In the first of this series of articles examining particle size analysis in the coatings industry (PCI, March 2005), Paul Kippax looked at the significance of particle size and its relationship to the performance of both raw materials and final products. Here he discusses laser diffraction, one of the most widely used technologies for particle size measurement, its applications and benefits.
Particle size is a variable of significant interest to coatings manufacturers, as it has a direct impact on the quality of the finished product. Optical properties, such as opacity, tinting strength, undertone, film appearance and weather resistance, as well as bulk properties, including dispersion and flocculation characteristics, and viscosity, are all, to some extent, a function of particle size. It is therefore clear that manufacturers intent on optimizing product quality need an effective and reliable method of particle size analysis. 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 can be used for the non-destructive analysis of wet or dry samples, with particles in the size range 0.02 to 2,000 microns, and has inherent advantages that 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 that generates surface-area-based data.
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
Laser diffraction has become one of the most widely used techniques for particle size analysis in the coatings industry, with applications from product development through to production and quality control. It 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 (Figure 2).
It is this behavior 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.
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.
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 behavior. 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. This is extremely important when assessing the mill end-point when producing paints and pigments.
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 the following advantages.
Application Study: Ink Jet Particle Size Measurement
In the ink jet industry there is a move away from the use of dye-based inks towards pigment-based inks, as these materials are more resistant to weathering and exposure to moisture. This application places stringent product requirements on the pigment - particle size must be very small (D50 = 200 nm or less) and the pigment dispersion must neither agglomerate nor settle during storage. If these requirements are not met then nozzle blockages, clogged jets and inconsistent color densities can occur. To produce pigment-based ink jet inks a two-stage process is adopted. First the pigment is dispersed in an appropriate solvent, and secondly this ‘pre-mix' material is milled using a ball mill to reduce particle size and break up any strongly bound aggregates. To ensure optimal milling, it is necessary to monitor particle size during the milling process.
Figures 5 and 6 show the data produced (using a Mastersizer 2000) to analyze samples removed at regular intervals during a milling process. Figure 5 shows how the relatively broad particle size distribution of the pre-mix is reduced to a narrow particle size distribution centered at around 137 nm after three hours of milling. The process is more clearly illustrated in Figure 6. This shows an initially rapid reduction in particle size that corresponds to the break up of agglomerated particles, followed by a more gradual reduction produced by the break up of larger primary particles. The ability of the particle size analyzer to track the milling process effectively and ensure a product with the required properties is evident.
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 7. 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.
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