Time of protection equivalence principle to allow design barrier layers for promoting the use of recycled materials for food contact

European and national environmental protection policies have programmed the forthcoming end of single-use plastics, including food packaging. Because plastic materials account for 50% of plastic waste, closed-loop recycling seems imperative. Still, plastics other than PET (Polyethylene terephthalate) are not widely recycled for food contact due to safety concerns. Among them, post-consumer polyolefins are heavily formulated, degraded, and contaminated by the previously contacting product. Using recycled materials behind a functional barrier (FB) could resolve the issue under specific provisions, but neither the European regulation nor the US FDA offer guidance concerning functional barriers evaluation and use. Mathematical modeling is the only viable method recognized by European and American agencies to evaluate recycled material under usage conditions. This study numerically explores the possibility of combining two effects: decontamination of the recycled material and a functional barrier to allow safe use of the recycled material.

particularly behind a functional barrier. The concept of a functional barrier is initially based on the idea of a diffusion barrier that delays migration without changing the final fate (Feigenbaum. 2005). This barrier is not absolute but only temporary. It must be appropriately chosen and scaled to ensure food safety. Modeling tools are already widely used in Europe, USA, and China. They are recognized in European (Hoekstra et al. 2015) and American (Schwope et al. 1990) practical guides and their state of the art has been taken up in the reference book . The use of a functional barrier is already accepted in the European plastic regulation (regulation (EC) 10/2011). The difficulty for the plastic material is related to contaminants whose nature, toxicity, and quantities are not known a priori. The analysis must be generic and robust. The working hypothesis is based on a dimensionless formulation that allows comparing a solution with or without a barrier for various levels of decontamination. This approach potentially covers all thermoplastics, substances, geometries, and uses. The novelty of the described concept lies in the fact that a lower decontamination rate is envisaged in the presence of a functional barrier when using nonauthorized materials for food contact. The text is organized as follows: the next part presents the mathematical model and the approximate solutions and the description of a case-study. The results are discussed in the third section. In particular, the aim is to show solutions where the barrier does not add waste and discuss the barrier's performance. The conclusions are finally summarized.

Acceptable thresholds
EFSA set rules to evaluate food contact materials regarding the risk of exposure to non-evaluated substances. Post-consumer recycled materials are a significant source of unknown chemicals potentially harmful. An acceptable level of exposure can be established according to analytical, chemical structure analogy (e.g., Cramer class) or a regulation threshold (e.g., the US TOR defined under 21 CFR 170.39), as summarized in Table 1.The most conservative thresholds have been jointly defined by EFSA and WHO and are coined thresholds of toxicological concern (TTC). For genotoxic substances, the TTC value corresponds to a maximum chronic daily exposure of 0.0025 µg −1 .kg −1 BW.day −1 . Its conversion into maximum acceptable concentration in food reads: A bodyweight of 60 and 5 kg is taken for adults and infants, respectively, with 1 and 0.75 kg daily intake respectively (Barthélémy et al. 2014). As discussed by , the ℎ ℎ , value of 0.15 mg⋅kg -1 for adults is far below the detection limit of the most commonly used analytical techniques, around 10 mg⋅kg -1 . Only modeling and numerical simulation can demonstrate that this threshold is not exceeded for low molecular weight surrogates. Current scenarios that EFSA considers use concentrations in recycled streams of 3 and 10 3 mg⋅kg -1 as conservative values for PET and polyolefins, respectively.

Mass transfer model
Without a loss of generality, the studied cases described mass transfer between recycled material (layer indexed = 2) and food (layer indexed = 0) separated by a functional barrier with an index = 1. Mass transfers are described in one dimension, as shown in Figure 1. The thicknesses are denoted { } =0,1,2 with an equivalent food thickness 0 = , where is the food volume and is the surface area in contact. The transport model of contaminants is like the one used in (Nguyen et al., 2013) and . It fulfils the assumptions recommended to evaluate the compliance of plastic materials intended to be in contact with food according to the European Regulation (EC) 10/2011. It assumes a diffusionsolubilization model in each layer and the food with a Henry-like isotherm with a constant Henry coefficient and a diffusion coefficient . By denoting the cumulated thicknesses: 0 Σ = 0, 1 Σ = 1 , 2 Σ = 1 + 2 , and the concentration profile , , the transport assumptions read in the polymer: An implicit model is used for the food layer ( = 0) and implemented as boundary layer of the third kind, also known as Robin boundary condition at the food-packaging interface ( = 0): This condition enables to account for the accumulation in the food and the partition coefficient between the food in contact and layer 1 ( 1 0 ). Far from the interface, the concentration in the food, , is assumed to be uniform. Close to the interface, ℎ is the mass transfer coefficient, with units in m 2 ⋅s -1 and representing the mass transfer resistance on the food side. The amount within the boundary layer is assumed to be negligible compared to . The initial concentration in the recycled layer at = 0 is given by Equation (4) where 0 ≤ Δ < 1 is the decontamination rate and the maximum concentration in the source of recycled materials.

Dimensionless mass transfer model
Migration from layer 2 to layer 1 starts during processing, as we showed (Dole et al., 2006), but coupling heat and mass transfer complicates the extrapolation of results from specific cases to more general ones. The difficulty can be partly circumvented by introducing a dimensionless formulation and cumulative time effects, as shown in . The dimensionless time can accommodate the variation of 2 with time due to temperature:  : Time at which concentration in food is the same in each system a,b,c).
For a given recycled stream (the same ) and plastic design (same 2 and 2 values), different values of * are therefore expected for different decontamination rates Δ and functional barrier thicknesses 1 . Two situations (see Figure ) are particularly relevant, denoted REF (reference) and TST (alternative): • REF: No barrier ( 1 = 0) but a decontamination level, Δ .
The reference situation * (Δ, 1 = 0) accepts a trivial approximate solution from Eq. 4.20 in Crank's book (Crank, 1975 . All effects are non-linear and should be explored rigorously before proposing a solution for a given polymer or application. The system is also strongly constrained. Since it is preferable to minimize the thickness of the barrier ( 1 * < 1) to minimize wastes, 1 * should be also lower than 1 ( 1 * ≪ 1 * ). That is to say that the functional barrier should be chosen among the best polymer or coating barriers and not interfere with the subsequent recycling of the material.

Studied case and simulation methodology
The studied case corresponds to 100µm thick PP trays covered internally with a 10µm PET layer. The simulation details are shown in Table 2. The considered contaminants of recycled PP are homologous aromatic surrogates: toluene, biphenyl and p-terphenyl, with a 1000 mg.kg -1 initial concentration and decontamination levels (∆ , ∆ ) range from 0% up to 99.9% (vacuum evaporation). Toluene is used as the reference evaluation substance with an acceptable threshold set to ℎ ℎ , .  Vitrac, O.,Hayert, M. (2005). (e) Typical value for trays and bottles.
As detailed by , all simulations were carried out with the open-source FMECAengine (Vitrac andNguyen 2014-2019). (Fang et al., 2013(Fang et al., ) et al. (2013 methodology was used to scale diffusion coefficients of linearly repeated aromatic jumping units according to Equation (11), 0 refers to the molecular weight of reference solute, toluene in this case.

Protection time equivalence of functional barrier with direct food contact
Simulated contamination kinetics for REF and TST conditions with toluene are plotted in Figure 3a.
As predicted by Eq. (10), a minimum thickness of the functional barrier can offer the same protection for the consumer as a decontamination level ∆ (equivalent times are marked by intersections). This protection is useful and robust only if it fulfils three conditions: (i) it is lasting longer than lag time (pure diffusion barrier), (ii) it does not double the amount of wastes ( 1 * < 1) and (iii) < ℎ ℎ , . Food shelf-life considerations are not introduced here, but it is more and more accepted to adjust the effective shelf life with the acceptable chemical risk for the consumers. For polyolefins and low molecular weight compounds (with high diffusivities), adding a functional barrier is not enough and a decontamination step is essential to get a protection equivalent to Δ > 0.99 or more. The depicted REF condition (dark red curve) describes a thermodynamic equilibrium achieved in about 2.3 days. That is to say that the concentration in food is entirely determined by (1 − Δ )/ 0 * after 3 days.
It corresponds to a value 6.7 times larger than ℎ ℎ , for REF at the decontamination level of Δ = 0.9999 which is the maximum value feasible realistically by the industry (for 0.999, the threshold is exceeded 67 times). The missing protection can be brought by combining a high Δ and a functional barrier delaying the equilibrium. As a rule of thumb and to avoid the production of extrawastes, the virgin functional barrier (layer 1) should be more barrier than the recycled polymer (layer 2). In the depicted TST condition, lag-time is comparable to equilibration time for toluene (1.5 days) and almost negligible. The protection is brought in the permeation regime when the concentration level is almost linear with time. In this regime, the linearity highlights those ten times higher protection (10 times longer shelf-life or service-life for the material) and requires either to multiply by ten the thickness or to divide by ten the factor 1-Δ .

Solute size effects
For bigger solutes, simulated conditions are plotted in Figure 3 b and c. As expected, a shift appears toward higher protection time equivalences. Table 3 show a report of those equivalent times for toluene and biphenyl, according to decontamination levels Δ for TST and Δ for REF situation. During a certain amount of time, the TST alternative solution is even safer than the REF condition. The risk assessment of a functional barrier relies on two conditions: (i) it has to be at least as safe as a highly decontaminated monolayer (today no recycling process is authorized and able to do such a thing, this is why the use of functional barriers has a big interest) and (ii) a compromise has to be found between the condition (i) and the fact that for large contaminants there is no need to target higher protection times than small ones since they migrate faster, allowing in some applications to lower the initial decontamination of large contaminants. The existence of a substance-dependant scaling law for equivalent times aims to target the decontamination needs according to the profile and extract good dimensioning practices to avoid considering large contaminants. The thickness of the functional barrier needs to be sufficient to accommodate shelf life and the storage of the material before use.

4-Conclusions
Conservative rules have been identified for homologous aromatic surrogates to assess the risk of using non-authorized materials for food contact behind functional barriers. The development of this concept