## 3 Results
### Migration Modeling
\begin{table}
\begin{tabular}{c c} \hline
**Temperature** & **Diffusion Coefficient** & **Activation Energy [kJ/mol]** & **Pre-Exponential** \\
[\({}^{\circ}\)**C]** & **[cm2/s]** & **Energy [kJ/mol]** & **Factor [cm2/s]** \\ \hline
25 & \(1.09\times 10^{-18}\) & & \\
30 & \(3.33\times 10^{-18}\) & & \\
40 & \(2.72\times 10^{-17}\) & 165.8 & \(1.22\times 10^{11}\) \\
50 & \(1.95\times 10^{-16}\) & & \\
60 & \(1.24\times 10^{-15}\) & & \\ \hline \end{tabular}
\end{table} 
Table 5: Predicted diffusion coefficients (D\({}_{\text{P}}\)), activation energies of diffusion (E\({}_{\text{A}}\)), and pre-exponential factors (D\({}_{\text{0}}\)) of BPA in PET according to the E\({}_{\text{A}}\)-based prediction model [36; 37] predicted with a molecular volume of BPA of 221.11 Å\({}^{3}\). of PET recyclates in beverage bottles [23; 26]. The results are shown in Tables 6 and 7 and Figure 3 as a correlation of the bottle wall concentration and the storage time. Regarding the new proposed threshold limit of 1 ug/L, maximum concentrations of 297 mg/kg (3% acetic acid), 255 mg/kg (10% ethanol), and 192 mg/kg (20% ethanol) in the PET bottle wall are predicted for 365 days of storage at 25 \({}^{\circ}\)C. Shorter storage times increase the above-mentioned maximum concentrations in the bottle wall. In addition to the storage conditions of up to 365 days at 25 \({}^{\circ}\)C, forced storage conditions of 10 days at 40 \({}^{\circ}\)C and 10 days at 60 \({}^{\circ}\)C were calculated. The forced contact conditions are used to accelerate the experimental migration testing and are part of the legal requirements according to Regulation 10/2011 [33]. Based on the experimentally determined activation energies (E\({}_{\text{A}}\)) for 20% ethanol, the test conditions of 10 d at 40 \({}^{\circ}\)C simulate storage for 195 days at 25 \({}^{\circ}\)C. In contrast, testing for 10 d at 60 \({}^{\circ}\)C very unrealistically simulates 18.3 years of storage at 25 \({}^{\circ}\)C. Similar results were obtained for 3% acetic acid at 100 days (10 days at 40 \({}^{\circ}\)C) and 7.2 years (10 days at 60 \({}^{\circ}\)C), respectively. The test conditions of 10 days at 40 \({}^{\circ}\)C are therefore much more suitable for real food applications than the current test conditions of 10 days at 60 \({}^{\circ}\)C in accordance with European Regulation 10/2011 [33]. The literature data \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Temperature** & **Storage Time [d]** & & & & **Concentration [mg/kg]** & \\  & & **3\% Acetic Acid** & **10\% Ethanol** & **20\% Ethanol** & **D\({}_{\text{P}}\) Predicted E\({}_{\text{A}}\)** & **D\({}_{\text{P}}\) Predicted** \\  & & **(E\({}_{\text{A}}\) exp)** & **(E\({}_{\text{A}}\) exp)** & **(E\({}_{\text{A}}\) exp)** & **Based Model** & **A\({}_{\text{P}}\) Predicted** \\ \hline
25 \({}^{\circ}\)C & 10 & 1792 & 1542 & 1167 & 1083 & 12.3 \\  & 20 & 1267 & 1108 & 825 & 765 & 8.67 \\  & 30 & 1033 & 892 & 672 & 624 & 7.09 \\  & 50 & 800 & 686 & 521 & 487 & 5.52 \\  & 90 & 597 & 514 & 387 & 361 & 4.12 \\  & 120 & 519 & 444 & 336 & 314 & 3.57 \\  & 150 & 462 & 397 & 300 & 279 & 3.19 \\  & 200 & 402 & 344 & 260 & 226 & 2.76 \\  & 300 & 327 & 281 & 212 & 198 & 2.25 \\  & 365 & 297 & 255 & 192 & 179 & 2.04 \\
40 \({}^{\circ}\)C & 10 & 542 & 395 & 263 & 218 & 4.68 \\
60 \({}^{\circ}\)C & 10 & 111 & 77.7 & 45.0 & 32.3 & 1.48 \\ \hline \end{tabular}
\end{table} 
Table 6: BPA concentrations in the bottle wall, which correspond to a migration of 1 ug/L (EU cube, layer thickness 300 \(\upmu\)m, diffusion coefficients calculated from the activation energies of diffusion from experimental migration kinetics or prediction models (E\({}_{\text{A}}\)-based and A\({}_{\text{P}}\) models)).