## 2 Cure Modeling and Heat Generation
### Heat Flow Measurements by Differential Scanning Calorimetry  
Several techniques exist to investigate the curing of polymers. Raman or infrared spectroscopy [PERSON] _et al._ (1989); [PERSON] _et al._ (1999); [PERSON] _et al._ (1999); [PERSON] _et al._ (1999) allows investigation of the reaction mechanisms. However, these techniques can not analyze the often very weak signals at high conversion. Measuring the dielectric properties (utilizing dielectric analysis -DEA) [33] or the change of the internal structure (using ultrasound) [34; 35] of the polymer are other methods to characterize the curing process. However, these provide the user not with thermal data. Judging from the literature curing characteristics are most often measured with Differential Scanning Calorimetry (DSC). DSC is a versatile, well known and long established material characterization technique [15; 16]. In this case DSC is used to determine the exothermic heat created by the curing process of the thermoset polymer, as it turns from a viscous liquid into a solid by cross-linking [36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50]. It is assumed that no other phase transitions occur absorbing or developing heat. Knowing the progression of the curing reaction and the related energy allows calculation of the heat release in a given volume in finite element simulations. In the following we will provide a brief overview of the DSC method, which should enable the reader to understand the results of this paper. More details can be found in [15]. The DSC related equations shown here are also taken from this reference and the same symbols are used. A DSC apparatus is basically a chamber with a defined gas flow (often nitrogen) that contains two similar pans on a constantan body. A sketch of such a setup can be seen in the Figure 1a. One pan contains the sample, the other one is empty and acts as reference. The temperature difference between both pans is measured while the temperature is ramped up. In isothermal experiments the heating rate is constant, while a temperature ramp is applied to both pans in dynamic experiments. Temperature differences occur either when the temperature of the constantan body is raised and the thermal inertia of the sample takes up more heat (this happens for any material) or when phase changes occur. Examples of the latter would be melting or transitioning from the glassy to  
Figure 1: (**a**) Sketch of a chamber of a Differential Scanning Calorimeter (DSC); \(Q_{\mathrm{s}}\) and \(Q_{\mathrm{r}}\) are the sample and reference heat flow as in Equation (3). (**b**) An idealized DSC curve of a heat flow peak due to an exothermic chemical reaction (taken from [15] and adapted). the rubbery state. However, none of these are relevant for the data and results presented here. Another cause for a temperature difference are chemical reactions taking place in the sample pan (as in the case of a curing polymer). Since both pans are similar (in material and mass) and are placed on the same constantan body, any difference in temperature between the sample and the reference pan is solely due to the sample itself. Leaving all particulars aside, the heat flow \(\mathrm{d}Q/\mathrm{d}t\) is simply proportional to the temperature difference between the containers:  
\[\Delta T\propto\frac{\mathrm{d}Q}{\mathrm{d}t}=\left(\frac{\mathrm{d}Q}{ \mathrm{d}t}\right)_{\mathrm{s}}-\left(\frac{\mathrm{d}Q}{\mathrm{d}t}\right)_ {\mathrm{r}}, \tag{3}\]  
\(Q_{\mathrm{s}}\) and \(Q_{\mathrm{r}}\) denote the sample and reference heat flow respectively. A DSC instrument measures the temperature difference very accurately, see e.g., [15]. Of interest here is the dependency of the released heat on time or (change of) temperature since it embodies the information needed to simulate the heat released during cure. A DSC curve shows the heat flow over time (or temperature in dynamic experiments). A curing reaction exhibits an exothermal heat flow peak over a baseline. A simplified sketch is shown in Figure 1b.