Structural, Electronic, and Mechanical Properties of Single-Walled

Article pubs.acs.org/JPCC

Structural, Electronic, and Mechanical Properties of Single-Walled Chrysotile Nanotube Models Maicon P. Lourenço,† Claudio de Oliveira,† Augusto F. Oliveira,‡ Luciana Guimaraẽ s,§ and Hélio A. Duarte*,† †

Department of Chemistry, ICEx, Universidade Federal de Minas Gerais, 31.270-901 Belo Horizonte, MG, Brazil School of Engineering and Science, Jacobs University Bremen, Campus Ring I, 28759 Bremen, Germany § Department of Natural Science, Universidade Federal de São João Del Rei, 36301-160, São João Del Rei, MG, Brazil ‡

S Supporting Information *

ABSTRACT: Structural, electronic, and mechanical properties of single-walled chrysotile nanotubes have been investigated using the self-consistent charge density-functional tight-binding method (SCC-DFTB). The naturally occurring chrysotile nanotubes (NTs) are composed of brucite, Mg(OH)2, layer in the outer side and tridymite, SiO2, in the inner side. The zigzag (17,0)−(45,0) and armchair (9,9)−(29,29) chrysotile nanotubes, which correspond to the radii ranging from 16 to 47 Å, have been calculated. The SCC-DFTB results are in good agreement with available experimental and previously published theoretical results. The chrysotile nanotubes are estimated to be insulator with band gap of 10 eV independently of their chirality and size, and the Young’s moduli are estimated to be in the range of 261−323 GPa. In addition, we have shown that the chirality of the NTs does not affect their stability, and the variant with brucite in the inner side and the tridymite in the outer side of the nanotube is indeed less stable with respect to the inverse case.

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INTRODUCTION The synthesis of inorganic nanotubes (NTs), such as WS2, BN, MoS2, and TiO2, opened possibilities of development of new advanced materials with enhanced properties.1−6 Therefore, much effort has been made to characterize these nanostructures and to modify them appropriately.1−4,6−16 However, the naturally occurring clay mineral NTs are not receiving much attention commensurate with their importance. For instance, imogolite,17 halloysite,18 and chrysotile19,20 are found in nature and can be synthesized in aqueous solution at mild conditions easily modified21−23 and functionalized.24 These minerals have been considered target materials to be used as components of hybrid materials, catalyst supports, ionic channels, molecular sieves, and gas storage.15,16,25−27 Chrysotile is possibly one of the most common nanostructured silicates which is easily found in nature. It is a nanosized and tube-shaped nonconducting material, which presents lower mechanical strength, and it is always uncapped. Stoichiometric chrysotile has been synthesized and characterized by structural and spectroscopic analysis.28,29 Yada30,31 reported spirals and multiwalled NTs of chrysotile with inner radii of 35−40 Å and outer radii of 110−135 Å. However, chrysotile structures with inner radii of 5−50 Å and outer radii of 50−250 Å can be found with lengths reaching up to the millimeter range.28 Chrysotile, together with lizardite and antigorite,25,26,30−35 is a natural fibrous phylosilicate of the serpentine group with 1:1 © 2012 American Chemical Society

structure and empirical formula Mg3Si2O5(OH)4. The chrysotile structure is composed of brucite (Mg(OH)2) and tridymite (SiO2) layers. The brucite octahedral sheet forms the outer side of the tube36 and tridymite SiO2 groups are anchored to the inner side of the tube as shown in Figure 1. Lizardite has the same formula but a lamellar structure. It can be seen as the opened chrysotile NT. Although chrysotile NTs and their structures were reported only in the 1950s,32−35 Linus Pauling,37 in 1930, speculated that some curved inorganic crystals could occur naturally. One of the inorganic crystals discussed by Pauling was chrysotile. Chrysotile has been targeted for synthesis and modifications of new materials with enhanced properties.24,38−42 The basic idea is to overcome the heterogeneity of the natural chrysotile strengthening the properties that can be useful for technological applications. Understanding the stability, electronic, and mechanical properties of chrysotile NTs is important for envisaging technological applications of such material. In the present work, the single-walled NTs have been investigated using the self-consistent charge density-functional tight-binding (SCC-DFTB) method.43−45Different chiralities have been investigated, and NTs up to 9 nm of diameter have been calculated. Lizardite has also been calculated aiming to Received: February 1, 2012 Revised: April 2, 2012 Published: April 5, 2012 9405

dx.doi.org/10.1021/jp301048p | J. Phys. Chem. C 2012, 116, 9405−9411

The Journal of Physical Chemistry C

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However, one could argue that lizardite could fold in the other direction forming NTs with tridymite in the outer side and brucite in the inner side (named Si:Mg chrysotile NTs). For this reason, we have calculated the Si:Mg chrysotile NTs with sizes (23,0)−(45,0) zigzag and (13,13)−(29,29) armchair NTs. The Si:Mg NTs are at least 30 meV/atom less stable than the respective Mg:Si NTs. Therefore, we focus our discussion on the Mg:Si chrysotile NTs. All chrysotile structures (Mg:Si and Si:Mg NTs) were fully optimized with respect to the atomic positions and the cell length without any symmetry constraint. Periodic boundary conditions were applied to the cell along the tube length. In this case, the first Brillouin zone was described by a 1 × 4 × 1 mesh of points in k space.54 All calculations have been performed using the DFTB+ program.55 X-ray powder diffraction (XRD) simulations were carried out using the Mercury program.56,57All diffractograms were calculated with the diffraction angle 2θ assuming values between 10 and 70 degrees. The X-ray wavelength λ used in this simulation was equal to 1.542 Å as for the copper filtered Cu Kα radiation. Electrostatic map was evaluated using the Visual Molecular Dynamics (VMD) software58 together with the Adaptive Poisson−Boltzmann Solver (APBS) package.59

Figure 1. Structure of (a) lizardite monolayer and (b) cross-sectional views of the zigzag (19,0) and (c) armchair (11,11) chrysotile nanotubes. Blue atoms, Mg; red, O; green, Si; black, H.

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RESULTS AND DISCUSSION Hereafter, for the sake of simplicity, chrysotile NTs refers to the naturally occurring Mg:Si chrysotile, shown at Figure 1, unless explicitly stated otherwise. Figures 1 and 2 show different views of the fully optimized zigzag (19,0) and armchair (11,11) chrysotile NTs. Information

provide information about the mechanism of formation of chrysotile. SCC-DFTB method has been applied to investigate imogolite46 and halloysite47 NTs with remarkable success. Recently, D’Arco et al.48explored the helical symmetry to perform B3LYP/6-31G* calculations of five single-walled chrysotile NTs, namely, (14,14), (17,17), (19,19), (22,22), and (24,24). This work has been used for benchmarking our SCC-DFTB method. The SCC-DFTB method is computationally less demanding and accurate enough to permit the investigation of larger chrysotile NTs and their derivatives.

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COMPUTATIONAL DETAILS Chrysotile NTs were calculated using the self-consistent charge density-functional tight-binding (SCC-DFTB) method.43−45 This method uses a minimum set of atomic basis functions and tight-binding-like approximations to the Hamiltonian.44,49,50 This method has been recently applied to investigate similar systems with remarkable success.46,47,51 Slater-Koster parameters for the Mg−X (X = Mg, Si, O, H) atomic pairs were developed following the protocol described elsewhere.45,46,52,53 The initial NT structures have been constructed by folding the 2D lizardite layer (Figure 1). The same convention for labeling the carbon, BN, and metal chalcogenides NTs was adopted for the chrysotile NTs. Depending on the rolling direction B in the 2D lattice B = na1 + ma2 (a1 and a2 are lattice vectors of the hexagonal lattice), three classes of NTs can be constructed: armchair (n,n), zigzag (n,0), and chiral (n,m) NTs; the latter has n ≠ m. The unit cell layer, with the chiral vectors a1 and a2 used to construct the NTs, is shown in Figure 1a. Experimental works have indicated that chrysotile has the brucite layer, Mg(OH)2, in the outer side and the tridymite, SiO2, in the inner side of the tube36(hereafter named Mg:Si chrysotile NT). In this work, the zigzag and armchair Mg:Si chrysotile NTs with sizes (17,0)−(45,0) and (9,9)−(29,29), which correspond to the radii ranging from 16 to 47 Å, were studied.

Figure 2. Optimized structures of the (a) zigzag (19,0) and (b) armchair (11,11) nanotubes. Blue atoms, Mg; red, O; green, Si; black, H.

about the type, number of atoms in the unit cell, radii (R), band gap (BG), and Young’s moduli (Y) of the fully optimized structures are shown in Table 1. The external radii of the zigzag and armchair NTs were calculated by the average distance between the center of the tube and the external hydrogen layer. For the zigzag NTs, in the range from (17,0) to (45,0), the external radii vary from 17.7 to 42.2 Å. For the (9,9) to (29,29) armchair NTs, the external radii range from 16.4 to 46.7 Å. 9406



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Table 1. Number of Atoms in the Unit Cell (N), Radii (R), Band Gaps (BG), and Young’s Moduli (Y) of the Zigzag (17,0)−(45,0) and Armchair (9,9)−(29,29) Chrysotile Nanotubes type

N

(17,0) (18,0) (19,0) (20,0) (21,0) (22,0) (23,0) (24,0) (25,0) (30,0) (35,0) (40,0) (45,0)

612 648 684 720 756 792 828 864 900 1080 1260 1440 1620

(9,9) (10,10) (11,11) (12,12) (13,13) (14,14) (15,15) (16,16) (17,17) (18,18) (19,19) (20,20) (21,21) (22,22) (23,23) (24,24) (25,25) (26,26) (27,27) (28,28) (29,29) layer

324 360 396 432 468 504 540 576 612 648 684 720 756 792 828 864 900 936 972 1008 1044 36

R (Å) Zigzag (n, 0) 17.68 18.57 19.45 20.34 21.21 22.10 22.97 23.86 24.73 29.15 33.45 37.82 42.22 Armchair (n, n) 16.38 17.89 19.44 20.97 22.49 24.01 25.56 27.06 28.60 30.11 31.65 33.12 34.64 36.16 37.68 39.15 40.65 42.20 43.71 45.21 46.71

BG (eV)

Y (GPa)

9.9 9.9 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

271 271 272 272 272 274 273 273 274 275 305 323 320

9.8 9.8 9.9 9.9 9.9 9.9 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.6

261 261 260 261 261 262 263 262 263 261 260 282 282 296 315 319 299 315 299 301 304

Figure 3. Strain energy per atom as a function of tube radius of the (17,0)−(45,0) zigzag (open circles) and the (9,9)−(29,29) armchair nanotubes (closed circles).

atom of the optimized NT and the energy per atom of the planar layer (lizardite). The strain energy of most of the inorganic and carbon NTs decreases with the squared radii (eq 1). Guimarães et al.46 have argued that this equation must be modified for the case of imogolite, which presents a minimum at 10 Å radius. A second term must be added to account for the difference between the inner and outer surface tensions since they have different crystalline structures (see eq 2). Therefore, the Estr (strain energy per atom) can be related to the elastic modulus Y, the thickness of the monolayer h, the tube radius R, and Δσ (the difference between the outer and inner surface tensions) Estr =

a Yh3 ≈ 2 2 R R

(1)

a b Yh3 Δσ + ≈ + 2 2 (2) R R R R It is important to highlight that eq 2 is also more adequate for fitting the strain energy of halloysite NTs.47 Although the range of the halloysite NT radii investigated was much smaller than the range of the radii found in nature, the authors argued that a very shallow minimum is expected for the halloysite. Following Guimarães et al.,46 the Estr shown in Figure 3 was fitted using eq 2 to give a = 26294.8 (meV Å2)/atom and b = 467.785 (meV Å)/atom. Conversely of what is observed for parent clay mineral NTs such as imogolite and imogolite-like structures, the strain energy curve for chrysotile follows the same tendency as other NTs such as carbon, WS2,1,4,60 BN,2,12 and MoS23,11,13NTs. The lamellar lizardite is the most stable structure and the limit for larger chrysotile NTs. In addition, it is important to highlight that there is no indication that the chirality of the NTs affects their stability. The strain energy of the zigzag and armchair NTs is nearly degenerated explaining the fact that chrysotile is normally found in nature as polydisperse multiwalled NTs.30−35 Contrarily, the strain energy of imogolite NTs favors the zigzag NTs compared to the armchair.46 The zigzag (12,0) imogolite NT is the most stable, and it is found as a monodisperse single-walled NT.46 The presence of chrysotile or lizardite is greatly related to the chemical conditions in which the mineral was formed. The strain energy for zigzag and armchair Si:Mg NTs has also been calculated, and the results are compared to the Mg:Si chrysotile NTs in Figure S1 of the Supporting Information. The Estr =

The optimized lattice parameters for the armchair (17,17) and (19,19) NTs are 5.432 and 5.450 Å, respectively. These values may be compared to the B3LYP/6-31G* optimized values of 5.330 and 5.335 Å for the armchair (17,17) and (19,19) NTs, respectively,48 obtained using helical symmetry. The SCC-DFTB lattice parameters are about 0.1 Å larger than those obtained by B3LYP/6-31G* calculations in reasonable agreement with the DFT calculations. The average Mg−O, Si− O, and Mg−Mg bond lengths are estimated to be about 2.12, 1.64, and 3.25 Å, respectively, for the optimized (11,11) NT (further details in the Supporting Information). The B3LYP/631G* calculations estimated the Mg−O, Si−O, and Mg−Mg bond lengths to be 2.09, 1.60, and 3.21 Å. This indicates that the SCC-DFTB results are in reasonable agreement with those obtained by B3LYP/6-31G* methodology using helical symmetry.48 The strain energy as a function of the radius of zigzag and armchair chrysotile NTs is shown in Figure 3. The strain energy (Estrain) is defined by the difference between the energy per 9407



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Figure 4. Experimental and simulated XRD of chrysotile nanotubes. The simulations were evaluated using the follow set of γ angles (in degrees): (a) γ = 60 and (b) γ = 90. The XRD curves are (1) experimental; (2) (21,21)@(26,26) double-walled nanotube; (3) (26,26) armchair nanotube; (4) (21,21) armchair nanotube; (5) (45,0) zigzag nanotube. (c) Definition of the lattice parameters a and c and the angle γ. The values of a and c were set to provide the distance between the external surface of the tubes equal to 3 Å. The experimental diffractogram was taken from the work of Anbalagan et al.20

observed for the different chrysotile NTs (21,21)@(26,26) (diffractogram 2), (26,26) (diffractogram 3), (21,21) (diffractogram 4), and (45,0) (diffractogram 5) regardless of the packing factor (γ = 60 or 90 degrees) used. The information about the arrangements of the atoms into the unit cell of chrysotile NTs is present in the 2θ region between 15 and 70 degrees. On the other hand, the region of lower angles (below 15) is not well described by XRD. The region of lower angles is responsible for the information of the unit cell packing and how the NTs are placed in one sample. However, we do not have much information about this in the simulation and even in the experimental diffractogram. Additional data of the simulated XRD, for different intertubular distances, can be seen in Figure S2 of the Supporting Information. Electronic Properties. The band gap (BG) for all NTs is estimated to be in the range of 9.8−10.0 eV indicating that they are insulators as expected. The B3LYP/6-31G* calculations estimate the band gap of chrysotile by 6.4 eV.48 It is well-known that the SCC-DFTB overestimates the BG. The BG evaluated by SCC-DFTB calculations is similar to that of imogolite46 and halloysite47 obtained by the same level of theory. The total (DOS) and partial density of states (PDOS) of the zigzag (40,0) and armchair (25,25) chrysotile NTs are similar indicating that the chirality and the size of the NT do not affect the electronic structure (Figure 5). In all valence bands ranging from −6 up to 0 eV as well as at the Fermi level, the predominant PDOS are those from O atoms. In the conduction region, the electronic states of Si atoms are responsible almost for the total DOS. The contribution of Mg and H atoms for the total DOS is smaller than that of Si and O in both valence and conduction bands. Furthermore, the DOS and PDOS of zigzag (40,0) and armchair (25,25) Si:Mg variant of chrysotile NTs were carried out and were compared with those of Mg:Si variant. The results are presented in Figure S3 of the Supporting Information. There is no significant change in the PDOS in the edge of the valence and conduction bands for both variants (Mg:Si or Si:Mg) of chrysotile. Figure 6 shows the electrostatic potential maps for the optimized zigzag (40,0) and armchair (25,25) chrysotile NTs. The NTs presented net positive charge on the outer part of the

Si:Mg NTs are at least 30 meV/atom less stable than the naturally occurring Mg:Si chrysotile NTs for the range of the NTs calculated in the present work. These results are in line with the experimental works showing that the external brucite is easily removed by mild acid leaching process to form nanofibriform silica.21,22 Structural Properties. The experimental and simulated Xray powder diffractions (XRD) of chrysotile NTs are shown in Figure 4. Falini et al.28succeeded to synthesize chrysotile single crystals prepared as a unique phase under controlled conditions. The Rietveld structure refinement led to a monoclinic crystal with the Cc space group and the following refined unit cell parameters: a = 5.340 Å, b = 9.241 Å, c = 14.689 Å, and β = 93.66 degrees. The simulations were performed for the fully optimized single-walled zigzag (45,0) NT and for the armchair (26,26) and (21,21) NTs. Furthermore, with the aim to evaluate possible effects of the multiwalled interactions on the XRD diffractogram, the XRD for the double-walled (21,21)@(26,26) NTs was simulated. XRD simulations were evaluated using different bundle configurations involving two values of the angle γ between the cell parameters a and c, Figure 4c. These angles correspond to hexagonal (γ = 60 degrees) and tetragonal (γ = 90 degrees) intertubular packings. It is well-known that the atoms in the hexagonal unit cell (γ = 60 degree) may have a better package factor.61 As a result, this package might contribute to a more realistic simulated XRD to be compared with that obtained experimentally.20 The intertubular distance (lattice parameter a = c) used to simulate the XRD of different NT sizes was 87.41 Å for the armchair (26,26) NT, 72.28 Å for the armchair (21,21) NT, and 87.44 Å for the zigzag (45,0). These values correspond to the distance between the external tube surfaces of about 3.0 Å. Figure 4 shows the results of the experimental20 and the simulated XRD for the (21,21)@(26,26), (26,26), (21,21), and (45,0) chrysotile NTs evaluated in the intertubular packings with γ = 60 and 90 degrees, Figure 4a and b, respectively. The main characteristic peaks of the chrysotile NTs20 were described by the XRD simulations. Furthermore, small differences in the shape of the simulated diffractograms were 9408



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over, the external positive charge may contribute to some chrysotile features such as its surface reactions with organic compounds25 as well as its immobilization properties.26 Mechanical Properties. Insights about the mechanical properties of chrysotile NTs are also of interest for technological applications such as in the synthesis of polymer nanocomposites.24 The Young’s moduli of the chrysotile NTs are experimentally accessible and provide information about the stiffness of the material. Following Hernandez et al.,62 the Young’s moduli of chrysotile NTs were calculated by a series of relaxations of the unit cell of the NTs in the direction of the tube axes and around the optimum cell parameter a. Then, it was possible to compute the energy as a function of the cell parameter along the tube axis. The following equation was used to calculate the Young’s moduli: Y=

Figure 5. Total and partial density of states (PDOS) of the (a) zigzag (40,0) and (b) armchair (25,25) chrysotile nanotubes. Color of lines: black, total DOS; orange, PDOS of H; blue, PDOS of Mg; green, PDOS of O; red, PDOS of Si. Gaussian broadening has been used to calculate the DOS and PDOS with a broadening width σ of 0.1 eV.

1 ⎛ ∂ 2E ⎞ ⎟ ⎜ V0 ⎝ ∂ε 2 ⎠ε= 0

(4)

where ε is the strain in the vicinities around the optimum lattice vector; E is the total energy; V0 is the equilibrium volume of the tube, which is evaluated by the cylinder equation V0 = πC0(R2ext − R2int); C0 is the cell length; Rext is the outer radius; and Rint is the inner radius. The Young modulus is estimated using numerical derivatives. The calculated Young’s moduli for the zigzag and armchair single-walled NTs are presented in Table 1 with values in the range of 261−323 GPa. These values are comparable to chrysotile experimental value of (159 ± 125)GPa.19 It is also in the same order of calculated values for imogolite (∼175−390 GPa),46 halloysite (∼230−240 GPa),47 WS2 (∼230 GPa),60 and GaAs (∼270 GPa)63NTs.

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CONCLUSIONS The stability, electronic, structural, and mechanical properties of the single-walled zigzag (17,0)−(45,0) and armchair (9,9)− (29,29) chrysotile NTs were studied with the SCC-DFTB method. The presented results are in very good agreement with recently reported B3LYP calculations of smaller chrysotile NTs using helical symmetry.48 Furthermore, the current work extends the previous theoretical work of chrysotile NTs48 for a larger range of NTs from 16 up to 47 Å providing insights about their stability, structural, electronic, and mechanical properties. In addition, we have shown that the chirality of the NTs does not affect their stability, and the variant with brucite in the outer side and the tridymite in the inner side of the NT is indeed the most stable with respect to the inverse case. The calculated strain energy curve for chrysotile follows the same tendency as observed for other carbon and inorganic NTs such as WS2, BN, MoS2, and halloysite. The lizardite lamellar structure is the most stable and energetically is the most favored in comparison to isolated chrysotile NTs. The zigzag and armchair NTs are close in energy, and there is no indication that one chirality is preferred. Chrysotile NTs are predicted to be insulators, and the Young’s moduli of the chrysotile NTs are in good agreement with the experimental values19 and are comparable to other inorganic NTs,60,63 for example, imogolite46 and halloysite.47 The charge distribution in the chrysotile NT, leading to the negative inner side and positive outer side, might have important implications to the solvation and hydrophilicity of the NT. The theoretical knowledge about chrysotile has been extended in the present work and provides perspective of

Figure 6. Electrostatic field of different chiralities of the chrysotile nanotubes: zigzag (40,0), view along the tube’s axis (1) and diagonal view (2); armchair (25,25), view along the tube’s axis (3) and diagonal view (4). Different colors show equipotential surfaces in e/Å.

tube while the inner part presented net negative charge as expected. The Mulliken population analysis for optimized structure indicates that the net atomic charges on magnesium and silicon were about +0.70e and +0.57e, respectively. Moreover, the oxygen atoms bound to magnesium and silicon had a net charge of −0.56e and −0.30e, respectively. Imogolite electrostatic field also indicated negative charge in the inner part of the NT showing that the tridymite layer is responsible for this behavior. The outer part of the NT (which is based on brucite in the case of chrysotile and on gibbsite in the case of imogolite) has positive charge.46 In the case of halloysite, the silicate layer is in the outer part of the NT leading to a negatively charged surface, and the inner part which is constituted by gibbsite layer is a positively charged surface.47 The positive charges on chrysotile external surface probably explain why the brucite layer can be leached under acidic conditions. Therefore, the reminiscent silica from the leaching is responsible for a new class of nanofibriform materials, which has been envisaged for technological applications.21,22 More9409



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application of this material. The study of the fibriform silica produced by mild acid leaching of chrysotile for the removal of the brucite layer is in progress.

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ASSOCIATED CONTENT

S Supporting Information *

Slater-Koster files for the atomic pairs MgX (X = Mg, O, Si, H), SCC-DFTB, and DFT structural properties of some armchair NTs, fitting of the strain energy, strain energy curves for Mg:Si and Si:Mg variants; X-ray powder diffraction simulations and PDOS of the Mg:Si and Si:Mg. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Prof. Thomas Heine for the fruitful comments and discussions during our stay at Jacobs University. The support of the Brazilian agencies Fundaçaõ de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Conselho ́ Nacional para o Desenvolvimento Cientifico e Tecnológico (CNPq), and Coordenaçaõ de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES) is gratefully acknowledged. This work has also been funded by the National Institute of Science and Technology for Mineral Resources, Water, and Biodiversity, ACQUA-INCT (http://www.acqua-inct.org).

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REFERENCES

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Structural, Electronic, and Mechanical Properties of Single-Walled

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