Inversion of Elastic Light Scattering Measurements to Determine Refractive Index and Particle Size Distribution of Polymeric Emulsions

Abstract

Polymeric emulsions are well characterized by the knowledge of their particle size distributions (PSD). Elasticlight-scattering (ELS) measurements can be inverted to estimate the PSD in the range from 50 nm up to several micrometers. The relative refractive index of the particles is required in computation procedures to obtain the PSD. Small differences in the assumed refractive index may cause significant differences in the resulting PSD. From the scattering data, the refractive index can be determined. In this article we present the corresponding technique. We consider polymeric emulsions where the nonabsorption assumption is reasonable. We propose a methodology based on Tikhonov regularization applied only to the distribution. However, we solve the minimization problem simultaneously with respect to the distribution and the refractive index. To select the regularization parameter, we include the Generalized Cross Validation (GCV) technique. From simulated ELS measurements we show that the problem is solved successfully.