Kinetic Analysis of Fractal Gel Formation in Waterborne Polyurethane Dispersions Undergoing High Deformation Flows

Abstract

Isothermal and nonisothermal kinetics studies of thermal-induced gelation for waterborne polyurethane dispersions have been investigated rheologically. The change in the viscoelastic material functions such as elastic storage modulus, G‘, viscous loss modulus, G‘‘ and complex dynamic viscosity, η* during the gelation process was evaluated accurately for the first time. The isothermal kinetics reaction was described using a phenomenological equation based on the Malkin and Kulichikhin model that was originally developed for predicting isothermal curing kinetics of thermosetting polymers from differential scanning calorimetery (DSC) data. The Malkin and Kulichikhin model was found to conform excellently well for the rheokinetics data presented here. The rate of the gelation process was found to be a second-order reaction regardless of the temperature and shear frequency, and to be in good agreement with literature data. The isothermal gelation kinetics was also analyzed using a standard isoconversional method that is based on replicated experimental data and model-free kinetics calculations. This isoconversional method evaluates an effective activation energy that is independent of the degree of conversion, indicating that the rate of gelation is controlled by a single step (homogeneous) process with no change in the fractal gel formation mechanism at different degree of conversions. The temperature dependence of the gelation rate constant was well described by an Arrhenius plot with an average apparent activation energy equal to 127 ± 2 kJ/mol, in reasonable agreement with the value obtained from the temperature dependence of gel time, tgel. The nonisothermal kinetics reaction rate was interpreted using the classical rate equation, the Arrhenius equation and the time−temperature relationships. A frequency-independent apparent activation energy was evaluated nonisothermally and found to be similar to that obtained from isothermal kinetics data. The high value of activation energy is thought to be due to the strong interaction between the PU-dispersed particles during the gelation process, making a significant contribution to the rate of structure formation. It is noteworthy that, in some respects, these results resemble those from other cross-linking polymer networks and gels measured by DSC, yet in very important ways the aqueous PUDs of the present study is quite unique.