Dynamic Light Scattering Methods
Dynamic Light Scattering (DLS) is nowadays used on a routine basis for the analysis of particle sizes in the sub-micrometer range. It provides an estimation of the average size and its distribution within a measuring time of a few minutes.
Sub-micron particles suspended in a liquid are in constant motion as a result of the impacts from the molecules of the suspending liquid. This movement is known as Brownian Molecular Movement and was correctly suggested by W. Ramsay in 1876 and confirmed by A. Einstein and M. Smoluchowski in 1905/06.
In the Stokes-Einstein theory of Brownian motion, the particle motion at very low concentrations is depending on the viscosity of the suspending liquid, the temperature, and the size of the particle. If viscosity and temperature are known, the particle size can be evaluated from a measurement of the particle motion. At low concentrations, this is the hydrodynamic diameter.
DLS probes this motion optically. The particles are illuminated by a coherent light source, typically a laser, creating a diffraction pattern, showing in FIG. 1 a fine structure from the diffraction between the particles, i.e. its near-order. As the particles are moving from impacts of the thermal movement of the molecules of the medium, the particle positions change with the time, t.
FIG. 1 Particles illuminated by a Gaussian shaped laser beam and it corresponding diffraction pattern, showing a fine structure.
The change of the position of the particles affects the phases and thus the fine structure of the diffraction pattern. So the intensity in a certain point of the diffraction pattern fluctuates with time. The fluctuations can be analyzed in the time domain by a correlation function analysis or in the frequency domain by frequency analysis. Both methods are linked by Fourier transformation.
The measured decays rate G are related to the translational diffusion coefficients D of spherical particles by
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and |
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were q is the modulus of the scattering vector, kB is the Boltzmann constant, T the absolute temperature, and h the hydrodynamic viscosity of the dispersing liquid. The particle size x is then calculated by the Stokes-Einstein equation from D at fixed temperature T and h known.
DLS covers a broad range of diluted and concentrated suspension. As the theory is only valid for light being scattered once, any contribution of multiple scattered light leads to erroneous PCS results and misinterpretations. So different measures have been taken to minimize the influence of multiple scattering.
The well established Photon Correlation Spectroscopy (PCS) is using highly diluted suspensions in order to avoid multiple scattering. The low concentration of particles makes this method sensitive to impurities in the liquid. So usually very pure liquids and a clean room environment have to be used for the preparation and the operation [ISO 13321:1996 Particle size analysis - Photon correlation spectroscopy].
Other technique utilizes an optical system which minimizes the optical path in and out of the sample – including the use of backscatter optics, a moving cell assembly, or set-ups with the maximum incident beam intensity located at the interface of the suspension to the optical window [Trainer, Freud, and Weiss, Pittsburg Conference, Analytical and Applied Spectroscopy, Symp. Particle Size Analysis (March 1990); Coming ISO 22412 Particle size analysis - Dynamic light scattering].
FIG. 2 Diagram of Leeds and Northrup Ultrafine Particle Size Analyzer (UPA), using fiber optics in a back-scatter set-up.
The novel Photon Cross Correlation Spectroscopy (PCCS) is using a 3-dimensional cross correlation technique which completely suppresses the multiple scattered fractions in a special scattering geometry. High concentrated, opaque suspensions can be measured, as long as scattered light is observed. High count rates result in short measuring times. High particle concentrations reduce the sensitivity of this method to impurities. So standard liquids and laboratory environments can be used, which simplifies the application [W. Witt, L. Aberle, H. Geers, Measurement of Particle Size and Stability of Nanoparticles in Opaque Suspensions and Emulsions with Photon Cross Correlation Spectroscopy, Particulate Systems Analysis 2003, Harrogate (UK)].
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FIG. 3 Scattering geometry of a PCCS set-up. The sample volume is illuminated by two incident beams. Identical scattering vectors 
and the scattering volumes are used in combination with cross correlation to eliminate multiple scattering.
