## 3 Results and Discussion
### Prediction of Migration into Food and Food Simulants  
Within this study, the diffusion coefficients were determined from permeation and migration experiments into the gas phase. Therefore, interaction of contact media like sorption and swelling of the polymer were minimized. Since swelling effects of the polymer matrix by sorption of the simulants is thereby negligible, the migration is independent of the simulant and the mass transfer is affected only by the diffusion of the migrant in the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **GPPS** & \multicolumn{2}{c}{**HIPS**} \\ \hline  & **below T\({}_{\mathrm{g}}\)** & **above T\({}_{\mathrm{g}}\)** & **below T\({}_{\mathrm{g}}\)** & **above T\({}_{\mathrm{g}}\)** \\ \hline a (1/K) & 2.59 \(\times\) 10\({}^{-3}\) & 2.44 \(\times\) 10\({}^{-3}\) & 2.55 \(\times\) 10\({}^{-3}\) & 2.46 \(\times\) 10\({}^{-3}\) \\ b (cm\({}^{2}\)/s) & 7.38 \(\times\) 10\({}^{-9}\) & 6.46 \(\times\) 10\({}^{-8}\) & 9.21 \(\times\) 10\({}^{-9}\) & 2.07 \(\times\) 10\({}^{-7}\) \\ c (Å\({}^{3}\)) & 55.71 & 25.51 & 73.28 & 45.00 \\ d (1/K) & 2.73 \(\times\) 10\({}^{-5}\) & 7.55 \(\times\) 10\({}^{-5}\) & 2.04 \(\times\) 10\({}^{-5}\) & 3.57 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Parameters for the prediction of diffusion coefficients according to Equation (3) for GPPS and HIPS below and above Tg.  
polymer. Interactions between contact media and polymers increase the migration which is an important parameter when using GPPS and HIPS in food packaging applications. The phenomena of sorption and swelling are well-known from migration kinetics into food simulants, e.g., the loss of functional barrier properties of PS functional barrier layers [32]. Strong interactions of PS with coconut oil, palm kernel oil, Miglyol, 10% ethanol, 50% ethanol and goat's milk have been reported [15] in the case of polystyrene (in this publication, it is unclear if it is GPPS or HIPS), which indicate that these foods and simulants can swell the polymer matrix and increase the diffusion of potential migrants into food and simulants. A similar behavior is reported for acrylonitrile butadiene copolymer (ABS) [33]. Interaction between the polymer and the food simulants mainly influences the migration into food, which was also reported for PET [34]. However, real food does not swell the packaging polymer significantly, especially at low temperatures, otherwise packaging polymer might be unsuitable for this purpose. Swelling of food simulants compared to real food is shown for ABS in Lit. [33]. However, for convenience and as specified in regulatory guidelines, food compliance testing is typically performed with simulants like 50% ethanol or _iso_-octane. This leads to a strong over-estimation of the level of migration [33; 34]. In addition, sorption and swelling had an influence also on the diffusion coefficients determined in PS. [PERSON] et al. determined the diffusion coefficients of styrene and styrene oligomers into the food simulant 95% ethanol at 40 \({}^{\circ}\)C [35]. The diffusion coefficients are significantly higher as predicted from the results of this study, which is most probably due to the swelling effect of 95% ethanol as food simulant. The influence of swelling is also visible in the proposed prediction parameters, if migration data in swollen PS is taken into account [36]. In this recent compilation study, most of the diffusion coefficients were determined under swollen conditions, e.g., PS in neat solvents at high temperature in [37; 38; 39]. This leads to a strong over-estimation of the diffusion coefficients and therefore also to the derived modelling parameters. Realistic diffusion coefficients as derived from this study might lead to a more realistic prediction of the migration of polymer constituents into food.