Particle Size Distribution

Particle size distribution (PSD) is a series of values, a histogram or a mathematical function indicating what sizes of particles, in what counts or proportions are present in the particle system. Particle size distribution information is critical for the analysis, control and optimization of a variety of processes, such as crystallization (and recrystallization), tablet dissolution and disintegration, emulsification, milling, flocculation and flow assurance.

To fully define "particle size distribution", we need to define "particle size". Spherical particle size is easy to be characterized by one number, the diameter (or the radius). Other types of particles have a wide variety of shapes, structures and phases, thus different three-dimensional elongations. A one-dimensional size function, such as spherical equivalent diameter, chord length, particle length or particle width, is frequently used in practice. Spherical equivalent diameter is defined as the equivalent diameter of a sphere having the same physical property. The volume based spherical equivalent diameter is obtained by calculating the diameter of a sphere with the same volume as that of the particle being studied.

However, while it is convenient to assign a single number to characterize a non-spherical particles system, it often does not reflect the full reality of the particles. The surface area of a needle 5 µm diameter X 50 µm length is 70% greater than that of a sphere with identical volume-based equivalent diameter (12.3 µm). This needle will handle and flow differently from the sphere during filtration or in a flow system. Therefore, it is critical to choose the right particle size parameter and analysis tool that fits the process being studied, and advantageous to be able to obtain PSD data three-dimensionally (e. g. via microscopy) and in-situ (by using in-process tools), which provides well-rounded understanding of the particles system in the native environment.

Particles (and crystals, droplets and bubbles) are present in the vast majority of manufacturing processes and their final products. The thorough understanding and proper control of particle size distribution is often a critical factor in final product quality and can greatly influence process efficiency.

For example, the effectiveness of medicines used to treat lung diseases has been shown to depend heavily on particle size. Large droplets (Figure A) deliver medicine in an ointment slower than small droplets (Figure B). It has also been reported that particulate process plants take longer to start up, and are less likely to achieve desired production rates, versus those processing liquids or gases. Multiphase systems involving combinations of particles, droplets, and bubbles result in additional complexity and magnify the challenge of understanding, optimizing, and controlling the processes used to produce, modify, or separate them. Crystallization in particular is a challenging particle formation process where the particle size after isolation can have a dramatic impact on all downstream processing operations. The separation time of a slurry (Figure C) can be heavily extended if there co-exists small particles (Figure D).

Using an offline analyzer is a powerful and widely used technique for the measurement of particle size in quality control (QC) labs. Examples of traditional particle size analysis techniques include sieving, laser diffraction, offline microscopy (more details below), dynamic light scattering, electrozone sensing, sedimentation and air elutriation. These approaches allow QC laboratories to check the dimensional information of the particles at the end of a process against a set specification and identify deviations from the required particle properties.

This approach involves passing particles through a series of sieves of different mesh sizes and measuring the amount/weight of material that is stopped by each sieve as a fraction of the total amount/weight. Sieving is intuitive, simple, cheap and easy to interpret, and usually works well for particles larger than 100 µm. However, smaller particles are difficult to be forced through the sieve, and the corresponding sieve can be too fragile to be practical.

When a laser beam passes through a dispersed particles system, large particles scatter light more intensely at small angles, and small particles scatter light less intensively but at larger angles. Laser diffraction analyzers do not directly measure the particle size, but collect the information of the angle and intensity of scattered light, and mathematically transform the information into the particle size distribution. Laser diffraction is one of the most commonly used measurement method, especially for particles from 0.5 µm to 1000 µm. This technique is a well validated analytical tool and an industrial standard for quality control (QC).

Traditional microscopic methods, such as optical microscopy and scanning electron microscopy, have long been used for particle analysis, although mostly through brutal force - manual counting and measuring. Recent development of image processing technology starts to allow the generation of particle size distribution information via automated image analysis. These tools are most suitable for particle systems that are robust against condition changes, such as cooling, drying, dilution and sonication, one or more of which the particle systems have to experience for offline measurement.

Inline particle size measurement typically relies on inserting a probe-based instrument or adding a flow-cell into a process stream for direct measurement of particles as they naturally exist in the process. Probes can be applied across a range of scales and installation environments, ranging from small-scale laboratory reactors (Figure A) to full-scale production pipelines (Figure B). Inline measurement provides in-situ data that requires no further processing and renders the true properties of the original particles system, full process trends that are recorded from the beginning to the end of the process, and real-time analysis that enables fast decision and immediate condition modification.

FBRM is the industry-standard measurement technique used for in-process measurement of particles. A rotationally scanning laser beam is launched down the probe tube and focused to a tight beam spot at the window contacting the process stream. During the scan, individual particles or particle structures will backscatter the laser light to the detector. The distances of the pulses of backscattered light are summarized into the particle size distribution, so called chord length distribution. Besides its inline nature, FBRM is a direct measurement method which records the sizes it actually "sees", not relying on indirect correlations such as particle size light scattering angle correlation.

Directly taking photos of the particles system and using software to analyze the photos can be rapid and accurate, and provide 3-D morphological information of the particles. For example, EasyViewer as a high-resolution microscope, in combination with its software's image analysis capability, can provide, in real time, not only images and a turbidity trend, but also particle size distribution, plus a variety of morphological parameters such as particle width, length, aspect ratio and circularity.

A successful laboratory analysis of particle and droplet systems requires the removal of a representative sample from the process, and the preparation of this sample for offline analysis. Most offline techniques have strict constraints on the range of concentration, size and shape of particles that can be measured accurately. This sample preparation procedure can be labor-intensive and expensive, since it often involves multiple steps necessary to meet these measurement constraints and can employ methods, such as filtration, rinsing, drying, subsampling, resuspension, surfactant addition, dilution and sonication.

These sample preparation steps may significantly alter the particles or droplets of interest. Even with the utmost care and precision in the sampling and sample preparation methods, the actual particles that are analyzed may be significantly different from the particles that were initially present in the process vessel. For example, mannitol crystals image taken by real-time microscopy (Figure A) is significantly different from that taken by a standard offline light microscope (Figure B). Sampling and preparation for offline microscope analysis have resulted in significant breakage and delicate dendritic structures observed in process go undetected.

The particle size of non-spherical particles is often reported using an equivalent diameter. For example, in the right figures, particles with different shapes but equivalent volumes are depicted. If particle size is reported based on volume, the spherical sample and the needle-shaped sample are identical. However, the behavior and throughput of sieving the two samples might be quite different, because their sieve diameters and shapes are far from identical. Therefore, care should be taken to determine how shape influences particle size analysis results, and if possible to determine particle shape using a technique, such as EasyViewer imaging.

Since most particle process streams operate at a solids loading much higher that anything traditional particle size analyzers can handle, careful and time consuming sample preparation is needed for the measurement. The measurement and analysis takes time as well, from minimum minutes (e.g. by light scattering methods) to even longer (e.g. by sieving and offline microscopy).

In order to obtain continuous information, samples would have to be manually extracted frequently and analyzed on the fly. This approach may also impose unacceptable level of risk, especially for processes at elevated temperatures and pressures with toxic or explosive slurries and solvents. The inevitable time delay between sampling and the receipt of results with offline tools makes them difficult to implement for true real-time measurement, and makes them unsuitable for monitoring process continuously as it changes over time. Inline particle size analyzers are the recommended alternative.

Typically, an in-process particle measurement is taken every few seconds, allowing discrete distributions to be recorded at user-defined intervals (Figure A). Statistics from each distribution can then be trended over time (Figure B and C), allowing scientists to monitor process trajectory in real time.

As exemplified in Figure C, it is straightforward to determine: 

1. When particle size and count starts changing
2. When particle size and count stops changing
3. The rate at which particles change
4. The degree to which particles change

With this information, scientists develop a deeper understanding of their processes compared to when they must rely on a single particle size analysis result from a single point in space and time.

By directly monitoring the impact of process parameters on particle size and count, it is possible to reliably determine the process parameters needed to target a specific set of particle attributes. For example, the impact of agitation rate on droplet size is clear, allowing scientists to readily choose a set of operating conditions that will deliver the desired droplet size.

Beyond the oversimplified particle size parameter, other shape parameters, such as particle width and length, are important because they impact process and product performance. One example of this is Carbamazepine, an anti-seizure drug (trade name Tegretol), used to prevent and control seizures. Carbamazepine has historically been problematic in terms of irregular drug performance.

Having multiple polymorphs, with different dissolution rates, control of the desired form is important for proper drug efficacy. By utilizing iC Vision software with image analysis, EasyViewer was able to track the changes of particle width and length in real time, and acquire kinetic and endpoint information that can be used to understand this conversion and ultimately introduce control into this process.

By monitoring particle size in real time directly in the process, it is possible to identify process deviations and take corrective action to minimize the impact of the upset. In Figure A, a continuous process is being monitored where particle size must be kept within tight specifications. Here it should be noted the specification that is set using the in-process instrument is not necessarily the same as the specification set using the traditional particle size analyzer in the QC lab. Here the in-process particle measurement instrument is simply identifying a dramatic process upset, and can support troubleshooting the problem before implementing a corrective action that will bring the process back into specification. For batch processes, in-process particle measurement can support the reduction of batch time by identifying when a process reaches steady state. In Figure B, most of the process changes occur during the first two hours of the process – however in-process particle measurement indicates that particles do not change for the remaining 10 hours of the batch. This is a good indicator that batch time could be reduced – and that a sample for offline quality control should be taken soon after the initial 2 hour period, where most change occurs.

A comprehensive particle engineering toolbox includes a reactor that mimics conditions at larger scales, as well as, probe-based tools that are inserted directly into the process to provide immediate and real time understanding of the impact of process parameters on particle mechanisms.

Process parameters and particle mechanisms are recorded and monitored automatically and can be linked to an offline particle size analysis result. Software ties all of this information together seamlessly, allowing scientists to concentrate exclusively on using high-quality data to make excellent evidence-based decisions.

• ParticleTrack tracks in-situ the change to particle size distribution. By understanding changes to particles in real time, scientists can quickly detect endpoints, ensure batch-to-batch consistency, and optimize downstream throughput and product quality.
• EasyViewer is a probe-based particle size analyzer with image analysis, and captures high-resolution images and calculate crystal, particle and droplet size distributions as they naturally exist in process.
• Automated synthesis reactors replace traditional round bottom flasks and jacketed lab reactors. These tools provide precise and automated control of an expanded range of process conditions and record parameters for analysis, repeat experiments and regulatory requirements.
• Raman spectrometers provide molecular and structural information to help scientists understand complex polymorphic landscapes and select process parameter to always achieve the desired crystal form.

• Crystallization
• Recrystallization
• Polymorphism Chemistry
• Flocculation
• Downstream Processing
• Formulations and Product Development
• Flow Assurance in Oil & Gas Production
• Process Analytical Technology (PAT)
• Quality by Design (QbD)
• Protein Crystallization
• Lactose Crystallization

Sirota, E., Kwok, T., Varsolona, R. J., Whittaker, A., Andreani, T., Quirie, S., Margelefsky, E., & Lamberto, D. J. (2021). Crystallization Process Development for the Final Step of the Biocatalytic Synthesis of Islatravir: Comprehensive Crystal Engineering for a Low-Dose Drug. Organic Process Research & Development, 25(2), 308–317. https://doi.org/10.1021/acs.oprd.0c00520

Clain, P., Ndoye, F. T., Delahaye, A., Fournaison, L., Lin, W., & Dalmazzone, D. (2015). Particle size distribution of TBPB hydrates by focused beam reflectance measurement (FBRM) for secondary refrigeration application. International Journal of Refrigeration, 50, 19–31. https://doi.org/10.1016/j.ijrefrig.2014.10.016

Kempkes, M., Eggers, J., & Mazzotti, M. (2008). Measurement of particle size and shape by FBRM and in situ microscopy. Chemical Engineering Science, 63(19), 4656–4675. https://doi.org/10.1016/j.ces.2007.10.030

Sankaranarayanan, S., Likozar, B., & Navia, R. (2019). Real-time Particle Size Analysis Using the Focused Beam Reflectance Measurement Probe for In Situ Fabrication of Polyacrylamide–Filler Composite Materials. Scientific Reports, 9(1). https://doi.org/10.1038/s41598-019-46451-x

Galata, D. L., Mészáros, L. A., Kállai-Szabó, N., Szabó, E., Pataki, H., Marosi, G., & Nagy, Z. K. (2021). Applications of machine vision in pharmaceutical technology: A review. European Journal of Pharmaceutical Sciences, 159, 105717. https://doi.org/10.1016/j.ejps.2021.105717

Kutluay, S., Şahin, M., Ceyhan, A. A., & İzgi, M. S. (2017). Design and optimization of production parameters for boric acid crystals with the crystallization process in an MSMPR crystallizer using FBRM® and PVM® technologies. Journal of Crystal Growth, 467, 172–180. https://doi.org/10.1016/j.jcrysgro.2017.03.027