Characterization of nanoparticle aggreates using inverse formulation and discrete-dipole approximation

Abstract

Characterization of nanostructures using numerical light scattering experiments without using polarization information and a priori particle size or number measure ments is investigated. Optimization and statistical methods are considered. The study focuses on particle clusters in the form of carbon nanoparticle aggregates generated with Filippov’s particle-cluster algorithm. Mutually well separated nanoparticle aggregates with same size are assumed. The scattering behavior is calculated by discrete dipole approximation. A database is developed and used for the solution of the direct prob lem. First, the inverse problem is formulated as a least squares minimization. Use of Tabu Search along with gradient based Levenberg-Marquardt algorithm is investigated as problem topology is prone to multiple extrema. Then, the same problem is treated statistically and classical Bayesian inference methods and Approximate Bayesian Com putation (ABC) methods are considered for the solution of the problem. Analytical likelihood function is obtained by additive noise assumption in classical Bayesian infer ence. On the other hand, four likelihood-free methods based on ABC that requires only simulation of the model without the need of evaluating a likelihood are considered. In particular, Rejection, Markov Chain Monte Carlo, Population Monte Carlo and Adap tive Population Monte Carlo are compared in terms of accuracy. All methods are able to predict the particle size and number for monodisperse aggregates with effective radius larger than 20 nm using a UV light source at a wavelength of 266 nm. Charac terization of soot aggregates is performed with less than 2 nm deviation in nanoparticle radius and 3-4 deviation in number of nanoparticles forming the monodisperse cases. Promising results are also obtained for the characterization of polydisperse case.