Differential scanning calorimetry analysis of thermoset cure kinetics: Phenolic resole resin

The Differential Scanning Calorimetry (DSC) trace for a commercial phenolic resole resin shows two distinct peaks. Assuming that these represent two independent cure reactions results in a kinetic model of the form:\documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{dx}}{{dt}} = p\kappa _1 \left({1 - x_1} \right)^{n_1} + \left({1 - p} \right)\kappa _2 \left({1 - x_2} \right)^{n_2} $$\end{document} with κ i = κ io exp(‐ B i / T ). The Arrhenius parameters were estimated from a plot of ln (β/ T   p 2 ) versus 1/ T p . The parameters, p , n 1 , and n 2 were obtained by writing the DSC response predicted by the equation above in terms of a function which contains temperature as the only variable.\documentclass{article}\pagestyle{empty}\begin{document}$$ \dot q = q_{tot} \left[{p\kappa _1 \left({1 - \theta _1 /r_1} \right)^{r_1 - 1} + \left({1 - p} \right)\kappa _2 \left({1 - \theta _2 /2} \right)^{r_2 - 1}} \right] $$\end{document} with \documentclass{article}\pagestyle{empty}\begin{document}$ \theta _i = \left({1/\beta} \right)\int_{T_0}^T {\kappa _i dT \le r_i} $\end{document} dT ⩽ r i and r i = 1/(1‐ n i ). Fitting this equation to the DSC response measured at a scan rate of 4°C/min obtains p ≈ 0.66; n 1 ≈ 0.55; n 2 ≈ 2.2; B 1 ≈ 8285; B 2 ≈ 7480; κ 1 ≈ 1. 12 × 10 8 s −1 ; κ 2 ≈ 0.99 × 10 6 S −1 .