Applying the Laplace transform to solve the kinetic equations of rubber vulcanization

Sulphur vulcanization is a complicated process, since here crosslinking occurs through both series and parallel reactions [1]. So proposing a quantitative macroscopic model enabling us to predict the rubber physical properties is still a real challenge. This process involves three steps, i.e. induction, curing, and post curing. In post curing, reversion could take place quite frequently giving rise to a remarkable decrease in rubber vulcanized properties. It was found out that, this phenomenon cause a decrease in sulfur crosslinking.In this work, the mechanism of curing and post curing will be investigated. To implement the task, Han et al. model [2, 3] was chosen as a base()Where A is sulfur available for the formation of crosslinks, Vu1 is the stable sulfur crosslinks formed during vulcanization, Vu2 is the unstable sulfur crosslinks, formed during vulcanization, D is product of the reversion reaction, and k1, k2,and k3 are rate constants. We managed to solve their three developed differential equations by using Laplace’s transform (equation1).()Whereis Laplace’s transform of product (Vu1+Vu2), A0 is initial sulfur concentration and p is independent variable for Laplace’s transform. Our analytical solution was in good agreement in comparing to literature [2, 3]. Mechanism by applying the Levenberg-Marquardt algorithm which were in consistent with experimental results obtained by the other researchers. In addition, the temperature effect on rate constants was examined and found that the rate constants follows the Arrhenius law.