The Optimal Aspect Ratio of Gold Nanorods for Plasmonic Bio-sensing

Abstract

The plasmon resonance of metal nanoparticles shifts upon refractive index changes of the surrounding medium through the binding of analytes. The use of this principle allows one to build ultra-small plasmon sensors that can detect analytes (e.g., biomolecules) in volumes down to attoliters. We use simulations based on the boundary element method to determine the sensitivity of gold nanorods of various aspect ratios for plasmonic sensors and find values between 3 and 4 to be optimal. Experiments on single particles confirm these theoretical results. We are able to explain the optimum by showing a corresponding maximum for the quality factor of the plasmon resonance.

Appendix

Methods

Simulations based on boundary element method

In our computational approach, we discretize the surface of the nanoparticle by a set of triangles and match the electromagnetic potentials at the triangle centers. By fulfilling the boundary conditions imposed by Maxwell’s equations through auxiliary surface charges and currents, we end up with a generic and flexible scheme that allows us to compute the optical properties of arbitrarily shaped nanoparticles with complex geometry embedded in dielectric environments.

The dielectric function of the gold nanorods was extracted from optical data [27] and the chosen mesh sizes allow for a spatial resolution of approximately 1 nm.

Determination of S, FOM, FOM*, and FOM*_layer

We calculated the light scattering cross-section C _sca for every particle shape (diameter 20 nm, length from 20 nm to 160 nm in steps of 2 nm) in n ₁ = 1.33 and in n ₂ = 1.34 as a function of wavelengths λ (in steps of 1 nm).

The FOM* was calculated according to the following equation:

$$ {\hbox{FOM}}* = {\left( {\frac{{\left| {{\text{Csc}}{{\text{a}}_1}(\lambda ) - {\text{Csc}}{{\text{a}}_2}(\lambda )} \right|}}{{1/2 \times ({\hbox{Csc}}{{\hbox{a}}_1}(\lambda ) + {\hbox{Csc}}{{\hbox{a}}_2}(\lambda ))}}} \right)_{\max }}/({n_2} - {n_1}) $$

The FOM*_layer was calculated in the same way in the quasi-static approximation for spheroids for layer thicknesses l = 0.01 nm to 10 nm in steps of 1 nm (0.01 nm until the first nanometer).

Gold nanorods preparation

Gold nanorods were synthesized according to the seeded growth procedure published by Nikoobakht et al. [36]. In this two-step synthesis, preformed seeds grow into rods in a concentrated surfactant solution. The samples used in this work were characterized by ensemble extinction spectroscopy and transmission electron microscopy to obtain the mean diameters and lengths of the different samples. The samples we used had the following properties:

Name	λ res	Width	Length
LC 12-1	634	57 ± 6	28 ± 4
S702	700	49 ± 4	18 ± 2
S740	743	55 ± 6	18 ± 3

Single particle spectroscopy

To investigate the spectral shift by changes in the refractive index of the environment on the single particle level, we dilute the nanorod suspensions 1:100 with distilled water and rinse them for 5 min through a flat glass capillary connected to PET tubing. Subsequent rinsing of 1 M sodium chloride solution for 1 min can increase the number of immobilized particles. Afterwards, the glass capillary is rinsed for at least 15 min with distilled water (n = 1.333) to remove as many of the molecules as possible that were attached to the particle surface, and the scattering spectra of all particles in the field of view recorded. After rinsing the glass capillary with glucose solution (25 wt.% n = 1.372) for 15 min, we again investigate the scattering spectra of the same particles and determine the quantities listed in Table 1.