Microtrac has played a leading role
in the development of light scattering particle size measurement. Commencing 25
years ago, diffraction measurements have been central to the Microtrac product
line.
A description of the basic diffraction concepts and the technology used in the
S3000 is presented below.
Basic concept
One method of describing the
phenomenon of the development of a pattern of light that is related to a
dimension has been shown by Young in his “double slit experiment” in which the
wavelength of light could be determined. In this experiment, monochromatic light
was directed to a card containing two very small slits cut very close to each
other. The waves may interact destructively (1800 out of phase or
peak of one wavelet superimposed on a valley of another wave) or they may
interact constructively when in phase (peak of one wave superimposed on the
valley of another wave). As the wavelets propagate in the forward direction the
interference continues.
A card placed in front of the
advancing superimposed waves will produce a pattern of lines (Figure 1.) due to
interference. The pattern begins at the center where highly intense light is
located. A dark line resulting from destructive interference follows. The next
line is bright and is a result of constructive interference of the wavelets. The
pattern of lines is related to the wavelength of the illuminating light and the
distance between the slits. This can be expressed by the formula:
This equation developed by Young provides the basis for determining the
wavelength of light, but is also related to the distance between the holes or
the size of a particle where the diameter equals the distance. The equation also
established the concept of interference patterns that was used by Bragg to
experimentally verify the concept of diffraction (bending) of light from layers
of atoms in a crystal.
The issues involving light scattering particle size are much more complex, but
these concepts form the basis that light is scattered from particles into a
definite pattern. The pattern is developed primarily by diffraction, which
spreads out more for fine particles and less for larger particles.
The issue for particle size
measurement is the ability to interpret the pattern from a mixture of particle
sizes covering a wide range of particle sizes (Figure 2). The mixed pattern is
mathematically analyzed to ascertain the particle sizes present.
Only a single pattern of light will correspond to a given particle size
distribution. To compute the distribution, Microtrac uses an advanced form of
interative deconvolution mathematics that has high sensitivity and resolving
capabilities without noise and spurious (“ghost”) peaks.
Use of a single wavelength source of laser light is required to apply the
mathematics to the fullest capability possible. The Tri-laser, single wavelength
system allows the same computations to be used over the entire angular range of
the diffraction pattern.
This avoids “connecting points” between distributions developed by different
wavelengths of light and the requirement for multiple Mie scattering treatments
(Mie scattering is wavelength dependent). For a complete explanation of the
principles, please
contact us.
Distance between holes= l
/ sin q
Distance between holes = Size of particle
Figure 1. Propagation of light as it interacts with two slits to produce
wavelets
That exhibit interference phenomena that in turn produce diffraction patterns.
S3000 Tri-laser Particle Size Analyzer
The advanced S3000 Tri-Laser uses a detector
system located at a precise distance from the point where the particles interact
with the light. A series of small silicon detectors produces electrical current
when light illuminates them (Figure 2). The detectors also respond to the amount
of light (intensity) reaching them, which is related to the amount present of a
particular particle size.
The angles of light determined from the illuminated detectors and the intensity
of the current produced provide the basis for providing the distribution of
particle sizes as well as the quantity of each present. The laser light (l =
780nm) in the S3000 allows for measurement of larger particles by detecting the
light scattered over an angular range of 0.02 to approximately 45 degrees.
Very small particles scatter light at very wide angles.
In order to illuminate the smallest
particles and detect the scattered light, lasers are strategically placed (Figure 3) at angles that allow detectors to be used more than one time. This arrangement reduces optical components (design elegance and simplicity) and reduces instrument space requirements (small lab bench foot-print). This combination provides an optical instrument having extremely stable alignment as well as being extremely portable.
Evaluating light that passes through
particles.
Diffraction of light occurs at the
edge of particles, but many substances have particles that are transparent and
allow light to pass though. This phenomenon is termed refraction. Particles
passing through the laser beam of the S3000 are constantly tumbling and pose
different faces of the particle to be exposed to the incident light.
In the case of spheres, all orientations of the particles are identical. Any
light passing through the particle will exit at the same place and illuminate
the same place on the detector. For particles that are not spherical, the
constant tumbling will cause the refracted light to illuminate a variety of
detector locations. This light also will undergo reflection inside the particle.
As shown in Figure
4, the entire pattern of light reaching the detector contains diffracted and
refracted light. The refracted light does not contain information of value in
determining size over all of the sizes measured by the S3000 and thus must be
eliminated by proper corrections. Since spheres represent well-defined shapes,
the effect of refracted light is easily corrected by the concepts proffered by
Gustave Mie (Mie theory). It has been estimated that spherical particle products
represent only 2% of all substances and makes the use of Mie corrections
limited.
The Microtrac S3000 and Ultrafine Particle Analyzer use Mie scattering
calculations that are related to the shape as defined as spherical or
non-spherical. The selection is made very easily as part of the measurement
set-up. It is based upon guidelines provided in the on-line operator’s manual.
Only Microtrac Particle Size Analyzers treat the refracted light according to
the rigorous treatment proposed by Mie for spherical particles and as well when
the particles are not spherical, using a modified Mie approach. The Microtrac
technical staff is also available to assist in this decision as well as answer
other questions.
Measurement of the Angular Scattered Light
Distribution
Angular (or
static) light scattering techniques are applicable over the particle size range
from .02 microns to above 3000 microns. The particle size distribution is
determined by measuring the scattered light intensity as a function of
scattering angle. A typical static light scattering configuration is shown in
Figure 1. A laser beam illuminates a group of particles, which may be dispersed
in a liquid or gas stream. Light scattered by the particles, and the incident
beam of light, are focused onto an optical detector array, which measures the
angular distribution of scattered light. Each point on the array collects a
single angle of scattered light, from all the particles in the beam; and the
angular resolution is independent of the sample volume size. The detector array
sums all of the scattered light distributions from individual particles in the
ensemble. This composite distribution is mathematically inverted to obtain the
particle size distribution, using a theoretical model for the scattering
process. The most widely used model is based on Mie theory, which solves
Maxwell’s equations exactly for the boundary conditions of a spherical particle.
For more information, please contact us. We are able to provide the product to meet exactly what you need.