Modeling cure depth during photopolymerization of multifunctional acrylates
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The photopolymerization of multifunctional acrylates leads to the formation of a complex and insoluble network due to cross-linking. This characteristic is a useful property for stereolithography applications, where solid parts of the desired shape are cured using a pre-determined energy exposure profile. Traditionally, the required energy exposure is determined using a critical energy--depth of penetration, or Ec--Dp, model. The parameters Ec and Dp, are usually fit to experimental data at a specific resin composition and cure intensity. As a result, since the Ec--Dp model does not explicitly incorporate cure kinetics, it cannot be used for a different set of process conditions without first obtaining experimental data at the new conditions. Thus, the Ec--Dp model does not provide any insight when a new process needs to be developed, and the best processing conditions are unknown. The kinetic model for multifunctional acrylate photopolymerization presented here is based on a set of ordinary differential equations (ODE), which can be used to predict part height versus exposure condition across varying resin compositions. Kinetic parameter information used in the model is obtained by fitting the model to double bond conversion data from Fourier Transform Infrared Spectroscopy (FTIR) measurements. An additional parameter, the critical conversion value, is necessary for determining the formation of a solid part of the desired height. The initial rate of initiation, Ri, combines all the factors that impact part height, and therefore, it is an important quantity that is required in order to find the critical conversion value. The critical conversion value is estimated using the Ri and Tgel value from microrheology measurements. Information about network connectivity, which can be used to get properties such as molecular weight, cannot be derived from models using traditional mass-action kinetics for the cross-linking system. Therefore, in addition to modeling the reaction using the ODE based model, the results from a statistical model based on Kinetic Monte Carlo (KMC) principles are also shown here. The KMC model is applicable in situations where the impact of chain length on the kinetics or molecular weight evolution is of interest. For the present project, the detailed information from network connectivity was not required to make part height predictions, and the conversion information from the ODE model was sufficient. The final results show that the kinetic ODE model presented here, based on the critical conversion value, captures the impact of process parameters such as initiator concentration, light intensity, and exposure time, on the final part height of the object. In addition, for the case of blanket cure samples, the part height predictions from the ODE model make comparable predictions to the Ec--Dp model. Thus, the ODE model presented here is a versatile tool that can be used to determine optimum operating conditions during process development.