On the Diffusion of Ionic Liquids in ILs@ZIF-8 Composite Materials: A Density Functional Theory Study

1. Introduction

Recently, the composite materials consisting of ionic liquids (ILs) and metal-organic frameworks (MOFs) have attracted considerable attention because of their exceptional properties^{1, 2}, therefore, they have been used in many important fields, e.g. the gas adsorption and separation, catalysis, and sensors^3-10. In particular, the large number of adsorption sites of MOFs with ILs play an important role in the mixture gas separation (e.g. CO₂/CH₄) ^11-14. For example, Ban et al¹⁵ loaded [C₄mim][TF₂N] into the cages of ZIF-8, and the results showed the adsorption selectivity for CO₂/CH₄ significantly increased from 7.5 to 41. Following this work, Kinik et al.¹⁶ examined the [C₄mim][PF₆]/ZIF-8 system via the density-functional theory (DFT) and Monte Carlo (MC) simulations. The authors found that the interactions between [C₄mim][PF₆] and ZIF-8 created certain new adsorption sites, which increases the ideal selectivity for CO₂/N₂ from 7.82 to 24.21. Burak et al.¹⁷ obtained a similar result by incorporating [C₄mim][BF₄] into ZIF-8, of which the selectivity of 13.3 has been obtained for CO₂/N₂. Afterwards, a large number of systems have been reported with different combination of ILs and MOFs¹⁸.

In general, the reasons for ILs@MOFs composites materials with high gas separation or selectivity have been attributed into the two main aspects. On the one hand, the rich hydrogen bonds network of ILs^{19, 20} could effectively dissolve CO₂ molecules against other gases, e.g. CH₄ or N_2,²¹ hence, it improves the separation performance compared to the pure MOF materials^22-24. For example, Thomas et al²⁵ performed DFT and Giant Canonical Monte Carlo (GCMC) simulations to investigate the selectivity for a series of IL@ZIF-8 systems. Their findings reveal that the hydrophobic fluorinated anion (e.g. [BF₄]^-, [Tf₂N]^-, and [PF₆]^-) exhibit higher selectivity compared to hydrophilic non-fluorinated anions (e.g. [NO₂]^-, [NO₃]^-, [SCN]^-). Kavak et al.²⁶ investigated the CO₂ separation efficiency of five different ILs encapsulated MIL-53 systems, and they found that the CO₂/CH₄ separation selectivity of [C₄mim][PF₆]/MIL-53 was 2.8 times higher compared to the pure MIL-53. Zhang et al.²⁷ conducted an investigation on ILs with three different cation functional groups, revealing that ILs containing amino functional groups exhibited the highest CO₂ molecule affinity and CO₂/CH₄ adsorption selectivity.

On the other hand, it is believed that the introduction of ILs could also modify the structures of the MOFs, and increase the gas selectivity, subsequently. Based on the experimental techniques (e.g. high pressure X-ray diffraction, XRD) with molecular simulations, Fairen et al.²⁸ demonstrated that the imidazolate linker of the ZIF-8 changed because of the swing effects, and change the gas selectivity, subsequently.²⁹ Uzun and colleagues³⁰ coated 1-(2-hydroxyethyl)-3-methylimidazolium dicyanamide ([Hemim][DCA]) on the ZIF-8 surface to eliminate the nonselective voids, and authors found that the CO₂ selectivity was increased by 45 times compared to pure ZIF-8. Chang et al.³¹ successfully constructed an zwitterionic MOF material (MOF UiO-66-SO₃^--NH₃⁺), and the adsorption capacity for CO₂ increased by 32-48%, because the positive and negative charges on the modified MOF material interacts with the ILs of [Emim][SCN]. Our previous theoretical studies ^{32, 33} revealed that the ZIF-8 aperture configurations have significant impact on the separation of CO₂/CH₄. Specific speaking, the DFT calculations showed that the pristine ZIF-8 aperture (with a pore size of 3.4 Å) exhibits the best separation performance, which has the largest energy barrier difference between CO₂ and CH₄, and the MD simulations revealed that ILs (e.g. [C₄mim][PF₆]) could effectively maintain pristine aperture configurations, and remain the high separation properties.

Yet, there is still an open question following the reported mechanistic studies, that is, how does the ILs diffusion into the cage of MOFs (e.g. ZIF-8), and the how many ILs could be accommodated per cage. For this vein, we performed DFT calculations to investigate the diffusion behavior of ILs into MOFs cages, by taking [C₄mim][PF₆] and ZIF-8 as an example. Firstly, the potential energy surface (PES) scan were performed to study the passing of [C₄mim]⁺ and [PF₆]^- through different ZIF-8 apertures. Secondly, several electronic analysis method, including frontier orbital energies, natural charge analysis, and energy decomposition analysis, were used to investigate the interactions between [C₄mim]⁺/[PF₆]^- and ZIF-8. Lastly, a series of ILs encapsulated ZIF-8 with different loading amount were investigated to obtain stabilities of ionic pairs in the SOD cage of ZIF-8.

2. Computational Details

The crystal structure of the ZIF-8 was obtained from the Cambridge Crystallographic Data Centre (CCDC) Crystal Library²¹, and the simplified SOD cage presentation is depicted in Figure 1a. We choose the five typical pore apertures of the ZIF-8 structure as the result of the rotation of the zinc-imidazole-zinc and methyl functional groups, as described by our previous work, ³², including "Pristine (3.4 Å)", "Closed" (4.1 Å), "Semi-open (4.2 Å)", "Closed (4.7 Å)", "Open" (6.9 Å), respectively, which are shown in Figure 1b – Figure 1f.

As demonstrated in Figure 2a, the [PF₆]^- and [C₄mim]⁺ were firstly placed at 10 Å away from the aperture of the ZIF-8, then gradually (e.g. with a step size of 0.1 Å), penetrate passed through the center of the aperture (in other words, the center of mass, COM). In principle, [PF₆]^- and [C₄mim]⁺ might have many orientations when pass through the five pore structures as shown in Figure 1. Here, we considered only the orientations which have possible low energy barriers. Summarizing in Figure 2 (b), three different orientations of [PF₆]^- have been studied, denoted as case I, II and III, with one, two, three fluorine atoms (F) towards the aperture, respectively. For the [C₄mim]⁺, one case was chosen towards the aperture, of which the imidazole ring is almost vertical to the aperture.

With above-described models, rigid PES scans with single point (SP) energy calculations were performed, where all atoms in the aperture of ZIF-8 and [PF₆]^-/[C₄mim]⁺ were kept frozen. Afterward, we performed the relaxation PES scan within the regions nearby the highest energy barrier positions from rigid PES scans (e.g. ca. -2 Å to 2 Å). In these cases, the atoms in the aperture of ZIF-8 were kept frozen, while [PF₆]^-/[C₄mim]⁺ were fully optimized. Both PES scans were carried out with the Gaussian16 software package⁴¹. Subsequently, the orbital energies and charge transfer were computed by natural population analysis (NPA)³⁴ using the Multiwfn³⁵ software package, and visualized using the VESTA³⁶ software package. To quantitatively study the interactions between [PF₆]^-/[C₄mim]⁺ and ZIF-8, the energy decomposition analysis were performed based on the generalized Kohn-Sham energy density analysis (GKS-EDA) method³⁷, which is implemented in the GAMESS program package ³⁸. All above-mentioned DFT calculations were performed at the B3LYP level of theory, and a basis set of 6-311+G*³⁹, together with the damping scheme of Becke and Johnson, which denoted as DFT-D3 (BJ)^{40, 41}.

Lastly, to study how many pairs are stable inside the SOD cage of ZIF-8, the periodic structures of ILs@ZIF-8 were examined by the BLYP functional with the dispersion correction scheme (DFT-D3). The geometry optimizations were performed to account for both changes in atomic positions and lattice dimensions, which were updated with the efficient L-BFGS algorithm. Within the DFT calculations, the DZVP-MOLOPT-SR-GTH basis set was adopt for Zn atoms, while the other atoms used the TZVP-MOLOPT -GTH basis set. The energy cutoff set to 400 Ry, and the energy convergence for the self-consistent field (SCF) calculation was set to 1 × 10^-5 Hartree. All those periodic calculations were performed by employing the CP2K’s Quickstep module⁴².

3. Results and Discussion

The PES scan of the [C₄mim]⁺ and [PF₆]^- passing through the pristine ZIF-8 aperture (with a pore size of 3.4 Å) were shown in Figure 3a. It is shown that both [C₄mim]⁺ and [PF₆]^- almost cannot pass through the pore, because of their large energy barriers. For [C₄mim]⁺, an energy barrier of 135. 5 kcal mol^-1 were obtained, and the corresponding structure is the one when the COM of imidazole is almost overlap with COM of the pristine ZIF-8 aperture. For [PF₆]-, three cases have been considered, as shown in Figure 2b. The lowest energy barrier, which is 69.17 kcal mol^-1, was found for the case III, in which three F atoms pointed to the plane of the ZIF-8 apertures. This finding could be explained by their molecular diameters, in which case I has a diameter of 3.29 Å, case II has a diameter of 3.20 Å, and case III has a diameter of 2.94 Å (Figure S1). Meanwhile, as shown in Figure S2, the results of the energy decomposition analysis show that the repulsive interactions between the [PF₆]^- and ZIF-8 is the smallest when [PF₆]^- adopted the case III. After obtaining the configurations with the highest energy barriers, we then refined the PES with the relax scan (see Figure 3b), and we found that both [C₄mim]⁺ and [PF₆]^- still have relative high energy barriers, being 39.87 kcal mol^-1 and 16.61 kcal mol^-1, respectively, which still prohibited [C₄mim][PF₆] diffusing into the SOD cage of ZIF-8 at finite temperatures, e.g. the room temperature. In details, only one energy barrier was found when [PF₆]^- moved from the left to the right side of the pore, and the highest energy point is corresponding to the structure of which the P atom is locating at the plane of the pristine ZIF-8, with three F atom locating at each side (see Figure S3a). The average distance between the H atoms of ZIF-8 and the F atom of the [PF₆]^- is computed to be 2.52 Å. While for the [C₄mim]⁺, two energy barriers were found when [C₄mim]⁺ moved from left to the right of the pristine ZIF-8 aperture. The first one, 14.60 kcal·mol^-1, is corresponding to passing of alkyl chain, in which the average distance between alkyl chain and ZIF-8 aperture is 2.61 Å. The second one, 39.87 kcal mol^-1, is corresponding to the passing of imidazole ring, in which the average distance between imidazole ring and ZIF-8 aperture is only 1.66 Å (Figure S3b), hence, such small distances result in large steric hindrances or strong repulsion interactions.

Afterwards, the frontier orbitals, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) were plotted in Figure 4. In general, the results indicate that there is no significant orbital interactions between the [C₄mim]⁺/[PF₆]^- and the pristine ZIF-8 aperture within the frontier orbital scheme. For example, both LUMOs and HOMOs of [C₄mim]⁺-ZIF-8 and [PF₆]^--ZIF-8 are almost the same compare to that of the free pristine ZIF-8 aperture, in other words, the frontier orbitals are mainly consisted by the contributions from ZIF-8 aperture. The HOMO-LUMO gaps of [C₄mim]⁺-ZIF-8 and [PF₆]^--ZIF-8 are also identical to that of the free pristine ZIF-8 aperture, e.g. 0.64 eV versus 0.65 eV. Moreover, the natural population analysis (NPA) was performed and the natural charges as summarized in Table S1. The values show that certain amount of charges (ca. 0.08 e) have been transferred between [C₄mim]⁺ and [PF₆]^- and the pristine ZIF-8 apertures.

To have a deep understanding of the interactions between [C₄mim]⁺/[PF₆]^- and the pristine ZIF-8 aperture, the GKS-EDA energy decomposition analysis has been performed based on the [PF₆]^--ZIF-8(3.4 Å) and [C₄mim]⁺-ZIF-8(3.4 Å) structures and the results are plotted in Figure 5. Generally, the interaction energies are decomposed according to following equations:

$$\Delta E^{total}=\Delta E^{ex}+\Delta E^{rep}+\Delta E^{corr}+\Delta E^{ele}+\Delta E^{pol}+\Delta E^{disp},$$

where $\Delta E^{ex}$, $\Delta E^{rep}$, $\Delta E^{corr}$, $\Delta E^{ele}$, $\Delta E^{pol}$, and $\Delta E^{disp}$ represent exchange, repulsion, correlation, electrostatic, polarization, and dispersion components, respectively. As shown in Figure 5, the interaction energies are dominant by three terms, including the repulsion, exchange and electrostatic energies, of which the repulsions are the main reasons for the high energy barriers shown in the Figure 3. The rest components are relatively small (e.g. less than 28 kcal mol^-1 in absolute values, and with a total ratio being less than 6.6%). Here, we take [C₄mim]⁺-ZIF-8(3.4 Å) as an example, and discuss those three terms individually: 1) The repulsion component. This term is responsible for steric repulsion, and it consists of the destabilizing interactions between occupied orbitals of the fragments. Usually, this term is repulsive (with a positive computed value). Here, a value of 304.27 kcal mol^-1 was obtained, which can be attributed to large steric repulsion between imidazole ring of [C₄mim]⁺ and the pristine ZIF-8 aperture. As discussed in the PES scan section, the pristine ZIF-8 aperture has a pore size of only 3.4 Å, hence, leaving the imidazole ring few spaces to pass through; 2) The exchange component. This term essentially is related to electrons with the same spin exchange their positions in degenerate orbitals, to increase stability of electronic structure states. Here, we found an value of -162.2 kcal mol^-1, in the case of [C₄mim]⁺-ZIF-8; 3) The electrostatic component. This term is the energy between the unperturbed charge distributions of the prepared fragments, which is usually attractive. As shown in Figure 5, the computed electrostatic interaction is -50 kcal mol^-1, which is much small compare to the repulsion and exchange interactions. This finding is somehow consistent with the NPA charge analysis, in which the pristine ZIF-8 is slightly charged (ca. 0.08 e) via the charge transfer from [C₄mim]⁺.

Our previous MD simulations showed that the pristine ZIF-8 aperture could be distorted because of the thermal oscillations³². When the simulations were performed at a temperature of 300 K, an average of 6.8 Å movements was obtained for the atoms defined the size and shape of pores, which are highlighted in Figure 1a. Following that study, here, we computed the PES scan of [C₄mim]⁺ and [PF₆]^- passing through the ZIF-8 aperture with the pore size of 4.1 Å, 4.2 Å, 4.7 Å, 6.9 Å, respectively, (the pore structures are depicted in Figure 1b ~ Figure 1e), and the results are summarized in Figure 6. Generally, the results show that the [PF₆]^- is able to freely pass through these pores with energies barriers under zero. However, [C₄mim]⁺ can only pass through the pore with a diameter of 6.9 Å. Together with our previous room temperature MD simulations, we conclude that a higher temperature might be needed to obtain larger swing effect and to encapsulate [C₄mim][PF₆] into the ZIF-8 SOD cage. These findings are rather qualitatively consistent with a reported experiment study, in which the authors employed a two-step adsorption/infiltration method to incorporate [C₄mim][PF₆] into ZIF-8⁴³. In that work, [C₄mim][PF₆] were firstly adsorbed on the outer-surface of ZIF-8, then through heat treatment (e.g. 105 ℃), [C₄mim][PF₆] molecules infiltrated into the SOD cage. Afterwards, the temperature was down to the room temperature, and then the [C₄mim][PF₆] encapsulated ZIF-8 composite materials were obtained.

Lastly, to study how many pairs of [C₄mim][PF₆] could be stable inside the ZIF-8 SOD cage, and to examine their impact of contents on the structures of the ZIF-8 apertures, the structural optimizations were performed by adding one, two, and three pairs of [PF₆][C₄mim] in the pristine ZIF-8 SOD cage. As shown in Figure 7a, it is shown that the interaction energies between [C₄mim][PF₆] and ZIF-8 was strongest when two pairs [C₄mim][PF₆] were added, with a computed value of -44.81 kcal·mol^-1, while the interactions energies of one and three pairs were computed to be -35.69 kcal·mol^-1 and -40.92 kcal mol^-1. As such, we conclude that most of the ZIF-8 SOD cage could accommodate two pairs of [C₄mim][PF₆], and some of them are even able to accommodate three pairs. Overall, a value slightly larger than 2 would be obtained for the pairs of [C₄mim][PF₆] per SOD cage. These finding are comparable to the experimental results obtained by Ban et al.¹⁵, in which average 1.4 pairs of [C₄mim][TF₂N] have been identified per single ZIF-8 SOD cage. The smaller value of 1.4 versus 2.0 could be attributed to the fact that the anion [TF₂N]^- is relatively larger than [PF₆]^- in the space size. Compared to the experimental values⁴⁴, we found that the volume of ZIF-8 SOD cage has been increased when [C₄mim][PF₆] was encapsulated, of which the smallest value was obtained (0.9%) for the case with two pairs. Moreover, we also observed certain confinement effects from the results shown in Figure 7c, e.g. the structure of one pair of [C₄mim][PF₆] is very similar compared to the free pair (e.g. gas phase calculations), while the two and three pairs show structures closer to the condense phase⁴⁵.

4. Conclusions

In summary, the DFT calculations and several electronic structure analysis have been performed to study the diffusion behavior of the ILs, [C₄mim][PF₆], through the different aperture configurations of ZIF-8, and their stability inside the ZIF-8 cage. The results indicate that the original aperture configuration (with a 3.4 Å pore size) eventually prohibit the diffusion of [C₄mim][PF₆] into the SOD cage of ZIF-8, as a minimum energy barrier of 39.87 kcal mol^-1 has been identified, which is mainly due to imidazole ring of the [C₄mim]⁺. The energy decomposition analysis based on the GKS-EDA method revealed that the large repulsion component are the main reason for the high energy barriers when [C₄mim]⁺ and [PF₆]^- passing through the pristine ZIF-8 aperture. Nevertheless, we found that the diffusion properties could be largely enhanced by modified the ZIF-8 apertures, e.g. the pore size, and the it is proved that this could be achieved via thermal contributions (e.g. employing a higher temperature during the synthesis procedure). Moreover, we found that two pairs of [C₄mim][PF₆] are the stable state to accommodate inside the ZIF-8 cage, according to interaction energies and volume changes. Certain confinement effects were obtained as well, in which the structure of one pair of [C₄mim][PF₆] is similar compared to the free pair, while the two and three pairs show structures closer to the condense phase.