Structural, electronic and optical properties of TiO 2 nanoparticles Matti Alatalo, Sami Auvinen, Heikki Haario Lappeenranta University of Technology Juho.

Structural, electronic and optical properties of TiO2 nanoparticles

Matti Alatalo, Sami Auvinen, Heikki Haario

Lappeenranta University of Technology

Juho Jalava, Ralf Lamminmäki

Sachtleben Pigments

Outline

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

Industrial use of TiO2 nanoparticles

− TiO2 pigments are widely used in the industry: whiteness, opacity

− Nano-TiO2: 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

200 300 400 500 600 700 800 900 1000 11000.05

0.1

0.15

0.2

0.25

Turbidity spectra of sample (normalized to 10 mg/l):XRDI-S 483.44 21.3.05/06.30

wavelength, nm

abso

rban

ce

p1011054 TUOTEKEH.LAB. weight 0.1204 g conc. 11.33 mg/llooseness 0.2 w%

measuredcalculatedcalculated and norm

Measurement of turbidity spectrum of rutile or anatase pigments

pigment + water + dispersing agent (MIPA)

Light to the sample

0

LI I e

− 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− Cext is the extinction coefficient− n is the refractive index− p refers to the particle and − m refers to the medium

Calculation of the turbidity

( , ) , , pext

m m

naN q a C q

n

Cext-matrix for spheroids as function of wavelength and crystal size diameter calculated by the T-matrix method

Length/width 1.1 Length/width 2.1

400600

8001000

0

200

400

6000

0.5

1

1.5

wavelength, nmvol. eq. crystal size diameter, nm

Cex

t

400600

8001000

0

200

400

6000

0.5

1

1.5

wavelength, nmvol. eq. crystal size diameter, nm

Cex

t

200 400 600 800 1000 12000

0.5

1

1.5

2

Turbidity spectra of sample (normalized to 10 mg/l):XRD: 8 nm

wavelength, nm

ab

sorb

an

ce

uvtsmfige8

mitattu weight 0.1000 g conc. 10.00 mg/l looseness -117.3 w% spektrin kunto 7 16 0 0 (koko UV VIS IR) wl(max) 278 nm abs(max) 1.991 abs(450 nm) 0.062 U/V*100 3191

measuredcalculatedcalculated and norm

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

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?

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

Details of the GPAW calculation

− Clusters of the size 18-38 TiO2 units were carved from anatase/rutile bulk (Smaller ones composed of TiO2 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

Results: Absorption spectra

Atomic vs. electronic structure

(TiO2)28

•Red: O•Blue: Ti

Effect of structure on the adsorption

spectra•A:

•B:

Effect of structure on the adsorption

spectra•A:

•B:

Contributions of different directions

•Note: Bulk anatase is birefringent

Observations

− Structure plays an important role on the absorption spectra

− Longest dimension dominates− Compact structures energetically favorable

Density functional tight binding,first results

•Green:•GPAW•Blue:•DFTB