SUPPORTING INFORMATION. Influence of plasmonic Au nanoparticles on the photoactivity of

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1 SUPPORTING INFORMATION Influence of plasmonic Au nanoparticles on the photoactivity of Fe 2 O 3 electrodes for water splitting Elijah Thimsen, Florian Le Formal, Michael Grätzel and Scott C. Warren* Interband Absorption. The goal here is to determine the functional form of the component in the absorbance spectrum arising from interband absorption, to subtract it from the measured uv-visible absorbance spectra and arrive at the absorbance from the surface plasmon resonance. The optical properties of a material can be described by its frequency dependent, complex dielectric function: (s1) Where Є 1 is the real component and Є 2 is the imaginary component. In free-electron metals, the dielectric function contains a component that arises from absorption by conduction electrons, resulting in an oscillation of the electron density at a resonance frequency, which is an intraband transition. In noble metals, the dielectric function also contains a component arising from the excitation of single electrons to an excited state above the Fermi level, which is an 1

2 interband transition. It is assumed here that the interband component is not size dependent, if the particle diameter is greater than 10 nm. 1 In Au, the frequencies of the intraband and interband transitions can partially overlap. 1 The total (experimental) complex dielectric function can be expressed in terms of its components from the two transitions: 2 (s2) (s3) (s4) Where Є f is the intraband component and δє b is the interband component. From equation (s2), it can be seen that once either component has been calculated, the other can be readily determined by simply subtracting from the experimental dielectric function. The intraband component can be calculated using the Drude-Lorentz-Sommerfeld model: 1 1 Γ 1 Γ Γ Γ (s5) Where is the Drude plasma frequency and 8.8 for Au, 2 Γ is the relaxation fequency, ν f = 1.39 x 10 6 m/s is the Fermi velocity, 3 and l = 42 x 10-9 m is the electron mean free path. 1 After calculation of the intraband component from equation (s5), the interband component is obtained from (s2) using experimental data from the literature. 4 The interband absorption is a function of the joint density of states of the Au band structure and the transition matrix. 5 If it is assumed that the transition matrix is constant, i.e. the transition probability is constant, then: 5 2

3 (s6) Where is the joint density of states and is the absorption cross section, which is proportional to the absorbance by the concentration and path length. The term is plotted as a function of photon wavelengthh along with the absorbance spectrum of the 48 nm Au nanoparticles on hematite in Figure S1. The term was adjusted using a linear scaling factor to set the two spectra equal at λ=350 nm, wheree the interband absorbance is expected to dominate the spectra. Figure S1: Measured absorbance spectrum for 48 nm Au nanoparticles on silicon-doped Fe 2 O 3 platelets taken from Figure 3 (black-solid) ); calculatedd interband absorbance spectrum using equation (s6) with rad s -1 as the frequency unit and a linear scaling factor of 2.2x10-33 (blue- dashed); difference spectrum ( dashed-red) between the measured spectrum and theoretical interband, which approximates the surface plasmon absorbance of the sample. 3

4 Calculation of the absorption and scattering cross sections of the Au nanoparticles. The ratio of the absorption to the scattering cross section can be used to estimate the probability of one process occurring over the other, with the larger cross section having a higher probability of occurrence. The absorption and scattering cross sections of spherical particles that are small with respect to the wavelength of light can be estimated by the following equations: 6 (s7) (s8) where k is the wave number, α is the complex particle polarizability, and Im{α} is the imaginary component of the complex polarizability. The complex polarizability can be calculated using the following equation: 6 4 (s9) where a is the particle radius, ε is the complex dielectric function for Au, and ε m is the dielectric constant of the embedding medium. The ratio of the absorption cross section to the scattering cross section is plotted in Figure S2 for embedding in air and Fe 2 O 3. In both cases it can be clearly seen that the absorption cross section is more than 10 times larger than the scattering cross section. 4

5 Figure S2: Ratio of the absorbance to the scattering cross sections for 48 nm diameter Au nanoparticles embedded in air and Fe 2 O 3. Comparison of nanoparticles in solution with those adsorbed onto an electrode Gold nanoparticles with a diameter of 50 nm were synthesized following literature protocols using a sodium citrate-driven growth to a 50 nm diameter. 7 UV-vis spectra were recorded between 380 nm and reduction to form seeds with a 20-nm followed by a hydroxylamine hydrochloride-driven 800 nm before and after adsorption of the gold particles onto platelet-type USP hematitee electrodes. Adsorption of the particles onto the hematite electrode was performed using electrophoretic deposition, as described below. 5

6 Figure S3: (a) uv-visible absorbance of the as-made hematite platelets and the hematite platelets modifiedd with 50-nm Au nanoparticles. (b) uv-visible absorbance: the blue line is the difference spectrum of the spectra in part (a) of the figure; the red line is for 50-nm gold nanoparticles in aqueous solution. Au nanoparticles deposited by electrophoresis. Citrate-stabili ized Au particles were synthesized following a procedure from the literature, 8 and had a mean size of 15.0 nm and standard deviation off 1.5 nm, as measured by TEM. The citrate-stabilized gold nanoparticles were deposited by electrophoretic deposition. A field of 30 V/cm was applied for 30 minutes to deposit the nanoparticles using a Pt counter electrodee held at negative potentials relative to the working electrodee (α-fe 2 O 3 nanoplatelet thin 6

7 film). After deposition, the particle size distribution had d broadened, with a mean particle size of 11.6 nm and a standard deviation of 3.8 nm as measured by SEM. Figure S4: SEM images of the hematite platelets (a) before and (b) after electrophorectic deposition of 15 nm Au nanoparticles; and (c) size distribution of Au nanoparticles measured from TEM images before deposition and SEM images after deposition onto the hematite platelets. 7

8 Figure S5: Current density as a function of electrode potential under (a) chopped simulated AM1.5 illumination at a frequency of 0.5 Hz (b) under continuous simulated AM1.5 illumination. 8

9 Figure S6: Spectral characteristi ics of the as-made (a) uv-visible absorbance, (b) IPCE measured at 1.4 V/RHE and (c) normalized IPCE measured at 1.4 V/RHE. The normalized IPCE in panel (c) was normalized with respect to the IPCE at 350 hematite platelets and hematite platelets modifiedd with 15 nm Au nanoparticles: nm. 9

10 Cited Literature. (1) Kreibig, U.; Vollmer, M. Optical properties of metal clusters; Springer: Berlin ; New York, (2) Cooper, B. R.; Ehrenrei.H; Philipp, H. R. Physical Review 1965, 138, A494. (3) Kittel, C. Introduction to solid state physics; 8th ed.; Wiley: Hoboken, NJ, (4) Johnson, P. B.; Christy, R. W. Physical Review B 1972, 6, (5) Christensen, N. E.; Seraphin, B. O. Physical Review B Solid State 1971, 4, (6) Bohren, C. F.; Huffman, D. R. Absorption and scattering of light by small particles; Wiley: New York, (7) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday Soc. 1951, 11, 55. (8) LizMarzan, L. M.; Giersig, M.; Mulvaney, P. Langmuir 1996, 12,