In a laser diffraction experiment the scattering intensity from particles in suspension is measured as a function of the scattering angle, light wavelength and light polarization. Mathematical calculations can be used to obtain particle size distribution from the raw intensity data. The size range, sensitivity and resolution of the measuring instrument is based on its hardware design, assembly quality and software algorithm. In order to obtain a good result, precise operation and sample preparation are also essential. In the process, the data analysis algorithm plays an important role in obtaining high resolution and accurate particle size distribution result from the raw data.
Generally for demonstration of the capability of a laser diffraction instrument, a mixture of well characterized spheres of narrow distribution is used, because for these samples, operator error and environmental impact are often minimal. This sample is known as a multimodal sample. In reality, most real industrial or research samples do not even come close to these narrow distributions. They typically have either a narrow single peak or a broad peak with one or more modals. Furthermore, distribution and modality of samples are often unknown.
Hence, a good algorithm should not presume any distribution or modality of the sample and yet it should be able to obtain accurate results with high resolution. When an algorithm cannot be applied to a broad range of samples for obtaining good and precise results, the addition of some constraints may help the math process and enhance the result. A typical constraint is to input the allowed modality and distribution width for each peak so the output will be the one satisfying the constraint. If the sample meets the requirements of the constraint as the ones used in the algorithm, a better result may (or may not) be obtained. Otherwise, either a non-realistic or biased result will be produced.
Examples of Different Fitting Modes
Detailed below is an example with and without the use of such a constraint. A laser diffraction instrument offers three options for the analysis mode selection, as described in the user’s manual:
A: “Single Mode - This is a special analysis routine for monomodal characterization lattices. “
B: “Multiple Narrow - This is an extension of the Single Mode routine which is designed so as to resolve two or more extremely narrow fractions produced by mixing two or more monodisperse materials.”
C: “General Purpose - The recommended analysis mode to always use unless characterization lattices are being measured.”
The sample used in this case study comprises a trimodal mixture of polystyrene microspheres with particle size of 0.15, 1.0 and 2.0 μm. The above three modes were chosen to analyze the same set of data from the sample. Completely different results were then obtained as shown in figure 1. It is obvious from the figures that, in order to obtain a particle size distribution, some data about the material needs to be known. Otherwise, it is impossible to determine which result is correct. In this case, if any mode other than the Multi Narrow is selected, a low resolution result will be obtained. But, for an unknown sample other analyses must be done before the sample can be analyzed.
Figure 1. Overlay of the trimodal sample from different analysis modes. Image credit: Beckman Coulter
If the hardware lacks the capability to measure particles at a certain range or the algorithm is not properly designed and tuned, even with the correct constraint, incorrect or low resolution results still will be produced. For example, when another submicron trimodal sample from the same vendor with modal sizes 81 nm, 200 nm, and 500 nm was used and the Multi Narrow mode was chosen to analyze the sample, only a low resolution bimodal result was obtained as shown in figure 2, "Low resolution" curve.
Figure 2. Trimodal results from two instruments of different brands. Image credit: Beckman Coulter
Another instrument from a different manufacturer who uses a patented Polarization Intensity Differential Scattering technology (PIDS) is able to achieve a high resolution. This technology enables the analyzes of samples without making any type of assumptions or putting any constraints even on narrow sample size distributions. This patent protected PIDS technology makes sure that an LD instrument can resolve multimodal samples at the size range as small as 81 nm without the need of mode-picking as shown in Figure 2, "High resolution" curve. It also proves that this PIDS instrument has a superior algorithm to provide high-resolution results than the first instrument. It measures what should be measured without the need to make assumptions or extrapolate the results in the submicron range.
For a laser diffraction instrument to measure any sample with prior knowledge or presumption, the essential things are: to design the instrument correctly so it can measure scattering intensity angular variation sensitively even in the submicron range, utilize a fitting algorithm smartly and thoroughly and offer users fool proof software. By asking input from the users so some constraints can be applied in the algorithm might work in certain cases. For most realistic samples, applying such constraints is not be applicable. Therefore, the real test of the performance of an instrument, its accuracy and resolution, has to be done without any need for fitting mode selection.
This information has been sourced, reviewed and adapted from materials provided by Beckman Coulter, Inc. - Particle Characterization.
For more information on this source, please visit Beckman Coulter, Inc. - Particle Size Characterization.