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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 as the Brookhaven BI-9000AT.
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.
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