Measuring nanoparticles in liquid: size and charge

Six principles for characterising a colloid: dynamic light scattering and what its hydrodynamic diameter includes, nanoparticle tracking analysis, the electrical double layer and the zeta potential, the electrophoresis cell that measures it, and small-angle X-ray scattering. Instruments and principles only, with every caption quoted from the cited papers.

1. Dynamic light scattering: DLS follows how fast particles diffuse in Brownian motion; the hydrodynamic radius is calculated from the diffusion coefficient and depends on size and shape (Stetefeld 2016). One set-up: a 633 nm laser with detection at 173° (backscatter) and further angles of 90° and 45° on a goniometer; q = (4πn/λ) sin(θ/2) (Tuoriniemi 2014). 2. What DLS measures: The hydrodynamic diameter is usually larger than the physical diameter because it includes waters of hydration; silica particles were an exception, about 10–15 % smaller, explained by a permeable gel layer (Tuoriniemi 2014). 10 nm Fe@FeOₓ cores with an 11 nm silica shell and 5 kDa PEG had hydrodynamic diameters in the 100 nm range (Mathieu 2019). 3. Particle tracking: In NTA the trajectories of particles in Brownian motion are tracked by video microscopy; lit from a 90° angle by an intense laser beam, particles well below the diffraction limit become visible, and diffusion constants follow from the distance each travels while visible. The beam’s Gaussian profile lets large, strong scatterers be seen further from its centre, which biased sizes of a poor scatterer such as silica upward (Tuoriniemi 2014). 4. The double layer: The electrical double layer has an inner Stern layer, where ions are strongly bound, and an outer diffuse layer; ions inside the slipping plane move with the particle, and its potential is the zeta potential; the Debye length follows from the ionic strength (Kaszuba 2010). With more salt the Stern layer is compressed and the zeta potential lower (Brown 2016). 5. Electrophoretic mobility: A voltage across electrodes at either end of the cell moves charged particles toward the oppositely charged electrode; laser Doppler electrophoresis measures the small frequency shift of light scattered by the moving particles, here at a forward angle of 13°; Henry’s equation converts mobility to zeta potential, with the Smoluchowski approximation f(κa) = 1.5 for a thin double layer (Kaszuba 2010). 6. Small-angle X-ray scattering: X-rays, with wavelengths typically of the order of 1 Å, are scattered by electrons, and the 2D pattern is radially integrated to I(q) (Di Cola 2016); solution SAXS gives statistically significant 3D structural information on monodisperse nanocrystals in their colloidal state (Krieg 2021).

Starting materials: A dilute nanoparticle dispersion in a cuvette, a thin chamber, a folded capillary or electrophoresis cell, or a capillary in the X-ray beam. Product: Hydrodynamic size, particle-by-particle size, zeta potential and core size and shape.

Stetefeld, McKenna & Patel, “Dynamic light scattering: a practical guide and applications in biomedical sciences”, Biophys. Rev. 2016 (doi:10.1007/s12551-016-0218-6); Tuoriniemi et al., “Intermethod comparison of the particle size distributions of colloidal silica nanoparticles”, Sci. Technol. Adv. Mater. 2014 (doi:10.1088/1468-6996/15/3/035009); Kaszuba et al., “High-concentration zeta potential measurements using light-scattering techniques”, Phil. Trans. R. Soc. A 2010 (doi:10.1098/rsta.2010.0175); Di Cola, Grillo & Ristori, “Small angle X-ray and neutron scattering: powerful tools for studying the structure of drug-loaded liposomes”, Pharmaceutics 2016 (doi:10.3390/pharmaceutics8020010); Krieg et al., “Monodisperse long-chain sulfobetaine-capped CsPbBr3 nanocrystals and their superfluorescent assemblies”, ACS Cent. Sci. 2021 (doi:10.1021/acscentsci.0c01153); Mathieu et al., “Silica coated iron/iron oxide nanoparticles as a nano-platform for T2 weighted magnetic resonance imaging”, Molecules 2019 (doi:10.3390/molecules24244629); Brown, Goel & Abbas, “Effect of electrolyte concentration on the Stern layer thickness at a charged interface”, Angew. Chem. Int. Ed. 2016 (doi:10.1002/anie.201512025).

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