## 3 Results
### Migration Modeling  
Migration modeling is a useful tool to predict the migration of BPA into food. Almost all applications of PET bottles and PET trays can be calculated with the experimentally determined activation energies (E\({}_{\rm A}\)) and pre-exponential factors (D\({}_{\rm 0}\)) from Table 3. The very low threshold values of BPA in particular are a big hurdle to determining the migration of BPA experimentally. Therefore, the migration of BPA can be predicted with the activation energies from this study. The experimental activation energies and pre-exponential factor (D\({}_{\rm 0}\)) of the migration kinetics (Table 3) were used for the predictions. Furthermore, a partition coefficient of K\({}_{\rm pF}\) = 1 is assumed, which simulates a good solubility of BPA in foodstuffs. Figure 2: Correlation between the diffusion coefficients (D\({}_{\rm P}\)) and the reciprocal temperature (Arrhenius plot). In addition to calculations with the activation energies (E\({}_{\text{A}}\)) determined in this study, two prediction models were also used. Regulation 10/2011 [33] allows the use of prediction models in the conformity assessment of FCMs. The so-called A\({}_{\text{P}}\) model was published in 2005 and is currently generally recognized for the prediction of diffusion coefficients [34; 35]. However, the A\({}_{\text{P}}\) model is highly overestimate. Therefore, another model was developed for the prediction of the diffusion coefficients of PET [36; 37]. It is based on experimentally determined activation energies (E\({}_{\text{A}}\)) and predicts migration much more realistically than the A\({}_{\text{P}}\) model. The predicted diffusion coefficients are given in Table 4 (A\({}_{\text{P}}\) prediction model) and Table 5 (E\({}_{\text{A}}\)-based model). Based on the experimentally determined activation energies of diffusion as well as of the two prediction models, the concentration of BPA in the bottle walls was predicted, which correlates with a migration of 1 ug/L as well as 0.012 ug/L. The storage conditions were assumed to be up to 365 days at 25 \({}^{\circ}\)C in contact with food with a surface/volume ratio of 6. These storage conditions were currently used by the EFSA for the evaluation \begin{table}
\begin{tabular}{c c} \hline
**Temperature**[\({}^{\circ}\)**C] & **Diffusion Coefficient [cm2/s]** \\ \hline
25 & \(8.45\times 10^{-15}\) \\
30 & \(1.65\times 10^{-14}\) \\
40 & \(5.84\times 10^{-14}\) \\
50 & \(1.92\times 10^{-13}\) \\
60 & \(5.87\times 10^{-13}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Predicted diffusion coefficients (D\({}_{\text{P}}\)) of BPA in PET according to the A\({}_{\text{P}}\) model [34; 35] (predicted with a molecular weight of BPA of 228.3 g/mol with Ap\({}_{\text{P}}\) = 3.1 and \(\tau\) = 1577 K). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Food** & **Temperature** & **Diffusion Coefficient** & **Activation Energy E\({}_{\text{A}}\)** & **Pre-Exponential** & **Correlation** \\
**Simulant** & [\({}^{\circ}\)**C] & **D\({}_{\text{P}}\) [cm2/s]** & **[kJ/mol]** & **Factor D\({}_{\text{0}}\) [cm2/s]** & **Coefficient r\({}^{2}\)** \\ \hline
3\% acetic acid & 30 & \(1.10\times 10^{-18}\) & & & \\  & 40 & \(4.14\times 10^{-18}\) & 131.2 & \(3.87\times 10^{4}\) & 0.9922 \\  & 50 & \(2.08\times 10^{-17}\) & & & \\  & 60 & \(1.19\times 10^{-16}\) & & & \\ \hline
10\% ethanol & 30 & \(1.67\times 10^{-18}\) & & & \\  & 40 & \(6.87\times 10^{-18}\) & 140.9 & \(2.63\times 10^{6}\) & 0.9901 \\  & 50 & \(3.68\times 10^{-17}\) & & & \\  & 60 & \(2.60\times 10^{-16}\) & & & \\ \hline
20\% ethanol & 30 & \(3.29\times 10^{-18}\) & & & \\  & 40 & \(1.37\times 10^{-17}\) & 153.6 & \(7.71\times 10^{8}\) & 0.9883 \\  & 50 & \(9.84\times 10^{-17}\) & & & \\  & 60 & \(7.72\times 10^{-16}\) & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Diffusion coefficients (D\({}_{\text{P}}\)), activation energies of diffusion (E\({}_{\text{A}}\)), and pre-exponential factors (D\({}_{\text{0}}\)) from experimentally determined migration kinetics of BPA from PET bottles into food simulants.