Authors: B. Benyahia, A. Latifi, C. Fonteix, F. Pla
Affilation: University of Nancy, France
Pages: 930 - 933
Keywords: fed-batch emulsion copolymerization, core-shell nano particles, modelling, multiobjective optimization, morphology control
This paper deals with the design and the control of the morphology of core-shell nanoparticles elaborated by emulsion copolymerization of styrene and butyl-acrylate in the presence of n-dodecyl mercaptan, as a chain transfer agent (CTA). Preliminary experimental studies of the process, carried out in batch mode, made it possible (i) to clearly highlight the influence of CTA on the kinetics of the reactions of copolymerization, (ii) to specify that styrene is consumed more quickly than butyl-acrylate (iii) to show the interest to carry out this copolymerization in fed-batch mode so that, thanks to the setting of the pre-emulsion feed rate, to control the monomers consumption and thus to manufacture copolymer particles of required composition, morphology and average diameters. In a second step, a mathematical model of the process was elaborated. It consisted of a system of differential algebraic equations, issued from population balance and involving 49 unknown kinetic and thermodynamic parameters, many of them being impossible to be accurately estimated, due to a lack of experimental data. So, considering that the main limitations to the parameters estimability are their weak effect on the measured out-puts and the correlation between these effects, a method based on the calculation of a sensitivity matrix was developed and allowed to determine a subset of the 21 most influential parameters. A stochastic optimization, followed by the determination of the corresponding confidence intervals, allowed then, using a genetic algorithm, to identify these parameters. The 28 non estimable parameters were taken from the literature. The model was then validated through additional experiments carried out in batch and fed-batch modes. Moreover, the results clearly showed that the model was also able to predict the time-evolution of the amounts of each residual monomer, the number and weight average molar masses and the glass transition temperature, Tg, of the resulting copolymers, for different experimental conditions. The model was then used to optimize, for a given recipe, the best profile of the pre-emulsion feed rate to control (i) the composition and average molar masses of the copolymer, (ii) the instantaneous glass transition temperature, Tgi, corresponding to a core-shell morphology adapted to special end-use properties. The optimization is a multiobjective procedure which used: (i) Pareto’s concept, to determine a large number of non-dominated solutions, (ii) ranking of these solutions according to the decision-makers’ preferences.