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.