## 2 Results
### Generic Diffusion Coefficient Approach
In the case the migration variation being dependent on the partition coefficient being less than 10%, it is considered that the impact of partitioning on migration is of low significance. A migration variation in this range would not be accessible by experimentation due to the uncertainty usually being in the range of 10% during migration measurements. If the migration range resulting from different \(K\) values has a maximum migration value that is no more 10% higher than the minimum migration value, then the point is colored in light green. For single-use applications, the smallest partition coefficient \(K=0.1\) provides the highest migration result, which is therefore the basis for the migration map. If the influence is higher than 10%, the color changes to dark green at 25%, bluish green at 50%, violet at 75%, blue at 100%, and white at >100%. The map shows the deviation d according to Equation (1), where \(m(K,t)\) is the migration mass for a given \(K\) at the time \(t\). \[d(t)=max_{K}(m(K,t))/min_{K}(m(K,t)), \tag{1}\]  
The migration map provides the possibility of deciding if partitioning needs to be considered at a given diffusion coefficient of the migrant in the material and at a different food contact time. At this point, it should be noted that the main factors of influence for the diffusion coefficient are the polymer type, the migrant, and the temperature. For a single-use food contact applications (Figure 4) at a diffusion coefficient of \(10^{-15}\) cm\({}^{2}\)/s and a contact time of 2 days, the impact of partitioning on migration is of low significance (neglectable < 10%); however, for the same contact time but higher diffusion coefficient of \(10^{-13}\) cm\({}^{2}\)/s, partitioning starts to become significant (75%). Compared to single-use food contact articles, where the food is in continuous contact with the material during a food's shelf life, in repeated-use food contact applications, the food is periodically removed from the material and is brought in contact with fresh portions of food during the service time of the material or article in question. A migration map for a repeated-use food contact application is given in Figure 5. As a result, a diffusion coefficient of \(10^{-18}\) cm\({}^{2}\)/s (position 1 in Figure 5) and a contact time of 6 days (=2 \(\times\) 3 days),  
Figure 4: Single-use: Map of time (t) in days against diffusion coefficient (D\({}_{\rm P}\)) in cm\({}^{2}\)/s. Deviation of migration in mg in dependence from partition coefficient (K\({}_{\rm pF}\)) 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). partitioning demonstrates a neglectable impact on migration (<10%). However, for the same contact time but higher diffusion coefficient of 10\({}^{-13}\) cm\({}^{2}\)/s (position 2 in Figure 5), partitioning plays a significant role (>100%). As seen in Figure 5, the impact of partitioning on migration is equal to that seen in the single-use graph for the first contact period (Figure 4) but differs significantly at the beginning of the second and third and following contact periods when fresh food or when a food simulant is brought in contact with the material. This behaviour can be explained by the time-dependent migration curves in Figure 6, which show time-dependent migration at a fixed diffusion coefficient (10\({}^{-13}\) cm\({}^{2}\)/s) for all partition coefficients (\(K\) = 0.1 to \(K\) = 10,000). It becomes visible that immediately after bringing the material or article in contact with fresh food again, the impact of partitioning is high and lowers over time until the next repeated use occurs. In the initial phase, the migrating amount is much higher for a high partition coefficient (\(K\) = 10,000) compared to a low one (\(K\) = 0.1). The reason for this observation is that in the diffusion-controlled part of the migration curve, the migration is proportional to the migrant's concentration.