One-click electromagnetism at the nanoscale

Silver nanoparticle UV-vis spectrum calculator

Questions & answers

Why are silver nanoparticles yellow?

Small silver spheres have their localized surface plasmon, the collective oscillation of the conduction electrons, near 390–400 nm in water. They absorb violet and blue light there, so a dilute colloid looks yellow. As the particles grow the peak moves into the visible and broadens, and the colour goes through orange towards grey-green.

How does the UV-vis peak of silver nanoparticles shift with size?

In water the plasmon peak sits near 385–390 nm for spheres up to about 20 nm, then red-shifts: about 400 nm at 40 nm, 408 nm at 50 nm, 446 nm at 80 nm and 481 nm at 100 nm. From about 60 nm a second, shorter-wavelength peak (the quadrupole) appears near 375–390 nm. Silver scatters strongly: above 40 nm most of the extinction is scattering, not absorption (table above).

What is the molar extinction coefficient of silver nanoparticles?

Silver's resonance is sharper and stronger than gold's: about 1.8 × 1010 M−1 cm−1 at the peak for 20 nm spheres and 6.9 × 1010 for 40 nm (table above). It follows from the extinction cross-section, ε = NA Cext / (1000 ln 10), and gives the particle concentration c = A / (ε ℓ).

What are the optical properties of silver nanoparticles?

Silver has the strongest and sharpest plasmon of the common metals: small spheres in water absorb and scatter strongly near 390–400 nm, with low damping, large near-field enhancement and, above about 35 nm, more scattering than absorption. The resonance moves through the visible as the particles grow or change shape (nanoprisms and nanocubes reach the red), which gives silver colloids colours from yellow to blue.

What is the UV-vis range of silver nanoparticles?

Spherical silver nanoparticles in water show their plasmon band between about 385 and 480 nm for diameters from 5 to 100 nm (table above); typical citrate-capped particles of 10–40 nm peak at about 390–410 nm. Peaks well beyond 450 nm point to large, non-spherical or aggregated particles.

How is UV-vis spectroscopy used for the characterization of silver (Ag) nanoparticles?

The plasmon band of plasmonic Ag nanoparticles in the UV-vis spectrum reports their size (peak position), size distribution and shape (width and shoulders), concentration (height) and stability (a red-shifted shoulder means aggregation). Compare a measured spectrum with the calculation for candidate sizes: a UV–visible spectroscopic assessment of the size distribution.

Why is my measured silver spectrum broader or shifted?

Silver is sensitive to its surface: oxidation or sulfidation and ligand layers red-shift and damp the peak (model them as a shell in the calculator), and the size distribution, non-spherical particles and aggregation broaden it. Particles under about 10 nm also show extra damping from electron surface scattering, which bulk optical constants do not include.

Silver or gold: which nanoparticles should I use?

Silver gives a stronger, sharper plasmon and larger near-field enhancement (useful for SERS and sensing) but oxidizes; gold is chemically stable and biocompatible, with its resonance in the green–red. Compare both in the calculator, or see the gold nanoparticle UV-vis page.

Is this an exact calculation?

Yes. Mie theory solves Maxwell's equations exactly for a sphere (and for layered core–shell spheres) at any size, unlike the quasi-static dipole approximation. The inputs are the measured optical constants of silver (Johnson & Christy) and of the medium.

Can I compute silver nanospheres, core–shell nanoparticles, arrays, near fields, heating or substrates?

Yes: silver 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.

The extinction (UV-vis), absorption and scattering spectrum of silver nanospheres of any size, in any solvent, with or without a shell: in one click, from exact Mie theory. Set the diameter and press Calculate.

Silver nanoparticle size vs UV-vis peak

Spheres in water, from exact Mie theory with this site's solver (the calculator above gives the full spectrum for any size, solvent or coating).

Diameter Plasmon peak (λmax) Molar extinction coefficient at λmax Scattering share
5 nm 384 nm 3.19 × 108 M−1 cm−1 < 1 %
10 nm 385 nm 2.52 × 109 M−1 cm−1 2 %
15 nm 386 nm 8.06 × 109 M−1 cm−1 8 %
20 nm 388 nm 1.75 × 1010 M−1 cm−1 17 %
30 nm 393 nm 4.36 × 1010 M−1 cm−1 41 %
40 nm 400 nm 6.89 × 1010 M−1 cm−1 62 %
50 nm 408 nm 8.84 × 1010 M−1 cm−1 76 %
60 nm 419 nm · 2nd peak 374 nm 1.04 × 1011 M−1 cm−1 86 %
70 nm 431 nm · 2nd peak 377 nm 1.18 × 1011 M−1 cm−1 92 %
80 nm 446 nm · 2nd peak 380 nm 1.29 × 1011 M−1 cm−1 94 %
90 nm 461 nm · 2nd peak 385 nm 1.39 × 1011 M−1 cm−1 95 %
100 nm 481 nm · 2nd peak 390 nm 1.50 × 1011 M−1 cm−1 96 %
125 nm 533 nm · 2nd peak 406 nm 1.82 × 1011 M−1 cm−1 97 %
150 nm 601 nm · 2nd peak 427 nm 2.20 × 1011 M−1 cm−1 98 %
200 nm 759 nm · 2nd peak 485 nm 3.19 × 1011 M−1 cm−1 99 %

Silver optical constants: Johnson & Christy (1972); water: Hale & Querry (1973). Plasmon peak: the dipole (longest-wavelength) extinction maximum; the second, shorter-wavelength peak of large particles is the quadrupole. Molar extinction coefficient ε = NA Cext / (1000 ln 10), so the particle concentration is c = A / (ε ℓ). Scattering share: Csca / Cext at the peak. Below about 10 nm real particles show broader, weaker peaks (electron surface scattering) than bulk optical constants give.

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