Metrics for Evaluation and Screening of Metal–Organic Frameworks for Applications in Mixture Separations

Abstract

For mixture separations, metal–organic frameworks (MOFs) are of practical interest. Such separations are carried out in fixed bed adsorption devices that are commonly operated in a transient mode, utilizing the pressure swing adsorption (PSA) technology, consisting of adsorption and desorption cycles. The primary objective of this article is to provide an assessment of the variety of metrics that are appropriate for screening and ranking MOFs for use in fixed bed adsorbers. By detailed analysis of several mixture separations of industrial significance, it is demonstrated that besides the adsorption selectivity, the performance of a specific MOF in PSA separation technologies is also dictated by a number of factors that include uptake capacities, intracrystalline diffusion influences, and regenerability. Low uptake capacities often reduce the efficacy of separations of MOFs with high selectivities. A combined selectivity–capacity metric, Δq, termed as the separation potential and calculable from ideal adsorbed solution theory, quantifies the maximum productivity of a component that can be recovered in either the adsorption or desorption cycle of transient fixed bed operations. As a result of intracrystalline diffusion limitations, the transient breakthroughs have distended characteristics, leading to diminished productivities in a number of cases. This article also highlights the possibility of harnessing intracrystalline diffusion limitations to reverse the adsorption selectivity; this strategy is useful for selective capture of nitrogen from natural gas.

1. Introduction

During the last 2 decades, there has been a substantial increase in the development and synthesis of novel microporous crystalline materials for use as selective adsorbents in a variety of industrially important separation applications; examples of such materials include metal–organic frameworks (MOFs), zeolitic imidazolate frameworks (ZIFs), porous organic cages, porous aromatic frameworks, covalent organic frameworks, and polymers with intrinsic microporosity. Such separations are normally carried out in fixed bed devices that are operated in a transient mode, consisting of adsorption and desorption cycles. In one class of applications, the motivation has been to afford energy-efficient and environmentally benign alternatives to conventional separations such as absorption, distillation, extraction, or crystallization. In other cases, there are incentives for enhancing the separation performance by replacing the currently used microporous adsorbents such as cation-exchanged zeolites and activated carbon (AC) with tailor-made MOFs. To set the scene and define the objectives of this article, we consider a number of mixture separations that may be targeted for the development of novel MOFs.

Arguably, the most important and successful industrial application of adsorption separations is for H₂ purification. The catalytic reforming of natural gas, when combined with a water gas shift reaction step, yields a hydrogen-rich product stream containing a number of impurities such as H₂O vapor, CO₂, CH₄, CO, and N₂.¹⁻³ These impurities must be removed in order to attain the 99.95%+ H₂ purity that is normally demanded.¹ In fuel cell applications, the purity demands are as high as 99.99%+.^2,4 Large-scale production of hydrogen, with the desired purity, is carried out in pressure swing adsorption (PSA) units that are operated at pressures reaching about 7 MPa using the Skarstrom cycle, involving multiple steps or stages; see the schematic in Figure 1. In the simplest case, the four steps in the sequence are as follows.⁵⁻⁷

• (a)Pressurization (with the feed or raffinate product)
• (b)High-pressure adsorption separation with the feed, with withdrawal of the purified raffinate product
• (c)Depressurization, or “blowdown”, countercurrent to the feed
• (d)Desorption at the lower operating pressure. This is accomplished by evacuation or purging the bed with a portion of the purified raffinate product.

Figure 1.

Sequential steps in the operation of a fixed bed adsorber in the Skarstrom cycle for H₂ purification.^2,5−7

The use of layered beds, consisting of three different adsorbents, is an important characteristic of the currently employed PSA technology for H₂ purification.^2,8 In order to rationalize and understand the use of multilayer adsorbent beds, Figure 2a,b presents simulations of transient breakthroughs of 73/4/3/4/16 H₂/N₂/CO/CH₄/CO₂ mixture, typical of steam methane reformer off-gas,³ in fixed bed adsorbers packed with (a) AC and (b) LTA-5A zeolite⁸⁻¹⁰ operating at 2 MPa total pressure and temperature T = 313 K. Purified H₂ can be recovered during the time intervals between the breakthroughs of H₂ and N₂, as indicated by the arrows. The stronger binding of N₂ in LTA-5A, as compared to AC, is due to the contribution of the quadrupole moment of N₂ and its interaction with the charges of extraframework cations Na⁺ and Ca²⁺.^5,11 The quadrupole moment of CO₂ also leads to stronger binding in LTA-5A, causing significantly higher CO₂ capture capacity, as evidenced by the strongly delayed breakthrough of CO₂ with LTA-5A as compared to AC.^5,11 The strong binding of CO₂ in LTA-5A is disadvantageous because deep vacuum will be required to reduce the CO₂ loading to the desired level during the purge step (d) in Figure 1. Consequently, despite the superior separation performance of LTA-5A, resulting in higher productivity of pure H₂ per kilogram of adsorbent, LTA-5A is not used on its own in the currently used PSA schemes.^2,3 Commonly, the first layer is either alumina or silica that retains the water vapor. Then, an AC layer is used to selectively adsorb CO₂. The main task of the alumina and AC layers is to prevent the H₂O vapor and CO₂ from reaching the zeolite layer.² The last layer is a cation-exchanged zeolite [such as LTA-5A, and NaX (=13X),¹² with Na⁺ cations] with enhanced capacity for CO and N₂. For H₂ purification applications,^3,13−15 it is evident that CO₂/H₂ adsorption selectivity is not the “key” determinant of the achieved purity of H₂.

Figure 2.

Transient breakthrough of 73/4/3/4/16 H₂/N₂/CO/CH₄/CO₂ mixtures in a fixed bed adsorber packed with (a) AC and (b) LTA-5A zeolite operating at a total pressure of 2 MPa and T = 313 K. For presenting the breakthrough simulation results, we use as x-axis the dimensionless time, τ = tv/L, where L is the length of the adsorber and v is the interstitial gas velocity.^63,122 Further information on input data and simulation details are provided in the Supporting Information.

For CO₂ capture from flue gases from power plants, and from natural gas streams, MOFs offer energy-efficient alternatives to conventionally used amine absorption technologies.¹⁶⁻²¹ In CO₂/flue gas and CO₂/natural gas separations, the process economics would demand high CO₂ capture capacity and concomitant ease of regeneration.²²

For the production of alkene feedstocks of 99.95%+ purity required for polymerization reactors, cryogenic distillation columns, operated at high pressures and high reflux ratios, are commonly employed for large-scale separations of C₂H₄/C₂H₆ and C₃H₆/C₃H₈ mixtures. Many MOF developments have targeted alkene/alkane separations with the objective of eventually supplanting the energy-intensive distillation technologies.²³⁻²⁹ Process economics would also demand high alkene productivities per kilogram adsorbent.

In steam cracking of ethane to produce ethene (C₂H₄), one of the byproducts is ethyne (C₂H₂). Typically, the C₂H₂ content of C₂H₂/C₂H₄ feed mixtures is 1%. Ethyne has a deleterious effect on the polymer products of ethene, such as polyethene. The impurity level of C₂H₂ in the C₂H₄ feed streams should be below 40 ppm in order to prevent the poisoning of catalysts used in the polymerization of C₂H₄. MOFs offer potential improvements to absorption technologies using dimethyl formamide as a solvent.^23,30−37 For 1/99 C₂H₂/C₂H₄ mixture separations, we would require that the MOF would have high productivity of pure alkene (<40 ppm C₂H₂) per kilogram of adsorbent.

Ethyne (C₂H₂) is an important building block in industrial chemical synthesis and is also widely used as a fuel in welding equipment. C₂H₂ is commonly manufactured by the partial combustion of CH₄ or comes from cracking of hydrocarbons. In the reactor product, C₂H₂ coexists with CO₂ or C₂H₄. Because of the similarity of molecular sizes and shapes (C₂H₂: 3.32 × 3.34 × 5.7 ų and CO₂: 3.18 × 3.33 × 5.36 ų), the separation of C₂H₂/CO₂ mixtures is particularly challenging.^38,39 Because the boiling points of C₂H₂ (189.3 K) and CO₂ (194.7 K) are close, distillation separations need to operate at cryogenic temperatures and high pressures. A number of recently developed MOFs offer the potential of use in adsorptive separations of C₂H₂/CO₂ mixtures.⁴⁰⁻⁵³

The selective capture of CO₂ from the reactor effluents from the process for oxidative coupling of methane essentially requires for CO₂-selective separation of CO₂/CH₄/C₂H₄/C₂H₆ mixtures; the number of candidate adsorbent materials is surprisingly limited.⁵⁴⁻⁵⁶

Noble gases such as He, Ne, Ar, Kr, and Xe find a variety of applications.⁵⁷ For example, heliox (a mixture of He and O₂) is used for patients with respiratory difficulties and in deep-sea diving,⁵⁸ Ne is used in the familiar “neon sign” for advertisements. Kr and Xe are used in flash bulbs and lasers. Ar is used in filament bulbs and in electric arc welding as a shielding gas. Based on the differences in the boiling points, Ne (27 K), Ar (87 K), Kr (120 K), and Xe (165 K) are commercially produced by liquefaction of air, followed by cryogenic distillation. Alternatively, adsorptive separations, relying essentially on the differences in polarizabilities (cf. Figure 3), are realizable with a number of MOFs.^57,59,60

Figure 3.

Boiling points and polarizabilities of noble gases culled from web sources.

The process demands in each of the aforementioned examples of mixture separations are different. The primary objective of this article is to provide a comparative assessment of the variety of metrics that are appropriate for screening and ranking candidate MOFs that are appropriate for the specific separation task in hand. The Supporting Information provides detailed structural information on the MOFs investigated, along with a detailed description of the methodology used for transient breakthrough simulations. For each of the chosen mixtures, the comparisons of the separation performance of various MOFs are on the basis of experimental data on the unary isotherms from published sources; the data sources are provided in the Supporting Information.

2. Adsorption Selectivities, Uptake Capacities, and Transient Breakthroughs

2.1. Xe/Kr Separations

To develop an understanding of the various metrics that determine the effectiveness of separations, let us consider the separation of 20/80 Xe(1)/Kr(2) mixtures in a fixed bed packed with CoFormate (=Co₃(HCOO)₆); the objective is to produce Kr with less than say 1000 ppm Xe. Because of the commensurate positioning of Xe within its cages, CoFormate displays high Xe/Kr selectivity.⁶¹ The continuous solid lines in Figure 4 represent transient breakthrough simulation results for the dimensionless concentrations c_i/c_i0 at the exit of the fixed bed. The breakthroughs have distended characteristics that are caused by intracrystalline diffusional limitations. For subsequent discussions, it is useful to also consider the limiting scenario in which the concentration fronts traverse the fixed bed in the form of shock waves;^62,63 the shock wave model approximation is shown by the dotted lines in Figure 4; further details of the shock wave model are provided in the Supporting Information. Because the shock wave model has sharp fronts, the separation performance is the maximum achievable, and this simplified model helps to derive simple expressions for the metrics that describe the performance of fixed bed adsorbers.

Figure 4.

Transient breakthrough simulations (indicated by the solid blue line) for separation of 20/80 Xe/Kr mixtures at 298 K and 100 kPa in a fixed bed packed with CoFormate; these simulations include intracrystalline diffusion limitations. The dotted lines represent the shock wave model approximation.⁶³ The input data and calculation details are available in earlier works.^57,63,121

In the shock wave model, the traversal velocity for the more strongly adsorbed Xe is significantly lower than that of the poorly adsorbed Kr.^6,7 The Xe capture capacity of CoFormate, q₁, expressed as moles captured per kilogram of adsorbent in the fixed bed can be calculated from a material balance

1

In eq 1, y₁₀ is the mole fraction of Xe at the inlet to the bed, Q₀ is the volumetric flow of the feed gas mixture with total molar concentration, c_t = p_t/RT, t₁ is the breakthrough time for Xe, and m_ads is the mass of the adsorbent. We define the displacement time interval Δt = t₁ – t₂ as the difference between the breakthrough times of Xe(1) and Kr(2); during this interval, pure Kr can be recovered. The productivity of purified Kr, Δq, that is collected during the displacement interval can be determined from the shock wave model⁶³

2

where q₂ is the uptake of Kr in the bed

3

Because its derivation is based on the idealized shock wave model, the quantity Δq, dubbed the separation potential, represents the maximum productivity of the less strongly adsorbed component that can be recovered.

The adsorption selectivity, S_ads, defined by

4

can be related to the breakthrough times by combining eqs 1–4

5

Increasing values of adsorption selectivities, S_ads, results in an increase in the values of Δt/t₁ and . This implies that as the selectivity increases, the breakthrough of Kr occurs increasingly earlier

6

Although a high value of S_ads is always a desirable characteristic, this metric does not guarantee a high productivity of pure Kr that is required of the “best” MOF. The highest productivity of Kr will be offered by the MOF that has the highest value of separation potential Δq = q₁y₂₀/y₁₀ – q₂, which should be regarded as a combined selectivity–capacity metric.⁶³ In order to underscore this observation, Figure 5a,b presents the ideal adsorbed solution theory⁶⁴ (IAST) calculations of (a) component loadings q₂ versus q₁ and (b) separation potential versus adsorption selectivity S_ads for adsorption of 20/80 Xe(1)/Kr(2) mixtures in NiMOF-74,^65,66 Ag@NiMOF-74,⁶⁶ CuBTC,^65,67 SBMOF-2,⁵⁹ CoFormate,⁶¹ and SAPO-34.⁶⁰ The MOF with the highest value of S_ads is CoFormate; however, the highest Δq is achieved by Ag@NiMOF-74. The presence of well-dispersed Ag nanoparticles in Ag@NiMOF-74 causes stronger van der Waals interactions of the polarizable Xe atoms; this results in the higher uptakes and the highest Δq.

Figure 5.

IAST calculations of (a) component loadings q₂ vs q₁ and (b) separation potential vs adsorption selectivity S_ads for 20/80 Xe(1)/Kr(2) mixture adsorption at 298 K and 100 kPa in six different MOFs: NiMOF-74^65,66 Ag@NiMOF-74,⁶⁶ CuBTC,^65,67 SBMOF-2,⁵⁹ CoFormate⁶¹ (=Co₃(HCOO)₆), and SAPO-34.⁶⁰ (c) Comparison of the transient breakthrough simulations for separation of 20/80 Xe/Kr mixtures at 298 K and 100 kPa in fixed beds packed with CoFormate and Ag@NiMOF-74. The dimensionless concentrations at the exit of the fixed bed are plotted as a function of Q₀t/m_ads, where Q₀ is the volumetric flow rate of the gas mixture at the inlet to the fixed bed, expressed in L s^–1, at STP conditions. (d) Plot of the productivity of pure Kr, determined from breakthrough simulations, vs the IAST calculations of for six different MOFs with y₁₀ = 0.2; y₂₀ = 0.8. Further information on input data and simulation details are provided in earlier works.^57,63,121

Because the productivity of pure Kr, Δq, is proportional to the displacement time interval, Δt = t₁ – t₂, an alternative procedure for screening MOFs for Xe/Kr separations would be on the basis of the displacement intervals, determined by comparing transient breakthroughs in fixed beds, that are determined from experimental data or transient breakthrough simulations. Figure 5c compares the transient breakthrough simulations for Ag@NiMOF-74 and CoFormate on this basis. The transient breakthrough simulation methodology is described in detail in the Supporting Information. Briefly, the assumptions made in the simulations are as follows: (1) axial dispersion effects are considered to be negligible, (2) the mixture adsorption equilibrium can be described using IAST, (3) the column pressure drop is of negligible importance, and (4) the total pressure remains constant during the operation. Because the breakthrough times are dependent on the mass of the adsorbent, m_ads, and the volumetric flow rate, Q₀, the appropriate comparison of transient breakthroughs for different MOFs is to use the parameter Q₀t/m_ads as the x-axis in place of time; indeed, this parameter may be viewed as a “corrected” time. It is also a common practice to use the value of Q₀ at STP conditions. Noteworthily, the breakthroughs of both Ag@NiMOF-74 and CoFormate have distended characteristics. Because of intracrystalline diffusion limitations, the breakthrough characteristics of CoFormate are more distended than that of Ag@NiMOF-74. In the industry, the process requirement would demand the production of Kr containing <1000 ppm Xe. During the displacement intervals indicated by the arrows, the industrial process requirements may be met.⁵⁷ To determine the actual amount of Kr of desired purity that may be recovered, the total amount of Kr that exits the fixed bed during the displacement interval is determined by sampling of the exit gas from the fixed bed; from such sampling, the productivities of pure Kr are 125 L (STP) kg^–1 for Ag@NiMOF-74 and 68 L (STP) kg^–1 for CoFormate. Despite having the highest S_ads value, the significantly poorer productivity of CoFormate is directly ascribable to its lower uptake capacity (cf. Figure 5a). Figure 5d plots the productivities of pure Kr from transient breakthroughs of six different MOFs as a function of the corresponding IAST calculations of Δq. The near-linear relation between the two sets confirms that IAST calculations of the separation potential Δq may be used for screening purposes. Also shown by the continuous solid line in Figure 5d is the parity line 22.4 × Δq for the productivities. Because of the distended nature of the transient breakthroughs in Figure 5c, the actual productivities are lower than 22.4 × Δq.

The MOF crystallites in the fixed bed at the end of the adsorption cycle are predominantly rich in the more strongly adsorbing Xe. Pure Xe can be recovered during the desorption cycle by the application of deep vacuum. The maximum productivity of pure Xe can also be derived from the use of the shock wave model⁶³

7

Figure 6 plots the productivities of pure Xe, containing <1000 ppm Kr, from transient desorption simulations using six different MOFs, against the corresponding IAST calculations of Δq, calculated using eq 7 with y₁₀ = 0.2; y₂₀ = 0.8. The relation between the actual productivities (symbols) and Δq is not perfectly linear. For example, the Xe productivity of CoFormate is slightly lower than that of CuBTC, despite the fact that the separation potential Δq of CoFormate is higher than that of CuBTC. IAST calculations of the separation potential Δq, from eq 7, for screening of MOFs will be of inadequate accuracy in cases of strong diffusional influences.

Figure 6.

Plot of the productivity of pure Xe determined from transient desorption simulations for 20/80 Xe(1)/Kr(2) mixtures vs the IAST calculations of separation potential for six different MOFs with y₁₀ = 0.2; y₂₀ = 0.8. Further information on input data and simulation details are provided in earlier works.^57,63,121

2.2. C₂H₂/CO₂ Mixture Separations

For separation of C₂H₂(1)/CO₂(2) mixtures, most of the suggested MOFs such as PCP-33,⁴⁷ HOF-3,⁴⁸ TIFSIX-2-Cu-i,⁴⁹ JCM-1,⁵⁰ DICRO-4-Cu-i,⁵¹ MUF-17,⁵² UTSA-74,⁴⁶ FJU-90,⁴³ and FeNi-M′MOF⁴¹ are selective to C₂H₂. Consequently, the desired ethyne product is available in the blowdown phase of the Skarstrom cycle of fixed bed operations, as shown in the schematic in Figure 7.

Figure 7.

Sequential steps in the operation of a fixed bed adsorber in the Skarstrom cycle for C₂H₂(1)/CO₂(2) separation.

For the nine selected MOFs, Figure 8a,b presents the IAST calculations of (a) component loadings q₂ versus q₁ and (b) separation potential versus adsorption selectivity S_ads. It is noteworthy that FJU-90 has the highest uptake capacity for ethyne, whereas the highest selectivity is afforded by FeNi-M′MOF. The separation performance in fixed bed adsorbers is dictated by a combination of selectivity and uptake capacities. Figure 8c presents the simulations of the vacuum blowdown cycle in which the equilibrated fixed bed of FJU-90 crystallites at the end of the adsorption cycle is subject to deep vacuum. During the time interval indicated by the arrow, C₂H₂ of the desired purity can be recovered from the gas mixture exiting the fixed bed. For a desired purity of 99%+, the amount of C₂H₂ that is recoverable can be determined from a material balance on the adsorber. These productivity values, expressed as L of the desired product (at STP) per kilogram of adsorbent in the packed bed, for the nine different MOFs are plotted in Figure 8d as the y-axis. The x-axis in Figure 8d is the separation potential, Δq, calculated using eq 7 with y₁₀ = y₂₀ = 0.5, which represents the maximum C₂H₂ productivity that is achievable if the concentration “fronts” traversed the column in the form of shock waves during the desorption cycle. We note that the productivities determined from the transient breakthrough simulations (denoted as symbols) are near linearly related to Δq. Also shown by the continuous solid line in Figure 8d is the parity line 22.4 × Δq for the productivities. Because of the distended nature of the transient desorption breakthroughs, the actual productivities are lower than the parity values. The important conclusion to emerge is that separation potential, Δq, is the appropriate metric to use in the screening of MOFs for C₂H₂/CO₂ mixture separations. The MOF with the highest C₂H₂ productivity is FJU-90, which does not possess the highest selectivity but the highest Δq.

Figure 8.

IAST calculations of (a) component loadings q₂ vs q₁ and (b) separation potential vs adsorption selectivity S_ads for the adsorption of C₂H₂(1)/CO₂(2) mixtures in nine different MOFs operating at 298 K and 100 kPa. (c) Simulations of transient desorption (blowdown) under deep vacuum (0.2 Pa total pressure and 298 K). During the time interval indicated by the arrow, the C₂H₂ product containing <1% CO₂ can be recovered. (d) Productivity of 99%+ pure C₂H₂ product determined by transient desorption simulations for PCP-33, HOF-3, TIFSIX-2-Cu-i, JCM-1, DICRO-4-Cu-i, MUF-17, UTSA-74, FJU-90, and FeNi-M′MOF at 298 K and 100 kPa, plotted as a function of the separation potential with y₁₀ = y₂₀ = 0.5. Further information on input data and simulation details are provided in earlier works.^41,43,63,121

2.3. C₂H₂/C₂H₄ Mixture Separations

With great potential for separation of C₂H₂/C₂H₄ mixtures are a series of three-dimensional (3D) coordination networks composed of inorganic anions of (SiF₆)^2– (hexafluorosilicate, SIFSIX).³⁰ The pore sizes within this family of SIFSIX materials can be systematically tuned by changing the length of the organic (=pyridine) linkers, the metal (=Cu, Ni, or Zn) node, and/or the framework interpenetration. Figure 9a compares the transient breakthroughs for 1/99 C₂H₂(1)/C₂H₄(2) mixtures using SIFSIX-1-Cu, SIFSIX-2-Cu-i, SIFSIX-3-Zn, Mg₂(dobdc), and NOTT-300; the ppm C₂H₂ in the gas mixture at the outlet of the fixed bed is plotted as a function of Q₀t/m_ads, where Q₀ is the volumetric flow rate of the gas mixture at the inlet to the fixed bed at STP conditions. From a material balance on the adsorber, we can determine the productivity of purified C₂H₄, containing less than 40 ppm. The productivity of pure C₂H₄ is found to be a near-linear function of the separation potential Δq determined from IAST; see Figure 9b. The highest productivity is obtained with SIFSIX-2-Cu-i (2 = 4,4′-dipyridylacetylene and i = interpenetrated);³⁰ in this case, each C₂H₂ molecule is bound by two F atoms from different nets. The binding of C₂H₄ with the F atoms is weaker because it is far less acidic than C₂H₂. This confirms that the separation potential Δq is the appropriate metric for screening MOFs for C₂H₂/C₂H₄ mixture separations.

Figure 9.

(a) Transient breakthrough simulations for 1/99 C₂H₂/C₂H₄ mixture adsorption at 298 K and 100 kPa in a fixed bed packed with five different MOFs. The ppm C₂H₂ in the gas mixture at the outlet of the fixed bed is plotted as a function of Q₀t/m_ads, where Q₀ is the volumetric flow rate of the gas mixture at the inlet to the fixed bed, expressed in m³ s^–1, at STP conditions. (b) Productivity of pure C₂H₄, containing less than 40 ppm C₂H₂, plotted as a function of the separation potential determined from IAST with y₁₀ = 0.01; y₂₀ = 0.99. (c) Separation potential, Δq, of SIFSIX-2-Cu-i and SIFSIX-1-Cu, plotted as a function of the % C₂H₂ in the feed mixture. Further information on input data and simulation details are provided in the Supporting Information.

Figure 9c compares the separation potentials of SIFSIX-2-Cu-i and SIFSIX-1-Cu as a function of the % C₂H₂ in the feed mixture. While the interpenetrated SIFSIX-2-Cu-i has the superior performance for feed compositions below 5% C₂H₂, SIFSIX-1-Cu, with a more open structure, has the better separation capability at higher % C₂H₂ in feed; this trend is verified in the experiments reported by Cui et al.³⁰

2.4. CO₂ Capture from Natural Gas

For CO₂ capture from natural gas streams, the process economics would demand the high capture capacity, concomitant with high productivity of pure CH₄. Li et al.⁶⁸ report on the experimental results of transient breakthroughs for 40/60 CO₂(1)/CH₄(2) mixtures in a packed bed with Mg₂(dobdc), Co₂(dobdc), MIL-100(Cr), and AC at 298 K temperature and 100 kPa total pressure. The masses of the adsorbents in the packed tube are not the same for each MOF, and therefore, their experimental data have been replotted in Figure 10a using Q₀t/m_ads as the x-axis. For each of the five materials, there is a displacement interval (indicated by the arrows) during which purified CH₄ can be recovered. The CH₄ productivities follow the hierarchy Mg₂(dobdc) > Co₂(dobdc) > MIL-100(Cr) > AC. Figure 10b presents a plot of productivity of 95%+ pure CH₄ as a function of the separation potential Δq = q₁y₂₀/y₁₀ – q₂. The 95%+ pure CH₄ productivities follow the same hierarchy as the Δq values, indicating that the separation potential can be used for screening purposes.

Figure 10.

(a) Experimental breakthroughs for CO₂/CH₄ mixtures in a packed bed with Mg₂(dobdc), Co₂(dobdc), MIL-100(Cr), and AC at 298 K. The partial pressures at the inlet are p₁ = 40 kPa, p₂ = 60 kPa, and p_t = 100 kPa. The experimental data, indicated by the symbols, are from Li et al.⁶⁸ The % CO₂ and % CH₄ in the exit gas phase are plotted as a function of Q₀t/m_ads. (b) Productivity of 95% pure CH₄ plotted as a function of separation potential.

2.5. N₂/CH₄ Mixture Separations

Although natural gas reserves may contain N₂ in concentrations ranging to about 20%,⁶⁹ the nitrogen content must be reduced to below 4% in order to meet pipeline specifications.⁷⁰ For large capacity wells, it is most economical to employ cryogenic distillation for nitrogen removal. However, for smaller natural gas reserves, PSA separations become more cost-effective, especially because the feed mixtures are available at high pressures.^69,70 The adsorbent materials in the PSA units need to be selective to N₂, which is present in smaller concentrations than CH₄. For most known adsorbents, the adsorption selectivity for separation of N₂/CH₄ mixtures is in favor of CH₄ because of its higher polarizability.

One practical solution is to rely on diffusion selectivities by using microporous materials, such as LTA-4A zeolite, ETS-4 (ETS = Engelhard Titano-Silicate; ETS-4 is also named as CTS-1 = Contracted Titano Silicate-1), and clinoptilolites, which have significantly higher diffusivities of N₂ compared to that of CH₄.^5,70−73 The “spherical” CH₄ (3.7 Å) is much more severely constrained inside the narrow pores of such materials, whereas the “pencil-like” nitrogen molecule (4.4 Å × 3.3 Å) hops lengthwise with higher diffusivity. By tuning the size of the microporous channels of cation-exchanged ETS-4, such as Ba-ETS-4, CH₄ can be practically excluded from the pores.

Bhadra^70,74 have developed a detailed mathematical model for a PSA scheme for purification of natural gas using Ba-ETS-4, using the steps shown in Figure 11. In this scheme, the inclusion of the cocurrent blowdown step (suggested by Jayaraman et al.⁷² for N₂/CH₄ mixture separations with clinoptilolites) increases the CH₄ recovery. At the end of the countercurrent blowdown step, the bed contains both nitrogen (fast diffusing) and methane (slow diffusing). Thus, if the bed is simply closed at one end and left for a period of time, the nitrogen will diffuse out first, followed by methane, so the system is, in effect, self-purging (fifth step in the sequence).

Figure 11.

Different steps in the production of purified CH₄ using an adsorbent such as LTA-4A zeolite, Ba-ETS-4, and clinoptilolites, which rely on kinetic selectivity. The scheme shows the sequence of processing of a single bed in a multibed PSA scheme. Adapted from Bhadra and Farooq⁷⁰ and Jayaraman et al.⁷²

In a recent article, Yoon et al.⁷⁵ have reported that MIL-100(Cr), activated at 523 K, shows adsorption selectivity in favor of N₂. However, an important disadvantage of this material for use in natural gas purification is that CH₄ is not completely excluded. Figure 12 compares the transient breakthrough of 20/80 N₂(1)/CH₄(2) mixtures in a fixed bed adsorber packed with MIL-100(Cr) and Ba-ETS-4, operating at 283 K and total pressure p_t = 1 MPa. We note that the breakthrough of CH₄ occurs significantly later than that with BaETS-4, implying that a significant amount of CH₄ gets adsorbed. Consequently, even after cocurrent blowdown, a significant proportion of CH₄ will remain in the void spaces of the fixed bed packed with MIL-100(Cr) and will be “lost” along with N₂ in the final blowdown step; this implies that recovery of 96%+ pure CH₄ is likely to be unacceptably low with MIL-100(Cr). Candidate adsorbents for N₂/CH₄ separations must disallow the ingress of CH₄ inside the pores.

Figure 12.

Comparison of the transient breakthroughs of 20/80 N₂(1)/CH₄(2) mixtures in a fixed bed adsorber packed with MIL-100(Cr) and Ba-ETS-4 operating at 283 K and total pressure p_t = 1 MPa. Further information on input data and simulation details are provided in the Supporting Information.

2.6. Separation of C₂H₄/C₂H₆ and C₃H₆/C₃H₈ Mixtures

Both ethene (C₂H₄) and propene (C₃H₆) are important precursors for the manufacture of a variety of polymers. Propene is a byproduct from the steam cracking of liquid feedstocks such as naphtha and liquefied petroleum gas, as well as off-gases produced in fluid catalytic cracking units in refineries. The key processing steps for preparing feedstocks for polymer production are the separations of C₂H₄/C₂H₆ and C₃H₆/C₃H₈ mixtures, which are traditionally carried out in distillation columns. Because of small differences in the boiling points, the relative volatilities of C₂H₄/C₂H₆ and C₃H₆/C₃H₈ separations are in the range 1.1–1.2. In order to satisfy the 99.95%+ purity requirement of alkene feedstocks to polymerization reactors, the distillation columns are tall (150–200 trays) and operate at cryogenic temperatures, high pressures, and high reflux ratios (≈15). Use of adsorptive separations may result in reduced energy consumption.

Each of the unsaturated alkenes C₂H₄ and C₃H₆ possesses a π-bond, and the preferential adsorption of alkene from the corresponding alkane with the same number of C atoms can be achieved by choosing zeolitic adsorbents with extraframework cations [e.g., LTA-4A zeolite^76,77 and NaX (=13X) zeolite^76,78] or MOFs with unsaturated “open” metal sites^23,79 (e.g., M₂(dobdc)^23,79 [M = Mg, Mn, Co, Ni, Zn, and Fe; dobdc^4– = 2,5-dioxido-1,4-benzenedicarboxylate] and CuBTC⁸⁰). All of the atoms of C₂H₄ lie on the same plane, and its dipole moment is zero; however, it does possess a quadrupole moment. It is to be noted that the polarizability of the alkane (C₂H₆, C₃H₈) is slightly higher than that of the corresponding alkene (C₂H₄ and C₃H₆).

An important disadvantage of the alkene/alkane separations with the adsorbents listed above is that the desired alkene product, required for the production of polymer-grade feedstock, can only be recovered in the desorption phase. In practice, it becomes necessary to operate with multiple beds involving five different steps, as schematized in Figure 13; the C₃H₆ product of the desired purity is recovered in the final step by countercurrent vacuum blowdown.^77,78,81 The recovery of high-purity C₃H₆ product in the final vacuum blowdown step is expected to be enhanced if C₃H₈ is (almost) excluded during the high-pressure adsorption cycle. Near-total exclusion of C₃H₈ is achievable by kinetically based separations using cage-type zeolites with eight-ring windows such as CHA and LTA-4A zeolites.^81,82 An alternative is to employ a customized MOF such as NbOFFIVE-1-Ni (=KAUST-7) with pyrazine as the organic linker.²⁴ The use of bulkier (NbOF₅)^2– pillars causes tilting of the pyrazine molecule on the linker, resulting in an effective aperture of 0.30 nm. This reduced aperture permits ingress of the smaller C₃H₆ molecules but practically excludes C₃H₈, relying on subtle differences in bond lengths and bond angles.

Figure 13.

Five-step PSA process for separating C₃H₆/C₃H₈ mixtures.^77,78,81

Figure 14a,b presents the simulations of the transient breakthroughs for the (a) adsorption and (b) desorption cycles for separation of equimolar C₃H₆(1)/C₃H₈(2) mixtures in a fixed bed adsorber packed with KAUST-7 operating at 298 K and 100 kPa. During the time interval indicated by the arrow in Figure 14b, the C₃H₆ product of desired purity can be recovered. Because of the significantly lower diffusivity of C₃H₈, the desorption process is self-purging.^7,83 In the last step shown in Figure 13, if the bed is simply closed at the one end and left for a period of time, C₃H₆ will diffuse out first, followed by C₃H₈. Figure 14c presents a comparison of the transient desorption using three different ratios of intracrystalline diffusivities Đ₁/Đ₂ = 1, 10, and 100. From a material balance on the adsorber, the productivities of 99%+ pure C₃H₆ can be determined; the values are, respectively, 15.7, 18.9, and 24.3 L kg^–1 at STP for the three scenarios. Because of the sensitivity of the C₃H₆ productivity to the values of intracrystalline diffusivities, a detailed process design exercise, such as that reported by Khalighi et al.,^81,82 will be required in order to compare the C₃H₆ productivities of KAUST-7, with other MOFs; simple IAST calculations of Δq and S_ads are unlikely to be sufficiently accurate for reliable screening.

Figure 14.

Transient breakthrough simulations for (a) adsorption and (b,c) desorption cycles for the separation of C₃H₆/C₃H₈ mixtures in a fixed bed adsorber packed with KAUST-7 operating at 298 K and 100 kPa; the feed compositions are y₁₀ = y₂₀ = 0.5. (c) Three different scenarios for the ratios of diffusivities Đ₁/Đ₂ = 1, 10, and 100 are compared, while maintaining Đ₁/r_c² = 1 × 10^–3 s^–1. Further information on input data and simulation details are provided in the Supporting Information.

For C₂H₄/C₂H₆ separations, near-total exclusion of C₂H₆ is achieved by use of ultramicroporous MOF [Ca(C₄O₄)(H₂O)] that possesses rigid one-dimensional (1D) channels.²⁵ The 1D channels are of similar size to C₂H₄ molecules (all atoms of which lie on the same plane), but owing to the size, shape, and rigidity of the pores, they practically exclude C₂H₆.

For C₂H₄/C₂H₆ separations, a number of microporous adsorbents such as Fe₂(O₂)(dobdc),²⁸ Cu(Qc)₂,⁸⁴ MUF-15,⁸⁵ PCN-250,⁸⁶ ZIF-7,^87,88 ZIF-8,^89,90 IRMOF-8,⁹¹ Ni(bdc)(ted)_0.5,⁹² MAF-49,⁹¹ CPM-233,²⁶ and CPM-733²⁶ adsorb the saturated alkane selectively exploiting the differences in van der Waals interactions, resulting from the higher polarizability of C₂H₆. Figure 15a presents the IAST calculations of the C₂H₆ uptake q₂ versus the separation selectivity S_ads of 90/10 C₂H₄/C₂H₆ mixture adsorption at 298 K and 100 kPa in four different MOFs. The hierarchy of separation selectivities is Cu(Qc)₂ > CPM-733 ≈ MUF-15 > CPM-233. However, because of the higher C₂H₆ uptake capacity of CPM-733, the separation potential, Δq, follows the hierarchy CPM-733 > CPM-233 > MUF-15 > Cu(Qc)₂. The separation potential of Cu(Qc)₂ is the lowest because it has the smallest C₂H₆ uptake. In order to verify the hierarchy of Δq determined from IAST, transient breakthrough simulations were carried out for CPM-733, CPM-233, MUF-15, and Cu(Qc)₂; see Figure 15b. The dimensionless concentrations at the exit of the packed bed are plotted as a function of Q₀t/m_ads. During the interval indicated by the arrows, purified C₂H₄ can be recovered. The productivities follow the hierarchy CPM-733 > CPM-233 > MUF-15 > Cu(Qc)₂, that is in line with the hierarchy of Δq values. From the transient breakthrough simulations, the amount of 99.95%+ pure C₂H₄ product recovered during the displacement intervals can be determined. The productivity values show a near-linear dependence on Δq; see Figure 15c. This implies that the IAST calculations of Δq = q₁y₂₀/y₁₀ – q₂ are appropriate metrics for screening and ranking MOFs.

Figure 15.

(a) IAST calculations of the C₂H₆ uptake q₂ vs the separation selectivity S_ads of 90/10 C₂H₄/C₂H₆ mixture adsorption at 298 K and 100 kPa in four different MOFs. (b) Transient breakthrough simulations for the separation of 90/10 C₂H₄/C₂H₆ mixture adsorption at 298 K and 100 kPa in fixed beds packed with Cu(Qc)₂, MUF-15, CPM-233, and CPM-733. (c) Productivity of 99.95%+ pure C₂H₄ product recovered during the displacement intervals, plotted as function of the separation potential Δq. Further information on input data and simulation details are provided in the Supporting Information.

2.7. Separation of Hexane Isomers

The values of the research octane number (RON) of alkane isomers increase with the degree of branching. For hexane isomers, for example, the RON values are n-hexane (nC6) = 30; 2-methylpentane (2MP) = 74.5; 3-methylpentane (3MP) = 75.5; 2,2 dimethylbutane (22DMB) = 94; and 2,3 dimethylbutane (23DMB) = 105. Consequently, dibranched alkane isomers are preferred blending components in high-octane gasoline.^90,93,94 As shown in the process scheme in Figure 16a, alkane isomers are currently separated on the basis of molecular sieving using LTA-5A zeolite. Linear alkanes can hop from one cage to the adjacent cage through the 4 Å windows of LTA-5A, but monobranched and dibranched alkanes are largely excluded. From an industrial perspective, it is desirable to adopt an alternative separation scheme (see Figure 16b) using an adsorbent that has the capability of separating the dibranched isomers from the linear and monobranched isomers that may be recycled back to the isomerization reactor.

Figure 16.

(a) Currently employed processing scheme for nC6 isomerization and a subsequent separation step using LTA-5A zeolite. (b) Improved processing scheme for the nC6 isomerization process. Further process background details are provided in the Supporting Information.

One candidate MOF that can be employed as an adsorbent in Figure 16b is Fe₂(BDP)₃ [BDP^2– = benzenedipyrazolate] that possesses one-dimensional triangular shape channels of 4.9 Å.⁹³ Simulations of transient breakthroughs of hexane isomers using Fe₂(BDP)₃ are shown in Figure 17a; the hierarchy of breakthroughs is dibranched, monobranched, and linear isomers; this hierarchy is dictated by a combination of adsorption strengths, dictated essentially by van der Waals interactions (nC6 ≫ 2MP ≈ 3MP ≫ 22DMB ≈ 23DMB), and diffusivities (nC6 > 2MP ≈ 3MP > 22DMB ≈ 23DMB). The RON of the product gas mixture exiting the adsorber is plotted in Figure 17b. During a certain time interval, the 92+ RON product can be recovered for incorporation into the gasoline pool. This requirement of 92+ RON implies that the product stream will contain predominantly the dibranched isomers 22DMB and 23DMB, while allowing a small proportion of 2MP and 3MP to be incorporated into the product stream. Also shown in Figure 17b, for comparison purposes, is the corresponding breakthrough simulation data for ZIF-77⁹⁴ that has a characteristic pore dimension of 4.5 Å. Because of stronger diffusional limitations in ZIF-77, the 92+ RON productivity of ZIF-77 is significantly lower than that of Fe₂(BDP)₃; this is evidenced by the significantly shorter time interval during which 92+ RON product can be recovered.

Figure 17.

(a) Simulations of transient breakthrough characteristics for a five-component nC6/2MP/3MP/22DMB/23DMB mixture in a fixed bed adsorber packed with Fe₂(BDP)₃ operating at a total pressure of 100 kPa and 433 K. The partial pressures of the components in the bulk gas phase at the inlet are p₁ = p₂ = p₃ = p₄ = p₅ = 20 kPa. (b) Plot of RON of product gas mixture exiting the fixed bed adsorber packed with ZIF-77 and Fe₂(BDP)₃, plotted as a function of Q₀t/m_ads. Further information on input data and simulation details are provided in the Supporting Information.

2.8. Separation of C8 Aromatics

The xylene isomers, o-xylene, m-xylene, and in particular p-xylene, are important chemical intermediates. Xylenes, along with other aromatic hydrocarbons, are commonly obtained from catalytic reforming of naphtha, as illustrated in the process scheme in Figure 18.^63,95,96 The products of catalytic reformer are fed to a distillation column called the reformate splitter. The bottom product of the reformate splitter, rich in xylenes, is further distilled in the xylene splitter, whose bottom product consists of C9+ aromatics. The recovery of p-xylene from the mixture of C8 aromatics (typically composition: 20% o-xylene, 44% m-xylene, 17% p-xylene, and 19% ethylbenzene) in the overhead product of the xylene splitter is the focus of attention in this section.

Figure 18.

Schematic showing the separations of the products from a catalytic reforming unit. Further process background details are provided in the Supporting Information.

Because of the very small differences in boiling points (cf. Figure 19), p-xylene recovery by use of distillation technology is not feasible. Two different technologies are currently in use for recovery of p-xylene: (a) fractional crystallization and (b) selective adsorption. Fractional crystallization relies on the differences in freezing points (cf. Figure 19). The freezing point of p-xylene is significantly higher than that of other C8 aromatics; on cooling, therefore, pure p-xylene crystals are the first to emerge from the solution. Selective adsorption of p-xylene from liquid-phase mixtures of C8 aromatics is achieved with cation-exchange FAU zeolite adsorbent, such as BaX, in a simulated moving bed (SMB) adsorption device.⁹⁷⁻⁹⁹ The hierarchy of adsorption strengths in BaX is dictated by molecular packing, or entropy, effects that prevail under pore saturation conditions in liquid-phase SMB separations.^95,97−100 Unlike PSA technologies for gaseous separations, the SMB process operates continuously under steady-state conditions; see the schematic in Figure 20.

Figure 19.

Boiling points and freezing points of C8 hydrocarbons, along with molecular dimensions, culled from Torres-Knoop et al.¹⁰⁷

Figure 20.

SMB adsorption technology for the separation of a feed mixture containing o-xylene/m-xylene/p-xylene/ethylbenzene. The SMB technology is depicted here with countercurrent contacting between the down-flowing adsorbent material and up-flowing desorbent (eluent) liquid. Also indicated are the liquid-phase concentrations of a mixture of o-xylene/m-xylene/p-xylene/ethylbenzene using the information presented by Minceva and Rodrigues.¹⁰¹

The C8 aromatic feed is introduced at a port near the middle of the SMB unit.^101,102 The desorbent p-diethylbenzene (boiling point 450 K) is introduced at the bottom.¹⁰³Figure 20 also indicates typical liquid phase concentrations of o-xylene, m-xylene, p-xylene, and ethylbenzene along the adsorber height. The extract phase, containing the more strongly adsorbed p-xylene, is recovered below the feed injection port in the bottom section of the column. The raffinate phase, containing the more weakly adsorbed o-xylene, m-xylene, and ethylbenzene, is tapped off above the feed injection port in the upper section of the column.

For realizing improvements in the SMB units, there is considerable scope for the development of MOFs that have both higher uptake capacity and selectivity to p-xylene as compared to BaX zeolite. Improved MOF adsorbents will result in lower recirculation flows of eluent, and microporous adsorbent in the SMB unit, and this will result in significant economic advantages. There are several MOFs such as DynaMOF-100,^104,105 Co-CUK-1,¹⁰⁶ MAF-X8,¹⁰⁷ JUC-77,¹⁰⁸ Co(BDP),²¹ and MIL-125^109−111 that have the potential for use in SMB units.

For preferential adsorption of p-xylene, and rejection of o-xylene, m-xylene, and ethylbenzene, the appropriate metric for comparing these MOFs is the separation potential Δq that is derived using the shock wave model for fixed bed adsorbers⁶³

8

In eq 8, the molar loadings of each of the four C8 aromatics, q_i, expressed in mol per kilogram of crystalline adsorbent are calculated using the IAST for mixture adsorption equilibrium. Figure 21 presents the plot of Δq versus p-xylene uptake for a few selected MOFs. The highest value of the separation potential is offered by DynaMOF-100 that is a Zn(II)-based dynamic coordination framework that undergoes guest-induced structural changes so as to allow selective uptake of p-xylene within the cavities. A slightly lower separation potential is offered by Co-CUK-1 that is composed of cobalt(II) cations and the dianion of dicarboxylic acid; the 1D zigzag-shaped channels of Co-CUK-1 allow optimal vertical stacking of p-xylene. Both these MOFs offer separation potentials about three to four times that achievable by BaX; there is a need for experimental verification of this expectation.

Figure 21.

Plot of the separation potential, Δq, vs the gravimetric uptake of p-xylene. Further information on input data and simulation details are provided in the Supporting Information.

2.9. Influence of Thermodynamic Nonidealities in Mixture Adsorption

In many cases, the IAST fails to provide a quantitatively correct description of mixture adsorption equilibrium and thus thermodynamic nonidealities come into play. Thermodynamic nonidealities are evidenced for water/alcohol mixtures because of molecular clustering engendered by hydrogen bonding.^112−117 Thermodynamic nonidealities also arise because of preferential location of CO₂ molecules at the window regions of eight-ring zeolites such as DDR, CHA, ERI, LTA-4A, and LTA-5A.^{55,56,117−119} For CO₂ capture with NaX zeolite, there is congregation of CO₂ around the cations, resulting in failure of IAST.^117,119 Thermodynamic nonidealities can be strong enough to cause selectivity reversals for CO₂/hydrocarbon mixture adsorption in cation-exchanged zeolites.^55,56,117 Framework flexibility and gate-opening behaviors may lead to failure of IAST.¹²⁰ In all the aforementioned cases, we need to use the real adsorbed solution theory (RAST) for quantitative description of mixture adsorption in transient breakthrough simulations. RAST calculations of Δq may be used for screening purposes.^116,119

3. Conclusions

The following major conclusions emerge from this study.

• (1)The separation performance in fixed bed devices is governed by a combination of adsorption selectivity, S_ads, and uptake capacities, q₁, q₂; low uptake capacities diminish the separation performance of MOFs with high values of S_ads.
• (2)The separation potential Δq, which is calculable on the basis of IAST, provides a simple and convenient metric to screen and rank the separation capability of MOFs. For a component that is recovered in pure form during the adsorption cycle, Δq can be calculated using eq 2, which is derived using the shock wave model. For a component that is recovered in pure form during the blowdown cycle, the separation potential Δq is defined by eq 7. The value of Δq defines the upper limit to the achievable separations in fixed bed units. The actual separations in fixed bed adsorbers will be lower than the IAST-calculated Δq values because of distended breakthroughs.
• (3)The composition of the feed mixture may have a significant influence on the separation potential of the MOF; this is illustrated in Figure 9c for C₂H₂/C₂H₄ mixtures.
• (4)Broadly speaking, high product purities are more difficult to achieve if the desired product is recovered in the blowdown cycle of PSA schemes, as presented in Figures 7, 11, and 13. In such cases, it is advantageous to have MOF adsorbents that virtually exclude the less strongly adsorbing component because this facilitates the achievement of high-purity products. The productivity calculations are very sensitive to intracrystalline diffusion limitations, as illustrated in Figure 14 for C₃H₆/C₃H₈ mixture separations using KAUST-7.
• (5)The concept of separation potential is particularly advantageous for multicomponent separations; several selectivities and uptake capacities are incorporated into one combined metric that quantifies the desired separation task. For example, eq 8 is the appropriate expression for Δq for separation of four-component mixture of C8 aromatics
• (6)As illustrated in Figures 5, 9, 10, 12, 15, and 17, transient breakthrough experiments or simulations can be directly used to compare the separation effectiveness of MOFs. In such cases, the appropriate x-axis for plotting purposes is Q₀t/m_ads; this parameter may be viewed as “corrected” time. Such comparisons are indispensable for comparison and screening of MOFs that are subject to severe diffusion limitations,^90,121
• (7)For situations in which the intracrystalline influences are strong, the separation performance will be significantly lowered and IAST calculations of Δq will not be adequate for screening purposes.
• (8)For kinetically driven separation, as used industrially for N₂/CH₄ and N₂/O₂ mixtures, some authors have suggested the use of as a metric to quantify kinetic influences.^71,81 The concept of the separation potential Δq is not of relevance in such cases.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c02218.

• Methodology used for transient breakthrough simulations, analytic solutions to the shock wave model for fixed bed transient operations, structural information on the MOFs investigated, unary isotherm data sources for each guest/host combination, and data inputs of simulation results for each of the investigated mixture separations (PDF)

The author declares no competing financial interest.