Light Extinction by Agglomerates of Gold Nanoparticles: A Plasmon Ruler for Sub-10 nm Interparticle Distances

Abstract

Plasmon rulers relate the shift of resonance wavelength, λ_l, of gold agglomerates to the average distance, s, between their constituent nanoparticles. These rulers are essential for monitoring the dynamics of biomolecules (e.g., proteins and DNA) by determining their small (<10 nm) coating thickness. However, existing rulers for dimers and chains estimate coating thicknesses smaller than 10 nm with rather large errors (more than 200%). Here, the light extinction of dimers, 7- and 15-mers of gold nanoparticles with diameter d_p = 20-80 nm and s = 1-50 nm is simulated. Such agglomerates shift λ_l up to 680 nm due to plasmonic coupling, in excellent agreement with experimental data by microscopy, dynamic light scattering, analytical centrifugation, and UV-visible spectroscopy. Subsequently, a new plasmon ruler is derived for gold nanoagglomerates that enables the accurate determination of sub-10 nm coating thicknesses, in excellent agreement also with tedious microscopy measurements.

Figure 1

(a) Evolution of D_f during agglomeration of gold NPs as a function of their d_g (bottom abscissa) and n_p (top abscissa) derived here by DEM (line and inset agglomerate images) along with microscopy data (symbols). (b) Evolution of d_h (solid line, symbols) and d_g (broken line) of gold NP agglomerates as a function of their n_p derived by DEM (lines and inset images) and measured using dynamic light scattering (DLS; symbols).

Figure 2

Normalized Q_ext as a function of λ of gold (a) spheres (dotted line, circles), dimers (dot-broken line, squares, inverse triangles), (b) 7- (broken line, diamonds) and 15-mers (solid and double dot-broken lines, triangles) with D_f = 1.67 (dot-broken, broken, and solid lines) or 1.9 (double dot-broken lines) estimated here by DDA (lines) and compared to those measured by Zook et al.(29) (circles, diamonds, and triangles) and Esashika et al.(4) (squares and inverse triangles). The DDA-derived Q_ext of gold NPs increases as single spheres (dotted line) form dimers (dot-broken line), 7- (broken line), and 15-mers (solid line) by agglomeration shifting λ_l from 530 to 680 nm, in excellent agreement with data^, (symbols).

Figure 3

Normalized Q_ext as a function of λ of gold dimers with d_p = 30 (a: dotted line) or 50 nm (b) at s = 50 (solid line), 2 (broken & dotted lines, triangles, and diamonds), and 1 nm (dot-broken line, squares) estimated here by DDA (lines) and measured using UV–visible spectroscopy and microscopy^, (symbols).

Figure 4

Au agglomerate λ_l as a function of normalized interparticle separation, s/d_p, estimated by DDA using dimers of monodisperse (squares and inverse triangles) and bidisperse (circles) NPs, and DEM-derived 7- (diamonds) and 15-mers (triangles) of monodisperse NPs with d_p = 20–50 (squares, circles, diamonds, and triangles) or 75 and 80 nm (inverse triangles) and s = 1–50 nm. A new plasmon ruler (eq 4, solid line and shaded area) is derived by regressing the DDA-derived λ_l evolution.

Figure 5

Estimated interparticle separation distance, s, as a function of normalized λ_l shift, Δλ/λ_s, using plasmon rulers for chains (dotted line), dimers (broken line), and 7- and 15-mers (eq 4, solid line) of gold NPs with d_p = 34 (a), 50 (b), 60 (c), and 80 nm (d) compared to microscopy and UV–visible measurements of dimers (triangles, and squares) and agglomerates (circles).

Figure 6

Separation distance, s, of gold agglomerates with d_p = 30 nm coated by fibrinogen (red), histone (green), albumin (orange), and γ-globulin (blue) estimated using UV–vis spectroscopy data with plasmon rulers for dimers (open bars), chains (lines bars) and agglomerates (eq 4, filled bars).