Sizing Particles

Many methods and numerous instruments are available from recognized vendors to measure particle size. Each method has advantages and disadvantages. In addition, most are not well suited for dealing with rods, needles, fibers, or other odd-shaped nonspherical particles, and need to be supplemented by a shape analysis.

Sieving method

Figure 1 - Standard test sieves.

A series of sieves (screens made of a woven cloth of stainless steel with rectangular openings of uniform size) are stacked on top of each other in order of size, and a sample is introduced on the top (the coarsest sieve). As the particles fall through the column, aided by vibration, the weight of material retained on each sieve produces a crude distribution of sizes (see Figure 1).

  1. Advantages. The method is simple and inexpensive, and inspires great confidence in the results.
  2. Disadvantages. It is practically impossible to measure sprays or emulsions and cohesive and agglomerated materials such as clays. Standard sieves range from 38 μm to 4.75 mm (0.187 in.). The method is usually labor intensive. Operators responsible for daily manual sieve shaking can develop carpal tunnel syndrome. Even with automated sieves, there is frequently a problem in determining when the fractionation process is complete. Sieving is inherently a low-resolution method. Other problems to be aware of are opening blocking by particles that are slightly larger than the sieve size, and variation in sieve apertures due to wear or lax manufacturing tolerances.
  3. Shape effect. The reported distribution depends very much on the shape of the particles and the duration of the test. Long, thin particles will give very different results when compared to spherical particles of the same weight. As particles orient themselves, longer test duration will produce smaller mean aperture results. Therefore, measurement times and operating methods need to be rigidly standardized to ensure repeatability.

Sedimentation method

Using light or X-ray beams, sedimentation apparatus determines the speed of particles falling in a suspension liquid. The particle size is then expressed in terms of the equivalent spheres, which have the same settling speed in laminar flow conditions. Stokes’ law indicates the impact of density and viscosity on the results. Streaming effects are countered by density gradients, and particles with low density (which would never settle) can be measured with an inverse disk. Centrifuges are sometimes used to accelerate the sedimentation process.

  1. Advantages. The technique has high resolution and excellent reproducibility. It became the method of choice for many applications, particularly in geology and oceanography explorations.
  2. Disadvantages. Sedimentation is limited at the high end (50 μm) by turbulence (large Reynolds numbers) and at the low end (below 2 μm) by diffusion due to Brownian motion (although some systems do a very good job in the submicron range). The method cannot be used for emulsions (the material does not settle), very dense materials that settle quickly, or mixtures of differing densities. It depends on the ambient temperatures that affect viscosity. Typical measurement is very long compared to other methods (it can take 20–60 min).
  3. Shape effect. Sedimentation generates accurate distributions for spherical particles only, since objects of the same weight but different shape and orientation will have different settling speeds.

Optical and electron microscopy methods

Figure 2 - Scanning electron microscope.

Many are familiar with the optical microscope. Electron microscopy extends the range of applications but essentially resorts to the same type of analysis, namely visual inspection, counting, and shape characterization. Automated optical systems (with video camera and computer) eliminate most of the drudgery of this approach (see Figure 2).

  1. Advantages. Microscopic evaluation allows one to see the particles and evaluate their shapes and sizes. The method inspires great confidence in the results. The microscope can be calibrated by looking at known size standards.
  2. Disadvantages. Even with some automation, analysis can be long and tedious, especially with the electron microscope. The number of measured particles is usually small compared to other methods. For both optical and electron microscopy, sample preparation is crucial. It is normally not possible to determine if two or more particles are just touching or if they are permanently stuck together. This can lead to significant errors in reported size distribution. Sample preparation for electron microscopes is slow, expensive, and requires considerable technical expertise, unless the state-of-the art devices that have recently become available to microscopists are used.
  3. Shape effect. Clearly, microscopy with a subsequent shape analysis is the best method for direct particle shape characterization.

Laser diffraction method

Figure 3 - Laser diffraction schematics.

In this method, a laser beam passes through particles while light intensity data are collected at different scattering angles by a fixed number of detectors. Two optical models can be employed to calculate particle size distributions from diffraction angles. Fraunhofer approximation (used for particles larger than 10 μm) is based on the assumptions that all particles scatter with equal efficiencies and that particles are completely opaque. Mie theory can be used for smaller particles but requires a priori knowledge of the refractive indices (see Figure 3).

  1. Advantages. Diffractometers can measure dry powders, liquid suspensions, emulsions, sprays, and aerosols. Data collection is very fast (a few minutes in most cases). With proper sample preparation, high reproducibility and precision can be achieved with a broad dynamic range (for some instruments, the applicable range is claimed to extend from 0.02 μm to several millimeters). The technique is relatively simple to use. Testing is nondestructive and nonintrusive. The entire sample is measured (this is the so-called "ensemble technique"). There is no need and, in fact, there is no real way to calibrate a laser diffraction instrument. The detectors, however, require a periodic check of operating performance. For Mie applications, the result is a volume distribution, which is equal to the weight distribution if the density is constant. Fraunhofer approximation yields projected area rather than a volume distribution.
  2. Disadvantages. Assumptions of Fraunhofer approximation are often violated and this can lead to huge errors. The results of Fraunhofer approximation are not volume proportional and therefore not mass equivalent. For Mie theory, incorrect refractive indices may lead to erroneous results. The method assumes that particles are optically homogeneous. Mixtures of particles with different optical properties cannot normally be measured. Resolution is limited by the number of detectors. The larger the measured particles, the lower the resolution of laser diffraction systems. Complex proprietary software employed by laser diffractometers is not open to independent validation. Software development standards may not apply. Validatability of computerized data acquisition systems is questionable.
  3. Shape effect. The method is based on the assumption of sphericity of the measured particles. Nonspherical particles have diffraction patterns that differ considerably from the spheres of equivalent diameter. The laser diffraction method is precise, but for particles with low aspect ratio, the results are inherently inaccurate, regardless of the definition of a “true” particle size.