## 4 Results and Discussion  
Diffusivity coefficients for C\({}_{1}\)-C\({}_{3}\) alkanes in PMPentene were calculated using a two-phase model for amorphous and crystalline phases. The results for the crystalline (\(D_{c}\)) and amorphous (\(D_{a}\)) PMPentene phases are given in Table 3.  
As can be seen from Table 3, \(D_{c}\) is significantly lower than \(D_{a}\) at temperatures above T\({}_{\text{g}}\). At the temperatures below T\({}_{\text{g}}\) the values of \(D_{a}\) and \(D_{c}\) are quite close. Detailed explanation of the calculation is done in [18]. Permeability coefficients for amorphous and crystalline phases were obtained from the experimental data using the same approach (Table 4). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **CH\({}_{4}\)** & **C\({}_{4}\)H\({}_{10}\)** \\ \hline \(S\), cm\({}^{3}\)/(cm\({}^{3}\)-cmHg) & 0.025 & 1.49 \\ \(\Delta H_{S}\), kJ/mol & \(-\)17.3 & \(-\)38.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Solubility parameters calculated for methane and butane in PMPentyne at 25 \({}^{\circ}\)C [31]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(D\times 10^{7}\), cm\({}^{2}\)/s & **CH\({}_{4}\)** & **C\({}_{2}\)H\({}_{6}\)** & **C\({}_{3}\)H\({}_{8}\)** \\ \hline \multicolumn{4}{c}{**t = 80 \({}^{\circ}\)C**} \\ \(D_{a}\) & 8.0 & 7.5 & 5.4 \\ \(D_{c}\) & 1.2 & 1.0 & 0.1 \\ \multicolumn{4}{c}{**t = 25 \({}^{\circ}\)C**} \\ \(D_{a}\) & 2.7 & 0.38 & - \\ \(D_{c}\) & 1.5 & 0.38 & - \\ \multicolumn{4}{c}{**t = 10 \({}^{\circ}\)C**} \\ \(D_{a}\) & 1.9 & 0.28 & - \\ \(D_{c}\) & 1.3 & 0.26 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The gas diffusion coefficients in the amorphous and crystalline phases of PMPentene at different temperatures. This approach allows estimation of the permeability and diffusion coefficients in the amorphous and crystalline phases as well as the contribution of the amorphous and crystalline phase influence on the gas transport and selective properties of the membranes based on semicrystalline polymers. The influence of crystallinity degree of PMP on the permeability parameters was investigated in our previous work [18]. It was shown that with increasing crystallinity, the permeability of some gases (namely, lower hydrocarbons) decreases, and at the same time the permeability of helium does not depend on crystallinity. In this case, the separation selectivity for such gas pairs as, for example, helium/methane and methane/butane, increases. In the present paper the theoretical approach to the description of permeability in two-phase systems is proposed as a part of a combined approach for evaluating the contribution of one of the phases (in this case crystalline and amorphous) to the gas transport properties of semicrystalline polymers (or other two-phase systems, such as block copolymers). As for PMPentyne, there is no direct quantitative method to obtain the gas diffusion coefficients in thin polymeric films (very low values of time-lag). One of the options to estimate the diffusion coefficients is to calculate them taking into account certain permeability coefficients (experimental) and the solubility coefficients (calculated, e.g., using Equations (4)-(6)). According to the experimental (\(p\) and \(E_{P}\)) and the calculated (\(S\) and \(\Delta H\)s) values, the diffusion coefficients \(D\) and the diffusion activation energies \(E_{D}\) for methane, ethane, propane and n-butane were estimated. The results of this evaluation for methane and butane are presented in Table 5.  
Thus, we fulfilled the estimation of the gas transfer parameters for the C\({}_{1}\)-C\({}_{4}\) alkanes through PMPentyne membranes, which allowed a comparative analysis of obtained values for PMPentyne and PMPentene. The results of this comparison at different temperatures (10, 25 and 80 \({}^{\circ}\)C) are shown in Figures 4-9.