An iterative approach for isothermal curing kinetics modelling of an epoxy resin system

In this work a novel iterative method for isothermal cure kinetic modelling of an epoxy resin system using differential scanning calorimetry (DSC) technique is presented. To reach the isothermal cure temperature, the sample has to be heated up from ambient temperature. This is commonly done with very high heat-up rates to minimise the time the sample reacts at temperatures other than the desired one. However, during heat up with high heating the amount of released energy rates cannot be measured directly because the shape of baseline is unknown. This means that the cure state at the beginning of the isothermal stage is unknown. For fast curing systems this unknown cure state causes significant inaccuracies in cure kinetics modelling. The presented iterative approach attempts to estimate the released enthalpy during heat-up of an isothermal run through an iterative numerical modelling of the heat-up phase. In each iteration the algorithm starts by estimating the enthalpy released during heat-up based on the recorded temperature profile and the calibrated model of the previous iteration. At the same time, it estimates the degree of cure at the end of the heat-up phase. Once the initial cure state is known the total heat of enthalpy can be recalculated for the current iteration. Subsequently the degree of cure and curing rate are re-evaluated with the newly estimated total enthalpy and used for determining the kinetics parameters. This is done by simultaneous fitting of the selected model to all experimental heat flow curves using a non-linear nonrestricted multivariable fitting method. The model with these new parameters is used again to estimate the released enthalpy and cure degree during the heat-up phase. The described loop is repeated until a predefined convergence criterion is satisfied. For modelling the reaction kinetics, the Kamal-Sourour equation accompanied with Rabinowitch approach to consider the diffusion effects is used. The diffusion reaction rate is modelled by the free volume model proposed by Huguenin and Klein. DiBenedetto model is applied to predict the evolution of glass transition temperature against the degree of cure. In order to compensate the effect of the initial values in the model's calibration, the algorithm is implemented in a routine, which assesses the quality of the fitting and consequently selects the cure kinetics parameter. The described algorithm and the routine are implemented in MATLAB. This paper demonstrates the application of this approach for using cure kinetics modelling to predict the degree of cure and the glass transition temperature. It supports the obtained results with validation tests using isothermal, dynamic and combined temperature profiles. (C) 2015 Elsevier B.V. All rights reserved.