*Condensation heat was evaluated at 40°C
Form the previously reported data 57, it was noticed that the ln(D 0) is proportional to the activation entropy change. Thus, the decreased diffusional activation energy in 15% Ni-ZIF-8 MMM confirms that the activation entropy change is less in the 15% Ni-ZIF-8 MMM relative to the pure PDMS, and 15% ZIF-8 MMM. Besides, Barrer’s “zone” theory of diffusion also states that a penetrant molecule executes a diffusion jump in an activated zone comprising segments of polymer molecules near the diffusing penetrant molecule. So, the size of the activated zone is also associated with both E D and activation entropy (lnD 0). Consequently, the larger the size of the activated zone required for diffusion, the higher is the diffusional activation energy and the entropy change, which is associated with the creation of the activated zone58. Therefore, it was concluded that the addition of Ni-ZIF-8 in PDMS reduced the size of activated zones for BD molecule jumps for diffusion, and also reduced the entropy change. Moreover, the permeation activation energy of BD reduced 66% in 15% Ni-ZIF-8 MMM from PDMS, and 27% less than 15% ZIF-8 MMM. Contrary, the permeation activation energy of N2 in 15% Ni-ZIF-8 MMM showed a 43% increased from PDMS and 19% higher than 15% ZIF-8 MMM.