by Mark Bumiller, Technology Manager, Entegris, Inc.
The “tail” of a particle size distribution refers to particles several standard deviations removed from the mean of the standard Gaussian distribution. A standard Gaussian distribution curve shows 95.5% of the total population lies within plus or minus two standard deviations (s) of the mean (µ). The tails could be defined as the 2.25% of the distribution outside of two standard deviations from the mean. The larger, or oversize particles to the far right of the distribution are within the coarse tail. These are often the “bad actors” that cause problems with either product quality or performance. The fines tail are the smaller particles to the far left of the distribution that can also cause problems with product behavior such as powder flow.
Although the word “tail” can be used to describe either the fine or course particles it is most often used to describe the course outliers in a particle size distribution. These particles are often missed, overlooked, or misinterpreted by conventional light scattering particle sizing techniques such as laser diffraction. The single particle optical sensing (SPOS) technique (1) is ideal for the measurement of distribution “tails”. This technique enables the user to count and size particles >0.5 microns with high resolution and accuracy. By measuring the distribution tail a user can acquire information such as whether or not an emulsion is stable or if a CMP slurry will cause damage to the silicon wafers it is used to polish.
Pharmaceutical emulsions
The relationship between coarse droplets and emulsion stability is well documented (2,3,4). The stability of lipid injectable emulsions is determined following the procedure described in USP <729> (5), “Globule Size Distribution in Lipid Injectable Emulsions”. Method I in USP <729> stipulates that the mean size must be below 500 nm as measured using either dynamic light scattering (DLS) or laser diffraction. Method II specifies that the coarse tail (volume % greater than 5 µm) be less than 0.05% as measured using the SPOS technique. This tail concentration has proven to be a good prediction for emulsion stability.
Figure 1: Old and new intralipid samples by DLS (upper) and SPOS (lower)
Figure 1 shows the particle size distributions for two pharmaceutical emulsions: a new and very old intralipid sample. These two emulsions have roughly similar mean diameter and would both pass the USP <729> Method I criteria of less than 500 nm. The upper graph shows the results from DLS and the lower graph was generated using SPOS.
Taking the old and new DLS results two standard deviations from the mean would equal 389.1 and 532.4 nm. It is obvious that the older sample would have more coarse particles, but DLS does not provide concentration information and does not extend well into the above 5 micron region (5000 nm). SPOS results for new and old intralipd samples clearly idicate that the old sample has a higher concentration in the greater than 5 µm range and fails the USP <729> Method II criteria. The graph provides qualitative evidence for this fact while the PFAT5 calculation provides the quatitative percentage value.
Tails in inkjet inks
Inkjet inks are colloidal dispersions of pigments in solution with mean sizes well below 1 µm. Oversized particles (coarse tails) pose a risk for clogging jets and causing other reductions in performance and image appearance. SPOS is often utilized to determine the concentration of large particles in inkjet inks.
A commercial black inkjet ink sample was analyzed using DLS to determine the mean size and zeta potential. The sample was diluted 1000:1 in deionized (DI) water and a quick study was performed to assure size did not change with additional dilution. The result for the mean size as measured by DLS system is shown in Figure 2, upper.
Figure 2: Inkjet ink DLS result (upper) and SPOS result (lower)
For this sample the volume mean = 98.31 nm and the standard deviation = 31.16. Here two standard deviations from the mean is 98.31 + (31.16 x 2) = 160.63 nm. One might think there would be few particles > 0.5 µm in this distribution of particles. But a high concentration of coarse tail particles was detected when this sample was tested on an SPOS system as shown in Figure 2, lower. Note that the actual concentration > 0.5 µm is over 20 million particles/mL, proving that SPOS is the best technique to quantify the concentration of this coarse tail.
Detecting fines
There are other industries and applications where the tail of small particles (the fines) is important. Examples include how small particles effect powder flow or packing density. SPOS can also accurately quantify concentration of fines and is again more accurate & higher resolution than laser diffraction. Additive manufacturing (AM), or 3-D printing, is an industry where the quantity of fines can play an important role in both the manufacture of parts and quality of final product (6-8). Several powder samples used in AM were analyzed on both SPOS and laser diffraction to investigate the ability of these techniques to define the population of fine particles (9). Figure 3, lower shows the volume distribution SPOS results for polymethyl methacrylate (PMMA) polymer. Figure 3, upper shows the same PMMA sample analyzed on a laser diffraction analyzer. The X axis scale is similar for all graphs. See reference (9) for details on the sample preparation and analysis details.
Figure 3: PMMA size distribution by laser diffraction (upper) and SPOS (lower)
The laser diffraction analyzer provided no useful information on the amount of fines in the particle size distribution while the SPOS results quantifiably defined the significant proportion of fines. The quantity of fines can be further characterized using an absolute volume fraction calculation within any desired size range. In addition, total number of particles within any size range can be determined by creating defined size regions and viewing the statistics with the region.
Conclusions
The tails of particle size distributions can have a significant effect on product quality and performance. While ensemble light scattering techniques such as DLS and laser diffraction are important and useful analytical tools, neither can provide accurate, high resolution concentration data for tails of particle size distributions. The SPOS technique is the preferred methos for quantifying both the coarse and fine tail of distributions and is used across a wide range of industries and applications for this purpose.
References
- Entegris White Paper “Particle Size Analysis Overview”
- Driscoll, D. et al., Physicochemical assessments of parenteral lipid emulsions: light obscuration versus laser diffraction, International Journal of Pharmaceutics 219 (2001) 21–37
- Driscoll, D., Globule-size distribution in injectable 20% lipid emulsions: Compliance with USP requirements, Am J Health-Syst Pharm—Vol 64 Oct 1, 2007
- Driscoll, D. et al., Pharmacopeial compliance of fish oil-containing parenteral lipid emulsion mixtures: Globule size distribution (GSD) and fatty acid analyses, International Journal of Pharmaceutics 379 (2009) 125–130
- USP <729> Globule Size Distribution in Lipid Injectable Emulsions
- Spierings A.B., Herres N., Levy G. Influence of the particle size distribution on surface quality and mechanical properties in AM steel parts. Rapid Prototyp. J. 2011;17:195–202. doi: 10.1108 /13552541111124770
- Liu B., Wildman R., Tuck C., Ashcroft I., Richard H. Investigation the effect of particle size distribution on processing parameters optimization in Selective Laser Melting process; Proceedings of the 22nd Solid Freeform Fabrication Symposium; Austin, TX, USA. 8–10 August 2011; pp. 227–2
- Spurek, M., Haferkamp, L., Weiss, C. et al. Influence of the particle size distribution of monomodal 316L powder on its flowability and processability in powder bed fusion. Progress in Additive Manufacturing 7, 533–542 (2022)
- Entegris application note Importance of Particle Size in Powders Used for Additive Manufacturing
About the author
Mark Bumiller, currently the Technology Manager at Entegris, Inc., has worked in the field of particle size analysis for over 35 years. Previous positions include product manager at Hiac Royco, technical support manager and vice president of business development at Malvern Instruments, vice president of particle products at Horiba and technology manager at Particle Sizing Systems, LLC. He has served as a member of the expert committee for USP <788>, the executive committee of the International Fine Particle Research Institute (IFPRI), and the executive committee of Particle Technology Forum of the American Institute of Chemical Engineers. Mark is an active member of Technical Committee 24 within ISO helping to write standards for particle size and zeta potential analysis. His B.S. in chemical engineering was earned at Carnegie Mellon University in Pittsburgh, PA.