Absorption cross section of gold nanoparticles based on NIR laser heating and thermodynamic calculations

Abstract

We present a method for measuring the optical absorption cross section ([Formula: see text]) of gold nanoparticles (GNPs) based on optically heating the solution of GNPs with an 808 nm near-infrared (NIR) laser and measuring the temperature increase of the solution. We rely on the theoretical calculations based on the heat diffusion equations and experimental measurements based on the energy balance equations to measure the [Formula: see text] and the temperature distribution of single GNPs. Several morphologies, including gold nanospheres (GNSs), spherical gold nanoparticle conjugate (AuNPC), which are 20 nm GNSs surface-functionalized with an IR 808 dye, gold nanorods (GNRs), and gold nanourchins (GNUs), were studied. The study found that a single 20 nm GNS has the lowest [Formula: see text] and temperature distribution as compared to 100 nm GNUs. By increasing the size of GNSs from 20 to 30 nm, the magnitude of [Formula: see text] as well as temperature distribution increases by a factor of 5. The [Formula: see text] values of 20 and 30 nm GNSs calculated by Mie theory and the experimentally measured are in a good agreement. GNRs with equivalent radius ([Formula: see text]) 9.16 nm show the second lowest [Formula: see text]. By increasing the [Formula: see text] by a factor of 2 to 19.2 nm, the measured [Formula: see text] and temperature distribution also increased by a factor of 2. We also estimated [Formula: see text] for GNUs with diameters at 80 and 100 nm, which also have higher [Formula: see text] values. This work confirms that we can use temperature to accurately measure the [Formula: see text] of a variety of GNPs in solution.

Figure 1

The extinction spectra of the different nanogold samples of (a) 20 and 30 diameters GNSs, (b) 25 and 10 diameters GNRs and (c) 80 and 100 nm diameters GNUs. All solutions were measured at a normalized optical density (OD) 1.

Figure 2

The evolution of δT as a function of irradiation time (s) for (a) 20 nm GNSs, (b) 30 nm GNSs, (c) AuNPC, (d) 25 nm × 60 nm GNRs, (e) 10 nm × 41 nm GNRs (f) 80 nm GNUs, and (g) 100 nm GNUs. All the solutions were measured over 25 min of irradiation by the CW NIR laser of densities of 0.3, 1.2, 2.5, and 5.1 W/cm². All solutions were excited at OD = 1.

Figure 3

Temperature elevation in the colloidal solutions as a function of power density; (a) the net values on different GNPs in the solutions after subtracting the background, with average values per single GNPs for (b) 20 nm and 30 nm GNSs and AuNPC, (c) 25 nm × 60 nm and 10 nm × 41 nm GNRs, and (d) 80 nm and 100 nm GNUs.

Figure 4

(a) Experimental ${\sigma }_{\mathit{abs}}$ (based on thermodynamic theory) and (b) theoretical ${\sigma }_{\mathit{abs}}$ (based on the Mie theory) for 20 nm and 30 nm GNSs, and 25 nm × 60 nm and 10 nm × 41 nm GNRs, wherein the error bars represent the standard deviation of triplicate measurements.

Figure 5

Experimental schematic for measuring temperature elevation in a nanocolloidal sample; HWP : a half-wave plate, PBS: a beam splitter, and PC: a computer.