Mathematical Modelling of 1,6-Hexanediol Diacrylate Photopolymerization with Spatial Gradients and Film Shrinkage

Abstract

Two dynamic models are proposed for the photopolymerization of 1,6-hexanediol diacrylate (HDDA) with bifunctional initiator bis-acylphosphine oxide (BAPO) in the presence of oxygen. The first accounts for spatial variations due to monomer and oxygen diffusion, while the second addresses spatial variations and film shrinkage. These partial-differential-equation (PDE) models predict overall vinyl-group conversion as well as time- and spatially-varying concentrations of monomer, initiator, oxygen, pendant vinyl groups and seven types of radicals. Measured diffusion coefficients for monomer, oxygen and initiator, provided by Canon Production Printing, are used in the models. Parameter estimation is performed using overall vinyl-group conversion data from Canon Production Printing, which were obtained using Fourier Transform Infrared (FTIR) spectroscopy for a range of operating conditions of film thicknesses (8-17 μm), BAPO levels (1-4 wt%) and light intensities (200-6000 W/m^2). The first model, which accounts for spatial variations but ignores shrinkage, gives reliable predictions for runs with high BAPO levels (4 wt%) and light intensities (≥5000 W/m^2). Model predictions are not accurate for runs conducted using low BAPO levels (1 wt%), indicating that some model parameters may be inaccurate. As predicted by the second model, shrinkage has a noticeable influence on the model predictions, where a ~9% discrepancy is observed between predictions of overall vinyl-group conversions obtained from the models with and without shrinkage. Prediction discrepancies are larger for simulated experiments involving thin films (8 μm) or low light intensities (1200 W/m^2). In future, it will be important to re-estimate the kinetic parameters, using the shrinkage model, so that accurate model predictions can be obtained over a wide range of operating conditions.