## 2 Results  
### Generic Diffusion Coefficient Approach  
Within this chapter, the influence of the partition coefficient on migration was investigated using a generic approach that was based on different diffusion and partition coefficients. This approach is based on the following well-known observations:  
* The migration rate of a substance in a polymer itself mainly depends on the diffusion rates of the migrant in the material. The diffusion rates depend on the material type (mainly mobility of the polymer at molecular level), migrant (mainly size of the migrant), and temperature (random movement induced by temperature). The diffusion rate is therefore represented by a diffusion coefficient. The diffusion coefficient can be considered to be a \"material\" constant for the combination of the polymer, substance, and temperature. * The migrating fraction is related to the initial amount of a substance from a polymer to a contact medium and mainly depends on the partition coefficient of the migrant between the polymer and contact medium, e.g., food, simulating solvent, cosmetic or pharmaceutical formulation, drinking water, etc. The partitioning might be also temperature dependent. The partition coefficient is the constant for a polymer, substance, contact medium, and temperature. * The migrating amount of the substance depends in addition on its initial concentration \(\rm c_{P0}\) in the polymer and the thickness of the material, i.e., the absolute amount in the system. Based on the above-mentioned well-known observations, the migration process in this generic approach can be displayed using diffusion coefficients, partition coefficients, material thicknesses, and concentrations. Due to the fact that the migration is directly proportional to the concentration in the material, the generic approach can be simplified if the migration is displayed as a percentage of the maximum migration at equilibrium. Based on the above summarized dependencies, the migrating amount in mg/L for a single use item is plotted against the storage time between the polymer and the contact medium for different partition coefficients. For each graph, the diffusion coefficient of the migrant in the material, the initial concentration of the migrant in the material, and the material thickness have fixed values. The migration was calculated for several packaging material thicknesses (50 \(\rm\upmu\)m, 100 \(\rm\upmu\)m, 200 \(\rm\upmu\)m, 500 \(\rm\upmu\)m, and 1000 \(\rm\upmu\)m) with an initial concentration of \(\rm c_{P0}=100\) mg/kg in the material. The surface volume ratio was set to V = 1000 mL and A = 600 cm\({}^{2}\), which represents a generic packaging, the so-called \"EU-cube\". Figure 1 (thickness 50 \(\rm\upmu\)m) and Figure 2 (thickness 500 \(\rm\upmu\)m) show the predicted migration in terms of the dependence of the diffusion coefficients \(\rm D_{P}\), which range from 10\({}^{-10}\) cm\({}^{2}\)/s to \(10^{-15}\) cm\({}^{2}\)/s, and partition coefficients, which range from K\({}_{\rm{PF}}\) = 0.1 to 10,000. These parameter ranges represent typical real scenarios for food contact materials. For parameter values that are outside of this range, the impact of the partition coefficient could be different. Similar graphs for other packaging thicknesses are given in the Supplementary Data. The storage time in this generic approach was assumed to be up to 365 d. Even if the topic of this publication concerns short-term contact, the migration results for storage times of up to 365 d seemed to be useful for understanding the diffusion and partitioning process in food contact materials. In case of short-term contact, the maximum storage time was below 10 d, and in most cases, it was below 1 d.  
As shown in the figures, high diffusion rates in combination with long contact times results in the partition coefficient demonstrating a strong influence on the migration results. In this case, maximum migration is reached within the storage time. As expected, the partition coefficient also has an influence on the migration amount.