## Better Analysis of Bulk Solids Six Errors in Particle Analysis and How to Avoid Them

Size distribution, shape factor, bulk density — there are numerous parameters that describe a bulk material as a whole. But their determination is also subject to many sources of error. These six tips for particle analysis show how to ensure that you end up with meaningful results when characterizing powders.

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Particle analysis is an integral part of the quality control of bulk materials and is routinely performed in numerous laboratories. The methods used have often been established for years and are hardly ever questioned. Nevertheless, procedures should be critically reviewed from time to time because various sources of error can negatively influence the results of a particle analysis. This article is intended to provide food for thought to make your own methods for particle characterization more accurate and reliable.

### 1. Inadequate Sampling

When sampling inhomogeneous bulk materials, it is important to make sure that the properties of the laboratory sample taken correspond to those of the total quantity. In this case we speak of representative sampling. This can be complicated by the fact that materials separate by size during handling (segregation). During transport, for example, small particles move down the interstitial spaces due to vibration and collect at the bottom of the container. In bulk cones, one usually observes a concentration of the small particles inside the cone. Sampling at a single location can therefore hardly be representative. Often, sub-samples need to be taken from several locations and combined into a composite sample to counteract the effect of segregation. Suitable aids such as sampling lances can further improve the situation.

### 2. Poor Sample Division

The sample quantity available for particle analysis is usually too large for the measuring instruments used. In many cases, the volume needs to be further reduced in the laboratory. Sample division done poorly — or not at all — is one of the main sources of error in particle analysis, especially for widely distributed bulk materials. Indiscriminate sampling produces sub-samples with different particle distributions, which can be seen in the poor reproducibility of measurement results (the left-hand curve in Figure 2, above). The use of sample dividers can remedy this situation. Even a simple sample splitter leads to significantly improved reproducibility when several sub-samples are analyzed. The best dividing results are achieved by automated rotating sample dividers such as the Retsch PT 100 (right-hand curve in Figure 2). The sample material used is standard sand with a particle size between 63 µm and 4000 µm.

### 3. Incomplete Dispersion

Dispersion is the process of separating particles so that they become accessible to measurement. Particles that stick together due to various attractive forces are called agglomerates. It is usually desirable to break up these agglomerates before measurement. However, it may also be of interest to create agglomerates in a targeted manner (granulation). In this case, care should be taken with dispersion so as not to destroy the structures to be measured.

For dry measurements, dispersion is usually done in a compressed air stream (Figure 1, left). Figure 4 (online) shows an example of dry measurements with Microtrac’s Camsizer X2 at different dispersion pressures. In the first example (Figure 4a, online), as the pressure increases the result becomes finer and finer until it stabilizes at 150 kPa and above. 150 kPa is therefore the optimum dispersion pressure for this sample.

In general, ‘as much as necessary and as little as possible’ applies when selecting the dispersion pressure. For most powdered materials, 20–30 kPa is sufficient for complete dispersion. In the second measurement example (Figure 4b, online), the dispersion becomes increasingly finer from a pressure of 100 kPa, indicating that the particles are ground. Pourable samples can even be analyzed in free-fall mode.

Agglomerates can also occur in suspensions. This can often be prevented by selecting a suitable dispersion medium (carrier fluid). Agglomerates that are still present in the suspension are broken up using ultrasound. Most modern particle analyzers have powerful ultrasonic probes built in, so that sample preparation is carried out entirely inside the instrument.

In general, the larger the particles, the higher the probability of errors in sampling and sample splitting. For finer particles, the error is more likely to be in dispersion.

### 4. Wrong Size Definition

Strictly speaking, particle size is only unambiguously defined for spherical structures, namely as the diameter of the sphere. For non-spherical particles, depending on the orientation and the measuring technique used, different measured values can be obtained. For example, imagine a sphere and a Lego brick that both fit through a 16 mm sieve aperture, while being retained by a 14 mm aperture. For sieve analysis, both objects have the same ‘equivalent diameter’ of 14–16 mm and it is not possible to be more precise. If we measure them with calipers, on the other hand, depending on the orientation it becomes clear that they are not the same size.

Even more advanced methods of particle measurement use different ‘size models’. With sieve analysis, particles ideally orient themselves so that their smallest projected area fits through the smallest possible mesh. Sieve analysis thus tends to determine particle width. In imaging techniques (as used by Camsizer), on the other hand, different size definitions are accessible. Size distributions can be reported separately for length and width.

In laser diffraction, all diffraction signals are evaluated as if they were generated by ideally spherical model particles. In contrast to methods based on image analysis, the particle shape cannot be determined. Furthermore, laser diffraction evaluates a signal generated by a particle collective with particles of different sizes. The calculation of the size distribution is therefore indirect. Nevertheless, laser diffraction is an established technique thanks to its great versatility and wide measurement range, from a few nanometers to the low millimeter range. Figure 3 compares the results of size measurement for a sample of coffee powder with sieving, Camsizer image analysis and laser diffraction.

From the considerations described above, it is clear that different methods for particle measurement will inevitably produce different results. While laser diffraction and sieve analysis are difficult to correlate, the results of sieve analysis and image analysis are often very close, since imaging techniques can determine particle width and sieve analysis tends to yield a measurement of width.

### 5. Incorrect Sample Amount

Using too much or too little material can negatively influence the measurement result. In laser diffraction, too high a particle concentration can lead to multiple scattering, and if too little sample is used, the signal-to-noise ratio is poor. However, modern laser analyzers indicate the ideal concentration for measurement and warn users as soon as the amount is too high or too low. In image analysis, you cannot actually use too much sample. If too little sample is analyzed, the result will be unreliable and poorly repeatable due to the small number of detections. Since the required amount of particle detections depends on the size of the particles and even more on the distribution width, it is difficult to make general recommendations here. Repeatability tests are helpful, especially looking at the ‘rough end’ of the distribution. Repeatability can be improved by using a larger sample volume. In dynamic image analysis with Camsizer instruments, enough particles are detected in 2–5 minutes under normal conditions to obtain a reliable measurement.

The strongest influence of sample quantity is in sieve analysis: a common error here is to overload the sieve. If too much sample material is used, particles can get stuck in the meshes and block them. Small particles then no longer fall through the blocked sieve, and the measured size distribution is ‘too coarse’.

In sieve analysis, the sample quantity must be matched to the particle size, the sieve stack used and the density. The simple rule of always using 100 g usually leads to a dead end, because 100 g can be too much or too little. In no case is a representative sample division given when weighing out 100 g.

### 6. Misunderstood Tolerances

Every measuring instrument has certain systematic uncertainties and tolerances which must be taken into account when interpreting the results. This will be illustrated here using the example of sieve analysis. Test sieves made of wire cloth are manufactured according to the standards DIN ISO 3310-1 or ASTM E11. These standards specify how the real mesh size of each sieve is to be tested. Each test sieve is inspected by an optical method before delivery and a specified number of meshes are measured. The mean value of the measured opening width must be within prescribed tolerances around the nominal mesh size. For a sieve of nominal mesh size 500 µm, the mean value of the real mesh size must lie within an interval of ±16.2 µm. A sieve conforming to the standard can therefore have an average opening width of 483.8 µm to 516.2 µm.

It is important to note that these are average values for a particular sieve; some openings can be even larger, thus allowing correspondingly large particles to pass through. The standard therefore also defines the maximum permissible aperture size for each sieve size. Calibration certificates are available for each sieve. These contain information on the real mesh sizes and their statistical distribution.

### Conclusion

Various methods are used for particle analysis, the most common being laser diffraction, dynamic image analysis and sieve analysis. Successful analysis and meaningful results can only be achieved if steps such as sampling, sample division and sample preparation are carried out correctly. Selection of the appropriate method for the sample material and a meaningful evaluation of the measurement data will lead to successful particle analysis.

Microtrac MRB is one of the leading suppliers of particle measurement technology from the fields of laser diffraction and dynamic light scattering, as well as static and dynamic image analysis, and offers a complete portfolio for particle characterization from a single source. n

* *K. Düffels, Microtrac Retsch, 42781 Haan/Germany, Phone: +49 2104 2333-300

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