Quantum Size Effect in TiO Nanoparticles Prepared by ......similarly contribute to the electronic...

S1

Supplementary information for

Quantum Size Effect in TiO2 Nanoparticles

Prepared by Finely Controlled Metal Assembly on

Dendrimer Templates

Norifusa Satoh, Toshio Nakashima, Kenta Kamikura, Kimihisa Yamamoto*

Department of Chemistry, Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan

*e-mail: [email protected]


Quantum Size Effect in TiO2 Nanoparticles Prepared by Finely Controlled Metal Assembly on Dendrimer Templates

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Supplementary Note

The following relationship between the bandgap of a semiconductor particle (Einfinite) and

the radius (R) is described by Brus, using the effective mass approximation1:

!

Einfinite " Eg +h2# 2

2R2

1

µ$1.8e

2

%R+ smaller terms (S1)

where ħ is Planck’s constant; e is the charge on the electron; Eg is the bandgap in the bulk; µ is the

reduced mass of the electron me and hole mh in the bulk; and ε is the dielectric constant of the bulk

semiconductor. Although this description is widely used in the study of TiO2 nanoparticles, the

failure of the Brus equation is generally known especially in the ultrasmall region; for example, in

the case of CdS.2, 3, 4 The main reason is the conventional infinite depth well model of the Brus

equation. Additionally, the electronic band structure of such small clusters is affected by their

surface state and related relaxation in the atomic positions.

Assuming an apparent reduced mass of the electron and hole µ´ and an apparent dielectric

constant ε´ in the infinite depth well model, we can replace the Nosaka equation4 for the excitation

energy Efinite using a finite depth well model with the following expression looking like a Brus

equation:

!

E finite ~ Eg +h2" 2

2R2

1

# µ $1.8e

2

%#R (S2)

In the case of TiO2, the normally used value of 1.63 mo as the µ, experimentally estimated from the

Brus equation using E* (∆E = 0.15 eV) at R = 1.2 by Kormann et al.5 would be the above µ´ to

describe the realistic finite potential well model in the rigorous meaning. As Kormann et al. also

mentioned, the real µ is believed to be less than 1 mo in the bulk because mh is much smaller than me

N. Satoh, T. Nakashima, K. Kamikura & K. Yamamoto*

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(e.g., me ~ 5–100 mo, mh ~ 0.01–0.8 mo)6, 7. By contrast, the ε in TiO2 is large enough to permit

ignoring the failure due to the infinite depth well model because of the small second term of the

Brus equation (cf. ε = 5.7 for CdS). For these reasons, the Brus equation for TiO2, generally

adopted, would correspond to the experimental data. Namely, the equation (S2) (= equation (1) in

the main text) is not the Brus equation based on the infinite depth well model but is equivalent to

the Nosaka equation based on the finite depth well model in physical meaning.

Additionally, this kind of semi-empirical prediction would essentially include the

information about the surface and the atomic character of the nanoparticles under the same

condition. Zunger and coworkers succeed in treating these problems in the calculation of the

electronic structure, using the semi-empirical pseudopotential method.8, 9, 10 Experimentally, it has

been shown that the surface modification of nanoparticles, e.g., CdSe and CdS, has little effect on

the absorption spectra without the electronic interaction with the aromatic rings of the

surface-capping molecules.11, 12

In contrast, Jorne and Fauchet et al. have observed the dramatic effect of the surface Si-H

and Si=O bonds on the electronic structure, such as absorption and luminescence, in Si nanocrystals

(1nm < 2R < 4 nm);13 Si is an indirect bandgap semiconductor. The phenomena are confined with

the theoretical computation by Zdetsis et al. and Brus et al.14, 15, 16 The H- and O-passivation

remarkably changes the chemical structure from almost pure Si in a bulk to a 1:1 ratio in the range

of 1.1–1.4 nm15, 16 and finally to the molecular structure, such as SiH4 and SiO2 (or Si(OH)4). In

the ultra-small range, the effect of the newly formed chemical bonds needs to be considered in the

electronic structure.

Although TiO2 is also classified as an indirect bandgap semiconductor (see S 23–25), the



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chemical structure changes less than that of Si; from TiO2 in the bulk to Ti(OR)4 in the final

molecular structure, where R is H or Si of the substrate SiO2 under the present study condition.17, 18

In both of the structures, a Ti atom is always surrounded by O atoms. Additionally, these atoms

similarly contribute to the electronic transitions; O of the valence band to Ti of the conduction band

in the bulk, and O of the ligands to Ti of the metal in the molecular structure. Therefore, we can

expect to observe the size dependency of an indirect bandgap semiconductor TiO2 in the ultra-small

region, based not on the surface effect but on the Q-size effect combined with a simple electrostatic

continuum, equation (1) in the main text.

In the theoretical field, numerous quantum mechanical calculations for free TiO2 clusters

have been performed. 19 However, these calculations neglect the chemical character of the Ti(IV)

ion, which tends to form a TiO4 tetrahedral or a TiO6 octahedral structure. Although these

calculations may successfully explain the experimental data for these free TiO2 clusters in a very

specific environment such as a high vacuum chamber20, these structures are too unstable in surface

energy and structure in an air atmosphere21. By contrast, Doren et al. have recently performed a

theoretical calculation for TiO6 octahedral chains. 22 They revealed that the Ti(3d) lowest

unoccupied state is delocalized in the 3Ti chain and that the lowest optical energy transition is an

O(2p) → Tibulk(3d). The theoretical calculation for Q-size TiO2 particles is beyond the scope of

our present study, but it will be needed to understand the detailed electronic structure in individual

particles.


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Supplementary Figure 1 1:1 complexation between phenylazomethine and

Ti(acac) Cl3. a, Changes in UV-vis spectra during addition of Ti(acac)Cl3 (in steps of 0.2

eq. until 1.0 eq.): b, titration curve, based on the spectral changes at 315 nm; c, scheme

of complexation of Ti(acac)Cl3 and phenylazomethine. These spectra changes are similar

to those of SnCl2 and FeCl3. Thus, the results indicate the complexation of the imine

ligand with Ti(acac)Cl3.



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Supplementary Figure 2 Changes in 1H-NMR spectra of phenylazomethine during

addition of Ti(acac)Cl3. a, phenylazomethine; b, c, d, e, phenylazomethine:

Ti(acac)Cl3 = 5:1 (b), 2:1 (c), 1:1 (d), 1:2 (e). With the addition of Ti(acac)Cl3, the

chemical shift moved upfield. This means the formation of a complex of

phenylazomethine with Ti(acac)Cl3. The shift is saturated at the ratio of 1:1. A similar

upfield shift is also observed during the complexation of phenylazomethine with SnCl2.


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Supplementary Figure 3 Changes in UV-vis spectra during addition of Ti(acac)Cl3.

a, DPA G3 (1 × 10–5 M) while adding 14 drops of 3 μl dehydrated acetonitrile solution of

Ti(acac)Cl3 (3 × 10–2 M); b, DPA G2 (3 × 10–5 M) while adding 6 drops of 3 μl dehydrated

acetonitrile solution of Ti(acac)Cl3 (1 × 10–2 M).

a

b



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Supplementary Figure 4 AFM image (50 nm × 50 nm) of [Ti(acac)Cl3]30@DPA G4.

a, top view; b, cross-sectional view.


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Supplementary Figure 5 Molecular modeling of [Ti(acac)Cl3]30@DPA G4. a, Top

view; b, side view. The size is in good agreement with that obtained in the AFM image

(Supplementary S5). An assembly of 30 equivalent Ti(acac)Cl3s increased the size from

2.3 × 2.5 × 2.9 nm to 3.0 × 3.9 × 4.0 nm; the size for this assembly is greater than that

reported using SnCl2.



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450455460465470 395400405410

N1s

Ti2p3/2

Ti2p1/2

[Ti(acac)Cl3]30@DPA G4




Ti(acac)Cl3

DPA G4

Binding energy (eV)

Supplementary Figure 6 XPS spectra of Ti-assembled DPA G4. The binding

energy of Ti(2p3/2) showed an upfield shift as complexing occurred with the imine groups on

the outer layer of DPA G4. The shift shows that the imine groups on the inner layer are

stronger bases than those on the outer layer. Ti(acac)Cl3 showed the lowest binding

energy, because it exists in a dimeric structure in the solid form; the chlorine atoms, which

bind two titanium atoms, acts as stronger donors than the N atoms of DPA G4.


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50 nm

Eg

A1gru

ru

300 400 500 600200 700Raman shift (cm-1)

a

b

Supplementary Figure 7 Hydrolysis of Ti-assembled DPA G4 under bulk

conditions. a, TEM image of hydrolyzed TiO2 under bulk conditions. b, Raman

spectrum of TiO2 obtained from hydrolysis of Ti-assembled DPA G4 in 10 %-HCl solution.



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Supplementary Figure 8 1H-NMR spectra of hydrolyzed DPA G4. DPA G4 was

hydrolyzed by the addition of a 10% HCl solution, forming small organic compounds, such

as benzophenone, diaminobenzophenone and a complex between diaminobenzophenone

and HCl.


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Supplementary Figure 9 Thermogravimetric curves of hydrolyzed DPA G4.

Benzophenone, diaminobenzophenone and the complex between diaminobenzophenone

diminished at about 180, 330, and 630 ºC, respectively, with a heating rate of 20 ºC/min.

under an air atmosphere. Although the ionic bonds of the complex are strong, the final

decomposition of the complex under HCl treatment starts at about 500 ºC.



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Supplementary Figure 10 Observed carbon remaining on substrate after

annealing of hydrolyzed Ti-assembled DPA G4. a, Changes in XPS spectra of

Ti-assembled DPA G4 hydrolyzed by vapor of HCl solution on a mica substrate after

annealing at 500 ºC; b, decay in the C1s peak area. The C(1s) peak area was determined

by subtracting the mica substrate background and normalizing to the Ti(2p) peak area.


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a

b

200 300 400 500 600 700Raman shift (cm-1)

50 nm

Eg

B1g

A1g

B1gan

an

an an

Supplementary Figure 11 Thermolysis of Ti-assembled DPA G4 under bulk

conditions. a, TEM image of thermolyzed TiO2 under bulk condition. b, Raman

spectrum of TiO2 obtained from thermolysis of solid Ti-assembled DPA G4.



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Supplementary Figure 12 Thermogravimetric curves of DPA G4 and Ti-assembling

DPA G4. Under a N2 atmosphere, DPA G4 has a high thermostability (Td-10% = 530 ºC)

and carbon remains on pan at 1000 ºC. Under an air atmosphere, however, DPA G4 was

largely removed at 800 ºC at the heating rate of 20 ºC/min. The amount of Ti-assembled

DPA G4 that remained on the pan was matched with the weight of Ti added as TiO2. The

final decomposition of the Ti-assembled DPA G4 starts about 500 ºC.


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Supplementary Figure 13 Observed carbon remaining on substrate after

annealing Ti-assembled DPA G4. a, Changes in XPS spectra of Ti-assembled DPA G4

on mica substrate after annealing at 500 ºC; b, decay in the C1s peak area. The C(1s)

peak area was determined by subtracting the mica substrate background, and normalizing

to the Ti(2p) peak area.



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Supplementary Figure 14 XPS spectra of the obtained TiO2. a. rutile particle and

hydrolyzed Q-size TiO2. b. anatase particle and thermolyzed Q-size TiO2. The y-axis is

Intensity (A.U.). In bulk, Eb (Ti2p3/2) is 458.9 and 458.7 eV for rutile and anatase,

respectively. The Eb of rutile is higher than that of anatase in bulk, which would also be

correct on a nanoscale as long as the TiO6 octahedrons exist. As a size-dependency, the

Eb of Q-size TiO2 shifted upfield with a reduction in the size. The difference in the

synthesis methods, hydrolysis and thermolysis, provide the Eb of Q-size TiO2 at different

peak positions: the Eb of the hydrolyzed one is higher than that of the thermolyzed one by

0.1-2 eV. These results also indicate the Q-size effect and crystal form existence.


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Supplementary Figure 15 Relation of observed size and bandgap energy of TiO2

molded on DPA G4. a. hydrolyzed TiO2 and the equation (S2) (= equation (1) in the main

text) for rutile. b. thermolyzed TiO2 and the equation (S2) for anatase. The equation (S2)

is plotted using with Eg = 3.0, ɛ = 173 (rutile) for the hydrolyzed samples and Eg = 3.2, ɛ = 31

(anatase) for the thermolyzed samples.

a

b



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Supplementary Figure 16 Molecular modeling structure, highlighted in

Supplementary Table 1. a, 7-rutile (O-center); b, 15-rutile (Ti-center); c, 31-rutile

(Ti-center); d, 7-anatase (O-center); e, 15-anatase (O-center); f, 34-anatase

(Ti-center).


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Supplementary Table 1 The number of TiO62– octahedral units within the TiO2

cluster models and the minimum radius R (Å) of the cluster models, approximated

as a spherical shape with a Ti or O atom as the center. The number of octahedral

units, included in a sphere with a radius increasing in steps of 0.01 Å, was counted in each

case of the Ti-center and O-center. Since the number quantumly increased with the

radius, we regarded the minimum radius as 6, 14, and 30 octahedrons as the radius of

these (highlighted).

number R (Ti-center, Å) R (O-center, Å) 3 4.62 3.97 5 ↓ 4.92

6TiO2 rutile

7 5.4 5.04 11 5.44

13 ↓ 6.44

15 6.16 ↓

14TiO2 rutile

17 6.46 26 7.26 27 7.12 ↓

30 ↓ 7.49 30TiO2 rutile

31 7.45

3 3.96 5 4.76 ↓

7 ↓ 5.46 6TiO2

anatase

9 5.7

9 5.7

13 6.04 15

↓ 6.16

14TiO2 anatase

17 6.6

29 7.25 7.65 33 ↓ 8.16

30TiO2 anatase

34 7.83



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Supplementary Figure 18 Crystalline phase formation from TiO62– octahedra

nucleus. The nucleus structure of the rutile and anatase phases differs at the point

where the 3rd octahedron is added to the dimer, giving a linear chain and zigzag chain,

respectively. These chains three-dimensionally grow to form TiO2 clusters and/or bulk

crystals.


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Supplementary Note

Titanium oxide is classified as an indirect bandgap semiconductor; a weak indirect

transition is observed from a lower energy point (3.0 eV for rutile and 3.2 eV for anatase) than a

strong direct transition bandgap (3.3 eV for rutile23 and 3.4 eV for anatase24, 25) in bulk.

Nanoparticles of indirect semiconductors would be considered to change the transition nature to

direct one by decreasing in size, because the structure finally reaches the molecular size17, 18 having

a direct transition property.

Serpone et al. inferred that the blue shift of TiO2 nanoparticles should be based not on the

quantum size effect but on the direct transition from the observation of the size-independent blue

shift using the size-uncontrolled samples (2R = 2.1 ± 1.1 nm, 13.3 ± 4.5 nm, and 26.7 ± 9.0 nm).26

However, this insistence is unacceptable because of the experimental error due to the enormous

large size-distribution. Additionally, they assigned the absorption spectra of the anatase particles

using the band calculation for the rutile single crystal27.

For direct transition in the templated TiO2, four regression lines could be obtained in the

Tauc plots of (αhν)2 versus energy (Supplementary Figure 19; estimated error in energies < 0.01 eV,

coefficients of determination > 95 %). All the obtained direct bandgap energies (E*direct) the cross

points of these lines and the x-axis are larger than the indirect bandgap (E* in the main text),

suggesting that the Q-size TiO2 would retain the nature of the indirect bandgap semiconductor.

Additionally, the differences between E*direct and E* in the 6, 14, and 30 TiO2 are almost the same

in each group, which agrees with the difference in the bulk (Supplementary Table 2; error in

energies ≤ 0.02 eV). This means that the size dependency of E*direct parallelly shifts to the upper

field of E* and that the Q-size effect (∆E) also affects these direct transitions comparably;



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!

"E = E *#Eg = E *direct #Eg#direct =h2$ 2

2R2

1

% µ #1.8e

2

&%R (S3)

!

E *direct "E* = Eg"direct " Eg (S4)

Here, Eg-direct is the bandgap energy of each direct transition in the bulk.

Comparing the hydrolyzed and the thermolyzed samples, we can observe the different

manner in the direct transition from the differences between E*direct and E*. The different manner

indicates that the band structure of anatase and rutile would be different because of the different

crystal structure and space group. The band structure of rutile is observed using the single crystal

and calculated sufficiently to discuss the electronic transition.27, To the best of our knowledge, the

experimental data24, 25 and theoretical calculation28 for anatase are not sufficient to assign the

electronic transition. The calculated values in the rutile band structure seem to compare with the

hydrolyzed samples (for rutile) better than the thermolyzed ones (for anatase). These results also

support the belief that the Q-size TiO2 would retain the crystal structure and nature in the range of 1

nm < 2R < 2 nm. hν

According to our conjecture, the crystal structure of TiO2 nanoparticles, such as rutile and

anatase, would lose their nature when the particle size reaches less than 0.68 nm (discussed in the

main text). At this point, the indirect bandgap, E*(0.68) is estimated to be 4.91 eV. On the other

hand, the electronic transition band of the molecular unit, such as TiO4 tetrahedral and TiO6

octahedral coordinations, can be assigned in terms of ligand-to-metal charge transfer (LMCT)

transition: O2–Ti4+ + hν → O–Ti3+. The energy of the molecular LMCT transition, ELMCT, is

calculated from a phenomenological relationship to be 5.39–5.96 eV, corresponding to the TiO6 and

TiO4 units.29 Thus, the ELMCT is higher than the E*(0.68) by 0.48–1.05 eV. The lowest indirect


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transition at 0.68 nm, E*direct(0.68), however, would exist in the upper field of the E*(0.68) by ca.

0.30–0.46 eV, which almost reaches the ELMCT of the TiO6 units. If the size dependence of E*direct

progressed to the dimer size, E*direct could reach the ELMCT of the TiO4 units. These conjectures

could well explain the shift of the indirect transition to the direct one at the point that would lose the

crystal nature. Needless to say, the possibility for the transition shift to happen in the range of

0.68 nm < 2R < 1 nm may be considerable.

0

2

4

6

8

10

3.5 4 4.50

10

20

30

40

50

60

Energy (eV)

b

c

d

a

b

a

c

d

b

ab

c

a

d

c

bb

a

c

A B

0

1

2

3

4

5

6

0

10

20

30

40

50

60

70

80

0

5

10

15

20

25

30

3.5 4 4.5 5

Energy (eV)

d d

c

d

5

b

a

0

2

4

6

3.5 4 4.5Energy (eV)

b

a

0

0.5

1

b

a

a

Supplementary Figure 19 Tauc plots for direct bandgap of 6TiO2 (green), 14TiO2

(red), 30TiO2 (blue). A, hydrolyzed TiO2. B, thermolyzed TiO2. The direct bandgap is

categorized into four groups, a, b, c, d.

Supplementary Table 2 Direct bandgaps of 6TiO2, 14TiO2, 30TiO2, and bulk (and

the difference with the indirect bandgap)

experimental* experimental‡group 30TiO2 14TiO2 6TiO2 bulk bulk transition 30TiO2 14TiO2 6TiO2 bulka 3.78 (0.44) 4.00 (0.45) 4.26 (0.45) 3.3 (0.3) 3.45 (0.45) X1 X1 3.77 (0.31) 3.93 (0.29) 4.18 (0.30) b 3.94 (0.61) 4.15 (0.60) 4.42 (0.60) 3.4 (0.4) 3.59 (0.59) X2 X1 3.97 (0.51) 4.15 (0.51) 4.39 (0.51)c 4.38 (1.05) 4.61 (1.07) 4.92 (1.10) 4.07 (1.07) 4.05 (1.05) 5 1 4.08 (0.62) 4.28 (0.63) 4.50 (0.62)d 4.45 (1.12) 4.73 (1.12) 4.95 (1.13) 4.15 (1.15) 4.3 (1.3) 2 1 4.15 (0.69) 4.36 (0.71) 4.58 (0.70)

* Reference 23. † Reference 27. ‡ Summarized in reference 25.

AnataseRutile

3.40 (0.20),3.63–3.67 (0.43–0.47),

and 3.80 (0.60)

hydrolysis calculated† thermolysis



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Supplementary Materials

DPA G2-4 and phenylazomethine were prepared according to a previous method30. Ti(acac)Cl3

was synthesized following a literature method31. The acetonitrile-d3 and chloroform-d used in the

NMR measurements (ACROS, 99% D) were dehydrated using activated molecular sieves (Wako

Pure Chemical Industries, Ltd., 4A/16) for titration. All other chemicals were purchased from

Kantoh Kagaku Co. and used as received.

Supplementary General Methods

The NMR spectra were recorded using a JEOL JMN400 FT-NMR spectrometer (400 MHz) in

CDCl3/CD3CN (v/v = 1/1, with tetramethylsilane as the internal standard) solution. UV-vis

spectra were recorded using a Shimadzu UV-3100PC spectrometer with a closed quartz cell (optical

path length: 1cm). AFM was performed using a SII SPA400 instrument under ambient conditions

with the tapping mode of imaging (DFM). Si probes having a spring constant of 42 N/m (SII

SI-DF40P for DFM) were used at a resonance frequency of 300 kHz. A 20-µm scanner

(SPA400-PZT (FS-20A), 970P3202) was used. The TEM images were obtained at 120 kV with a

JEOL JEM-2010 instrument. The molecular modeling of the Ti-assembled DPA G4 was

performed using Fujitsu CAChe 5.0 Molecular Mechanics software with MM3 parameters

according to a previous method32. The XPS spectra were measured using a JEOL JPS-9000MC

photoelectron spectrometer without the plasma etching process. The binding energy calibration is

based on the measurement of the mica O(1s) signal, Eb = 531.61 eV33. The thermogravimetric

measurements were performed using a Rigaku TG8120 TG-DTA/MS system. The OWG spectra

were obtained using a System Instruments Co., Ltd., SIS-5000 spectrophotometer. The structures

of the TiO2 clusters were drawn using the CrystalMaker software CrystalMaker 7.


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