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Prediction of the breakthrough performance of “gating” adsorbents using osmotic framework adsorbed solution theory Francisco J. Sotomayor, and Christian Lastoskie Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02036 • Publication Date (Web): 09 Aug 2017 Downloaded from http://pubs.acs.org on August 11, 2017

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Predicting the breakthrough performance of “gating” adsorbents using osmotic framework adsorbed solution theory

Francisco J. Sotomayor, Christian M. Lastoskie* Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Michigan 48109

We present an experimental and theoretical study of the breakthrough performance of the flexible metal-organic framework Cu(bpy)2(BF4)2 (bpy = 4,4’-bipyridine), termed ELM-11. Pure CO2, He, and N2 gases, as well as binary gas mixtures of those species, were used to perform breakthrough experiments on ELM-11. ELM-11 exhibits a stepped breakthrough curve for CO2 not seen in rigid adsorbents. By comparing the step heights observed in the experimental breakthrough curves with predictions of the gate pressure obtained from the osmotic framework adsorbed solution theory (OFAST) method, we show that the OFAST method can be used to predict the occurrence and height of the steps observed in the breakthrough curves of flexible metal organic frameworks. For specific gas mixtures, breakthrough curves on ELM-11 show a “doorstop” type effect, wherein the observed step heights for CO2 breakthrough curves are reduced when the gas mixture contains small kinetic diameter gas species such as helium.

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INTRODUCTION Metal-organic frameworks (MOFs), also known as porous coordination polymers (PCPs)1, are a relatively novel class of hybrid materials built from organic ligands that bridge metal ions with well-defined coordination geometries. Through careful choice of the metal and organic building blocks, MOFs can be conceptually designed and synthesized to control how the building blocks come together to form a net, allowing fine tuning of pore size and crystal structure. Over 20,000 different MOFs have been reported and studied within the past decade.2 The enormous structural and chemical diversity of MOFs has resulted in an enormous growth of research into their potential application for gas storage, ion exchange, molecular separation, and heterogeneous catalysis.3 The exceptional tunability of these materials has allowed MOFs to break several records in porous material properties such as specific surface area, hydrogen (H2) uptake based on physical adsorption, and methane (CH4) and carbon dioxide (CO2) storage.4 Their large surface areas, adjustable pore sizes, and controllable pore surface properties make MOFs especially appealing as next-generation porous adsorbents. Flexible MOFs, also known as soft porous crystals (SPCs)5, are a subset of MOFs that possess both a highly ordered network and structural transformability. In contrast with rigid MOFs, which retain their structure and porosity irrespective of environmental factors, SPCs can undergo structural transformations depending on external stimuli such as temperature, mechanical pressure, or guest adsorption, due to their bi-stable or multi-stable natures.6 The multi-stable nature of SPCs has led to the observation of previously unanticipated gas adsorption phenomena. A subset of SPCs that are representative of these exotic adsorption behaviors are the elastic layer-structured metal-organic frameworks (ELM)7,8. ELMs are two dimensional grid sheets composed of metal vertex ions, connecting ligands, and charge-balancing counter ions arranged


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in three-dimensional stacked structures. These materials show a latent porosity9 such that adsorption of gas molecules above a specific pressure, termed the “gate pressure”, results in expansion of the layer planes and a vertical jump in the adsorption profile. These “gated” isotherms do not fall into any of the adsorption isotherm categories identified by the International Union of Pure and Applied Chemistry.10 Because of their exotic adsorption characteristics, which are not observed in traditional porous materials or in rigid MOFs, ELMs have attracted interest as potential next-generation carbon capture materials. Of particular interest is their apparent high selectivity for CO2 and their low energy requirements for adsorbent regeneration and CO2 recovery.8 To be suitable for carbon capture applications, flexible MOFs like ELMs must demonstrate suitable CO2 separation performance under working conditions. Short of operating a full temperature swing, pressure swing, or vacuum swing adsorption system, it is challenging to predict how well a material will capture CO2 under working conditions. However, it is possible to evaluate the CO2 capture performance of adsorbent materials in flow-through systems by performing breakthrough experiments, wherein a gas mixture is flowed through a bed of the adsorbent of interest. By monitoring the composition of the outflow gas stream, using gas chromatography or mass spectrometry, the separation performance of the adsorbent may be assessed.11 A very limited number of breakthrough experiments using flexible MOFs have been reported in the literature. These include: separation of CO2 and CH4 on MIL-53(Cr)12, MIL-53(Al)13, CID55, and CID-65; separation of ethane and ethene on ZIF-714; and separation of xylene isomers on MIL-53(Al)15. Even within this limited set, novel and unexpected properties have been observed. For example, the breakthrough curves collected for CO2 separation from CH4 on MIL-53(Cr) exhibit distinct changes in the slope of effluent CO2 concentration with time, which the authors


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concluded were most likely caused by the breathing of the MOF structure. An even more peculiar “stepped” breakthrough curve was observed for separation of xylenes with MIL-53(Al) and separation of CH4 and CO2 on CID-5. A comparison of a typical breakthrough curve profile using a rigid adsorbent and a representative “stepped” breakthrough curve of a “gating” type flexible MOF is shown in Figure 1.

Figure 1. Comparison of typical breakthrough curves (blue) and isotherms (purple) for rigid microporous adsorbents (top) and “gating” type flexible MOFs (bottom). Gating adsorbents have defined gate opening (point A) and gate closing (point B) pressures that mark the start of transitions between an easily accessible expanded structure and an inaccessible closed structure. The breakthrough curves for gating adsorbents have a “stepped” feature not seen in rigid adsorbents, defined by a plateau in the effluent fraction (defined by a “step height”) prior to ultimate breakthrough.


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Horike et al.5 postulated that the stepped breakthrough of CID-5 could be attributed to rapid and selective adsorption of CO2 when the relative pressure was above the gate opening pressure, and the absence of adsorption when the relative pressure dropped below the gate opening pressure. Finsy et al.15 rationalized the unconventional breakthrough profile in terms of a transition from non-selective adsorption in a single-file adsorption mode for the closed form of the pores, to selective adsorption in a double-file adsorption mode for the open form of the pores. If the unusual breakthrough step is indeed a result of the transition between open and closed structures, then it stands to reason that methods that predict gating or breathing transitions in flexible frameworks can also be used to predict the step heights in breakthrough profiles for these materials. The appropriate thermodynamic method to describe adsorption of fluids in flexible frameworks is the osmotic framework adsorbed solution theory (OFAST) method proposed by Coudert and coworkers6,16–23. The OFAST method has been successfully applied to study breathing and gating effects in flexible frameworks. For example, Tanaka et al.24 used a combination of grand canonical Monte Carlo (GCMC) simulation and OFAST to predict the gate transition that occurs during static adsorption in the elastic layer-structured metal-organic framework Cu(bpy)2(BF4)2 (bpy = 4,4’-bipyridine), commonly referred to as ELM-11. To better understand the novel and unexpected breakthrough behaviors of flexible MOFs additional breakthrough curves for ELM-11, a representative flexible MOF, are reported and analyzed herein using the OFAST approach. The operating hypothesis is that application of the OFAST method to mixed gas adsorption in ELM-11 can be used to predict the occurrence and the height of the steps in a flexible adsorbent’s breakthrough profile.


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EXPERIMENTAL SECTION Material

Preparation.

To

obtain

ELM-11,

its

un-activated

precursor,

[Cu(bpy)(BF4)2(H2O)2]bpy, termed pre-ELM-11, was purchased from the Tokyo Chemical Industry Co., Ltd. (CAS Number: 854623-98-6, Product Number: C2409) at >98% purity. PreELM-11 is readily converted to ELM-11 by degassing under vacuum (99.99%) CO2 gas at 258, 273, 304, 308, 318, 328, 338, and 348 K using a Micromeritics ASAP 2050 extended pressure volumetric adsorption analyzer. The temperature in the sample tube was controlled by an external recirculating bath. The measured CO2 adsorption isotherms used for model fitting are shown in Figure S4. Adsorption isotherms for He, N2, and CH4 on the expanded ELM-11 structure were calculated using grand canonical Monte Carlo (GCMC) simulation performed in MCCCS Towhee26. The rigid ELM-11 structure used for the GCMC simulations was the expanded structure reported by Kondo et al.27, with an additional 5% expansion of the interlayer distance included to achieve better agreement with experimental CH4 isotherms reported by Kanoh et al.8 Supporting Information section S5 contains additional simulation details. A sample Towhee input file is included in Supporting Information section S6.


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RESULTS AND DISCUSSION Stepped Breakthrough Curves of ELM-11. Figure 2 shows CO2 breakthrough curves for ELM-11 for a 60:40 CH4/CO2 gas mixture displacing helium at 258 K and for pure CO2 displacing helium at 273 K. What is immediately apparent in both graphs is a step in the breakthrough curve not seen for rigid adsorbents or inflexible MOFs, but observed for other flexible frameworks as discussed in the introduction. Closer inspection of Figure 2 reveals that

Figure 2. CO2 breakthrough curves for 60:40 CH4/CO2 à He at 258 K (top) and CO2 à He at 273 K (bottom). CO2 and CH4 are represented by closed and open symbols respectively. A sharp drawdown in CO2 concentration, indicative of rapid adsorption, is noted in the bottom figure.


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the steps occur at 20% CO2 at 258 K, and at 30% CO2 at 273 K. This corresponds to CO2 partial pressures of 22 kPa at 258 K, and 33 kPa at 273 K, both of which are comparable to the gate opening pressures observed for pure CO2 isotherms at these temperatures (21 kPa at 258 K and 35 kPa at 273 K). This lends credence to the interpretation of Horike et al.5 that the step height in the breakthrough curve is related to the gate-opening phenomenon. Another observation that provides evidence of a connection between gate opening and the step in the breakthrough curve is the sharp reduction in the gas flow through the column that occurs when the influent gas mixture containing CO2 reaches the adsorbent bed. A reduction in gas flow is consistent with a sharp drop in the column pressure as CO2 rapidly adsorbs onto ELM-11 after gate opening. A pressure wave at the onset of a rise in the CO2 effluent concentration, such as that shown in the bottom panel of Figure 2 was observed in many of the CO2 breakthrough curves measured on ELM-11. Because the gas flow influent to the column is kept constant with time, measurement of breakthrough becomes problematic when adsorption of CO2 is so rapid that it exceeds the rate at which gas is supplied to the column, and the effluent flow rate falls to zero. This was particularly an issue for breakthrough measurements in which pure CO2 was used as the displacing fluid. Without continuous gas flow at the column exit to monitor the effluent gas composition, it is not possible to collect accurate data on the breakthrough step height. To work around this experimental limitation, the remainder of the results presented herein were obtained from CO2 release experiments in which a gas that does not adsorb or that sparingly adsorbs is flowed over an adsorbent bed that has been pre-loaded with CO2. For this type of breakthrough measurement, a carrier gas is always present in the effluent, and this prevents the occurrence of a sudden pressure drop and ensures a nonzero effluent flow rate.


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Rather, as CO2 desorbs from the ELM-11 adsorbent and joins the flush gas stream, the gas flow rate through the column increases slightly. Figure 3 shows a representative sample of CO2-release curves obtained by passing pure CH4, N2, and He at various temperatures over an ELM-11 adsorbent bed preloaded with CO2. It is seen that the observed step height is a function of both temperature and the gas species used to displace CO2 in the column, as one would expect if the step height is related to the gating transition. As might be anticipated, the step height corresponding to the effluent CO2 concentration increases and the duration of the step decreases as the column temperature increases. The higher the temperature, the higher the corresponding pressure for gate closing, and the more swiftly expulsion of CO2 occurs from the collapsing framework as CO2 is purged from the gas phase of the column. Interpretation of the effect of the displacing gas species on the breakthrough release profile is decidedly less straightforward, however. With respect to the molecular properties one might expect to be important in determining the gating transition, methane, nitrogen, and helium have significant distinctions. CH4 is a nonpolar

Figure 3. CO2 release curves on ELM-11 for CH4àCO2 (left), N2àCO2 (center), and HeàCO2 (right) at temperatures ranging from 258 to 302 K.


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spherical molecule that is larger than CO2 and undergoes gated adsorption on ELM-11 at high pressure (20 to 40 bar at 303 K)8. N2 is a quadrupolar linear molecule similar in size to CO2 that has gated adsorption on ELM-11 at cryogenic temperatures (P/P0 ~ 0.1 at 77 K)7. Helium is a nonpolar inert monatomic gas that is considerably smaller than CO2 and has no reported adsorption, gated or otherwise, on ELM-11. The isotherms for these three gases on ELM-11 obtained from molecular simulation do not show a gating transition at the temperatures and pressures of the experimental measurements reported in Figure 3. Moreover, it is interesting to note that when He, the molecule with the smallest kinetic diameter of the three gases is used as the flush gas, the CO2 release curves have significantly lower step heights than those obtained when CH4, the molecule with the largest kinetic diameter, is the flush gas. Although pure CH4 and pure N2 do not induce gating at the temperatures and pressures shown in Figure 3, they are known to gate adsorb at higher pressures and lower temperatures, and so it might reasonably be expected that the co-adsorption of CH4 or N2 could assist CO2 with gate opening or gate closing on ELM-11, i.e., a lower CO2 partial pressure would be required for gating. If this were the case, breakthrough experiments using these gases to displace preloaded CO2 should show lower CO2 step heights than corresponding experiments using He, a gas for which no significant co-adsorption is anticipated. However, the CO2 release curves of Figure 3 do not fit these expectations. Comparison with OFAST. To better understand co-adsorption on flexible MOFs and interpret the breakthrough measurements obtained for ELM-11, experimental isotherms and breakthrough results were compared against predictions obtained using the three OFAST models described previously. Figure 4 shows the comparison between the expected values of Pgate (or equivalently, the gas composition Ygate) obtained from the OFAST model predictions and the


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partial pressure of CO2 (or gas composition) at the step height observed in breakthrough/release curves for temperatures ranging from 255 to 315 K. The diagonal line represents a 1:1 match of predicted and measured values. Points above the line indicate that the model overestimates the partial pressure of CO2 required to cause the gating transition (as indicated by the step height) at a given temperature, whereas points below the line indicate the model underestimates the pressure at which gating occurs.

Figure 4. Correlation of expected values obtained from OFAST model 1 (top row), model 2 (middle row), and model 3 (bottom row) with values of the CO2 step height observed from pure He displacing pure CO2 (HeàCO2; far left column; open circles), pure N2 displacing pure CO2 (N2àCO2; middle left column; open triangles), pure CH4 displacing pure CO2 (CH4àCO2; middle right column; open squares), and CO2 mixtures displacing He (CO2/MixàHe; far right column; closed circles) breakthrough experiments. CO2 release curves and CO2 breakthrough curves are outlined in black and blue respectively. Each experimental value is represented by two points determined by tracking CO2 as CO2 (black) or CO2 as CO (red) by mass spectrometry.


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Two points are shown for each experiment. The first point, shown in black, is obtained using mass spectrometer readings for ion mass 44, which is a direct measure of the CO2 concentration in the effluent. The second point, shown in red, is obtained using mass spectrometer readings for ion mass 28, which is an indirect measure of CO2 from the generation of carbon monoxide by CO2 ionization within the mass spectrometer. (Only one point is used for the experiments where N2 displaces CO2, since N2 and CO share the same molecular weight.) As seen in the top row of Figure 4, Model 1 overestimates the CO2 partial pressure required to cause gating in ELM-11. Of the four breakthrough tests conducted (CH4àCO2, N2àCO2, HeàCO2, and CO2/MixàHe), Model 1 yields the best correlation with the step height observed in the release curves when methane is the flush gas (CH4àCO2). Because the parameter estimation method used to develop Model 1 implicitly assumes that only CO2 is important in determining the gating transition, the implication is that CH4 molecules do not impact the gating transition when CO2 is the controlling gas species. Meanwhile, Model 1 performs the most poorly when helium is the flush gas (HeàCO2), implying that He molecules do significantly impact the gating transition when CO2 is the controlling gas species. Relative to the expectations of Model 1, the presence of He lowers the partial pressure of CO2 required to maintain the expanded structure or initiate gate closing. Since helium is chemically inert, its influence on the gating transition must be due to a physical interaction between He, CO2, and the ELM-11 framework. The effects of He could be due simply to co-adsorption of He and CO2; however, the results of Model 2 cast doubt upon this interpretation. Model 2 uses IAST to determine mixture co-adsorption, using both simulated and experimental single-component isotherms, before applying the OFAST method to predict the gating pressure. In general, the inclusion of co-adsorbed species into the OFAST calculation has


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the effect of lowering the predicted partial pressure of CO2 required to maintain the expanded structure or initiate gating. This can be rationalized in that the presence of another adsorbing species compensates for a smaller number of CO2 molecules adsorbed between the layer planes of the adsorbent. Because this model specifically accommodates the inclusion of multiple gas species, the predictions for Model 2 in Figure 4 are reported as the minimum mole fraction Ygate of CO2 in the adsorbing gas mixture at a specified total pressure (in this case, 108 kPa) that can maintain the expanded ELM-11 structure or initiate a gating transition. Note that the experimental results used for evaluation of Model 2 are the same as those used to compare against the Model 1 predictions. Based on a comparison of the top and middle rows of Figure 4, using IAST to estimate mixed gas adsorption on ELM-11 does not significantly improve the predictions for the step height in release curves where He or N2 is the flush gas (N2àCO2 and HeàCO2), but it does make the predictions where methane is the flush gas (CH4àCO2) noticeably worse. In other words, including co-adsorption effects through the use of IAST in Model 2 does not account for the true influence of N2 and He on the gating process, and it overestimates the influence of CH4. Based on IAST, CH4 should co-adsorb with CO2 on ELM-11 more readily than N2 or He. From the OFAST formulation, co-adsorption of CH4 and CO2 should stabilize the expanded ELM-11 structure, preventing gate closure until the partial pressure of CO2 has reached a new, lower, critical threshold. For CO2/He and CO2/N2 mixtures, IAST suggests that He and N2 do not readily co-adsorb with CO2 and should therefore not impact the threshold when gate closure occurs. Yet the experimental breakthrough curves clearly show the opposite. The presence of N2 or He has a large impact on the observed step height, and by proxy on gate closure, while the presence of CH4 has no noticeable impact on these features. Flexible MOFs like ELM-11 are clearly more


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sensitive to gas composition than has previously been recognized, such that current coadsorption models cannot reproduce the effects of composition on breakthrough characteristics. Model 3 also uses IAST to determine mixture co-adsorption before applying the OFAST method, but in this case the estimate of Pgate is taken from the observed step height. Model 3 is thus a direct semi-empirical fitting of the observed breakthrough curves. Model 3 can only be used in a predictive capacity after a suite of breakthrough curves have already been measured and used for fitting. By contrast, Models 1 and 2 can be developed a priori and used in a predictive capacity prior to experimental measurement of breakthrough, as these models are based solely on adsorption theory and fittings of pure component isotherms. The alternative route for fitting Pgate in Model 3 results in a modified estimate of the free energy difference (ΔFhost) between the closed and open structures of ELM-11 for different gas mixtures. The critical threshold of CO2 expected to cause gating is again reported in Figure 4 for Model 3 as the mole fraction of the adsorbing gas mixture (Ygate) at a specified total pressure (108 kPa). If the simplified OFAST formulation of equation (4) used in this work is mathematically sufficient to describe mixed gas adsorption under dynamic conditions, then direct fitting of the experimental breakthrough curve in Model 3 should yield predictions for the breakthrough step height that closely match experimental results. In Figure 4, it is indeed observed that fitting the OFAST model directly to Ygate values obtained from breakthrough experiments better aligns predicted and measured values for all purge gas compositions and temperatures. This suggests that the poor agreement between theory and experiment for Model 1 and Model 2 was due to the underlying limitations of parameter estimation from pure component isotherms and IAST, rather than from a fundamental inapplicability of the underlying mathematical prescription of the OFAST model.


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It should be emphasized that the good fit for Model 3 does not mean that the fitted parameters are inherently “correct”. For example, the poor accounting of gas co-adsorption effects in Model 2 can be compensated for by adjusting the value of the free energy difference (ΔFhost) to obtain a good fit to the experimental breakthrough curves. However, the resulting model is only predictively useful in the temperature, pressure, and mixture composition range of the breakthrough curves used for the fitting. To understand why Model 1 and Model 2 had poor predictive capabilities, even while the OFAST formulation appears mathematically satisfactorily to model the breakthrough and release of gas mixtures on flexible adsorbents, it is necessary to explore both the assumptions underlying IAST and the impact that gas molecular properties might have on the gating transition. The two main assumptions of IAST are that the components of the gas mixture behave as ideal gases and that the surface of the adsorbent is homogeneous.11 The latter assumption is a problem in flexible frameworks, where the pore surface can adjust to accommodate absorbate molecules. The solution proposed by Coudert, and used here in Model 2, is to apply IAST separately to rigid approximations of the expanded and closed forms of the framework.23 However, the rigid approximation obtained from single component isotherms may fail to correctly estimate coadsorption if the interlayer distance required to accommodate one molecule between the layer planes is significantly different from the interlayer distance required to accommodate a differently sized molecule between layers. If we compare the molecular diameters of CH4 (4.046 Å), N2 (3.578 Å), CO2 (3.469 Å), and He (2.557 Å), as calculated by quantum mechanical methods, we see that CH4 is significantly larger than CO2 and N2, while He is significantly smaller.28 If CO2 is the controlling species during the gating transition, the layer plane expansion caused by gated adsorption of CO2 may not necessarily be large enough to accommodate the


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larger CH4 molecules. The IAST estimate, which uses single component methane isotherms to develop the estimate of co-adsorption, implicitly assumes that there is only one expanded structure, one that is large enough to accommodate either CO2 or CH4. Size exclusion of CH4 from the ELM-11 structure, which is not taken into account by the expanded structure approximation obtained from combined single-component isotherms, would explain the good correlation of Model 1 and the poor correlation of Model 2 with the CO2 step heights observed in the CO2-release curves where methane is the flush gas. This conclusion is in keeping with reported studies that have shown that breakthrough curves of flexible frameworks are highly sensitive to adsorbate size and shape. For example, Gücüyener et al.14 found that the gating framework ZIF-7 could selectively adsorb ethane over the similarly sized but differently shaped ethylene, in contrast with most microporous materials which selectively adsorb olefins over paraffins. The significant overestimation of the CO2 step heights obtained from both Model 1 and Model 2 for the N2àCO2 and HeàCO2 breakthrough release curves requires a more subtle interpretation. It is possible that the simulated isotherms used in this work for He and N2 significantly underestimate the adsorption capacity for these gases on the expanded ELM-11 structure. If this is the case, then IAST, and by extension Model 2, will also underestimate the co-adsorption of these molecules with CO2. However, as discussed previously, one of the main attractions of elastic layered MOFs like ELM-11 is their apparent high selectivity for CO2 over other gas species like N2. For example, Kanoh et al.8 were able to recover highly pure (>99%) CO2 from a CO2/N2/O2 mixture at 268 K through a single adsorption and desorption cycle on ELM-11. This argues against significant co-adsorption of N2 with CO2 on ELM-11. Size exclusion, which can explain the outcomes of the CH4àCO2 experiments, would not apply to


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the N2àCO2 and HeàCO2 displacements as N2 is similar in size to CO2 and He is much smaller. Instead, N2 and He must have an impact on the gating transition that is unrelated to the total quantity of molecules adsorbed ∆𝑁!"! , which is the parameter by which the OFAST method determines the gating transition for co-adsorption of gas mixtures. Previous work by Cheng et al.29 showed that the gate pressure of ELM-11 can be modified through the inclusion of trace amounts of alcohol during adsorbent synthesis. It was postulated that these trace molecules serve to prop open the ELM-11 framework, making it easier to dehydrate the structure and lowering its gate pressure. Since N2 and He are respectively similar in size to and smaller than CO2, it is possible that a small number of these molecules can infiltrate the expanded ELM-11 structure while CO2 is desorbing, but before the ELM-11 structure has entirely collapsed. Acting somewhat like “doorstops”, N2 and He molecules would prop open the ELM-11 framework in a manner analogous to that of the alcohols in the synthesis of pre-ELM-11, allowing CO2 molecules to remain adsorbed or to reabsorb at pressures significantly below the gate closing pressure expected from the single component isotherm for CO2. This interpretation is bolstered by the OFAST results of Model 3, which brings the Model 2 approach into agreement with the experimental breakthrough curves by modification of the ∆𝐹 !!"# parameter. As discussed previously, ∆𝐹 !!"# is the free energy difference between the collapsed and open structures of the ELM-11 framework. Changes in this parameter suggest changes in the underlying energetics of the crystal structure that are independent of the amount adsorbed, which is accounted for by other terms of the OFAST equation. The combined processes of size exclusion and small molecule infiltration leading to a “doorstop” type effect are visually summarized in Figure 5.


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Figure 5. Visualization of size exclusion and “doorstop” effects in the gating transition of an elastic layer-structured metal organic framework pre-loaded with adsorbed CO2 molecules during purging with either methane or helium. Shown in the lower right corner is a comparison of typical breakthrough curves for CH4àCO2 (orange solid line) and HeàCO2 (grey dashed line) at the same temperature.


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Implications for Carbon Capture with Flexible MOFs. The unique stepped breakthrough curves, characteristic of flexible MOFs, warn against the assumption that these materials can simply be substituted for rigid framework adsorbents to achieve similar results in gas separation applications using, for instance, pressure swing adsorption. While the gating transition does in principle allow for low-energy regeneration of a flexible adsorbent in a flow-through system, the trade-off for this energy benefit may be a hard ceiling on the amount of CO2 that can be removed from the gas feed mixture. For example, suppose CO2 removal in excess of 90% is desired from a flue gas stream that has a CO2 partial pressure of 10 kPa. This requires a CO2 partial pressure in the effluent from the adsorbent bed of less than 1 kPa. If a gating adsorbent is used, then the gate pressure for CO2 will also need to be less than 1 kPa to reach the desired threshold. A flexible framework with a gate pressure of 5 kPa, for example, will not adsorb CO2 below a partial pressure of 5 kPa, and so as the CO2 partial pressure decreases along the direction of flow in the adsorber unit, gate opening will not occur in the downstream portion of the bed where the CO2 partial pressure remains below 5 kPa. Recalling the breakthrough curve in Figure 2, in the scenario described here, only 50% of the CO2 in the feed will be captured prior to breakthrough, and the adsorbent bed will discharge an effluent with a step height corresponding to 5 kPa CO2. Whereas a rigid adsorbent will adsorb some CO2 at low partial pressure, single-step gating frameworks like ELM-11 that have no microporosity in the “collapsed” configuration will not adsorb any CO2 below the gate pressure. While this result may seem obvious in retrospect, its implications for adsorbent bed and column design heretofore have not been discussed in the literature. As compared to rigid frameworks, the suitability of a particular flexible framework for carbon capture may thus depend more on the temperature dependence of its gating transition than on its measured heat of adsorption or its CO2 capacity. A straightforward solution to this


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potential limitation is to overpressure the feed gas so that the CO2 partial pressure remains above the gate pressure along the entire length of the column. This approach will however incur an energy penalty in the work input required to pressurize the feed gas. Another, more subtle workaround was demonstrated by Horike et al.5, who used a solid solution of two zinc-based 2D porous coordination polymers, CID-5 and CID-6, to cleanly separate methane from binary mixtures of carbon dioxide and ethane. CID-5 has more structural flexibility than CID-6 and exhibits selective gated adsorption for CO2 and C2H6 over CH4, whereas CID-6 has permanent microporosity and non-selectively adsorbs all three gases. In breakthrough experiments with a 60:40 vol% CH4 / CO2 mixture and a 90:10 vol% CH4 / C2H6 mixture on CID-5, the CH4 fraction in the effluent was about 90%, well below the desired target near 100%, on account of gate closure effects noted earlier when the partial pressure of the gateopening species is insufficient to yield access to the gated pore volume. Neither was an effluent nearly pure in methane produced when breakthrough experiments for the same gas mixtures were performed on CID-6, as this material co-adsorbs both species from the gas mixtures in substantial amounts. However, Horike et al. demonstrated that a solid solution of CID-5 and CID-6 with gated adsorption characteristics for both CO2 and C2H6, prepared by substituting 10% of the nitroisophthalate ligands of CID-5 with the methoxyisophthalate ligands of CID-6, cleanly separated methane from both carbon dioxide and ethane for retention times of eight minutes and 25 minutes respectively in breakthrough column experiments. Hence, by judicious selection of the ligand composition, the gate-opening pressure of a CID-5/6 solid solution was successfully tuned so as to optimize its gas separation properties under dynamic conditions. Other categories of flexible framework adsorbents should be expected to have breakthrough behaviors and application limitations similar to ELM-11. It should be noted that ELM-11


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exhibits rapid kinetics7 for gas adsorption and desorption. The absence of internal mass transfer resistance contributes to the distinct step in the CO2 breakthrough profile for ELM-11. By contrast, a gated adsorbent with slow sorption kinetics may not exhibit as distinct a step in its breakthrough curve.

SUMMARY AND CONCLUSIONS The breakthrough performance of the elastic layered metal-organic framework ELM-11 was systematically explored as this material constitutes a representative example of a gated adsorbent. ELM-11 exhibits a stepped breakthrough curve for CO2 not seen in rigid adsorbents. The CO2 step height observed in the breakthrough experiment was a function of temperature, pressure, and mixture composition, consistent with evidence that the step originates from the ELM-11 gating transition. Osmotic framework adsorbed solution theory, which has previously been shown to correctly predict the gating transition in flexible frameworks, was used to predict the breakthrough step height for CO2 uptake and release on ELM-11. Three OFAST models were developed and compared with CO2 breakthrough and release curves obtained from experimental measurements. It was determined that the OFAST method can be used to predict the step height in breakthrough curves from single component isotherms of the target gas species, in this case CO2, although the model predictions consistently err on the conservative side. Using ideal adsorbed solution theory within the OFAST method to account for co-adsorption of gas molecules on the expanded structure of the framework did not result in improved model accuracy, unless the estimate for the free energy difference between the open and closed structures (∆Fhost) was also modified through the fitting of the OFAST model parameters directly from the experimental breakthrough/release curves. It was found that the CO2 step height


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observed in the breakthrough experiments is sensitive to the kinetic diameters of the component species in the influent gas mixture. When a gas species such as helium with a comparatively small kinetic diameter is used as the flush gas, the resulting CO2 step height shows a greater deviation from OFAST model expectations than when a flush gas with a large kinetic diameter relative to the target gas species is used. These unexpected phenomena can be explained through a combination of size exclusion and “doorstop” effects, wherein co-adsorbing species are either too large to insert into the open framework (as in the case of CH4/CO2 co-adsorption), or appropriately sized to “prop open” a closing framework and sustain transfer between the adsorbed and gas phases (as observed for N2/CO2 and He/CO2 co-adsorption).

ASSOCIATED CONTENT Supporting Information. The reader is referred to the supporting information for additional details regarding material characterization; the breakthrough column experimental apparatus; OFAST model development; sample MATLAB codes; GCMC simulation parameters; and a sample Towhee input file. This material is available free of charge at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author Email: *[email protected]

ACKNOWLEDGMENT The authors gratefully acknowledge support from the National Science Foundation for this work under award number 1034116.


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