An Equation for Conversion and Cure Curves of Nitrile Rubbers

Abstract

The first order equation: -d(A)/dt = k(A) becomes, on integra tion, A = A ₀( 1 - exp(-k(t - t ₀))). This second equation (with A ₀ = 100) does not give a good correlation with the data for free radical emulsion poly merization of acrylonitrile-butadiene copolymers, particularly at low conver sion. It is found that modifying the above equation by introducing a square term gives a better fit for the data. The new equation is of the form: A = A ₀(1 - exp(- k(t - t ₀) ²)), which-on differentiation-becomes the time- modified first order equation: -d(A)/ dt = 2kt(A). The inflexion point of this S-shaped curve is found to occur at the point at which A = 39.3% of A ₀. At con versions less than 10% the conversion is closely proportional to the square of time in agreement with the observations of Gardon. Not only does the S-shaped curve fit the data for emulsion polymerization but also it appears to have much wider applications. One of these applications is the oscillating disc rheometer curves of peroxide cured nitrile rubbers. Subtracting the curve for a compound without curative from one with a curative gives the same type of S-shaped curve observed with emulsion polymerization. The effects of different levels of curative and carbon black are examined.