Numerical kinetic model with regularization for NR–PB natural and poly-butadiene rubber blends: implementation and validation against experimental data

  • G. MilaniEmail author
  • F. Milani
Original Paper


A simple and versatile numerical approach of experimental data regularization plus a kinetic model to predict the vulcanization behavior in a rheometer for natural rubber (NR) and poly-butadiene (PB) blends is presented. The numerical model proposed uses generic rheometer experimental curves to estimate kinetic constants of the cure reactions, preliminarily regularizing input data through Cn continuous polynomial splines of degree n, with spline knots equally spaced or placed at user’s discretion. Splines coefficients are efficiently evaluated through a standard non-linear least squares optimization procedure. In this way a set of meta-data fitting optimally experimental values is obtained, with a smooth prediction of the local curing rate. The kinetic approach adopted is classic but adaptable to a wide class of cases and characterized by only three kinetic constants, describing two reactions occurring in parallel and two in series (reversion phenomenon). The determination of the three kinetic constants characterizing the model is performed graphically in quasi analytical form. The model is benchmarked by means of an ad-hoc conducted experimental campaign carried out with different typologies of rubber blends constituted by NR and PB at 70–30% and 50–50% concentrations, with sulfur at 1 phr and two accelerants (TBSS and DPG) at 1 and 3 phr, under standard vulcanization conditions (rheometer) at 150 °C, 170 °C and 180 °C.


NR/high cis PB blends Vulcanization Rheometer experimental data Kinetic numerical model Experimental data fitting Predictive behavior 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Politecnico di MilanoMilanItaly
  2. 2.Chem.Co ConsultantOcchiobelloItaly

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