Resumo:
The analysis of particle systems by means of Static Light Scattering (SLS) measurements may procure different types of information about morphological characteristics of the particles. Their size, shape, constitution and distribution can be known when experimental setups and appropriate models are available. The use of an appropriate model in each case depends on some parameters of the system such as its concentration and polydispersity. The mathematical model complexity is another relevant issue which in some cases may require building approximations due to excessive computational costs.
The interpretation of measured data through models leads to a formulation of an inverse problem, where the solution is represented by a set of parameters and/or functions that characterizes the analyzed system. Furthermore, the formulated inverse problem falls into the category of the ill-conditioned ones which means high variability of solutions for minimal changes in data. As a consequence of this, there is a need of stabilizing the given problem by some regularization technique.
The developed work in this thesis corresponds to the estimation of the Particle Size Distribution (PSD) for concentrated systems by using two different accuracy models for spherical particles with one or two layers: the model known as Local Monodisperse Approximation (LMA) and the Finite Mixture Model (FMM). These models work for media with refractive index close to the one of particles (low contrast condition) in which is possible to neglect the multiple scattering effect, simplifying in a significative way the mathematical difficulties. The scope and limitations of the used models are studied in regard with concentration and polydispersity of systems and with several resolution methods for the inverse problems. In this sense, valuable quantitative results are obtained related to the errors in the use of the less-exact model (LMA) taking as evaluation criteria the functioning of this model in solving the inverse problem. The performed analysis firstly uses a deterministic approach of minimum-squares based methods with three data sources: two coming from simulations corresponding to each model with numerical normal noise added and a third one from experimental measurements. As a consequence of some errors observed using this deterministic approach, it is also presented a new alternative one based on Bayesian methods. This new approach has been successfully applied to combine processing from SLS measurements with data coming from alternative techniques, in this case, from Scanning Electron Microscopy (SEM). Finally, the FMM is used in a parametrical form due to its mathematical complexity following a deterministic approach equivalent to the one implemented for the LMA.
