not exist. Thus, the situation [0 1]-[<1 1] can be simulated by assuming that the layer 1 is
stands for the removed layer.
The configurations, which present a "reservoir effect" with unknown Henri like coefficient, can
be approximated similarly. The configurations [1 0]-[1 <1] and [1 0]-[1 >1] are appropriately
overestimated respectively by [1 0]-[1 1] and [1
The proposed approximations are summarized in Figure 8 for a general configuration including n
layers of different thicknesses. The reasoning is applied to each layer individually by applying the
principle of independence of each layer. When reservoir effects are minimized, this reasoning
maximizes the concentration gradient and therefore maximizes the desorption rate. It is
emphasized that this reasoning is different from a superposition principle, because the desorption
rate of the assembled system at a given time is not expected to be equal to the sum of desorption
rates due each individual layer. This is only true at equilibrium according to Equation (19). In the
proposed scheme, the contamination from a trilayer material [C
] is thus calculated from
the cumulated contamination from 3 trilayer materials [C
0 0], [0 C
0] and [0 0 C
trilayer configuration is subsequently approximated by a configuration that overestimates the
contamination from the layer, which contains the substance of interest (see Figure 8a).
The rules of overestimation presented in Figure 8b are applied to a layer (here in position 2)
intercalated between two layers. It is highlighted that the proposed estimation scheme is a
recursive process. Thus, if a configuration [0 0 C
0 ... 0] is replaced by [0 C'
0 0 ... 0] (i.e.
layer 3 is removed), the last configuration can also be replaced by [C"
0 0 0 ... 0] (i.e. the
previous layer 2 is removed). It is worth to notice that this process is accompanied by a change of
the formulation of layers on the left so that the amount of substance is strictly preserved (see the
approximation of layer 3 in Table 3). The removing of formulated layers "in cascade" is
systematic when the chemical affinity of the layer on the left is assumed to be higher than the
currently formulated layer. This process happens also on the right of the formulated layer for all
layers, whose chemical affinity is lower than for the formulated one.
The choice of deciding whose layer has a higher chemical affinity than the reference layer may
seem arbitrary. On the basis of polarity of both the substance and the polymer, it is almost always
possible to justify if the chemical affinity (or almost equivalently the solubility) of the substance
is expected to be higher or not. This kind of reasoning can be applied for several migrating
substances simultaneously according to the partition coefficient of the substance between water
and octanol (also known as logP). Several models are available in the literature to predict logP
values. In absence of data, a worst-case overestimate of
v can be derived by assuming that all
the substance is only contained within the layer 1 in contact with F by discarding all other layers.
A detailed example
The methodology to predict the contamination from multilayer materials in presence of
is tested for a trilayer material presented in Table 3. The equivalent
configurations to overestimate the contribution of each layer to the overall contamination are also
detailed. Several approximations are illustrated via the proposed example: overestimation of a