ARTICLE pubs.acs.org/JPCC
Origin of the Strain Energy Minimum in Imogolite Nanotubes Sang Uck Lee,*,† Young Cheol Choi,† Sang Gil Youm,‡ and Daewon Sohn‡ † ‡
LG Chem. Ltd./Research Park, 104-1, Moonji-dong, Yuseong-gu, Daejeon, 305-380, Korea Department of Chemistry, Hanyang University, Seoul, 133-791, Korea
bS Supporting Information ABSTRACT: We have systematically analyzed the structure of imogolite and their energetics, to understand the physics governing control over imogolite nanotube diameter and strain energy. In this work, we have presented evidence that the arrangements of inner and outer hydroxyl (OH) groups, that is hydrogen bond (HB) networks, play an important role in the formation of imogolite nanotubes and their structural stability. The outer HB significantly affects the Al-O distances and generates two different structures. Even though the relaxation of inner and outer Al-O and Si-O bond distances is the driving force for tubular imogolite formation, we show that the origin of the strain energy minimum, that is high monodispersity of diameter in imogolite nanotubes, is the inner HB networks. The preference for zigzag chirality and the formation mechanism of tubular imogolite also can be understood based on HB networks. Therefore, we present that a comprehensive understanding of the origin of high monodispersity of diameter and the preference for zigzag chirality in imogolite nanotubes provide useful insight into the researches of technical applications of imogolite nanotubes.
’ INTRODUCTION Nanotubes have been increasingly investigated in the past decade and have become a symbol of the new developing area of nanotechnology.1 The widespread attention can be traced not only to their interesting structure but also to their wide range of electrical, chemical, and mechanical properties. However, the defining characteristic of a nanomaterial is that its properties vary as a function of its size. Therefore, as most practical technologies require predictable and uniform performance, researchers have been aggressively seeking strategies for preparing samples of nanotubes with well-defined diameters, lengths, chiralities, and electronic properties. Despite extensive studies on nanotubes, it is still tricky task to obtain monodisperse nanotubes of diameter because of a lack of understanding of the mechanism of nanotube formation.2-4 Various theoretical studies on several nanotubes, such as C,5,6 BN,5,6 BC2N,5 GaS,7 MoS2,8 and TiO2,9 have shown that the strain energy necessary to roll a monolayer into a tube decreases monotonically with increasing tube diameter. Therefore, no suitable energy minimum has been identified to produce nanotubes with a desired diameter.10 An exception to the above considerations is the unique single-walled aluminosilicate nanotube, imogolite. Several types of experimental evidence, that is, nitrogen adsorption, X-ray diffraction, TEM, and dynamic light scattering, show that imogolite nanotubes are highly monodisperse in diameter.11 Recently, a minimum in the diameterdependence of the strain energy of the imogolite nanotubes was observed in the harmonic force-constant model, molecular dynamics, and first-principle calculations.12-21 Although extensive studies have been performed on the electronic structure of imogolite nanotubes, and it has been suggested that the curvature r 2011 American Chemical Society
of nanotubes could be due to the differing energies of the Al-O and Si-O bonds,22 the physics governing control over imogolite nanotube diameter and strain energy is still unclear. Moreover, the role of inner silanol and outer hydroxyl groups remain murky, even though it is expected that their effects on the structure and stability are significant because of their hydrogen bond networks. To resolve the issues, we must ask what is the driving force of tubular imogolite formation, and what is the origin of strain energy minimum, that is high monodispersity of diameter in imogolite nanotubes? Here, we systematically analyze the structure of imogolite nanotubes and their energetics. We also discuss the reasons why imogolite nanotubes prefer zigzag chirality. A comprehensive knowledge of the origin of high monodispersity of diameter and the preference for zigzag chirality in imogolite nanotubes allow us to access controllable dimension and chirality of imogolite nanotubes. In this work, we present evidence that the arrangements of inner and outer hydroxyl (OH) groups, that is hydrogen bond (HB) networks, play an important role in the formation of imogolite nanotubes and their high monodispersity of diameter.
’ COMPUTATIONAL DETAILS All the calculations were performed using the SIESTA code.25-27 A linear combination of localized numerical atomicorbital basis sets was adopted for the valence electrons, and norm-conserving nonlocal pseudopotentials constructed using Received: September 9, 2010 Revised: February 10, 2011 Published: March 07, 2011 5226
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Figure 1. Structures of gibbsitelike imogolite sheet with zigzag and armchair types of rolling vectors: views at the (a) inner surface and (b) outer surface are shown. (c) Two types of outer OH arrangements and resulting HB networks, HB1 and HB2. Orientations of OH bonds are indicated by red open arrows with respect to orthosilicate tetrahedron. HB networks are described by ball-and-stick and space-filled notation.
the Trouiller-Martins scheme28 were employed for the atomic core. The nonlocal components of the pseudopotentials were expressed in the fully separable form of Kleinman and Bylander.29,30 The Perdew-Burke-Ernzerhof (PBE) parametrizations of the generalized gradient approximation (GGA) corrections were used for the exchange-correlation potential.31 The atomic orbital basis set was of double-ζ quality with inclusion of polarization functions (DZP). An auxiliary basis set of a real-space grid was used to expand the electron density for numerical integration. A kinetic energy cutoff of 200 Ry was employed to control the fineness of this mesh. Imogolite nanotubes were placed in a rectangular supercell repeated along the z direction with a vacuum region of up to 10 Å along the x and y directions to exclude the mirror interactions. The Brillouin zone was sampled with a k-point grid of (1 1 4), according to the Monkhorst-Pack scheme.32 The atomic positions along with the lattice vectors were optimized by using a conjugate gradient (CG) algorithm, until each component of the stress tensors was reduced below 0.02 GPa and the maximum atomic forces were less than 0.04 eV/Å.
’ RESULTS AND DISCUSSIONS The aluminosilicate mineral, imogolite, occurs naturally in soils of volcanic origin and is composed of single-walled nanotubes. The tube walls consist of a curved gibbsitelike imogolite sheet (Al(OH)3), in which the inner hydroxyl surface of the gibbsite is substituted by (SiO3)OH groups. This structure
possesses a composition of (HO)3Al2O3SiOH, which is the sequence of atoms encountered on passing from the outer to the inner surface of the tube (Figure S1 of the Supporting Information). There is a controversy as to whether the assembly of tubular imogolite occurs through a thermodynamically controlled self-assembly process or a kinetically controlled growth/ polymerization process.23,24 In any case, to become imogolite nanotubes, gibbsitelike imogolite sheets must be rolled up. There are two possible rolling vectors in gibbsitelike imogolite sheets, zigzag- and armchairlike rolling vectors (part a of Figure 1). Interestingly, depending on the rolling vectors, OH groups of inner silanol (SiOH) generate distinct hydrogen bond (HB) networks: disk- and helixlike inner HB networks occur for zigzag and armchair imogolite nanotubes, respectively, because inner OH groups are aligned with zigzaglike rolling vectors in parallel (part c of Figure 1). For outer OH groups, there is no alignment with rolling vectors, instead, one-third of outer OH groups are oriented toward the corner, whereas the remaining two-thirds of them are oriented on the side of the orthosilicate tetrahedron (part b of Figure 1). Therefore, it is expected that outer OH groups are susceptible to the tubular curvature. When gibbsitelike imogolite sheets are rolled up into imogolite nanotubes, some outer OH groups change their orientation, thereby all outer OH groups have the same arrangement. In this process, if all outer OH groups are oriented at the corner of the orthosilicate tetrahedron, additional HB networks are created at the outer surface as helix- or linearlike HB networks. Therefore, we denote the two different outer OH arrangements as HB1 having only an 5227
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Figure 2. Calculated energies and structural parameters as a function of the number of gibbsite units(N) for zigzag imogolite nanotubes. (a) Strain energy, Estrain, and (b) inner HB energy, EHB, and the variations of outer and inner Al-O and Si-O bond distances compared to those of gibbsitelike imogolite sheet, (c) ΔdAl-O(out) and ΔdAl-O(in), and (d) ΔdSi-O.
inner HB network and HB2, which contains inner and outer HB networks. Further, we represent the designed imogolite nanotubes as “[Chirality][Number of gibbsite unit]-[Inner substituent]Imo[HB networks]”, where chirality is armchair (A) or zigzag (Z), inner substituents are silanol (SiOH) or silane (SiH), and HB networks are HB1 or HB2. Such characteristic structures imply that the arrangement of inner or outer OH groups, that is HB networks, play an important role in the formation of imogolite nanotubes and their structural stability. Despite the importance of the OH arrangement and HB networks, there has been no consideration of these factors in previous studies. Here, we provide unambiguous answers to the above-mentioned issues based on a thorough understanding of the structure of imogolite nanotubes, the driving force for tubular imogolite formation and the origin of the strain energy minimum in imogolite nanotubes. All calculations were performed using SIESTA code based on the DFT.25-27 Calculated all structural and energetic parameters are listed in Tables S1-2 of the Supporting Information. The strain energies of designed zigzag imogolite nanotubes (Z-Si0 ImoHB0 , where Si0 means SiOH or SiH, HB0 is HB1 or HB2) as a function of the number of gibbsite units (N) are plotted in part a of Figure 2. The plot shows that Z-Si0 ImoHB0 (N > 6) except Z-SiHImoHB2 has lower energy than gibbsitelike
imogolite sheets. Therefore, gibbsitelike imogolite sheets spontaneously roll up into imogolite nanotubes by releasing their strain energy. However, it is clearly seen that structural stability is significantly affected by inner substituent (SiOH and SiH) and outer OH arrangement (HB1 and HB2). In the comparison of inner substituents, Z-SiOHImoHB0 has a minimum strain energy at N = 8 and 9 for HB1 and HB2. In contrast, there is no strain energy minimum in SiHImoHB0 . Further, because of the effect of outer OH arrangements, Z-Si0 ImoHB1 (N > 6) is more stable than Z-Si0 ImoHB2 by about 20 meV/atom. From a structural point of view, the distinct behaviors of the strain energy in imogolite nanotubes can be explained by changes in structural parameters, such inner and outer Al-O and Si-O bond distances, because of the size misfit caused by bonding of orthosilicate anions with the gibbsite sheet. The variations of inner and outer Al-O and Si-O bond distances compared to those of gibbsitelike imogolite sheets, ΔdAl-O(in), ΔdAl-O(out), and ΔdSl-O, are plotted in parts c and d of Figure 2. Negative and positive values of ΔdAl-O(in), ΔdSl-O, and ΔdAl-O(out) indicate shortening and stretching of inner Al-O and Si-O, and outer Al-O bond distances respectively during the formation of imogolite nanotubes. Thus, both inner and outer Al-O and Si-O bonds are strongly constrained in gibbsitelike imogolite sheets. Therefore, the relaxation of inner and outer Al-O and 5228
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The Journal of Physical Chemistry C Si-O bond distances (Al-O/Si-O bond competition effects10) become the driving force for tubular imogolite formation. In the case of Z-Si0 ImoHB2, the change in inner and outer Al-O bond distances is exceeded compared to Z-Si0 ImoHB1 because of the additional outer helixlike HB network. Therefore, destabilization of Z-Si0 ImoHB2 can be understood by the excessive change of inner and outer Al-O bond distances. However, we also would like to present that the Si-O/Al-O bond competition effects cannot explain entire phenomena of imogolite nanotubes. Looking at the Z-SiHImoHB2 in part a of Figure 2, tubular imogolite is less stable than gibbsitelike imogolite sheets with positive strain energy, even though it also has the relaxation of inner and outer Al-O and Si-O bond distances, as shown in parts c and d of Figure 2. However, if the inner silane groups are changed to silanol groups, Z-SiOHImoHB2, tubular imogolite is stabilized with negative strain energy. Furthermore, |ΔdAl-O(in)|, |ΔdAl-O(out)|, and |ΔdSi-O)| should monotonically decrease with increases in the tubular curvature because the curvature decreases with increasing diameter. However, Z-SiOHImoHB0 has minimum values of ΔdAl-O(in) at N = 8. In contrast, there is no minimum in Z-SiHImoHB0 . It means that the relaxation of inner and outer Al-O and Si-O bond distances is not the only driving force for tubular imogolite formation. Therefore, we have taken note of the role of inner HB networks created by OH of SiOH, because the structural difference between Z-SiOHImoHB0 and Z-SiHImoHB0 is due only to the inner substituent, SiOH or SiH. We obtained inner HB energy by difference between their strain energies because Z-SiHImoHB0 has only the Al-O/Si-O bond competition effects and Z-SiOHImoHB0 includes additional hydrogen bond effect. The inner HB energy in part b of Figure 2 shows both Z-SiImoHB1 and Z-SiImoHB2 have a maximum HB energy at N = 8. The behavior is in good agreement with the feature of ΔdAl-O(in) and strain energies of Z-SiOHImoHB0 . Furthermore, Durate et al. have investigated halloysite nanotubes and they have found that there is no minimum strain energy.20 The halloysite nanotubes have simply opposite inner and outer surfaces of imogolite nanotubes, which means there is no inner HB networks. Therefore, we provide the HB energy of inner HB networks for a supplementary explanation. The minimum values of ΔdAl-O(in) and strain energy originate from the inner HB energy, even though the Al-O/Si-O bond competition effects mainly work as a driving force for tubular imogolite formation. In addition, the fact that the inner HB energy of Z-SiImoHB2 is larger than the strain energies of Z-SiOHImoHB2 reveals that the destabilization of Z-SiOHImoHB2 that is caused by excessive change of Al-O bond distances can be compensated for by the inner HB energy. Thereby, Z-SiOHImoHB2 also can be spontaneously created, and has minimum strain energy. To evaluate a correlation between the strain energy and the inner HB networks, we have investigated mixed inner substituent systems (Z-SiOHþHImoHB1) for the imogolite nanotubes containing even number of gibbsite units (N = 6, 8, 10, and 12), where SiOH and SiH groups are alternately arranged. Thus, the inner HB networks are disrupted and their HB energy is weakened. Therefore, the strain energy increases due to the decrease of the HB energy contribution to the strain energy, and which causes a shift of minimum strain energy to larger diameters of imogolite nanotube, N = 10. (Table S3 of the Supporting Information). Previously, S. Nair et al. also reported that a minimum internal energy progressively shifts to larger nanotube diameters with increasing Ge content.15 The behavior may be
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Figure 3. Calculated strain energies, Estrain, as a function of the outer diameter for Z-SiOHImoHB1 (red circles) and A-SiOHImoHB1 (blue squares).
Figure 4. Structural relaxation of a hydrogen terminated curved gibbsitelike imogolite patch.
understood on the same bases of our results, HB networks, because the shift of a minimum internal energy is due to the increase of HB distance (i.e., the decrease of HB energy) with increasing Ge content, even though further studies are required to confirm our assertion, such as the change of HB energy and strain energy according to the ratio of Si and Ge. The distinct behaviors of zigzag imogolite nanotubes are identically seen in armchair imogolite nanotubes because the role of the inner and outer HB in imogolite nanotubes is the same irrespective of their chirality (Figure S2 of the Supporting Information). If that is so, why do imogolite nanotubes prefer zigzag chirality? The plot of strain energies in Figure 3 as a function of the outer diameter (Dout) obviously shows the preference for zigzag chirality, where zigzag nanotubes are more stable than armchair nanotubes for Dout < 26 Å. The result is well agreement with previous simulation studies on stability of zigzag versus armchair imogolite nanotubes10 and experiment, where no armchair nanotubes were observed. As mentioned before, the 5229
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Figure 5. Optimized structures including additional two water molecules (a) inside the inner hydrogen bond networks and (b) above the inner hydrogen bond networks.
zigzaglike rolling vectors are well aligned with inner hydroxyl (OH) groups. Therefore, the zigzag nanotubes can effectively construct inner HB networks. Comparison of the HB distance between Z- and A-SiOHImoHB0 shows Z-SiOHImoHB0 has relatively short HB distances, as shown in Figure S3 of the Supporting Information. So, the HB energy of Z-SiOHImoHB0 becomes stronger than that of A-SiOHImoHB0 , and, accordingly, imogolite nanotubes prefer zigzag chirality. To evaluate the preference, we have investigated structural relaxation of hydrogen terminated curved gibbsitelike imogolite patches with armchair chirality. We removed a piece of gibbsitelike imogolite from A5-SiOHImoHB2, which has minimum strain energy, and then terminated the dangling bonds with hydrogen atoms, as shown in Figure 4. The calculation shows that the curved gibbsitelike imogolite patch spontaneously changes its chirality from armchair to zigzag by shortening inner HB distances and changing the rolling vector. The results give insight into the zigzag preference and the formation mechanism of tubular imogolite. To investigate the effect of hydration on the inner HB networks, we have considered additional water molecules at the model of the hydrogen terminated curved gibbsitelike imogolite patch as shown in Figure 5. Although hydration may provide different environment, the Al-O/Si-O bond competition effects still work as the driving force for tubular imogolite formation. Therefore, the curvature of gibbsitelike imogolite sheet is created by the relaxation of inner and outer Al-O and Si-O bond distances. As the gibbsitelike imogolite sheet is rolled up, inner silanol gropus (Si-OH) are biased toward formation of the inner HB networks because the HB distances between two silanol groups are decreased and optimized. Here, we found that it is hard to insert the additional water molecules into the inner HB networks, because the inserted water molecules suppress the relaxation of Al-O and Si-O bond distances by reducing the curvature. So, structure of part a of Figure 5 is energetically unstable than structure of part b of Figure 5 by about 2 kcal/mol. In this work, we just used less curved small gibbsitelike imogolite patch. But, if we used more curved large gibbsitelike imogolite patch, the difference of energy stability will be reinforced. It means that the inner HB networks are rigid against the hydration effect, in contrast the outer HB networks are significantly affected by hydration as describe by Zang et al.21
’ CONCLUSIONS In conclusion, we have presented evidence that the unique arrangement of inner silanol groups (Si-OH) and their
hydrogen bond (HB) networks in imogolite nanotubes are shown to be the origin of the strain energy minimum (i.e., high monodispersity of diameter) and the preference for zigzag chirality, even though the relaxation of inner and outer Al-O bonds and Si-O bond distances is the driving force for tubular imogolite formation. The results allow at least a qualitative description of the potential for engineering the dimensions and chirality of imogolite nanotubes by subtle control over inner HB networks. Therefore, we present that the relation between inner HB networks and the strain energy minimum provides guidelines for the synthesis of tunable nanotube diameters with appropriate control of inner HB networks at hydrothermal or solvothermal synthesis conditions.
’ ASSOCIATED CONTENT
bS
Supporting Information. Formation of gibbsitelike imogolite sheet from a gibbsite sheet, calculated structural and energetic parameters, and optimized geometries (Cartesian coordinates) of Z8-Si0 ImoHB0 and A5-Si0 ImoHB0 . This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT D.S. thanks to the financial support from Nano Core Project in Korea (KRF 20100646). ’ REFERENCES (1) Saito, R.; Dresselhaus, M. S.; Dresselhaus, G. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998; p 272. (2) Dresselhaus, M. S.; Dai, H. Carbon Nanotubes: Continued Innovations and Challenges. MRS Bull. 2004, 29, 237–239. (3) Ago, H.; Ohshima, S.; Tsukuagoshi, K.; Tsuji, M.; Yumura, M. Formation Mechanism of Carbon Nanotubes in the Gas-Phase Synthesis from Colloidal Solutions of Nanoparticles. Curr. Appl. Phys. 2005, 5, 128–132. (4) Klinke, C.; Bonard, J. M.; Kern, K. Thermodynamic Calculations on the Catalytic Growth of Multiwall Carbon Nanotubes. Phys. Rev. B 2005, 71, 035403. (5) Hernandez, E.; Goze, C.; Bernier, P.; Rubio, A. Elastic Properties of C and BxCyNz Composite Nanotubes. Phys. Rev. Lett. 1998, 80, 4502–4505. 5230
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