Choosing the right particle analysis instrument requires an understanding of the basic operating principles of the different analysis techniques, as well as how variations in size and shape affect the results.

A basic idea of particle size and shape can be gained by microscopically examining the particles in a sample. However, reducing this visual perception to quantitative values is not straightforward and requires the right selection of specialized analysis equipment. Selecting the right system requires an understanding of what particle characteristics are being measured and interpreted as "size" and "shape," as well as the basic operating principles of the different analysis techniques, and how variations in size and shape affect the results. Figure 1 (p. 15) illustrates the challenge.

The primary measure of a particle's size is its volume. For a particle with a regular shape, such as a cube or sphere, a measure of the diameter is enough to define the particle. This measurement can usually be reduced to a single value, such as the diameter of a spherical particle or the length of one face of a cubic shape. However, as the shape begins to vary, a simple diameter measurement becomes inadequate, and additional values such as maximum and minimum diameter, aspect ratio and others are required to represent the shape. Image analysis software libraries can have more than 50 different measures of shape.

Fortunately, knowing the shape of the particles in such detail is unnecessary for the majority of applications, and simplifying assumptions can be made. In fact, the majority of instruments for particle size analysis assume a spherical shape, and this is entirely adequate for most applications. Some users combine techniques to gain additional information about their samples.

Laser Light Scattering

Laser light scattering is one of the most commonly used techniques for particle size analysis because of its speed and relative ease of analysis. The two theories widely applied for interpreting the results of this technique are the Mie and Fraunhofer theories, both of which almost always assume a spherical particle shape. The Mie theory is considered to be an exact solution and includes all interactions between the laser light and the particle (diffraction, reflection, absorption and refraction) but requires knowledge of the complex refractive index of the particles under analysis. The Fraunhofer theory only considers light diffraction and does not require a refractive index value. As a result, it loses accuracy as the size of the particle is reduced and is generally not suitable for use on particles smaller than 30 to 50 micrometers. Figures 2 and 3 (p. 16) represent a sample for which either the Mie or Fraunhofer theories could be used.

Laser light scattering works by suspending the particles in a fluid medium (usually air or water) and exposing the particles to a collimated laser beam. The light is scattered by the particles, and the light scattering pattern is measured by a detector system. Since the light scattering pattern depends on the particle size, the measured light scattering pattern can be analyzed by the mathematical process of deconvolution to determine the particle size distribution that produced the light scattering pattern. In general, the greater the number of detectors available, the higher the measuring resolution of the system for particle size analysis and for the study of shape analysis effects. High resolution is important in detecting small differences in particle size and in enabling the early detection of process trends that affect particle size.

The equations of the Fraunhofer and Mie theories can be developed for a variety of shapes, although a spherical shape is always used in commercially available instruments. At this point, no theory exists that enables laser light scattering instruments to determine the shape of the particles under analysis, so shape would have to be assumed prior to the size analysis. The sphere is the dominant choice because it is close to most particle shapes and is the most practical to use. The resulting particle size is referred to as the "equivalent spherical diameter," or the diameter of spherical particles that would have produced the measured light scattering pattern.

The Mie theory was developed beginning with Maxwell's Equations of electromagnetic fields. "Light" is simply the visible part of the electromagnetic spectrum; however, any of the portions of the electromagnetic spectrum-including radio waves, microwaves, infrared and ultraviolet light, X-rays, and gamma rays-could be used in a light scattering analysis. Shorter wavelengths of the electromagnetic spectrum can be used to characterize smaller particles, and longer wavelengths can be used for larger particles.

Electrical Sensing Zone Method

A particle sizing technique that directly measures the volume of the particles under analysis is the electrical sensing zone method, as defined in ISO 13319:2000. In this method, the particles to be analyzed are suspended in a conductive electrolyte solution and are pumped one at a time through a precisely sized orifice.

A constant current flows through the orifice; as the particle passes through, electrolyte is displaced so that the voltage required to maintain a constant current must be increased. This action produces a voltage pulse with an area under the pulse that is proportional to the volume of electrolyte displaced, which is the volume of the particle. In practice, the particles can be pumped through the orifice very rapidly so that a complete analysis can take place in a few minutes.

As with laser light scattering, the particle shape has to be assumed prior to the size analysis. Again, the shape assumed in the electrical sensing zone analysis is a sphere, and the sizes are reported as equivalent spherical diameters, or the diameter of spheres that have the measured volumes. Since the basic measurement is the volume of the particles, converting the reported sizes to other shapes is straightforward.

Some information about the shape of the particles can be obtained from the shapes of the pulses generated. Given two particles of the same volume, one spherical and the other rod-shaped, the pulses generated as the particles pass through the analysis orifice would have the same area but different widths. If the widths are also measured and reported, this information can provide additional detail about the shape of the particles. Some instruments can report the width of the pulses in a three-dimensional plot with particle size along one axis, particle counts along another axis, and pulse widths along the third axis. However, deriving shape information from the electrical sensing zone method is still in its early stages.

Image Analysis

The technique that is most capable of determining particle shape is image analysis. Just as a visual examination gives significant information regarding particle shape, image analysis can also give shape information. The difficulty is in defining "shape" in a way that can be reduced to a measurement that can be made by a computer.

Image analysis has been used for a number of years, and the software libraries for measuring size and shape are common and quite mature. Image analysis instruments work by digitizing the particle image. The computer then identifies the perimeter of the particles and measures the cross-sectional area of the particles by simply counting the number of image pixels within the perimeter. The shape of the line representing the perimeter is used to determine the particle shape. At least one image analysis library* has more than 50 different particle shape measures, so a large number of shapes can be measured along with particle size. Particles are positioned so that they can be imaged by a camera or even an electron microscope. The images acquired can then be analyzed for size and shape.

A variety of instruments exist for performing this type of analysis. Many systems require the particles to be placed by hand, so that analyzing enough particles to get a good statistical sampling can be time-consuming. More recently, instruments that incorporate a sample handling system with an imaging system have been developed and are capable of analyzing enough particles to yield good statistical sampling in a relatively short amount of time.

Choosing the Right Technique

For the majority of applications, an equivalent spherical diameter is a useful measure of particle size. This provides a good method to compare samples and to determine changes in particles from sample to sample. Increasingly, particle shape is also of interest, and the effect of different shapes on the various techniques of particle size analysis is important to understand.

Research is being performed to determine techniques for analyzing a large number of particles for size and shape. At this stage, image analysis is the most powerful technique for determining particle shape, but other techniques are also capable of providing some shape information. In most cases, however, it is still necessary to begin the analysis with information regarding the particle shape, as few techniques can determine the shape of particles in an unknown sample.

Ultimately, the application will dictate the type of instrument that is required. If the particle shape must be measured, image analysis is likely the best tool. If particle volume is a critical measurement, the electrical sensing zone method or X-ray sedimentation technique can provide the most accurate results. If a high sample concentration is required (as in many ceramic applications), X-ray sedimentation is often used since it allows a higher sample concentration than most other techniques. And for applications in which the speed of the analysis is the most important consideration, an instrument that uses laser light scattering or the electrical sensing zone technique can be a good choice.

Understanding the basic operation and limitations of the different instruments can help users select the right tool (or combination of tools) to ensure accurate particle characterization-and high-quality finished products.

For more information about particle size and shape characterization, contact:
Micromeritics Instrument Corp
One Micromeritics Dr.
Norcross, GA 30093
Phone: (770) 662-3620
e-mail: mike.strickland@micromeritics.com.

Links

• mike.strickland@micromeritics.com
• www.ni.com
• www.eng.uc.edu/~gbeaucag/BeaucageResearchGroup.html
• For more Information visit www.micromeritics.com
• www.iso.org
• www.A9.com
• www.sciencedirect.com