Least-mean-squares algorithm to determine submicrometer particle diameter, volume fraction, and size distribution...

A computationally fast method to determine values and their uncertainty for particulate system volume median diameter, volume fraction, and size distribution width is presented. These properties cannot be obtained for submicrometer particulate by diffraction-based methods. The technique relies on a least-mean-squares method applied over a prespecified size range and distribution width. Prespecifying the range significantly reduces the number of calculations required to determine the particulate parameters from experimental data, allowing the practical evaluation of large data sets. The solution method that was developed has significant advantages over ratio-style calculations that are more commonly performed, the primary of which is a simple method to determine errors in the measurement parameters. We evaluated the predicted performance for a specific experimental system for various levels of noise, with monodisperse and log-normal distributions, by analyzing synthetic data with the algorithm. Results were a quantitative statement of system accuracy. In addition, synthetic log-normal data evaluated with monodisperse models revealed significant and systematic errors in the predicted volume median diameter. These errors indicate that, in general, systems with a significant size distribution width must be analyzed with a model that includes this size distribution. Finally, calibrated polystyrene spheres were measured with an experimental system that used four simultaneous scattering measurements, and all diameters were within the reported uncertainty.