## 6 Finite Element Simulations
### Isothermal and Dynamic Experiments  
All heat flow data is baseline corrected as described in Section 5.1 and Appendix C to obtain the heat flow related to the curing of the polymer. Figure 4 shows the measured heat flows and corresponding conversion (calculated according to Equation (2); cf. also Figure 1b) for the isothermal experiments. The lower row of Figure 4 shows that the material more quickly reaches higher conversion at higher temperatures, as was to be expected according to Equation (1) since the Arrhenius term increases with higher temperature. Thus, at higher temperatures more heat is released early in the experiment, as the upper row of Figure 4 shows. Hence, at lower temperatures the amount of heat released at any time is smaller than at higher temperatures, but heat is released over a longer period. This is shown on two heat flow curves in Figure 4a. The heat flow signal for the experiment at 323 K falls below the heat flow curve for the experiment at 293 K after approximately 70 min. In the former experiment 100% conversion is reached after ca. 500 min and no heat flow is measured any longer, the signal reached the baseline level. In the latter experiment 100% conversion is not reached before ca. 2000 min. As for the isothermal data Figure 5 shows the heat flows and corresponding conversion for the dynamic experiments. Figure 4: **Upper row**: DSC heat flows for isothermal experiments at the given temperature. **Lower row**: Time Development of the conversion \(\alpha\) of the corresponding experiments shown in the upper row. **Left column**: Development of the heat flow/conversion for two selected experiments over the first day of the experiment at 293 K and the first 1000 min for the experiment at 323 K. **Right column**: Development of the heat flow/conversion over the first hour for all performed isothermal experiments. It can be seen that the position of the heat flow peak occurs at higher temperatures for higher heating rates. In addition Figure 5 shows that the experiments do not reach full cure during the temperature ramps (with the exception of the experiment at 1 K/min). The reason for the right shift of the peak in the temperature dependent dynamic data in Figure 5b is the following: At slower heating rates the material spends more time at lower temperatures and reaches higher conversion earlier, temperature-wise (cf. Figure 5d). The Arrhenius term in Equation (1) still increases with rising temperature. Thus, the reason for a decreasing heat flow is to be found in \(f(\alpha)\). As said above \(f(\alpha)=(1-\alpha)^{n}\) is often assumed as the kinetic model to describe polyurethane. Hence, \(f(\alpha)\) decreases with increasing conversion. Temperature-wise, the heat flow peak occurs earlier in slow heating rate dynamic data, because the decreasing kinetic function \"outpaces\" the increasing Arrhenius term. The isothermal and dynamic data shows quite different curing behaviour at different temperatures and heating rates. Any set of model parameters must be able to characterize this wide range of curing behaviour. Table 3 presents the determined total heats of reaction for all experiments. The total heat is the integral of the curves shown in Figures 4 and 5 (cf. also Figure 1b). Figure 5: **Upper row**: DSC heat flow data for dynamic experiments with the given heating rates. **Lower row**: Time Development of the conversion \(\alpha\) of the corresponding experiments shown in the upper row. **Left column**: development of the heat flow/conversion over time. **Right column**: development of the heat flow/conversion over temperatur. The legends in the left column are valid for both columns. As Table 3 reveals, the total heats of reactions are all similar. For the isothermal values a mean value of 67 J/g was found, while it was 73 J/g for the dynamic experiments.