NANO LETTERS
Thermodynamic Stability of Discrete Fully Coordinated SiO2 Spherical and Elongated Nanocages
2004 Vol. 4, No. 8 1427-1432
S. T. Bromley Ceramic Membrane Centre “The Pore”, Delft UniVersity of Technology, Delft, Julianalaan 136, 2628 BL Delft, The Netherlands Received May 5, 2004; Revised Manuscript Received June 9, 2004
ABSTRACT Atomically well-defined discrete fully coordinated spherical and elongated nanocages constructed from SiO2 are shown, via density functional calculations, to be structurally stable. Generally the spherical nanocages are energetically preferred over the elongated nanocages. With increasing size, both types of nanostructures are shown to be increasingly thermodynamically stable with respect to known terminated silica nanostructures and bulk alpha-quartz. The structural and low-energy cluster growth characteristics of SiO2 are compared with that of carbon nanostructures showing intriguing correspondences.
Silica nanostructures with dimensions on the order of a single nanometer can now be controllably fabricated in a variety of distinct topological forms (e.g., nanopores,1 nanospheres,2 nanotubes3), giving rise to applications in optics,4 drugdelivery,5 microelectronics,6 and catalysis.7 The incredible diversity of silica nanoarchitecure is also exhibited in some microorganisms,8 exhibiting distinct intricate shell details down to the 10 nm scale. Although other oxides have also been tailored on the nanoscale,9 silica is particularly interesting as a molecular building material due to its bulk stability and the ease with which its inherent structural richness can be exploited via a range of synthetic methods. Furthermore, SiO2 can act as a prototype nanooxide, with the recent demonstration that silica nanostructures can be isostructurally transformed into other technologically important oxides (e.g., TiO2, ZrO2) via shape-preserving displacement reactions.10 Although the range of synthetic and natural silica nanostructures is impressive, almost all are based upon the condensation and/or manipulation of amorphous silica constituted from essentially random molecular networks. In this letter we show via density functional theory (DFT) calculations that, at the nanoscale, SiO2 may not only be stabilized as atomically well-ordered fully coordinated discrete structures (i.e., without terminating defects) but that such well-defined silica nanostuctures appear to be thermodynamically favorable, pointing to new levels of control and functionality for oxidebased nanotechnology. Recently, by way of a simple topological transformation of a terminated SiO2 chain into a fully connected nanoring, we demonstrated that fully coordinated silica nanostructures could be thermodynamically favored over certain terminated 10.1021/nl049330y CCC: $27.50 Published on Web 07/17/2004
© 2004 American Chemical Society
clusters.11 Fully coordinated silica clusters have subsequently been utilized as model systems for studying the vibrational modes on bulk silica surfaces12 and for investigating the hydration properties of nanosilica structures.13 We have further pointed to the potential of fully coordinated SiO2 clusters as building blocks for new materials11,14 and suggested possible routes to their synthesis.15 Atomically wellordered SiO2 cages and tubes are known to exist, but only (thus far) as integral constituent parts of extended periodic frameworks known as zeolites.16 Such materials, although having open topologies, are also only marginally higher in energy than alpha-quartz, the lowest energy form of bulk silica. The high stability of zeolitic crystalline SiO2 materials based upon well-ordered nanoscale cages together with their recognized utility for molecular control begs the question of whether such cages can exist as stable discrete nanoscale structures independent of a host framework. In former investigations we found that it was tractable to efficiently survey the phase space of different small cluster polymorphs ((SiO2)N N ) 6-12) using global optimization methods. Due, however, to the exponentially increasing number of cluster isomers with increasing number of atoms and the growing complexity of the potential energy landscape, such an approach was not adopted for the larger clusters (consisting of 54 and 72 atoms for the N ) 18 and N ) 24 clusters, respectively) presented herein. From previous work, however, we noticed that, although with an increasing number SiO2 units (all of which can be considered to be at the “surface” of the cluster) the potential for more surface defects is greater, larger low energy clusters tend to have proportionally fewer terminating defects than smaller
Figure 1. Formal vertex topology correspondence between hybridized carbon centers and silica centers.
clusters.18 Another study on nanoscale SiO2 clusters also noted that the passivation of terminating defects seemed to lead to lower energy (SiO2)24 cluster structures.19 The above considerations have led us to concentrate on the interesting limiting case of discrete silica nanocluster cages exhibiting no terminating defects, i.e., fully coordinated clusters, to investigate their energetic and structural stability. When constructing fully coordinated nanostructures from a formally tetrahedrally coordinated material such as SiO2, it should be noted that there is no natural planar-like coordination center that can facilitate the formation of sheets and cages. Planar triply connected sp2 vertices are common in carbon nanostructures due to the electronic flexibility of the carbon atom. Similarly, for materials such as BN,20 Al2O3,21 and ZnS,22 the bonding requirements of the atoms make sheets and cages formed from meshes of planar threeconnected vertices more feasible. Although silica is apparently hindered in this respect, SiO2 displays an immense structural versatility, allowing for structures far more diverse than simple close-packed crystals as found in many other oxides. This propensity for structural richness can be largely traced to the relatively covalent character of the Si-O bond
and the high flexibility of the Si-O-Si bridge. In the bulk limit, porous zeolites typify these characteristics whereby silicon atoms sit at the center of SiO4 tetrahedra forming complex three-dimensional networks in a manner analogous to carbon atoms in materials such as diamond; the Si-OSi bridge and the C-C single bond performing a similar role. To form discrete, fully coordinated nanostructures in silica, however, it is desirable to similarly have a mechanism whereby silicon centers can also be at near-planar threeconnected vertices. The sp2 three-connected carbon center is formally depicted as two single bonds and one double bond. In silica, due to the relaxed nature of the Si-O-Si linkage, we can form such a center, whereby the double ‘bond’ becomes two Si-O-Si linkages joining two vertex atoms, forming a so-called ‘two-ring’ (Si2O2). This formal correspondence between carbon hybridized centers and SiO2 centers is shown in Figure 1. For both spherical and elongated, fully coordinated (SiO2)N nanocage clusters, we examined structures for N ) 12, 18, and 24, utilizing various combinations of tetrahedral (four single-oxygen-bridged structure centers) and planar (one double-oxygen bridge and two single-oxygen bridges) SiO2 centers. The elongated nanocages were obtained as naturally truncated versions of the large repeated six-ring (SiO)48 nanotube reported previously as a part of a classical interatomic potential study.13 For our elongated nanocages, energy-minimized using DFT, it was found that the two sets of three double-oxygen bridges at either end of the tubes should be anti-aligned (as opposed to aligned as in ref 13) in order to obtain a lower energy tubular structure, see Figure 2. For the (SiO2)N N ) 12, 18, 24 spherical nanocages, regular three-coordinated polyhedra were used as templates from which silica cages, using only “planar” SiO2 centers, were built. For N ) 12 we employed the truncated tetrahedon (B-12) and the hexagonal prism (A-12), see Figure 3. The hexagonal prism is also known as the double six-ring in the zeolite literature, being a common interlinking building unit
Figure 2. DFT energy minimized (SiO2)N N ) 12, 18, 24 fully coordinated elongated nanocages. 1428
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Figure 3. DFT energy minimized (SiO2)N N ) 12, 18 fully coordinated nanocluster structures. A-12 is a fully coordinated double six ring (structurally distinct from the smallest elongated nanocage, T-12, due to a different, lower energy arrangement of double oxygen bridges), B-12 is a truncated tetrahedron, and A-18 a fully coordinated version of a cage often found in zeolites.
in numerous zeolite framework types,23 e.g., MSO and OFF. For N ) 18, a discrete, fully coordinated polyhedron consisting of six square faces and five hexagonal faces, as found in the silica-based frameworks ERI, OFF, and SAT, was constructed, see structure A-18 in Figure 3. For the fully coordinated (SiO2)24 cluster structures, we constructed a truncated cube (C-24), a truncated octahedron (B-24), as found in, e.g., SOD, FAU, and LTA, and (A-24), the 20-
vertex fullerene structure, as found in MEP and in carbon as a discrete fullerene cage,24,25 see Figure 4. All sets of fully coordinated silica nanostructures were subsequently energyminimized as closed shell systems, employing no symmetry constraints, using the B3LYP exhange-correleation functional26 and a 6-31G(d) basis set for both oxygen and silicon atoms using the GAMESS-UK27 DFT module. This level of theory has previously been shown to be suitable for assessing both the energetics and geometries of silica nanoclusters.28 For each nanocage of formally fixed connectivity between silicon vertices, various alternative structures with different choices of the arrangement of the double-oxygen bridges were also energy minimized and the lowest energy forms reported herein. In Figures 3 and 4 the energies of the nanocage clusters are ordered alphabetically (isomer A being lowest in energy). First it is noted that in all cases the discrete, fully coordinated silica nanostructures were structurally stable after DFT energy minimization and did not collapse into other lower lying terminated states. It is important to stress that no restrictions on the symmetries of the clusters were imposed and that all structures possesed well-defined energetic minima having all positive Hessian eigenvalues. From a previous study employing classical molecular dynamics, it is also noted that the larger spherical nanocages also appear to be particularly thermally stable.15 The total energies (eV/ SiO2) of all DFT energy-minimized stable nanocages,
Figure 4. DFT energy minimized (SiO2)N N ) 24 fully coordinated spherical nanocluster structures. A-24 has the connectivity of the C24 fullerene, B-24 is a fully coordinated version of the sodalite beta-cage and C-24 a fully coordinated truncated cube. Nano Lett., Vol. 4, No. 8, 2004
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Figure 5. Energies per molecule of (SiO2)N nanoclusters for N ) 12, 18, 24 with respect to the estimated total energy of alpha-quartz (see Figure 6). The open diamonds indicate fully coordinated cages, the open triangles correspond to fully coordinated nanotubes and the horizontal bars indicate the energies of lowest-energy reported terminated nanoclusters found by global optimization approaches.18,19 The single data point showing the lowest energy (SiO2)24 cage is actually two overlying data points for clusters A-24 and B-24.
calculated with respect to the individual oxygen and silicon atoms in the triplet state at the 6-31G(d)/B3LYP level of theory, for N ) 12, 18, and 24, are plotted in Figure 5, showing that, in nearly all cases, the spherical nanocages are lower in energy than the elongated nanocages. One exception to this is found for the (SiO2)24 truncated cube nanocage (C-24), which is higher in energy than the respectively sized elongated nanocage. Also in Figure 5 we include the energies of the lowest energy-terminated (SiO2)12 cluster as found by us18 and the lowest energy-terminated (SiO2)24 cluster reported in a recent study.19 Both these terminated clusters were obtained by first using silica interatomic potentials together with global optimization strategies to deliberately search the nanosilica energy landscape for low energy structures, followed by DFT energy minimizations. From Figure 5 it can be seen that for N ) 12 the low-energy terminated cluster is considerably lower in energy than the fully coordinated cages. For N ) 24, however, our deliberate targeted design of fully coordinated nanostructures has produced clusters lower in energy that that found thus far by global optimization searches. We do not claim that our lowest energy (SiO2)24 nanocage cluster is a ground-state cluster but feel that this result shows that such cluster topologies appear to be surprisingly low in energy with respect to known cluster isomers. Further evidence that fully coordinated (SiO2)N structures become more energetically favorable with respect to other isomers with increasing N can be obtained by considering an extrapolation of the energies of our best candidate ground1430
state clusters for (SiO2)N N ) 1-12.18 We have found that these twelve data points can be fitted well by a simple power law (R2 ) 0.995), see Figure 6. We also note that the functional form of the fitted function has the appropriate asymptotic behavior for large N, which should approach a limiting value for the bulk energy. Although it should not be expected that all clusters for N > 12 also closely follow this fitted energy dependence (e.g., due to finite size fluctuations), it is encouraging that the limit tends toward a value of -17.9 eV/SiO2 (a vertical shift of 17.92 eV/SiO2 is applied in Figure 6), which is surprisingly close to the experimentally measured bulk energy of alpha-quartz (-19.2 eV/SiO2).29 This limiting energy is also respectable when considering the magnitude of the overestimations of the total energy of quartz predicted by periodic DFT calculations, which give values between -20.2 eV/SiO230 and -22.4 eV/ SiO231 depending on the methodology employed. The relatively smaller limiting value of the bulk energy obtained by us is based upon extrapolation from energies obtained from cluster DF calculations which employ localized basis functions rather than the plane wave basis sets as in periodic DF calculations. These and other differences in the DF methodologies employed are the likely reason for the differing theoretical estimations of the bulk energy, both of which, however, give relatively close agreement with experiment. For our DFT cluster calculations, taking into account the goodness of the fit of the power law to the ground-state energies for the (SiO2)N clusters N ) 1-12, together with its sensible limiting value, we take a limited extrapolation Nano Lett., Vol. 4, No. 8, 2004
Figure 6. Power law fit to the twelve lowest known energy nanoclusters (SiO2)N N ) 1-12 (filled diamonds). The nearness of the energies of the fully coordinated nanotubes (open triangles) and nanoclusters (open diamonds) to the extrapolated region N > 12, for N ) 18 and 24 suggests that these structures lie relatively low on the silica nanoscale energy landscape. A vertical shift of all data points is applied such that zero corresponds to the extrapolated bulk limit of the power law fit, which is interpreted to be an estimation of the total energy of alpha quartz.
(from 12 < N < 24) as an approximate guide to the relative thermodynamic stability of the fully coordinated clusters we propose for N ) 12, 18, 24. From Figure 6 we can see that, although the (SiO2)12 nanocage clusters are well above the trend line, our fully coordinated cages and tubes for (SiO2)18 and (SiO2)24 lie very close to the extrapolated energetic trend, indicating again their relatively low energy with respect to other similarly sized nanostructures. The low energy of our fully coordinated N ) 24 silica nanocages, with respect to known correspondingly sized lowenergy terminated clusters, is particularly surprising when one considers the strain inherent in both the numerous double-oxygen bridges necessary to form our fully coordinated silica structures and in the closed topological form of the clusters themselves. The observed energy stabilization of fully coordinated clusters with increasing size, when considered together with what is known for other topologically comparable systems, is perhaps indicative of more general cluster growth behavior. Specifically, considering only vertex topology (see Figure 1), it is interesting to further compare the low energy cluster characteristics reported for CN with those suggested by calculations and experiments by us and other authors for (SiO2)N. For both (SiO2)N and CN with N < 10, linear chains of repeating doubly linked centers (see Figure 1) are found to be among the lowest energy Nano Lett., Vol. 4, No. 8, 2004
structures. Specifically, as confirmed by both theoretical32 and experimental33 studies, for (SiO2)N N < 7 doubly linked linear chains are ground-state structures. For N < 10, CN linear chains dominate other isomers in experiments34 and are theoretically also predicted to be ground states (at least for odd N).35 For 10 < N 11,11 explicitly demonstrating that fully coordinated (SiO2)N clusters may be stabilized over terminated clusters. For 6 < N
