Many different techniques have been devised for determining particle size distribution, but for a wide range of industries laser diffraction has become the preferred choice. Laser diffraction, alternatively referred to as Low Angle Laser Light Scattering (LALLS), can be used for the non-destructive analysis of wet or dry samples, with particles in the size range 0.02 to 2000 micron and has inherent advantages which make it preferable to other options for many different materials.
In this article the issues surrounding the measurement of particle size are examined. Different definitions of particle size are considered and the theory underpinning laser diffraction analysis is outlined. The benefits of laser diffraction as an analytical technique for particle sizing are discussed with reference to the Mastersizer 2000, an instrument developed by Malvern Instruments to provide easy and efficient analysis.
What is particle size?
Before discussing methods for particle sizing, it is worth understanding how particle size distributions are defined. Particles are three-dimensional objects for which three parameters (the length, breadth and height) are required in order to provide a complete description. As such, it is not possible to describe a particle using a single number that equates to the particle size. Most sizing techniques therefore assume that the material being measured is spherical, as a sphere is the only shape that can be described by a single number (its diameter). This equivalent sphere approximation is useful in that it simplifies the way particle size distributions are represented. However, it does mean that different sizing techniques can produce different results when measuring non-spherical particles.
An example of the application of the equivalent sphere approximation is shown in figure 1. Here the spherical equivalent diameters reported using different techniques for the same particle are shown. In each case, the reported diameter will be dependent on the physical property measured using the chosen technique. For example, a technique could measure the mass or volume of the particle. This would lead to the diameter of the sphere that has the same volume as the measured particle being reported as the particle size. Each representation is equally valid, although they are not equally relevant to any given process. A catalyst engineer, for example, may be particularly interested in surface area as this influences reaction rate, and might therefore prefer a technique which generates surface-area based data.
|Fig. 1: Equivalent sphere representation for an irregularly shaped particle.|
It is clear then that any instrument or technique selected for particle size analysis needs to generate data in a form that is relevant to the process. In addition, the technique needs to be reliable, simple to use and capable of generating reproducible data, if acceptance and usefulness are to be maximized.
Laser diffraction based particle size analysis relies on the fact that particles passing through a laser beam will scatter light at an angle that is directly related to their size. As particle size decreases, the observed scattering angle increases logarithmically. Scattering intensity is also dependent on particle size, diminishing with particle volume. Large particles therefore scatter light at narrow angles with high intensity whereas small particles scatter at wider angles but with low intensity (see figure 2).
|Fig. 2: Light scattering patterns observed for a large particle (upper part) and a smaller particle (lower part).|
It is this behaviour that instruments based on the technique of laser diffraction exploit in order to determine particle size. A typical system consists of a laser, to provide a source of coherent, intense light of fixed wavelength; a series of detectors to measure the light pattern produced over a wide range of angles; and some kind of sample presentation system to ensure that material under test passes through the laser beam as a homogeneous stream of particles in a known, reproducible state of dispersion. The dynamic range of the measurement is directly related to the angular range of the scattering measurement, with modern instruments making measurements from around 0.02 degrees through to beyond 140 degrees (figure 3). The wavelength of light used for the measurements is also important, with smaller wavelengths (e.g. blue light sources) providing improved sensitivity to sub-micron particles.
|Fig. 3: Typical laser diffraction instrument layout.|
Particle Size Calculations
In laser diffraction, particle size distributions are calculated by comparing a sample’s scattering pattern with an appropriate optical model. Traditionally two different models are used: the Fraunhofer Approximation and Mie Theory.
The Fraunhofer approximation was used in early diffraction instruments. It assumes that the particles being measured are opaque and scatter light at narrow angles. As a result, it is only applicable to large particles and will give an incorrect assessment of the fine particle fraction.
Mie Theory provides a more rigorous solution for the calculation of particle size distributions from light scattering data. It predicts scattering intensities for all particles, small or large, transparent or opaque. Mie Theory allows for primary scattering from the surface of the particle, with the intensity predicted by the refractive index difference between the particle and the dispersion medium. It also predicts the secondary scattering caused by light refraction within the particle – this is especially important for particles below 50 microns in diameter, as stated in the international standard for laser diffraction measurements (ISO13320-1 (1999)).
Analysis of calcium carbonate
The following example illustrates the superiority of Mie Theory. Figure 4 shows comparative, cumulative particle size data for a sample of calcium carbonate, a filler used in papermaking to give a smooth printing surface.
|Fig. 4: Calcium carbonate size distributions reported using Mie Theory and the Fraunhofer Approximation.|
Using the Fraunhofer Approximation the measured size distribution is shifted to larger particle sizes. This error stems from the inability of the Fraunhofer Approximation to correctly predict the sample’s true scattering behaviour. For calcium carbonate, the scattering efficiency decreases rapidly below 2 microns, but the Fraunhofer approximation is based on the assumption that scattering efficiency is independent of particle size. The use of this approximation therefore causes a significant underestimation of the volume of sub-micron material within the sample. Mie Theory, which is able to predict effectively the fall off in scattering efficiency, gives appropriate weighting to the fine sizes and hence correctly predicts the overall particle size distribution.
The benefits of laser diffraction
Laser diffraction is a non-destructive, non-intrusive method that can be used for either dry or wet samples. As it derives particle size data using fundamental scientific principles there is no need for external calibration; well-designed instruments are easy to set up and run, and require very little maintenance. Additionally, the technique offers:
- A wide dynamic measuring range – modern systems allow users to measure particles in the range from 0.02 micron to a few millimetres without changing the optical configuration, ensuring that both well-dispersed and agglomerated particles are detected equally well
- Flexibility – the technique is equally applicable to sprays, dry powders, suspensions and emulsions, allowing different product formulations to be compared in a realistic way
- Generation of volume-based particle size distributions – this is normally equivalent to a weight distribution and is relevant to many processes as it indicates where most of the mass of material is located in terms of particle size
- Rapid data acquisition – a single measurement across the entire dynamic range can be made in 0.4 milliseconds, allowing dynamic events to be studied
- High repeatability – the ability to acquire data rapidly allows many thousands of measurements to be averaged when reporting a single result, providing repeatability. This, coupled with standardized operating procedures, ensures that the instrument-to-instrument variation is less than 1%, enabling direct comparison of data from different sites.
- Ease of Verification – as a first principles technique laser diffraction does not require calibration but can be easily verified using a variety of readily available NIST-traceable standards (eg from Duke Scientific, Whitehouse Scientific, NIST).
The Mastersizer 2000
The generic benefits of the technique of laser diffraction have been exploited and enhanced in the design of the Mastersizer 2000, (see figure 5), which is used worldwide for the analysis of a diverse range of particles. The Mastersizer has a fully optimized optical design which allows particles in the size range 0.02 - 2000 micron to be characterized effectively. A range of dispersion units ensures optimum sample presentation, and switching between units is relatively easy allowing different samples to be analyzed rapidly, in close succession. Automated, standard operating procedure (SOP) driven operation delivers a consistent analysis, and minimizes training requirements, whilst flexible software allows results presentation to be tailored to the requirements of the customer.
|Fig. 5: Mastersizer 2000.|
Application study : Powder coating characterization
One of the strengths of the laser diffraction technique is its ability to detect out-of-specification material at both the fine and coarse ends of a particle size distribution. As such, the technique is routinely applied to determine the end point of milling when producing powder coatings. Here particle size control is important as it defines the properties of the finished film as well as the ease of application. Large particles can lead to defect formation within the finished coating. However, the use of too fine a powder can lead to dusting and a reduction in the overall transfer efficiency. Achieving optimum particle size distribution in the powder coating material (often in a tightly specified range) is therefore essential to its usability and efficacy, and to the appearance and durability of the final film.
An example of the sensitivity of laser diffraction in detecting out-of-specification material is shown in figure 6. Here, the size distribution reported for a typical powder coating is shown following the addition of known fractions of coarse particles. As can be seen, the technique is extremely sensitive to the presence of the oversized material, detecting its presence at a concentration of only 2% by weight. This sensitivity derives from the intense scattering observed from coarse particles due to their large volume.
|Fig. 6: Particle size distributions measured for a powder coating containing differing volumes of a coarse particle fraction.|
Relevant, reproducible particle size data are essential in many areas of manufacturing industry and laser diffraction is a widely used technique. The Mastersizer 2000, for example, is a fully optimized laser diffraction instrument which allows manufacturers to simply and rapidly generate high quality data. These data are invaluable for quality control and in the optimization and development of materials.