Modeling the Formation of TiO2 Ultra-Small Nanoparticles
Update: 2018-02-24 08:59:26      Author:

Titanium dioxide has been widely used as a heterogeneous photocatalyst for various photocatalytic oxidation and reduction reactions with many applications including water treatment and water splitting.[[i]] Further improvements in TiO2-based catalysts may impact solutions for major environmental and energy problems. Researchers have shown that the nanoparticle forms of TiO2 exhibit better catalytic activities than does the bulk phase.[[ii]] Recent studies also showed that the photoelectrochemical performance of TiO2 nanoclusters is enhanced as the size of the nanocluster is reduced.[[iii]] When the particle size falls below 10 nm, the particles become the so-called ultra-small nanoparticles (USNPs) and display unique properties.[[iv]][[v]] Despite that he properties of the solid, the surface, and nanoparticles of TiO2 have been studied extensively, very little has been known about TiO2 USNPs.[[vi]][[vii]][[viii]] It is important to predict the atomistic structures and the structure-property relationships for TiO2 USNPs. An extensive range of low energy (TiO2)n clusters and USNPs (n up to 384) were predicted and validated by Chen and Dixon[[ix]] using a novel bottom-up global optimization approach that is based on all-atom real-space calculations, and the structural evolution pathway from cluster to bulk nanoparticle was proposed (Fig. 1). This is a remarkable improvement over the previous studies on this research topic. Before this work, the largest (TiO2)n predicted was (TiO2)13 by Chen and Dixon.[[x]]


Fig. 1. (a) Selected global energy minima structures for (TiO2)n (b) Structural phase diagram for (TiO2)n USNPs.

To understand the structure-property relationships for the metal oxide cluster, USNP and bulk material, Chen and Dixon developed a novel fragment-based scheme (Fig. 2) [9] [[i]] to approximate the size-property relationships by the more computationally convenient fragment-property relationships. Surface energy densities were predicted for the surface fragments of the anatase-like USNPs using this new model. Based on the predicted surface energy densities and the partial density of states, the most catalytically active sites for the anatase-like 3-D USNPs were predicted to be the kink sites on Face-x surfaces consisting of an octahedral-Ti, the step (edge) sites between the Face-x and Face-y surfaces consisting of a square pyramidal-Ti (on Face-x), and the step sites consisting of trigonal bipyramidal Ti on the Face-y surfaces.


Fig. 2. Fragmentation of (TiO2)320.

Table 1. Surface energy densities for the anatase-like (TiO2)n USNP series.

Fragment Types

Surface Energy Density
  kcal/mol per TiO2

Corners 1-4


Edge-x1 + Edge-x2


Edge-y1 + Edge-y2


Edge-z1 + Edge-z2











In a follow-up work on the formation of brucite-related USNPs by Chen and Dixon, [11] the fragment-based energy decomposition model was further extended. The generated fragment-based thermodynamic parameters from the energy decomposition not only can be used to predict the stabilities of the fragment types, but also to predict a range of thermodynamics-related properties for the nanoparticle series, including the structural phase diagram, ideal aspect ratio (morphology), and surface reactivities (Fig. 3). The fragment-based energy decomposition provides a “multum in parvo” way to compute the thermodynamic properties of large nanoparticles with CCSD(T)-level of high accuracy at a minimal computational cost. The high accuracy is achieved by choose appropriate DFT functional and basis set for energy calculations that produce energy landscape very close to the CCSD(T) results for the small clusters (of the benchmark set) and meanwhile produce the correct normalized dissociation energy at the thermodynamic limit. 


Fig. 3. (a) Structural phase diagram for brucite-related (Mg(OH)2)n USNPs. (b) Solvent effects on the structural phase diagram for (Mg(OH)2)n USNPs.


[[i]] M. Chen, D. A. Dixon, J. Phys. Chem. C, 2017, 121, 21750-21762.

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[[ii]] H. Han, R. Ba, Ind. Eng. Chem. Res., 2009, 48, 2891-2898.

[[iii]] S. Srivastava, J. P. Thomas, Md. A. Rahman, M. Abd-Ellah, M. Mahapatra, D. Pradhan, N. F. Heinig, K. T. Leung, ACS Nano, 2014, 8, 11891-11898.

[[iv]] O. Regan, M. Grätzel, Nature, 1991, 353, 737-740.

[[v]] M. R. Hoffmann, S. T. Martin, W. Choi, D. W. Bahnemann, Chem. Rev., 1995, 95, 69–96.

[[vi]] M. Amin, J. Tomko, J. J. Naddeo, R. Jimenez, D. M. Bubb, M. Steiner, J. Fitz-Gerald, S. M. O’Malley, Applied Surface Science, 2015, 348, 30-37.

[[vii]] Q. Wu, F. Huang, M. Zhao, J. Xu, J. Zhou, Y. Wang, Nano Energy, 2016, 24, 63-71.

[[viii]] N. Bayat, V. R. Lopes, J. Schölermann, L. D. Jensen, S. Cristobal, Biomaterials, 2015, 63, 1-13.

[[ix]] M. Chen, D. A. Dixon, Nanoscale, 2017, 9, 7143-7162.

[[x]] M. Chen, D. A. Dixon, J. Chem. Theory Comput. 2013, 9, 3189-3200.

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