Molecular simulations of adsorption and separation of ethylene/ethane and propylene/propane mixtures on Ni2(dobdc) and Ni2(m-dobdc) metal-organic frameworks

Abstract Porous solid adsorbents have received considerable attention as a promising alternative to the traditional cryogenic distillation for separating olefin/paraffin mixtures. In this work, we studied pure components as well as ethylene/ethane and propylene/propane binary mixtures uptakes and selectivities at 318 K and 1 bar into metal-organic frameworks Ni2(dobdc) and Ni2(m-dobdc) using GCMC simulations. We used DFT method to modify the potential model of carbon–carbon double bond in unsaturated hydrocarbons. GCMC results show that ethylene and ethane uptakes on Ni2(m-dobdc) are higher than that of Ni2(dobdc) but propylene and propane uptakes are equal in Ni2(m-dobdc) and Ni2(dobdc). Also, Ni2(m-dobdc) has higher selectivity than Ni2(dobdc) for separation of ethylene/ethane and propylene/propane mixtures.


Introduction
In recent decade, metal-organic frameworks (MOFs) have received considerable attention as an interesting subset of porous materials [1][2][3]. As these materials take advantage of high surface areas, adjustable pore size, chemical tenability, good thermal and mechanical stabilities and high porosities, they have been studied extensively for gas adsorption and separation applications [4][5][6]. MOFs can be alternative to high energy costs cryogenic distillation in the process of olefin/paraffin separation. The cryogenic distillation process demands high pressure and low temperature, but MOF-based process can be used at moderate conditions and great energy saving is expected [7].
The cationic sites of M 2 (m-dobdc) have a higher charge density than M 2 (dobdc) and show 0.4−1.5 kJ/mol larger H 2 binding enthalpies [13]. While several studies have been recently addressed the adsorption and separation of light hydrocarbons using M 2 (dobdc) [7,11,14,15], there is no comparative study of the olefin/paraffin separation performances in M 2 (dobdc) and M 2 (m-dobdc). This motivated us to study ethane, ethylene, propane and propylene adsorption and their selectivities on Ni 2 (dobdc) and Ni 2 (m-dobdc) by Grand Canonical Monte Carlo (GCMC) simulations. Molecular simulation methods are powerful tools to study the physicochemical process at the molecular scale. Exploring the structural effects on the adsorption/ separation of molecules into isostructural MOFs by molecular simulations can help understand the underlying mechanism and design the task-specific adsorbents [16].

Computational details
GCMC simulations were performed using a code developed by Prof. T. Woo research group [17,18] in the University of Ottawa based on DL_POLY MD code [19]. Three types of trial moves were randomly attempted in GCMC simulations, translation, insertion and deletion. The size of the simulation box was set to 2 × 2 × 4 unit cells. Each point of the pure component isotherms was equilibrated for 10 7 steps followed by subsequent 10 7 moves for data collection. Mixtures simulations consist of a total of 10 8 steps where the last half of the configurations is used for data collection. functional with 6-31 + G(d,p) basis set was used for the calculation of binding energy of ethylene to Ni 2 (dobdc) and Ni 2 (mdobdc) representative clusters. All DFT calculations were performed using Gaussian 09 software [29]. The cluster model of Ni 2 (dobdc) and Ni 2 (m-dobdc) was used to perform the DFT calculations. The energy profiles of hydrocarbons adsorptions on Ni 2 (dobdc) and Ni 2 (m-dobdc) were obtained as a function of the distance between the centre of mass of the adsorbed molecule and Ni atom. For each value of the molecule-Ni distance, the interaction energies were computed from Equation (1): where, E MOF-molecule represents the total energy of the MOF cluster and the molecule, while E MOF and E molecule are the total energies of the MOF cluster and the molecule, respectively. Figure 2 displays simulated ethane and ethylene adsorption isotherms on Ni 2 (dobdc), as well as experimental data of Geier et al. [11]. The simulated uptake of ethane on Ni 2 (dobdc) in Figure  2(a) reproduces the shape of the experimental isotherm [11] satisfactorily although it overestimates the experimental uptake in the studied pressure range, especially at high pressures. Usually, the simulated uptake overestimates the experimental ones due to some assumptions made in performing simulations such as assumption of ideal crystal structure and accessibility of all pores in simulation and the inability of applied force field to reproduce the adsorbate-adsorbent interaction energies. Figure 2(b) compares the simulated isotherms for ethylene on Ni 2 (dobdc) using the unmodified interaction energy parameters with the experimental uptakes of Geier et al. [11]. The experimental isotherm [11] of ethylene in Figure 2(b) rapidly increases with pressure at low pressure range and reaches saturation for pressures larger than 0.6 bar. However, the simulated uptake using unmodified potential parameters underestimates significantly the experimental uptakes and increases linearly for all studied pressures. The observed disagreement is a result of the inability of the TraPPE force field to properly account for the interaction between ethylene and open metal sites of the MOF.

Pure components adsorption isotherms
It was shown that the interaction between π-orbital electrons of unsaturated hydrocarbons and empty d-orbitals of metal caused higher uptake of unsaturated hydrocarbons in Van der Waals (vdW) interactions were described by Lennard-Jones 12-6 potential model. The Lennard-Jones parameters for the interactions between unlike interactions have been obtained from Lorentz−Berthelot mixing rules [20]. A cut-off radius of 12.5 Å was applied. Periodic boundary conditions were applied in all three dimensions.
The studied MOFs were modelled as rigid frameworks with atoms frozen at their crystallographic positions reported by Kapelewski et al. [13]. The LJ potential parameters of the framework atoms were adopted from the OPLS all-atom force field [21], except those for the Ni atom, which were not available in OPLS and were taken from the UFF force field [22]. OPLS was shown to accurately describe the saturated hydrocarbon adsorptions into MOFs [23][24][25].
Hydrocarbon molecules were described using the united atom model, where the CH x groups are treated as an electronically neutral LJ interaction site, so the electrostatic interactions were not considered. The TraPPE force field was used for LJ potential parameters of propane and ethane [26]. The unmodified LJ parameters for ethylene and propylene were adopted from the works of Weitz et al. [27] and Gutiérrez-Sevillano et al. [28], respectively.
DFT calculations were used to reparametrise the LJ interaction parameters of ethylene and propylene with Ni atoms of MOFs. Perdew Burke Ernzerhof (PBE) exchange-correlation  comparison with the saturated hydrocarbons [23,30]. Previous attempts to overcome this shortcoming of classical force fields are based on two main approaches: (1) ad hoc adjustment of the metal-carbon Lennard-Jones energy parameters to gain a satisfactory agreement between the simulated and the experimental isotherms [23,31], (2) the calculation of the interaction energy between the adsorbate and the metal by means of quantum mechanical methods and then incorporation of the QM-calculated interaction energy into the classical force field [32][33][34][35]. The implementation of the first approach is easy but gives no insight and relies on the availability of the experimental data. To the best of our knowledge, there is no experimental data for the uptake of ethane, ethylene, propane and propylene on Ni 2 (m-dobdc) so we used the second approach for adjusting the energy parameter of ethylene and propylene with Ni on Ni 2 (dobdc) and Ni 2 (m-dobdc).
At first, the interaction potential energy of ethylene adsorbed on Ni 2 (dobdc) as a function of centre of mass of ethylene and Ni distance was calculated using the DFT method. In order to model the special interaction of π-electrons with the Ni atoms and achieving a better fitting performance, a new massless LJ interaction site (X) was placed at the centre of mass of the ethylene. The Ni-X potential energy parameters were obtained by fitting Ni-X LJ potential energy to the DFT-calculated energies where the two energies are shown in Figure 3. The obtained potential energy function of Ni-X interaction was added to the standard force field [26], and the modified potential was used in GCMC simulations.
The GCMC-calculated ethylene uptake using the DFTmodified force field is shown in Figure 2(b). Although the modified uptake underestimates the experimental uptakes slightly at low pressure and overestimates at high pressure, it is obvious that it reproduces the shape of the experimental isotherm [11] and shows more satisfactory agreement with the experimental values [11] than the unmodified TraPPE force field.
The binding energy of a molecule on a MOF has a crucial effect on the observed uptake. The DFT-calculated binding energies of ethane, ethylene, propane and propylene on Ni 2 (dobdc) and Ni 2 (m-dobdc) are depicted in Table 1. The adsorbates' binding energies on Ni 2 (m-dobdc) are higher than that of Ni 2 (dobdc). So, one can expect a higher adsorption of a hydrocarbon on Ni 2 (m-dobdc) than Ni 2 (dobdc). Also, the calculated binding energies for the unsaturated hydrocarbons are higher than that of the corresponding saturated one on the same MOF which cause a higher uptake of an unsaturated hydrocarbon than that of saturated one on the same MOF. The results of Table 1 motivated us to study the adsorption isotherms and separations of ethane, ethylene, propane and propylene on Ni 2 (dobdc) and Ni 2 (m-dobdc) by molecular simulation.
The GCMC-simulated adsorption isotherms of ethane on Ni 2 (m-dobdc) and Ni 2 (dobdc) using the standard force field in Figure S5 show that the ethane uptake on Ni 2 (dobdc) at moderate pressures are higher than that of Ni 2 (m-dobdc). While, according to Table 1, the DFT-calculated binding energies of ethane on Ni 2 (m-dobdc) is 3.8 kJ/mol higher than Ni 2 (dobdc). So, it is apparent that the applied force field is unsuccessful in reproducing the correct trend of ethane adsorption into Ni 2 (m-dobdc). In order to obtain the correct trend of ethane uptakes, the LJ energy well-depth parameter representing Ni-CH 3 (ethane) interaction for the adsorption of ethane on Ni 2 (m-dobdc) was adjusted in such a way that the difference between the calculated binding energies of ethane into Ni 2 (m-dobdc) and Ni 2 (dobdc) using the applied classical force field be equal to the quantum mechanical calculated energy differences in Table 1. The ethane-Ni 2 (dobdc) and modified ethane-Ni 2 (m-dobdc) potential energy as well as adjusted Ni-CH 3 parameters are shown in Figure S6 and Table  S3 of ESI, respectively. Figure 4 shows the calculated adsorption isotherms of ethane on Ni 2 (dobdc) and Ni 2 (m-dobdc) using the modified Ni-CH 3 potential. The adsorption of ethane on Ni 2 (mdobdc) is higher than that of Ni 2 (dobdc) in agreement with quantum mechanically calculated binding energies in Table 1. Figure 5 compares the simulated isotherms for ethylene on Ni 2 (dobdc) and Ni 2 (dobdc). For adsorption of ethylene on Ni 2 (m-dobdc), we adjusted the ethylene-Ni interaction energy parameters using the same method as described above for ethylene adsorption on Ni 2 (dobdc). The obtained LJ classical as well as the quantum mechanical calculated interaction energy of Ni 2 (mdobdc) cluster models and ethylene are shown in Figure S7, and the adjusted LJ parameter for new inserted interaction site (X) of ethylene on Ni 2 (m-dobdc) are depicted in Table S4 of ESI.   parameters for the Ni-X for ethylene was used. The simulated propylene uptakes on Ni 2 (dobdc) with the modified model in Figure 7 are higher than the experimental values [11] which is reasonable for a GCMC simulation. Like propane adsorption, uptakes of propylene on Ni 2 (mdobdc) and Ni 2 (dobdc) in Figure 7 are nearly equal for all studied pressures. This similar uptake can be related to the larger molecular sizes than ethane and ethylene which causes the MOF pore volume fill rapidly. As propane or propylene uptake get saturated, the pore volume is mainly filled with adsorbed molecules and only a small amount of pore volume left unoccupied due to matching between the pore size and the size of a propylene molecule (see Figures S11 and S12). Thus, increasing the interaction energy between propylene (or propane) and open metal site can't increase their adsorption on Ni 2 (m-dobdc). Figure 8 shows the calculated isosteric heats of adsorptions of ethane, ethylene, propane and propylene on Ni 2 (dobdc) and Ni 2 (m-dobdc).
For all studied adsorbates, the calculated isosteric heats of adsorption are smaller than the experimental values [11]. A detailed comparison between our simulated isosteric heats of adsorption and experimental values of Geiere [11] is not possible due to the lack of statistical uncertainties of the experimental values. However, we can count some factors for the observed discrepancy. First, a neat and perfect crystal structure is used in the simulations, where the samples used in the experiments may have impurities and crystal defects. The dispersed impurities in the real samples can enhance the adsorbate-adsorbent As it can be seen from Figure 5, the ethylene adsorption on Ni 2 (m-dobdc) are higher than that of Ni 2 (dobdc) for all studied pressure ranges. Differences in ethylene adsorptions on Ni 2 (mdobdc) and Ni 2 (dobdc) at low pressures are larger than that of high pressures. It is well known that at low pressures, adsorption is controlled by the interaction between the guest molecule and the framework where at high pressures the surface area or free volume of adsorbent determines the adsorption capacity [6,36]. The calculated binding energies in Table 1 show that the interactions of the ethylene with Ni 2 (m-dobdc) is stronger than Ni 2 (dobdc). At low pressures, the uptake is controlled mainly by the interaction energy of the guest molecules and framework, so one can expect a larger binding energy between ethylene and Ni 2 (m-dobdc) led to a higher uptake on Ni 2 (m-dobdc) than Ni 2 (dobdc). However, comparable surface area and free volume of Ni 2 (m-dobdc) and Ni 2 (dobdc) caused small difference in ethylene adsorption on Ni 2 (m-dobdc) and Ni 2 (dobdc) at high pressure. Figure 6 displays the simulated adsorption isotherms of propane on Ni 2 (dobdc) and Ni 2 (m-dobdc). One can see that there are good agreements between simulated and experimental uptakes of Geier et al. [11] for the propane adsorption on Ni 2 (dobdc).
For simulating the propane adsorption on Ni 2 (m-dobdc), the obtained Ni-CH 3 (ethane) potential parameters for the adsorption of ethane on Ni 2 (m-dobdc) in Table S3 was used. Also, the potential parameters of Ni-CH 2 (propane) interaction were adjusted by the same method as Ni-CH 3 and results are depicted in Table S5. The resulted potential energies for the adsorption of propane on Ni 2 (dobdc) and Ni 2 (m-dobdc) are shown in Figure  S8 of ESI. As it can be seen from Figure 6 uptakes of propane on Ni 2 (m-dobdc) and Ni 2 (dobdc) are nearly equal for all studied pressures.
The adsorption isotherm of propylene into Ni 2 (dobdc) and Ni 2 (m-dobdc) are shown in Figure 7.
The simulated uptake of propylene on Ni 2 (dobdc), using unmodified force field, underestimates the experimental adsorptions. Similar to the adsorption of ethylene on Ni 2 (dobdc), it is necessary to augment the standard force field with a term for representing the specific interactions between the π-orbitals of the propylene and Ni d-orbitals. The same model used for the adsorption of ethylene on Ni 2 (dobdc) and Ni 2 (m-dobdc) was employed for describing propylene on studied MOFs. A new interaction site (X) has been considered at the centre of the C=C bond of propylene where the obtained Lennard-Jonnes

Separation of binary mixtures
To study the performance of Ni 2 (m-dobdc) and Ni 2 (dobdc) for the components separation of ethylene/ethane and propylene/ propane binary mixtures, we conducted GCMC simulations on these mixtures. The adsorption selectivity S of an adsorbent to separate the components A and B from their mixture is defined by where x i and y i are the mole fractions of components in the adsorbed and the bulk phases, respectively. The simulated ethane/ethylene and propane/propylene selectivity at 318 K are shown in Figure 9(a) and (b), respectively, and compared with IAST (Ideal Adsorbed Solution Theory) prediction [11].
There is a good quantitative agreement between our results using the modified model of ethylene and IAST predicted selectivity [11] of ethylene over ethane on Ni 2 (dobdc) in Figure 9(a). In Figure 9(b), the unmodified model of propylene underestimates propylene/propane selectivity on Ni 2 (dobdc) with respect to the experimental IAST [11] prediction while the modified model overestimates it.
(2) S = x A ∕x B ∕ y A ∕y B , interaction energy. Second, the simulated isosteric heats of adsorption are obtained directly from interaction energies in the course of simulation but the experimental heat is estimated from the fitted experimental adsorption isotherms to some models. Third, the applied force fields might be unable to correctly capture the adsorbate-absorbent and adsorbate-adsorbate interaction energies.
The isosteric heats of adsorption is controlled by both guest-guest and framework-guest interactions. Increasing the isosteric heats of ethane and propane with loading indicates the significance of intermolecular interaction for the adsorption of these gases. For all hydrocarbons, the isosteric heats of adsorption on Ni 2 (m-dobdc) at low pressures are higher than that of Ni 2 (dobdc) where they are nearly the same at high pressures. It is well known that at low pressures the guest molecules are mainly adsorbed by the open metal sites of the MOF. This leads to higher isosteric heat of adsorption on Ni 2 (m-dobdc) than Ni 2 (dobdc) at low pressures in Figure 8. As the pressure increases, the adsorbed molecules accumulate in the centre of pore and increase the repulsion which decreases the heat of adsorptions differences between Ni 2 (m-dobdc) and Ni 2 (dobdc) at high pressures.

Conclusion
In this study, we conducted a comparative study of ethane, ethylene, propane and propylene adsorption and separation on Ni 2 (m-dobdc) and Ni 2 (dobdc). Our results show that the TraPPE and OPLS classical force fields are unable to reproduce the experimental adsorption isotherms especially for the adsorption of unsaturated hydrocarbons on the unsaturated metal centres of MOFs. The applied force fields were modified using the DFT calculations results on the model cluster of MOFs. The simulation results using the modified model for ethylene predicted the pure component adsorption isotherm into Ni 2 (dobdc) in acceptable agreement with the experimental values. Also, the predicted adsorption selectivities for ethane/ethylene mixture are in good agreement with IAST prediction. Based on our simulation results, Ni 2 (m-dobdc) has higher ethylene adsorption than Ni 2 (dobdc), especially at low pressure range. This is due to stronger interaction between ethylene and Ni 2 (m-dobdc). Ni 2 (mdobdc) has higher selectivity than Ni 2 (dobdc) in all studied mole fractions of ethylene too. Both of unmodified and modified model of propylene can predict pure component adsorption isotherm of Ni 2 (dobdc) in acceptable agreement with the experimental observations but none of them are in agreement with IAST. Based on our simulation results, Ni 2 (m-dobdc) has higher selectivity in propylene/propane separation.