Companies that manufacture or use powdered materials may need to produce identical products at many different plants on several continents. This can create quality control headaches that underscore the importance of having effective methods and instrumentation for measuring and controller product quality.
Until recently, companies found it frustrating to use laser light scattering instruments to monitor particle size distribution in different plants due to the inadequate resolution and repeatability results. Instruments located at different plants, even of the same brand and model, are often unable to produce matching analyses for identical samples.
On the surface, this problem is puzzling because light scattering theory is based on fundamental principles and instruments measuring particle size distribution using light scattering should always produce similar results from similar light scattering patterns. Textbooks derive the equations dealing with the propagation and scattering of light beginning with Maxwell's equations which are the fundamental equations dealing with the properties of electromagnetic fields.
The light scattering pattern measured during a laser particle size analysis should be well-defined, repeatable, and predictable. Why, then, do light scattering instruments from different manufacturers and even from the same manufacturer give different results for the same material?
The obvious answer is that the differences are because different instrument vendors have implemented their instruments differently, with different detection systems, different numbers of detectors, different data reduction methods, and even different sample handling systems. Yet, there are many examples of the same brand, model, and therefore design, of instruments giving different results.
A not-so-obvious answer is that the previously available instruments have been designed in a way that prevents them from measuring the scattered light in enough detail and with the accuracy necessary to extract all of the information inherent in the light scattering pattern.
In fact, the detector systems used are the same technology used in the earliest laser light scattering instruments in the 1970s. These instruments use ring detectors based on photodiode technology, dividing the richly detailed light scattering pattern into a relatively small number of measurements made by anywhere from 32 to 128 detectors. To illustrate the effect of such a small number of detectors, look at a high-resolution photograph on a computer screen (say, 4 x 4 k pixels) and see how much detail is there. Then use a photo editor to reduce the resolution to 128 x 128 pixels. The scene is no longer recognisable and cannot be recovered because most of the information in the original image has been lost.
A second problem with the legacy laser light scattering technology is that the signal-to-noise ratio for low intensity areas of the light scattering pattern makes it very difficult to measure the intensity accurately. The net result is a low resolution representation of the original light scattering pattern with inadequate measurement accuracy. A third problem of previous instruments is that the dynamic range of the light scattering intensity pattern is so large (in the order of a billion to one) that photodiode technology cannot be used at a high enough resolution to significantly improve the situation. Making higher resolution ring detectors would require making individual detectors significantly smaller. However, measuring low intensity regions of the light scattering pattern requires increasing the photodiode area so that the photodiode signal is high enough to be detected. The legacy technology is at an impasse.
A breakthrough technology was needed to overcome the limitations of the technology. This was found to be available as an outgrowth of the space program in the form of a scientific charge coupled device, or CCD.
CCDs were originally developed and used for astronomical imaging and have been steadily increasing in performance and quality. Recent photographs from the Cassini space probe and the current level of performance of the Hubble Space telescope show what can be accomplished with these devices.
Astronomical imaging requires the ability to accurately measure a very wide range of intensities and digital techniques have been developed that allow multiple exposures to be digitally combined. This permits both high and low intensity light levels to be imaged in the same region while maintaining accurate intensity measurements. Another technique developed by astronomers enables multiple images taken over a wide field of view to be combined to produce a detailed panorama of the entire scene.
Building on these techniques from the space program has enabled Micromeritics to produce an instrument that can accurately measure a light scattering pattern over 45° of scattering angle with a dynamic intensity range of 1 x 1010 to 1 at an effective resolution of over 15,000,000 pixels. This is as compared to 128 data points or so on legacy instruments. The level of detail, accuracy, and resolution enables the extraction of all available information from the static light scattering pattern.
Users can now measure the same material on multiple instruments located at different points around the world and get the same highly detailed size distribution measurement on each instrument. The instrument is able to produce correct, repeatable results based on first principles of light propagation and is able to do this reliably from instrument to instrument.
Mie and Fraunhofer Theory
Depending on the size range of the particles being analysed, one of two light scattering theories has typically been selected for interpreting the light scattering pattern and converting it to a size distribution. The two theories are Fraunhofer Theory, which is useful if all particles are larger than about 10 micrometres, and Mie Theory which gives accurate results for particles both above and below 10 micrometres.
The primary difference between the two theories is that Fraunhofer is based on the action of light diffracting around the particles and Mie adds the effects of the refraction of light through the particles and the absorption (or reflection) of light by the particles. An accurate measure of the refractive index is needed to get accurate results from Mie theory.
The refractive index is measured as a real part (representing the refraction of light through the particle) and an imaginary part (representing the amount of light absorbed or reflected by the particle). Even on instruments that are able to provide a Mie analysis, obtaining the refractive index has been a problem. Micromeritics has developed techniques for easily determining the effective refractive index that make Mie analysis so easy to use that many customers are using it for all their analyses.
Fraunhofer is still available and gives excellent results on the Saturn DigiSizer for larger particles.
The Saturn DigiSizer has such a high degree of accuracy and resolution that it is sensitive to even small errors in the value of the refractive index. Legacy instruments are relatively insensitive to the value of refractive index since there isn't enough resolution to detect subtle differences in the light scattering pattern. In addition, refractive index values are often published for different wavelengths than used by light scattering instruments, plus the effective value can actually change due to variations in particle shape and surface texture. The amount of porosity in a particle can even make a difference.
For these reasons, the optimum value of the real and imaginary parts of the refractive index must be known at the wavelength of the Saturn's laser diode (658 nm). Micromeritics has an analytical tool that simplifies determining the optimum refractive index values. The technique used to determine the size distribution from the measured light scattering pattern is mathematical deconvolution. This technique uses a series of models based on the refractive index and scattering angles to determine the size distribution that would produce a light scattering pattern that closely fits the measured light scattering pattern. The difference in fit between the calculated and measured light scattering pattern for this distribution is the residual error and the correct model (based on the complex refractive index) is the one with the smallest residual error. This property of mathematical deconvolution is the basis for Micromeritics' method of determining the refractive index for an unknown material.
A software tool examines a range of real and imaginary refractive index values over a range of scattering angles and develops light scattering models for all of these values. It performs the deconvolution for all of these models and then compares the results to the measured data to determine how well the models fit the data.
The optimum model and therefore the correct effective refractive index values will produce an excellent fit to experimental data with a smooth, noise-free size distribution. This refractive index scanning technique is very powerful and makes it practical to accurately measure the effective refractive index of samples. By combining this technique for optimising the real and imaginary refractive index values, Micromeritics is now able to provide paid laboratory analysis for size distribution measurement using the Saturn DigiSizer. With the optimum models identified by their internal analysis tool, Micromeritics is confident that the results produced by our Material Analysis Laboratory will match the results obtained on any Saturn DigiSizer located anywhere in the world. Customers are able to set up unified standards for the size distribution of their products produced at multiple locations and reduce their quality control headaches.
