Particle size measurements of materials in the dry dispersed state are increasingly being used as an alternative to wet or liquid dispersion methods. There are several advantages to using dry powder dispersion for laser diffraction measurements:
If a material is processed in the dry state then measuring the particle size in the same state may be more representative than wet dispersion.
For some materials dry measurement may be the only option, due to dissolution in common dispersants or changes in the size of the particles in wet dispersion (due to hydration).
In general, measurements in dry dispersion are quicker than wet, enabling you to measure a larger mass of material in a short time. This is particularly useful for achieving reproducible results for coarse or polydisperse materials.
However, not every sample is suitable for dry dispersion. Very fine or cohesive materials may be more suited to wet measurement, as surfactants and additives may be required to achieve full and reproducible dispersion. Dry dispersion may not be suitable for extremely fragile materials due to the more aggressive nature of the dispersion mechanisms. Finally, while it is possible to measure very small sample masses using a dry system, improved result reproducibility is often achieved using wet dispersion.
Achieving reproducible results from any kind of particle characterization system depends upon three factors:
The relative importance of each of these factors depends on the size of the particles being measured. Figure 1 shows the relative risk factors associated with measurements of fine or coarse particles in dry dispersion.
Therefore, if you are measuring fine particles then the air pressure will have the greatest influence on the results as it affects the samples state of dispersion. However, if you are measuring coarse particles, the greatest possible source of error will be sub sampling of the material.
Air pressure and dispersion
Achieving reproducible results from a particle size measurement relies on the sample being in a stable state of dispersion. The ease with which particles can be dispersed depends on the particle size, as the relative forces of adhesion between particles increase as the particle size decreases. This is why air pressure, and dispersion, is at the top of the list of risk factors for measurements of fine particles.
Samples in the dry state are dispersed using a venturi driven by compressed air. For each venturi, the amount of energy available to disperse the sample will depend on the pressure of the compressed air. The state of dispersion for a dry sample is assessed by carrying out a pressure titration and comparing the results to a well dispersed wet measurement. A pressure titration generally shows a decrease in particle size with increasing pressure as agglomerates are dispersed. However, the particle size can also decrease due to particle attrition and these two processes can overlap. The results of a pressure titration are compared to a well dispersed wet measurement to determine the pressure at which the agglomerates are dispersed but the primary particles are not being broken. A pressure titration for a milk powder sample is shown in Figure 2.
The dry result showing the closest agreement to the well dispersed wet result will indicate the appropriate pressure. If the results of a dry measurement are finer than the wet measurement this indicates that the primary particles are being broken at that pressure. Figure 3 shows a dispersed wet result for the milk powder sample, compared to dry results measured at 0.5 bar and 3 bar. The 0.5 bar measurement shows a larger size compared to the wet measurement, indicating that the sample is not fully dispersed at 0.5 bar. However, the 3 bar measurement shows excellent comparability to the wet measurement. Therefore, for this material the appropriate pressure to disperse the sample to its primary particle size is 3 bar.
The pressure titration shown in Figure 2 was carried out using the standard venturi supplied with the Mastersizer 3000 dry powder disperser the Aero S. This venturi makes use of two of the mechanisms available for dry powder dispersion, as shown in Figure 4: (a) velocity gradients caused by shear stress and (b) particle-to-particle collisions.
For the majority of materials these two mechanisms are sufficient to disperse the sample. However, some highly agglomerated and robust samples may require the additional higher energy dispersion mechanism of particle-to-wall collisions, Figure 4 (c). As the standard venturi is applicable to the vast majority of samples then this will be your starting point for developing a dry method. However if full dispersion is not achieved for a robust material then the Aero's high energy venturi , which makes use of all three dispersion mechanisms, may be required.
If we measure the milk powder sample using the high energy venturi then we see a different pressure titration. Full dispersion is achieved at a lower pressure, due to the higher energy dispersion mechanism. Figure 5 shows that the dry result at 1 bar using the high energy venturi shows good agreement to wet result, whereas the dry result at 4 bar shows a smaller particle size which indicates particle attrition.
Figure 6 shows the Dv50 vs. pressure measured using both the standard venturi and high energy venturi, with the Dv50 from the wet result added as a dashed line for comparison. This shows that results comparable to the wet measurement are achieved at between 3 bar and 4 bar using the standard venturi and at 1 bar using the high energy venturi. In this case the standard venturi would be recommended, as the dry results are comparable to the wet dispersion over a wider range of pressure which improves the robustness of the method.
The feed rate controls the rate at which material is fed through the venturi to the measurement cell by vibrating the sample tray. The amount of material passing through the measurement cell is recorded via the obscuration (the percentage loss of laser light through the measurement cell). The feed rate must be set so that the obscuration is in range for the majority of the measurement duration, as illustrated in Figure 7. The obscuration filtering feature in the Mastersizer software ensures that detector scans where the obscuration is outside the target range are not included in the results. The percentage of the measurement duration where the obscuration was within range can be checked using the 'Snap collection percentage' parameter. The higher this percentage the more scans of the detector were within the obscuration range, and the more representative and reproducible the results. This is one of the parameters checked by the Mastersizer 3000s data quality report for dry measurements, which will show a warning when poor obscuration control is detected.
The appropriate obscuration range will depend on the size and nature of the sample. Cohesive, fine samples may need to be measured at a lower obscuration in order to maximize the efficiency of the disperser, whereas coarser materials can be measured at a higher obscuration. If poor dispersion is observed for fine, or cohesive, materials then the upper obscuration limit should be reduced to improve the efficiency of the disperser.
On the Aero S dispersion unit, the stability of the sample flow can be optimized by adjusting the set-up of the sample tray and hopper. For free flowing materials a lower hopper height will prevent material flowing off the tray too quickly. For cohesive materials an increased hopper height may improve flowability. The basket and ball bearing can also be used to improve the flow of cohesive materials. If you only have a small amount of sample available then the hopper may not be necessary and the Macro or Micro sample trays may be more suitable.
If you are measuring coarse particles then amount of sample you measure and how you take the sub sample become the largest possible source of error.
To get a representative result you need to measure a minimum number of particles. For example, to get the Dv90 to within a 5% standard error requires at least 400 particles to be measured during the analysis. Therefore, for a material with a density of 1.5g/cm3 and a Dv90 of 500μm you would need to measure about 0.5g to get the Dv90 to within a 5% standard error. As the size of the particles increases the mass containing sufficient particles increases, and the minimum mass required to achieve reproducible results also increases.
Figure 8 shows the minimum mass required to achieve a 5% standard error as a function of particle size. You can test whether your sample mass, or technique, is sufficient by measuring several separate sub samples and assessing the variability of the results.
The precision of laser diffraction measurements can be assessed using the coefficient of variation.
(also referred to as the relative standard deviation)
The ISO standard for laser diffraction  recommends that the %COV should be less than 3% for central parameters such as the Dv50, and less than 5% for parameters at the extremes of the distribution such as the Dv10 and Dv90. The Mastersizer 3000 has a variability check in its data quality tab to allow you to check the variability of your measurements against the limits set in the ISO standard.
The duration of the sample measurement can also affect the variability of results, as it can become another sampling step. As the sample tray vibrates it is possible for a sample to become segregated. The larger, more free flowing, particles within a sample may arrive at the measurement cell before the finer more cohesive particles. Therefore it is important, when making dry measurement, to ensure that the entire sub sample put onto the tray is measured. During method development it can be useful to make repeat measurements of shorter duration in order to help optimize parameters, such as the obscuration range. However, once the measurement conditions have been defined a long measurement, with sufficient duration to measure all of the material on the tray, should be set.
The mass of the sub sample required to achieve reproducible results will depend on the size and polydispersity of the sample. Samples containing larger particles or with very polydisperse distributions will require a larger mass of material to be measured and, therefore, a longer measurement duration.
For example, Figure 9 shows several 5 second measurements of a sample with a median size of approximately 600μm. The relative standard deviation of the percentiles shows quite a high variability which can be improved by increasing the measurement duration and thereby improving the sampling of the material.
For finer, or monodisperse, samples it is possible to measure a very small mass of sample and still get representative results. Figure 10 shows the results of dry measurements of a baby powder sample from a sub samples with masses between 50mg and 5mg. The table in Figure 10 contains the resulting percentiles and relative standard deviations which show reproducibility well within the expected repeatability for a laser diffraction measurement, according to the ISO standard .
Getting reproducible results from dry laser diffraction measurements is dependent on three main factors: taking a representative sample of the bulk material, using the correct pressure to disperse the sample and setting appropriate measurement conditions. The relative importance of each of these factors will depend on the particle size of the sample that you are measuring. For fine particles achieving a reproducible state of dispersion will be the most important factor. Whereas for coarse particles ensuring that a sufficient mass of material is measured will be the most important factor.
In this application note we have covered the process of setting up a method for dry laser diffraction measurements. We have also covered some tests that you can carry out to assess the reproducibility and robustness of your method. By following this process you will be able to increase your understanding of the materials that you measure, and improve the reproducibility of your particle size results.
 ISO13320 (2009). Particle Size Analysis - Laser Diffraction Methods, Part 1: General Principles