What is the Haiss method for gold nanoparticle sizing?

The Haiss method uses UV-Vis spectroscopy to determine gold nanoparticle size and concentration. It employs either the SPR peak wavelength position or the ratio of absorbances (Aspr/A450) to calculate particle diameter, with different equations optimized for different size ranges.

What size range is valid for the Haiss method?

The SPR peak position method works best for 35-100 nm particles (±3% error), while the absorbance ratio method is optimized for 5-80 nm particles (±6% error). Below 5 nm, the SPR peak becomes severely damped, making UV-Vis sizing unreliable.

Why is 450 nm used as the reference wavelength?

At 450 nm, gold exhibits interband transitions that are relatively insensitive to particle size, shape, and aggregation state. This makes A450 a reliable reference for concentration measurements regardless of nanoparticle morphology.

How accurate is UV-Vis sizing compared to TEM?

For spherical, monodisperse gold nanoparticles in water, the Haiss method achieves ±3-6% accuracy compared to TEM. Accuracy decreases for polydisperse samples, non-spherical particles, or particles with thick surface coatings.

Gold Nanoparticle Size Estimator

Estimate AuNP size and concentration from UV-Vis spectra using the Haiss method

Sizing Method

⚡ Auto-Update

Select Method

The absorbance ratio method is generally more robust as it doesn't require precise wavelength calibration.

UV-Vis Spectral Data

SPR Peak Wavelength (λ_SPR) Typically 515-570 nm

Wavelength at the maximum of the surface plasmon resonance peak.

λ_SPR must be between 500 and 600 nm for valid results

Absorbance at SPR Peak (A_SPR)

Maximum absorbance value at the SPR peak wavelength.

Absorbance must be greater than zero

Absorbance at 450 nm (A₄₅₀)

Absorbance at the interband transition region. Used for both sizing and concentration.

Absorbance must be greater than zero

Optical Path Length Cuvette path length

Standard cuvettes are 1 cm. Microvolume instruments may use shorter paths.

Data quality: Use blank-subtracted absorbance values. Ensure the sample is well-dispersed (no aggregation) and the absorbance is within the linear range of your instrument (typically 0.1–2 AU).

Results

Estimated Particle Diameter

— nm

Concentration

—

particles/mL

Molar Concentration

—

Gold Mass Conc.

— µg/mL

ε₄₅₀ (Extinction Coeff.)

— M⁻¹cm⁻¹

Expected Color

Ruby Red

AuNP Color vs Size Guide

Validation: Results should be verified with TEM or DLS for critical applications. Polydispersity and non-spherical particles can lead to inaccurate estimates.

The Haiss Method for AuNP Characterization

The Haiss method, published in Analytical Chemistry in 2007, provides a rapid, non-destructive approach to estimate gold nanoparticle size and concentration directly from UV-Vis spectra. It exploits the size-dependent optical properties arising from the surface plasmon resonance (SPR) of gold nanoparticles.

Key insight: As gold nanoparticle size increases, the SPR peak redshifts (moves to longer wavelengths) and the ratio A_SPR/A₄₅₀ increases due to enhanced scattering contributions at larger sizes.

Sizing Methods

Method 1: SPR Peak Position (35-100 nm)

For particles larger than 35 nm, the SPR peak position provides reliable sizing. The Haiss forward equation relates size to wavelength:

SPR Peak Redshift with Increasing Particle Size

As particle diameter increases, λ_SPR shifts to longer wavelengths

λ_SPR = λ₀ + L₁ × exp(L₂ × d)

Inverted to solve for diameter:

d = ln((λ_SPR − λ₀) / L₁) / L₂

where L₁ = 6.53, L₂ = 0.0216, λ₀ = 512 nm

This method achieves ~3% error for spherical particles in water but is sensitive to refractive index changes from surface coatings or different solvents.

Mathematical constraint: The SPR peak method requires λ_SPR > 518.5 nm. Below this threshold, the logarithm yields undefined or negative values. For small particles with λ_SPR in the 510-518 nm range, use the Absorbance Ratio method instead.

Method 2: Absorbance Ratio (5-80 nm)

The ratio of SPR absorbance to the interband transition absorption at 450 nm provides a more robust sizing method:

d = exp(B₁ × (A_SPR/A₄₅₀) − B₂)

where B₁ = 3.00, B₂ = 2.20

This method is less sensitive to concentration errors and achieves ~6% accuracy. It works well for smaller particles where the SPR peak position is less size-dependent.

Concentration Determination

Particle concentration is calculated from the absorbance at 450 nm, which is relatively independent of particle shape and aggregation:

N = A₄₅₀ × 10¹⁴ / d² (particles/mL)

This can be converted to molar concentration by dividing by Avogadro's number (6.022 × 10²³).

Why 450 nm?

The wavelength 450 nm falls in the interband transition region of gold, where:

Absorption is dominated by electronic transitions rather than plasmon resonance
The extinction coefficient scales predictably with particle volume
The signal is insensitive to particle shape, aggregation state, and surface chemistry

Limitations

Spherical particles only: Rods, cubes, and other shapes have fundamentally different optical properties
Aqueous dispersions: Different solvents shift λ_SPR significantly due to refractive index changes
Monodisperse samples: Polydispersity leads to peak broadening and inaccurate size estimates (biased toward larger particles)
No aggregation: Aggregated samples show red-shifted, broadened peaks that invalidate the analysis
Size limits: Below ~5 nm, the SPR is severely damped; above ~100 nm, multipolar modes complicate the spectrum

Surface coating effects: Thick coatings (>2 nm) with high refractive index can redshift λ_SPR by 5-10 nm, leading to size overestimation. For functionalized particles, the absorbance ratio method is preferred.

References

Haiss, W., Thanh, N. T. K., Aveyard, J., & Fernig, D. G. (2007). Determination of Size and Concentration of Gold Nanoparticles from UV−Vis Spectra. Analytical Chemistry, 79(11), 4215–4221. doi:10.1021/ac0702084

Amendola, V., & Meneghetti, M. (2009). Size Evaluation of Gold Nanoparticles by UV−vis Spectroscopy. The Journal of Physical Chemistry C, 113(11), 4277–4285. doi:10.1021/jp8082425

Shard, A. G., Wright, L., & Minelli, C. (2018). Robust and accurate measurements of gold nanoparticle concentrations using UV-visible spectrophotometry. Biointerphases, 13(6), 061002. doi:10.1116/1.5054780

Jain, P. K., Lee, K. S., El-Sayed, I. H., & El-Sayed, M. A. (2006). Calculated Absorption and Scattering Properties of Gold Nanoparticles of Different Size, Shape, and Composition. The Journal of Physical Chemistry B, 110(14), 7238–7248. doi:10.1021/jp057170o

Particle Size

— nm

AI & Computational Tools for Researchers

Explore our curated guides to the best free AI tools for literature discovery, data analysis, computational modeling, and more.