Störmer et al.
10.3389/fchem.2024.1397913
equation for B2 with functional consideration of the vapor pressure of the migrants and provided a general migration model for speci fi c and global mass transfer of impurities from the recycled board into the dry food. Barnkob and Petersen (2013) studied the applicability of the paper migration model by fi tting the migration of benzophenone from paper at several humidities (40% to > 73% rH) at 34 ° C, using the approach of Zülch and Piringer (2010). The authors found some differences concerning the applicability of the one- and two-layer approaches, which were small within the quality of the fi ts between both approaches. Han et al. (2016) investigated the migration of photoinitiators into MPPO at 50 ° C – 100 ° C and derived effective diffusion and partition coef fi cients by fi tting the experimental curves to Fickian second law. Huang et al. (2013) included a term for the paper porosity into their model according to Fickian second law. 5.3.3 Other models Contrary to the above-described work, Poças et al. (2011) reported that Fick ’ s second law of diffusion gave poor fi ts in some cases. They studied the migration of several substances with different chemical functionalities from fi ve different paper materials to investigate the in fl uence of molecular size, chemical characteristics of the migrants, and paper characteristics (such as type, thickness, and recycling content). To fi t the migration curves, they explored the potential of Weibull model, which is based on a distribution function triggered by two parameters (scale and shape parameter). It can be empirically applied without the use of physical – chemical parameters, such as D paper and K paper/food . Migration from paper was found to be much faster than those from plastics. The volatility and polarity of the migrants determined their transfer into food (simulant) and the losses from the system due to evaporation. The authors concluded that this simple model allows them to describe the pattern of migration curves for a wide range of migrant volatilities. Guazzotti et al. (2015) applied the Weibull model to fi t kinetic migration curves obtained from paper, spiked with a series of n-alkanes at 40 ° C and 60 ° C in contact with MPPO, con fi rming that this model can effectively be used to describe a diffusional process of the paper. Another statistical approach to correlate physical – chemical properties with migration behavior was recently published by Jaén et al. (2022) using MOAH surrogates (experimental details are given in Section 5.2). The authors applied multivariate analysis algorithms to correlate and group the migration of model substances and built a partial least squares regression model to predict the worst case MOAH migration. The migration patterns showed strong correlations along with the volatility of the surrogates. The elaborated model was capable of predicting migration values from the physical – chemical substance properties and was a useful tool to be further explored. Aurela and Ketoja (2002) studied the diffusion of volatile compounds in fi ber networks by experimental determination and modeling using random walk simulation, which is based on the porosity of the paper sample and the diffusion speed through the pores — assumed to be the diffusion constant in free air. The compounds were volatile solvents, such as ethanol and butyl acetate. The experimental and modeled effective D paper values matched and were in the range of approximately E-7 m 2 /s (E-3 cm 2 /s) at ambient temperature. The estimate of effective
on the effective diffusion constants D paper (understood as the overall diffusion effect within the paper matrix) and partition coef fi cients K paper/food orK paper/MPPO . Effective D paper andK paper/food values were obtained from migration experiments into MPPO and dry foods at temperatures 50 ° C, 60 ° C, and 70 ° C, with eight different paper types spiked and a set of eight migrants. The partition coef fi cients con fi rmed that MPPO serves as a more severe adsorbent than foods. From the D paper values, the effective diffusion behavior of the paper samples was found to be similar to LDPE polymer. In general, at temperatures of 40 ° C and above, migration was dominated by partitioning due to the relatively rapid achievement of equilibrium. At room temperature, diffusion played a bigger role, especially for larger molecules. Therefore, the kinetic model appeared to be more useful in describing short-term contact at ambient temperature and above, e.g., fast foods, and at low temperatures, e.g., chilled and frozen foods. An important fi nding was that no considerable kinetic differences were noted between the different paper materials, as known for different plastic types. Zülch and Piringer (2010) developed an adaptation of the plastics migration model for paper. They studied the migration behavior from different paper samples, spiked with model substances and non-spiked with foodstuffs and MPPO as food simulant at − 18.5 ° C and 22 ° C, and a blotting paper as the acceptor at 40 ° C. From fi tting the migration curve using the plastics multilayer mode of the model (Tosa et al., 2008), they found that in this temperature range transfer from paper will be best described by considering paper as a two-layer system, which is represented by a core layer B1 with relative high diffusion rates and a thin surface layer B2 with different migration behavior. Effective diffusion coef fi cients were estimated in analogy to the A P value approach for plastics (Begley et al., 2005), based on the molecular mass of the migrating substance up to 400 g mol − 1 . For paper, A B1 andA B2 are used as speci fi c parameters with constant A B1 = 6. A B2 value of the virtual surface layer depended on the polarity, humidity in the paper, the water activity of the food, and properties of the migrant ranging between − 10 and − 1 for contact with dry food and up to 6.0 for contact with butter. This two-layer approach is particularly relevant in the case of low temperatures and migrants with high molecular weight. At high temperatures, the best fi t of predicted versus experimental migration data was obtained with a one-layer approach and a common value of A B1 = A B2 = A B = − 2. The authors concluded that the differentiation between the diffusion in B1 and B2 is unnecessary for migrants with low polarity, molecular weights below 350 g mol − 1 at high temperatures ( ≥ 40 ° C), and high humidity due to the strongly increased desorption rate. With this model, the authors present a full migration model into food for foods like butter, chocolate, pasta, wheat fl our, and biscuits at low temperatures (5 ° C, 22 ° C). In 2013, the same group (Hauder et al., 2013) published further work to better understand the necessity of the changing the model behavior from a two- to a one-layer approach, depending on the temperature and tore fi ne the model. The speci fi c diffusion behavior in paper and migration modeling from recycled board into dry foodstuffs using n-alkanes with 15 – 35 carbon atoms and other substances in the board (no spiking) was studied. For the surface region (B2) determining the diffusion rate, the diffusion coef fi cients of these migrants decreased proportionally to their vapor pressures. Based on these fi ndings, the authors modi fi ed the diffusion coef fi cient
Frontiers in Chemistry
10
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