## 2 Cure Modeling and Heat Generation
### Heat Flow Measurements by Differential Scanning Calorimetry
The baseline is the heat flow during steady state conditions [15]. The peak above the baseline is the total heat of curing \(Q_{\mathrm{total}}\). By integrating Equation (2) the time (or later temperature) dependent degree of cure \(\alpha\) can easily be calculated directly from the DSC measurements. It is necessary to determine the baseline of the DSC curve to be able to calculate \(Q_{\mathrm{total}}\) and \(\alpha\). In reality the baseline is a sigmoid and several, more or less complicated, techniques exist to calculate it. However, very often simply a straight line is used between the start- and end-point of the exothermic peak [15; 42; 51; 52; 53; 54; 55; 56]. If the change in heat capacity during the exothermic peak is insignificant a straight line is justified [15; 55]. The procedure to obtain the baseline will also influence \(Q_{\mathrm{total}}\). However, choosing a straight line gives just a small error of \(Q_{\mathrm{total}}\) relative to the scatter of \(Q_{\mathrm{total}}\) between samples [56]. Appendix C gives a detailed example on how to perform the baseline correction of the heat flow data for isothermal and dynamic measurements. Dynamic DSC experiments are typically run at a constant rate of increasing temperature. The rate may be changed from experiment to experiment. Since the time to cure depends on the characteristics of chemical reaction, dynamic DSC experiments under different conditions allows obtaining the kinetic triplet parameters from Equation (1). The standard way to obtain the kinetic triplet is regular fitting of DSC data with a given kinetic function [4; 57]. Here, and in the following, the term \"regular fitting\" shall describe that the parameters of a given function are optimized until said function describes the data in question. If for example it is assumed that \(f(\alpha)=(1-\alpha)^{n}\) in Equation (1) than the function that needs to be optimized is \(A\cdot\mathrm{e}^{-E/RT}\cdot(1-\alpha)^{n}\). In this example the values for \(A\), \(E\) and \(n\) are initially guessed and said function will be calculated. Then the values for these three parameters will be changed and the function calculated again until the deviation between the function with optimized parameters and the data is below a given threshold. If the chemical composition of the constituents and the chemical pathways are known, it is possible to arrive at the kinetic function by studying the rate equations of the underlying chemical reactions [58; 59]. However, this research was done for the practical case where no detailed information of the involved chemicals was available (cf. Section 5.2). Two other methods shall be mentioned which enable a user to simulate the curing process of a polymer: Molecular dynamic calculations [60] and thermodynamic frameworks [61]. However, these are rather involved, require extensive mathematical frameworks, can not easily be used in standard finite element software and are not suitable for the simulation of large structures with today's computational technology. Utilizing the Isoconversional Method and the Compensation Effect to Calculate the Actual Kinetic Model  
If the polymer under investigation does not behave according to an idealized reaction model or if this model \(f(\alpha)\) is not known it may not be possible to acquire the correct kinetic triplet by regular fitting of the DSC data as described above. In such cases the isoconversional method allows obtaining the activation energy in dependency of the conversion without having to know anything about the kinetic model. Below we present just the final results of the theory extensively laid out in the works of [PERSON] and others [19; 20; 21; 22; 23; 25; 27; 29]. The theory assumes that the Arrhenius prefactor \(A\) and the activation energy \(E\) in Equation (1) are also dependent on the degree of cure, thus becoming \(A_{\alpha}\) and \(E_{\alpha}\). A more detailed derivation and justification for these equations can be found in Appendix A.