Molecular Simulation of Nanosized Tubular Clay Minerals

Chapter 14

Molecular Simulation of Nanosized Tubular Clay Minerals H.A. Duarte* ^ Grupo de Pesquisa em Quı´mica Inorganica Teo´rica (GPQIT), Instituto de Ci^ encias Exatas, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil * Corresponding author: e-mail: [email protected]

14.1 INTRODUCTION Nanostructured materials have been known to exist in nature for a long time. Pauling (1930), analysing the structure of some clay minerals, pointed out that hollow materials might exist in nature. The tubular shape of halloysite (Bates et al., 1950), chrysotile (Yada, 1971) and imogolite (Cradwick et al., 1972) have been determined. Naturally occurring nanotubular materials such as imogolite and halloysite are per se fascinating, but with the advent of nanotechnology, these natural nanotubes have become a target for developing advanced materials with enhanced properties. The aluminosilicate nanotubes are isolators, so applications in electronic devices are limited. However, these natural nanotubes are the perfect target for developing nanocatalysts, gas storage, controlled delivery systems, nanowires, clay polymer nanocomposite agents and many other relevant technological applications. Furthermore, the outer and inner surfaces of clay mineral nanotubes can be easily modified and different organic groups anchored, providing new chemical functionalities. Investigations based on sophisticated experimental techniques and computational chemistry have contributed to a complete understanding of the structure and chemical properties of clay mineral nanotubes at an atomistic level. Computational chemistry techniques have been used to explore aspects such as the stability of clay mineral nanotubes and the role of hydrogen bonding at the surface, their electronic structure, their mechanical properties such as Young’s moduli and the chemical properties of possibly synthesisable

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nanotubes. Such information has been shown to be essential for envisaging new strategies for developing different modified clay mineral nanotubes. In this chapter, the contributions that computational chemistry have made over the last 10 years for understanding clay mineral nanotubes are presented. The different approaches used to model the clay mineral nanotubes are briefly reviewed. The most studied one, from the computational chemistry point of view, is imogolite, probably because it is a unique nanotube that is monodisperse and single-walled (SW) with a well-defined diameter. Computational chemistry investigations of other nanotubes have been reported, and their main achievements are presented here as well.

14.2 COMPUTATIONAL ASPECTS The detailed fundamentals of the methodologies used to perform computer simulations of the nanostructured aluminosilicates are beyond the scope of this chapter. However, the main concepts behind the state-of-the-art computational chemistry techniques are important to highlight in order to present their uses and limitations. For details about the theory and methodology, see the cited references throughout the text. The chemical model of aluminosilicate nanotubes is usually a cylinder with its respective unit cell, and the periodic boundary condition is applied along the cylinder axial. On the other axis, the size of the unit cell is large enough to avoid lateral interactions of the nanotubes. It is important to note that normally, the calculated nanotubes are considered to be in the gas phase without any effect of the solvent or lateral interactions due to the bundle formation, for example.

14.2.1 Force Field Simulations The molecular and covalent bounded systems can be reasonably modelled as a set of atoms that are connected through force constants. The two-, three- and four-atom interactions due to bond lengths, angles and dihedrals are adequately modelled using suitable equations. For nonbonding interactions, such as van der Waals and hydrogen bonding, the Lennard–Jones potential is usually used. The topology of the systems is established by providing all the connections between the atoms and their types. Different parameters are used depending on the hybridisation involved and the type of the material. The set of parameters that describe the molecular structure is called a ‘force field’. Experimental data such as geometries, heat of formation, reaction energies, vibrational frequencies and other properties are normally used to assess the quality of a force field. There are many different force fields, which have been developed for a class of systems such as proteins, materials and clay minerals

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(Cygan et al., 2004; Zeitler et al., 2014). Normally, the total energy is adequately described for clay minerals by Eq. (14.1): "   o 6 # 12 R e2 X qi qj X o Roij + Dij  2 rijij E¼ rij 4pe0 i6¼j rij i6¼j |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Coulomb van der Waals (14.1) X  X   2 2 1 2 + kij rij  r0 + kijk yijk  y0 : i6¼j

i6¼j6¼k

|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} bond stretch

angle bend

The partial charges qi and qj and the force constants k1ij and k2ijk are parameters normally derived from quantum-mechanical calculations. Doij and Roij are empirical parameters derived from structural and physical properties. Due to the relative simplicity of the method, calculations of thousands of atoms can be performed. Force fields are often applied in molecular dynamics (MD), in which the system is evolved along the time at a given pressure and temperature. With the gradients of the force field and the velocities, the classical equations of motion can be established and integrated along the normal time for using periodic boundary conditions (Allen and Tildesley, 1987). The MD can be evolved up to nanoseconds using a time step in the range of femtosecond. MD can be used for investigating the dynamics of the solvent around the aluminosilicate nanotubes and the formation mechanism of nanotubes and nanoscrolls.

14.2.2 Density-Functional Theory The density-functional theory (DFT) is probably the highest-level theory used for investigating large systems such as aluminosilicate nanotubes. Based on the published Hohenberg–Kohn theorems (Hohenberg and Kohn, 1964), the electron density is legitimized as the principal variable that permits calculating the total energy of an electronic system. Then Kohn and Sham (1965) published a method that permits the performance of DFT calculations in a computationally efficient manner. As explained by Levy (1982), the Kohn–Sham equations [Eqs (14.2)–(14.5)] use a noninteracting electron system as a reference for providing one-electron Kohn–Sham orbitals, ci, that lead to the electron density of the real interacting electron system:   1  r2 + vef ðr Þ ci ¼ ei ci ; (14.2) 2 where vef ðr Þ ¼

M X A

and

ZA  + j r  RA j

Z

rðr 0 Þ 0 dr + vxc ðr Þ; jr  r 0 j

(14.3)

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vxc ðr Þ ¼ rðr Þ ¼

dExc ½r ; dr

N X

ni c2i ðr Þ:

(14.4)

(14.5)

i

In Eq. (14.2), the first term is the kinetic energy operator and the second term is the effective local potential felt by the electrons. The effective potential, Eq. (14.3), includes the external potential due to the nuclei charges, the Coulomb term due to the classical repulsion between the electrons and the exchange-correlation (XC) potential, which includes all nonclassical interactions between the electrons. ZA, N and M are the atomic number of atom A, the number of electrons and the number of atoms, respectively. The XC potential is defined by Eq. (14.4) as the derivative of the XC energy functional, and the electron density, r(r), is defined by Eq. (14.5), where ni is the occupation of the KS orbitals. The Schr€ odinger equation Eq. (14.2) is solved by expanding the oneelectron KS orbital in a set of basis functions {fm}: X ci ¼ Cmi fm : (14.6) m

The basis functions can be localized using Gaussian, Slater or numerical basis sets, depending on the strategy used for implementing the method in the different program packages. The XC functional [Eq. (14.4)] is simultaneously the strength and weakness of the DFT method. The Hohenberg–Kohn theorems show that an XC functional of the electron density does exist, and consequently, so does the total electronic energy functional. However, the exact form of the XC functional is still unknown, although many properties of the exact XC functional have been reported (Parr and Yang, 1994). Different approximations for the XC functional define the different DFT methods. Most of the XC functionals are based on the homogeneous electron gas approach. The simplest XC functional named SVWN (for Slater, Vosko, Wilk and Nusair) is due to the work of Slater (1951) and Vosko et al. (1980), based on a local approach of the homogeneous electron gas approximation. The generalized gradient approximation (GGA) takes into account part of the inhomogeneity of the electron density of the molecular calculations incorporating the electron density gradients in the XC functional. The GGA XC functional proposed by PBE (named for Perdew, Burke and Ernzerh€ of; Perdew et al., 1996) is nonempirical and largely used for solid-state calculations and molecular systems. The hybrid XC functional includes part of the exact exchange term of the Hartree–Fock method. The three-parameter hybrid method called B3LYP (named for Becke, Lee, Yang and Parr; Becke, 1988, 1993; Lee et al., 1988) is largely used mainly for organic molecular systems.

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14.2.3 Self-consistent-Charge Density-Functional Tight-Binding Method Frauenheim and collaborators developed the density-functional tight-binding (DFTB) method (Porezag et al., 1995; Seifert et al., 1996) that is an approximate DFT method (Oliveira et al., 2009). Basically, the tight-binding approximation is evoked, a minimal basis set is used for all atoms and the three-centre integrals present in the Hamiltonian (Eq. 14.2) are disregarded. Therefore, only one- and two centre integrals are present in the Hamiltonian and can be easily tabulated in a pairwise manner. The set of the tabulated integrals are called ‘Slater-Koster files’. The DFTB method has been applied with success for investigating materials such as carbon and simpler inorganic nanotubes (Frauenheim et al., 1995; Seifert et al., 2001). However, for more heterogeneous systems where charge transfer may occur, the DFTB method fails. An extension of the DFTB method, called the ‘self-consistent-charge density-functional tight-binding method (SCC-DFTB)’ was developed (Elstner et al., 1998). The SCC-DFTB total energy is given by Eq. (14.7): ESCC ¼

N M X    1X ni ci H^0 ci + g Dqa Dqb + Erep : 2 a, b ab i

(14.7)

The SCC-DFTB method allows charge transfer to occur through a self

! !  consistent procedure driven by gab ¼ gab Ua , Ub , jR a  R b j , which is related to the Hubbard parameter, Ua, of each atom present in the structure. It is interesting to note that the Hubbard parameter is related to the hardness of the atoms. Here, Dqa is estimated from Mulliken population analysis, and ci is expanded in a minimal basis set according to Eq. (14.6). The Hamiltonian H^0 is exactly the same as in the standard DFTB scheme, as shown here: 8 free atom em , m¼v > > >  >   <  1

 o (14.8) Hmv ¼ fm  r2 + uef rA0 + rB0 fv , m 2 fAg, v 2 fBg : > 2 > > > : 0, otherwise Eq. (14.8) depends only on atoms A and B following the tight-binding atom approach. In this instance, rA0 and efree are the electron density of the atom m A and one-particle energy for the free atom, respectively. It is important to highlight that the lack of the three-centre integrals in the Hamiltonian leads to the necessity to incorporate a repulsive contribution, Erep, to the total energy estimate. This repulsive contribution is incorporated in order to reproduce the DFT total energy of reference systems. Erep is usually fitted to a polynomial function or to a series of splines. The parameterization of the repulsive contribution is crucial for the quality of the results to be obtained and to its transferability between different systems. Parameter sets for general and specific purposes are available (see K€oskinen and Ma¨kinen,

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2009). The SCC-DFTB method provides an efficient and reasonably accurate way to calculate the electronic energy of large systems.

14.3 IMOGOLITES Carbon nanotubes and other inorganic nanotubes are normally polydisperse, with a large range of diameters. Many studies have shown that the strain energy necessary to roll a monolayer into a tube decreases smoothly with the increase in diameter, such as for carbon, MoS2, TiS2 and GaS nanotubes (Seifert et al., 2001; Kohler et al., 2004; Enyashin et al., 2007). The synthesis of the nanotubes normally leads to a kinetic polydisperse and multiwalled (MW) product. However, the imogolite nanotube is monodisperse, uncapped, and SW, with a well-defined diameter. Understanding this intriguing property of imogolite was probably the ultimate goal for these theoretical investigations.

14.3.1 Imogolite Model Imogolite has the composition of (HO)3Al2O3SiOH, which is the sequence of atoms going from the outer to the inner surface of the nanotube. Hereafter, this is referred as ‘imogolite-Si’, while ‘imogolite-M’ denotes other minerals sharing the same imogolite-like local structure, in which silicon was replaced by atom M. The hypothetical monolayer is built by taking a sheet of gibbsite structure and replacing the hydroxyl groups in one vacant site by orthosilicate anions (Fig. 14.1A). The convention for labelling carbon nanotubes is

FIG. 14.1 (A) Gibbsite unit and its vacant site where the silanol group is placed; (B) hypothetical 2D imogolite layer with vectors a1 and a2; (C) zigzag (12,0) imogolite nanotube. White atoms, H; red (dark grey in the print version), O; blue (grey in the print version), Al; yellow (light grey in the print version), Si. Adapted with permission from Guimara˜es et al. (2007). Copyright 2007 American Chemical Society.

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normally adopted for the aluminosilicate nanotubes. In Fig. 14.1, the lattice vectors a1 and a2 of the hexagonal lattice are used to define the rolling direction B in the two-dimensional (2D) lattice, where B ¼ na1 + ma2. Two classes of nanotubes have been considered in the computer calculations: armchair (n, n) and zigzag (n, 0). The diameter of the nanotubes is easily estimated from theoretical simulations and experiments. However, it is important to note that the estimates can vary depending on the model or reference used. Normally in the computer simulations, the diameter is based on the outer hydrogen layer of imogolite, and experimental estimates are usually based on small-angle X-ray scattering (SAXS), gas adsorption and cryo-electron microscopy (cryo-EM) (Maillet et al., 2010; Thill et al., 2012b), which is only slightly affected by light atoms such as hydrogen. Therefore, the nanotubes are normally estimated to have smaller diameters compared to the computersimulated structure.

14.3.2 Imogolite: Aluminosilicate Nanotubes Tamura and Kawamura (2002) were among of the first researchers to perform calculations on the molecular models of imogolite using an interatomic potential model. For comparison, they also calculated the hypothetical gibbsite nanotube. Presumably, they have constructed models of zigzag (n, 0) symmetry. In their computer simulations, these authors showed that the total energy of the nanotubes have a minimum of n ¼ 16, with a diameter of 2.93 nm. Imogolite is more stable than the hypothetical gibbsite due to the tetrahedra (silanol group) bounded near the vacant octahedral sites of the gibbsite framework that stabilize the tubular structure. Konduri et al. (2006) used the clay force field (CLAYFF) (Cygan et al., 2004) to investigate in detail the strain energy, defined as the energy necessary to roll a planar monolayer to the nanotube. The contributions of the stretching potentials of the Al–O (VAl–O) and Si–O (VSi–O) bonds to the total energy behave in a different manner with respect to the diameter. The VAl–O decreases with the increase of the diameter, since it is approaching the ideal gibbsite structure. However, VSi–O increases with the diameter of the structure, since the ideal tetrahedral of the silanol is deformed. The sum of these two contributions leads to the minimum total energy, with a diameter of 2.26 nm. Guimara˜es et al. (2007) used the SCC-DFTB method for investigating the electronic, mechanical and structural properties of imogolite. The quantummechanical approach used here permitted the exploration of the electronic properties and the stability of the nanotubes. They investigated the armchair (n, n) and zigzag (n, 0) chiralities. The structures have been fully optimized, showing that the cylindrical structure is a stable local minimum. Born– Oppenheimer MD simulations at 300 K was performed using the potential

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FIG. 14.2 Comparison of the different naturally occurring nanotubes. Squares mark imogolite-Si, circles mark imogolite-Ge, triangles mark halloysite and diamonds mark chrysotile; and solid objects are zigzag (n, 0) nanotubes and open objects are armchair (n, n) nanotubes. Strain energy curves were obtained from Guimara˜es et al. (2007, 2010); Lourenc¸o et al. (2012, 2014).

energy surface (PES) obtained from the SCC-DFTB method. This is important to note that at the quantum-mechanical level, the bonds can be broken and distorted. The strain energy per atom was estimated by taking as a reference the ideal planar layer. A comparison of the strain energy curves of the different imogolite-like nanotubes, halloysite and chrysotile is reported in Fig. 14.2. The strain energy curves of the different nanotube configurations as a function of the diameter have a minimum for the zigzag and armchair conformations. The zigzag configurations are the most stable for the n < 16. The (12,0) zigzag is the most stable, with a diameter of about 1.97 nm, taking as a reference the oxygen atoms on the outer surface. Recently, the imogoliteSi nanotubes were recalculated using a new set of Slater-Koster files, and the estimated value for (12,0) zigzag was 2.16 nm (Lourenc¸o et al., 2014) in close agreement with the classical MD simulations (Tamura and Kawamura, 2002; Konduri et al., 2006). The imogolite band gap of about 10 eV confirms that it is an isolator with wide band gap material. The Young’s

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14 339

modulus was estimated to be about 242 GPa, which is similar to other nanotubes such as chrysotile but less stiff than other nanotubes such as carbon (Hernandez et al., 1999). The radial breathing mode was estimated to be about 54 cm1 for the zigzag (12,0) nanotube, but these results indicate that with more than 17 gibbsite units in the circumference, the nanotube could became instable since imaginary frequencies of the radial breathing mode were predicted. MD of the hydrated imogolite-Si were performed containing 12 water molecules inside of the nanotube and 82 water molecules in the intertubular void corresponding to mass percentage of about 14.1% similar to the experimental low relative humidity (Creton et al., 2008). The results pointed out that the breathing motions of the nanotube does not reduce to a single mode but rather a narrow band in the range of 30–50 cm1 is observed containing modes involving all atoms of the nanotube. These are important contributions from the computational chemistry investigations for understanding the properties of imogolites such as to be monodisperse, SW and with well-defined dimensions. The minimum in the strain energy curves and the mild conditions that the imogolite are synthesized in aqueous solution over 72 h of reflux lead invariably to the thermodynamic most stable structure with well-defined diameter. Cradwick et al. (1972) reported that natural imogolites are composed by 10 gibbsite units and the first imogolite nanotubes synthesized by Farmer et al. (1977) contained 12 gibbsite units around the circumference according to X-ray diffraction (XRD) analysis. Indeed, the experimental conditions (temperature, ionic strength, type of ions in the solution) can significantly change the diameter of the nanotube (Yucelen et al., 2012). This is a unique characteristic compared to the other nanotubes that may be considered as kinetic product of the syntheses since they are not the global minimum structure. The planar is normally the most stable for carbon and other inorganic nanotubes (Lourenc¸o et al., 2012). It seems that for one-atom-thick nanotube wall, such as carbon nanotubes, it is not possible to obtain a structure with a minimum in the strain energy curve. The four-atom-thick imogolite nanotube wall with nonsymmetric bond strengths leads to a difference between the outer and inner surface tensions, and an optimal curvature is found for the nanotube. Density-functional calculations have been performed for the imogolite. Alvarez-Ramı´rez (2007) and Li et al. (2008) investigated the electronic structure of the imogolite using localized numerical basis sets and the PW91 (named for Perdew and Wang; Perdew et al., 1992) and PBE XC functional, respectively. The calculations indicate a direct band gap with a value of 4.7 (PW91) and 3.67 (PBE) eV. However, this value might be taken with caution since it is known that the GGA XC functional underestimates the band gap. The projected density of states indicates that close to the Fermi level the valence band is mostly contributed by the Si–OH groups and the conduction band is mostly contributed by the Al–OH groups. Demichelis et al. (2010) used the roto-translational symmetry to perform DFT calculations using

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localized Gaussian basis sets with the three-parameter B3LYP hybrid XC functional. They found similar results compared to the SCC-DFTB calculations. The (10,0) zigzag nanotube was found to be the most stable with inner diameter of 1.45 nm and the (8,8) armchair is less stable of about 10.6 kJ mol1 per formula unit. The B3LYP estimated value for the band gap is 7.2 eV. This is considered the best value since B3LYP is known to estimate accurate band gaps, and this value is in between the two extremes of PBE XC functional and the SCC-DFTB estimates. The experimental and calculated diameters of imogolites are reported in Table 14.1.

TABLE 14.1 Experimental and Calculated Diameters of SW and DW Imogolite-Si and SW and DW Imogolite-Ge Nanotubes

Nanotube SW: Imogolite

Diameter (A˚)

Method a

Exp.

Band gap (eV)

Structure

5.7

(9,0)/(12,0)

7.2

(10,0)

23.0 b

17.50

PBE/DFT

c

B3LYP/DFT e

d

14.52 17.18

PBE/DFT

(8,0)

f

23.48

4.8

(12,0)

g

19.72

10.0

(12,0)

h

21.6

10.2

(12,0)

h

PW91/DFT SCC-DFTB

SCC-DFTB DW: Imogolite

SCC-DFTB

18.50 (internal) 32.42 (external)

8.1

SW: Ge-imogolite

Exp.

33.0i

3.6

(10,0)@(19,0)

j

33.0

30.04  0.10k 30l 35.0  1.6m 23.0  5.0n 38o PW91/DFTf SCC-DFTB

4.8 h

26.46

9.6

(14,0) Continued

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TABLE 14.1 Experimental and Calculated Diameters of SW and DW Imogolite-Si and SW and DW Imogolite-Ge Nanotubes—Cont’d

Nanotube

Method

Diameter (A˚)

DW: Ge-imogolite

Exp.

24.0  1.0 (internal)m 40.0  1.0 (external)m

Band gap (eV)

Structure

30.0  5.0 (external)n 26 (internal)o 43.0 (external)o SCC-DFTB

23.42 (internal)h 37.46 (external)h

8.5

(12,0)@(21,0)

a

Mukherjee et al. (2005). Zhao et al. (2009). Demichelis et al. (2010). d Internal diameter. The external diameter can be roughly estimated to be 20 A˚. e Lee et al. (2011). f Alvarez-Ramı´rez (2007). g Guimara˜es et al. (2007). h Lourenc¸o et al. (2014). i Wada and Wada (1982). j Mukherjee et al. (2005). k Levard et al. (2008). l Levard et al. (2010). m Maillet et al. (2010), diameter estimated from SAXS. n Maillet et al. (2011), diameter estimated from AFM. o Thill et al. (2012b). Adapted with permission from Lourenc¸o et al. (2014). Copyright 2014 American Chemical Society. b c

One important aspect of the imogolite is the role of the hydrogen bonding between the silanol groups in the inner surface of the nanotube in the stabilization of the structure. The orientation of the hydrogen bonding is an important aspect that has been investigated by Demichelis et al. (2010) and Lee et al. (2011). These authors argue that the zigzag is favoured with respect to the armchair due to the hydrogen bonding in the inner surface. The different orientation of the hydrogen bonding can explain up to 2 kJ mol1 per unit cell of difference in the strain energy curves. However, it seems that the favoured zigzag structure cannot be explained solely on the basis of the hydrogen bonding network in the inner surface of the imogolite, as discussed by Guimara˜es et al. (2013). Zhao et al. (2009) also performed PBE DFT calculations using numerical localized basis sets and estimated the band gap to be 5.7 eV. They found two minima in the strain energy curves for (9,0) and (12,0) zigzag nanotubes and tried to correlate with the natural and synthetic imogolites. However, analysing the results of the Demichelis et al. (2010)

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shows that the hydrogen bonding configuration in the inner surface is very sensitive to the starting structures used for geometry optimization. In fact, with the increase of the diameter the orientation of the hydrogen bonding can be changed leading to an extra stabilization and the artefact of appearing a second minimum in the strain energy curve.

14.3.3 Aluminogermanate Nanotubes For the first time, Wada and Wada (1982) synthesized imogolite-like nanotubes in which the silicon atoms were replaced by germanium atoms. The aluminogermanate nanotube (imogolite-Ge) has a larger external diameter of about 4.0 nm and it can be synthesized in large amounts as was shown by Levard et al. (2008, 2011). Alvarez-Ramı´rez (2007) performed a detailed analysis of the imogolite structure with different silicon-germanium content. The XRD pattern of imogolite-like structures was simulated, and they are in good agreement with the available experimental data for imogolite-Si and imogolite-Ge. The packing of the nanotubes in bundles has been discussed and its effect on the XRD pattern analysed. The band gap of the imogolite-like structure with different contents of germanium varies between 4.3 eV (for imogolite-Ge) up to 4.8 eV (imogolite-Si) at the PW91/plane wave level of theory. Konduri et al. (2007) also investigated imogolite with a different silicon-germanium content using a modified CLAYFF force field. The results indicated that a larger diameter for the imogolite-Ge is favoured in comparison to the imogolite-Si. They discussed the effect of increasing Ge content on the XRD pattern and on the outer diameter. By controlling the pH, concentration and ionic strength, it is possible to synthesize the double-walled (DW) imogolite-Ge (Maillet et al., 2010; Thill et al., 2012b). Lourenc¸o et al. (2014) used the SCC-DFTB calculations to investigate the electronic, mechanical and structural properties of the SW and DW imogolite-Ge. The zigzag (n, 0) SW imogolite-Ge nanotubes are favoured in comparison to the armchair (n, n) SW nanotubes. The (14,0) SW imogolite-Ge nanotube was predicted to be the most stable, with an external diameter of about 2.46 nm, while the (11,0) imogolite-Si nanotube is the most stable, with an external diameter of about 2.16 nm. It is important to note that computer simulations are performed on idealized structures calculated at the gas phase, while synthetic nanotubes can vary their diameters according to the electrolyte used and experimental conditions, as has been shown by Yucelen et al. (2012). The (p, 0)@(q, 0) DW imogolite-Ge nanotubes have been calculated at the SCC-DFTB level of theory with the aim of understanding why the synthesis of DW imogolite-Ge was successful and DW imogolite-Si seems to not be achievable. Fig. 14.3 indicates clearly that the most favoured DW imogoliteGe occurs for the combination (p, 0)@(p + 9, 0) nanotube, and the most stable is the (12,0)@(21,0) DW imogolite-Ge nanotube.

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FIG. 14.3 Strain energy per atom as a function of the outer radius for double-walled (p, 0)@ (q, 0) imogolite-Ge nanotubes, taking into account different sizes and wall interactions: q  p ¼ 8, 9, 10 and 11. Dashed lines are related to the same inner nanotube but different outer nanotube. The reference used to calculate the double-walled nanotubes strain energies was the bilayer. Reproduced with permission from Lourenc¸o et al. (2014). Copyright 2014 American Chemical Society.

The external diameter is estimated to be about 3.75 nm. It is interesting to observe that it does not contain the (14,0) nanotube, which is the SW most stable nanotube. This is a characteristic of the imogolites that are synthesized in aqueous solution and in mild conditions leading to the thermodynamic product. Two contributions are involved in the DW nanotube formation: (i) the stabilizing contribution due to the hydrogen bonding interaction between the surfaces of the nanotubes; (ii) the destabilizing contribution due to the strain energy of the (12,0) and (21,0), which are not the most stable compared to the SW (14,0) nanotube. In fact, when one compares to the hypothetical DW imogolite-Si nanotubes (Fig. 14.4), it is clear that larger strain energy is paid to form the DW imogolite-Si and the stabilizing hydrogen bonding interaction is much smaller due to the larger distances between the two tube walls of about 0.207 nm. This value must be compared to the 0.143-nm measurement for the DW imogolite-Ge nanotube. A similar explanation was given by Thill et al. (2012a,b) based on qualitative analytical models of the imogolite energy as a function of radius. The band gap is predicted to be smaller with respect to the imogolite-Si, and the estimates are about 9.6 and 8.5 eV for the SW and DW imogolite-Ge nanotubes. This is an upper bound value since SCC-DFTB overestimates band gaps.

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FIG. 14.4 Strain energy curves for the SW and DW nanotubes of the imogolite-Si and imogolite-Ge systems. Reproduced with permission from Lourenc¸o et al. (2014). Copyright 2014 American Chemical Society.

14.3.4 Other Imogolite-like Nanotubes It is disturbing that since the synthesis of the aluminogermanates nanotubes in 1982 by Wada and Wada, no other imogolite-like nanotubes have been successfully synthesized. The chemical intuition indicates that any replacement of the group III elements (Al, Ga, In) or group IV elements (C, Si, Ga, Sn) should be stable and synthesisable. Alvarez-Ramirez (2009) investigated the electronic and structural properties of such hypothetical structures showing that the band gap could vary from 4.6 eV for Al–Si (imogolite-Si) to 2.6 eV for In–Ge, as expected. Although all these possible imogolite-like structures are predicted to be stable with different external diameters and electronic properties, the right experimental conditions to achieve such a syntheses remains to be designed. Actually, it has been shown that the syntheses of the imogolites (imogolite-Si or imogolite-Ge) are very sensitive to pH, ionic strength and concentrations. The nanotubes are formed upon self-organizing mechanisms from the hydrolysis of the species, oligomerization and the formation of proto-imogolites (Levard et al., 2010; Yucelen et al., 2011). The understanding of the chemical speciation in aqueous solution seems very important to establish the right conditions for nanotube formation. Guimara˜es et al. (2013) were interested for the replacement of the silanol by other fragments other than the Ge(OH)4. Actually, any element that forms tetrahedron in aqueous solution is, in principle, a candidate to replace the silanol fragment. They have investigated the possible imogolite-like structures

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replacing the fragment (O3SiOH)3 by PO4 3 , PO3 3 , AsO4 3 and AsO3 3 . The basic idea is that on the inner side of the nanotube, there is the dP]O group instead of –Si–OH, which could be easily reduced to –P. The same stands for the dAs]O, which could be reduced to –As. For all these structures, a minimum is observed for the strain energy curves with respect to the diameter. The band gap is much decreased to the reduced species, such as phosphite and arsenite (about 5.2 and 4.2 eV, respectively). For the imogolite-P-ate (phosphate), the band gap is predicted to be about 10 eV (similarly to imogolite-Si) and for the imogolite-As-ate, the band gaps are about 7.6 eV. It is interesting to note that the zigzag (n, 0) structures are more stable than the armchair structures (n, n), similar to imogolite-Si and imogolite-Ge. This indicates that the hydrogen bonding present in the imogolite-Si and imogolite-Ge is not responsible for stabilizing the zigzag with respect to the armchair. The internal hydrogen bonding of imogoliteSi is responsible for the larger stabilization and more pronounced minimum in the strain energy surface. Duarte et al. (2012) speculated that the pKa of the precursor reactants could indicate the feasibility of a different imogolite-like structure. Table 14.2 lists the pKa of the components of the possible species that could be used to

TABLE 14.2 Possible Elements to Form Imogolite-like Nanotubes Element

Species

pKa

Group III elements Al(III) Ga(III)

[Al(H2O)6]3+ [Ga(H2O)6]

3+

3+

5.52 2.85

[In(H2O)6]

3.7

Si(IV)

Si(OH)4

9.84

Ge(IV)

Ge(OH)4

In(III) Group IV elements

Sn(IV)

Sn(OH)4

a

9.16 –

Group V elements P(V)

H3PO4

2.12; 7.21; 12.67

P(III)

H3PO3

1.3; 6.7

As(V)

H3AsO4

2.19; 6.94; 11.5

As(III)

H3AsO3

9.2

The aqueous species are indicated with its respective pKa. a Little information is available due to the very low solubility of SnO2(s) (Seby et al., 2001).

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form imogolite-like structures, and that has been investigated by computational chemistry, as have the species and the pKa of possible candidates to replace silicon or aluminium in the imogolites. Carbon and nitrogen species are not considered since they lead to the carbonate and nitrate species which are trigonal planar and not suitable for replacing the silicon. As it was pointed out by Duarte et al. (2012), the species Si(OH)4 and Ge(OH)4 have similar pKa; therefore, the replacement of the Si by Ge is easily achieved using a very similar protocol of synthesis. Other elements, such as Ga(III) and In(III), are more acidic (small pKa), and therefore, the synthesis must be done in a more acidic medium in order to obtain similar chemical speciation. For the replacement of the Si, only As(III) seems to be possible using a similar protocol, since the pKa is very similar to the Si(IV). The understanding of the chemical speciation and the formation mechanism of imogolite at a molecular level seems to be a key point to manage the synthesis of other imogolite-like structures. Important insights have been provided about this mechanism using different experimental techniques such as 27Al and 29Si nuclear magnetic resonance (NMR), electrospray ionization mass spectrometry (ESI-MS), dynamic light scattering (DLS), extended X-ray absorption fine structure (EXAFS) and inductive coupled plasma atomic emission spectroscopy (ICP-AES) (Levard et al., 2010, 2011; Yucelen et al., 2011, 2012). Recently, Gonza´lez et al. (2014) used classical MD to investigate the selfrolling of an aluminosilicate sheet model into an imogolite. They used flat models of the aluminosilicate sheets with 9 < N < 24 (where N is the number of the hexagons to form the nanotube) and CLAYFF force field (Cygan et al., 2004) to perform the MD in different temperatures (10–368 K). These authors were able to reproduce the results showing a minimum in the strain energy curve. They found that the length of the unit cell of the tube varies with the ˚ at 10 K up to 8.50 A ˚ at 368 K. Furthermore, temperature between 8.39 A the starting flat models of different sizes were evolved for up to 200 ps at different temperatures. A small increase of temperature was sufficient to shift the minimum from the n ¼ 10 to n ¼ 11. At 368 K, the most stable nanotube is shifted to the N ¼ 12. The tendency to form nanoscrolls is observed (n ¼ 15) for higher temperatures. A precursor of the DW nanotubes has also been observed for higher temperatures and larger models (N > 15). It is important to note that Thill et al. (2012a) showed that for the synthesis of (OH)3Al2O3SixGe1xOH nanotubes with x ¼ 0.10, the formation of nanoscrolls also occurs. In spite of the fact that Gonza´lez et al. (2014) investigated only the imogolite-Si system, to the best of our knowledge, this is the first attempt to understand the mechanism of imogolite formation considering the effect of the temperature. However, the mechanism of the imogolite formation involves the formation of proto-imogolites, which are self-organizing to form nanotubes, allophanes or amorphous aluminosilicates depending of the pH, ionic strength, temperature and concentration (Yucelen et al., 2011, 2012,

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2013). The acidic constants of the hydrolysed species forming aluminates and silicates are key points for understanding the whole process. The computer modelling of such complex systems is still a challenge, and much effort has to be made towards understanding the imogolite formation at the atomistic level.

14.3.5 Modification of Imogolite The internal and external surfaces of imogolite-Si can be easily modified using different strategies such as creating vacancies, decorating it with different organic groups, changing the reactants to form modified structures or through thermal treatments. The reaction with organophosphonic acids and organosilanes (Bac et al., 2009; Ma et al., 2011, 2012; Amara et al., 2015) modifies the external nanotube surfaces. New developments for modifying the interiors have been reported (Bottero et al., 2011; Kang et al., 2011, 2014; Zanzottera et al., 2012; Amara et al., 2015) enhancing the adsorption properties of the material. A different way of modifying the interior has been suggested by Kang et al. (2010) through dehydroxylation using controlled thermal treatment. These authors have shown that the dehydroxylation occurs predominantly in the interiors of the nanotube. Teobaldi et al. (2009) investigated the hydroxyl vacancies in the outer- and inner-nanotube surfaces using PW91/plane wave calculations. The results indicated that the structure of the nanotube is only slightly modified upon hydroxyl vacancies but occupied and unoccupied states are created, reducing the band gap to 1.8 and 1.1 eV for imogolite-Si and imogolite-Ge, respectively. The orientation and the distances between radial and axial inner hydroxyl surfaces are shown in Fig. 14.5. Kang et al. (2011) carried out reactions of the

OH OH OH OH

3.4 Å OH

OH OH OH OH OH 4.6 Å FIG. 14.5 Inner-surface hydroxyl orientation and the main distances between the radial and axial inner hydroxyl. Adapted from da Silva et al. (2015).

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FIG. 14.6 (A) Inner-surface representations for the modified zigzag (12,0) imogolite nanotube. (B) The optimized structures of the substituted (12,0) imogolite. Adapted from da Silva et al. (2015).

methyltrimethoxysilane, CH3Si(OCH3)3, with imogolite-Si as shown at Fig. 14.6, leading to the formation of methanol. From 29Si NMR data, they have shown that about 24–38% of the silanols are substituted, leading mostly to Z2-imogolite. SCC-DFTB calculations showed that CH3Si(OCH3)3 prefers radial Z2-imogolite, in which the two silanol groups in the same radial line are substituted (da Silva et al., 2015). The Z1-imogolite product leading to one substitution is about 9.1 kJ mol1 (unit cell)1 larger in energy with respect to the most favoured Z2-imogolite product. Furthermore, the axial Z2-imogolite and Z3-imogolite products involving silanol groups in different ˚ between silanol groups radial lines are not favoured. The distance of 4.6 A of different radial lines leads to bonding stress. Calculations were performed for different substitutions (up to 66% of the silanol groups). The calculations performed by da Silva et al. (2015) indicated that the reaction energy is not much affected by the number of substitutions, about 122 kJ mol1 (unit cell)1 on average. Other properties, such as the band gap and Young’s modulus, are slightly affected. However, the dehydroxylation of the silanol groups, leading to Si–O–Si bonding in the inner surface due to the thermal treatment, affects substantially the geometry, band gap and Young’s modulus of the material, as shown in Fig. 14.7. Kang et al. (2010) using 29Si and 27Al NMR experiments showed that up to 73% of the silanol groups were dehydroxylated. Recent calculations performed by da Silva et al. (2015) for dehydroxylation of up to 50% of the silanol groups indicated that the nanotube is much deformed. For 50% of dehydroxylation, the nanotube is hexagonalized and the reaction energy of

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FIG. 14.7 (A) Dehydroxylation reaction scheme in the inner surface. (B) Optimized structures of the dehydroxylated zigzag (12,0) imogolite nanotube. Adapted with permission from da Silva et al. (2015).

dehydroxylation is increased with the number of dehydroxylations in the unit cell. The dehydroxylated nanotube, with 50% of the silanol groups modified, presents a bang gap of about 3.8 eV, which must be compared to 10 eV of the ideal structure. The bulk volume and the Young’s modulus remain practically the same. These authors suggested that the band gap of the imogolite could be controlled by heat treatment upon dehydroxylation. If one takes into account that SCC-DFTB method overestimates the band gap, it is reasonable to conclude that the dehydroxylated imogolite is a semiconductor.

14.4 HALLOYSITE Halloysite nanotubes are more abundant in nature than imogolites. They are mined from natural deposits, and therefore, their use in technological applications has been developed (Rawtani and Agrawal, 2012). Halloysite is a 1:1 layer with the formula Al2Si2O5(OH)4 and it is polydisperse, with lengths of 500–1000 nm and diameters varying between 15 and 100 nm (Veerabadran et al., 2007; Lvov et al., 2008). Halloysite is chemically similar to kaolinite, and it is usually MW, but it can also present as nanoscrolls or nanorolls

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II Structure and Properties of Nanosized Tubular Clay Minerals

C

B

HO

Al

Si O

FIG. 14.8 (A) Side and (B) top view of the monolayer. (C) (12,0) Halloysite nanotube. Adapted with permission from Guimara˜es et al. (2010). Copyright 2010 American Chemical Society.

(Ece and Schroeder, 2007). Fig. 14.8 shows the cross-sectional views of halloysite. SW halloysite nanotube models have been calculated using SCCDFTB (Guimara˜es et al., 2010). The strain energies have been calculated for up to (20,0) halloysites with external diameters of about 3.63 nm. The band gap was estimated to be about 8.4 eV, and the Young’s modulus about 280 GPa. A comparison of the strain energy curves for different aluminosilicate nanotubes was shown in Fig. 14.2 earlier in this chapter. In the range of the diameters investigated, no minimum was found in the strain energy curves. However, extrapolating the curve to larger diameters, it is predicted that a very shallow minimum may exist. In fact, this has been used to explain the large range of diameters normally found for halloysite. Furthermore, according to the SCC-DFTB calculations, no preference is found for zigzag or armchair nanotubes. The hydrated and anhydrous halloysite spiral nanotubes were also calculated using SCC-DFTB (Ferrante et al., 2015). Models consisting of an inner diameter of 5 nm and overlapping arms between one-half and one-third of a revolution were built. Water molecules in the hydrated halloysite nanospirals have been added following the Al2Si2O5(OH)42H2O stoichiometry. The bond lengths are not affected by the spiralization of the kaolinite layer. The spiralization of the kaolinite favours the approach of the water to the surface, leading to some degree of disorder. In the overlapping of the arms, the water molecules are between an upper layer of aluminium oxide and a lower layer of silicon oxide. Water molecule pairs make bridges that connect the two surfaces of the arms. For the anhydrous halloysite, a larger number of AlO–H…(O–Si)2 interactions compensates for the absence of water making

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hydrogen bonds. It has been argued that the disorder of the hydrogen bonding is related to the many minima in the PES with similar energies and very tiny barriers. Therefore, it is more a dynamic linkage between the two surfaces of the arms than a static one.

14.5 CHRYSOTILE AND NANO-FIBRIFORM SILICA Chrysotile is easily found in nature, and it is one of the most common nanostructured silicates. Synthetic and natural MW nanotubes and scrolls have been reported on (Yada, 1967, 1971). The inner and outer diameters have been stated to be in the range of 1–10 and 10–50 nm, respectively, and lengths in the millimetre range (Falini et al., 2004). The formula of chrysotile is Mg3Si2O5(OH)4. The layer of Mg is normally associated with brucite (Mg(OH)2) and the Si layer with tridymite (SiO2) (Fig. 14.9). In addition, SW models have been calculated using SCC-DFTB for both possibilities with tridymite in the outer or inner side of the nanotube (Lourenc¸o et al., 2012). The SCC-DFTB calculations indicated that the tridymite on the inner side is at least 30 meV/atom more stable than the other option. Fig. 14.2 also showed the strain energy curves for zigzag and armchair of SW chrysotile nanotubes calculated in the range of (17,0)–(45,0) and (9,9)–(29,29), corresponding to external diameters in the range between

FIG. 14.9 Structure of (A) lizardite monolayer, (B) cross-sectional views of the zigzag (19,0) and (C) armchair (11,11) chrysotile nanotubes. Reproduced with permission from Lourenc¸o et al. (2012). Copyright 2012 American Chemical Society.

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3.2 and 9.4 nm. The strain energy curves do not present minima. Their stability is not affected by the chirality. It is estimated to be an insulator with a band gap of 10 eV and Young’s modulus are estimated to be in the range of 261–323 GPa. D’arco et al. (2009) performed B3LYP/DFT calculations on SW chrysotile models. Helical symmetry was used for calculating nanotubes in the range of (17,17)–(24,24) armchair. The band gap was estimated to be 6.4 eV, which is about 3.6 eV less than the SCC-DFTB estimated values. Nano-fibriform silica nanotubes (SNT) can be synthesized by removing the brucite layer using acid leaching of chrysotile (Wang et al., 2006a,b). The external surface of the SNT can also be easily modified using organosilanes to produce a functionalized nanotubular silica (MSNT) material (Wang et al., 2009). da Silva et al. (2013) used the same SCC-DFTB approach to investigate the electronic, structural and mechanical properties of SNT and MSNT (Fig. 14.10A). Armchair and zigzag SNT with inner diameter in the A

(n,n) SNT

(n,0) SNT

(n,n) MSNT

(n,0) MSNT

B

Strain energy (meV/atom)

−2 12 10 8 18

−6

20

22

16

−10

14

8

26

28 30 28

30

22

34

24

24

26

16

18

(n,n) SNT (n,0) SNT (n,n) MSNT (n,0) MSNT

16

10

28

20

12

8

30

22

20

10

−12

26 28

38

24

18

12 10

24

22

14

−8

18

16

14

−4

20

14

−14 5

10

15

20

25

30

35

40

45

Inner radius (Å)

FIG. 14.10 (A) Side views of the armchair (n, n) and zigzag (n, 0) of SNT and MSNT; (B) below is the strain energy curves with respect to the inner radius for armchair and zigzag SNT and MSNT. Adapted with permission from da Silva et al. (2013).

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range of 1.6–7.2 nm have been calculated. SNT and modified silica nanotubes (MSNT) are insulators with band gaps estimated to be about 8–10 eV. The strain energy curves showed at Fig. 14.10B present different behaviour than for the other inorganic nanotubes. First, the zigzag is predicted to be more stable for SNT, but upon functionalization with organosilanes, armchair MSNT are more stable than the respective zigzag MSNT. It is interesting to observe that these nanotubes are always more stable than the respective planar layer, as is the case for imogolites. But no minima are observed for SNT and MSNT. The strain energy decreases smoothly up to the smallest nanotube investigated (about 1.6 nm in diameter). According to da Silva et al. (2013), decreasing the diameter of the system will make it collapse to the silica structure. Young’s modulus is predicted to be about 232–260 GPa for the most stable armchair SNT and 150–194 GPa for the zigzag SNT. For the MSNT, the Young’s modulus is estimated to be in the range of 77–89 GPa for the most stable zigzag and 110–140 GPa for the armchair MSNT. These values must be compared to the chrysotile values of 261–323 GPa. The brucite layer outer of the chrysotile nanotubes increases the stiffness of the nanotube. However, it also increases the strain energy favouring the layered structure of the chrysotile called lizardite.

14.6 CONCLUDING REMARKS Computational chemistry investigations of imogolites, halloysites and chrysotiles have been reported using different methodologies. Detailed analysis of the structure and energetics of the rolling of the ideal layer to form the nanotube has been provided. The comparison of the strain energy curves of the different nanotubes shown at Fig. 14.2 is very important for understanding the uniqueness of imogolite. The gibbsite is like a template for developing new nanotubes, in which, depending on the group placed on the octahedral site, replacing the silanol could lead to nanotubes with enhanced properties. From the theoretical point of view, the replacement of the silanol by germanate, phosphate, phosphite, arsenate and arsenite leads to stable structures. The aluminogermanate was already synthesized; however, the synthesis of new imogolite-like structures is still a challenge. The DW imogolite-Ge nanotube also presents a minimum strain energy curve for the (12,0)@(21,0) nanotube. The imogolite-Ge presents a more flat strain energy curve and a more efficient hydrogen bonding interaction between the two tubes, favouring its formation. The same is not predicted for imogolite-Si; since the strain energy curve presents a more pronounced minimum and higher energetic cost, the DW imogolite-Si nanotube formation is not favoured. The synthesis of nanocables based on carbon nanotube@imogolite has been proposed based on computer simulations (Kuc and Heine, 2009). The concept is interesting since the electron transport in the carbon nanotubes would not be affected by

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the environment due to the presence of the isolator imogolite shielding the nanowire. The synthesis of imogolite in the presence of an emulsion of carbon nanotubes could lead to the nanocable. It is expected that self-organization of the proto-imogolites around the carbon nanotube can be achieved by controlling the temperature and ionic strength of the system. Halloysite and chrysotile have also been investigated by means of theoretical calculation. The lack of a minimum in the strain energy curves makes them behave like other inorganic NT that are polydisperse with a wide range of diameters. Insights about the electronic, structural and mechanical properties of SW halloysite and chrysotile nanotubes have been provided. One crucial point is the chemical modification of the inner and outer surfaces of the nanotubes. The computational modelling can provide insights about the effect on the geometry, electronic structures and mechanical properties. Some theoretical calculations have been reported about the modified structures, indicating that the dehydroxylation of the imogolite could be used to fine-tune the band gap. On the other hand, functionalization of the inner silanol groups with organosilanes does not change significantly the structure and band gap of the imogolite. Much effort has been made to understand the mechanism of the formation of imogolites from experimentation. However, the computational modelling of the formation mechanism of the imogolites (or halloysites) in aqueous solution is a challenge. The system is very complex, with an initial oligomer formation of aluminates and silicates, followed by the formation of larger aggregates called ‘proto-imogolites’, which is self-organized to form the nanotube. The structure and the acidic properties of these species are crucial for modelling the nanotube formation. Indeed, the type of acid used (HCl, HClO4, CH3COOH) in the synthesis can significantly change the diameter of the nanotube (Yucelen et al., 2012). However, the solvent effects, the role of the water and ions to the formation of such species are very difficult to be adequately modelled. In fact, the importance of the understanding of this mechanism at a molecular level is an important motivation for improving and developing new approaches for studying species in solution. In spite of the many theoretical calculations reported in the present chapter, computational chemistry has not been fully explored as a way to investigate the aluminosilicate nanotubes. Theoretical calculations can predict spectroscopic data such as NMR, X-ray photoelectron emission, Fourier transform infrared spectroscopy (FTIR), RAMAN, ultraviolet visible (UV-vis) and many other techniques, and the results can be compared directly with the experiments. Actually, a combined experimental/theoretical approach based on sophisticated spectroscopic techniques could fulfil the lack of information about the acid/base behaviour, dynamics of ions and molecules inside of the nanotube, charge distribution between outer and inner-nanotube surfaces at aqueous solution and the mechanism of formation of nanotube and nanoscrolls.

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ABBREVIATIONS B3LYP CLAYFF DFT DFTB DW GGA MD MSNT MW NMR NT PBE PES PW91 SAXS SCC-DFTB SNT SVWN SW XC XRD

three-parameter hybrid method expressed for Becke, Lee, Yang and Parr Clay Force Field developed by Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. density-functional theory density-functional tight-binding double-walled generalized gradient approximation molecular dynamics modified silica nanotubes multiwalled nuclear magnetic resonance nanotubes expressed for Perdew, Burke and Ernzerh€of potential energy surface expressed for Perdew and Wang small-angle X-ray scattering self-consistent-charge density-functional tight-binding silica nanotubes expressed for Slater, Vosko, Wilk and Nusair single-walled exchange-correlation X-ray diffraction

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