Simultaneous Estimation of the PSD and the Particle Refractive Index of an Unknown Latex from Combined Optical Measurements

J.R. VEGA, V. D.G. GONZALEZ, G. L. FRONTINI, G. E. ELIÇABE, AND L. M. GUGLIOTTA

Graz , Austria

Congreso; 8th. International Congress on Optical Particle haracterization; 2007

Independent measurements of Elastic Light Scattering (ELS), I(q) at several angles q, and Turbidity (T), t(l) at several wavelength l, are combined to simultaneously estimate the particle size distribution (PSD), f(D), and the particle refractive index (PRI), np(l), corresponding to a dilute polymer colloid of unknown composition. The problem is solved in 3 sequential steps: (i) an initial PSD estimate f0(D) is obtained from I(q), on the basis of an “a priori” guess (or measurement) of the PRI at the ELS wavelength l0, np(l0); (ii) np(l) is estimated from t(l) and f0(D); and (iii) an improved PSD is estimated by combining I(q), t(l), and np(l), in a single inverse problem[1]. The rationale of the proposed sequence is supported by a relatively low sensitivity of f0(D) to moderate uncertainties in np(l0); a high sensitivity of t(l) to uncertainties in np(l); and an increased information content about the PSD, due to the combination of the two independent measurements. The proposed method was validated through numerical and experimental examples. For the experimental validation, an industrial latex for pressure-sensitive adhesive was considered. A Brookhaven Instrument BI-2000 photometer [q=30°–118°], and a Perkin-Elmer Lambda 20 spectrophotometer [l=350 nm–700 nm] were used. At l0 = 632.8 nm (He-Ne laser), np(l0) = 1.4681 was estimated from off-line measurements at 3 different l´s, and on the basis of a Cauchy correlation. The measurement models respond to the Mie theory; and all inverse problems were solved through standard regularization techniques. The estimated np(l) exhibits a Cauchy shape. The estimated PSD was compared with an independent estimate obtained from single-angle dynamic light scattering measurements (taken at 90°).