Photothermal effects in small gold nanorod aggregates for therapeutic applications

Abstract

Proximity of the metal nanoparticles enhance the plasmonic coupling and shifts the resonance. This article presents a numerical study of the photothermal effect in aggregates of small gold nanorods considering the ordered as well as random aggregates. In the ordered aggregates, there is lateral coupling which causes blueshifts in the plasmonic resonance, while in the random aggregates, there are redshifts in the plasmonic resonance. The plasmon response of latter could be tailored up to the second infrared biological therapeutic window. It has been observed that the aggregates show higher absorption power, and therefore, higher temperature rise compared to the single gold nanorod or monodispersive nanorods. The absorption resonance peak position of the random aggregate depends on the incident and polarization angles of the incident light. The aggregation of the nanoparticles often inherently occurs in the biological medium which affects the photothermal process. This study helps to understand the photothermal heating of nanoparticle aggregates and the use of the optimal light source concerning the absorption peak of the aggregates suspension for therapeutic uses.

Appendices

Appendix 1. Aggregate projections

All considered six aggregates, ordered as well as random, are three-dimensional entities. The geometric structure projections in the xy, yz and zx planes are shown in the Fig. 10, 11.

Fig. 10

Projected views of aggregates C1, C2, C3, C4, C5 and C6 in the xy, yz and zx planes used for computation. Each nanorod has length 25 nm and diameter 5 nm

Fig. 11

Projected views of aggregate C7 in the xy, yz and zx planes used for computation. In this aggregate, three nanorods have the size 25 nm $\times$ 5 nm (NR1, aspect ratio = 5), four have the size 23 nm $\times$ 4.7 nm (NR2, aspect ratio = 4.9) and two have the size 21 nm $\times$ 4.4 nm (NR3, aspect ratio =4.8)

Appendix 2. Model validation

Heat generation study of a 100 nm gold nanosphere situated in water was carried out as a benchmark problem. The permittivity of the gold was from Johnson and Christy (1972). All values of other parameters had been kept identical as used by Baffou et al. (2010). Figure 12 shows the computation of the normalized electric field intensity, energy density, temperature evolved in the nanosphere at incident wavelength 530 nm. The total absorption power of the nanosphere from 400 nm to 800 nm is also shown. The irradiance of the light was 1 mW/$\mu$m$^2$. In our case, the maximum raised temperature was 52.2 $^\circ$C which was 55 $^\circ$C in Baffou case and 52.5 $^\circ$C in Chen et al. (2012). The maximum absorbed power was obtained 28.27 $\mu$W at 543 nm while the maximum absorbed power reported by Baffou was 20.5 $\mu$W at 530 nm and by Chen 21.45 $\mu$W at 540 nm.

Fig. 12

Comparison validation of algorithm: a normalized electric field intensity, b absorbed power density, c temperature field and d total absorbed power of a gold nanosphere of 100 nm diameter at incident wavelength 530 nm and irradiance 1 mW/$\mu$m$^2$