## 3 Results
### Migration Kinetics into Food Simulants  
Migration kinetics from PET into food simulants were used to determine the diffusion coefficients of BPA in PET. Similar approaches have been used in previous studies for antimony in PET as well as for the acetaldehyde-scavenging substance anthranilamide in PET [27; 28]. The migration of BPA from PET bottles into food simulants was determined experimentally after contact up to 90 days and temperatures up to 60 \({}^{\circ}\)C in a migration kinetic experiment with seven kinetic points for each temperature and simulant. The concentration of BPA in the PET bottles used for the kinetics was determined to be 26.2 \(\pm\) 0.4 mg/kg. An area of 100 cm\({}^{2}\) was then cut out of the PET bottles and totally immersed with the food simulants 3% acetic acid, 10% ethanol, and 20% ethanol, respectively. The samples were then stored at 30 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C for up to 90 days in total. Below 30 \({}^{\circ}\)C, the migration is very slow, so that the concentrations of BPA are below the detection limits, and therefore no diffusion coefficient can be determined. The glass transition temperature of PET is between 60 and 70 \({}^{\circ}\)C. Therefore, 60 \({}^{\circ}\)C was chosen as the highest temperature for the migration experiments.  
Samples of the food simulants were taken at regular intervals and analyzed for their BPA content. The results of the migration kinetics are given in Table 2. The migration kinetics are visualized in Figure 1. The results of the migration kinetics show that, as expected, migration increases over time and with increasing temperature. The kinetics follow [PERSON]'s law, which is confirmed by the fact that the migration of BPA increases linearly with the square root of time. It is therefore possible to calculate the diffusion coefficient (D\({}_{\text{P}}\)) from the experimental data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Food Simulant** & **Storage Time [d]** & \multicolumn{4}{c}{**Concentration [ug/L]**} \\  & & **30 \({}^{\circ}\)C** & **40 \({}^{\circ}\)C** & **50 \({}^{\circ}\)C** & **60 \({}^{\circ}\)C** \\ \hline
3\% acetic acid & 10 & 0.128 \(\pm\) 0.010 & 0.242 \(\pm\) 0.010 & 0.511 \(\pm\) 0.022 & 1.11 \(\pm\) 0.06 \\  & 20 & 0.188 \(\pm\) 0.005 & 0.287 \(\pm\) 0.007 & 0.716 \(\pm\) 0.012 & 1.45 \(\pm\) 0.08 \\  & 30 & 0.141 \(\pm\) 0.005 & 0.310 \(\pm\) 0.012 & 0.710 \(\pm\) 0.029 & 1.57 \(\pm\) 0.05 \\  & 40 & 0.155 \(\pm\) 0.003 & 0.316 \(\pm\) 0.005 & 0.841 \(\pm\) 0.039 & 1.93 \(\pm\) 0.11 \\  & 50 & 0.182 \(\pm\) 0.006 & 0.341 \(\pm\) 0.012 & 0.790 \(\pm\) 0.007 & 1.89 \(\pm\) 0.15 \\  & 60 & 0.159 \(\pm\) 0.004 & 0.301 \(\pm\) 0.009 & 0.634 \(\pm\) 0.029 & 1.61 \(\pm\) 0.04 \\  & 90 & 0.225 \(\pm\) 0.008 & 0.460 \(\pm\) 0.026 & 0.926 \(\pm\) 0.106 & 2.42 \(\pm\) 0.22 \\ \hline
10\% ethanol & 10 & 0.154 \(\pm\) 0.014 & 0.296 \(\pm\) 0.026 & 0.688 \(\pm\) 0.024 & 1.69 \(\pm\) 0.044 \\  & 20 & 0.221 \(\pm\) 0.016 & 0.349 \(\pm\) 0.012 & 0.863 \(\pm\) 0.033 & 2.02 \(\pm\) 0.042 \\  & 30 & 0.172 \(\pm\) 0.009 & 0.423 \(\pm\) 0.035 & 0.969 \(\pm\) 0.034 & 2.44 \(\pm\) 0.07 \\  & 40 & 0.215 \(\pm\) 0.002 & 0.409 \(\pm\) 0.002 & 1.10 \(\pm\) 0.01 & 2.64 \(\pm\) 0.25 \\  & 50 & 0.235 \(\pm\) 0.033 & 0.462 \(\pm\) 0.009 & 0.990 \(\pm\) 0.017 & 2.53 \(\pm\) 0.13 \\  & 60 & 0.198 \(\pm\) 0.013 & 0.424 \(\pm\) 0.002 & 0.953 \(\pm\) 0.009 & 2.59 \(\pm\) 0.12 \\  & 90 & 0.260 \(\pm\) 0.010 & 0.547 \(\pm\) 0.029 & 1.22 \(\pm\) 0.043 & 3.72 \(\pm\) 0.070 \\ \hline \end{tabular}
\end{table}
Table 2: Results of the migration kinetics of BPA into 3% acetic acid, 10% ethanol, and 20% ethanol as food simulants.