## 2 Materials and Methods
### Sample Materials and Model Compounds for Desorption Testing
#### 2.1.3 Determination of Diffusion Coefficients  
Migrations into the gas phase of the spiked model compounds were determined according to [19; 20] using an automated method that involved placing sheet samples of 15.6 cm diameter (area 191 cm\({}^{2}\)) in a migration cell. One sheet per temperature was analyzed. The migration cell was heated up to the measuring temperature and the compounds migrating from the polystyrene sheets were purged out of the extraction cell by a helium stream of 20 mL/min. The migrants were trapped (Carbopack B 20 mm, Supelco) at a trap temperature of -46 \({}^{\circ}\)C. Subsequently, the loaded trap was completely desorbed and transferred directly to the connected gas chromatograph (GC) by heating it to 300 \({}^{\circ}\)C within  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sheet** & **Substance** & \multicolumn{2}{c}{**Spiked Concentration (mg/kg)**} \\ \hline  & & **General Purpose Polystyrene** & **High Impact Polystyrene** \\  & & **(GPPS)** & **(HIPS)** \\ \hline sheet 1 & \(n\)-Octane & 422 \(\pm\) 5 & 474 \(\pm\) 37 \\  & \(n\)-Decane & 486 \(\pm\) 4 & 354 \(\pm\) 4 \\  & \(n\)-Dodecane & 518 \(\pm\) 3 & 610 \(\pm\) 8 \\  & \(n\)-Tetradecane & 531 \(\pm\) 4 & 692 \(\pm\) 15 \\  & \(n\)-Hexadecane & 538 \(\pm\) 5 & 709 \(\pm\) 19 \\  & \(n\)-Octadecane & 522 \(\pm\) 5 & 674 \(\pm\) 19 \\  & \(\mathrm{Styrene}^{\,1}\) & 627 \(\pm\) 22 & 354 \(\pm\) 2 \\ sheet 2 & Acetone & 180 \({}^{\circ}\) & / \\  & Ethyl acetate & 270 \({}^{\circ}\) & 500 \({}^{\circ}\) \\  & Toluene & 464 \(\pm\) 3 & 763 \(\pm\) 11 \\  & Chlorobenzene & 521 \(\pm\) 4 & 821 \(\pm\) 13 \\  & \(\mathrm{Phenyl cyclohexane}\) & 627 \(\pm\) 6 & 1229 \(\pm\) 33 \\  & \(\mathrm{Benzophenone}\) & 538 \(\pm\) 7 & 1002 \(\pm\) 27 \\  & \(\mathrm{Styrene}^{\,1}\) & 595 \(\pm\) 5 & 363 \(\pm\) 6 \\ \hline \hline \end{tabular} \({}^{\dagger}\) residual monomer, not artificially added, \({}^{\circ}\) estimated from headspace gas chromatography.  
\end{table}
Table 1: Experimentally determined concentrations of model compounds in the spiked polystyrene (PS) sheets.  
about 10 s. Subsequently, a new trapping cycle started. By using this automated method, every 40 min a kinetic point was determined. The migrants were separated during the GC run and quantified during the chromatographic measurements. Calibration was achieved by injection of undiluted standard solutions of the migrants into the migration cell. Gas chromatograph: Column: Rai 624; 30 m length; 0.32 mm inner diameter; 1.8 \(\upmu\)m film thickness, temperature program: 40 \({}^{\circ}\)C (2 min), rate 20 \({}^{\circ}\)C/min, 270 \({}^{\circ}\)C (8 min), pressure 70 kPa helium, detector temperature: 280 \({}^{\circ}\)C.  
The diffusion coefficients \(\mathrm{D_{P}}\) were calculated from the area related migration into the gas phase according to Equation (1). Within this equation, \(\mathrm{m_{t}}\)/A (in \(\mathrm{\mu g}\)/cm\({}^{2}\)) is the mass transfer into gas phase per area A (in cm\({}^{2}\)) and \(\delta\) (in g/cm\({}^{3}\)) is the density of the polymer. The concentration of the migrant at the start of the tests is \(\mathrm{c_{P0}}\) (in mg/kg) and \(\mathrm{D_{P}}\) (in cm\({}^{2}\)/s) is the diffusion coefficient in the polymer. The parameter t is the run time (in s) of the experiment.  
\[\frac{\mathrm{m_{t}}}{\mathrm{A}}=\frac{2}{\sqrt{\pi}}\delta\,\mathrm{c_{P0} }\sqrt{\mathrm{D_{P}}\,\mathrm{t}} \tag{1}\]