The adsorption and mass transport of CO2 and CH4 in CHA zeolite were studied experimentally. First, large and well-defined CHA crystals with varying Si/Al ratios and morphologies ideal for adsorption studies were prepared. Then, adsorption isotherms were measured, and adsorption parameters were estimated from the data.
Microporous and Mesoporous Materials 332 (2022) 111716 Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso Mass transport of CO2 over CH4 controlled by the selective surface barrier in ultra-thin CHA membranes Mojtaba Sinaei Nobandegani *, Liang Yu , Jonas Hedlund Chemical Technology, Luleå University of Technology, SE-971 87, Luleå, Sweden A R T I C L E I N F O A B S T R A C T Keywords: Adsorption Mass transport Surface barrier Surface diffusion Activation energy The adsorption and mass transport of CO2 and CH4 in CHA zeolite were studied experimentally First, large and well-defined CHA crystals with varying Si/Al ratios and morphologies ideal for adsorption studies were prepared Then, adsorption isotherms were measured, and adsorption parameters were estimated from the data In the next step, permeation experiments for pure components and mixtures were conducted for a defect-free CHA mem brane with a Si/Al ratio of 80 and a thickness of 600 nm over a wide temperature range A maximum selectivity of 243 in combination with a CO2 permeance of 70 × 10− mol/(m2 s Pa) was observed for a feed of an equimolar CO2/CH4 mixture at 273 K and 5.5 bar Finally, a simple model accounting for adsorption and diffusion through the surface barriers and the interior of the pores of the membrane was fitted to the permeation data The fitted model indicated that the surface barrier was a surface diffusion process at the pore mouth with higher activation energy than the diffusion process within the pores The model also showed that the highly selective mass transport in the membrane was mostly a result of a selective surface barrier and, to a lesser extent, a result of adsorption selectivity Introduction Natural gas and biogas are mainly composed of a mixture of methane and carbon dioxide [1–3], and the removal of CO2 is usually required to satisfy grid and fuel specifications Water scrubbing, pressure swing adsorption (PSA), amine sorption, cryogenic separation, and membrane techniques [4–13] have been employed to remove CO2 from CH4 However, the existing technologies have some drawbacks such as low selectivity, complexity, high energy consumption, and high cost [14] Due to their high efficiency, low energy demand, compact equipment, and straightforward operation, membrane-based techniques have been studied intensively [11,15] and polymeric membranes have been used for gas separation on a large scale However, polymeric membranes display relatively poor selectivity, permeability, and stability, which makes them disadvantageous and less applicable For instance, for cel lulose acetate membranes that are used on a large scale for CO2/CH4 separation, a CO2 permeance of approximately 0.6 × 10− mol/(m2 s Pa) in combination with a CO2/CH4 ideal selectivity of 35 has been observed in the laboratory [16] For commercial polymeric membranes, the CO2 permeance is even lower; for example, polyetherimide (Ultem® 1000) has an indicated CO2 permeance of 0.09 × 10− mol/(m2 s Pa) coupled with a CO2/CH4 selectivity of 40 [17] Zeolites are ceramic materials with well-defined pores and much higher chemical and thermal stabil ities than polymeric materials and have been used as adsorbents for industrial gas upgrading [18–20] Ceramic zeolite membranes have the potential to display a higher selectivity, permeability, and stability than polymeric membranes for gas separations; however, zeolite membranes have not yet been commercialized for gas separations Consequently, much research and development work has been devoted to zeolite membranes during the past decades [21] The pore system of CHA zeolite has a window size of 3.7 × 3.7 Å Because this window size is in between the kinetic diameters of CO2 (3.3 Å) and CH4 (3.8 Å), CHA zeolite can separate CO2/CH4 mixtures by molecular sieving [22–29] The CHA membranes with different chemi cal compositions and Si/Al ratios but the same CHA pore system have been reported for CO2/CH4 separation “Pure silica” (implying an infinite Si/Al ratio) CHA membranes [30] and “high silica” (implying a finite Si/Al ratio) membranes [25,31,32] have also been reported These “pure silica” and “high silica” CHA membranes are alternatively denoted as SSZ-13 membranes There are also reports on SAPO-34 membranes [33,34], in which the CHA framework comprises phosphate in addition to silica and alumina * Corresponding author E-mail address: mojtaba.nobandegani@ltu.se (M.S Nobandegani) https://doi.org/10.1016/j.micromeso.2022.111716 Received 30 October 2021; Received in revised form 30 December 2021; Accepted 20 January 2022 Available online 29 January 2022 1387-1811/© 2022 The Authors Published by Elsevier Inc This is an open (http://creativecommons.org/licenses/by-nc-nd/4.0/) access article under the CC BY-NC-ND license M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 In previous studies [35,36], we have prepared and evaluated CHA membranes for the separation of CO2/CH4 mixtures A high CO2/CH4 separation factor of 99 in combination with a high CO2 permeance of 60 × 10− mol/(m2 s Pa) was observed for a feed of an equimolar CO2/CH4 mixture at room temperature A high separation factor in combination with high permeance is a desirable membrane property The observed CO2 permeance was approximately 2–20 times higher than that reported for CHA membranes in the literature [25,37,38] This high permeance was attributed to the very thin CHA film (approximately 450 nm) sup ported on a highly permeable support Furthermore, the CO2 permeance was about 100 times higher than that typically observed for polymeric membranes, e.g., cellulose acetate membranes in the laboratory [16], and more than 600 times larger than the indicated permeance for commercial polyetherimide (Ultem® 1000) membranes [17] Conse quently, these highly permeable CHA membranes are promising for in dustrial applications, but the fundamental mass transfer process in thin membranes has hitherto been poorly understood A fundamental un derstanding of the mass transfer process is essential for the development of tools for engineering and, in the next step, to enable the design of industrial CO2/CH4 separation processes Adsorption, surface diffusion, and desorption are the main mass transfer steps in nanoporous materials In sufficiently large crystals, the surface diffusion step must be rate-limiting Krishna et al modeled the mass transport of molecules through zeolite membranes with a thickness of 50 μm using the Maxwell–Stefan equations to describe the surface diffusion process in the pores [39,40] Similar work has also been re ported by Kapteijn et al for silicalite-1 membranes having a thickness of 20–60 μm [41–44] Surface barriers may influence the mass transfer as first described by Bülow et al [45], and in small crystals and thin membranes, the mass transfer may even be limited by the surface barrier [46–48] The effect of surface barriers on the molecular mass transport ărger and Bỹlows groups using various in zeolites has been studied by Ka experimental methods such as micro-imaging, NMR tracer desorption, frequency response (FR), and barometric (or piezometric) techniques [49–54] However, the origin of the surface barrier has been unknown [51], although pore narrowing and pore blockage have been suggested as possible reasons for the barrier [55] We have studied the surface barrier in ultra-thin MFI and CHA membranes by careful permeation experiments over a wide temperature range [56] The results indicated that the surface barrier was the rate-limiting mass transfer step and that it was a surface diffusion process with higher activation energy than that for the surface diffusion process within the pores It appeared that the activation energy was higher because there were fewer molecular in teractions at the pore mouth than within the pores themselves The pore mouth was in direct contact with the gas phase where the concentration of molecules was very low compared to the concentration in the pores Consequently, the origin of the surface barrier may be due to the dif ference in geometries between the pore mouth and the pore interior In our previous work [56], the adsorption parameters were taken from the literature However, the chemical properties of the zeolite, such as the Si/Al ratio and the concentration of silanol groups, affect the adsorption parameters In addition, most of the reported adsorption data has been determined in a narrow temperature range [27,57–59] Determination of the parameters in a temperature range similar to the membrane experiments may serve to avoid systematic errors caused by taking the two measurements at different temperatures Thus, the determination of adsorption parameters for a zeolite with the same chemical properties as the zeolite in the membrane as well as the use of similar temperature ranges for the adsorption and membrane experi ments are essential to accurately determine the surface permeability and the corresponding activation energy Experimental studies of both adsorption and permeation over CHA zeolites are rare, however, due to the more extensive experimental work that they require In the present work, the adsorption isotherms of CO2 and CH4 were measured for CHA crystals with Si/Al ratios of 45, 77, and ∞ over a wide temperature range of 150–350 K; the adsorption parameters were determined from the isotherms In the next step, permeation experi ments for the same components in their pure forms and as mixtures were conducted for an ultra-thin CHA membrane with a Si/Al ratio of 80 The crystals and membrane were synthesized in fluoride media, which has been shown to eliminate silanol groups (i.e., the concentration of silanol groups should be very low or even zero in both the crystals and the membrane) [60,61] Furthermore, the synthesis of the crystals was optimized to produce large and well-defined crystals with morphologies that were optimal for adsorption studies (e.g., a low external area/ internal area ratio) Finally, a simple mathematical model [56] ac counting for adsorption and surface diffusion through the two surface barriers and the pores of the membrane was fitted to more extensive permeation data for the CHA membrane than in previous work [56] The permeation experiments were conducted over a wider temperature range than the CO2 adsorption experiments, i.e from 210 to 450 K This also allowed a more precise estimation of the surface permeability and the corresponding activation energy In addition, the permeance selec tivity (usually denoted as permselectivity), adsorption selectivity, and surface permeability selectivity were evaluated, which led to a deeper understanding of the selective mass transfer processes Material and methods 2.1 Synthesis of CHA crystals To synthesize relatively large pure silica CHA crystals in fluoride media [35], distilled water, colloidal silica (40%, Ludox AS-40), N,N, N-trimethyl-1-adamantyl ammonium hydroxide (TMAdaOH 25%, SACHEM, Inc.), and hydrofluoric acid (48%) were mixed in a plastic bottle and stirred overnight at room temperature The mixture was then freeze-dried, and a small amount of water was added to obtain a gel with a molar composition of 1.0 SiO2:1.4 TMAdaF:9.4H2O The gel was placed in an autoclave that was kept in an oven at 175 ◦ C for day The crystals were purified by repeated centrifugation and re-dispersion in a 0.1 M NH3 solution a total of times This sample will be furthermore denoted as Si-CHA Two additional CHA samples with Si/Al ratios of 45 and 77 were synthesized using a similar procedure; these samples will be furthermore denoted as CHA45 and CHA77, respectively These samples were prepared by adding aluminum isopropoxide (99.99%, Sigma-Aldrich) to the synthesis gel, followed by stirring for 15 before freeze-drying The compositions of the synthesis mixtures used to prepare CHA45 and CHA77 were 1.0 SiO2:0.01 Al2O3:1.4 TMA daF:9.4H2O and 1.0 SiO2:0.005 Al2O3:1.4 TMAdaF:9.4H2O, respec tively Finally, the crystals were calcined at 480 ◦ C in ambient air for 16 h to remove the template molecules from the pores 2.2 CHA membranes CHA membranes supported on graded α-alumina discs with a diameter of 25 mm were provided by ZeoMem Sweden AB The thick ness of the top layer of the support was about 35 μm with a pore size of approximately 100 nm, and the thickness of the base layer was mm with a pore size of about μm 2.3 Characterization Scanning electron microscope (SEM) images of the samples were recorded by using an extreme-high-resolution SEM (XHR-SEM) (Magellan 400, FEI Company, Eindhoven, The Netherlands) The in strument was operated using an accelerating voltage of kV and a probe current of 6.3 pA No conductive coating was applied to the samples prior to imaging A PANalytical Empyrean X-ray diffractometer equip ped with a Cu LFF HR X-ray tube and a PIXcel3D detector was employed to record XRD patterns of the zeolite crystals and the membrane in the 2θ range of 5◦ –35◦ The accelerating voltage and current were 45 kV and 40 mA, respectively The Si/Al ratios of the CHA crystals were measured M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 by inductively coupled plasma-sector field mass spectroscopy (ICPSFMS, ALS Analytica) The samples were prepared by digesting 0.1 g zeolite powder in LiBO2 followed by dissolving in HNO3 Loss on ignition was estimated by heating the sample to 1000 ◦ C 2.5 Modeling 2.5.1 Gas adsorption To consider the heterogeneity of the adsorbate, Toth adsorption isotherms were fitted to the measured adsorption data [63]: 2.4 Adsorption and permeation experiments C = Csat A Micromeritics ASAP 2020 Plus instrument equipped with a Micromeritics Cryostat I was used to measure the adsorption isotherms of CO2 (99.995%) and CH4 (99.9995%) at pressures up to 125 kPa The CO2 and CH4 isotherms were measured over the temperature range of 230–350 K and 150–300 K, respectively A lower temperature range was selected for CH4 to arrive at sufficient adsorption The samples were degassed under vacuum conditions at 350 ◦ C for 12 h before measure ment The equilibrium time for CO2 and CH4 was 40 and 630 s, respectively To evaluate membrane quality, the permeance of H2 and SF6 was measured at a feed pressure of bar(a) and a permeate pressure of bar(a) at room temperature Since H2 molecules are small enough to permeate the CHA pores while SF6 molecules can only permeate defects, a high H2/SF6 permeance ratio indicates a high membrane quality The membrane was mounted in a stainless steel cell and sealed with graphite gaskets for permeation measurements over a wide temperature range using equipment that has been detailed in previous work [62] The membrane was dried at 573 K for h in a flow of dry He, and then the permeation experiments with pure CO2 and CH4 were conducted in the temperature ranges of 220–450 K and 210–450 K, respectively The membrane experiments were carried out in a slightly wider temperature range than the temperature range for the CO2 adsorption measurements in order to more accurately determine the activation energy for surface permeability The pure components were fed to the membrane through a mass flow controller, and the pressure on the feed side of the membrane was controlled by a backpressure regulator set to 1.5 or bar(a) The pressure on the permeate side was maintained at bar(a) The permeate flow was measured by a bubble flowmeter Finally, permeation experi ments for the feeds comprised of the CO2/CH4 mixtures with molar ra tios of 50/50 and 80/20 were carried out at feed pressures of and bar (a) and a permeate pressure of bar(a) A drum-type flowmeter was used to measure the permeate flow rate, and the composition of the permeate was analyzed using an online GC (Micro GC 490, Agilent) bP / [ t] t + (bP) (1) In this equation, C represents the adsorbed concentration and Csat represents the adsorbed concentration at saturation The parameter b is the affinity constant, t is the Toth heterogeneity parameter, and P is the pressure The parameter Csat was estimated by fitting the isotherm to the adsorption data recorded at the lowest temperature, while the param eters b and t were fitted at all temperatures The heat of adsorption (ΔHads.) for the three samples with varying Si/Al ratios was estimated by fitting the van’t Hoff equation to the experimental data: ln b = − ΔHads ΔSads + RT R (2) where ΔSads is the adsorption entropy, which was assumed to be con stant for all three samples 2.5.2 Gas permeation Fig illustrates the mass transfer process in the zeolite membrane at steady conditions, and for component i, the flux through the zeolite film Jfi can be described as [56]: Jfi = α i i fD ( f ) αif αip Di p C − Ceq,i ε + αif αip L + αip Di eq,i (3) where αif and αip are the surface permeabilities of i at the surface barrier at the feed side f and permeate side p of the zeolite film, respectively Di is the diffusion coefficient of i in the zeolite pores, ε is the fractional pore f volume (0.382 for CHA [40]), and L is the zeolite film thickness Ceq,i and Cpeq,i are the concentrations of i in the zeolite pores at the feed and permeate sides, respectively As shown in previous work [56], the mass transfer process in these thin membranes is controlled by the surface barrier and not by the diffusion process inside the pores Adsorption equilibrium was assumed at the feed and permeate sides of the zeolite film, and consequently, the concentrations in the zeolite pores at the f feed (Ceq,i ) and permeate (Cpeq,i ) sides were estimated from the f Fig Schematic of the mass transfer process through a zeolite membrane Ceq denotes the concentration within the pores in equilibrium with the feed gas with (partial) pressure f pg , f Cb is the concentration at the other side of the barrier, Cpb is the concentration within the pores before the barrier at the permeate side, and Cpeq is the concentration after the barrier within the pores in equilibrium with the gas with (partial) pressure ppg at the permeate side of the membrane M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 f corresponding pressures (pg and ppg ) using Equations (1) and (2) with the fitted adsorption parameters The surface permeability is a function of the concentration and temperature as follows [56]: α=( 1− α* C Csat ( ( )) E 1 )n exp α − R 300 T (4) In Equation (4), Eα is the activation energy for surface permeability, α* is the surface permeability at 300 K and zero concentration, and the parameter n is equal to 1.2 [56] The diffusion coefficient D is considered Fig SEM images of CHA crystals and a membrane: a) Si-CHA, b) CHA77, c) CHA45, d) Cross-sectional view of a CHA membrane, e) High resolution image of the cross-section rotatated 90◦ anti-clockwise as compared to the image in d), and f) Top-view of a CHA membrane M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 to be a function of temperature and is independent of loading [64]: D = A2 e for pure components and as “mixture” when estimated for mixtures (5) − EDiffusion /RT Results and discussion EDiffusion is the activation energy for diffusion in the zeolite pores The flux through the support Js was considered to be a combination of Poiseuille flow and Knudsen diffusion [56]: ( √̅̅̅̅̅ ) B0 P 194K0 T dP Js = (6) + M dx μRT RT 3.1 General characterization of CHA crystals and membrane The Si/Al ratios of the CHA45 and CHA77 crystals were determined by ICP-SFMS to be 45 and 77, respectively The Si/Al ratio of a CHA membrane was estimated to be 80 by first performing an ion exchange of the membrane to the Cs+ form and then measuring the Cs signal by EDS analysis, as described in previous work [66,67] Fig shows SEM images of the crystals and CHA membrane The CHA crystals displayed the typical pseudo-cubic habit [28,35] No crystals with other morphologies or any amorphous materials were observed by the SEM The width of the crystals was approximately 10 μm with a narrow size distribution for the three samples (Fig 2a–c) Consequently, the ratio of the external-to-internal surface areas of these large crystals was as small as 1/1000 (i.e., the adsorption data reflected only the internal surface of the crystals) Fig 3a shows the XRD patterns recorded for the CHA crystals (black traces) All observed reflections are typical for the CHA phase, as indicated by the reference pattern (ICDD-00-052-0784) for CHA crystals (blue bars) No signal from amorphous material was observed Fig 2d and e shows SEM images of the cross-section of a CHA membrane A continuous film with a thickness of around 600 nm (Fig 2d) was observed In addition, the pores of the support were completely open, which indicated that the support was highly perme able (Fig 2d) Furthermore, this demonstrated that the mass transfer in the support could be described using Equation (6) with parameters fitted to the permeation data for the support (without zeolite) Fig 2e shows a high-resolution image of the cross-section of the film, which is rotated 90◦ anticlockwise compared to Fig 2d The high-resolution image of the cross-section (Fig 2e) shows that the grain boundaries within the film were closed The SEM image of the membrane surface (Fig 2f) dem onstrates that the film was comprised of well inter-grown zeolite crys tals, and no cracks or pinholes were present The XRD pattern of the CHA membrane (black trace in Fig 3b) only displayed reflections from the CHA and alumina phases, which confirmed the high purity of the CHA membrane where B0 (1.90 × 10− 16 m2) is the Poiseuille structural parameter, K0 (2.40 × 10− m) is the Knudsen structural parameter, M is the molar mass (g/mol), μ is the viscosity (N⋅s/m2), and x is the thickness (35 μm) of the top layer of the support, which is where the main mass transfer resistance in the support is generated The Sutherland model was used to estimate the viscosity [65]: T Tref )32 / ( μ = μref Tref + S T +S (7) In this model, S is the Sutherland constant equal to 275 and 179 K for CO2 and CH4, respectively The parameter μref is the viscosity of the gas at the reference temperature Tref of 273 K, which is 1.37 × 10− and 1.03 × 10− (N s)/m2 for CO2 and CH4, respectively The adsorption selectivity, permeance selectivity, surface perme ability selectivity, and driving force were estimated according to Equations (8)–(11): AdsorptionSelectivity = PermeanceSelectivity = θfCO2 (8) θfCH4 πfCO2 πfCH4 SurfacePermeabilitySelectivity = (9) αfCO2 αfCH4 (11) Drivingforce = θf − θp Here, θ is the loading (θ = Ji f p ), pi − pi (10) Ceq ) Csat and π represents the permeance (π i = where Ji and pi are the flux and partial pressure, respectively, of 3.2 Gas adsorption component i These selectivities are denoted as “ideal” when estimated The points in Fig represent the measured adsorption isotherms of Fig XRD patterns of the as-synthesized: a) CHA crystals and b) CHA membrane (black trace) Blue bars represent reflections from the reference database and the red bar represents the reflection from the α-alumina support (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 Fig Adsorption isotherms of single components over CHA crystals Measured data are shown by points and curves represent the fitted model M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 CO2 and CH4 for the CHA crystals The adsorption measurements were repeated and almost the same results were obtained, see Fig S1a All the isotherms appeared to be of type I [68], which is typical for microporous materials, although saturation was not reached even at the lowest investigated temperatures The observed CO2/CH4 ideal adsorption selectivity was around 4.3 at 298 K and 100 kPa for Si-CHA, which is comparable with the reported adsorption selectivity of 4.06 at 298 K and 100 kPa [29] Fig also shows that the Toth adsorption isotherms (curves) are fitted well to the adsorption data; the R-squared values (>0.99) are summarized in Table S1 Single site Langmuir isotherms were also fitted to the adsorption data, but the fit was not as good, particularly for CH4 at low temperatures, as illustrated by much lower R-squared values, see Table S1 Fig S2 shows Toth and Langmuir isotherms fitted to CO2 adsorption data over Si-CHA crystals It shows that a Langmuir isotherm cannot be fitted well to the data recorded at the lowest temperature, and that the Toth isotherm can be fitted well to data recorded at all tem peratures To determine the adsorption capacities at saturation, the Toth adsorption isotherms were fitted to the adsorption data recorded at the lowest temperatures, e.g., 230 and 150 K for CO2 and CH4, respectively The parameters b and t were then estimated by fitting the Toth adsorption isotherms to the data recorded at all temperatures Finally, the parameters ΔHads and ΔSads were estimated from the fitted b-values by fitting the van’t Hoff equation (Equation (2)) to the data As illus trated by the van’t Hoff plots in Fig S3, the fit was excellent (R2 > 0.99) The fitted parameters are presented in Tables and and discussed below The fitted adsorbed concentration at saturation was 35.0 and 30.0 kmol/m3 for CO2 and CH4, respectively These values are quite similar to those estimated by configurational-bias Monte Carlo (CBMC) simulation and reported by Krishna et al (34.98 and 30.61 kmol/m3 for CO2 and CH4, respectively) [40] A higher CO2 adsorption capacity is mainly be an effect of the smaller size of the CO2 molecule compared to the CH4 molecule As shown in Tables and 2, the same adsorbed concentration at saturation was observed for all samples independent of the Si/Al ratio This can be rationalized by the facts that only a small amount of aluminum was introduced in the samples CHA77 and CHA45, and that protons are the counterions, which should result in a minor influence of the pore volume accessible for pore filling by the adsorbates The estimated b-values at 300 K for Si-CHA of 2.9 × 10− and 5.25 × 10− 7/Pa for CO2 and CH4, respectively, are also quite similar to those reported by Krishna et al (1.7 × 10− and 6.1 × 10− 7/Pa for CO2 and CH4, respectively) [40] The higher b-value for CO2 should be an effect of the larger polarizability of CO2 compared to that of CH4 [69] Higher b-values were observed for samples with lower Si/Al ratios For CO2, this should be an effect of the increased basicity and polarity of the frame work [70,71], and for CH4, this should be an effect of the increased polarity [72,73] caused by the introduction of Al in the zeolite The fitted Toth heterogeneity parameter (t) deviated further from unity by decreasing the Si/Al ratio This indicated that the adsorption sites became more heterogeneous when more Al was introduced in the zeolite, as observed for other zeolites [74–77] The fitted heterogeneity parameter was also lower for CH4 than for CO2, which indicated that the adsorption sites for CH4 are more heterogeneous than those for CO2 The heats of adsorption ΔHads for CO2 and CH4 were estimated within the ranges of − 26.75 to − 25.82 kJ/mol and − 17.76 to − 17.23 kJ/mol, respectively, which are close to the values reported by other groups [27,40,78] A more negative heat of adsorption is expected for adsorption systems with larger polarities [47,79], which is in concert with the observed heat of adsorption for CO2 Fig shows plots of -ΔHads (Fig 5a), b-values (Fig 5b), and t (Fig 5c) as a function of the Al/Si ratio, i.e., the inverse of the more common Si/Al ratio More details can be found in Fig S4 It is evident that the parameters -ΔHads and b are increasing nearly linearly with the Al/Si ratio, while the parameter t is decreasing nearly linearly with the Al/Si ratio, as shown by the fitted lines The values of -ΔHads., b, and t for the membrane with an Al/Si ratio of 1/80 were estimated from these linear dependencies, and the estimated values are given in Tables and These estimated values differ only slightly from the literature data that we used in previous work [56] 3.3 Single-component permeation experiments The permeances of pure H2 and SF6 over the membrane were measured to be 52 × 10− and × 10− 11 mol/(m2 s Pa), respectively The H2/SF6 permeance ratio was as high as 75,000, which was indica tive of a high membrane quality [25,30] and shows permeation data should reflect only mass transfer in the pores of the zeolite, and not in the defects This ratio is much higher than the ratios previously reported for CHA membranes [25,30], which were in the range of 200–600 In the next step, single-component permeation experiments with CO2 and CH4 at feed pressures of 1.5 and bar(a) were carried out at various temperatures The maximum CO2 fluxes were observed at 280 K and were 0.42 and 0.88 mol/(m2⋅s) for feed pressures of 1.5 and bar(a), respectively (Fig 6a) Comparable results were obtained from repeating the permeation measurement, e.g Fig S1b shows the results for CH4 permeation at bar(a) feed pressure The corresponding CO2 per meances were as high as 82 × 10− and 86 × 10− mol/(m2 s Pa), which is similar to the permeance of 78 × 10− mol/(m2 ⋅ s ⋅ Pa) that we have reported for an ultra-thin MFI membrane [80] and significantly higher than the permeance reported by Falconer et al for SSZ-13 membranes [23] High CO2 permeance must have been a result of the low membrane thickness of 600 nm in combination with a highly permeable and open support as observed by the SEM At the same temperature, considerably lower CH4 fluxes of 2.6 × 10− and 5.8 × 10− mol/(m2⋅s) were observed, which corresponded to low CH4 permeances of 0.51 × 10− and 0.57 × 10− mol/(m2 s Pa) at feed pressures of 1.5 and bar(a), respectively Consequently, a high maximum ideal CO2/CH4 permeance selectivity of 160 was observed (see Fig 6b) This selectivity is much higher than the reported selectivities of 54 [30] and 76 [35] at com parable test conditions and membrane types Based on the parameters estimated from the adsorption data (see Tables and 2), Equation (3) was fitted to the data Since the mass transfer process is controlled by the surface barrier in thin membranes [56], the experimental data could not be used to determine the diffusion coefficient; thus, diffusion coefficients (Di) were taken from the litera ture (2.5 × 10− and × 10− 11 m2/s at 300 K for CO2 and CH4, respectively [40]) These diffusion coefficients were assumed to be in dependent of loading, while the surface permeability at zero concen tration (α*), the activation energy of the surface permeability (Eα), and Table Fitted parameters for CO2 adsorption in CHA Sample ΔHads (kJ/mol) Si-CHA CHA77 CHA45 Membrane (Si/Al = 80) − − − − 25.82 26.29 26.75 26.32 ΔSads (J/mol) − − − − 132.7 132.7 132.7 132.7 b (at 300 K) (/Pa) 2.94 × 3.86 × 4.28 × 3.74 × 10− 10− 10− 10− 6 6 t (at 300 K) Csat (kmol/m3) 0.9367 0.9201 0.8952 0.9159 35.0 35.0 35.0 35.0 Ref ΔHads (kJ/mol) [40] − 25.0 [27] − 23.1 [78] − 23.2 M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 Table Fitted parameters for CH4 adsorption in CHA Sample ΔHads (kJ/mol) Si-CHA CHA77 CHA45 Membrane (Si/Al = 80) − − − − 17.23 17.46 17.76 17.50 ΔSads (J/mol) − − − − 117.9 117.9 117.9 117.9 b (at 300 K) (/Pa) 5.25 × 10− 5.93 × 10− 6.52 × 10− 5.94 × 10− 7 7 t (at 300 K) Csat (kmol/m3) 0.8387 0.8012 0.8006 0.8121 30.0 30.0 30.0 30.0 Ref ΔHads (kJ/mol) [40] − 16.0 [27] − 16.8 Fig a) -ΔHads, b) b-values, and c) t-values as a function of the Al/Si ratio Circular red-filled and empty blue symbols indicate the measured values for CO2 and CH4 adsorption for the crystals, respectively Lines are fitted to the data by linear regression and the stars indicate the estimated values for the membrane (For inter pretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) diffusion in the pores (EDiffusion) were fitted to the experimental data As shown by Teixeira et al [81], the activation energy for diffusion EDiffusion can be correctly estimated from experimental data independent of crystal size Consequently, the activation energy for diffusion was esti mated from the experimental data in the present work, which has also been demonstrated in previous work [56] The fitted parameters are summarized in Table 3, and the agreement between the fitted model and the experimental data is illustrated in Fig 6a A surface permeability at zero concentration (α*) of 2.0 × 10− m/s was observed for CH4, which is 40 times lower than that of CO2, which was 8.0 × 10− m/s This is presumed to be the main reason for the highly selective mass transfer of CO2 across the membrane For a deeper analysis of this selective mass transfer, the ideal surface permeability selectivity is plotted in Fig 6b This selectivity was 25 at 450 K and increased to 1500 at 220 K As shown in Fig 6b, the ideal surface permeability selectivity was always much higher than the ideal adsorption selectivity, and the difference was particularly large at low temperatures The highly selective mass transfer through the membrane was mostly an effect of the selective surface barrier, i.e., a high ideal surface permeability selectivity The high surface permeability selec tivity at low temperatures was largely due to the high adsorbed con centration of CO2 at low temperatures, which resulted in a small denominator in Equation (4) and thereby a large surface permeability f for CO2 For instance, at 230 K and a feed pressure of bar(a), CCO2 was 33.1 kmol/m3, which is close to the Csat of CO2 (35 kmol/m3) This produced a denominator value in Equation (4) of 0.03 and an αCO2 of 5.8 × 10− m/s Under the same conditions, CCH4 was 14.8 kmol/m3, which is less than half of the Csat of CH4 (30 kmol/m3) This resulted in a f M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 Fig a) Single-component CO2 and CH4 fluxes and b) Ideal CO2/CH4 permeance selectivity, ideal surface permeability selectivity, ideal adsorption selectivity, and driving force Filled symbols and lines show the experimental data and model, respectively, for a feed pressure of bar(a), while empty symbols and dashed lines show the experimental data and model, respectively, for a feed pressure of 1.5 bar(a) The permeate pressure is bar(a) in all cases Fig 6b also shows the driving force for the mass transfer across the membrane expressed as the loading difference θf − θp , which is a func tion of the temperature and corresponds to the concentration difference Table Fitted parameters in Equation (3) Single Component CH4 α* at 300 K (m/s) E300K (kJ/mol) α E300K Diffusion (kJ/mol) α* at 300 K (m/s) 2.0 × 10− 16.5 CO2 8.0 × 10− 13.0 15.5 CH4 3.0 × 10− f Ceq − Cpeq in Equation (3) In the case of CO2 and a feed pressure of bar (a), a maximum driving force was observed at about 285 K This maximum driving force was a result of increasing CO2 adsorption to f wards saturation at the feed side (Ceq ) when the temperature was decreasing to 285 K At temperatures lower than 285 K, the driving force of CO2 was reduced due to increased adsorption towards saturation at the permeate side (Cpeq ) The presence of the maximum driving force for CO2 mass transfer was the main reason for the maximum CO2 flux at 280 K, as shown in Fig 6a However, the maximum CO2 flux was observed at a slightly lower temperature than the temperature at which the maximum driving force occurred, due to the increasing surface perme ability of CO2 with decreasing temperature As mentioned above, a maximum ideal permeance selectivity of 160 was observed at 280 K, which was because the maximum driving force for CH4 occurred at a lower temperature (220 K) than the temperature at which the maximum driving force for CO2 occurred (285 K) Table demonstrates that the activation energy for surface 7.0 Mixture CO2 8.0 × 10− denominator value in Equation (4) of approximately 0.44, a small αCH4 value of 6.1 × 10− m/s, and an ideal surface permeability selectivity of 943 In addition, the activation energy for surface permeability Eα of CH4 (16.5 kJ/mol) was larger than that of CO2 (13.0 kJ/mol) (see Table 3) Thus, there was a higher temperature sensitivity and a greater reduction of the surface permeability for CH4 at lower temperatures, which supports the observation that surface permeability selectivity increases with decreasing temperature M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 permeability was higher than the activation energy for diffusion in the pores This indicates that surface permeation was the limiting mass transfer step across the membrane and, consequently, this higher acti vation energy caused the surface barrier [56] Furthermore, the ratio Lα0 αL D(α0 +αL ) can be used to determine if either the surface permeability or the pores, with more significant interactions within the pores than at the pore mouth Consequently, it appeared that the surface barrier is a geometrical effect The excellent fit between the model and the more extensive experimental data for a CHA membrane at two different pressures and over a wide temperature range in the present work in dicates that Equation (3) provides an adequate description of the mass transfer and that Equation (4) provides an adequate description of the temperature and concentration dependencies of the surface permeability diffusivity was limiting the mass transfer [56] For single-component permeation of CO2 and CH4, this ratio was 0.18 and 0.13, respec tively These low ratios indicate that the surface barrier controls the ărger et al [50,51] observed mass transport in the thin membranes Ka increasing surface permeability with increasing concentration of adsorbed molecules However, no mathematical description of this de pendency was suggested In our previous work [56], we showed that when Equation (4) accurately describes the surface permeability, it can be fitted well to our experimental data as well as to the experimental data reported by Kă arger et al [50,51] Equation (4) is similar to the HIO model derived for surface diffusion [82] under the assumption that molecules jump from site to site, and if a site is occupied, the molecule is scattered to another site In the HIO model, it is further assumed that molecular interactions are negligible, which results in n = 1.0 The successful fitting of Equation (4) to the experimental data suggests that the surface permeation pro cess is a surface diffusion process [56] We observed that the fitted activation energy for surface permeability Eα was higher than the acti vation energy for surface diffusion EDiffusion within the pores and that the molecular interactions increased n to 1.2, which reduced these activa tion energies We suggested that the surface barrier is a result of the geometrical differences between the pore mouth and the interior of the 3.4 Mixture permeation experiments The points in Fig 7a represent, as a function of temperature, the experimental permeation data for a feed of CO2/CH4 mixtures with compositions of 50/50 and 80/20 (molar ratios) at a feed pressure of 5.5 bar(a), and a permeate pressure of bar(a) The observed CO2 flux was consistently about two orders of magnitude higher than the observed CH4 flux The membrane was highly CO2 selective across the entire studied temperature range and a maximum separation factor of 156 was observed at 273 K (Fig S5), which corresponded to a mixture permeance selectivity of 243 (Fig 7b) Table summarizes CO2/CH4 separation data reported for zeolite and MOF membranes in the literature and in the present work As shown in Fig 7b, the selective mass transfer across the membrane was a result of the high mixture surface permeability selectivity (approximately 54 at 300 K) and high mixture adsorption selectivity (6.7 at 300 K) The curves in Fig 7a illustrate that the same model and Fig a) Fluxes observed for CO2/CH4 mixtures with compositions of 50/50 and 80/20 (molar ratios), b) Mixture selectivities and driving forces for a 50/50 CO2/ CH4 mixture, and c) Mixture selectivities and driving forces for an 80/20 CO2/CH4 mixture Points indicate experimental data and curves indicate the fitted model 10 M.S Nobandegani et al Microporous and Mesoporous Materials 332 (2022) 111716 The model demonstrated that the surface barrier was a surface diffusion process with higher activation energy than the surface diffusion process in the pores Furthermore, the model showed that the highly selective mass transfer for single components and mixtures through the ultra-thin CHA membrane was mostly a result of a high surface permeability selectivity, i.e., a selective surface barrier, and, to a lesser extent, the CO2/CH4 adsorption selectivity Table Reported CO2/CH4 separation data for zeolite and MOF membranes in the literature and in the present work Membrane Temperature (K) Pressure (bar) Selectivity Permeance 10− mol/ (m2 s Pa) Ref SAPO-34 MFI 293 250 1.4 7.0 152 7.1 39.0 98 [34] [83] SSZ-13 DDR DDR NaX ZIF-8 LTA MOF-5/ Matrimid Si-CHA 303 293 303 308 298 303 308 2.0 1.0 1.0 1.0 1.0 3.0 3.0 300 150 400 28 2.2–32 20.5 29 2.0 8.6 0.65 3.0 0.3–2.5 0.002 [22] [84] [85] [86] [87] [88] [89] 276 9.0 47 84 [35] Si-CHA 295 5.0 103 60 [90] Si-CHA 293 6.0 198 14 [91] Si-CHA 273 5.5 243 70 This work a a CRediT authorship contribution statement Mojtaba Sinaei Nobandegani: Writing – original draft, Writing – review & editing, Visualization, Validation, Formal analysis, Concep tualization, Investigation Liang Yu: Investigation, Supervision, Writing – review & editing, Conceptualization, Formal analysis Jonas Hed lund: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization a a Declaration of competing interest a The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Our previous work Acknowledgments similar parameters that were fitted to the single-component permeation data could also describe the permeation data for the mixture In the mixture, the same surface permeability for CO2 and a slightly larger surface permeability for CH4 were observed This is consistent with observations in our previous work [56] and indicates that the highly mobile CO2 molecules interacted with the less mobile CH4 molecules, thereby increasing the surface permeability for CH4 The concentration of molecules in the zeolite pores was estimated using the ideal adsorp tion solution theory (IAST) The difference in flux between the experi mental data and the model at low temperatures (