(2b) A Comprehensive Mathematical Model of Vinylidene Fluoride Emulsion Polymerization in a Semi-Batch Reactor

Polyvinylidene fluoride (PVDF), the second most important fluoropolymer, exhibits a unique combination of desired end-use properties including excellent chemical resistance, high thermal stability, and good mechanical as well as piezoelectric properties. Due to these unique characteristics, PVDF is widely used in wire and cable insulation, as sheet and melt-cast films in electronics, in fittings, valves and pumps, etc. PVDF is produced commercially by emulsion and suspension polymerization processes.

In the present paper a comprehensive mathematical model of the vinylidene fluoride (VDF) emulsion polymerization process for a semi-batch reactor is developed. The model can predict the molecular (e.g., molecular weight distribution, etc.) and morphological (e.g., particle size distribution) properties of the particulate PVDF in agreement with experimental measurements. The mathematical model includes a comprehensive kinetic mechanism, a gel-effect model based on the generalized free-volume theory, thermodynamic equilibrium models for calculating monomer partitioning in the different phases present as well as the reactor pressure, a physical model for calculating the crystalline and amorphous polymer mass fractions, and a full set of differential equations describing the conservation of various molecular species and energy in the reactor. The method of moments is employed for the calculation of the average molecular weight properties. In addition, a population balance model is included to describe the dynamic evolution of the particle size distribution in the polymerization reactor.

The predicting capabilities of the model are demonstrated by a direct comparison of model predictions with experimental data on the monomer feed rate, monomer conversion, mean particle size and particle size distribution, as well as the molecular weight distribution of PVDF obtained from a pilot-scale polymerization reactor. Detailed experimental measurements on the polymerization rate, monomer feed rate, operating pressure, molecular weight distribution and particle size distribution of PVDF (measured in a 30 lt semi-batch reactor) were provided by an industry. In the experiments, the reactor pressure was kept constant throughout the polymerization via the control of the monomer feed rate into the reactor. The initiator and chain transfer agent were added in the beginning of the polymerization as well as at various discrete times during the polymerization. Simulation results show a very good agreement between model predictions and experimental measurements on the total amount of VDF fed to the reactor as well as with   measured particle size and the molecular weight distributions.