Nanoparticle heating calculator

Plasmonic heating of nanostructures turns absorbed light into heat at the particle's plasmon resonance. In gold-nanoparticle-mediated photothermal therapy, gold nanoshells or nanorods, whose resonance lies in the near-infrared where tissue is most transparent, are delivered to a tumour and heated with a laser focused on it; the gold nanorod photothermal effect is strongest with light polarized along the rods. The temperature rise follows from the absorption cross-section, the intensity and heat conduction, as computed here (and for rods on the nanorod heating page).

Light absorbed by a particle is turned into heat, which flows into the surroundings: the photothermal effect. Plasmonic nanoparticles do this very efficiently at their resonance, which is used in photothermal therapy, drug release, catalysis and solar steam generation. The photothermal conversion efficiency is the share of the incident energy that becomes heat; for small gold particles nearly all extinction is absorption, so it is close to 100 %, while large particles lose part to scattering.

In steady state the temperature rise at its surface is ΔT = σ_abs I / (4π κ r): absorbed power over the heat conduction of the surroundings. A 40 nm gold sphere in water under 1 mW/µm² at its plasmon resonance warms by about 23 K.

For small particles the absorption cross-section grows with the volume (r³) while conduction grows with r, so ΔT grows about as r². Larger particles scatter more and absorb less per volume, so the trend flattens.

Outside the particle the temperature rise falls off as 1/distance; the map shows it. Many particles heat each other collectively: see array heating.