Sorption and diffusion analysis
For a better understanding of permeation mechanism across the pure PDMS membrane and MMMs, sorption tests were conducted at different temperatures, and a constant pressure range from 0-1.5 bar. As the gas separation in rubbery polymers follows the solution-diffusion model so that both the sorption and diffusion properties of BD and N2 have been measured for pure PDMS, ZIF-8/PDMS MMMs, and Ni-ZIF-8/PDMS MMMs. The isotherm of BD sorption in PDMS is linear, while the ZIF-8 and Ni-ZIF-8 based MMMs showed a slight curve with respect to the ZIFs filling in the membrane (Figure 5 (a) and Figure S11). The concentration of BD in the membrane increased with respect to the loading of the ZIFs particles in the PDMS matrix. The details are given in supplementary information.
The solution coefficients of both gases and solution selectivity are determined by using equations (5) and (6), as shown in Figure 5 (b) and Figure S14(a). The BD solution coefficient enhanced from 24.67 to 35.13 (cm3(STP).cm-3 membrane. bar-1) by incorporating Ni-ZIF-8 particles up to 15% in the PDMS matrix, which is quite similar to the calculated theoretical sorption values of MMMs by using pure Ni-ZIF-8 and PDMS adsorption capacity data (supporting information Table S11). Consistency of experimental and theoretical solution coefficient values verified that no pore blockage of the fillers existed due to polymer chains in the MMM synthesis. The maximum solution selectivity measured was 27.43 for 15% Ni-ZIF-8 MMM at 40°C and 1.5 bar pressure, which was 31% improved by PDMS, and 18% higher than 15% ZIF-8 MMM value. This phenomenon should be ascribed to the intrinsically high adsorption capacity and adsorption selectivity of Ni-ZIF-8 than those of the ZIF-8, and PDMS. The rise in solubility due to the Ni-ZIF-8 filling, possibly due to the decrease in polymer density or high fractional free volume of the MMMs51.
The penetrant solubility in the polymer matrix mainly depends upon two factors. One factor is dependent, and the other is independent of polymer-penetrant interaction52. The values of Hansen solubility parameters of PDMS and BD are given in Table S10, which indicates the difference of 0.94 between BD and PDMS. The lower difference in solubility parameters shows higher polymer-penetrant interaction. The other parameter that influences the penetrant solubility is its critical temperature (T c), which is used to calculate the penetrant condensability. Consequently, the penetrant, which has a high value of T c, shows high condensation and high solubility. The critical temperature of BD is 425K (Table S5), which is much higher than the N2critical temperature (126 K). According to these considerations, BD solubility is higher in PDMS membrane than N2, while the introduction of ZIF-8 and Ni-ZIF-8 also affects the solubility of both the penetrants in MMMs.
Molecular diffusivity is positively correlated with diffusion coefficient (D ) and concentration difference driving force. The diffusion coefficient and diffusion selectivity (α D) data are given in Figure 5(c) and Figure S14. The diffusivity of 15% Ni-ZIF-8/MMM 45% improved by pure PDMS, and 18% higher than 15% ZIF-8/MMM. The increase in diffusivity with respect to Ni-ZIF-8 loading was due to an increase in the fractional free volume of the membrane, and the nano-sized particles enhanced the polymer-filler interface, which provided the efficient gas diffusion channels as compared with pure PDMS, and ZIF-8/MMMs. The diffusion selectivity also improved with respect to the ZIFs loading in the PDMS matrix. Diffusion selectivity of 15% Ni-ZIF-8 MMM showed 39% improvement from pure PDMS, and 16% from 15% ZIF-8 MMM, respectively. The diffusional selectivity has been improved mainly due to the provided channels of Ni-ZIF-8 cavities to BD molecules and less interaction of N2with respect to the Ni-ZIF-8 loadings. As the ideal selectivity is the multiplication of solution and diffusion selectivities, so that the contribution of diffusion selectivity (0.7) of 15% Ni-ZIF-8 MMM to the ideal selectivity (19.5) is low compared to the solution selectivity (27.4), shown in Figure 5(d).
In order to explain the diffusion of penetrants briefly, the effective diameter of a gas molecule for diffusion in the membrane should be known. For this purpose, either collision diameter of Lennard-Jones potential σ LJ or kinetic diameterα kt given by Breck often been used53. The effective diameter of BD estimated at 0.43 nm ( supporting information), which is smaller than its Leonard Jones diameter (0.51 nm)54, but similar to its cross-section diameter (0.44 nm) of the molecule. Therefore, it was estimated that the diffusion of BD molecules through the membrane was based on its kinetic molecule diameter.