Permeation activation energies
For finding the effects of temperature over permeability, gas sorption, and gas diffusion, the permeation activation energies were calculated for detecting the contribution of each parameter in the permeation of penetrants through the membrane. Permeation activation energy provides a qualitative analysis for testing the permeation mechanism. The temperature dependency of gas sorption, diffusion, and permeability can be described by using the following Arrhenius–Van’t Hoff equations:
\(S=S_{0}\exp{(-\frac{{H}_{S}}{\text{RT}})}\) (9)
\(D=D_{0}\ exp(-\frac{E_{D}}{\text{RT}})\) (10)
\(P=P_{0}\ exp(-\frac{E_{p}}{\text{RT}})\) (11)
here S 0, D 0,and P 0 representing pre-exponential factors of sorption, diffusion, and permeation, respectively. R is used for general gas constant (8.314 kJ.mol-1. K), and Tis the operating temperature (K). ΔH S,E D, and E P are representing the enthalpy of sorption, the apparent activation energy of diffusion, and apparent activation energy of permeability, respectively.
Penetrant sorption in the membrane may be considered as a two-step thermodynamic process: (1) penetrant condensation from a gas phase density to a liquid-like density and (2) opening a gap in the membrane to allow the condensed penetrant to be mixed with the active membrane layer. In order to better understand the role of each thermodynamic phase in the determination of penetrant solubility, these two factors are dealt with separately. The condensation step value was directly measured by reversing the penetrant heat of vaporization, while the other step value was measured by using the following equation,
\({H}_{S}={H}_{\text{cond}}+{H}_{\text{mix}}\) (12)
here the \(H\)S is the enthalpy change of sorption, ΔH cond is the heat of condensation of the penetrant, and ΔH mix is the heat of mixing, which is required for the mixing of gas molecules with the membrane surface.
The equation (12) was used for the qualitative dissolution analysis of penetrants in the membrane. It was noticed that the low mixing heat demonstrated a strong penetrant affinity to the membrane55. The lower mixing value of 15% Ni-ZIF-8 MMM confirmed the higher BD affinity with this membrane relative to pure PDMS, and 15% ZIF-8 MMM. The values are given in Table 1, which shows that ΔH S has negative values for both the gases as the solubility decreased by temperature increase. On the other hand, the N2 showed a positive mixing heat in pure PDMS, 15% ZIF-8 MMM and 15% Ni-ZIF-8 MMM. The positive mixing heat showed less affinity of N2 with pure PDMS while mixing heat increased by 28% in 15% ZIF-8 MMM and 67% in 15% Ni-ZIF-8 MMM. The high mixing heat value strongly supports the low N2interaction with 15% Ni-ZIF-8 MMM.
Table 1. Energy analysis for penetrant permeation through PDMS, 15% ZIF-8 MMM, and 15% Ni-ZIF-8 MMM.