To ensure high-quality finished products, the analytical
technique used to determine the particle size distribution of the raw material
must be sensitive enough to detect changes between lots.
Figure 1. Overlay of analyses of six individual samples
of medium garnet.
Quality departments and laboratories perform literally
millions of particle size distribution analyses each year. Most are performed
to allow suppliers and users of particles to predict expected process behavior
without having to prepare a test batch of the final product. All quality
managers hope that analyses of each new lot will produce results that are
within published product specifications. These lots can then be shipped to end
users, who will be able to use them in some type of finished product.
Both the supplier and user want each new lot to behave
like the last, which they should, if we can make two assumptions: the particle
size distribution analysis results for the new lot are within product
specifications, and the analytical technique used to determine the size
distribution is sensitive enough to detect changes. A number of methods can be
employed to determine the particle size distribution of particulate materials,
including microscopy and image analysis, sedimentation, laser light scattering
(static and dynamic), the electrical sensing zone method, and others based on
the interaction of particles with light and sound.
Figure 2. Overlay of analyses of six individual samples
of coarse garnet.
Static laser light scattering can provide these analyses
very quickly (within minutes) and covers a wide range of particle diameters
(from nanometers to millimeters) for almost any particulate materials, as long
as the individual particles can be separated from one another. Once the
particles are dispersed, they are directed into a sensing area where polarized,
monochromatic light strikes the particles. The light interacts with the
particles in such a way that some of the light energy is redirected away from
the incident direction, with the angles of deflection and the intensity at each
angle dependent on the size of the particles. Using scattering models for known
particle sizes, the combined light scattered by all of the particles in the
sample can be deconvoluted to determine the relative amounts of particles
present at each size.
What is sensitivity as it relates to particle size
distribution analysis? In the case of laser light scattering, clause 6.7 of the
current ISO standard describing the general principles of the technique (ISO
13320-1:1999) provides a very brief definition. Essentially, sensitivity is the
ability to detect small differences in the amount of material present at a
given particle size.
The same clause also offers brief advice regarding how we
can measure the sensitivity of a particular technique or instrument. The
sensitivity of a specific analytical instrument can be determined by comparing
analysis results for blends of known composition with those predicted for such
a blend, given the particle size distribution of the individual components.
This study will provide an example of such a sensitivity study performed for a
laser particle size distribution analyzer using known mass blends of two
abrasive powders, a medium garnet and a coarse garnet.
Table 1. Percentage of each of two garnet powders in
analyzed blends, based upon mass of each component in the blend.
To ensure confidence in the data produced, each of the
two garnet powders were analyzed six times using a high-definition digital
laser particle size analyzer.* Overlays of the repeat analyses are shown in
Figures 1 and 2 for the medium and coarse garnet, respectively. Repeatability
must be demonstrated to ensure that the differences seen in succeeding
distributions are due to differences in the sample and not random errors.
Once it was demonstrated that results for each of the two
materials met or exceeded reproducibility expectations, nine different blends
of the two powders were prepared, with the mass of each component determined
using an analytical balance. The resulting mass percentages of each component
in the nine blends are given in Table 1.
*Micromeritics Saturn DigiSizer 5200.
Figure 3. Overlay of volume frequency distribution from
analyses of two garnets and nine blends, with percentage of coarse garnet in
the sample indicated in the plot legend.
The particle size distribution of each blend was
determined, and Figure 3 shows an overlay of the volume percent frequency
distribution for the nine blends, as well as the pure components. Note that the
differences in the distributions are obvious, even with only 5% of one component
blended with the other.
Figure 4. Overlay of calculated and measured volume
frequency for blend of 65.76% coarse garnet and 34.24% medium garnet, along
with the difference between
calculated and measured distributions.
The results of each analysis were exported into
a spreadsheet, where measured results were compared with calculated distributions
based on adding the distributions for the two components; these were then
scaled according to the mass of each component in
the blend. Figures 4 and 5 show the measured and calculated
distributions overlaid with the distribution difference for the nominal 67% and
90% coarse blends, respectively.
Figure 5. Overlay of calculated and measured volume
frequency for blend of 90.02% coarse garnet and 9.98% medium garnet, along with
the difference between calculated and measured distributions.
The difference between the measured and calculated
distribution was determined for each size class in the distribution for all
nine blends. The quality of agreement between the two distributions (measured
and calculated) for each blend was quantified using the root mean square (RMS)
of the differences between the distributions. The calculated RMS data, in units
of volume percent of the distribution at a given particle diameter, are given
in Table 2 for the nine analyzed blends of the two garnet powders. The maximum
difference in volume percent of the distribution at a given particle diameter
is included in the table.
Table 2. Root mean square of differences and absolute
maximum difference at a given diameter between measured and calculated
distribution for each of nine garnet blends.
The close agreement between the measured and calculated
particle size distributions of the nine blends, evidenced by small RMS
differences for each blend and small maximum difference at any given particle
size, indicates that in the present study laser light scattering particle size
distribution results are sensitive to the amount of material present. A similar
study can be performed by quality managers to ensure confidence in the results
obtained on their instruments.
For more information regarding particle size
distribution analysis, contact Micromeritics Instrument Corp., One Micromeritics Dr., Norcross, GA 30093-1877; (770)
662-3633; fax (770) 662-3696; e-mail firstname.lastname@example.org;
or visit www.micromeritics.com.