step of 0.2 fs. As we would like to determine whether chemical reactions between layers could occur and these events have a fast dynamics, we chose a small time step to avoid any spurious effect. Because of the chosen initial number of turns and radius, all the nanoscrolls were out of equilibrium. During the thermalization, these initial parameters changed. To properly quantify these variations, we used the internal nanoscroll radius values, which are defined as the distance between the line that passes through its center of mass (main axis) and the innermost line of atoms in the scroll (see Figure 1c). It is important to point out that these values are obtained for each atom in the innermost line and averaged to take into account the thermal fluctuations.

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METHODOLOGY Graphyne and graphdiyne nanoscrolls were investigated through MD simulations using the open-source software named largescale parallel molecular dynamics simulation code (LAMMPS).23 The atomistic pair interactions were described by the reactive force field ReaxFF.24 First, atomic coordinates of the planar sheets of graphyne (α, β, and γ-types) and graphdiyne (α, β, and γ-types) were built using the corresponding unit-cell parameters. Subsequently, the sheets of width W and length L were rolled into an Archimedean spiral shape (Figure 1b). The set of points that follows an Archimedean spiral are described by the following equation in polar coordinates: r = a + bθ

(1)

where a is the starting point of the spiral or internal radius, b is related to the separation among subsequent turns; that is, 2πb ≈ 3.4 Å is the interlayer distance, and θ is the number of turns. Notice that, since the sheet is finite, the value of a must vary according to the number of turns. The suitable values of a were obtained through numerical calculations solving the arc length equation of the Archimedean spiral. A series of scrolls was generated with θ varying from 0 to 8π. After the scroll coordinates B


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Figure 2. Schematics of the obtained α-, β-, and γ-graphyne nanoscrolls (left) from their corresponding planar configurations (right). The highlighted regions (left and right) indicate the structural topological motifs.

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RESULTS AND DISCUSSION Graphyne. Our MD results indicate that existence of stable scroll configurations for all different types and within the temperature range investigated here (up to 1000K). We did not observe broken bonds and/or the formation of new covalent bonds, even at high temperatures. Moreover, the scroll maintains its structure with inner radius values fluctuating around a constant value, as we can observe in the time evolution of inner radius displayed in Figure 3. The α-graphyne inner radius values fluctuates around ∼5−6 Å at temperatures below 500 K (see Figure 3a). At high temperatures (>700 K), these values increase to ∼10−11 Å. This effect of temperature is explained observing that the interlayer interaction energy that maintains the scroll cohesion/integrity is surpassed by the atomic kinetic energy, making the scroll “breathe”. The temperature has not the same effect in β- or γ-graphynes, where its inner radius is kept at ∼10−11 Å, independently of temperature. This radius is comparable to ∼10 Å of graphene nanoscroll.15 For β-graphyne in Figure 3b for the case of 100 K the stability radius value is ∼8.5 Å and displays the smallest radius value among the different temperatures considered here. The same is similarly observed for α-graphyne. But differently to what occurs for α-graphyne, β-graphyne is less sensitive to temperature changes, showing already at 300 K a radius comparable to ∼10 Å, the same value as at 500, 700, and 1000 K. In Figure 3c we can observe that the radius values present large amplitude oscillations, which disappears when the nanoscroll achieves its equilibrium configuration. The equilibrium radius

values for all temperatures considered are very close and reflect the higher invariance with respect to temperature of the γ-graphyne in comparison to the other graphyne structures. This suggests that γ-graphyne is the most thermally stable configuration (see Video 2 in the Supporting Information). To understand how the graphyne sheets change in terms of energy when they are rolled up, it is necessary to determine the balance between the energetic cost to bend the sheet, that is, the torsion energy and the energetic gain due the cohesion forces, that is, vdW interactions, whose variations are the more pronounced. In Figure 4 we present the torsion energies (a) and the vdW energies (b) for each graphyne structure during its scrolling processes. Notice that the torsion energy increases while the scroll is being rolling up. The torsion energy cost is more relevant for the β-graphyne and less important for γ-graphyne, while α-graphyne represents an intermediate case. The vdW energy is zero until it reaches the value 2π. For rounds infinitesimally larger than this value we start to have a sheet overlap and, consequently, a nonzero vdW interaction among the atoms of the overlapped surface can be observed (see Figure 4b for radius > 2π). The energetic gain from vdW interactions is proportional to the overlap area, which means that increasing the scrolling implies increasing the vdW interaction energy gain. In Figure 4c we present the sum of torsion and VDW peratom energies. Starting the bending, but before the layer overlap occurs, the total energy of all the structures is increasing (because of the bending), clearly dominated by the torsion C


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can be even more stable than the planar configuration. However, we stress that, to achieve the scrolled configuration, this process needs to be energy-assisted. Each graphyne type possesses a different energy minimum, and the most stable structure is the γ-graphyne. Even if β-graphyne is less porous (more vdW) than the α-graphyne, it is the least-stable structure among the graphynes studied here. We stress that the thermal stability ordering is not the same of structural stability one, since they have origin in different aspects of the scrolls. Graphdiynes. MD simulations were also performed for three type of graphdiynes, considering the same structural parameters as for the graphynes; that is, W ≈ 200 Å, L ≈ 100 Å, and initial configuration being rolled up to 4π turns. The structures of the graphdiynes and their corresponding nanoscrolls are shown in Figure 5. The MD simulations have shown that these nanoscrolls also reached thermal stability for the temperature considered here (100 to 1000 K). The total simulation time was between 400 and 600 ps. As mentioned above graphdiynes present twice as many acetylenic groups as graphynes. Consequently, graphdiynes present higher porosity than graphyne structures. More porosity results in lower π−π stacking interactions, which results in a smaller number of turns when compared to graphynes (see Video 3 in the Supporting Information). The graphdiyne scroll dynamics is similar to the graphynes ones, but the structural and thermal stability ordering are not the same. α-Graphdiyne is the allotrope that exhibits the most evident elliptical-shaped structure, as shown in the snapshots of Figure 6a, as well as the graphdiyne structure with the largest radius value (a summary of the density and average radius values for graphyne and graphdiyne scrolls is presented in Table 1). By density we mean the total number of carbon atoms in the unit cell divided by its area. As in the case of α-graphdiyne, β-graphdiyne (Figure 6b) nanoscroll also presents a cylindrical shape with an elliptic base. α-Graphdiyne and β-graphdiyne are the most porous structures in this study with atomic densities of 0.153 and 0.179 atoms·Å−2, respectively. Because of this, even at low temperatures, they form scrolls with a small number of turns (∼4π), and as a consequence these nanoscrolls have large radius values. Their larger deformation capability is directly related to the structural arrangements of their atoms, a feature that can be understood looking at the low torsion energies for these structures. In fact, their torsion energies are very close, and the differences in the nanoscroll rolling comes mainly from the vdW interactions. The general trends are quite similar to the ones presented in Figure 4. In Figure 6c we present the radius values variation and snapshots of the final configuration of γ-graphdiyne for different temperatures. Taking into account the γ-graphdiyne density and base shape low eccentricity, we can conclude that this structure is the least flexible and most stable allotrope among the graphdiynes. It possesses an average radius of ∼11 Å for all the temperatures considered here. This radius value is very similar to those found in the literature for graphene13 and in the graphynes structures studied earlier. In Figure 7 we present the equivalent of Figure 4 for the graphdiyne structures. We present the torsion energies (a) and the vdW energies (b), for each graphdiyne structure during its scrolling processes, as well as their total energy (c). The torsion energies have very similar values and nonlinear behavior. The vdW energy contribution is larger for γ-graphdiyne than for β-graphdiyne and α-graphdiyne, which has the smallest vdW energy contribution. This is expected because the vdW

Figure 3. (left) Inner radius (r) values vs the MD simulation time (in ps) for (a) α-graphyne; (b) β-graphyne; (c) γ-graphyne. (right) MD snapshots of the obtained final configuration for temperatures 100, 300, 500, 700, and 1000 K, respectively. The red marks indicate the inner and outer edge of the corresponding nanoscroll.

Figure 4. (a) Torsion energy; (b) van der Waals energy; and (c) total energy for the static case for α-graphyne, β-graphyne, and γ-graphyne.

energy. When the graphyne is highly rolled, the vdW gains surpass the bending elastic cost, and the scrolled configuration D


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Figure 5. Schematics of the obtained α-, β-, and γ-graphdiyne nanoscrolls (left) from their corresponding planar configurations (right). The highlighted regions (left and right) indicate the structural topological motifs.

that graphyne and graphdiyne scrolls also present the same features. From Table 1 we can conclude that, once the scrolls are provided with enough thermal energy to go beyond the radial expansion barrier values (see, e.g., the results for 1000 K), the inner radius values are more or less type- and chiralityindependent. However, for low temperatures the radial expansion has different energy barriers, which are type- and chirality-dependent. For instance, in the case of α-graphyne, which has a large barrier, the significant changes in inner radius values only happens at 600 K, while for β-graphyne it occurs at just 300 K.

energy depends on the density of the structures (see Table 1). As we can see from Figure 7, the general trends are the same as discussed for the graphyne structures. As all graphynes and graphdiyne are porous and can easily have out-of-plane distortions, the linear regime for the torsion angles is not expected. In fact, just one of the six structures (see Figures 4a and 7a) exhibits a linear regime. One important issue regarding formation and stability of the scrolls is the role played by defects (such as vacancies). The detailed analysis of this issue is beyond the subject of the present work, but it was already shown28 that vacancies can facilitate carbon nanoscroll (CNS) formation by decreasing the energy barriers during the nanoscroll formation. This energy barrier is the result of competing interactions between the vdW forces, which favor the layer overlap and the torsional or bending forces, which oppose the scrolling process. These conclusions were based on static analysis (similarly to what is shown in Figures 4 and 7). However, when dynamical aspects are taken into account, these defects/vacancies can create more reactive sites, which increases (proportional to temperature values) the probability of forming covalent bonds across different layers compromising the scroll structural stability and/or formation. Thus, the type and number of defects will determine which aspect (facilitating or compromising) will be dominant for each scroll structure. With relation to conformational chirality, it was shown for graphene scrolls that they are metastable states.15 Our results show (see Figure S1 and Video 4 in the Supporting Information)

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CONCLUSIONS Graphynes and graphdiynes are generic names for families of 2D carbon allotropes, where acetylenic groups connect benzenoid-like hexagonal rings. In this work we studied through molecular dynamics simulations, using reactive potentials (ReaxFF force field), the structural and thermal (up to 1000 K) stability of α, β, and γ graphyne and graphdiyne scrolls. These structures are graphynes and graphdiyne membranes rolled up into papyrus-like structures. Our results show that stable (we did not observe broken bonds and/or the formation of new covalent bonds, even at high temperatures) nanoscrolls can be formed for all the structures investigated here, although they are less stable than corresponding graphene scrolls (see Table 1 and Figure S2). This can be elucidated as a result of the higher graphyne/ graphdiyne structural porosity in relation to graphene, and as a E


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Figure 7. (a) Torsion energy; (b) vdW energy; (c) total energy for the static case for α-graphdiynes, β-graphdiynes, and γ-graphdiynes.

(see Figure S3 in the Supporting Information) an almost complete recovery (only a very small hysteresis was observed). We hope the present work can stimulate further works along these lines.

Figure 6. (left) Inner radius (r) values as a function of the simulation time for (a) α-graphdiyne; (b) β-graphdiyne; (c) γ-graphdiyne. (right) MD snapshots of the obtained final configuration for temperatures 100, 200, 500, and 700 K, respectively. The red marks indicate the inner and outer edge of the corresponding nanoscroll.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.8b03481. Energy variation as a function of the simulation time, thermal dependence of graphene nanoscroll inner radius (PDF) MD simulation (MOV) MD simulation (MOV) MD simulation (MOV) MD simulation (MOV)

consequence, the π−π stacking interactions diminish. Interestingly, the structural and thermal stability ordering for these structures are not the same. Also, under heat excitation they undergo significant radial expansion, for instance, the α-graphyne radius value can vary from 5.77 to 11.33 Å, which could be exploited in a large variety of applications, such as thermal actuators, sensors, etc. Considering that graphynes and graphdiyne membranes have been already experimentally realized, their scroll fabrication is feasible with our present-day technology. As mentioned above, the significant scroll radial expansion can be the basis for a large variety of applications, but one critical issue is the scroll thermal reversibility, that is, if decreasing the temperature the scroll would go back to its original configuration. To test this, we performed some MD runs (from 1000 up to 100 K), and indeed we observed

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AUTHOR INFORMATION

Corresponding Author

*E-mail: galvao@ifi.unicamp.br. ORCID

Douglas S. Galvão: 0000-0003-0145-8358

Table 1. Density and Inner Radius at Temperatures of 100, 200, 300, 500, 600, 700, and 1000 K for α-, β-, and γ-Graphynes, α-, β-, and γ-Graphdiynes, and Graphene radius (Å) structure

density atoms·Å−2

100 K

200 K

300 K

500 K

600 K

700 K

1000 K

α-graphyne β-graphyne γ-graphyne α-graphdiyne β-graphdiyne γ-graphdiyne graphene

0.238 0.259 0.335 0.153 0.179 0.253 0.393

5.77 8.82 10.57 12.52 11.25 10.86 10.15

5.68 8.51 10.68 12.32 11.35 10.72 10.11

5.62 10.33 10.08 11.44 10.88 10.86 9.94

5.32 10.32 9.94 12.11 11.07 10.76 9.95

9.73 10.47 10.37 11.97 10.93 10.80 10.04

9.57 10.09 9.92 11.16 10.54 10.99 9.88

11.33 10.14 10.78 10.44 10.88 10.81 10.01

F


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ACS Applied Materials & Interfaces Author Contributions

(17) Stankovich, S.; Dikin, D. A.; Dommett, G. H. B.; Kohlhaas, K. M.; Zimney, E. J.; Stach, E. A.; Piner, R. D.; Nguyen, S. T.; Ruoff, R. S. Graphene-Based Composite Materials. Nature 2006, 442 (7100), 282−286. (18) Petkov, V.; Zavalij, P. Y.; Lutta, S.; Whittingham, M. S.; Parvanov, V.; Shastri, S. Structure beyond Bragg: Study of V2O5 Nanotubes. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69 (8), 85410. (19) Wu, B.; Li, M.; Xiao, S.; Qu, Y.; Qiu, X.; Liu, T.; Tian, F.; Li, H.; Xiao, S. A graphyne-like porous carbon-rich network synthesized via alkyne metathesis. Nanoscale 2017, 9, 11939. (20) Perim, E.; Galvao, D. S. The Structure and Dynamics of Boron Nitride Nanoscrolls. Nanotechnology 2009, 20 (33), 335702. (21) Coluci, V. R.; Braga, S. F.; Baughman, R. H.; Galvao, D. S. Prediction of the Hydrogen Storage Capacity of Carbon Nanoscrolls. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75 (12), 125404. (22) Perim, E.; Machado, L. D.; Galvao, D. S. A Brief Review on Syntheses, Structures, and Applications of Nanoscrolls. Front. Mater. 2014, 1, 31. (23) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (24) van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396−9409. (25) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14 (1), 33−38 27−28. (26) Nosé, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. J. Chem. Phys. 1984, 81 (1), 511−519. (27) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31 (3), 1695− 1697. (28) Wallace, J.; Shao, L. Defect-induced Carbon Nanoscroll Formation. Carbon 2015, 91, 96−102.

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the Brazilian Agencies CAPES, CNPq, and FAPESP. The authors also thank the Center for Computational Engineering and Sciences at Unicamp for financial support through the FAPESP/CEPID Grant No. 2013/08293-7. D.D.B. and C.F.W. thank FAPESP Grant Nos. 2015/14703-9 and 2014/24547-1, respectively, for financial support.

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Structural and Thermal Stability of Graphyne and Graphdiyne

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