High‐Throughput Discovery of Ni(IN)2 for Ethane/Ethylene Separation

Abstract Although ethylene (C2H4) is one of the most critical chemicals used as a feedstock in artificial plastic chemistry fields, it is challenging to obtain high‐purity C2H4 gas without any trace ethane (C2H6) by the oil cracking process. Adsorptive separation using C2H6‐selective adsorbents is beneficial because it directly produces high‐purity C2H4 in a single step. Herein, Ni(IN)2 (HIN = isonicotinic acid) is computationally discovered as a promising adsorbent with the assistance of the multiscale high‐throughput computational screening workflow and Computation‐Ready, Experimental (CoRE) metal–organic framework (MOF) 2019 database. Ni(IN)2 is subsequently synthesized and tested to show the ideal adsorbed solution theory (IAST) selectivity of 2.45 at 1 bar for a C2H6/C2H4 mixture (1:15), which is one of the top‐performing selectivity values reported for C2H6‐selective MOFs as well as excellent recyclability, suggesting that this material is a promising C2H6‐selective adsorbent. Process‐level simulation results based on experimental isotherms demonstrate that the material is one of the top materials reported to date for ethane/ethylene separation under the conditions considered in this work.

Center of Sogang University. Infrared (IR) spectra were obtained with an ATR module using a Nicolet iS10 FT-IR spectrometer.

Breakthrough experiments:
The breakthrough curves of mixed gas C 2 H 6 /C 2 H 4 (1:1 or 1:15, v/v) for Ni(IN) 2 were performed by a BELCAT-II linked with BELMASS mass spectrometer. A fixed-bed column filled with the pelletized samples (425 -600 μm) was prepared and the total gas flow rate was fixed to total 100 sccm for 1:1, and 50 sccm for 1:15. The flow rates of binary mixutre C 2 H 6 /C 2 H 4 were controlled at 2 sccm for 1:1, and 1 sccm for 1:15, respectively, balanced with He gas. Before breakthrough measurements, all samples were activated at 160 o C for 12 h. The composition of the activated sample was determined: elemetal analysis (%) calcd. for for C 12  exposure to air during elemental analysis measurements.) All outgas were continuously monitored by the mass spectrometer. The adsorbed amount of each gas was calculated with the ChemMaster program. [3] In case of the cyclic test, the samples were regenerated at 160 o C for 2 h before each cycle.
Computational methods: For molecular-level evaluation, the grand canonical Monte Carlo (GCMC) simulations were carried out to compute binary component (50:50) adsorption data for C 2 H 6 and C 2 H 4 in 6,830 MOFs from CoRE MOF 2019 database [4] at 1 bar, and 298 K. The single and binary component (50:50) adsorption isotherms were computed for C 2 H 6 and C 2 H 4 in top candidates (10 top-performing MOFs) in high-throughput computational screening with a range of pressure (from 1 Pa up to 100,000 Pa) at 298 K. Each GCMC simulation composed of a total 10,000 cycles where the first 5,000 cycles for initialization and the remaining 5,000 cycles for production run to compute ensemble average. The additional GCMC simulations were performed for 10,000 initialization cycles followed by 10,000 production cycles to compute single component C 2 H 6 and C 2 H 4 adsorption isotherms for the reported MOFs in the literature. The swap (insertion and deletion), rotation, re-insertion, translation, and identity change moves for C 2 H 6 and C 2 H 4 were considered equal probabilities for binary component GCMC simulations. For single-component GCMC simulations, the identity change move was not included in calculations. The potential energy surface of the materials were calculated by placing a single adsorbate molecule inside the unit cell and using MC moves to sample the inside of the framework. Energy histograms were computed based on 5,000,000 MC cycles. The Widom particle insertion simulations with 20,000 cycles were carried out at 298 K for top candidates (10 top-performing MOFs + 12 reported MOFs in the literature) in high-throughput computational screening to predict the heat of adsorption of C 2 H 6 and C 2 H 4 in the MOFs. Additionally, the Widom particle insertion simulations of 25,000 cycles were carried out at 298 K for C 2 H 6 and C 2 H 4 in the empty box (30 Å x 30 Å x 30 Å size) to predict the internal energy of C 2 H 6 and C 2 H 4 . The heat of adsorption was computed using the following equation (Eq. S1): is the heat of adsorption of the adsorbate (C 2 H 6 and C 2 H 4 ) in the framework (MOFs), is the interaction energy between the adsorbate and the framework, is the framework energy (which is set to zero for rigid framework), is the adsorbate's internal energy (which is zero for rigid molecules), R is gas constant, and T is the temperature of the system in Kelvin. For the N 2 adsorption isotherm in 2 with a range of pressure (up to 1 bar) at 77 K, the GCMC simulation was performed for 5,000 initialization cycles followed by 5,000 production cycles.
The Lennard-Jones (LJ) 12-6 potential was used to model the nonbonded interactions between framework atoms and atoms of adsorbates (Eq. S2): where is the interaction energy between atom i and j, is the distance between atoms i and j, and are the LJ well-depth and diameter, respectively. For the framework atoms, the interaction parameters were obtained from the DREIDING force field [5] . The TraPPE force fields were used to model C 2 H 6 , C 2 H 4 [6] and N 2 [7] molecules. The LJ parameters for different atom type interactions were approximated with the Lorentz-Berthelot mixing rules (Eq. S3-4): The non-bonded interactions for both adsorbate-adsorbate and adsorbate-framework interactions were truncated at 14.0 Å with the analytic tail correction. Periodic boundary conditions (PBC) were applied to x, y, and z directions to satisfy the minimum image conventions with respect to the 14.0 Å cutoff. The framework atoms forming the MOFs are held fixed at their crystallographic positions during MC and GCMC simulations. All MC and GCMC simulations were carried out using the open-source RASPA 2.0. [8] The potential energy surface of Ni(IN) 2 was calculated with methane molecule as a probe using iRASPA software. [9] Molecular Dynamics (MD) simulations were carried out to obtain relaxed Ni(IN) 2 . NPT MD simulations were carried out for 1 ns for pristine Ni(IN) 2 at 298 K and 1 atm. Following the NPT MD simulation, Ni(IN) 2 structure was relaxed under the NVT ensemble at 0 K. The Nose-Hoover thermostat and barostat were used to maintain the system's temperature and pressure damping parameters of 0.1 ps and 1.0 ps, respectively. Velocity-verlet integrator was used to numerically integrate the Newton's equations of motion with 0.1 fs time steps. Conjugated gradient (CG) and fire algorithms, as implemented in the LAMMPS simulation package (ver 12 Dec 2018) were used for the energy minimization step. The energy difference between subsequent cycles becomes less than 1.0 x 10 -6 kcal/mol. Bonded interactions between framework atoms were approximated based on UFF4MOF force field, as reported by Coupry et al. [10] Force field parameters were assigned using the LAMMPS interface python module developed by Boyd et al. [11] All MD simulations were carried out using LAMMPS. [12] Material Studio [13] was used for Density functional theory (DFT) calculations were carried out using CP2K package [15] The PBE functional [16] with the Grimme D3 correction [17] was used. The Goedecker−Teter−Hutter (GTH) pseudopotentials [18] and DZVP-MOLOPT-GTH basis sets [19] were utilized with energy cutoff of 1000 Ry. For the adsorbent evaluation at the process-level, an ideal vacuum swing adsorption (VSA) process is adopted in this work [20] , which models the VSA process by excluding the heat and dispersion and void volume effects. The method computes the best possible performance that an adsorbent material can achieve under the ideal circumstances. The ideal VSA simulation only consists of adsorption and desorption steps, and we calculated the C 2 H 4 recovery during the adsorption and desorption step to evaluate the performance of adsorbent materials. Here, C 2 H 4 is a raffinate component produced during the adsorption step, while the unreacted ethane was recovered during the desorption step. The purity of C 2 H 4 8 is 100% for all materials evaluated in this work since the materials preferentially adsorb C 2 H 6 over C 2 H 4 during the adsorption step. Depending on the adsorbents, some C 2 H 4 is adsorbed during the adsorption step, which is lost during the desorption step. The extent of loss and the recovery of C 2 H 4 is closely related to the economic performance of the VSA process. A high C 2 H 4 recovery is directly related to a higher production rate of C 2 H 4 and a smaller loss of the raw material.
The ideal VSA process produces 100% purity of raffinate, which is ethylene in our case. This high-level of purity can be achieved by judiciously selecting the operating conditions of the process, such as step times, rinse flowrate, which has been experimentally demonstrated by Park et al. [21] However, the modification of the operating conditions leads to the trade-offs between the recovery and purity of ethylene product. One of the key materials properties that can be tuned from the operating condition is mass transfer coefficient. Unfortunately, the accurate estimation of the mass transfer coefficients of all adsorbents are computationally and experimentally difficult and time consuming. Ideal VSA simulation allows us to remove the need to use the mass transfer coefficient to evaluate the performance of adsorbent materials at the process-level. Figure S1. VSA process schematic and its key parameters.
We modified the original method that has been developed for the CO 2 /N 2 separation for the case of C 2 H 4 /C 2 H 6 separation. The key parameters are marked in Figure S1. Based on the assumption that the process produces 100% ethylene through the raffinate flow, we can write down the mass conservation of ethylene as in Eq. S6: Here, is the mole fraction of ethylene in the feed flow, is the mole fraction of ethylene in the extract, ̇ and ̇ are the total molar flow rate of feed and extract in the unit of mol per time.
The ethylene purity in the raffinate, , is formally defined as: By combining the Equations S5 and S6, we can obtain the equation for the raffinate recovery as below: Here, is the recovery of ethylene in the raffinate, and are the molar fraction of C 2 H 4 in the extract and feed flows, respectively. For the application of the adsorbent properties, the ideal adsorbed solution theory (IAST) was employed with the quadratic, Langmuir or dual-site Langmuir isotherm parameters explaining the pure adsorption isotherm (see the Supplementary Information S7).
Each molecular simulation result or the experiment dataset was fitted with the most suitable model among the isotherm models supported in pyIAST. [22] The mixture isotherms were predicted using the pure component isotherms as input. Details of fitting isotherm parameters are provided as Section S7 of the Supplementary Information (SI).

Isosteric heat of adsorption calculations:
The coverage-dependent adsorption enthalpy profiles were calculated from the sorption data measured at 273, 298, and 323 K by Virial fitting method and Clausius-Claperyron equation. A Virial-type expression was used (Eq. S9), which is composed of parameters ai and bi, which are independent of temperature. In Eq. S9, P is the pressure in atm, N is the adsorbed amount in mmol g -1 , T is the temperature in Kelvin, a i and b i are the Virial coefficients, and m and n represent the number of coefficients required to adequately describe the isotherms.
To calculate Q st , the fitting parameters from the Eq. S9 were used for the Eq. S10.

Derivation of the propagation rate of saturated adsorbent area
From the process engineering point of view, the main advantage of C 2 H 6 selective material is that the product (ethylene) exits first during the adsorption step. To see if this is true for all the materials considered in this work, we derived the propagation rates of the saturation region for both ethane and ethylene, and compared if the ethane is always small. The propagation rate is calculated in the following way: (Eq. S11) (Eq. S12) (Eq. S13) where, is a propagation rate of the saturated adsorbent area for component i during the adsorption time.

S4. Comparison of experimental and simulated results
To obtain relaxed Ni(IN) 2 structure, MD simulations were carried out for pristine Ni(IN) 2 structure. As shown in Figure S12 and Table S2, the relaxed Ni(IN) 2 has relatively larger pore size and pore volume than the pristine Ni(IN) 2 . Both MOFs were used to compare experimental and simulated isotherms. Figure S13 shows that the N 2 isotherm of the relaxed Ni(IN) 2 is similar to experimental isotherm compared with data of pristine Ni(IN) 2 . Additionally, as shown in Figure S14 and

S5. Ideal VSA simulations results with different operating conditions
Additional process-level analyses with different vacuum pressure (i.e., desorption pressure) were performed to elucidate the parameter's sensitivity on the performance. The results are shown in Figure   S16 -S18. For varying vacuum pressure, we tested the top 10 candidates selected in the screening work with the CoRE MOF 2019 database. Figure S16 shows the VSA process performances of the top 10 candidates. This evauation was performed for the varying vacuum pressure from 0.01 mbar to 10 mbar.
The ethylene recoveries of the VSA processes with each adsorbent are displayed as different vaccum pressures are used during the desorption step. In Figure S17, the adsorbents from the literature are compared with Ni(IN) 2 for the varying vacuum pressure with the same setting of Figure S16. Figure S18 has the results of ideal VSA process where 16.44% of ethane is used as a feed flow, which has been reported by Park et al. [21] In these three cases, as the vacuum pressure decreases, the recovery values of all the MOFs become improved. This trend can be explained with the correlation where the energy input and the extent of separation in this process. Stronger vacuum needs increased energy for the process operation, but the process can harness more energy to separate the target gas. Thus, more energy input to the process leads to lower vacuum pressure, which makes better separation of C 2 H 6 /C 2 H 4 . Moreover, depending on the adsorption isotherm properties, the slope of the recovery is shown to be different. While MAF-49 and

S6. Correlation of process-level and molecular-level metrics
To see the correlation of process-level and molecular-level metrics, we computed the Spearman's ranking correlation coefficients (SRCC) which is a nonparametric measure of rank correlation using Eq. S14: (Eq. S14) where and are ranks of raw scores and , is the covariance of the rank variables, and are the standard derivations of the rank variables. We calculated SRCC for recovery, 1 bar selectivity (50:50) and 1 bar ethane uptake obtained from experimental and simulated isotherm data used in this paper. As shown in Figure S19, SRCC between recovery and selectivity is high, while SRCC between recovery and uptake is low. This data supports our approach to select the best performing MOFs based on selectivity.

S8. Comparison of productivity and recovery metrics
We obtained the productivity values that have been frequently proposed in the literatures. The results are shown from Figure S86 to S87. For breakthrough simulations with the adsorbents we evaluated in this study, we used the following model equations, from Eq. S18 to Eq. S21. Based on the gas and solid phase concentrations, the model adopts linear driving force model to describe the mass transfer between the two phases. For different adsorbents, different isotherm models and corresponding parameters were applied in Eq. S20, which are listed in Section S7.
(Eq. S18) (Eq. S19)    such as product recovery, that we considered in this work. This is because the recovery from the VSA and the productivity from the breakthrough simulation (or experiment) represent completely different process information. In the breakthrough simulation (or experiments), the inert gas (typically helium) is employed to regenerate the adsorbents packed in advance of the column. However, in the actual operation of VSA process for ethane/ethylene separation, the inert gas is not injected because the use of inert gas increases the operating cost by causing to the loss both in the quality and the recovery of the ethylene due to the diluted gas concentration in the column. Moreover, the feed concentration is assumed to be 50:50 in a typical breakthrough work, while actual VSA processes have lower ethane concentration.
The product recovery metric tells us how much of ethylene can be produced out of the invested ethylene in the feed flow, which critically influences on the operating cost of the process. Computation of the metric reflects the effect of the remaining gas component after the desorption (i.e., regeneration) step, which impacts the adsorption characteristics of feed gas components in subsequent adsorption step.