## 3 Results and Discussion
### Diffusion Coefficients from Permeation Kinetics  
The permeation curves of six 1-alcohols through a 34 \(\upmu\)m biaxially oriented GPPS film were determined in this study. The diffusion coefficients were determined from the lag times of the permeation curves according to Equation (2). The lag time tlag is defined as the intercept of the asymptote to the permeation curve on the time-axis [22]. In previous studies, the same method was applied on thin films of oriented polyamide (PA6) [24], polyethylene terephthalate (PET) [23; 25], polyethylene naphthalate (PEN) [26] and ethylene vinyl alcohol copolymer (EVOH) [27]. Examples for the experimental permeation curves for 1-butanol through the investigated GPPS film at temperatures between 60 \({}^{\circ}\)C and 90 \({}^{\circ}\)C are given in Figure 2. The permeation curves of the other substances measured within this study follow a similar behavior. The diffusion coefficients D\({}_{\text{P}}\) for the applied 1-alcohols are summarized in Table 5. Permeation tests with \(n\)-alkanes failed because the film became brittle and broke under the applied temperature and concentration conditions. The lag times and diffusion coefficients in the biaxially oriented GPPS film were determined at temperatures between 0 \({}^{\circ}\)C and 90 \({}^{\circ}\)C. However, it was only for methanol and ethanol diffusion that coefficients could be determined at temperatures of 0 \({}^{\circ}\)C and 25 \({}^{\circ}\)C, because the diffusion coefficients D\({}_{\text{P}}\) of all other 1-alcohols were too low at ambient  
Figure 2: Experimental permeation curves for 1-butanol at 60 \({}^{\circ}\)C, 70 \({}^{\circ}\)C, 80 \({}^{\circ}\)C and 90 \({}^{\circ}\)C (lag time at 70 \({}^{\circ}\)C: intercept of the red line on the time-axis). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Temperature (\({}^{\circ}\)C)** & \multicolumn{5}{c}{**Diffusion Coefficient (cm\({}^{2}\)/s)**} \\ \hline  & **Methanol** & **Ethanol** & **1-Propanol** & **1-Butanol** & **1-Pentanol** & **1-Hexanol** \\ \hline
0 & \(1.2\times 10^{-9}\) & \(2.8\times 10^{-11}\) & & & \\
25 & \(2.2\times 10^{-9}\) & \(1.7\times 10^{-10}\) & & & \\
40 & \(3.1\times 10^{-9}\) & \(3.8\times 10^{-10}\) & \(2.5\times 10^{-11}\) & \(2.7\times 10^{-12}\) & \\
60 & \(2.7\times 10^{-9}\) & \(1.0\times 10^{-9}\) & \(1.0\times 10^{-10}\) & \(1.7\times 10^{-11}\) & \\
70 & \(2.1\times 10^{-9}\) & \(1.0\times 10^{-9}\) & \(2.0\times 10^{-10}\) & \(4.1\times 10^{-11}\) & \(9.3\times 10^{-12}\) \\
80 & \(2.4\times 10^{-9}\) & \(1.4\times 10^{-9}\) & \(3.5\times 10^{-10}\) & \(8.5\times 10^{-11}\) & \(2.1\times 10^{-11}\) & \(4.2\times 10^{-12}\) \\
90 & \(2.4\times 10^{-9}\) & \(1.6\times 10^{-9}\) & \(5.6\times 10^{-10}\) & \(1.7\times 10^{-10}\) & \(4.8\times 10^{-11}\) & \(1.3\times 10^{-11}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Experimentally determined diffusion coefficients D\({}_{\text{P}}\) in GPPS of 1-alcohols from permeation kinetics. temperatures. Diffusion coefficients increase significantly with molecular volume and therefore the lag time increases accordingly. For example, given a diffusion coefficient \(\mathrm{D_{P}}\) of 9.2 \(\times\) 10\({}^{-15}\) cm\({}^{2}\)/s, which is the expected diffusion coefficient of 1-butanol from the results of this study, a lag time of 6.6 years is predicted according to Equation (2). Raising up the temperature to 30 \({}^{\circ}\)C, the lag time is still around 3 years and hard to be measured in a reasonable time. Thinner GPPS films, which will lead to significantly lower lag times for larger molecules, are not available on the market and also the handling with such thin and brittle films is difficult. Therefore, higher temperatures need to be applied for 1-alcohols starting from 1-propanol. It is interesting to note that the diffusion coefficients for methanol are more or less similar in the range of 1 to 3 \(\times\) 10\({}^{-9}\) cm\({}^{2}\)/s at all applied temperatures, which indicates that the activation energy of diffusion is virtually zero.