## 3 Results and Discussion
### Diffusion Coefficients from Desorption Kinetics  
The applied desorption method determines the migration of spiked substances from PS sheets into the gas phase at elevated temperatures. Diffusion coefficients D\({}_{\mathrm{P}}\) were determined from the slopes of the linear correlation between the square root of time and the area-dependent migration according to Equation (1). By use of this desorption method, several migrants can be determined simultaneously provided the model compounds are distributed homogenously in the spiked PS sheet and separation on the GC column is attained. In order to obtain a homogenous distribution of the migrants in the sheet, the organic substances were spiked into the polymer melt during sheet production. Notably, a proportion of the migrants evaporate during the thermal step of sheet production, especially in case of volatile substances. Thus, compounds of higher volatility are removed in greater amounts during sheet production, leading to lower concentrations in the final spiked PS sheet. It was therefore necessary to analyze the final PS sheets according to their residual concentration of the artificially spiked compounds (Table 1). As a result, the concentrations of the \(n\)-alkanes were quantified between 400 and 700 mg/kg. A broader concentration range was determined for the applied solvents like acetone, ethyl acetate, toluene and chlorobenzene with concentrations of 180 mg/kg up to around 800 mg/kg. The substances phenyl cyclohexane and benzophenone were determined at concentrations of 500 to 1200 mg/kg. The concentration of styrene in both sheets was determined in the range of 350 mg/kg up to 600 mg/kg. Styrene was not artificially added, but detectable in polystyrene polymers as residual monomer. The diffusion coefficients D\({}_{\mathrm{P}}\) derived from the desorption kinetics are summarized in Table 3 (\(n\)-alkanes) and Table 4 (other substances with various functional groups and aromatic rings). Examples of the desorption kinetics into the gas phase for \(n\)-octane and chlorobenzene in GPPS as well as for \(n\)-dodecane and toluene in HIPS are given in Figure 1. Desorption kinetic curves all other applied substances had a similar shape. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Temperature** & & & & & & \\ (\({}^{\circ}\)C) & & & & & & \\ \hline  & **Methanol** & **Ethanol** & **1-Propanol** & **1-Butanol** & **1-Pentanol** & **1-Hexanol** \\ \hline
0 & 9.16 & 12.8 & 9.29 & 7.49 & 5.65 & 3.76 \\
25 & 27.5 & 28.3 & 27.9 & 22.5 & 17.0 & 11.3 \\
40 & 54.9 & 76.7 & 55.8 & 45.0 & 33.9 & 45.0 \\
60 & 201 & 281 & 204 & 165 & 124 & 82.8 \\
70 & 330 & 460 & 335 & 270 & 203 & 135 \\
80 & 549 & 767 & 558 & 450 & 339 & 226 \\
90 & 916 & 1280 & 929 & 749 & 565 & 376 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: 1-Alcohols and their upstream concentrations used in permeation testing. The desorption kinetics were determined at temperatures between 75 \({}^{\circ}\)C and 115 \({}^{\circ}\)C. For all investigated migrant kinetic points, they were determined every 40 min. Therefore, several kinetic points are available for each diffusion coefficient. From this migration, it could be shown that the diffusion process is following Fickian laws of diffusion resulting in a linear correlation between the migrated amount and the square root of time ([PERSON] et al., 2017). However, it should be noted that the kinetic curves shown in Figure 1 do not go through the zero point. This is due to the fact that during sheet manufacturing, a portion of the spiked substances are lost from the hot surface of the sheets during sheet production, which reduces slightly the concentration at the surface of the sheets. This leads to a slightly lower desorption at the beginning of the kinetics. Due to the high temperatures during the kinetic tests, the concentration is gradually replenished at the surface of the sheets.