Dynamic light scattering (DLS) and zeta potential: how they work and how to read size, PDI and ζ

Brownian motion and scattered light. Particles in a liquid move randomly because of collisions with solvent molecules; small particles move fast and large ones slowly (Rodriguez-Loya et al. 2023). When a laser lights the sample, light scattered by all the particles interferes, and as they move the total scattered intensity fluctuates. DLS records these fluctuations in time, whereas static light scattering records only the time-averaged intensity (Wishard & Gibb 2019).

From fluctuations to size. A correlator compares the intensity at time t with the intensity a delay τ later. For short delays the signal is well correlated; as τ grows the correlation decays, usually exponentially, as g₂(τ) = 1 + β·exp(−2Dq²τ), where D is the translational diffusion coefficient and q the scattering vector (Wishard & Gibb 2019). In a typical measurement the correlation falls away within about 1–10 ms (Rodriguez-Loya et al. 2023). The diffusion coefficient is then converted to a hydrodynamic radius with the Stokes–Einstein equation, D = k_BT / (6πηr_H), where η is the viscosity of the liquid and T the temperature (Wishard & Gibb 2019). The result is a sphere-equivalent hydrodynamic size: for non-spherical particles the measured diffusion mixes translation and rotation (Wishard & Gibb 2019).

Zeta potential. In electrophoretic light scattering, the instrument applies an electric field and measures how fast the particles move, using laser Doppler velocimetry: the scattered light is Doppler-shifted by the moving particles (Rodriguez-Loya et al. 2023). The velocity per unit field is the electrophoretic mobility U_E, and Henry's equation, U_E = 2εζf(κa)/3η, converts it to the zeta potential ζ, the electrical potential at the slipping plane between the particle and the bulk liquid. For particles that are large compared with the double layer in aqueous salt solutions f(κa) = 1.5 (the Smoluchowski limit); for small particles in low-salt or low-dielectric media f(κa) = 1.0 (the Hückel limit) (Rodriguez-Loya et al. 2023). These two measurements belong with the other characterisation techniques for anything dispersed in a liquid.

Start with the correlation function. It is the raw data of DLS. A clean curve starts high and decays smoothly to a flat baseline; a noisy, poorly correlated curve, caused by weak scattering, dust, precipitation or sedimentation, gives unreliable sizes whatever the software reports (Wishard & Gibb 2019).

Mean size and PDI. The cumulants method fits the correlation function of a single population and gives a mean size and the polydispersity index (Wishard & Gibb 2019; Danaei et al. 2018). PDI runs from 0 for a perfectly uniform sample to 1 for a very broad one; below 0.05 is seen only with highly monodisperse standards, and above 0.7 the distribution is probably too broad for DLS. In practice 0.2 or less is accepted for polymer nanoparticles and 0.3 or less for liposomes and other lipid carriers (Danaei et al. 2018).

Intensity, volume and number distributions. For several populations, software fits the decay with an NNLS-type algorithm and reports a size distribution (Wishard & Gibb 2019). The intensity distribution is the primary result; volume and number distributions are calculated from it with Mie theory (Rodriguez-Loya et al. 2023). Because scattered intensity scales with the sixth power of diameter, a 1:1 mixture by number of 1 nm and 10 nm particles shows up as 1:10⁶ by intensity and about 1:1000 by volume (Wishard & Gibb 2019). Likewise, equal numbers of 50 nm and 100 nm particles give an intensity ratio of 1:64 (calculated from I ∝ d⁶). A small peak of large particles in the intensity plot can therefore be only a tiny number of aggregates.

Zeta potential. The result is a value in millivolts with its sign, usually shown as a distribution. A value beyond about ±30 mV is generally taken as the line between stable and unstable dispersions, values near zero as unstable; some authors ask for ±40 to ±60 mV for good stability (Rodriguez-Loya et al. 2023). Always quote the pH and the medium alongside it (Rodriguez-Loya et al. 2023).

• Keep it dust-free. Because of the d⁶ scaling, one dust particle can swamp the signal of nanometre particles; use clean, capped cuvettes and wipe the outside (Wishard & Gibb 2019).
• Centrifuge or filter. Centrifuging for about 10 min at 10,000 rpm or filtering removes stray particles; measure an unfiltered reference too, so you know the filter did not remove your own aggregates (Wishard & Gibb 2019).
• Dilute. The sample must be dilute enough to avoid multiple scattering (Rodriguez-Loya et al. 2023); concentration effects are also one cause of DLS–TEM disagreement (Filippov et al. 2023).
• Enter the right solvent data and wait for temperature. The viscosity and refractive index of the solvent at the measurement temperature are needed, and each degree away from thermal equilibrium adds about 2% error to the size (Wishard & Gibb 2019).
• Choose the angle. Back-scatter at about 173° suits large particles; about 90° suits small ones, where forward scatter from large species would otherwise dominate (Wishard & Gibb 2019).
• Add background salt for charged particles. Unscreened polyelectrolytes diffuse anomalously fast and look too small; salt or buffer removes the effect (Wishard & Gibb 2019). For zeta potential, control pH and ionic strength, which set the double-layer thickness (Rodriguez-Loya et al. 2023).

Colloidal stability and aggregation. DLS follows particle size over time, so it shows aggregation as it happens, and zeta potential gives the electrostatic part of the stability (Rodriguez-Loya et al. 2023). In DLVO theory, the stability of a dispersion is the balance of van der Waals attraction and electric double-layer repulsion; adding salt compresses the double layer and screens the repulsion, which is why dispersions that are stable at low salt aggregate at high salt (Rodriguez-Loya et al. 2023).

Isoelectric point. Measuring zeta potential across a pH range finds the isoelectric point, where the dispersion is least stable (Rodriguez-Loya et al. 2023). The same size and zeta measurements apply to dispersions of MOF nanoparticles such as ZIF-8 or UiO-66 and to sheets such as graphene oxide, whose non-spherical shape limits what a sphere-equivalent size means (Wishard & Gibb 2019).

Nanocarriers and quality control. Size and PDI are critical quality attributes of lipid nanoparticles and liposomes, measured by DLS against ISO 13321 and ISO 22412 (Danaei et al. 2018).

Size in solution, not dry size. DLS gives an ensemble hydrodynamic size of particles in their liquid; it complements TEM and SEM, which image dry particles one by one (Danaei et al. 2018). For crystallite size from diffraction, see XRD; for gold nanoparticles, the plasmon band in UV–vis gives another size estimate.

• Reporting the number distribution as "the size". The intensity distribution is what DLS measures; volume and number distributions are conversions from it through Mie theory (Rodriguez-Loya et al. 2023; Wishard & Gibb 2019). Report the intensity result and say which weighting you show.
• Expecting DLS to match TEM. Many papers report DLS and TEM sizes that differ by 200–300%; concentration and angle effects are common causes, and correct procedures bring the two much closer (Filippov et al. 2023). DLS also counts an aggregate of several particles as one particle (Danaei et al. 2018).
• Applying it to non-spheres without care. For rods and sheets the measured diffusion mixes translation and rotation, so the sphere-equivalent size is only indicative (Wishard & Gibb 2019); DLS gives no shape information (Danaei et al. 2018).
• Measuring broad or concentrated samples. A PDI above about 0.7 means the sample is probably not suitable for DLS (Danaei et al. 2018); high concentration, high viscosity and turbidity reduce reliability (Rodriguez-Loya et al. 2023).
• Quoting ζ without conditions. Zeta potential depends on pH, conductivity, temperature and the ions present (Rodriguez-Loya et al. 2023); a value without pH and medium cannot be compared.
• Forgetting that ELS can change the sample. The applied current can damage sensitive samples, so measure size before zeta potential (Wishard & Gibb 2019).

In the LabCanvas figure editor, the Library has a DLS / zeta potential analyser as an editable object, including a cutaway of the laser path through the cuvette to the detector at the back-scatter and side-scatter angles and the electrodes of the zeta cell, plus an editable data plot for correlation functions, intensity, volume and number distributions and zeta potential curves. You can label the peaks with their hydrodynamic diameters and the PDI, mark the ±30 mV stability band, and export the figure for a methods section or a graphical abstract.