Question 1

What are the optical properties of polystyrene nanoparticles and beads?

Accepted Answer

Polystyrene has a refractive index of about 1.59 in the visible and does not absorb, so polystyrene beads only scatter light. They have no plasmon resonance: their extinction spectrum is pure scattering, rising towards the blue for small beads (Rayleigh, about λ−4) and showing broad Mie oscillations for beads around a micrometre and larger. That predictability makes them the standard calibration particles for DLS, flow cytometry, particle sizers and turbidity.

Question 2

How do I calculate the extinction spectrum of polystyrene beads?

Accepted Answer

Choose polystyrene and water in the calculator above, set the diameter and press Calculate: the extinction (turbidity) spectrum follows from exact Mie theory. The table gives the extinction efficiency, the molar extinction coefficient and the wavelength exponent of the turbidity for common sizes.

Question 3

How can I estimate bead size from a turbidity spectrum?

Accepted Answer

The wavelength exponent of the turbidity falls as the beads grow: about 4 for small beads, 3 for 200–300 nm polystyrene, 2.4 at 500 nm and about 1 at 1 µm (table above). Comparing the measured exponent, or the full spectrum, with the calculation gives the size.

Question 4

What are the optical properties of silica nanospheres?

Accepted Answer

Silica (index about 1.46) is barely different from water (1.33), so silica nanospheres scatter weakly, several times less than polystyrene of the same size, and do not absorb in the visible. That makes them good transparent cores and shells: gold-coated silica (nanoshells) and silica-coated gold are both layered spheres the calculator solves exactly.

Question 5

Can Mie scattering be used for nanoplastics detection?

Accepted Answer

Yes. Polystyrene and other plastics scatter light according to Mie theory, with Mie resonances once they approach the wavelength, so their size and concentration can be inferred from scattering or extinction spectra, and dark-field or interferometric microscopes detect single particles down to tens of nanometres. Exact Mie calculations give the expected signal for each size and plastic.

Question 6

Do polystyrene nanoparticles have a plasmon resonance or near-field enhancement?

Accepted Answer

No plasmon: polystyrene is a dielectric. Its near-field enhancement is modest (|E|2/|E0|2 of a few) for small beads; micrometre beads focus light into a photonic nanojet. Polystyrene beads on substrates and in arrays are available in all the calculators, including near fields, arrays and lattice resonances and particles on a substrate.

Diameter	Extinction efficiency at 550 nm	ε at 550 nm	Wavelength exponent (450–650 nm)
50 nm	0.00087	4.45 × 10⁶ M⁻¹ cm⁻¹	4.38
100 nm	0.013	2.57 × 10⁸ M⁻¹ cm⁻¹	4.13
200 nm	0.117	9.65 × 10⁹ M⁻¹ cm⁻¹	3.07
300 nm	0.336	6.21 × 10¹⁰ M⁻¹ cm⁻¹	2.99
500 nm	1.048	5.38 × 10¹¹ M⁻¹ cm⁻¹	2.38
1 µm	3.096	6.36 × 10¹² M⁻¹ cm⁻¹	1.10
2 µm	2.500	2.05 × 10¹³ M⁻¹ cm⁻¹	-1.82

Diameter	Extinction efficiency at 550 nm	ε at 550 nm	Wavelength exponent (450–650 nm)
50 nm	0.00021	1.07 × 10⁶ M⁻¹ cm⁻¹	4.06
100 nm	0.00291	5.98 × 10⁷ M⁻¹ cm⁻¹	3.75
200 nm	0.027	2.19 × 10⁹ M⁻¹ cm⁻¹	2.75
300 nm	0.073	1.34 × 10¹⁰ M⁻¹ cm⁻¹	2.65
500 nm	0.243	1.25 × 10¹¹ M⁻¹ cm⁻¹	2.31
1 µm	0.983	2.02 × 10¹² M⁻¹ cm⁻¹	1.94
2 µm	2.817	2.31 × 10¹³ M⁻¹ cm⁻¹	1.04

Polystyrene and silica bead scattering calculator

Questions & answers

What are the optical properties of polystyrene nanoparticles and beads?

How do I calculate the extinction spectrum of polystyrene beads?

How can I estimate bead size from a turbidity spectrum?

What are the optical properties of silica nanospheres?

Can Mie scattering be used for nanoplastics detection?

Do polystyrene nanoparticles have a plasmon resonance or near-field enhancement?

Polystyrene beads: scattering by size

Silica beads: scattering by size

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