Störmer et al.
10.3389/fchem.2024.1397913
comparable adsorptive properties of MPPO versus dry foods. These K values largely overlapped with those obtained by curve fi tting of migration kinetics within FAIR-CT98-4318 (Raffael and Simoneau, 2002; Castle and Franz, 2003). Triantafyllou et al. (2005) determined partition coef fi cients of additional substances between paper and air at 70 ° C and 100 ° C. Migration kinetics at these temperatures into Tenax (Triantafyllou et al., 2002) and semolina, instant baby cream, and milk powder (Triantafyllou et al., 2007) up to equilibrium are reported from this group; however, partition coef fi cients were not calculated. Within the German research project IGF 19016N (Fengler et al., 2019), partition coef fi cients for mineral oil components (MOSH and MOAH) were determined and published in the guideline document (Gruber et al., 2019). Partition coef fi cients of MOSH and MOAH between paper and food range between 1,000 (crystalized sugar or honey) and 1 (chocolate or chopped nuts).
diffusion constants was based only on that of the compound present in free air. Laine et al. (2016) added a term describing sorption to a one-dimensional diffusion equation to simulate migration into MPPO through cardboard in indirect contact and solely through air. The simulated data fi tted well with experimental data on migration into MPPO during an indirect contact in an air- fi lled chamber and after permeation through cardboard using MOSH and MOAH surrogates. Serebrennikova et al. (2022) described the transport by partial differential equations for transporting within the gas phase of the pores in the paper coupled to those describing the sorption process. The transport processes are determined by complex interactions. Diffusion coef fi cients and sorption constants cannot be easily derived from experiments but by fi tting the parameters of the model to the experimental data (solution of an inverse problem). The example was the diffusion of dimethyl sulfoxide in a stack of paper (23 ° C, 50% rH), measured at four time points and spatially dissolved in fi ve paper sheets. For solving the complex differential equations (derived from models for water vapor transport), fi tting to the experimental data, and obtaining the parameters, they used physics-informed neural networks (PINNs) and successfully compared with fi nite element methods. In Serebrennikova et al. (2024), the dimethyl sulfoxide experiment (polar component), extended to 12 weeks, and another one with tetradecane (non- polar) were compared with fi ve different mathematical models, which were evaluated by PINN. Three of them were based on Fick ’ s law of diffusion, with and without a speci fi c term for sorption and desorption. In addition, pseudo- fi rst-order adsorption and second-order reversible sorption models were included. The Fickian behavior models did not fi t the data. The best fi t was observed for a pseudo- fi rst-order adsorption model (without desorption from the fi ber); however, a further search for a suitable function was called for. In general, the authors concluded that PINNs represent a versatile mathematical tool either to validate or to refute the capability of theoretical models to describe experimental data.
6 Discussion
From the published results, key fi ndings, and interpretations summarized under Sections 4 and 5, several discussion points arise, which are presented in the following, concise way: Standard methods to estimate the transfer to foods are extracts with water (cold and hot), solvents (ethanol and isooctane), and migration testing into MPPO. From a physical – chemical point of view, the extracts determine concentrations at partitioning equilibrium in water or solvent. These standard methods have been found to hold potential for overestimation and, in some cases, underestimation of migration into foods, either due to differences in partitioning coef fi cients of paper versus food or extractant and/or being far away from reaching equilibrium in real applications. Therefore, the extracts cannot be considered to reliably represent the real exposure of the consumer from paper food contact materials in most cases. However, only a little study efforts were made toward wetting or aqueous and fatty contacts. Migration into MPPO is used for simulating dry foods (EU food contact material simulant E) and heat contact in oven applications. For the latter, there are diverging protocols regarding the test temperature between Member States, EU reference laboratories, and Council of Europe Technical Guide that will need harmonization. However, for the evaluation of these high- temperature applications, no scienti fi c work was found. For a sound decision, not only oven temperatures but also the usually lower temperatures at the direct contact area in real baking applications for large food pieces (cakes and roast) or the shorter times at these high temperatures for cookies should be considered. Furthermore, for setting harmonized test conditions, temperature limitations to MPPO should be taken into consideration. At temperatures of 200 ° C and higher and in the presence of oxygen from air, MPPO starts to degrade oxidatively, which limits the number of possible reuses after reconditioning. To experimentally simulate migration from paper into dry foods, there is a broad discussion in the reviewed literature if MPPO is suitable at all, or suitable under which test conditions. MPPO has a highly adsorptive power due to its porosity with a large inner surface and its chemistry. If comparing MPPO and dry foods
5.4 Partition coef fi cients
Although mainly the diffusion processes and estimation of diffusion coef fi cients D paper are addressed for the migration modeling, access to other crucial parameter — the partition coef fi cient K paper/food — is also limited. The partition coef fi cients describe the concentration ratio (mass/volume) in the equilibrium. For volatiles, a promising approach determines the partition coef fi cients of paper and food or MPPO versus air. From the quotient of both, the partition coef fi cients K paper/food can be derived. Haack (2006) determined the adsorption isotherms of the volatile model substances such as hexanol and others into paper material (at 40 ° C – 120 ° C), as well as into the foodstuff chocolate, cookies, and pasta — including MPPO as food simulant at 100 ° C — and calculated partition coef fi cients from the data. For hexanol, butyl acrylate, nonanal, and diphenyl oxide, K paper/food values for the three foods ranged from 0.03 to 0.88 and K paper/MPPO for MPPO from 0.02 to 0.08, being strongly on the food side. For butanol, K paper/food was between 1 and 4.3 for foods and K paper/MPPO was 3.3. Overall, these data demonstrate the high or at least
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