Störmer et al.
10.3389/fchem.2024.1397913
introduced a virtual surface layer to describe the experimental data by Fickian diffusion (Zülch and Piringer, 2010), allowing the use of the same software established for plastics. The diffusion coef fi cients are estimated from a semiempirical equation using 95% con fi dence upperbound parameters. This and other statistical approaches (Weibull and partial least square regression) might be applicable ways for conformity testing but would need further exploration on applicability outside the datasets used for establishment of the parameters. The major research focused on relatively volatile substances (Supplementary Table S1). For non-volatiles and transfer mechanisms other than those via the gas phase, only little work is published. For understanding the impacts of in fl uencing parameters, de fi ning overestimating parameters is not suf fi cient. Transport in the gas phase of the pores and desorption and adsorption on the fi bers need to be considered. These highly complex interactions cannot be simply derived from experiments. However, initial steps are already taken: Hauder et al. (2013) implemented a term for the vapor pressure; Huang et al. (2013) introduced paper porosity in the modeling equation. For volatiles, the random walk simulation in the pores (Aurela and Ketoja, 2002) will be applicable but for less volatiles, adsorption and desorption on the fi bers will play a non- negligible role. Computational approaches by multivariate data analysis and neuronal networks, in combination with physical considerations, are promising. These can help identify the interrelations of various parameters and test the applicability of proposed differential equations and boundary conditions to experimental data. However, the tested models in Serebrennikova et al. (2024) could not yet suf fi ciently describe the processes and demand for further work.
at identical test conditions, MPPO often highly overestimates migration into foods but may also be in the same range (chocolate) or even less severe (milk powder). However, this conclusion depends not only on the properties of the food but also on that of the substances, mainly the volatility. For room temperature applications, migration may increase over months or years, without reaching equilibrium. Thus, accelerated tests are necessary. However, because of the completely different transport mechanism of gas phase transfer, desorption, and adsorption on the paper fi bers in comparison to plastic polymers, an increase in temperature not only accelerates the diffusion rate but also mobilizes substances of lower volatility that would not migrate at detectable amounts at room temperature. The combination of the high adsorptive power of MPPO and acceleration by increased temperature in many cases leads to a high overestimation of migration, as shown in many of the reviewed papers. The conclusions differ: some appreciate the conservative characteristics (Van Den Houwe et al., 2018), whereas others judge MPPO as unsuitable because of the overestimative characteristic (Zur fl uh et al., 2013; Eicher et al., 2015). One approach to overcome this problem is to de fi ne a certain time – temperature condition for migration tests (e.g., 30 min at 70 ° C for short-term contacts), which covers the migration into food in a slightly overestimating way (Dima et al., 2011). Such approaches will need a good statistical basis. Because of the manifold in fl uence factors on migration, a certain time – temperature condition is expected to be valid for a restricted range of substances and food applications. Another approach is to de fi ne conventional transfer rates into foods (i.e., typical or worse case percentage of concentration in material) and analyze the paper material (Zur fl uh et al., 2013). Such a concept ignores the in fl uence of the material thickness on the transfer rate. Furthermore, and more importantly, it will impede developments for the implementation of barrier properties within the papermaking process. Reduction factors applied to the result of migration into MPPO are a further possibility (Castle, 2015). From comparative data of migration into certain food groups or storage applications, typical overestimating factors of MPPO test were derived and conservative factors were de fi ned, which shall be applied for the evaluation of MPPO test results. However, this must be differentiated based on the volatility of the migrating substance and the type of food. Simple reduction factors will be too crude. Therefore, Bradley et al. (2014) proposed further development of modeling as the better solution. Adapting the geometry of the simulant to that of foods using rods instead of fi ne particulate adsorbents is an experimental way to reduce the differences to real foods (Fengler and Gruber, 2022) or using real foods (Eicher et al., 2015; Van Den Houwe et al., 2018). Accepted and validated models — which can simulate the migration out of paperboards into various foods considering the properties of the substances, in fl uences of humidity, paper and food properties, and temperature — will be a solution to overcome all these shortcomings of the experimental tests. However, there is a high demand for research. In the words of Nguyen, the mechanisms and relationships are still poorly understood (Nguyen et al., 2017). At room temperature and below, a non-Fickian behavior was mainly observed. Piringer
7 Conclusion
Numerous scienti fi c attempts have been made — and are still ongoing — to explore the de fi ciencies are and the alternative scienti fi c solutions to overcome the shortcomings of existing testing approaches and data gaps. The scienti fi c efforts were focused, in the fi rst place, on the transfer from paper into dry foods under two aspects: (i) how and under which time – temperature conditions migration into dry foods could be simulated and (ii) what would be an appropriate model to simulate and predict migration into food. Aspect (i): MPPO seems to be the most suitable dry food simulant due to its high adsorptive properties, which makes it a more severe test medium than any dry food but in many cases, a too severe one. For speci fi c applications, representative model foods like polenta or adsorbing rods may serve as options. However, when it comes to the choice of time – temperature contact conditions, there is not enough clarity and targeted precision to match exactly or, at least, very closely the food contact application to be simulated. Several options are discussed but a general approach seems to be dif fi cult. Most of them are related to speci fi c substance groups or volatility ranges and applications. It needs to be explored if the humidity conditions in the experiments need to be de fi ned or not, and
Frontiers in Chemistry
12
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