While considering a model porous structure, we have set the following criteria: i) preconceivable nanometer pore size and geometry, ii) periodically arranged pores with specific orientation, iii) chemical tunability, and iv) ease of assembly as a thin film at micrometer length scale (so that it can be related to a membrane-type structure). Among the contemporary porous materials, MOFs qualify with these criteria. MOFs consist of inorganic metal or metaloxo nodes and functionalized organic linkers,37,38 which are linked by reversible and directional coordination bonds. The choices for metal and linkers are virtually infinite, and the possible structural topologies are also numerous. To name a few benchmark examples where molecular diffusion and gas adsorption selectivities have been studied in details and possible applications for membrane based gas separation have also been performed, are ZIFs (Zeolitic imidazolate frameworks), UiOs (University of Oslo), MILs (Material Institute Lavoisier).35,39−43 In our present approach, we have considered a rather simple PCU topology that can afford biporous (two different pores), 3D connected nanochannels. One advantage of this type of topology, otherwise also known as pillared-layer MOFs,44–46 is that these structures can be grown as a thin film in an oriented fashion47–49 and two different types of pores can be arranged in a preconceived orientation.
The selected model structure is Cu(BDC)(pillar) MOF, where the pillars are Py-X = X-Py (Py = pyridyl, X = CH and N) (Fig. 1a). The Cu(BDC) 2D square grids are formed by linking Cu-paddle-wheels with benzenedicarboxylic acid (BDC) linker along the ab plane and these 2D sheets are pillared by Py-X = X-Py along the c-axis (along [001]) forming an extended pillared-layer structure (Fig. 1a). This 3D structure features two types of pores, one of them has a window size of ~ 7.3 × 4.3 Å along the c-axis while the other one comes with a pore size of ~ 9.7 × 6.9 Å along the ab plane. These pore sizes are estimated by adding van der Waals radii of the atoms in the simulated structures (see computational details). Herein, we have two types of pillared-layer (PL) structures, denoted as PLC=C and PLN=N. The only difference between the two structures is their pillar linker functionality, one having -C = C- while the other one with -N = N-. Note that the smaller pores are chemically equivalent but different chemical functionalities are present at the larger pore (2-times larger), (see Fig. 1a).
To synthesize the model structures and perform the molecular diffusion studies, we have grown oriented thin films of both PLC=C and PLN=N using well-known LPE method in an lbl fashion. The surface functionalization with –OH end groups is used to grow the oriented thin films. Each cycle progresses by alternately exposing the substrate surface to a solution of copper (II) acetate (1 mM) and mixed organic linkers (BDC (0.2 mM) and one of the pillar linkers (0.2 mM)) using an automatized pump system (see experimental section for details). By repeating the number of cycles we could obtain homogenous and pinhole free ~ 250 nm thick films (Fig. 1a, Figure S1). These synthesized films were characterized using powder X-ray diffraction (PXRD) and Raman spectroscopy (Figures S2 and S3). Figure 1b shows the out-of-plane (OP) PXRD along with the simulated PXRD patterns. In the OP PXRD, the diffraction peaks appear at ~ 5.4, 10.8, and 16.3°. Comparison of these peaks with simulated PXRD suggests that these peaks are related to (00l) planes of the PLC=C. In the in-plane PXRD, we have observed the diffraction peaks corresponding to the orthogonal planes ((100), (010) and (110), see Figure S2). This observation confirms that the PLC=C structure is oriented along the (001) or c-direction where the smaller pores are vertically aligned, (hereafter called as WV) and the larger pores are parallel to the substrate plane (along the ab plane, hereafter called as WH). PLN=N thin film also exhibits similar growth orientation, as can be confirmed from the PXRD patterns (Figs. 1b and S2).
Because of the crystal growth preference along the c-axis, the surfaces of both thin films are populated with the WV pore windows as shown in Fig. 1a. Hence, during the molecular diffusion into the thin film steps A and B (vide supra) should be similar for both PLC=C and PLN=N. Diffusivity will differ, only if the different chemical functionalities come into play or the larger pores WH controls the diffusivity. To study this, we have measured mass uptake rates of the PL thin films grown on quartz crystal microbalance (QCM)25 sensors with –OH functionalized Au-surface. Methanol (kinetic diameter ~ 3.6 Å) is used as a probe molecule because it is compatible with the pore size of the WV pores and has high vapour pressure at ambient temperature. The QCM sensors coated with the PL thin films were mounted in a fluidic cell in a temperature controlled environment. The saturated methanol vapor (~ 15.8 kPa) uptake profiles were recorded at 298 K by monitoring the fundamental frequency change (Δf) over time (t). The mass change (Δm) per area is calculated using the Sauerbrey equation:
\(\varDelta m= -c\frac{\varDelta f}{n}\) …Eq. (1)
where n denotes the overtone order and c is the mass sensitivity constant.25
In Fig. 2a, the fractional mass uptake is plotted against the uptake time in linear and logarithmic scale. At lower fractional uptake (< 20%; molecules entering from the vapour phase into the pore, i.e. steps A and B) both PLC=C and PLN=N shows linear uptake behavior and almost no difference in the uptake rate. But beyond this regime, when the interpore diffusion step C, dominates the mass uptake rate, the uptake rate slowed down for PLN=N as compared to that of PLC=C for similar thickness of the films (~ 250 nm, saturation mass uptake time is ~ 2x slower for PLN=N compared to that of PLC=C) (see Figure S4). For a larger molecule (1-butanol; kinetic diameter ~ 4.6 Å) also we observed the uptake rate difference at the higher mass loading regime only (see Figure S5). These observations indicate that at lower mass loading, i.e. when methanol molecules are mostly near the surface, diffusivity rates are controlled by the pore windows which are similar in PLC=C and PLN=N, i.e. WV. Note that at this regime of mass uptake, concentration gradient is maximum, and it is probably obvious that methanol molecules will diffuse along the gradient through WV. The surprising difference in the uptake saturation time indicates that the larger pores WH do play an important role even though diffusion through these pores are orthogonal to the concentration gradient. Moreover, the WH sizes are similar for PLC=C and PLN=N, hence it must be the different chemical functionalities that are controlling the diffusion rate. In the following discussion, we reveal that diffusion through WH pores is indeed rate limiting for the interpore diffusion and can be tuned by chemical design.
To ascertain that the dominating diffusion path for steps A and B involves WV pores only, we have compared the methanol diffusivities of the different types of PLs (designed by using different pillars; 1,4-diazabicyclo[2.2.2]octane or DABCO, Py-S–S-Py, Py-N = N-Py and Py-CH = CH-Py with Cu(BDC) 2D layer) at lower mass uptake regime (Figs. 2b and S4). In these PLs, WV dimensions, orientations and chemical functionalities are identical (see the out and in-plane XRDs in Figures S6, S7). For PLDABCO, WH pore dimension (~ 3.1 × 4.0 Å) is smaller than the other PLs. The estimated diffusivity values at 298 K are found to be similar; D = 1 × 10− 16 for PLC=C, 1.6 × 10− 16 for PLN=N, 1.8 × 10− 16 for PLDABCO and 1.7 × 10− 16 m2s− 1 for PLS−S (see Figure S8). Note, that change in the pore structure and chemical functionalities can change the diffusivities by an order of magnitude or higher, as we observed for ZIF-8 methanol diffusivity (Fig. 2b, Figures S9 and S10, ZIF-8 is a cage like 3D porous structure having pore window dimension of ~ 3.5 Å). We have also compared the activation energy (EA) and enthalpy of adsorption (ΔH) for the PLC=C and PLN=N for methanol (see Figures S11, S12) by measuring mass uptake at different temperatures. We found that the differences are very small (ΔH = ~ 24.3 (± 2.1) and 27.4 (± 3.2) kJ/mol and ΔEA = 26.9 (± 2.4) and 30.8 (± 2.7) kJ/mol for PLN=N and PLC=C), Fig. 2c and 2d). The EA is estimated by the diffusivities at lower uptake regime, hence similar EA values confirms the hypothesis that steps A and B involve mostly WV pores. Similar ΔH values indicates that the adsorbate-adsorbent interaction differences are small enough, to be identified by the present experimental setup.
The PLs presented in Fig. 1a do exhibit distinct time differences in the saturation uptake, and this can be attributed to the following features: i) structural defect densities, ii) cooperative effect between adsorbed molecules, iii) lateral diffusion through WH pores with different functionalities. We rule out the defect densities, because in that case mass uptake rate will be affected also at the lower mass loading (steps A and B). To test the impact of cooperative effect, we have compared the percentage change in the rate of mass uptake (slope %) vs. fractional mass loading at two different temperatures (298 and 315 K, Fig. 2e). We observed that with increasing mass uptake, rate increases. It indicates that the methanol-methanol cooperative interaction at higher loading accelerates mass uptake. Furthermore, at lower temperature the change in the slope percentage is higher for both the PLs. This is probably due to the stronger methanol-methanol interaction at the lower temperature, indicating presence of similar cooperativity in both the PLs. Hence, methanol cooperative interaction is not rate limiting at higher mass loading.
In light of the dependence of interpore diffusivities the WH pores, which are stationed orthogonal to the concentration gradient, we postulate that the effective diffusion is governed not only by the concentration gradient but also by the pore window size. At the lower uptake regime, during steps A and B, concentration gradient is highest and hence, it dominates the mass uptake rate. At higher mass loading (when the interpore diffusion dominates) concentration gradient continuously decreases, and the pore window size becomes the rate limiting factor. In the present case 2x larger size of WH, as compared to WV, dictates the diffusion path during interpore diffusion at low concentration gradient. This is contrary to the common notion of Fickian diffusion, and can be generalized to any 3D porous structure, in which more than one type of pore window exists. Evidently, as the chemical functionalities of the WH are changed, uptake rates change sharply. Comparing the mass uptake time of methanol and 1-butanol, for the different PLs with different pillar functionalities indicate that (size-based) selectivities are higher at saturation, compared to the lower mass loading region (Table S1). Using this approach, the permeation and selectivity of the chemical mixtures can be regulated rationally, in a preconceived manner.
To get an insight into the energy barriers along the WV and WH pores for methanol, we performed force field based molecular dynamics simulations (see computational section). The comparative free energy profiles are illustrated in Fig. 3. It is evident from these simulations that during the diffusion along the WV pores (from A to A'), the free energy changes are similar for PLC=C and PLN=N. On the contrary, it is energetically uphill to traverse along the WH pores (from B to B') for PLN=N but energetically downhill for PLC=C. This finding is in tune with the observed the higher mass uptake rate in PLC=C. The preferential interaction between methanol and the pillar functionalities is clearly visible at the energy minimum (see Figures S13-S15) ascertaining the hypothesis of chemically controlled interpore diffusion.