Viscosity-dependent frequency factor for modeling polymerization kinetics

Abstract

The simulation of polymer-forming reactions can be a powerful tool to reduce the time and cost of developing new polymer formulations; formulations that can be potentially both more sustainable and less costly. A critical aspect of advancing such simulations is the reduction in the number of fitted parameters, and more specifically, the identification of fundamentally-correct parameters that can be applied to a range of reactions as opposed to parameters specific to each reaction. This paper presents an innovative approach focusing on the frequency factor of the Arrhenius equation resulting in insight to how this frequency factor is a characterization of mass transfer that can be broadly applied to a range of similar reactions. The result is a reduction in the number of fitted parameters needed for simulation and providing a more fundamental, efficient, and robust method to simulate thermoset polymerization reactions. Impacts of mass transfer limitations due to the large increase of resin viscosities during thermoset polymer reactions were reflected in the frequency (pre-exponential) factor of Arrhenius equation. By representing the frequency factor as the sum of viscosity-dependent and a viscosity-independent terms to account the impact of inter- and intra-molecular diffusion/movement of the reacting moieties in the resin, the same pre-exponential factor was able to be used for catalytic and non-catalytic paths. Impacts of catalysts were reflected in lower activation energies. Temperature profiles of urethane gel reactions were used to characterize the reactivities of different polyols based on the fractional content of primary (versus secondary) hydroxyl moieties. This approach the simulation results of reaction temperature show good agreement with the experimental data.