Investigation of accelerated sulfur vulcanization by irreversible consecutive mechanism

The most mathematical application in chemical kinetics is to find analytical solutions for the rate equations. Rate equations describe how the rate of concentration change depends on concentrations. By solving these equations, the relationship between species concentration and time are sought. Solutions of the rate equations for single step reactions (elementary reaction) are often well known but for reactions involving several steps (complex reaction) are difficult. Since the accelerated sulfur vulcanization involves a large number of parallel and series steps [1], it is impossible to obtain a complete analytical solution, therefore, a mechanism involving several steps for this reaction is suggested. A typical schematic of the cure-curve obtained from an ODR exhibits three main regions, scorch delay, cure and postcure. The regions, cure and postcure could be modeled using a two-step consecutive mechanism as follow.()The concentration of the intermediate, B(t), can be defined by the following general differential equation:()Considering B as a product, the second stage represents a reversion in postcuring. The analytical solution derived from the above equation is dependent on f(t) and thus with the type of reaction of the first step[2]. In this research, the order of zero, one, two (two modes with identical and different materials) and three order reaction were considered as the first step and the analytical solutions of this equation were investigated. Validity of reaction behavior in the first stage was evaluated by comparing the error of fitting the equations with experimental data. The order of reaction rate in the first step was evaluated by comparing fitting the obtained equations with experimental data.