2.5. Gas Permeation Measurement

Gas permeability of membranes was measured using single gases with high purity (H₂, CO₂, CH₄) by the barometric technique using a laboratory high-vacuum apparatus with a static permeation cell with an effective area of 5.25 cm² at 30 °C. The membrane sample was placed and sealed in a module which was evacuated. At the beginning of the permeation experiment, the gas under constant pressure, p (150 kPa), was brought into the feed part of the permeation cell. The permeability was determined from the increase of pressure Δp_p in a calibrated volume V_p of the product part of the cell per the time Δt interval during steady-state permeation. The gas permeability coefficient, P_exp, was estimated by the following equation [41]:

where l is a membrane thickness, S is its area, T is the absolute temperature, and R is the gas constant. The permeability coefficient P was expressed in Barrers (1 Barrer = 10⁻¹⁰ cm³ (STP)cm/(cm² s cmHg)). Each experiment was repeated 3–5 times; several membranes of approximately the same thickness and prepared under the same conditions were used. The relative error of permeability value was 1–3%.

The ideal selectivity of gas i relatively gas j, α_i/j, was calculated with the accuracy ± 0.05 according to the following equation:

The diffusion coefficient, D, was calculated from the initial transient regime, which determines the x-intercept that is a time-lag, θ:

The solubility coefficient, S, was calculated using the main gas transport equation:

Correlation analysis of gas transport parameters was performed using the data in Table 1.

Effective diameter, d, and the depth of the Lennard-Jones potential, (ε/k), for the gases under study [42].

The gas permeability coefficient for P84/ND film prepared by inclusion of non-porous impermeable filler in a continuous polymer matrix, P_Maxwell, was calculated using Maxwell model [43]:

where P_P84 is the gas permeability coefficient for pure polymer and ϕ_ND is the volume fraction of nanodiamonds.

The volume fraction of the filler in the polymer matrix was estimated using the equation:

where ρ_P84 and ρ_ND are the density of P84 and ND, respectively, and wt_ND is the weight fraction of the filler in the polymer matrix.