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Structural, electronic and optical properties of TiO2 nanoparticles
Matti Alatalo, Sami Auvinen, Heikki Haario
Lappeenranta University of Technology
Juho Jalava, Ralf Lamminmäki
Sachtleben Pigments
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Outline
− Motivation, earlier studies− Methods: Brief description− Ab initio results− Simpler approaches− Outlook
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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
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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
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− 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
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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
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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.
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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?
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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
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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
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Results: Absorption spectra
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Atomic vs. electronic structure
(TiO2)28
•Red: O•Blue: Ti
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Effect of structure on the adsorption
spectra•A:
•B:
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Effect of structure on the adsorption
spectra•A:
•B:
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Contributions of different directions
•Note: Bulk anatase is birefringent
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Observations
− Structure plays an important role on the absorption spectra
− Longest dimension dominates− Compact structures energetically favorable
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Density functional tight binding,first results
•Green:•GPAW•Blue:•DFTB