Drastic Surface Plasmon Mode Shifts in Gold Nanorods Due to Electron Charging

Abstract

The color of small gold rods changes dramatically when electrons are injected by chemical reductants. The longitudinal and transverse plasmon modes are both found to blue-shift, and the shift is larger for rods with larger aspect ratios. The color changes are visible to the eye for rods with aspect ratios around 2–3. It is found that the surface plasmon band is damped when charging becomes high. The effects are in qualitative agreement with a model in which the gold plasma frequency increases due to an increase in electron density.

Appendix

Calculation of the Spectra in Figure 6

To calculate the spectrum of polydisperse, charged gold nanorods within the dipole approximation, we first decompose the complex dielectric function [12] into an interband component, which is independent of size, shape, and charge, and a free electron or Drude component,

$$ \varepsilon {\left( \omega \right)} = \varepsilon _{{\operatorname{int} }} {\left( \omega \right)} + \varepsilon _{{{\text{free}}}} {\left( \omega \right)} $$

(A1)

We then subtract the free electron contribution and add a modified Drude function in which the plasma frequency is modified by an amount $\omega ^{{\text{2}}}_{{\text{p}}} = {\left( {1 + \Delta N} \right)}{Ne^{2} } \mathord{\left/ {\vphantom {{Ne^{2} } {m\varepsilon _{0} }}} \right. \kern-\nulldelimiterspace} {m\varepsilon _{0} }$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.

$$ \varepsilon {\left( {\omega ,\Delta N} \right)} = \varepsilon _{{\operatorname{int} }} {\left( \omega \right)} - \varepsilon _{{{\text{free}}}} {\left( \omega \right)} + \varepsilon _{{{\text{free}}}} {\left( {\omega ,\Delta N} \right)} $$

(A2)

The Drude term becomes:

$$\varepsilon _{{{\text{free}}}} {\left( {\omega ,\Delta N} \right)} = \frac{{N{\left( {1 + \Delta N} \right)}{e^{2} } \mathord{\left/ {\vphantom {{e^{2} } {m\varepsilon _{0} }}} \right. \kern-\nulldelimiterspace} {m\varepsilon _{0} }}}{{\omega ^{2} + i\omega \gamma }}$$

(A3)

The uncharged metal has ΔN = 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 the standard equations for absorption of light by ellipsoids within the dipole approximation and numerically integrated over the size distribution.