## 2 Results
### Generic Diffusion Coefficient Approach
High partition coefficients indicate low solubility in the contact medium and therefore lower concentrations of the low partition coefficients (e.g., \(K\) = 1, good solubility). Figure 1 shows the generic approach for a thin food contact item with a material thickness of 50 \(\upmu\)m. For graphs (a), (b), and (c), which depict high diffusion rates (D\({}_{\text{P}}\) = 10\({}^{-10}\) cm\({}^{2}\)/s to 10\({}^{-12}\) cm\({}^{2}\)/s), the equilibrium is reached after storage for 365 d, and therefore, the partition coefficient plays the main role in the migration process. In terms of short-term contact, at the very fast diffusion coefficient of 10\({}^{-10}\) cm\({}^{2}\)/s, the equilibrium is also reached after a storage time of 10 d. For the material thickness of 100 \(\upmu\)m (see Supplementary Data), equilibrium is reached in graphs (a) and (b) after 365 d storage. All of the other diffusion coefficients result in non-equilibrium situations after 365 d of storage. After short-term storage (10 d), equilibrium is only reached for a diffusion coefficient of 10\({}^{-10}\) cm\({}^{2}\)/s. The diffusion coefficient of 10\({}^{-11}\) cm\({}^{2}\)/s resulted in a non-equilibrium situation for the partition coefficients of \(K\) = 0.1 to \(K\) = 100, whereas the equilibrium is still (nearly) reached for \(K\) = 1000 and \(K\) = 10,000. For a material thickness of 200 \(\upmu\)m, the equilibrium is (nearly) reached only for \(K\) = 1000 and \(K\) = 10,000 for D\({}_{\text{P}}\) = 10\({}^{-10}\) cm\({}^{2}\)/s (see Supplementary Data). Similar situations were achieved with material thicknesses of 500 \(\upmu\)m (Figure 2) and 1000 \(\upmu\)m (see Supplementary Data). As a result, the partitioning coefficients play a main role in combination with high diffusion coefficients and thin food contact materials. When considering lower diffusion coefficients and higher material thicknesses, the diffusion coefficient plays the most important role, especially at short storage times. In order to translate the generic graphs into a practical tool for migration prediction, the diffusion coefficients must be assigned to polymers, substances, and temperatures. For the typical polymers and migrants that are used in food contact applications at ambient temperatures, the diffusion coefficient ranges between \(10^{-10}\) cm\({}^{2}\)/s (high diffusivity polymer, small molecule) and \(10^{-15}\) cm\({}^{2}\)/s (low diffusivity polymer, huge molecule). Figure 3 shows examples for polypropylene (PP) [21], general-purpose polystyrene (GPPS), high-impact polystyrene (HIPS) [22], acrylonitrile butadiene styrene copolymer (ABS) [21], styrene acrylonitrile copolymer (SAN [21]), and polyethylene terephthalate (PET) [10]. The impact of the partition coefficients can be summarized using a so-called migration map (Figure 4). The migration map is generated by calculating the migration in a diffusion coefficient range from \(10^{-10}\) cm\({}^{2}\)/s to \(10^{-16}\) cm\({}^{2}\)/s and in a time range between 0 and 10 days (single use) independently of a partition coefficient range from \(K\) = 0.1 to \(K\) = 10,000. The migration map visualizes the influence of the partition coeffici  
Figure 3: Diffusion coefficients at 20 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C in different polymers: **(a)** PP, **(b)** GPPS, **(c)** HIPS, **(d)** ABS, **(e)** SAN, and **(f)** PET (without bars: molecular weight \(>\) 1000 mg/mol). results. As a quantitative criterion, we suggest considering the partition coefficients in migration modelling when the migration values are above 10% of the migration at equilibrium. Such a 10% criterion is supported by the fact that analytical approaches are also typically associated with a measuring uncertainty in the range of 10%. Therefore, this percentage seems to be a suitable indicator as to whether the dependence of the migration from partitioning is significant or not.