Rheokinetics of Thermal-Induced Gelation of Waterborne Polyurethane Dispersions

Thermal-induced gelation for waterborne polyurethane dispersion has been studied rheologically under isothermal condition over a wide range of frequencies at different constant temperatures (55, 60, 65, and 70 °C). The elastic storage modulus, G ‘, at a constant temperature in the vicinity of the gel point increases abruptly, and the magnitude of the elevation in G ‘ was found to be temperature dependent. Similar behavior has been observed for both the viscous loss modulus, G ‘ ‘, and the complex dynamic viscosity, η*. The gel point, t gel, was determined from the point of intersection in tan δ vs gelation time for different constant shear frequencies, where tan δ is frequency independent and all curves cross over, indicating the validity of the Winter−Chambon criterion. The value of t gel obtained from the coincidence of G ‘ and G ‘ ‘ was in excellent agreement with that obtained from tan δ vs t . At the gel point, G ‘ and G ‘ ‘ showed a power law with shear frequency, i.e., G ‘ ∼ G ‘ ‘ ∼ ω n with critical exponents n ‘ and n ‘ ‘ for G ‘ and G ‘ ‘, respectively. The values of n ‘ and n ‘ ‘ are identical at t gel ( n ‘ and n ‘ ‘ ∼ 0.58), and both decreased exponentially with gelation time at 70 °C. The exponent values n ‘ and n ‘ ‘ are in good agreement with that predicted from the percolation theory (i.e., n = 2/3). In addition, the temperature dependence of n ‘ and n ‘ ‘ was investigated in the vicinity of the gel point. Both n ‘ and n ‘ ‘ decreased with temperature and intersected at the gel temperature, i.e., n ‘ = n ‘ ‘ at T gel = 67 °C. The value of T gel = 67 °C was in good agreement with that obtained previously from the temperature at which tan δ is frequency independent and also from the temperature at which G ‘ and G ‘ ‘ coincided. The zero shear viscosity, η 0, and the equilibrium shear modulus, G eq, conformed well with power law scaling functions of the relative distance from the gel point, ε, i.e., η 0 ∼ ε - k and G eq ∼ ε z (where k and z are scaling parameters).