Computational Screening of Metal-Organic Frameworks for Ethylene Purification from Ethane/Ethylene/Acetylene Mixture

Abstract

Identification of high-performing sorbent materials is the key step in developing energy-efficient adsorptive separation processes for ethylene production. In this work, a computational screening of metal-organic frameworks (MOFs) for the purification of ethylene from the ternary ethane/ethylene/acetylene mixture under thermodynamic equilibrium conditions is conducted. Modified evaluation metrics are proposed for an efficient description of the performance of MOFs for the ternary mixture separation. Two different separation schemes are proposed and potential MOF adsorbents are identified accordingly. Finally, the relationships between the MOF structural characteristics and its adsorption properties are discussed, which can provide valuable information for optimal MOF design.

1. Introduction

Ethylene (C₂H₄) is one of the major chemicals in the petroleum industry, which can be produced by thermal cracking from various sources; for instance, natural gas, naphtha, and gasoline [1]. In C₂H₄ production, the separations of acetylene (C₂H₂) and ethane (C₂H₆) from C₂H₄ are achieved through catalytic partial hydrogenation and cryogenic distillation, respectively [2]. However, they are very energy-consuming processes due to extreme operating conditions. Over decades, adsorptive separation under mild conditions on a novel class of nano-porous materials, known as metal-organic frameworks (MOF), has been suggested as a substitute [3]. Due to their structural diversities, MOFs feature many outstanding properties such as tunable pore sizes and high surface areas [4], making them ideal for many applications, such as membranes based purification [5], removal of environmental pharmaceutical contaminants [6,7], gas storage, and in particular gas separation.

A number of MOFs have been reported as promising materials for the separation of C₂H₂/C₂H₄ based on different mechanisms. Some utilize a size-selective sieving effect. For example, Xiang et al. discovered that M’MOF-3a could separate C₂H₂ and C₂H₄ with a high selectivity of 25.53 at 195 K and 5.23 at 295 K based on the different sizes of the solutes [8]. Hu et al., (2015) revealed that the suitable pores and opening windows of UTSA-100a could lead to a high C₂H₂ uptake of 4.27 mmol/g and a C₂H₂/C₂H₄ selectivity of 10.72 at 296 K and 1.0 bar. Besides, MOFs featuring open metal sites (OMS) have been found effective for the C₂H₂/C₂H₄ separation due to large affinity. However, the OMS bind strongly with both C₂H₂ and C₂H₄, resulting in a relatively low selectivity. For instance, Bloch et al. demonstrated that Fe₂(dobdc) had a high C₂H₂ uptake of 6.8 mmol/g, but a low C₂H₂/C₂H₄ selectivity of 2.08 at 318 K and 1.0 bar [9]. In addition to that, Yang et al. showed that NOTT-300 could separate the mixture through weak supramolecular interactions aligned within the host [10]. Finally, MOFs containing anions (such as SIFSIX) have been also found to be promising for C₂H₂/C₂H₄ separation [11].

For the separation of C₂H₄/C₂H₆, there have been many MOFs reported to be C₂H₄ selective, such as Fe₂(dobdc) [9], PAF-1-SO₃Ag [12], NOTT-300 [10] etc. However, only limited MOFs with reverse selectivities towards C₂H₆ have been reported. Gücüyener et al. first demonstrated the C₂H₆ selectivity of ZIF-7 and concluded that its selectivity was induced by a gate-opening mechanism [13]. Liao et al. found that MAF-49 had a C₂H₆ selectivity of 2.7 and a capacity of 1.73 mmol/g at 298 K [14]. Later, Lin et al. studied Cu(Qc)₂ and found that its capacity towards C₂H₆ was 1.85 mmol/g and the C₂H₆/C₂H₄ selectivity was 3.4 at 298 K and 100 kPa [15]. Chen et al. reported an iron-based MOF PCN-250 as another C₂H₆ selective adsorbent. Its adsorption capacity towards C₂H₆ and C₂H₄ was 5.21 mmol/g and 4.22 mmol/g at 298 K and 100 kPa, respectively, and the C₂H₆/C₂H₄ selectivity was in the range of 1.9−4.0 [16].

Unlike the widely investigated binary separations, a direct purification of C₂H₄ from the ternary mixture C₂H₂/C₂H₄/C₂H₆ has been much less studied. There have been basically two different strategies. Hao et al. synthesized a MOF TJT-100 that can simultaneously trap C₂H₂ and C₂H₆, thus leading to high selectivities for C₂H₂/C₂H₄ of 8.5 and C₂H₆/C₂H₄ of 5.75 [17]. Chen et al. purified a four-component mixture (C₂H₂/C₂H₄/C₂H₆/CO₂) in one column packed with three different MOFs with each capturing one impurity [18]. It is worth noticing that both of these novel approaches, where a direct purification of C₂H₂ from the ternary C₂ mixture instead of performing two separate binary separations, can yield intensified process configurations with less unit operations.

To identify candidates with great potential in the direct purification of the ternary C₂ mixture is a challenging task. Fortunately, the grand canonical Monte Carlo (GCMC) simulation can predict adsorption equilibria fast and efficiently. In fact, it has been tested and proven useful in various gas separations, such as CO₂/N₂/CH₄ [19,20,21], H₂/CH₄ [22,23], C₂H₂/CH₄ and C₂H₂/CO₂ [24], C₂H₆/C₂H₄ and C₂H₆/CH₄ [25], C₂H₂/C₂H₄ [26], CO₂/H₂ [27], C₃H₈/C₃H₆ [28], hexane and heptane isomers [29], xylene isomers [30], and process-centric CO₂ capture [31,32].

In this work, we perform a high-throughput screening over 4764 experimentally synthesized MOFs for the separation of C₂H₂/C₂H₄/C₂H₆. First, we validate the accuracy of GCMC simulations by comparing the simulated and experimental uptakes of pure C₂H₂, C₂H₄, and C₂H₆ in a few MOFs. Next, we compute the separation capacity and selectivity for each candidate. Based on that, a new separation performance index (SPI) is defined and discussed in detail. The best MOFs are selected accordingly and the structural characteristics are revealed.

2. Computational Details

2.1. MOF Database

The computation-ready, experimental metal-organic framework (CoRE MOF) database [33] containing totally 4764 MOF candidates was chosen as the screen basis due to the following reasons. First, this database consists of a variety of MOF structures, which provide a rich search space for finding promising adsorbents; second, the structures in the database are immediately suitable for molecular simulations without any further modifications; third, each MOF has already been experimentally reported and recorded with a unique Cambridge Structural Database (CSD) code [34] so that the screened materials can be synthesized.

2.2. Molecular Simulation

Molecular simulation enables multifaceted investigations of intermolecular and intramolecular phenomena on the microscopic scale by advanced computational algorithms. GCMC simulation, with constant chemical potential, volume, and temperature, but variable number of molecules, has been widely used for studying adsorption equilibrium [35]. In this work, we implement GCMC simulations using the software RASPA [36] to estimate the adsorption equilibria of the ternary mixture C₂H₂/C₂H₄/C₂H₆ over the 4764 MOFs.

For the GCMC simulation, various parameters need to be specified properly. First, general parameters such as Monte Carlo moving probabilities, cut-off radius, cell size, and number of cycles are defined. Here, four types of Monte Carlo moves (i.e., translation, rotation, reinsertion, and swap) are considered. The probabilities of the occurrences of these moves are set equal. In addition, a cut-off radius of 12.0 Å is used. The simulation cell size is expanded to at least 24.0 Å along all the three spatial dimensions and the corresponding periodic boundary conditions are applied. Each simulation is carried out with first 30,000 cycles for equilibration and subsequent 20,000 cycles for production. Additionally, the Peng−Robinson equation of state is used to estimate the gas phase fugacities of species.

Next, to calculate the energy state of the whole system, the following force field equation is used [37].

$$U=\sum 4{\epsilon }_{ij}\left[{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^6\right]+\sum \frac{q_i{q}_j}{4\pi {\epsilon }_0{r}_{ij}}$$

(1)

where ε_ij is well depth, σ_ij is collision diameter, r_ij is the distance between atoms i and j, q_i is the atomic charge of atom i, and ε₀ is 8.8542 × 10⁻¹² (C²N⁻¹m⁻²). The first term describing Van der Waals interactions is the Lennard-Jones (LJ) potential and the second term representing electrostatic interactions is the columbic potential.

In addition to the force field equation, force field parameters are provided. First, for adsorbate molecules (C₂H₂, C₂H₄, and C₂H₆), the Lennard-Jones (LJ) potential parameters (σ and ε), partial charge (q), and bond length (l) are specified.

Table 1. Molecular Parameters of C₂H₂, C₂H₄, and C₂H₆.

	Atoms	σ (Å)	ε (K)	q (e)	Bond Length l (Å)
C2H2	C in C2H2	3.800	57.875	−0.278	1.211 (C≡C)
	H in C2H2	0	0	0.278	1.071 (C—H)
C2H4	CH2 (sp2)	3.685	93.0	0	1.330 (C=C)
C2H6	CH3 (sp3)	3.750	98.0	0	1.540 (C—C)

lists all the molecular parameters of the gas components where those of C₂H₂ are taken from [38] and those of C₂H₄ and C₂H₆ are adopted from [39]. Next, for host frameworks, the LJ potential parameters are adopted from the DREIDING force field [40] and those of the missing atoms are taken from the UFF force field [41]. The charges on the MOF atoms are estimated using the EQeq method [42]. MOFs are considered as rigid and thus the interactions between MOF atoms are ignored. The cross LJ parameters are computed using the Lorentz–Berthelot combining rule [41] except those between Cu of MOF and C of C₂H₂ that are modified according to [38].

3. Results and Discussion

3.1. GCMC Validation

The reliability of GCMC simulations was validated by experimental data. In the literature, the amount of C₂H₂ and C₂H₄ adsorbed on different MOFs (i.e., MOF-5, ZIF-8, and UTSA-20) has been measured at 298 K and 10⁵ Pa [9,43,44]. In addition, the adsorption uptakes of C₂H₆ on Fe-MOF-74, MOF-505, and UTSA-20 have also been measured at 318 K and 10⁵ Pa [43]. Under the same experimental conditions, the pure component uptakes of C₂H₆ were simulated and those of C₂H₂ and C₂H₄ were directly taken from our previous work [26].

The comparison of the GCMC results and experimental data is presented in Figure 1. Clearly, the majority of the data lies close to the parity line, indicating an overall good agreement between experimental and simulated uptakes. However, some MOFs such as Mg-MOF-74 and Fe-MOF-74 lie far away from the parity line. This is mainly due to the fact that the M-MOF-74 (where M=Mg, Fe et al.) family contains open metal sites (OMS), which can strongly bind with the adsorbates [45]. In this case, the standard force field parameters are unable to appropriately capture these interactions. For better illustration, we calculated the zero coverage isosteric heat of adsorption $Q_{st}^0$ for the two outliers. Note that the absolute value of $Q_{st}^0$ indicates the strength of the MOF-adsorbate interactions. As shown in

Table 2. Isosteric heat of adsorption at zero coverage $Q_{st}^0$.

	$\mathbf{Simulated} {\mathit{Q}}_{\mathit{s}\mathit{t}}^0 (\mathbf{kJ}/\mathbf{mol})$	$\mathbf{Experimental} {\mathit{Q}}_{\mathit{s}\mathit{t}}^0 (\mathbf{kJ}/\mathbf{mol})$
C2H6 in Fe-MOF-74 at 318 K	−20.1	−28.2
C2H4 in Mg-MOF-74 at 298 K	−22.8	−43.0

, the two $Q_{st}^0$ derived from molecular simulation are significantly lower than the corresponding experimental values, which demonstrates the lack of accurate force field parameters for the description of coordination interactions between OMS and adsorbates. Some methods such as quantum mechanics (QM) calculations [46,47] have been developed to improve the accuracy of force field parameters. However, the identification of MOFs containing OMS is very laborious and the re-adjustment of force field parameters through rigorous QM calculations is computationally expensive. Therefore, to facilitate the large-scale MOF screening, we adopted the general force field parameters to keep a compromise between simulation precisions and computational cost.

3.2. Capacity and Selectivity

For the evaluation of separation performance of adsorbent, the capacity and selectivity are two important indicators. The adsorption capacity $q_i$ ($i$ = C₂H₂, C₂H₄ and C₂H₆) is usually defined as the amount of gas adsorbed in the solid adsorbent. Additionally, the selectivity is typically defined for a binary system (component = i, j):

$$S_{i/j}=\frac{K_i}{K_j}=\frac{x_i}{y_i}/\frac{x_j}{y_j}$$

(2)

where K_i is the equilibrium constant. y_i and x_i are the molar fractions of species i in the gas and solid phases, respectively. In a ternary system, selectivity can be defined likewise. For instance, the task of this work is to separate C₂H₂ and C₂H₆ from the ternary mixture in order to obtain a purified C₂H₄ product. Obviously, MOFs with high C₂H₂ and C₂H₆ uptakes and low C₂H₄ uptake are desired. Thus, two selectivity indicators ($S_{{\mathrm{C}}_2{\mathrm{H}}_2/{\mathrm{C}}_2{\mathrm{H}}_4}$ and $S_{{\mathrm{C}}_2{\mathrm{H}}_6/{\mathrm{C}}_2{\mathrm{H}}_4}$) can be defined for MOF screening where the first is the selectivity of C₂H₂ over C₂H₄ and the second is the selectivity of C₂H₆ over C₂H₄ in the ternary mixture.

We conducted GCMC simulations for all the 4764 MOFs in the CoRE MOF database. The concentrations of the three components C₂H₂/C₂H₄/C₂H₆ were set to 5.0/90/5.0 (mol/mol/mol), and the adsorption simulation was conducted at ambient conditions (i.e., 298 K and 1.0 bar). Note that only 4462 of the 4764 MOFs show valid non-zero uptakes. The obtained equilibrium adsorption loadings of the 4462 MOFs are plotted in Figure 2 with each point representing a single MOF. From this figure, we found that the adsorption uptakes of the three components are roughly in the order of q_C2H2 > q_C2H4 > q_C2H6. This can be explained by the differences in the molecular model parameters. As indicated in Table 1, for both C₂H₆ and C₂H₄ we used two-site models with three parameters. In contrast, C₂H₂ was modeled as a four-site molecule with additional point charge parameters. The introduction of point charges on the C and H atoms provides additional electrostatic interactions between C₂H₂ and the MOF atoms, which leads to the highest adsorption uptake of C₂H₂. Furthermore, a strong correlation between the uptakes of C₂H₄ and C₂H₆ can be observed from Figure 2. This is primarily due to their similar molecular models and parameters (see Table 1).

In addition to the adsorption capacity, we calculated the separation selectivity of C₂H₆/C₂H₄ and C₂H₂/C₂H₄ for each MOF candidate. The results are shown in Figure 3. It can be found that the selectivity of C₂H₂/C₂H₄ spans a wide range. By contrast, the distribution of C₂H₆/C₂H₄ selectivity is much narrower. Moreover, most of the C₂H₆/C₂H₄ selectivity is lower than 2.0 (red dash line), which reveals the relative difficulty for the separation of C₂H₆ from C₂H₄.

3.3. Selection of Potential MOFs

The product of selectivity and capacity has been widely used as a criterion for the selection of MOFs for binary gas separations [24,48]. However, this simple performance indicator needs some modifications before it can be used to rank MOF candidates for ternary separation systems. First, unlike binary systems where a unique pair of selectivity and capacity is involved, for ternary mixtures, selectivity and capacity must be carefully defined to give an appropriate description of the separation performance. Second, the selectivity and capacity often differ in several orders of magnitude. Thus, the direct product of selectivity and capacity can be dominated by one single factor. Such a biased metric is not useful for the screening of best adsorbents. Based on these considerations, we propose a new selection performance indicator (SPI) for the evaluation of the performance of MOFs for the separation of the ternary C₂H₂/C₂H₄/C₂H₆ mixture.

$${SPI=log(\mathit{S}}_{{\mathrm{C}}_2{\mathrm{H}}_2{/\mathrm{C}}_2{\mathrm{H}}_4}{) \times \mathit{q}}_{{\mathrm{C}}_2{H}_2}{ \times \mathit{l}\mathit{o}\mathit{g}(\mathit{S}}_{{\mathrm{C}}_2{\mathrm{H}}_6{/\mathrm{C}}_2{\mathrm{H}}_4}{) \times \mathit{q}}_{{\mathrm{C}}_2{\mathrm{H}}_6}$$

(3)

$${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}{=\mathit{l}\mathit{o}\mathit{g}(\mathit{S}}_{{\mathrm{C}}_2{\mathrm{H}}_2{/\mathrm{C}}_2{\mathrm{H}}_4}{) \times \mathit{q}}_{{\mathrm{C}}_2{\mathrm{H}}_2}$$

(4)

$${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}{=\mathit{l}\mathit{o}\mathit{g}(\mathit{S}}_{{\mathrm{C}}_2{\mathrm{H}}_6{/\mathrm{C}}_2{\mathrm{H}}_4}{) \times \mathit{q}}_{{\mathrm{C}}_2{\mathrm{H}}_6}$$

(5)

To provide a deeper insight of the selection metrics, we divide the SPI into two parts. The product of the first two terms denoted as ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}$ represents the performance of MOF for C₂H₂ separation. Similarly, the product of the last two terms denoted as ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ measures MOF’s performance for C₂H₆ separation. Figure 4 plots the ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}$ and ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ for all the MOF candidates. It can be observed that ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ is generally much smaller than ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}$. This confirms that the separation of C₂H₆ from C₂H₄ is more difficult than the separation of C₂H₂ from C₂H₄. Moreover, the distribution of ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}$ and ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ forms a Pareto-like front, which indicates a competitive relation between the separation of C₂H₂ and C₂H₆.

Two different separation schemes are proposed for the ternary mixture: i.e., single-step separation and multi-step separation. As illustrated in Figure 5a, in the single-step separation process, C₂H₂ and C₂H₆ are adsorbed simultaneously in a single sorption cycle and a pure C₂H₄ product stream can be obtained directly. This separation process uses only one adsorbent material, which significantly reduces the process complexity. Accordingly, the MOF selection criterion is the maximization of SPI that compromises the material performance for both C₂H₂ and C₂H₆ separations.

Table 3. Structural properties, selectivity, capacity, and SPI of the top 10 MOF candidates for the single-step separation of C₂H₂/C₂H₄/C₂H₆.

Rank	CSD Code	Metal	LCD (Å)	Pore Volume (cm3/g)	${\mathit{S}}_{{{C}}_2{{H}}_2{/{C}}_2{{H}}_4}$	${\mathit{q}}_{{{C}}_2{{H}}_2}$ (cm3/g)	${\mathit{S}}_{{{C}}_2{{H}}_6{/{C}}_2{{H}}_4}$	${\mathit{q}}_{{{C}}_2{{H}}_6}$ (cm3/g)	SPI (cm6/g2)
1	CUNXIS	Al	4.73	0.22	22.2	22.2	18.7	18.6	705.8
2	CUNXIS10	Al	4.73	0.22	16.6	20.4	13.3	16.3	455.0
3	GIHBII	Ga	4.58	0.17	17.5	18.3	6.56	6.85	127.4
4	NEXXEV	Li	10.14	0.92	36.7	128.8	1.18	4.15	60.8
5	JAVTAC	Al	5.08	0.21	147.4	51.5	2.97	1.04	54.7
6	BEKSAM	Ga	4.04	0.13	30.8	27.1	2.99	2.63	50.4
7	XEDPON	Zn	7.48	0.56	48.0	114.6	1.17	2.80	37.6
8	LEVNOQ01	Mg	5.91	0.58	16.4	56.1	1.32	4.52	37.0
9	XEKCAT01	Mg	5.92	0.67	11.5	61.1	1.22	6.50	36.4
10	EYACOX	Eu	8.14	0.72	15.3	64.5	1.23	5.17	34.9

lists the best 10 MOFs for the single-step separation as well as their corresponding structural properties, selectivity, capacity, and SPI values. As depicted, the most promising MOF is CUNXIS, showing a maximal SPI of 705.8 cm⁶/g².

Although the single-step process is easy to operate, it may be difficult to find an adsorbent that shows excellent separation performance for both C₂H₂ and C₂H₆. Additionally, the regeneration of MOF produces a C₂H₆/C₂H₂ mixture, which needs to be further separated and recycled back to the cracking reactor for maximizing the C₂H₄ yield. Considering these factors, another multi-step separation process shown in Figure 5b is introduced. Unlike the single-step separation, the multi-step process separates each impurity on an individual adsorbent sequentially. For purifying C₂H₄ from C₂H₂/C₂H₄/C₂H₆, two different strategies can be employed. Specifically, one can first select a C₂H₂-selective MOF to separate C₂H₂ and then employ another C₂H₆-selective MOF to adsorb C₂H₆. Alternatively, the opposite separation sequence can also be applied. The top five C₂H₂-selective MOFs and C₂H₆-selective MOFs are listed in

Table 4. Structural properties, selectivity, capacity, and SPI of the top five MOFs for C₂H₂ separation (ranked according to $SP{I}_{{\mathrm{C}}_2{\mathrm{H}}_2}$ ) as well as the top five MOFs for C₂H₆ separation (ranked according to $SP{I}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ ) for the multi-step separation of C₂H₂/C₂H₄/C₂H₆.

Rank	CSD Code	Metal	LCD (Å)	Pore Volume (cm3/g)	${\mathit{S}}_{{{C}}_2{{H}}_2{/{C}}_2{{H}}_4}$	${\mathit{q}}_{{{C}}_2{{H}}_2} ({\mathbf{cm}}^3/\mathbf{g})$	$\mathit{S}\mathit{P}{\mathit{I}}_{{{C}}_2{{H}}_2} ({\mathbf{cm}}^3/\mathbf{g})$
1	ORAQUU	Bi, Zn	8.39	0.68	5216.4	354.7	1318.5
2	FENVOL	Zn	6.69	0.44	39528.8	281.4	1293.7
3	ZUQVIQ	Mn	5.78	0.66	5033.4	232.8	861.6
4	OHOFEW	Co	7.31	0.68	5735.7	202.6	761.5
5	VEHNED	Na, Ni	3.81	0.22	454736.8	115.0	650.5
Rank	CSD Code	Metal	LCD (Å)	Pore Volume (cm3/g)	${\mathit{S}}_{{{C}}_2{{H}}_6{/{C}}_2{{H}}_4}$	${\mathit{q}}_{{{C}}_2{{H}}_6} ({\mathbf{cm}}^3/\mathbf{g})$	$\mathit{S}\mathit{P}{\mathit{I}}_{{{C}}_2{{H}}_6} ({\mathbf{cm}}^3/\mathbf{g})$
1	CUNXIS	Al	4.73	0.22	18.7	18.6	23.6
2	CUNXIS10	Al	4.73	0.22	13.3	16.3	18.3
3	GIHBII	Ga	4.58	0.17	6.56	6.85	5.6
4	UFATEA01	Ni	5.37	0.42	2.02	7.41	2.3
5	CEYPUT	Co	5.37	0.42	1.82	6.71	1.7

according to their individual SPI values. The numerous combinations of one adsorbent from each group provide a big chance for the successful implementation of the multi-step separation process. For example, out of all the 25 combinations, ORAQUU and CUNXIS can be selected due to their highest ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_2}$ and ${SPI}_{{\mathrm{C}}_2{\mathrm{H}}_6}$ values.

3.4. Structure-Property Relationship Study

Some valuable insights can be extracted from the screening results by conducting the structure–property relationship study. These insights provide useful information for the experimental design of novel high-performing adsorbents. First, to quantify the influence of structural parameters on the adsorption selectivity, the relationship between the largest cavity diameter (LCD) and the selectivity of C₂H₂/C₂H₄ and C₂H₆/C₂H₄ is shown in Figure 6. As depicted in Figure 6a, the majority of the C₂H₂/C₂H₄ selectivity are higher than 1.0 and the highest selectivities are generally achieved at very low LCDs (below 4.0 Å). When only looking at the data, the C₂H₂/C₂H₄ selectivity of which is above 1.0, the selectivity generally decreases as the LCD increases. Similar trends in relations between LCD and selectivity were reported in the literature [21,49]. In Figure 6b, however, one can see that the selectivity of C₂H₆/C₂H₄ increases with LCD and reaches its highest value at around 4.7 Å. As the LCD increases further, both selectivities tend to converge to 1.0. This indicates that MOFs with very large LCDs are neither C₂H₂-selective nor C₂H₆-selective. This is not surprising because when the LCD is small, where three components have to compete for limited adsorption space, molecules with smaller size will be bound more easily. When LCD increases, more adsorption sites become available, hence all the components eventually will have equal chances to be adsorbed on frameworks.

Figure 7 shows the dependency of adsorption capacity on pore volume of MOF. As indicated in Figure 7a, the adsorption capacity of C₂H₂ increases with the pore volume until it achieves a maximal value of 354.7 cm³/g at pore volume of 0.68 cm³/g. As the pore volume increases further, the capacity of C₂H₂ starts to decline and finally converges to 2.5 cm³/g. Figure 7b,c shows a similar trend. Generally, the adsorption capacities of both C₂H₄ and C₂H₆ increase with pore volume until reaching the peak. Further increasing the pore volume, the adsorption capacities of C₂H₄ and C₂H₆ gradually decline to a limit value of 25.0 cm³/g and 1.5 cm³/g, respectively. It is observed that high capacities are achieved at moderate pore volumes. This might be explained by the fact that the pore volume is inversely proportional to framework density as demonstrated by Kong et al. [50]. Thus, adsorption capacities are always subjected to a balance between pore volume and MOF density. Comparing Figure 7a–c, although increasing the pore volume until 0.68 cm³/g leads to a larger adsorption capacity of impurities C₂H₂ and C₂H₆, it also causes a higher loss of product C₂H₄. Besides, due to the very analogous dependency of adsorption capacities of C₂H₄ and C₂H₆ on pore volume, the amount of removed C₂H₆ is always proportional to the amount of lost C₂H₄.

4. Conclusions

In summary, we studied the separation of C₂H₄ from the C₂H₂/C₂H₄/C₂H₆ mixture and screened the MOF adsorbents from the CoRE MOF database by GCMC simulation. We first validated its accuracy and showed that the force field in general yielded satisfactory results for adsorption equilibrium prediction, except for a few MOFs with the OMS effect. Next, new evaluation metrics SPI were proposed for single-step and multi-step separation strategies for C₂ ternary mixtures. For single-step separation processes, among all, CUNXIS with the highest SPI value at 705.8 cm⁶/g² was identified as the best. For multi-step separation processes, ORAQUU and CUNXIS with SPI being 1318.5 cm³/g and 23.6 cm³/g, respectively formed the best combination. Finally, we discovered that S_C2H2/C2H4 decreased with increasing LCD, and S_C2H6/C2H4 increased with increasing LCD. For all three components, capacities increased first with pore volume until reaching the peak and after that slowly converged.

However, there are two drawbacks of our study. First, we assumed that thermodynamics is the dominant controlling mechanism in our adsorption system, hence kinetics are ignored. Consequently, MOFs that achieved separations by exploiting the differences in diffusion rates of different species were out of the scope of the search. Second, the selection criteria SPI may not necessarily guarantee a success in practical processes, because it is derived from the phase level properties alone. So future studies containing detailed process modelling or experiments can be carried out for improvement.