Novel approaches to improve the particle size distribution prediction of a classical emulsion polymerization model

A recent investigation on the homopolymerization of styrene (Hosseini et al., 2012a) showed that the classical population balance models are incapable of predicting the evolution of the breadth of the experimental particle size distributions correctly when a high resolution discretization method is used to suppress the numerical errors. Also by re-tuning the model parameters the model predictions did not fit the experimental results which points to a structural inadequacy of the conventional deterministic growth models in describing the experimentally observed broadening phenomenon. Two novel approaches are suggested in this work to improve the predictions. In the first approach, a possibly size dependent stochastic term is added to the deterministic growth kernel to account for the inhomogeneities of the growth process. The probability distribution of the resulting stochastic differential equation evolves over time based on the Fokker–Planck equation. The parameters of the (possibly size dependent) dispersion term of the Fokker–Planck equation are used as tuning parameters to fit the model to the experimental results. In the second approach, the growth kernel is extracted from the characteristics of the transient experimental particle size distributions. The extracted growth kernel is described in terms of the states of the system which affect the growth phenomenon. The advantages and disadvantages of both approaches are highlighted.

► We proposed two novel approaches to improve the PSD prediction of the classical emulsion polymerization PBE models.
► Addition of a particle size dependent stochastic term to the growth kernel is investigated in the first approach.
► In second approach, the growth kernel is extracted from the evolution of the experimental PSDs.
► Two proposed approaches are effective in overcoming the limitations of the original PBE models of emulsion polymerization.