As
particles become smaller, the ratio
of particle dimension to light wavelength
(d/λ) is reduced and the scattering
pattern becomes smoother and less angularly
dependent, causing more difficulty in
determining the correct size values.
To enhance the ability to measure small
particles, there are three approaches
one may take to extend the lower size
limit when measuring particles using
laser diffraction.
The first approach to extend the lower
sizing limit is by increasing the angular
detecting range. If we use the angular
location of the first minimum in the
scattering pattern as the criterion
to correctly size a sphere, we will
find that in order to size a sphere
having a diameter smaller than 0.5 µm,
the maximum detecting angle has to be
greater than 90 degrees. Thus, in order
to size a submicron particle, the detection
angular range has to be designed to
cover angles at least as large as 90
degrees; practically, the maximum detecting
angle can be as large as 175°.
Scattering patterns are a function of
light wavelength and particle size.
Their variations are related to the
ratio between particle dimension and
wavelength (d/λ). Obviously,
if the wavelength of light is shorter
the ratio will be greater and the lower
sizing limit will be effectively extended.
Practically, the shortest wavelength
is about 350 nm because most materials
exhibit strong absorption at wavelengths
shorter than 300 nm. Using a light of
λ = 375 nm, the lower sizing
limit can be extended to half of that
using light of λ = 750 nm.
Pioneered by Beckman Coulter, most laser
diffraction manufacturers now use the
above two approaches to size small particles.
However, for particles smaller than
200 nm, even using wide angular range
and short wavelength, it is still difficult
to obtain an accurate size. The third
approach is to use the polarization
effects of the scattered light.
Vertically polarized scattered light
has different scattering patterns and
fine structures from that of horizontally
polarized light for small particles.
The main characteristic of the horizontal
scattering intensity (Ih)
for small particles is that there is
a minimum around 90 degrees. This minimum
shifts to larger angles for larger particles.
Thus, although both vertical scattering
intensity (Iv) and Ih have
only small contrast in the case of small
particles, the difference between them
can reveal a more distinguished fine
structure, thereby making the sizing
of small particles possible. Combining
polarization effects with wavelength
dependence at large angles, we can extend
the lower sizing limit to as low as
40 nm without extrapolation. This combined
approach is known as the Polarization
Intensity Differential Scattering (PIDS)
technique patented by Beckman Coulter1.
When the light beam is polarized in
either the v direction or the h direction,
the scattering intensity Iv and Ih for
a given angle will be different. The
difference between Ih and
Ih (Iv - Ih) is
termed the PIDS signal. For small particles
the PIDS signal is roughly a quadratic
curve centered at 90 degrees. For larger
particles the pattern shifts to smaller
angles and secondary peaks appear due
to the scattering factor. Since the
PIDS signal is dependent on particle
size relative to light wavelength, valuable
information about a particle size distribution
can be obtained by measuring the PIDS
signal at several wavelengths.
Figure 1. displays the shift in the
peak value and the change in contrast
of the PIDS signal for particles of
various diameters. In addition, because
the PIDS signal varies at different
wavelengths (it becomes flatter at longer
light wavelengths), measurement of the
PIDS signals at several wavelengths
will provide additional scattering information
that can be used to further refine the
size retrieval process.
From Figure 1., the angular patterns
for 100 nm and even for 50 nm particles
are recognizable, in addition to the
shift in the axis of symmetry. It has
been verified through both theoretical
simulation and real experimentation
that accurate sizing of particles smaller
than approximately 200 nm by scattering
intensity without the use of the PIDS
technique is practically difficult and
probably unrealistic. The combination
of the three approaches (wide angular
range, wavelength variation, and polarization
effect) improves the accurate characterization
of submicron particles using light scattering.
There is no mixing of technologies.
All signals are from the same scattering
phenomenon and treated integrally in
a single data retrieval process just
like in an ordinary laser diffraction
measurement.
