## 2 Experimental Methodology and Materials
\[V=\frac{R\cdot T}{p} \tag{3}\]  
where:  
\(V\) = molar volume in test conditions, m\({}^{3}\cdot\)mol\({}^{-1}\)  
\(R\) = gas constant: 8.314463 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\)  
\(T\) = gas temperature, K  
\(p\) = gas pressure, Pa  
An amount of hydrogen diffused through the sample in a certain time can be calculated, using the Equation (4). In this case the volume of the downstream side of the setup needs to be determined. This was done by approximation of the inner volume of the pipes, based on the manufacturer's data and measurements of the setup. The volume of the downstream in the setup was 12.0 cm\({}^{3}\)  
\[N_{H_{2}}=\frac{c\cdot\left(\frac{N_{A}}{V}\right)\cdot v_{downstream}}{10^{6}} \tag{4}\]  
where:  
\(N_{H2}\) = amount of hydrogen, diffused through the sample  
\(c\) = measured hydrogen concentration on downstream side, ppm  
\(N_{A}\) = Avogadro's constant: 6.02214076\(\cdot\)10\({}^{23}\), mol\({}^{-1}\)  
\(V\) = molar volume, m\({}^{3}\cdot\)mol\({}^{-1}\)  
\(v_{downstream}\) = volume of downstream side of setup, m\({}^{3}\)  
By knowing the molar volume of one mole of gas in Standard Temperature and Pressure conditions (STP: 0 \({}^{\circ}\)C, 100 kPa), the volume of gas in STP can be calculated, using Equation (5). \[V_{H_{2}}=\frac{N_{H_{2}}\cdot 22.414}{N_{A}} \tag{5}\]  
where:  
\(V_{H2}\) = volume of hydrogen diffused through the sample, cm\({}^{3}\)STP  
\(N_{A}\) = Avogadro's constant: 6.02214076\(\cdot\)10\({}^{23}\), mol\({}^{-1}\)  
22.414 = mole volume of ideal gas in STP, cm\({}^{3}\)  
Using the calculation above, gas permeability coefficient can be calculated with Equation (6). \[P_{H_{2}}=\frac{V_{H_{2}}\cdot l}{A\cdot t\cdot p} \tag{6}\]  
where:  
\(P_{H2}\) = hydrogen permeability coeficient, barrer  
\(V_{H2}\) = volume of hydrogen diffused through the sample, cm\({}^{3}\)STP  
\(l\) = sample length, cm  
\(A\) = sample cross section area, cm\({}^{2}\)  
\(t\) = time, s  
\(p\) = gas pressure (feed gas), cmHg (1 bar = 75 cmHg)  
Permeability coefficient of hydrogen is given in Barrer unit [18], presented in Equation (7). Barrer unit is commonly used for presenting the permeability of membranes. However, it does not refer to the SI system, because of the pressure given in cmHg. Transforming the pressure into the SI unit (for example bar or Pa) is possible, however the results will not be comparable with the common literature data. \[1 barrer=\frac{\mathrm{cm}_{\mathrm{STP}}^{3}\cdot\mathrm{cm}}{\mathrm{cm}^{2} \cdot\mathrm{s}\cdot\mathrm{cmHg}}10^{-10} \tag{7}\]  
Hydrogen diffusion is calculated as a diffusion coefficient D, given in m\({}^{2}\)/s, using the Fick's law [19] and following set of Equations (8)-(12), as well as values received from the Equations (3) and (4). For a gas diffusion through the polymer materials, the transport mechanism described by Fick's Law is accepted [20]. Figure 1:0  
where:  
\(J=\) flux, amount of hydrogen diffusing through the area in time, mol\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)  
\(D=\) diffusion coefficient, m\({}^{2}\cdot\)s\({}^{-1}\)  
\(\phi=\) hydrogen concentration, mol\(\cdot\)m\({}^{-3}\)  
\(x=\) length of hydrogen path, m  
Figure 1:1  
where:  
\(D=\) diffusion coefficient, m\({}^{2}\cdot\)s\({}^{-1}\)  
\(J=\) flux, amount of hydrogen diffused through the area in time, mol\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\)  
\(\phi_{upstream}=\) concentration of hydrogen (upstream), mol\(\cdot\)m\({}^{-3}\)  
\(\phi_{downstream}=\) concentration of hydrogen (downstream), mol\(\cdot\)m\({}^{-3}\)  
\(x_{2}-x_{1}=\) diffusion distance (sample length), m  
For a non-porous polymer material, the tortuosity is equal to 1, thus the assumption can be made, that the hydrogen path is equal to sample length [21].