A Neural Network Approach for Estimating the PSD of a Polymer Latex from Combined Optical Measurements

STEGMAYER, GEORGINA S.; GONZALEZ, VERÓNICA D.G.; GUGLIOTTA, LUIS M.; CHIOTTI, OMAR A.; VEGA, JORGE R.

Graz

Congreso; 8th International Congress on Optical Particle Characterization OPC 2007; 2007

Several optical techniques, such as elastic light scattering (ELS), dynamic light scattering (DLS), and turbidity, are often used to estimate the particle size distribution (PSD) of a diluted latex. However, all optical techniques are recognized to have a low information content about the PSD; and sometimes two or more independent measurements are combined in a single problem to improve the PSD estimate[1]. In any case, an ill-posed inverse problem must be solved; and only oscillating (or artificially smoothed) approximated solutions are obtained through standard regularization techniques. This work aims at developing an artificial neural network for estimating the PSD of a diluted latex, from combined ELS and DLS measurements, and without solving any inverse problem[2]. The network is fed with: (i) the ELS measurement; i.e. the light intensity scattered at different detection angles (qr); and (ii) the average diameter at each qr, obtained from the DLS measurement. A general regression neural network was trained with a large set of measurements simulated on the basis of the Mie scattering theory. As a first approximation, only log-normal PSDs with mean diameters in the range [140?800] nm were simulated, at regular intervals of DD = 5 nm. At each mean diameter, 20 PSDs were generated, with standard deviations in the range [0.01?0.20] nm. The measurements were assumed to be taken each Dq = 10°, in the range [10°?170°]. Hence, a total of 2660 training patterns were generated, all of them normalized in the range [0,1]. The model perfectly learned the training data, with an approximate root mean square error (RMSE) of 10-9. The model was tested through synthetic and experimental examples. The synthetic examples considered (unimodal) log-normal and exponentially-modified Gaussian PSDs. The trained neural model accurately predicted all the PSDs. The experimental PSD was a narrow standard latex, that was also measured by electron microscopy and capillary hydrodynamic fractionation. At present, the model is restricted to deal with unimodal PSDs; but in the future, a larger spectrum of PSD shapes (including bimodal PSDs) will be included in the training set.