Article pubs.acs.org/JPCC
Spherical versus Faceted Anatase TiO2 Nanoparticles: A Model Study of Structural and Electronic Properties Gianluca Fazio, Lara Ferrighi, and Cristiana Di Valentin* Dipartimento di Scienza dei Materiali, Università di Milano Bicocca via R. Cozzi 55 20125 Milano Italy
Downloaded via OPEN UNIV OF HONG KONG on January 23, 2019 at 13:57:23 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: TiO2 nanoparticles are fundamental building blocks of many TiO2-based technologies. However, most of the computational studies simulate either bulk or surface titania. Structural and electronic properties of nanoparticles are expected to differ much from extended systems. Moreover, nanoparticles of different size and shape may also present peculiar features. In this study we compare nanocrystals and nanospheres of various sizes (up to a diameter of 3 nm) in order to highlight analogies and differences. In particular, we focus the attention on the surface-to-bulk sites ratio, the surface sites coordination distribution, the atomic distortions or curvature, and the surface energies from the structural point of view. Regarding the electronic properties, we investigate the difference between Kohn−Sham and fundamental gaps of these finite-sized systems, the frontiers orbitals space distribution, ionization potentials, and electron affinities, and finally, the densities of states projected on the various coordination sites present in the nanoparticles. This detailed analysis proves that faceted and spherical nanoparticles present different structural and electronic properties, which make each of them better suited for different uses and applications.
1. INTRODUCTION Titanium dioxide nanoparticles are fundamental building blocks in many technological applications,1 especially in those involving light irradiation and photochemical processes, such as photovoltaics, photoelectrochemistry, and photocatalysis.2−5 However, more recently, titania nanoparticles have also attracted the interest of the biomedical community.6 Typically, TiO2 nanoparticles are grown via sol−gel synthesis.7 Several studies during the past few years have proven that the shape and size of titanium dioxide nanoparticles can be efficiently and successfully tailored by controlling the conditions of preparation and by using ad-hoc surface chemistry.8−12 Below a certain nanoparticle dimension, the anatase phase is found to be more stable than rutile.13 The formation rate and the shape of anatase nanoparticles in aqueous solution are dependent on the pH value.14 Another growth determining factor is the particle density during synthesis: an excessive dilution may cause a partial dissolution of titania nanocrystals leading to the formation of spherical nanoparticles.6 The latter, analogously to nanotubes and nanorods, are characterized by a high curvature profile, which is expected to trigger higher binding properties. In fact, highcurvature nanoparticles present many undercoordinated sites, which are very reactive.6 Undercoordinated sites are particularly important for nanoparticles smaller than 20 nm since the fraction of surface atoms becomes comparable to that of bulk atoms. Surface-to-bulk aspect ratios intimately depend also on the shape of the nanoparticle. Additionally, the coordination and structure of Ti © 2015 American Chemical Society
surface sites, which are the surface binding sites for molecular and adsorbate species, are expected to be highly affected by the size and the shape of the nanoparticles. Commonly, computational first-principle studies are devoted to either bulk of surface slabs of TiO2. The object of this work is to systematically investigate and compare structural and electronic properties of faceted and spherical anatase nanoparticles of different size in order to get insight into the intimate differences between these two commonly observed nanoparticles shapes. State-of-the-art density functional methodologies will be used in order to accurately describe the quantum size effects on the electronic structure of the semiconducting oxide system. In particular, the hybrid functional HSE06,15 which is considered to be the best suited to describe semiconducting oxides, will be compared to the more popular, at least in the quantum chemical community, B3LYP.16,17 Faceted nanoparticles have been the object of a number of previous first-principles studies,18−24 with full relaxation for a maximum diameter size considered of 2.7 nm. Spherical nanoparticles have only been studied by means of force field approaches,25 which, however, lack any information on the electronic properties. Here we will consider nanocrystal/ nanosphere diameter sizes up to 3 nm. The paper is organized as follows: in Section 2 the Computational Details are presented; in Section 3.1 we will Received: July 3, 2015 Revised: August 11, 2015 Published: August 12, 2015 20735
DOI: 10.1021/acs.jpcc.5b06384 J. Phys. Chem. C 2015, 119, 20735−20746
Article
The Journal of Physical Chemistry C
For the 3D plots of the molecular orbitals we have used an isovalue of 0.0005 au for all the orbitals except for very localized ones for which we have used a 0.001 au isovalue. Geometric surfaces of the nanocrystals have been designed as the smallest Wulff-shape decahedron, with a specific angle θ, uniquely determined by the cell parameters (θ = tan−1(c/a)), between (101) and (001) planes. We can then determine the values of the parameters A, B, and H (see Figure 1) for that
discuss the Structural Properties of the nanoparticles in terms of shape (3.1a), size, morphology (3.1.b), distortions with respect to bulk (3.2.c), and surface energies (3.2.d); in Section 3.2 we will analyze the Electronic Properties of the nanoparticles in terms of Kohn−Sham vs fundamental gaps (3.2.a), frontier orbitals (3.2.b), and total and projected densities of states (3.2.c); Section 4 is devoted to a summary and to the conclusions of the work.
2. COMPUTATIONAL DETAILS All the calculations were performed with the CRYSTAL1426 package, where the Kohn−Sham orbitals are expanded in Gaussian-type orbitals (the all-electron basis sets are O 8− 411(d1), Ti 86−411 (d41), and H 511(p1)). Some test calculations have been performed with a diffuse basis set (Ti diffuse 86−411(d411), O diffuse 8−4111(d1), H diffuse 5111(p1)) on all the surface atoms and the hydrogen atoms, showing negligible effects that will be discussed in the following. The HSE0615 and B3LYP16,17 hybrid functionals have been used throughout this work. The values of the optimized lattice parameters are 3.766 and 3.789 Å for a and 9.663 and 9.777 Å for c, respectively, for HSE06 and B3LYP (see Table 1 for experimental values).27 Table 1. Optimized Cell Parameters a and c (in Å), and a/c Ratio of Bulk Anatase, as Obtained with the HSE06 and B3LYP Functionals, Together with the Corresponding Experimental Values HSE06 B3LYP exp.
a
c
a/c
3.766 3.789 3.782
9.663 9.777 9.502
2.569 2.580 2.512
Figure 1. Top: Space-filling representation of the faceted anatase nanoparticles and the corresponding schematic representation of the Wulff-shape decahedron with its parameters A, B, and H. Bottom: Space-filling representation of the spherical anatase nanoparticles and the corresponding schematic representation of the sphere with radius RM. The HSE06 optimized nanostructures are shown. The surface-tobulk % ratio and the stoichiometry of each nanoparticle are indicated on the side of the model.
To describe the (101) surface, we used a slab of 10 triatomic layers with 60-atoms and a unit cell periodicity along the [101]̅ and [010] directions; no periodic boundary conditions were imposed in the direction perpendicular to the surface. The kspace sampling for the surface geometry optimization included 43 k-points. Nanoparticles have been treated as molecules in the vacuum without any periodic boundary conditions. Simulated total densities of states (DOS) of the nanoparticles have been obtained through the convolution of Gaussian peaks (σ = 0.01 eV) centered at the Kohn−Sham energy eigenvalue of each orbital. Projected densities of states (PDOS) have been obtained by using the coefficients in the linear combination of atomic orbitals (LCAO) of each molecular orbital: summing the squares of the coefficients of all the atomic orbitals centered on a certain atom type results, after normalization, in the relative contribution of each atom type to a specific eigenstate. Then, the various projections are obtained from the convolution of Gaussian peaks with heights that are proportional to the relative contribution. The zero energy for all the DOS is set to the vacuum level, corresponding to an electron at an infinite distance from the surface. Similarly, the extended X-ray adsorption fine structure (EXAFS) simulated spectra have been constructed with the Gaussian convolution of peaks (σ = 0.0005 Å) centered at the distance lengths between each Ti atom and other atoms (O or Ti) from its first, second, and third coordination shells. Projections have been performed by taking into account groups of titanium atoms with the same coordination sphere.
specific decahedron. The surface area, Sgeom, is then calculated as ⎛ (A2 − B2 ) ⎞ Sgeom = 2⎜B2 + ⎟ cos θ ⎠ ⎝
For nanospheres, the geometric surfaces are those of a sphere of radius RM, which has been used to truncate the bulk. Connolly surfaces (SConn) for nanoparticles have been created using the algorithm developed by Connolly.23,24 First, we build the surface resulting from the overlap of all the atomic van der Waals spheres; second, a probe sphere of a certain chosen radius (i.e., 3.0 Å) is rolled on that surface and the contact points are used to form arcs that smooth the van der Waals surface. The resulting surface is the Connolly surface.
3. RESULTS AND DISCUSSION 3.1. Structural Properties. 3.1.a. Nanoparticle Shapes. Nanoparticles have been carved from the optimized anatase TiO2 bulk, as calculated with both the HSE06 and B3LYP functionals (see Table 1). A Ti atom was set at the origin of the coordinate axis and an overall D2d point group symmetry was kept when cutting the nanoparticle. Faceted nanoparticles or nanocrystals (NC) have been cut from the bulk anatase crystal according to the minimum energy shape predicted by Barnard et al.13 for dimensions below 10 nm, which is a decahedral shape where the two lowest energy 20736
DOI: 10.1021/acs.jpcc.5b06384 J. Phys. Chem. C 2015, 119, 20735−20746
Article
The Journal of Physical Chemistry C
Table 2. Optimized Geometrical Parameters, at the HSE06 and B3LYP Level of Theory, for the Nanoparticles, as Shown in Figure 1a A
nanoparticle NCS (TiO2)159·4H2O NCL (TiO2)260·6H2O NSS (TiO2)223·26H2O NSL (TiO2)399·32H2O
1.56 1.93
NCS (TiO2)159·4H2O NCL (TiO2)260·6H2O NSS (TiO2)223·26H2O NSL (TiO2)399·32H2O
1.57 1.94
B
H
0.39 0.77
B/A
2.83 2.85
0.39 0.78
RM
Deq or DM
SConn
VConn
DConn
1.22 1.50
1.79 2.19 2.44 3.00
18.4 25.0 21.4 32.0
5.7 9.3 8.1 14.6
2.22 2.61 2.49 3.03
1.23 1.51
1.81 2.21 2.56 3.02
18.7 25.4 21.8 32.5
5.8 9.4 8.3 15.0
2.23 2.62 2.52 3.06
HSE06 0.25 0.40
B3LYP 0.25 0.40
2.87 2.89
a The decahedron parameters A, B, and H are reported, as well as the B/A ratio for the faceted nanoparticles, whereas the cutting radius RM is reported for the nanospheres. The diameter DM = 2 × RM for nanospheres and the equivalent diameter Deq = (6V/π)1/3 (where V = 1/3H(A2 + B2 + AB) is the geometrical volume of the nanocrystal) for nanocrystals are also given. SConn and VConn are the surface area and the volume estimated with the Connolly method (see Computational Details), while DConn is the equivalent diameter of a sphere with the same Connolly volume. Parameters are reported in nm, surfaces in nm2, and volumes in nm3.
Table 3. Number of O and Ti Atoms with a Specific Coordination Sphere in the HSE06 and B3LYP Optimized Structures (When Different, B3LYP Value Is in Bracket) and Their Percentage with Respect to the Total Number of Atomsa NCS number
a
NCL %
NSS
number
OH O2c O3c
8 88 226
2.5 27.3 70.2
12 120 394
Ti4c Ti5c Ti6c Ti4c(OH) Ti5c(OH) Ti6c(OH) Ti5c(OH)2 Ti6c(OH)2
4 76 71
2.5 47.8 44.7
4 106 138
8
5.0
12
% O Atoms 2.3 22.8 74.9 Ti Atoms 1.5 40.8 53.1 4.6
NSL
number
%
number
%
52 124 (128) 296 (292)
11.0 26.3 62.7
64 192 (200) 574 (566)
7.7 23.1 69.2
24 46 105 24 8 (12) 12 (8)
10.7 20.6 47.1 10.8 3.6 5.4
36 64 (72) 243 (235) 32 16
9.0 16.1 60.9 8.0 4.0
8
2.0
4
1.8
The cutoff radius for a Ti−O bond is 2.5 Å.
representations for the parameters (A, B, H, and RM) defining the size of the nanostructures are shown. Further details on the spatial dimensions are provided in Table 2 for both the HSE06 and B3LYP functionals. We may notice that B3LYP calculations produce somewhat larger nanoparticles, in particular, regarding the nanocrystals, the dimension along the z-axis is slightly elongated, in line with a longer lattice parameter c (see Table 1). In Table 2, the nanoparticles surface (SConn) and volume (VConn), as determined with the Connolly method28,29 (see Computational Details), are reported. This type of surface and its inner volume are conceived for three-dimensional molecular objects, which involve protruding atoms and take atomic van der Waals radii into account. The equivalent diameter (DConn) is the diameter of a corresponding ideal sphere that has the same volume (VConn) of the nanoparticles. This parameter allows direct comparison between nanocrystals and nanospheres. Noteworthy is that the size, in terms of number of atoms and equivalent diameter, of NCL is about that of NSS. The average size of the nanoparticles is between 2 and 3 nm, which is consistent with real small nanocrystallites.31−33 The coordination/undercoordination of all the atomic species in the designed nanoparticles is quantitatively detailed
anatase surfaces, (101) and (001), are exposed. The horizontal sides of the decahedron are defined A and B, with A > B (see Figure 1). B/A ratio was determined to be typically around 0.32.30 When cutting the nanocrystal, excess atoms were removed and monocoordinated oxygen atoms were saturated with H atoms. This sequence of operations resulted in stoichiometric nanocrystals saturated with few dissociated water molecules, as described in Figure 1: (TiO2)159·4H2O (NCS) and (TiO2)260·6H2O (NCL). Spherical nanoparticles or nanospheres (NS) have been obtained by carving a sphere of radius RM from the bulk anatase crystal. Then, all the 2-fold Ti atoms on the surface were removed, while 3- and, when necessary, 4-fold Ti atoms were coordinated to hydroxyl groups. Analogously, monocoordinated O atoms were saturated with H atoms. These operations result in the creation of stoichiometric nanospheres saturated with a bunch of water molecules, as described in Figure 1: (TiO2)223·26H2O (NSS) and (TiO2)399·32H2O (NSL). 3.1.b. Nanoparticle Size and Morphology. A representation of the nanocrystals and nanospheres, together with their stoichiometry and coordination data, is provided in Figure 1, as well as in Tables 2 and 3. In particular, in Figure 1 the surfaceto-bulk % ratio for each nanobject is indicated, and the sketch 20737
DOI: 10.1021/acs.jpcc.5b06384 J. Phys. Chem. C 2015, 119, 20735−20746
Article
The Journal of Physical Chemistry C
the distance of about 2 Å (first coordination sphere) are the Ti−Oeq (eq = equatorial) and Ti−Oax (ax = axial) bonds, which are well-known to be slightly different in the D2D symmetry, with the former shorter than the latter; then the third line (second coordination sphere) is the distance between the selected central Ti atom and the next-neighboring Ti atoms (Ti···Ti) of about 3 Å; finally, the fourth and the fifth lines (third coordination sphere) are the distances between the central Ti atom and the second shell of Ti and O atoms (Ti···Ti and Ti···O) of about 3.8−3.9 Å. The EXAFS spectra of the nanocrystals and of the nanospheres under investigation are more complex since, after relaxation, these systems become less ordered than bulk, with the various lines converted into peaks after convolution. We first analyzed the EXAFS spectra of the nanocrystals NCS and NCL, focusing on the first coordination sphere (Figure 3b,c). The Ti−O distance critically depends on the Ti coordination number. Thus, there are two main contributions (green and blue) that are associated with the Ti5c (shorter Ti− O bonds) and to Ti6c (almost bulk Ti−O distances). The ratio between equatorial and axial contribution is not the typical 4:2 as for Ti6c in the bulk because the number of Ti−Oax bonds is higher, as a consequence of their shape, where H > A (elongated decahedron). The green curve (Ti5c) presents three features at low bond (about 1.8 Å), at bulk (about 2.0 Å), and at high bond (about 2.2 Å) distances. These features are due to the typical relaxation associated with 2-fold coordinated oxygens and 5-fold coordinated titanium atoms on the prevalent (101) surfaces, as previously reported.39 Finally, the red curve, to be associated with Ti4c species, presents a low peak at short distances (about 1.8 Å). As regards the EXAFS spectra of the nanospheres NSS and NSL, we observed a broader variety of features contributing to the peak of the first coordination sphere, in the bottom two panels of Figure 3 (Figure 3d,e). For both nanospheres there is a predominant contribution of Ti6c (blue line), which is more evident for the larger nanosphere. Then, there are various contributions at short Ti−O distances of about 1.8 Å due to all the undercoordinated species on the surface, such as 4- and 5fold coordinated Ti atoms or Ti atoms bound to an OH group. For both types of nanoparticles, the Ti···Ti feature presents peaks centered at the bulk distance with some broadening due to surface, edge, and corner species. The faceted nanoparticles are characterized by a sharper Ti···Ti peak because of the higher percentage of bulk-like atoms with respect to the nanospheres. The larger the size of the nanoparticles, the more the EXAFS peaks approach the bulk line. For the large nanosphere NSL, which has an average diameter (DConn) of about 3 nm, we notice a general compression of the Ti−O bonds accompanied by a slight average increase of the Ti···Ti distances, in line with the experimental EXAFS data observed for 3 nm size nanoparticles.34 3.1.d. Surface Energies. In this section we investigate the cost to form nanoparticles from bulk systems in terms of surface energies. The standard free energy of formation of nanocrystals is the sum of two terms:13
by the data in Table 3. The number and percentage of each coordination-type atomic species is given, ranging from O3c to OH and from Ti6c to Ti4c(OH). The position of the atoms of different coordination in the nanoparticles is then visually shown by the color coding in Figure 2. We can note that the
Figure 2. Position of the Ti atoms with different coordination sphere within the various nanoparticles is visually shown by the color coding indicated on the right side.
percentage of Ti5c atoms is much larger in the nanocrystals than in the nanospheres, with an increasing trend for smaller particles. On the contrary, the balance between O3c and O2c is not that different when comparing nanocrystals and nanospheres. Small nanocrystals (NCS) have about the same contribution of fully coordinated O atoms than larger nanospheres (NSL; 70.2 vs 69.2%). The number of OH groups is larger in the nanospheres since those are required to achieve a minimum 4-fold coordination that we have set as necessary for chemical stability. It is noteworthy that nanocrystals of different sizes (NCS and NCL) present the same atomic species at the analogous positions: 4-fold Ti atoms at corners between the upper and the lower part of the decahedron, 5-fold Ti atoms at the edges and on the (101) lateral surface, and finally, 5-fold Ti atoms involving an OH group on the top (001) surfaces. Nanospheres (NSS and NSL) are characterized by a larger percentage of undercoordinated Ti atoms (especially
