## 3 Results  
### IRMS Analysis  
Data concerning the \(\xi^{13}\)C values of the shopping bags analyzed in this study are reported in Table 1. Mater-Bi\({}^{\circledR}\) bags were found to be made principally with corn starch (the only declared component) and PCL [22; 23] or partially _bio-based_ copolyester prepared from vegetable oils [24]. Instead, [PERSON] et al. (2015) [25] mentioned that the Mater-Bi\({}^{\circledR}\) bag analyzed in their study consisted of a starch-based biopolymer/polyethylene terephthalate (PET) blend. The \(\xi^{13}\)C values of \(-21.14\pm 0.13\)% and \(-22.87\pm 0.09\)% for ULB and LSB, respectively, suggest a mixed composition of the used blends. In particular, the contribution of starch and polyester components to the bag's composition was estimated by applying a two end-member mixing model. Considering the literature, references [22; 23; 24; 26; 27] and \(\xi^{13}\)C values determined for different polyesters and natural raw materials, corn starch and biodegradable polyesters PCL and PBS were chosen as end-members. Potential raw materials, such as polymers, potato and corn starches (C3 and C4 plants, respectively) \begin{table}
\begin{tabular}{c c c c c} \hline
**Sample Type** & **Mean \(\xi^{13}\)C (\%)** & **SD (\%)** & **n** & **Reference** \\ \hline
**Shopping bags** & & & & \\ \hline Ultra-lightweight food bag—ULB T0 & \(-21.14\) & \(0.13\) & \(5\) & This study \\ Lightweight shopping bag—LSB T0 & \(-22.87\) & \(0.09\) & \(5\) & This study \\ Polyethylene bag—PE T0 & \(-30.41\) & \(0.51\) & \(5\) & This study \\ \hline
**Natural samples** & & & & \\ \hline Corn starch & \(-12.23\) & \(0.10\) & \(3\) & This study \\ Corn & \(-11.38\) & \(0.55\) & \(3\) & [15] \\ Corn & \(-10.7\) to \(-10.8\)** & & \(3\) & [16] \\ Potato starch & \(-25.52\) & \(0.00\) & \(2\) & This study \\ Potato & \(-27.80\) & \(0.01\) & \(2\) & [15] \\ Potato & \(-27.2\) to \(-25.8\)** & & \(3\) & [16] \\ Sunflower oil & \(-29.04\) & \(0.10\) & \(2\) & This study \\ Rapeseed oil & \(-30.14\) & \(0.08\) & \(2\) & This study \\ \hline
**Polymer samples** & & & & \\ \hline Polylactic acid (PLA) & \(-9.48\) & \(0.40\) & \(2\) & This study \\ Polylactic acid (PLA) & \(-13.87\) & \(2.18\) & \(6\) & [15] \\ Polyhydroxybutyrate (PHB) & \(-11.83\) & \(0.20\) & \(3\) & This study \\ Polycaprolactone 10000 (PCL) & \(-27.15\) & \(0.40\) & \(3\) & This study \\ Polycaprolactone 80000 (PCL) & \(-27.33\) & \(0.20\) & \(3\) & This study \\ Polybutyrate succinate (PBS) & \(-27.47\) & \(0.20\) & \(3\) & This study \\ Polyethylene terephthalate (PET) & \(-27.84\) & \(1.71\) & \(7\) & [15] \\ IAEA CH-7 polyethylene standard (PE) * & \(-32.04\) & \(0.04\) & \(3\) & This study \\ \hline \end{tabular}
\end{table} 
Table 1: \(\xi^{13}\)C values for matrices analyzed: mean, standard deviation (SD) and number of replicates (n); * certified value \(-32.151\pm 0.050\)%; ** only range reported. and vegetable oils were considered in this study as possible end-members for isotope mixing analysis. A similar approach was adopted for several environmental studies ([28] and authors cited therein). The following equations were used for mixing calculations (Equations (2) and (3)):  
\[\mathrm{F_{starch}+F_{polyester}=1} \tag{2}\]  
\[\mathrm{\delta^{13}C_{bag}=F_{starch}\times\delta^{13}C_{starch}+F_{polyester} \times\delta^{13}C_{polyester}} \tag{3}\]  
where F is the fraction percentage, \(\mathrm{\delta^{13}C_{starch}}\) and \(\mathrm{\delta^{13}C_{polyester}}\) are the two end-members (\(-11.45\%\) and \(-27.32\%\), respectively) calculated as the mean of values reported in the literature [15; 16] and those determined in this study. The results of mixing calculations showed a higher percentage of polyesters in LSB with respect to ULB (72% and 61%, respectively).