## 2 Cure Modeling and Heat Generation  
The conversion \(\alpha\) (or degree of cure) is the amount of bonds formed in a certain amount of polymer. The rate \(\mathrm{d}\alpha/\mathrm{d}t\) at which bonds are formed with time \(t\) during a chemical reaction is typically described with a general rate equation [15; 16]:  
\[\frac{\mathrm{d}\alpha}{\mathrm{d}t}=k(T)\cdot f(\alpha)=A\cdot\mathrm{e}^{-E/ RT}\cdot f(\alpha) \tag{1}\]  
The so called kinetic function \(f(\alpha)\) will be discussed below, \(T\) is the absolute temperature and \(k\) the rate coefficient. The latter relates to the temperature according to the empirical Arrhenius equation [17; 18] which appears in the right hand side of Equation (1) instead of \(k\). In the Arrhenius equation \(R\) is the universal gas constant, \(E\) the activation energy and \(A\) the pre-exponential factor. The exact physical meaning of \(A\) is out of scope of this article, but in general it determines how often molecules collide with each other. Note that \(\alpha\) is given as a normalized quantity ranging from 0 (no bonds) to 1 (fully cured). The rate of reaction \(\mathrm{d}\alpha/\mathrm{d}t\) should change with the number of bonds that have already formed. This change can be described by the kinetic function \(f(\alpha)\). Intuitively one could think that the reactants can find possible sites for bonding easily at the beginning of the curing process. Once many bonds have formed the reaction rate slows down due to a limited number of available sites. Depending on the chemistry involved many scenarios are possible. Much work has been done to determine the functions \(f(\alpha)\) for various chemical reactions and we refer to Table 1 in Section 3.2 for some of them. While traditionally it was assumed that \(k\) is only dependent on the temperature, a growing body of works shows that both \(E\) and \(A\) can be dependent on \(\alpha\) (see for example [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]).  
The formation of polymer bonds is an exothermic reaction. During each bond formation a certain amount of heat \(Q\) is released. If, in a given amount of polymer, all bonds are formed, the total heat \(Q_{\mathrm{total}}\) (usually normalized to one gram) is released (cf. Figure 1b and text). The heat set free during a chemical reaction can be measured with a standard experimental procedure as described in more detail below. The rate at which bonds are forming is related to the released heat. This relationship is expressed in the equation:  
\[\frac{\mathrm{d}\alpha}{\mathrm{d}t}=\frac{1}{Q_{\mathrm{total}}}\frac{ \mathrm{d}Q}{\mathrm{d}t} \tag{2}\]The quantities \(\alpha(t)\) and \(Q(t)\) are of primary interest for the practical user. If the former can be calculated as the integral of Equation (1), the latter can easily be obtained as the integral of Equation (2). This has an important implication. It is sufficient to model the integral of the reaction equations accurately. This means typically that certain inaccuracies in the reaction equations can be acceptable, because they play a minor role in the integrated quantities. This will be discussed in more detail throughout the paper.  
The equations also show that the main parameters to be obtained are: \(E\), \(A\) and \(f(\alpha)\); which is often called the \"kinetic triplet\". The following will describe how these parameters can be obtained at sufficient accuracy.