Particle size and zeta potential analysers

Suspended particles are struck unevenly by solvent molecules and execute Brownian motion, with small particles diffusing faster than large ones. Illuminate the suspension with a coherent laser and the scattered light from many particles interferes; as the particles move, the speckle pattern at the detector fluctuates. Dynamic light scattering measures nothing but the timescale of those fluctuations. An intensity autocorrelation function is built from the signal, its decay rate gives the translational diffusion coefficient, and the Stokes–Einstein relation converts diffusion at known temperature and viscosity into a hydrodynamic diameter. The method is standardised as ISO 22412.

Three assumptions are buried in that chain. The result is the diameter of a sphere that would diffuse at the observed rate, so an elongated or heavily hydrated particle reports larger than its geometric size. The viscosity used is that of the solvent, so a concentrated or polymer-containing formulation is misread unless the true medium viscosity is known. And the particles must be moving freely — at high concentration, light scattered by one particle is scattered again by another, and multiple scattering corrupts the correlation function, which backscatter detection geometry mitigates but does not abolish.

The sixth-power problem#

For particles well below the wavelength, scattered intensity rises with roughly the sixth power of diameter. A single one-micrometre aggregate therefore scatters about as much light as a million ten-nanometre particles. This makes dynamic light scattering exquisitely sensitive to the appearance of aggregates — useful, since aggregation is often the thing being watched — and simultaneously a poor tool for quantifying them, because the intensity-weighted distribution it produces overstates the large tail enormously. Converting to a volume or number distribution requires assumptions about refractive index and particle shape that add their own error.

The same physics limits resolution. Two populations closer than roughly a factor of three in diameter cannot be reliably separated; the fit returns one broad peak. The routinely quoted z-average and polydispersity index come from fitting the correlation decay as if the sample were monomodal, so for a genuinely mixed sample they are descriptors of the fit, not of the material. Nanoparticle tracking analysis avoids the weighting problem by following individual particles and counting them, giving number-weighted concentration, at the price of a narrower usable size range and statistical noise from finite track lengths. Laser diffraction, used above the micrometre range, inverts a Mie scattering pattern and needs the refractive and absorptive indices of the material as inputs — values often not accurately known.

Zeta potential is inferred, not measured#

The instrument measures electrophoretic mobility: an alternating field is applied, and the Doppler shift of light scattered by drifting particles is recovered by phase analysis. Mobility is a real observable. Zeta potential is not — it is the electrostatic potential at the hydrodynamic shear plane, a surface whose position cannot be located independently, and mobility is converted into it through Henry’s function, using the Smoluchowski limit for a thin double layer or the Hückel limit for a thick one.

The choice between those limits depends on the ratio of particle radius to Debye length, and this is where the method fails where it is most wanted. In physiological ionic strength the double layer is compressed to about a nanometre, mobility is small, conductivity drives Joule heating and electrode polarisation, and the assumptions behind the conversion are strained. Zeta potentials are therefore normally measured in diluted low-salt buffer — a useful comparative ranking of colloidal stability, but not the value the formulation actually has in the vial.