J. Phys. Chem. C 2008, 112, 10013–10020
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Molecular Dynamics Study of Hydrated Imogolite. 1. Vibrational Dynamics of the Nanotube Benoıˆt Creton,†,§ Daniel Bougeard,† Konstantin S. Smirnov,*,† Jean Guilment,‡,⊥ and Olivier Poncelet‡,¶ LASIR, UniVersite´ des Sciences et Technologies de Lille, CNRS; Baˆt. C5, Cite´ Scientifique, 59650 VilleneuVe d’Ascq, France, and KODAK European Research, 332 Science Park, Milton Road, Cambridge CB4 0WN, U.K. ReceiVed: January 24, 2008; ReVised Manuscript ReceiVed: April 17, 2008
An atomistic model of imogolite was defined and tested in molecular dynamics simulations. The model is based on the structure by Cradwick et al. (Nature, Phys. Sci. 1972, 240, 187). The interatomic interactions were defined by a generalized valence force field. As the experimental samples are mostly hydrated, water molecules were also included into the model. X-ray diffraction pattern computed from molecular dynamics trajectory well corresponds to the experimental one, thus confirming the validity of structural model. Calculation of the vibrational dynamics of imogolite nanotube shows a good overall agreement between the experimental and the calculated infrared and Raman spectra. The detailed analysis of the vibrational spectra leads to the conclusion that there exist strong couplings between internal coordinates preventing from the complete assignment of the observed bands to a particular coordinate or structural unit. These strong couplings also lead to the appearance of breathing vibrations involving in-phase displacements of all atoms at low frequencies. Origins of the Raman activity of some peaks are analyzed in detail. 1. Introduction Since the discovery of carbon nanoballs and nanotubes in the late eighties, research about this family of compounds has developed to an important part of the work about nanoobjects. The studies in this field were extended by the appearance of inorganic nanotubes like boron nitride, MoS2 or WS2. Other inorganic nanotubes, like imogolite, were rediscovered. Imogolite is a part of the clay fraction of soils originating from volcanic ashes. Its tubular structure was recognized as early as 1972,1 and a synthesis protocol based on the heating of weakly acidic solutions containing hydroxyaluminum orthosilicate complexes was derived some years later.2 The synthesis procedure leads to a very monodisperse distribution of nanotubes suitable for the inbetween proposed potential applications: catalysis,3,4 molecular sieves or absorbents,5,6 composite materials with polymers.7,8 As a consequence of this renewed interest a better knowledge of the structure and properties of imogolite became necessary, but unfortunately the natural as well as the synthetic compound exists only as poorly crystalline hydrated samples. Therefore, the study of the structural and dynamical properties of imogolite has to rely on a complementary approach involving spectroscopic methods assisted by computer simulations in order to improve the interpretation of data obtained earlier in X-ray crystallographic works. Cradwick et al.1 proposed a structure which is the basis of all structural works about imogolite. Imogolite can be understood as a curved gibbsite cylinder in which ortho* To whom correspondence should be addressed. † LASIR, Universite ´ des Sciences et Technologies de Lille. ‡ KODAK European Research. § Present address: IFP, 1 et 4 Avenue du Bois Pre ´ au, 92852 RueilMalmaison, France. ⊥ Present address: ARKEMA-CERDATO, Laboratoire d’Etude des Mate´riaux, 27470 Serquigny, France. ¶ Present address: CEA-Liten, 17 rue des Martyrs, BP 85, 38054 Grenoble, France.
silicic acid is coordinated via oxygen with three aluminum atoms. Aluminum occurs only in octahedral coordination while all silica sites are tetrahedral. The ideal formula (HO)3Al2O3SiOH indicates the order in which the various chemical elements are encountered when going from outside to inside; it also manifests that, in opposition to single-walled carbon nanotubes, the aluminosilicate wall has an important thickness. Another difference appears in the relative stability of the nanotubes with increasing diameter. While the strain energy of carbon nanotubes monotonically decreases with increasing diameter,9 the corresponding curve for imogolite shows a minimum related to the difference of the energies of the Al-O and Si-O bonds.10 This difference can explain the tube curvature1 and the monodispersity of the distribution of the tubes diameters. However, the position of the minimum is still object of discussions. Experimentally Cradwick et al.1 determined a repetition of ten gibbsite units along the tube circumference for natural imogolite. Recently a similar determination for synthetic imogolite led to a repetition of 12 units.11 Several theoretical studies addressed this question with various success.10,12 In ref 10, a molecular dynamics (MD) calculation using the CLAYFF force field finds the minimum at this value, while an earlier MD work12 using a specially designed three-body potential found the minimum for 16 gibbsite units. In a recent DFT study13 fitting the X-ray diffraction patterns the authors concluded that the best agreement was obtained for a repetition of 12 units. Finally things appear to converge in a recent work by Guimaraes et al.14 treating the question with the tight-binding method. A complete scan of (9,0) to (19,0) zigzag and (5,5) to (14,14) armchair imogolite models clearly showed that the zigzag configurations between (9,0) and (15,0) were more stable than all other models and that the minimum was located at the (12,0) repetition. Taking into account the remark that “no claim can be made that the C20h is a closer approach to the true structure than C22h and C24h”1 one can definitely conclude
10.1021/jp800802u CCC: $40.75 2008 American Chemical Society Published on Web 06/14/2008
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Figure 1. C24h model of imogolite with three cylindrical units along the tube axis according to ref 1.
that the C24h symmetry implying the repetition of 12 units is a model representing both natural and synthetic imogolites. Concerning the periodicity along the tube axis all works agree about a translation unit of 8.4 Å.1,15 Finally imogolite is rarely observed as an isolated tube, but usually appears in bundles. Most of the studies assumed a hexagonal close-packed organization of the nanotubes1,12,15,16 and converged to a center-to-center distance of 27 Å. In fact, a more detailed analysis of the X-ray diffraction patterns led to the proposition that the unit cell could be monoclinic (a ) b ) 21.05 Å, c ) 8.51 Å, R ) β ) 90°, γ ) 78°).11 An extensive DFT study13 showed that the best agreement between calculated and observed X-ray pattern is obtained for a ) b ) 24.8 Å and γ ) 64°, i.e., near the hexagonal case with γ ) 60° (in that case the intertubular distance is 26 Å), but that a model with an intertubular distance of 28-30 Å and γ ) 80° would also satisfactory reproduce the experimental data of ref 15 and thus would confirm a monoclinic unit cell. It seems that if one takes into account the eventual systematic errors of the theoretical approach and the quality of the experimental data for such low-crystalline materials, where impurities and water can affect the structure as well as the diffraction data, it is presently impossible to define the structure more precisely. While the preceding presentation shows that several structural questions are already well studied, dynamical processes which are highly relevant for characterization and applications are only poorly understood. The vibrational spectra have been used as fingerprints17–22 but their interpretation is not complete and most of the theoretical works were concentrated on the evaluation of the frequency of a ring breathing mode (RBM) analogous to the mode observed in carbon nanotubes14 or on a comparison of the total density of vibrational states with the infrared spectra.13 Therefore there is a need for a detailed analysis of the vibrational dynamics at the microscopic level in order to assign the spectroscopic patterns and particularly to address the question of the meaning of the concept of RBM in a structure which is not “single-walled” but consists of a wall built of at least five layers of heavy atoms. In the present paper, we will summarize our results concerning the vibrational dynamics of imogolite, while a subsequent one will use the model presented here in order
to study the behavior of confined water molecules.23 For aluminosilicates the most informative part of the vibrational spectra lies in the region up to 1200 cm-1, where the framework modes are localized. That is why the discussion concentrates on the midfrequency range. The paper starts with a presentation of the structural model, of the interatomic potential and of the procedure of the MD simulations. The analysis of the MD results will begin with a validation of the imogolite model through a presentation of structural data which will be followed by a discussion of the vibrational spectra with a particular emphasis on the results relevant to the tubular structure. 2. Computational Procedure and Experiment 2.1. Structural Model of Imogolite. On the basis of the structural data discussed in Introduction, the model of imogolite was defined using a tube with symmetry C24h, i.e., containing 12 repeating units along the circumference, and the cylindrical coordinates of atoms reported by Cradwick et al.1 As the positions of the hydrogen atoms are not given in ref 1, these atoms were added perpendicularly to the outer tube’s surface and with a Si-O-H angle of 117.0° for the inner surface. In both cases, the O-H distance was set to 1.0 Å. Taking into account the still active discussion about the monoclinic and hexagonal crystalline system we decided to choose a hexagonal packing of the nanotubes with one tube in the unit cell and a unit cell dimension of 29 Å for the a and b directions, which is of the order of magnitude of the experimental values.15,24–27 In order to ensure similar sizes of the simulation box in all directions, three cylindrical units were used along the tube axis; therefore the MD box had following dimensions: a ) b ) 29.0 Å, c ) 25.2 Å, R ) β ) 90°, γ ) 60°. The resulting model is presented in Figure 1, where the notation used throughout the paper for the atoms of the structure is defined. In order to treat hydrated imogolite the volumes inside and outside of the nanotube in the MD box have to be filled with water molecules. The internal volume of a tube was evaluated as the volume of a cylinder with a radius corresponding to the distance of the internal oxygen atoms (Oi) to the tube axis. Accordingly, the intertubular void was evaluated as the difference between the volume of the MD box and the volume of the cylinder with a radius equal to
MD Study of Hydrated Imogolite
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TABLE 1: Parameters of Charge-Free Potential (2) for the Interactions between Hydroxyl Groups on Imogolite Surfaces -1
DHB (kJ mol
)
37.674
σHB (Å)
CHH (kJ mol
2.60
-1
Å 6)
564.656
n
m
l
atom
Ho
Oo
Al
Oc
Si
Oi
Hi
9
6
2
charge
0.3225
-0.9662
1.7782
-1.2744
2.8933
-1.0726
0.3773
the mean radius of the outer hydrogen atoms Ho. In the present study it was assumed that the water density was identical for both the internal and external spaces. Thirty water molecules were randomly inserted inside the tube and 82 in the outer void. The corresponding weight percentage of 14.1% with respect to the weight of imogolite, or 12.4% with respect to the total weight of the sample, is of the order of the experimental values under low relative humidity.28 2.2. Potential Model. The potential energy U of the system was represented as
U ) UWW + UI + UWI ,
(1)
where the three terms stand for the potential energy due to the water-water, intraimogolite, and water-imogolite interactions, respectively. As we were not interested in the vibrational dynamics of the water molecules, they were considered as rigid bodies and the intermolecular UWW interactions were described with the SPC model.29 The imogolite structure was treated as flexible and the UI interactions were described with a generalized valence force field model. Values of the force constants for the imogolite were transferred from our previous studies on aluminosilicates30–32 The equilibrium values of the internal coordinates (bond lengths and bond angles) were taken to be equal to those determined by Cradwick et al.1 for natural imogolite. As the electrostatic and van der Waals interactions are implicitely included into the UI potential model, they were not considered for atoms of the solid. Consequently, to account for the interactions between the hydroxyl groups of the imogolite surfaces, a charge-free hydrogen-bond potential used in modeling hydrated allophane nanosphere33 was employed to describe the interactions between the OH groups of imogolite. The functional form of the potential is similar to chargefree H-bond potential of the DREIDING force field34 and reads
[( ) ( ) ] [ ( ) ( )]
UOH ) 4εOO
σOO rOO
12
-
σOO rOO
6
s
+ DHB p σHB rOO
m
TABLE 2: Charge of Imogolite Atoms (in au) Determined with the Electronegativity Equalization Method; the Atoms’ Names As in Figure 1
σHB n rOO
cosl θOHO +
CHH 6 rHH
(2)
where s ) n/(n - m) and p ) s - 1. In eq 2, rOO, rHH, and θOHO are the distances between the oxygen and hydrogen atoms of the OH groups and the O-H-O angle, respectively. The values of the parameters OO and σOO are equal to those of the SPC water model, whereas the parameters DHB, σHB, l, m, n, and CHH were determined by optimizing the heat of formation, the three radial distribution functions, and the center-of-mass vibrational spectrum of water molecules in the bulk liquid water. The corresponding reference data were calculated using the SPC model for a system of 256 H2O molecules at density 1 g cm -3 at the temperature 293 K. Values of the optimized parameters are listed in Table 1. Additional calculations of the self-diffusion coefficient, the relaxation times of the molecular dipole and HH vectors, and the number of hydrogen bonds for molecules in the liquid water have shown a good agreement of these quantities with their experimental and/or calculated values.35
The water-imogolite UWI interactions were represented as the sum of electrostatic and Lennard-Jones (12-6) potential functions. The electrostatic interactions were considered between all types of atoms, whereas the van der Waals interactions were taken into account only between the oxygen atoms of the water molecules and those of the imogolite tubes through potential parameters of the SPC water model. The partial charges of atoms in the imogolite structure were determined by the electronegativity equalization method with the parameters taken from ref 36. The charge values are gathered in Table 2. The comparison of the charge values with other sets of charges available in the literature13,14 for the imogolite structures shows that the relative values of the charges are in a fair agreement taking into account the methodological differences used for their derivation. The electrostatic energy and forces deriving from the UWW and UWI terms in eq 1 were computed with the Ewald sum method. 2.3. Molecular Dynamics Calculations. The model of imogolite presented above was used in MD calculations. The hexagonal MD simulation box contained 1008 atoms of the solid and 336 atoms of the water molecules. At time t ) 0, the water molecules were distributed randomly in the available space and the initial atomic and angular velocities were taken from a Maxwell distribution. The equations of motion of the imogolite atoms and of the centers of mass of the water molecules were integrated with the velocity Verlet algorithm, while a 4th-order predictor-corrector algorithm was used to solve the equations for the rotational degrees of freedom of the H2O molecules. The integration time-step was equal to 0.5 fs. The simulation began with a 50 ps equilibration period and then continued in the canonical ensemble for the next 150 ps. The atomic coordinates and velocities were stored every 2.5 fs during the last 100 ps (production period). The first ten picoseconds of the equilibration period were performed for the temperature 700 K and they were then followed by 40 ps of annealing stage during which the system was cooled down from 700 to 300 K. Such a scheme permitted to avoid possible artifacts due to the choice of initial conditions. The stored trajectory was used to derive structural characteristics and the vibrational spectra of the system. The infrared spectrum was computed from the charges and atomic velocities. The Raman spectrum was calculated from the time history of the polarizability tensor of the system. The tensor was obtained with the bondpolarizability model (BPM). The electro-optical parameters (EOPs) of BPM are reported in ref 37. The interested reader can find an in-depth discussion of the methodology of the spectra calculations in refs 37-41. Both the MD calculations and the analysis of the MD trajectories were carried out using codes developed in the laboratory. 2.4. Experiment. Imogolite sample was synthesized by the procedure described elsewhere.8,42 The quality of the samples was verified with the inductive coupled plasma atomic emission spectroscopy (ICP-AES) method on a Varian Vista X apparatus. The solid state MAS 29Si and 27Al NMR spectroscopy (300 MHz Bruker spectrometer) was used to
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Figure 2. Experimental (solid line) and calculated (dashed line) X-ray diffraction pattern of imogolite. The experimental spectrum was adapted from Figure 1 of ref 28. Figure 3. Density of vibrational states (DVS) and power spectra of atoms of imogolite structure.
quantify the environment of Si and Al atoms in the samples. Further characterization was done by transmission electron microscopy using a TEM Philips CM12 (120 kV) microscope; ethanol and propanol were used to disperse the gels and prepare the samples. The infrared spectra were obtained from imogolite dispersed in KBr pellets (2.5 mg of imogolite for 1 g of KBr) and were recorded on Bruker IFS 66 spectrometer with 4 cm-1 resolution, 64 scans. The Raman spectra were measured from powder imogolite samples on FT-Raman Bruker RFS 100 spectrometer with the excitation wavelength 1024 nm, laser power of 800 mW, 512 scans. The scattered radiation was collected in a back-scattering mode (180° geometry) with a hemicylindrical mirror objective allowing compensation for the powder form of the samples. TEM image and NMR spectra of representative imogolite samples are available as Supporting Information to this paper. 3. Results and Discussion 3.1. Structural Characteristics. Figure 2 compares the XRD pattern measured28 with CuK R radiation with that calculated for the same wavelength. The calculation was performed as43
[
I(2θ) ) (1 + cos2 2θ)
∑ fi2(s, i) + ∑ fi(s)fj(s) i
i,j>i
sin srij srij
]
(3) where s ) 4π sin θ/λ, λ being the wavelength of the incident radiation, rij is the distance between atoms i and j, and fi(s) is atomic scattering factor for atom i. The latter were computed by using their analytical approximation (CromerMann coefficients).44 Because of the finite size of the MD simulation box, the calculated XRD pattern does not cover small values of 2θ angles (long distances). Analysis of Figure 2 reveals a good correspondence between the measured and calculated XRD spectra and thus justifies the use of the structural model. The agreement between the patterns is as good as in other works treating this issue.13,14 The authors of ref 12 observed a deformation of the circular section of their anhydrous model during the molecular dynamics. A similar behavior was also observed in our study of a hydrated model. In order to quantify this effect the ellipticity of the tube was followed as a function of time. For this purpose the tube diameters were defined as distance between opposite Oc atoms; at the beginning of the production
period the shortest and largest diameters were identified and followed all along the run. It appears that the imogolite’s section remains elliptical during the whole run and the diameters can be evaluated to 15.78 ( 0.46 and 17.57 ( 0.42 Å, indicating a permanent and significant departure from a circular section. 3.2. Vibrational Spectra. The analysis of the vibrational spectra is obviously aimed at finding correlations between features in the spectra and the structure of imogolite nanotube. Figure 3 shows the calculated density of vibrational states (DVS) in the region of framework vibrations (up to 1200 cm -1). Completing the DVS with the power spectra of atoms obtained by Fourier transformation of the velocity of atoms of different types (Figure 3) permits to separate the spectra into two regions. In the first region from 700 to 1100 cm-1 only the atoms constituting the SiO4 tetrahedra move (Oi, Si and Oc). The spectrum of aluminum atoms does not reveal a notable intensity in this zone and one can therefore assume that the outer layer of the imogolite tube (Al and, to a lower extent, Oo atoms) is at rest. Further analysis shows that in the lowfrequency part of this region (at ca. 840 cm -1) the silicon atoms do not move, while Oi and Oc atoms do. Such vibrations involving displacements of four terminal atoms of a tetrahedron while leaving the central atom in place are due to the totally symmetric stretching mode of the tetrahedron. The bands at 940-970 cm -1 can then be ascribed to asymmetric stretching modes of the tetrahedra. This supposition can be verified by calculating the power spectrum of the symmetry coordinates formed by the Si-O bond stretching coordinates in the assumption of Td symmetry of the tetrahedra. The result is presented in Figure 4 (curves a and b) and the interpretation of the spectra deserves some comments. The four symmetry coordinates used correspond to an ideal isolated SiO4 tetrahedron and should lead to two modes of A1 and F2 symmetries. However, the site symmetry of the tetrahedra in imogolite is different from Td. As the Si-Oi bond differs from the three other Si-Oc bonds, a C3V symmetry could be supposed; in that case the totally symmetric mode would remain of A1 symmetry, whereas the F2 mode would split into one A1 mode and one doubly degenerate E mode. Furthermore, the symmetry of the
MD Study of Hydrated Imogolite
Figure 4. Spectra of the symmetry coordinates of SiO4 tetrahedra and AlO6 octahedra. Curves a and b present the spectra of the A1 and F2 coordinates of the tetrahedra, respectively. Curves c and d show the spectra of A1 coordinate of Al(Oc)3 and Al(Oo)3 entities, respectively.
crystallographic site reduces to a mirror plane so that finally in the Cs symmetry the two modes expected for the Td symmetry could give rise to four bands (3A′+1A′′). The spectra a and b in Figure 4 nicely correspond to the expectation as one mode generated by the totally symmetric A1 coordinate is calculated at 842 cm-1, while three peaks due to the F2 coordinates appear at 943, 958, and 970 cm -1 We have further to consider that each imogolite structural unit contains two tetrahedra connected by a screw axis and that the unit is repeated 12 times around the circumference of the tube. Therefore, each vibrational mode can give rise to 2 × 12 ) 24 vibrations which can dynamically couple and appear as band splitting. Probably for this reason the calculated bands have not a symmetric profile. In the second spectral region, below 700 cm-1, the power spectra of atoms show that the DVS is due to modes involving displacements of all atoms. Nevertheless one can attempt an assignment of some modes to structural subunits of imogolite, in particular to the AlO6 octahedra. Assuming the Oh symmetry the six Al-O bonds of an isolated ideal octahedron should result in three bands (1A1g + 1Eg + 1F1u) from which only the Eg and F1u ones should appear in the power spectrum of aluminum because the totally symmetric mode A1g yields no displacement of the atom. Calculation of spectrum of the A1g coordinate of the octahedron model shows a spectrum spread over the whole spectral range thus revealing that the totally symmetric linear combination of Al-O bond stretchings is not a normal coordinate of the structure. Taking into account the chemical environment of aluminum it is also possible to conceive the octahedron as a superposition of two C3V entities (AlOc and AlOo pyramides) giving rise to four bands (two times 1A1 + 1E modes). Results for the C3V model are not convincing as well (curves c and d Figure 4). The totally symmetric A1 combinations of the two AlO3 entities have resembling spectra but can by no means be considered as normal coordinates. Similar spectral patterns are obtained for the degenerate E symmetry coordinates (not presented in the figure). The matter is obviously complicated by the fact that the site symmetry of these entities is lower than the symmetry of the entities and that, like for the tetrahedra, a splitting due to the descent in symmetry could appear. Furthermore, the octahedra cannot be considered as isolated
J. Phys. Chem. C, Vol. 112, No. 27, 2008 10017
Figure 5. Experimental and calculated infrared spectrum of imogolite. Dashed line shows calculated infrared spectrum of liquid water in the region of imogolite lattice vibrations.
Figure 6. Experimental (a) and calculated (b and c) Raman spectra of imogolite. The spectrum b was obtained with modified set of electro-optical parameters; see text for discussion.
because the spectrum of the Oc side has a contribution above 800 cm-1 indicating a coupling of the Al-Oc and Si-Oc bond stretchings. Note that it is not the case for the Oo side. Therefore, we come to the conclusion that in this spectral region it is rather difficult to assign a vibrational mode to a definite motion of structural units. The infrared and Raman spectra are presented in Figure 5 and Figure 6, respectively. As for many aluminosilicates the information content of the infrared spectrum is rather low due to the fact that the samples are usually hydrated and consequently, the highest intensity in the spectrum results from water adsorbed in the voids between imogolite bundles and on the surface of microcrystals. Thus, the band around 600 cm-1 in the experimental spectrum in Figure 5 can be attributed to the libration motions of such water molecules, which are calculated in the same region for the model of liquid water (dashed line in Figure 5). It is, however, possible to recognize some spectral features due to the nanotube vibrations (430, 505, 690, 950, and 985 cm -1), some of which appear as shoulders of the large band at 600 cm-1. Bands at similar positions are also present in the calculated spectrum. Using the previous discussion the band at 690 cm-1 can be assigned to asymmetric stretching vibrations of the octahedra while the bands at 950 and 985 cm-1 belong to the antisymmetric stretching modes of the tetrahedra.
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Figure 7. Raman spectra of imogolite in the zone 600-1100 cm-1 calculated with (a) longitudinal valence electro-optical parameter of the Si-Oc bond scaled by the factor 0.5; (b) longitudinal valence electro-optical parameter of the Al-Oc bond scaled by the factor 0.5; (c) modified set of EOPs (see text for discussion); the complete Raman spectrum is shown in Figure 6, curve b. (d) The curve presents the experimental spectrum.
The information can better be extracted from the Raman spectrum because the scattering cross-section of water is low and thus, the spectrum generally reflects the dynamics of the solid. The comparison of the experimental and the calculated spectra in Figure 6 (curves a and c) shows a good general agreement; each experimental peak finds its calculated counterpart, except for the band around 860 cm-1. In a previous paper on allophane,33 where a similar peak was also observed but not calculated, we suggested that the missing intensity could be due to the use of the zero-order bond polarizability model. We introduced parameters taking into account in imogolite the variation of the Si-Oi bond polarizability upon the Si-Oi-H angle variations, thus using a first-order BPM, but unfortunately this was not sufficient for reproducing the intensity of that band. Therefore, a more detailed analysis of the Raman activity of the modes in the region between 600 and 1100 cm-1 had to be performed. As it was discussed above the mode around 860 cm-1 can be ascribed to a symmetric stretching mode of the SiO4 tetrahedra. On the other hand, because of the particular structure of imogolite, such a mode also belongs to the AlO6 octahedra through the motions of the Oc atoms (see Figure 3). Accordingly the valence electro-optical parameters (EOPs) of the Si-Oc and Al-Oc bonds were varied one by one and were then used in the calculations of the Raman spectra of imogolite. Taking into account that the transversal EOPs have a better transferability, only longitudinal EOPs were changed.37 The results of these calculations are presented in Figure 7 (curves a and b) and show that a new peak at 825 cm-1 appears in the calculated Raman spectra that can account for the observed Raman intensity at 860 cm-1. After several trials aimed at understanding the EOPs driving the intensities of peaks in this frequency range an extreme solution was found. It consists in setting the parameters for Si-Oc bonds to zero and dividing those of Si-Oi ones by a factor of 2. The resulting calculated Raman spectrum shown in Figure 7 (curves c) clearly indicates a good agreement of the intensities without deterioration of the quality of the complete Raman spectrum (Figure 6, curve b). It is not the aim of the present paper to develop a new set of EOPs for the study of the particular system, but the result puts in
Creton et al.
Figure 8. Spectrum of the radial breathing coordinate B(t) (eq 4) defined with the use of Oo, Oc, and Oi atoms (cf. Figure 1 for the notation).
evidence the limitation of the set of parameters in the present case. A first possible reason for this is that the molecule database used for the calculation of the EOPs did not contain molecules with Si-O-Al bridges involving octahedral aluminum atoms.37 Second, the folding of the aluminosilicate layer in imogolite certainly induces strains in the bonds which can result in unusual values of the EOPs. The extreme values used in the last calculation cannot be considered as basis for a physical interpretation but the trend indicates that in the present structural configuration the polarizability of the Si-Oc bonds of the tetrahedra seems to vary very little when the bond length is changed by comparison with their behavior in other silicates. Finally, it is worthy of noting that the difference of 35 cm-1 in the positions of the observed and calculated peak is obviously due to the use of a generic force field, which equally well works for the spectra calculation of numerous aluminosilicate structures (silica polymorphs, zeolites, clays). At the other end of the Raman spectrum a high intensity band with a maximum at 47 cm-1 is calculated which can correspond to the ring breathing mode (RBM) postulated in analogy to the corresponding mode in carbon nanotubes by previous authors10,14 at 46 and 54 cm-1. While in singlewalled carbon nanotubes the RBM concerns only one layer of carbon atoms, the correlation with imogolite is not obvious because the aluminosilicate nanotube is built from five layers of heavy atoms over a thickness of about 5 Å and connected by a complex network of bonds oriented in different ways with respect to the tube’s axis. Therefore, nothing warrants that all layers vibrate at the same frequency corresponding to one single breathing normal mode. To investigate this issue, we defined a breathing coordinate B(t) for each atomic layer as N⁄2
B(t) )
∑ di(t),
(4)
i)1
where N is the number of units forming the tube circumference (N ) 12 in the present case) and d is the distance between the opposite atoms. The Fourier transformation of the autocorrelation function of this coordinate yields for each type of atom the corresponding spectrum of the breathing coordinate. The results obtained for the different oxygen types are presented in Figure 8. The main feature is the presence in the spectra for all
MD Study of Hydrated Imogolite atoms (including silicon and aluminum not shown in the figure) of one intense structured feature at the place where the high intensity band appears in the Raman spectrum (see Figure 6). No other vibrational mode in another frequency range shows a significant participation in any of these coordinates. The detailed analysis of the spectrum permits the identification of at least three peaks at 32, 42, and 47 cm-1. These peaks can also be identified in the calculated Raman spectrum with different properties in terms of polarization (the first band is present exclusively in the anisotropic part of the spectrum, while the two others components are partly polarized). We can therefore conclude that, as the complex structure can suggest, breathing motions of the tube do not reduce to one single mode, but give rise to a narrow band between 30 and 50 cm-1 containing several modes involving all atoms of the tube. The fact that the spectra of the breathing coordinates have a broader signal than expected in previous works and that this signal also appears as broad and partly as polarized bands in the Raman spectrum can probably be assigned to the fact that the finite temperature and the presence of water molecules in the MD simulations induce a dynamical elliptical deformation of the tube (cf. Section 3.1) leading to a variation of the modes frequencies. The presence of the RBM at rather low energy in comparison with carbon nanotubes is due to the fact that, while the stretching force constants are of the same order of magnitude for all nanotubes, the reduced mass is much higher for the thick flexible wall of imogolite than for the singlewalled carbon and BN nanotubes. One should finally notice that these normal modes are a combination of most of the totally symmetric combinations of the various internal coordinates and also include participations of angle deformations necessary to conserve the tube symmetry during a breathing vibration. It could appear interesting to pursue the analogy with single-walled nanotubes and to look for analogues to the tangential G modes.45 Unfortunately, such a search seems to be hopeless for at least two reasons. First, no mode of the structure can be identified as such a mode as in the case of the graphene band around 1600 cm-1 in the spectra of carbon nanotubes. In aluminosilicates, characteristic bands could only be assigned to small three- or four-membered rings in aluminosilicates; however even this assignment is still under discussion.46,47 In the case of imogolite, the feature would be due to six-membered rings for which no characteristic modes are expected.48 Second, even if a correlation between structure and spectral pattern would exist the corresponding bands would appear in the region between 600 and 200 cm-1, where the density of vibrational states is so high that their identification could not be unequivocal. Finally, as we have seen in the middle-frequency range, the complex structure of the imogolite wall leads to couplings impeaching the localization of vibrations on structural units. Therefore, such a search of a G mode analogue was not performed. 4. Conclusions In an attempt to improve the description of imogolite at the microscopic level and as a support for the analysis of experimental data a molecular dynamic model of imogolite was defined and tested. The structural model is based on the well accepted structure of Cradwick et al.1 The potential was defined with the help of a generalized valence force field transferred without modification from previous works on aluminosilicates, zeolites, and clays. As the experimental samples generaly exist in hydrated form, water molecules
J. Phys. Chem. C, Vol. 112, No. 27, 2008 10019 were also included into the model. It turns out that this model is able to reproduce experimental X-ray pattern. The model was then applied to study the vibrational spectra of the nanotube. The overall agreement between the experimental data and the calculated infrared and Raman spectra are very satisfactory. However, the discrepancies caused by the use of generic models for the calculation of both the frequencies and intensities in the vibrational spectra point to particular characteristics of the chemical bonds in the curved aluminosilicates. The infrared data are characterized by the strong spectral signature of water, but the imogolite pattern appears in the middle-frequency range of the spectrum. A detailed analysis of the Raman spectra leads to two main conclusions. It turns out that the complex structure of the imogolite wall and strong couplings of the various internal coordinates permit only partial assignment of the observed bands to modes localized on particular internal coordinates or structural subunits. These strong couplings also result in the appearance of ring breathing vibrations involving in-phase displacements of all atoms at low frequencies. These results concerning the imogolite nanotube will be followed by a detailed analysis of the behavior of confined water in the hydrated structure.23 Acknowledgment. B.C. is grateful to Eastman Kodak Inc. for the financial support in the framework of KODAK Research Fellowship program. Supporting Information Available: TEM image and NMR spectra of imogolite samples. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Cradwick, P. D. G.; Farmer, V. C.; Russel, J. D.; Masson, C. R.; Wada, K.; Yoshinaga, N. Nature, Phys. Sci. 1972, 240, 187. (2) Farmer, V. C.; Fraser, A. R.; Tait, J. M. J. Chem. Soc.; Chem. Commun. 1977, 13, 462. (3) Imamura, S.; Kokubu, T.; Yamashita, T.; Okamoto, Y.; Kajiwara, K.; Kanai, H. J. Catal. 1996, 160, 137. (4) Marzan, L. L.; Philipse, A. Colloids Surf. A 1994, 90, 95. (5) Denaix, L.; Lamy, I.; Bottero, J. Y. Colloids Surf. A 1999, 158, 315. (6) Wilson, M. A.; Lee, G. S. H.; Taylor, R. C. Clays Clay Miner 2002, 50, 48. (7) Yamamoto, K.; Otsuka, H.; Takahara, A. Polym. J. 2007, 39, 1. (8) Poncelet, O. J. C.; Rigola, J. U.S. Patent 5,888,711, 1999. (9) Mintmire, J. W.; White, C. T. Carbon 1995, 33, 893. (10) Konduri, S.; Mukherjee, S.; Nair, S. Phys. ReV. B 2006, 74, 033401. (11) Mukherjee, S.; Bartlow, V. M.; Nair, S. Chem. Mater. 2005, 17, 4900. (12) Tamura, K.; Kawamura, K. J. Phys. Chem. B 2002, 106, 271. (13) Alvarez-Ramirez, F. Phys. ReV. B 2007, 76, 125421. (14) Guimaraes, L.; Enyashin, A. N.; Frenzel, J.; Heine, T.; Duarte, H. A.; Seifert, G. ACS Nano 2007, 1, 362. (15) Bursill, L. A.; Peng, J. L.; Bourgeois, L. N. Philos. Mag. 2000, 80, 105. (16) Pohl, P. I.; Faulon, J. L.; Smith, D. M. Langmuir 1996, 112, 4463. (17) Wada, S. I. Clays Clay Miner. 1987, 5, 379. (18) Koenderink, G.; Kluitmans, S.G.J.M.; Philipse, A. P. J. Colloid Interface Sci. 1999, 216, 429. (19) Tani, M.; Liu, C.; Huang, P. M. Geoderma 2004, 118, 209. (20) McCutcheon, A.; Hu, J.; Kannangara, G. S. K.; Wilson, M. A.; Reddy, N. J. Non-Cryst. Solids 2005, 351, 1967. (21) Abidin, Z.; Matsue, N.; Henmi, T. J. Comput.-Aided Mol. Des. 2007, 14, 5. (22) Konduri, S.; Mukherjee, S.; Nair, S. ACS Nano 2007, 1, 393. (23) Creton, B.; Bougeard, D.; Smirnov, K. S.; Guilment, J.; Poncelet, O. Phys. Chem. Chem. Phys., 2008, DOI: 10.1039/b803479f. (24) Ackermann, W. C.; Smith, D. M.; Huling, J. C.; Kim, Y. W.; Bailey, J. K.; Brinker, C. J. Langmuir 1993, 9, 1051. (25) Farmer, V. C.; Fraser, A. R. International Clay Conference, Oxford; Elsevier: Amsterdam, 1978; p 547. (26) Clark, C. J.; McBride, M. B. Clays Clay Miner. 1984, 32, 291.
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