## 3 Results and Discussion
### Prediction of Diffusion Coefficients  
Diffusion coefficients at various temperatures were determined in this study from which activation energies of diffusion were derived. Based on these experimentally determined activation energies, a correlation between activation energies of diffusion E\({}_{\rm A}\) and the molecular volume of the migrant V was established for GPPS and HIPS (Figure 4). Similar correlations between E\({}_{\rm A}\) and V were found in the literature for other polymers like PET [25], polycyclicin polymer (COP) [20], polyethylene naphthalene (PEN) [26] and polyethylene vinylalcohol copolymer (EVOH) [27]. All tested compounds follow the correlation between the E\({}_{\rm A}\) and V nearly independent from chemical nature, functional groups or polarity of the molecules. Therefore, most probably also other organic molecules in PS might follow similar correlations. Due to slight effects of polarity or experimental uncertainties, the correlation of the activation energies of diffusion E\({}_{\rm A}\) and the molecular volume V shows a slight variance. As expected, the diffusion below and above the glass transition temperature is different, resulting in different correlations between the activation energies of diffusion E\({}_{\rm A}\) and the molecular volume V. As discussed above, for a given molecular volume V, the activation energies of diffusion E\({}_{\rm A}\) above T\({}_{\rm g}\) are lower than below T\({}_{\rm g}\) as indicated for the substances styrene, \(n\)-octane, \(n\)-decane, \(n\)-dodacane, \(n\)-tetradecane, and \(n\)-hexadecane. As shown in Figure 5, also the pre-exponential factor D\({}_{0}\) correlates also with the activation energy E\({}_{\rm A}\) for GPPS and HIPS, above as well as below the glass transition temperature. The role of the correlation between the pre-exponential factor D\({}_{0}\) and the activation energy E\({}_{\rm A}\) has been discussed in the literature as a so-called \"compensation effect\" [29] or \"Meyer-Neldel rule\" [30] and was also found in previous studies [20; 25; 26; 27]. As a consequence of this effect, the activation energy E\({}_{\rm A}\) and the pre-exponential factor D\({}_{0}\) are not independent from each other. This correlation was established over 16 orders of magnitude in the case of PET [25], 29 for COP [20], 23 for PEN [26], 30 for EVOH [27] and 74 orders of magnitude for PS in this study. It is noteworthy that in the case of GPPS and HIPS, the correlation does not significantly change below and above T\({}_{\rm g}\), whereas the correlation between the molecular volume V and the activation energy of diffusion E\({}_{\rm A}\) is different below and above the glass transition temperature. From the correlations given in Figures 4 and 5, the activation energies of diffusion E\({}_{\rm A}\) as well as the pre-exponential factor D\({}_{0}\) can be predicted for other non-tested substances. From both values, the diffusion coefficients are available at any temperature within the measured temperature intervals. Assuming that the Arrhenius plot is linear over a broader temperature range, diffusion coefficients can also be predicted at lower temperatures, e.g., room temperature. An equation was established combining both correlations and is given in Equation (3). The prediction of diffusion coefficients might be an important tool for the prediction of the mass transfer from PS into contact media, e.g., foodstuffs. Based on the correlations shown in Figures 4 and 5, the parameters \(a\) to \(d\) in Equation (3) were derived according to the procedure published in [25]. The parameters \(a\) to \(d\) for Equation (3) below and above the glass transition temperature are given in Table 8. It should be noted that the parameters for GPPS above the glass transition temperature are derived only from six individual activation energies of diffusion and pre-exponential factors, whereas the correlation below the glass transition temperature is based on 17 activation energies of diffusion.