## 3 Results and Discussion
### D\({}_{\text{app}}\) Values of Additives in Neat and Nanocomposite Aged Materials  
The estimation of the D\({}_{\text{app}}\) of each additive from the biopolymer into fatty food simulants is reported in Figure 7 (PHBV) and Figure 8 (PBSA), showing the respective impacts of: polymer type, food simulant, nanoparticle incorporation and accelerated aging. Figure 6: Univariate plot summarizing the distribution of relative migration values as a function of aging treatment applied to neat and nanocomposite PBSA (**a**) and PHBV (**b**) materials in contact with 95% ethanol and isooctane. Figure 7: Comparison of D\({}_{\text{app}}\) values of additives in PHBV, PHBV NCP and the corresponding aged materials in contact with 95% ethanol (**a**) and isooctane (**b**). The differing scales of the histograms highlight the impacts of the polymer type and the food simulant, these observations having already been established and commented on a previous study performed on untreated material [11]. The accelerated aging does not impact this range of scales; the apparent diffusion coefficient ranking is as follows: PBSA/95% ethanol > PBSA/isooctane > PHBV/95% ethanol > PHBV/isooctane. However, contrasted results due to the treatment of materials were obtained depending on polymer type and food simulant in contact. The effect of the presence of nanoclays in the PHBV is very significant (\(n<0.0001\)), leading to a dramatic increase in the diffusivity values of almost all additives, whatever the food simulant in contact. However, this effect does not apply to the particular case of higher molar mass compounds for which the influence of nanofillers is more difficult to identify. This increase in the diffusivity of low molar mass molecules may appear in opposition to an expected tortuosity effect due to the presence of nanofillers and an increase in crystallinity induced by UV treatment. The most tangible hypothesis to explain this behavior is the macroscopic damage of the films induced by the aging process. It is indeed likely that the accelerated aging of materials will produce microcracks, generating diffusion channels, particularly for the most volatile compounds. This effect should be enhanced by the presence of inorganic nanoclays whose differences in mechanical strength with the polymeric matrix could generate channels at the non-cohesive interface between the two phases. The effect of UV treatment is noticeably different for PBSA-based materials. For aged PBSA materials in contact with 95% ethanol (Figure 8a), a significant decrease of the D\({}_{\rm app}\) was observed (\(n<0.0001\)) for each additive compared to each unaged one. These results are in accordance with those of the degree of crystallinity reported in Section 3.1. This decrease was additionally observed for PBSA NCP, suggesting an apparent tortuosity effect associated with a nucleating effect of nanoclays. Surprisingly, the UV treatment induces, on the contrary, an increase in the diffusion of the compounds in the neat PBSA when it is placed in contact with isooctane, this behavior being difficult to explain at the scale of observation of this study. Regarding the influence of nanoclays on aged materials, a conventional impact was observed for PBSA and PBSA NCP; that is, nanoclays decrease the D\({}_{\rm app}\), while a non-conventional impact was evidenced in the case of PHBV and PHBV NCP. These results suggest that the degree of crystallinity is not sufficient to explain the transfer properties of a material, since the measure of the crystallinity degree measured on all of the samples does not evidence any impact of the incorporation of nanoclays. It is therefore likely that the combined effects of nanoclay and UV treatment induce structural reorganizations of polymer chains which need  
Figure 8: Comparison of D\({}_{\rm app}\) values of additives in PBSA, PBSA NCP and the corresponding aged materials in contact with 95% ethanol (**a**) and isooctane (**b**).