Parabola-Hyperbola P-H kinetic model for NR sulphur vulcanization

A Parabola-Hyperbola (P-H) kinetic model for NR sulphur vulcanization is presented. The idea originates from the fitting composite Parabola-Parabola-Hyperbola (P-P-H) function used by the authors in [1,2] to approximate experimental rheometer curves with the knowledge of a few key parameters of vulcanization, such as the scorch point, initial vulcanization rate, 90% of vulcanization, maximum point and reversion percentage. After proper normalization of experimental data (i.e. excluding induction and normalizing against maximum torque), the P-P-H model reduces to the discussed P-H composite function, which is linked to the kinetic scheme originally proposed by Han and co-workers [3]. Typically, it is characterized by three kinetic constants, where classically the first two describe incipient curing and stable/instable crosslinks and the last reproduces reversion. The powerfulness of the proposed approach stands into the very reduced number of input parameters required to accurately fit normalized experimental data (i.e. rate of vulcanization at scorch, vulcanization at 90%, maximum point and reversion percentage), and the translation of a mere geometric data-fitting into a kinetic model. Kinetic constants knowledge from simple geometric fitting allows characterizing rubber curing also at temperature different from those experimentally tested. The P-H model can be applied also in the so-called backward direction, i.e. assuming Han's kinetic constants known from other models and deriving the geometric fitting parameters as result. Some existing experimental data available, relying into rheometer curves conducted at 5 different temperatures on the same rubber blend are used to benchmark the P-H kinetic approach proposed, in both backward and forward direction. Very good agreement with previously presented kinetic approaches and experimental data is observed.