SPECIAL SECTION/INSTRUMENTATION: Measuring Sensitivity in Particle Size Distribution Analysis

May 1, 2007
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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.

Analysis

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.

Sensitivity Quantification

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 ussales@micromeritics.com; or visit www.micromeritics.com.

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