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.