1. Structural, electronic and optical properties of TiO 2 nanoparticles Matti Alatalo, Sami Auvinen, Heikki Haario Lappeenranta University of Technology Juho Jalava, Ralf Lamminmäki Sachtleben Pigments

2. Outline −Motivation, earlier studies −Methods: Brief description −Ab initio results −Simpler approaches −Outlook

3. Industrial use of TiO 2 nanoparticles −TiO 2 pigments are widely used in the industry: whiteness, opacity −Nano-TiO 2 : Plastics, coatings, cosmetics −Particle size and shape distribution important for applications −These distributions can be solved by measuring the turbidity spectrum of a dilute solution: A nontrivial inverse problem

4. Measurement of turbidity spectrum of rutile or anatase pigments pigment + water + dispersing agent (MIPA) Light to the sample

5. −When the refractive index of a material is known at different wavelengths, the turbidity can be calculated rigorously, e.g., for spheroid −N is the number of particles, −a is the width of spheroid −q is the length/width −C ext is the extinction coefficient −n is the refractive index −p refers to the particle and −m refers to the medium Calculation of the turbidity

6. C ext -matrix for spheroids as function of wavelength and crystal size diameter calculated by the T-matrix method Length/width 1.1Length/width 2.1

7. Limitations of the T-matrix modeling Fitting is moderate but the error in numerical results is much larger than expected.

8. Limitations of the T-matrix modeling −The results are not good at particle sizes below 200 nm and wavelengths below 360 nm −Quantum size effect?

9. Methods −Structures, spectra: Density functional calculations as implemented in the GPAW code −Projector augmented wave method in real space grids −Structures, spectra: Density functional tight binding as implemented in the Hotbit code −First attempts (testing of the parametrization) −T-matrix modeling −Particle size distributions

10. Details of the GPAW calculation −Clusters of the size 18-38 TiO 2 units were carved from anatase/rutile bulk (Smaller ones composed of TiO 2 molecules) −For small particles, anatase is known to be the ground state structure −The structures were allowed to relax −Several different structures per particle size were tested −Absorption spectra were calculated using time propagation TDDFT −Grid parameter h=0.17 for structural relaxations, h=0.3 for the calculation of the absorption spectra

11. Results: Absorption spectra

12. Atomic vs. electronic structure (TiO 2 ) 28 Red: O Blue: Ti

13. Effect of structure on the adsorption spectra A: B:

14. Effect of structure on the adsorption spectra A: B:

15. Contributions of different directions Note: Bulk anatase is birefringent

16. Observations −Structure plays an important role on the absorption spectra −Longest dimension dominates −Compact structures energetically favorable

17. Density functional tight binding, first results Green: GPAW Blue: DFTB