Gold nanoparticle UV-vis spectrum calculator

The conduction electrons of a small gold particle oscillate together when light hits it: a localized surface plasmon. For spheres in water this resonance absorbs strongly near 520 nm, in the green, so the light that passes through a colloid is mostly red. That is the ruby colour of stained glass and of a fresh citrate-gold sol.

Larger particles shift the resonance to longer wavelengths and scatter more, which is why the colour moves to purple and then blue-grey (see the colour column in the table).

In water the plasmon peak stays near 520 nm up to about 30 nm, then red-shifts and broadens: about 525 nm at 40 nm, 530 nm at 50 nm, 549 nm at 80 nm and 570 nm at 100 nm. Above roughly 150 nm a second, shorter-wavelength peak (the quadrupole) appears. The table above lists every size; the calculator gives the full spectrum for any diameter in one click.

For spheres larger than about 35 nm the peak position alone is a good size gauge: compare it with the table, or enter candidate diameters in the calculator and match the measured peak. Below about 30 nm the peak barely moves, so use the ratio of the absorbance at the peak to that at 450 nm (Haiss et al., Anal. Chem. 2007) or electron microscopy. Check the solvent (water, ethanol…) and any coating: both shift the peak by several nanometres, and the calculator models a coating as a shell.

It grows roughly with the particle volume: about 1.1 × 10⁹ M⁻¹ cm⁻¹ at the peak for 20 nm spheres, 9.8 × 10⁹ for 40 nm and 1.4 × 10¹¹ for 100 nm (table above). It follows from the extinction cross-section: ε = N_A C_ext / (1000 ln 10). With it the particle concentration of a colloid is c = A / (ε ℓ), from the absorbance A at the peak and the path length ℓ.

Gold nanoparticles absorb and scatter light through their localized surface plasmon: a strong extinction band near 520 nm for small spheres (ruby-red colloids), shifting to longer wavelengths for larger, elongated, shell-coated or aggregated particles. Small particles mostly absorb (and heat); above about 85 nm in water they mostly scatter. Near the surface the field is enhanced, the basis of SERS and plasmonic sensing. All of these follow from gold's dielectric function and the particle's size and shape, which the calculator handles exactly.

The color follows the plasmon peak. When gold nanoparticles aggregate, for example when a target molecule bridges them, neighbouring particles couple and a new red-shifted band appears, so the solution turns from red to purple or blue. Colorimetric assays read this change by eye or as the ratio of absorbance at about 520 and 650 nm. The two-sphere calculator shows the coupled band.

UV-vis spectroscopy of Au nanoparticles gives their plasmon band: its position and width indicate size, shape and aggregation, its height the concentration. Gold nanoparticles of different sizes show different colours and spectra (table above), which is the basis of size evaluation by UV-vis (Haiss et al. 2007) and of quick quality checks after synthesis.

Shape tunes the plasmon into the red and near-infrared: gold nanorods (often called the most versatile plasmonic nanoparticles) through their aspect ratio (nanorod calculator), star-shaped gold nanoparticles through their sharp tips, and gold or hollow gold nanoshells through the ratio of shell thickness to core (add a shell over a silica or water core in the Mie calculator). Nanoshells and rods are the classic photothermal-therapy particles.

The calculation is exact for one ideal sphere. Real samples differ through the size distribution and non-spherical particles (broader peaks), ligand or silica shells (a red shift: add a shell in the calculator), aggregation (a new red-shifted band, see the two-sphere calculator), the solvent refractive index, and for particles under about 10 nm, extra electron surface scattering that damps and broadens the peak.

Exact. Mie theory is the full solution of Maxwell's equations for a sphere (and, with the shell option, for layered core–shell spheres), valid at every size, unlike the quasi-static (dipole) approximation that only holds for particles much smaller than the wavelength. The only inputs are the optical constants of gold and of the medium, taken from published measurements.

Yes: gold nanospheres and core–shell nanoparticles (add a shell) are available in every calculator, from spectra to optical properties: near-field enhancement maps, dimers and hot spots, nanoparticle arrays and lattice resonances, particles on a substrate, emitters and the Purcell factor, nanorods and laser heating.