A Novel Method to Model Emulsion Polymerization Kinetics: The Explicit Radical-Particle Size Distribution Approach

Abstract:

An alternative approach to model emulsion polymerization is presented that is capable of rigorously solving both particle and radical kinetics for emulsion polymerization: the explicit radical-particle size distribution approach. The method is based on a direct solution of all population balances and fully covers the strong influence of compartmentalization on rates of reactions between macroradicals and, consequently, on chain length averages. An essential and new feature is the compartmentalization factor (D_f), which accounts for compartmentalization in a transparent manner. The generic approach allows for studying the complete emulsion polymerization conversion range, including gel-effect, and the effect of various parameters on both chain length and particle size distribution. Well-known kinetic regimes for emulsion polymerization naturally arise as limiting cases from our model. The dynamic behavior of the model was studied by simulating several realistic seeded emulsion polymerization reactions for styrene. The model dealt with compartmentalization accurately and was able to correctly reproduce the dynamic behavior known to be typical for emulsion polymerization.

Keywords:

• Modeling
• styrene
• seeded emulsion polymerization

ACKNOWLEDGMENT

The authors would like to thank the employees at Computing in Technology GmbH for their great customer support and the Foundation of Emulsion Polymerization (SEP) for financially supporting this work.

Notes

D_f for several highly simplified r-psd's with particles of equal volumes with n radicals in total.

D_f for several highly simplified r-psd's with 2 particles with various volumes with n radicals in total.

Linear set of algebraic Equations as a solution for the population balance Equations using a QSSA and equal particle volumes.

Recipes used for modeling with the full model, the bold recipe was the “standard recipe” as frequently used for experimental work in our lab²⁸.

Parameters used for modeling the seeded emulsion polymerization of styrene at 50°C.

Particle numbers calculated for each PSD at different times and conversions for the standard recipe of the seeded emulsion polymerization of styrene at 50°C.