Supplementary Information

Transcription

1 Electrochemical Charging of Single Gold Nanorods Carolina Novo, Alison M. Funston, Ann K. Gooding, Paul Mulvaney* School of Chemistry & Bio21 Institute, University of Melbourne, Parkville, VIC, 3010, Australia Supplementary Information 1

2 Appendix A. Calculation of the Spectra of charged particles To calculate the spectrum of polydisperse, charged gold nanorods within the dipole approximation, we first decompose the complex dielectric function into an interband component, which is independent of size, shape and charge and a free electron or Drude component 1 ε(ω) = ε int (ω) +ε free (ω) [A1] We then subtract the free electron contribution and add a modified Drude function in 2 which the plasma frequency is modified by an amount ω p = (1+ N)Ne 2 /mε o, and recalculate the new dielectric function. This enables us to calculate the entire spectrum of the charged gold rods, not just the region around the plasmon modes. ε(ω, N) = ε int (ω) ε free (ω) +ε free (ω, N) [A2] The Drude term becomes: ε free (ω, N) = N(1+ N)e2 / mε o ω 2 + iωγ [A3] The uncharged metal has N=0. In an aqueous environment, the metal particles may be cathodically or anodically charged causing electron density changes of up to 10-15%. This modified dielectric function is used in equation 3 to calculate the scattering spectrum of the charged rod and in equation 4 to calculate the change in scattering when the charge is altered. Equation [A3] may be combined with equation 3 in the text to yield equation 2, which gives a direct relationship between the plasmon peak and the excess electron density. These equations apply in the dipole limit, where the rod dimensions are much smaller than the wavelength of the incident light in the medium. 2

3 Appendix B: Plasmon Shifts & Simple Capacitance Calculation: 66.7nm H 31.2nm We need the volume of the spherically-capped cylindrical rods. For the rod shown in Figure 2F, the full length is 66.7nm and the full width 31.2nm by SEM. The volume is then V= (HπR 2 + 4π/3*R 3 ) = 43,000 nm 3. The volume of a gold atom is nm 3, therefore the number of gold atoms in the nanorod is N = 2.53 x10 6. Within the dipole approximation, the plasmon resonance wavelength is given by equation 2 in the text 1 λ = λ p ε + 1 L L ε m [B1] where the symbols have the same meaning as outlined in the manuscript, λ p is the bulk plasma wavelength which for neutral gold is 131 nm, ε is the high frequency contribution to the metal dielectric function (12.2 for gold), ε m is the dielectric constant of the medium and L is the particle shape factor. The particles are immersed in water and the refractive index of the medium may be approximated as 1.33 (neglecting the effect of the substrate), therefore the dielectric constant is = The plasmon resonance for the particle in Figure 2F is nm. Using these data it is possible to calculate that for this particle, L = Using Equation 2, for a shape factor of L = 0.12 and λ p =131nm, ε =12.2, ε m =1.78 and λ = 11 nm. λ = N 2N λ p ε + 1 L L ε m [B2] we find N =0.0334*2.53x10 6 = 85,000 electrons. The reader is referred to reference 1 in the Supplementary Information for a full derivation of this equation. The capacitance, C = dq/adv where q = surface charge (the number of electrons multiplied by the elementary charge 1.6 x coulomb) and A is the electrode area. While the electrons are not distributed homogeneously over the surface (see reference 12 for a discussion of electron distribution on metal ellipsoids in dilute electrolytes), we can get an overall estimate using the surface area of the rod: The surface area of the rod is A = 4πR 2 + 2πHR = 6540 nm 2. Hence, C = 85,000*1.6 x10-19 /(1.4V*6.54x10-11 cm 2 ) = 150 µf/cm 2. This is about a factor of 2-3 higher than for compact electrodes, but given the assumption of homogeneous charge density, which is poor for rods, this is considered good agreement and reconfirms the essential physics of the spectral shift. 3

4 Figure S1. Gold Nanorod sample: A) Dark field image of gold rods in air on glass, before electron injection, scale bar = 50 µm. B) Spectrum of gold nanorod ensemble (black line) and calculated spectra of nanorods (within the dipole approximation) of width 30nm, in water, of aspect ratios 2.75 (pink) and 4 (purple). C) Low resolution TEM of ensemble, on a carbon-coated Cu grid. 4

5 Figure S2. Control experiment: Spectra of a single gold nanorod on glass, in water, over time, showing system stability is to within a nanometre. Variations observed during charging experiments are therefore due to charging only, and are not due to temperature changes or to fluctuations in the dielectric properties of the surrounding. 5

6 Figure S3. Electrochemical Charging: The electrochemical cell consists of a transparent conducting ITO working electrode. The gold nanocrystals are spin coated onto the surface. The NCs have a single monolayer of cationic surfactant CTAB (not shown). A silver wire functions as the quasi-reference electrode and a Pt wire serves as the counter electrode. An Autolab PGSTAT 302 potentiostat is used to apply a linear, negative potential ramp to the electrode. This causes electrons to be "pumped" from the counter electrode to the working electrode. The electrons are distributed over the ITO and tunnel to the adsorbed gold crystals. The whole surface is assumed to be at the same electrochemical potential (applied voltage). In response to this negative charge distribution, counter ions from solution build up next to the electrons, but the ions are unable to undergo reduction, so the voltage drop occurs between the ITO surface and the adsorbed counter ions. The thickness of this layer is about 0.3nm and is determined by the size of the hydrated counterions. This is termed a Helmholtz capacitor; the voltage drop is proportional to the surface charge density and is denoted VH. It changes with applied potential. There is a fixed but undetermined potential difference at the reference electrode, but this does not change during the experiment. The capacitance of the Helmholtz layer is much higher than attainable in air because of the screening by the counterions. (1) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer-Verlag: Berlin Heidelberg, 1995; Vol. 25; Mulvaney, P.; Pérez-Juste, J.; Giersig, M.; Liz- Marzán, L. M.; Pecharromán, C. Plasmonics 2006, 1, 61; Pérez-Juste, J.; Pastoriza- Santos, I.; Liz-Marzán, L. M.; Mulvaney, P. Coord. Chem. Rev. 2005, 249,