Outlier Detection in Highly Concentrated Solutions Using the Coulter Principle

Particle characterization techniques are classified into "ensemble" techniques (multiple particles are analyzed simultaneously), or "discrete" techniques (individual particles are measured one at a time).

Ensemble techniques such as light scattering or laser diffraction, are poorly suited for outlier detection, since they are designed to give highly accurate and reproducible information about the entire population of particles, rather than individual particles. However, discrete techniques are excellent for outlier detection since particles are analyzed individually.

This article focuses on an industrially relevant example: “Large Particles in Highly Concentrated Solutions of Chemical Mechanical Planarization (CMP) slurries".

Overview of the Coulter Principle

The Coulter Principle is a discrete technique which is well-suited for outlier detection. This is because of its wide dynamic range and reliance on electrical impedance to individually count and size particles suspended in dilute conducting liquids.

Examples of successful application of the Coulter Principle include characterization of: ink toners, plant cells, abrasive grit, chromatography media, protein aggregates, in vitro diagnostic beads, rocket fuel, and ocean plankton.

Experimental Design

In order to test if the Coulter Principle could be used in this environment, a model system was devised which consisted of:

  • Ludox HS-40 (Sigma Aldrich), which is a 40 wt% suspension of colloidal silica particles approximately 20 nm in diameter;
  • Beckman Coulter LI000, which is a suspension of latex beads with a nominal 1.0µm diameter; and
  • Beckman Coulter LI0, which is a suspension of latex beads with a nominal 10µm diameter

In the Ludox system, the 1.0 µm particles act as the large outlier contaminant, in another experiment, the 1.0-micron particles act as a smaller contaminant in a solution of 10 µm beads. 0.1 M sodium triphosphate buffer was used as a diluent due to its previously proven ability to dilute Ludox stably.

Several experiments using a 20 µm aperture (dynamic range of 0.400-16 pm) installed on a Multisizer 4 instrument was designed to probe the model system.

Studies were first done to determine if or not background signals would be generated by the highly concentrated Ludox suspensions. For this test, the stock-concentrated Ludox was diluted to concentrations ranging from 3wt% to 15wt% solid.

The hypothesis driving these experiments was that highly concentrated particles can cause an interference in electrical current to produce a background signal, which should increase with time.

The next series of experiments were done to determine whether or not 1.0 µm particles could be detected above background of the same highly concentrated Ludox suspensions (6.0 wt%) used in the first experimental set. For the positive test case, one drop of Beckman Coulter LI000 standard was added to each of the same vials used for background measurements.

The third series of experiments aimed to determine whether or not the 1.0 µm particle concentration could be quantitatively assessed above background.

For this, a stock solution of 6.0 wt% Ludox in 10 mL of sodium triphosphate buffer was prepared and mixed with either 50 or 100µL of LI000 I-micron beads. The experiment was run in volumetric mode (50µL), so that the total concentration of LI000 beads/mL could be calculated.

The final set of experiments focused on multiple outlier detection as the Coulter Principle is more adept at detecting small amounts of large outliers than typical light scattering techniques and is better than any other technique at detecting low amounts of smaller outliers.

The differentiating power of the Coulter Principle is demonstrated by making a solution with 1:10,000 dilution of I-micron beads, and 1:1,000 dilution of I0-micron beads. The dual outliers were analyzed in series of mixtures with and without Ludox to assess the influence of the concentrated background particles on small outlier detection.

Results

Figure 1 shows that background noise (in the form of particulate counts) was indeed observable and increased with concentration of Ludox. Despite background noise, the absolute level of background counts was relatively low and stable.

Average background particle counts in Ludox suspensions.

Figure 1. Average background particle counts in Ludox suspensions.

The second experiment was done determine whether or not particles could be detected accurately above these backgrounds. Figure 2 shows the results of these tests.

Average background subtracted counts between 0.75 and 1.5m in Ludox suspensions.

Figure 2. Average background subtracted counts between 0.75 and 1.5m in Ludox suspensions.

The third experimental data set, shown in Figure 3, proved that particles suspended in highly concentrated Ludox could be accurately detected in proportion with their concentration.

Quantitative determination of 1.0-micron particles mixed with 6% Ludox at two concentrations.

Figure 3. Quantitative determination of 1.0-micron particles mixed with 6% Ludox at two concentrations.

At 1:200 dilution, an average of 54,900 particles was counted (ranging from 0.4 µm to 12 µm) in 50 µL of analyzed sample; at 1:100 dilution, an average of 104,600 particles were counted. Thus, even with a huge excess of Ludox, the Multisizer is able to quantitatively determine the concentration of larger outlier contaminants.

The final experimental data is shown in Figure 4.

Signals generated 1-micron and 10-micron beads in Ludox-free buffer, plotted with respect to total number of particles counted in 20s (Trial 1) or 50 mL of volume (Trial 2).

Figure 4(a). Signals generated 1-micron and 10-micron beads in Ludox-free buffer, plotted with respect to total number of particles counted in 20s (Trial 1) or 50 mL of volume (Trial 2).

Signals generated 1-micron and 10-micron beads in Ludox-free buffer, plotted with respect to total volume. Note that on a per-volume basis, the 10-micron beads occupy 94.6 e6(µm)3/mL while the 1-micron beads occupy 42.7(µm)3/mL.

Figure 4(b). Signals generated 1-micron and 10-micron beads in Ludox-free buffer, plotted with respect to total volume. Note that on a per-volume basis, the 10-micron beads occupy 94.6 e6(µm)3/mL while the 1-micron beads occupy 42.7(µm)3/mL.

Using pure sodium triphosphate buffer and 6.0 wt% Ludox, both 1.0 micron particles and 10 micron particles were suspended. In pure buffer, the 1.0 micron particles have a narrow peak as shown in Figure 4, which broadens when the particles are mixed with Ludox (Figure 5).

In both cases inspite of a large excess of 10 micron beads (roughly 10-fold), the 1 micron beads were easily detectable. When particle diameter is plotted against volume, the 10 micron beads dominate; a small but detectable signal can be seen near 1-micron as shown in Figures 4b and 5b.

Contrastingly, when the particle diameter is plotted against particle number, the smaller but more numerous 1-micron beads dominate the signal (Figures 4a and 5a).

The data from Figure 4 indicates that the Multisizer 4 is able to pick up small outliers from the main distribution, while the data from Figure 5 displays how the Multisizer 4 is able to pick up several distributions of larger outliers.

Signals generated 1micron and 10 micron beads in 3.0 wt% Ludox, plotted with respect to total number of particles counted in 20s (Trial 1) or 50 mL of volume (Trial 2).

Figure 5(a). Signals generated 1micron and 10 micron beads in 3.0 wt% Ludox, plotted with respect to total number of particles counted in 20s (Trial 1) or 50 mL of volume (Trial 2).

Signals generated 1 micron and 10 micron beads in 3.0 wt% Ludox, plotted with respect to total volume. Note that on a per-volume basis, the 10 micron beads occupy 220.4e6 (µm)/mL while the 1-micron beads occupy 7.1 (µm)3/mL.

Figure 5(b). Signals generated 1 micron and 10 micron beads in 3.0 wt% Ludox, plotted with respect to total volume. Note that on a per-volume basis, the 10 micron beads occupy 220.4e6 (µm)/mL while the 1-micron beads occupy 7.1 (µm)3/mL.

Discussion

This data shows that the Coulter Principle, as implemented in the Multisizer 4, is a powerful and capable tool for monitoring outliers, even in extremely concentrated solutions. The instrument proved capable of detecting extremely low concentrations of large particles mixed with very high concentrations of small particles.

While this data set focused on a system designed to mimic CMP slurries, it proves a point which is more broadly applicable to the Coulter Principle: the Multisizer Series is capable of detecting very low concentrations of outliers, both larger and smaller than the main distribution.

This information has been sourced, reviewed and adapted from materials provided by Beckman Coulter, Inc. - Particle Characterization.

For more information on this source, please visit Beckman Coulter, Inc. - Particle Size Characterization.

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