## 2 Results
### Material, Temperature and Migrant Specific Approach  
The main deficiency of the generic \"short-term contact\" considerations that are solely based on diffusion coefficients and partition coefficients if relevant is the missing link to real case applications where migration assessment is material, substance, and temperature dependent. This limitation of the generic approach can be exemplified by the following two case examples for PET computed with the Welle estimation procedures [10]: (i) A molecule  
Figure 5: Repeated-use: Map of time (t) in minutes against diffusion coefficient (Dp) in cm\({}^{2}\)/s. Deviation of migration in mg in dependence from partition coefficient (K\({}_{\text{PF}}\)) expressed in % at a given initial concentration (1000 mg/kg), material thickness (2000 \(\upmu\)m), and area to volume ratio (6 dm\({}^{2}\) per kg food). For a description of positions 1 to 3 see text. with a molecular volume of M\({}_{\rm V}\) = 195 A\({}^{3}\) at a temperature of T = 40 \({}^{\circ}\)C results in (nearly) the same diffusion coefficient of D = 7.8 \(\times\) 10\({}^{-17}\) cm\({}^{2}\)/s as a molecule with M\({}_{\rm V}\) = 326 A\({}^{3}\) at T = 60 \({}^{\circ}\)C. (ii) Substances with M\({}_{\rm V}\) = 130 A\({}^{3}\) at T = 70 \({}^{\circ}\)C and M\({}_{\rm V}\) = 65 A\({}^{3}\) at T = 30 \({}^{\circ}\)C both have a diffusion coefficient of about D = 2.3 \(\times\) 10\({}^{-13}\) cm\({}^{2}\)/s. Decomposing the diffusion coefficient into the contributions of the material, substance, and temperature makes a graphical representation very complex and impractical. Therefore, in the following section, an attempt is made to show the dependence of amount of migration from a substance resulting from a partition coefficient between the polymer and food for different time points at a fixed temperature and molecular mass (equivalent to size of migrant). These results are given in Figure 7. The significant dependence of the migration from the partition coefficient becomes visible in Figure 7 by drop of the curve, i.e., a decrease in migration as the partition coefficient increases. For a small molecule (50 g/mol), the impact of partitioning on migration becomes relevant at the partition coefficient \(K\) = 1000, and for bigger molecules (250 g/mol), the impact of partitioning in impact becomes relevant at the partition coefficient \(K\) = 100,000. A benefit of this representation is that the migrating amount is included in the graph, which means that a compliance evaluation with a restriction or a risk assessment that is based on toxicological considerations are possible. In the following figures, the migration maps for various polymers (PET, ABS, PA6 and PP) are presented and discussed. These maps were generated from Figure 7 using  
Figure 6: Repeated-use 3 \(\times\) 72 h (= 3 \(\times\) 3 days) with diffusion coefficient 10\({}^{-13}\) cm\({}^{2}\)/s and partition coefficient \(K\) = 0.1 to \(K\) = 10,000. Figure 7: Plot of migration (m) in mg for a generic migrant of molecular weight of 50 g/mol (**a**) and 250 g/mol (**b**) from a PET layer against partition coefficient (K\({}_{\rm pF}\)) at 40 \({}^{\circ}\)C in dependence of time. the diffusion coefficients available from Figure 3. Figure 8 show the deviation in the migration in mg/dm\({}^{2}\) that is independent of the partition coefficient (K\({}_{\text{PF}}\)) that is expressed in % at a given initial concentration (1000 mg/kg), material thickness (2000 \(\upmu\)m), and area to volume ratio (6 dm\({}^{2}\)/kg) for PET. For PET and the contact times under 10 days, the impact of partitioning on migration is neglectable (<10%) at the temperature of 40 \({}^{\circ}\)C and with a migrant with a molecular mass of 200 g/mol, which is significant at 100 \({}^{\circ}\)C. For a comparison of a single-use scenario (10 days) with a repeated-use scenario, the migration maps were generated for the time period of 6-9 days from three consecutive uses of 3 \(\times\) 3 = 9 days.