Introduction
When a beam of light passes through a colloidal dispersion, the particles or droplets scatter some of the light in all
directions. When the particles are very small compared with the wavelength of the light, the intensity of the scattered light
is uniform in all directions (Rayleigh scattering); for larger particles (above approximately 250nm diameter), the intensity is
angle dependent (Mie scattering).
If the light is coherent and monochromatic, as from a laser for example, it is possible to observe time-dependent
fluctuations in the scattered intensity using a suitable detector such as a photomultiplier capable of operating in photon
counting mode.
These fluctuations arise from the fact that the particles are small enough to undergo random thermal (Brownian) motion
and the distance between them is therefore constantly varying. Constructive and destructive interference of light scattered
by neighbouring particles within the illuminated zone gives rise to the intensity fluctuation at the detector plane which, as it
arises from particle motion, contains information about this motion. Analysis of the time dependence of the intensity
fluctuation can therefore yield the diffusion coefficient of the particles from which, via the Stokes Einstein equation,
knowing the viscosity of the medium, the hydrodynamic radius or diameter of the particles can be calculated.
The time dependence of the intensity fluctuation is most commonly analysed using a digital correlator. Such a device
determines the intensity autocorrelation function which can be described as the ensemble average of the product of the
signal with a delayed version of itself as a function of the delay time. The "signal" in this case is the number of photons
counted in one sampling interval. At short delay times, correlation is high and, over time as particles diffuse, correlation
diminishes to zero and the exponential decay of the correlation function is characteristic of the diffusion coefficient of the
particles. Data are typically collected over a delay range of 100ns to several seconds depending upon the particle size and
viscosity of the medium.
Analysis of the autocorrelation function in terms of particle size distribution is done by numerically fitting the data with
calculations based on assumed distributions. A truly monodisperse sample would give rise to a single exponential decay to
which fitting a calculated particle size distribution is relatively straightforward. In practice, polydisperse samples give rise to
a series of exponentials and several quite complex schemes have been devised for the fitting process. One of the methods
most widely used today is known as Non-Negatively Constrained Least Squares (NNLS); the Brookhaven correlator
software includes this along with several other approaches to the problem.
Particle size distributions can be calculated either assuming some standard form such as log-normal or without any such
assumption. In the latter case, it becomes possible, within certain limitations, to characterise multimodal or skewed
distributions. The size range for which dynamic light scattering is appropriate is typically submicron with some capability to
deal with particles up to a few microns in diameter. The lower limit of particle size depends on the scattering properties of
the particles concerned (relative refractive index of particle and medium), incident light intensity (laser power and
wavelength) and detector / optics configuration.
Dynamic light scattering (also known as Quasi Elastic Light Scattering [QELS] and Photon Correlation Spectroscopy
[PCS]) is particularly suited to determining small changes in mean diameter such as those due to adsorbed layers on the
particle surface or slight variations in manufacturing processes.
