Theoretical investigation of CO₂ capture in the MIL-88 series: effects of organic linker modification

Abstract

CO₂ capture is a crucial strategy to mitigate global warming and protect a sustainable environment. Metal–organic frameworks with large surface area, high flexibility, and reversible adsorption and desorption of gases are good candidates for CO₂ capture. Among the synthesized metal–organic frameworks, the MIL-88 series has attracted our attention due to their excellent stability. However, a systematic investigation of CO₂ capture in the MIL-88 series with different organic linkers is not available. Therefore, we clarified the topic via two sections: (1) elucidate physical insights into the CO₂@MIL-88 interaction by van der Waals-dispersion correction density functional theory calculations, and (2) quantitatively study the CO₂ capture capacity by grand canonical Monte Carlo simulations. We found that the 1π_g, 2σ_u/1π_u, and 2σ_g peaks of the CO₂ molecule and the C and O p orbitals of the MIL-88 series are the predominant contributors to the CO₂@MIL-88 interaction. The MIL-88 series, i.e., MIL-88A, B, C, and D, has the same metal oxide node but different organic linkers: fumarate (MIL-88A), 1,4-benzene-dicarboxylate (MIL-88B), 2,6-naphthalene-dicarboxylate (MIL-88C), and 4,4′-biphenyl-dicarboxylate (MIL-88D). The results exhibited that fumarate should be the best replacement for both the gravimetric and volumetric CO₂ uptakes. We also pointed out a proportional relationship between the capture capacities with electronic properties and other parameters.

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1 Introduction

The energy consumption activities of industries, vehicles, and daily demands intensively depend on fossil fuels and natural gases. The by-products of such processes contain harmful emissions, especially CO₂, a greenhouse gas related to the global warming phenomenon.¹ Also, there is a huge amount of CO₂ emitted by agricultural activities and forest exploitation and reclamation.² For sustainable environment and energy usage, CO₂ capture and reduction are indispensable. Until now, post-combustion (mainly used in coal-gasification plants), pre-combustion, and oxyfuel combustion (primarily used in gas and coal-fired plants) have been crucial technologies for carbon capture.³ However, these technologies face many challenges such as CO₂ separation and purification from flue gas streams and gas mixtures.⁴ The solution to these problems is searching for solid materials that meet the requirements,⁵ i.e., high adsorption capacity, high selectivity, fast adsorption and desorption, and durability for CO₂ capture based on adsorption effects.^6–8 Solid sorbents that have been used to adsorb CO₂ include rigid classical adsorbents (activated carbon and zeolites) and novel porous adsorbents (covalent organic frameworks, zeolitic imidazolate frameworks, and metal–organic frameworks). Nowadays, metal–organic frameworks (MOFs)^9,10 have become the most popular CO₂ capture material due to their many outstanding features: ultra-large surface area, high porosity, and remarkable chemical, thermal, and mechanical stabilities.^11,12

So far, MOF-200 and MOF-210 recorded the highest capacity for the gravimetric CO₂ uptake of 2400 mg g⁻¹ (74.2 wt%) and 2396 mg g⁻¹ (73.9 wt%) at 298 K and 50 bar.¹³ At the same condition of the temperature and pressure, MOF-117 was the best sorbent among the considered MOFs with the gravimetric and volumetric CO₂ uptakes of 33.5 mmol g⁻¹ and 320 cm³ (STP) per cm³, respectively.¹⁴ Besides, MIL-100(Cr) and MIL-101c(Cr) also achieved 18 mmol g⁻¹ and 40 mmol g⁻¹ (280 cm³ (STP) per cm³ and 390 cm³ (STP) per cm³ for volumetric loading) at 304 K and 50 bar; MIL-47(V) with 11 mmol g⁻¹ and 250 cm³ (STP) per cm³ at 302 K, 20 bar, IRMOF-1 with 21.7 mmol g⁻¹ and 290 cm³ (STP) per cm³ at 298 K, 35 bar.¹⁵ Other MOFs were also investigated for CO₂ capture as NU-100 (69.8 wt%, at 298 K and 40 bar), Mg-MOF-74 (68.9 wt%, at 278 K and 36 bar), MOF-5 (58 wt%, at 273 K and 10 bar), and HKUST-1 (19.8 wt%, 298 K and 1 bar).¹⁶

Among the successfully synthesized MOFs, the MIL-88 series have attracted our attention due to their exceptionally high flexibility and stability that MIL-88 series could swell upon immersion in various liquids with reversible variations in unit cell volume from 85% (MIL-88A) to 240% (MIL-88D) depending on the nature and length of the organic spacer without breaking the bonds, and fully retains its open framework topology.¹⁷ Therefore, the MIL-88 series became a good candidate for CO₂ capture. In reality, MIL-88A(Fe) has been studied for catalysis,^18,19 NO adsorption,²⁰ and drug transportation.²¹ Besides, MIL-88s (s = A, B, C, D) were investigated for hydrogen storage.^22–24 In 2016, the experiment measured CO₂ sorption capacity of MIL-88A as a function of temperatures, and the value achieved was 4.95 mmol g⁻¹ at 30 °C and the pressure of 1 bar.²⁵ MIL-88 family has been synthesized by experiment,^26,27 where the structure of MIL-88A, B, C, and D has the same metal site but different organic linkers, i.e., fumarate, 1,4-benzene-dicarboxylate, 2,6-naphthalene-dicarboxylate, and 4,4′-biphenyl-dicarboxylate, respectively. However, no research is available to systematically investigate the CO₂ capture capacity in the MIL-88 series and the physical meanings of the CO₂-MOF interaction under the influences of replacing organic linkers. Therefore, we elucidated these topics in the present work using the van der Waals dispersive correction density functional theory calculations for the earlier via electronic structure properties and the grand canonical Monte Carlo simulations for the later via adsorption isotherms, and isosteric heat of adsorption for the pressures below 100 bar. Elucidating the effects of defects and structural flexibility is out of the scope of the current work.

2 Computational techniques

2.1. Density functional theory calculations

We used the van der Waals dispersive correction density functional theory (vdW-DF) calculations with the revPBE-based exchange–correlation energy^28,29 via the Vienna Ab initio Simulation Package (VASP).^30,31 The projector augmented-wave technique was used to describe the electron–ion interactions and a cut-off energy of 700 eV for the plane-wave basis set.^32,33 The first Brillouin zone was sampled with a special k-point mesh of 3 × 3 × 3 for MIL-88A and B, 3 × 3 × 2 for MIL-88C and D, centred at the Gamma point following the Monkhorst–Pack method. The Methfessel–Paxton smearing of order 1 with the smearing width of 0.1 eV was used to support the convergence speed of geometry relaxation and the electronic density of states (DOS).³⁴ Besides, the tetrahedron method with the Bloch corrections has been selected for the total energy calculations.³⁵ Because the magnetic moments of the iron atom of the MIL-88 series are inconsistent with the spin-polarized calculations due to the structural flexibility, we, therefore, performed the non-spin polarized scheme in the present study. The structure and unit cell of the MIL-88 series are shown in Fig. 1. MIL-88A, B, C, and D share the same metal oxide node (Fe₃O) but different ligands, i.e., fumarate or FMA (OOC–C₂H₂–COO), 1,4-benzene-dicarboxylate or BDC (OOC–C₆H₄–COO), 2,6-naphthalene-dicarboxylate or NDC (OOC–C₁₀H₆–COO), and 4,4′-biphenyl-dicarboxylate or BPDC (OOC–C₁₂H₈–COO), respectively.

Fig. 1 The structure of MIL-88 series. The dotted frame indicates the unit cell. Fe (blue), O (red), and C (brown), and H (light-grey).

Before exploring the CO₂ adsorption configurations, we have to fully optimize the atomic positions and the unit cell volume of the MIL-88 series, which followed the procedure of our previous publications.^22,23 We then carried out the geometric optimization to search for the CO₂ adsorption configurations and favorable sites. The adsorption energy of the CO₂ molecule in the MIL-88 series was calculated by

ΔE_ads = E_MIL+CO2 − (E_MIL + E_CO2), (1)

where E_MIL+CO2, E_MIL, and E_CO2 are the total energy of the [MIL-88 + CO₂] system, the pristine MIL-88, and the isolated CO₂ molecule, respectively. Besides, we calculated the charge density difference of the [MIL-88 + CO₂] system via the expression

Δρ = ρ_MIL+CO2 − (ρ_MIL + ρ_CO2), (2)

here ρ_MIL+CO2, ρ_MIL, and ρ_CO2 are the charge density of the [MIL-88 + CO₂] system, the pristine MIL-88, and the isolated CO₂ molecule, respectively.

2.2. Grand canonical Monte Carlo simulations

After optimizing the volume and structure of the MIL-88 series, we obtained the charge distribution in the unit cell. We then used the density-derived electrostatic and chemical charge (DDEC6) method^36–39 to calculate the partial point charge for the atoms of the MIL-88 series. This charge assignment was used to parameterize the force fields as follows.

The interaction between the CO₂ molecule and the MIL-88 series was modelled by

U(r_ij) = U_vdW(r_ij) + U_elec(r_ij), (3)

where r_ij is the distance between the i^th and j^th atoms. The above interaction consists of two parts:

(i) The van der Waals (vdW) interaction was described by the Lennard-Jones (LJ) potential,

where, the parameters ε_ij and σ_ij are the Lennard-Jones (LJ) potential well depth and diameter, respectively. These parameters were determined by the Lorentz–Berthelot mixing rule for a pair of unlike atoms:here, σ_i and ε_i (i = the Fe, H, C, O atoms of MIL-88A, B, C, and D) were taken from the generic force fields for MOFs.⁴⁰ Notice that the cutoff radius of 22 Å has been checked for the convergence of the vdW interaction.

(ii) The electrostatic interaction with a cutoff radius of 13 Å,

Here, ε₀ is the dielectric constant of the vacuum, and q_i is the partial charge of the i^th atom, which was obtained by the DDEC6 method.^36–39 The atomic charge of the atoms in the MIL-88 series was listed in Table 1.²³ Where, Fe, H, C1, C2, C3, C4, C5, O1, and O2 were also displayed in Fig. 2. The force field parameters for the CO₂ molecule were described as a rigid three-site molecule using the EPM2 model (elementary physical model).^41,42

Table 1 The Lennard-Jones parameters, the atomic charges of the CO₂ molecule and the MIL-88 series^a

Ions	ε/kB (K)	σ (Å)	Partial charges (e^−)
a μ3-O: the oxygen atom at the center of the trimer of the MIL-88 series. The A, B, C, and D letters indicate MIL-88A, MIL-88B, MIL-88C, and MIL-88D, respectively.
Fe_MIL	6.54	2.59	1.222 (A), 1.212 (B), 1.208 (C), 1.306 (D)
H_MIL	7.65	2.85	0.118 (A), 0.099 (B), 0.096 (C, D)
C1_MIL	47.86	3.47	0.734 (A), 0.689 (B), 0.700 (C), 0.718 (D)
C2_MIL			−0.178 (A), −0.095 (B), −0.071 (C), −0.135 (D)
C3_MIL			−0.059 (B), −0.062 (C), −0.026 (D)
C4_MIL			−0.114 (C), −0.139 (D)
C5_MIL			0.058 (C), 0.073 (D)
O1_MIL	48.16	3.03	−0.570 (A, B), −0.574 (C), −0.603 (D)
O2_MIL (μ3-O)			−0.875 (A), −0.844 (B), −0.849 (C), −0.939 (D)
C_CO2 (ref. 41 and 42)	28.129	2.757	0.6512
O_CO2 (ref. 41 and 42)	80.507	3.033	−0.3256

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Fig. 2 The structure of MIL-88 series. Fe (blue), O (red), and C (brown), H (light-grey).

With the obtained force fields, we carried out the GCMC simulations using the RASPA code⁴⁰ to calculate the CO₂ adsorption isotherms in the MIL-88 series with μVT ensembles (i.e., fixed the temperature, volume, and chemical potential) for various pressures up to 60 bar and 298 K (room temperature). In the GCMC simulation process, the MIL-88 series was kept fixed while the CO₂ molecule could move by inserting, translating, rotating, and deleting operations. We obtained the total (n_tot) and excess (n_exc) uptakes of CO₂, satisfying the relationship

n_exc = n_tot − V_gρ_g. (7)

Here, V_g and ρ_g are the pore volume of the MIL-88 and the molar density of the bulk gas phase, respectively.

To evaluate the strength of the adsorbate–adsorbent interaction within the GCMC simulations, the total heat of adsorption (or the isosteric heat of adsorption) was also calculated from the average energies of the [MIL-88 + CO₂] system:

Q_st = [〈U_gh〉 − 〈U_h〉 − 〈U_g〉] − RT. (8)

where 〈U_gh〉, 〈U_h〉, and 〈U_g〉 are the average potential energy of the guest–host (CO₂ + MIL-88), the host (MIL-88), and the gas (CO₂), respectively.

3 Results and discussion

3.1. Adsorption configurations and energies

After optimizing the atomic positions of MIL-88s using the vdW-DF calculations, we loaded a CO₂ molecule into the MIL-88s structure to create the CO₂@MIL-88s systems, then continued fully relaxing their atomic positions. With many possibilities of the CO₂ adsorption sites on the Fe metal, the organic linker, and iron–oxygen hollow sites, see Fig. 3, we obtained the stable configurations of the CO₂ molecule and the corresponding adsorption energies. With three stable adsorption sites and two configurations (end-on and side-on) for each MOF, see Fig. 4 and Table 2, we found that there is a similarity among MIL-88A, B, and D that the side-on configuration is more stable than the end-on configuration on the hollow and linker, while the reverse tendency holds for the CO₂ molecule on the Fe metal. MIL-88C does not adsorb the CO₂ molecule on the linker. Even though the most favourable adsorption configuration of CO₂ is end-on on the Fe metal for MIL-88A, B, and C, while it is side-on on the linker for MIL-88D. We also observed that the CO₂ molecule adsorbed in the pore position among the metal site and the iron–oxygen hollow (see Fig. S2 in the ESI†). Therefore, the CO₂ molecule belongs to both the metal end-on and hollow end-on or metal side-on and hollow side-on configurations in MIL-88C. The bond distance from the CO₂ molecule to the nearest atoms of the MIL-88s is about 3 Å, Table 2. Besides, we found that the average adsorption strength of CO₂ at the favourable sites is in the order of MIL-88A (−37.52 kJ mol⁻¹) > MIL-88D (−19.33 kJ mol⁻¹) > MIL-88B (−14.25 kJ mol⁻¹) > MIL-88C (−2.9 kJ mol⁻¹). Notably, the adsorption of the CO₂ molecule is strongest and weakest on MIL-88A and C, respectively. The number of the favourable adsorption sites of MIL-88C is fewer than that of the others because its organic linker does not offer negative adsorption energy. A more detailed analysis revealed that the adsorption strength is MIL-88A (FMA linker) > MIL-88B (BDC linker) > MIL-88D (BPDC linker) > MIL-88C (NDC linker) for the metal, but it is MIL-88A > MIL-88D > MIL-88B > MIL-88C for the linker and hollow sites. The latter has the same tendency as the average adsorption energy. Also, the adsorption energy is significantly large on the linkers compared to the metal and hollow sites of MIL-88A, B, and D, which implies a significant role of the linkers.

Fig. 3 The possible adsorption regions in a unit cell of MIL-88 series. Fe (blue), O (red), C (brown), and H (light-grey).

Fig. 4 The favorable CO₂ adsorption configurations in MIL-88A. Similarly, the CO₂ adsorption configuration in MIL-88B, C, and D was presented in the ESI (Fig. S1–S3).†

Table 2 Adsorption energy ΔE_ads (kJ mol⁻¹), the distance between the nearest atoms of CO₂ and MOF, d_MIL–CO2 (Å)

Site	Configuration	MIL-88A		MIL-88B		MIL-88C		MIL-88D
		ΔEads	dMIL–CO2	ΔEads	dMIL–CO2	ΔEads	dMIL–CO2	ΔEads	dMIL–CO2
a These adsorption configurations are identical.b These adsorption configurations are identical.
Metal	Side-on	−30.65	3.39	−0.46	3.37	−0.870^a	3.36	−12.73	3.42
	End-on	−57.88	2.42	−37.23	2.38	−4.962^b	2.33	−24.96	2.44
Hollow	Side-on	−28.59	3.16, 3.11	−6.87	3.08, 3.09	−0.870^a	3.58, 3.36	−20.84	3.17, 3.19
	End-on	−20.62	2.97, 3.06	−6.26	3.49, 3.67	−4.962^b	3.22, 3.17	−11.01	2.99, 3.01
Linker	Side-on	−45.16	3.48, 3.52	−15.55	3.57, 3.58	—	—	−26.88	3.39, 3.45
	End-on	−42.23	3.03, 3.07	−5.36	3.44, 3.57	—	—	−19.57	3.27, 3.27
Average adsorption energy		−37.52		−11.96		−2.916		−19.33

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3.2. Electronic properties

The nature of the CO₂@MIL-88s interaction can be understood via the analysis of point charges, which were calculated by the Bader partition technique^43,44 and then excluded the neutral charge value of the corresponding atoms.^45,46 Table 3 shows that the C and O atoms of the CO₂ molecule always donate and accumulate the negative charge for all cases, respectively. However, the CO₂ molecule can gain (in most cases) or lose the charge. For MIL-88s, the Fe and C atoms always lose, while the O atoms always gain the negative charge. The charge of the H atoms of MIL-88s can vary depending on case by case, resulting in the total charge of MIL-88s, which can compensate for the charge losses or gains of the CO₂ molecule. Based on the obtained charge exchange of the CO₂ molecule and the MIL-88s, we found that the maximum value of the charge exchange of 11% e⁻ was achieved for the CO₂ adsorption with the side-on configuration at the Fe metal site in the MIL-88D. Therefore, the nature of the CO₂@MIL-88s interaction is the weak charge exchange.

Table 3 The Bader charge transfer (e⁻) between the CO₂ molecule and the MIL-88 series. Positive and negative values implied the negative charge (e⁻) accumulation and donation, respectively

Site/configuration		Metal		Hollow		Linker
		Side-on	End-on	Side-on	End-on	Side-on	End-on
CO2@MIL-88A	1C	−1.949	−2.071	−1.995	−2.013	−2.074	−2.057
	2O	1.954	2.097	2.059	2.065	2.100	2.068
	CO2	0.006	0.025	0.065	0.052	0.026	0.011
	12H	0.132	0.068	−0.013	0.073	0.146	0.129
	24C	−19.016	−18.923	−18.892	−18.996	−19.069	−19.029
	26O	27.221	27.239	27.360	27.269	27.340	27.315
	6Fe	−8.343	−8.409	−8.382	−8.398	−8.443	−8.426
	MIL-88A	−0.006	−0.025	−0.065	−0.052	−0.026	−0.011
CO2@MIL-88B	1C	−2.072	−2.064	−1.966	−1.983	−2.055	−2.070
	2O	2.080	2.053	1.973	1.991	2.085	2.098
	CO2	0.008	−0.011	0.007	0.008	0.030	0.028
	24H	−0.186	0.093	−0.101	−0.110	−0.172	−0.239
	48C	−18.771	−18.945	−18.910	−18.894	−18.727	−18.785
	26O	27.356	27.296	27.424	27.369	27.300	27.431
	6Fe	−8.407	−8.434	−8.420	−8.374	−8.431	−8.436
	MIL-88B	−0.008	0.011	−0.007	−0.008	−0.030	−0.028
CO2@MIL-88C	1C	−2.021			−2.090
	2O	2.039			2.069
	CO2	0.018			−0.021
	36H	0.316			0.263
	72C	−19.275			−19.286
	26O	27.166			27.288
	6Fe	−8.225			−8.245
	MIL-88C	−0.018			0.021
CO2@MIL-88D	1C	−1.935	−2.029	−1.943	−1.999	−1.974	−2.050
	2O	2.045	2.014	1.951	2.006	1.994	2.076
	CO2	0.110	−0.016	0.008	0.007	0.020	0.026
	48H	0.256	0.249	0.207	0.228	0.117	0.220
	85C	−19.288	−19.248	−19.331	−19.385	−19.160	−19.248
	26O	27.340	27.427	27.556	27.549	27.440	27.416
	6Fe	−8.418	−8.413	−8.440	−8.399	−8.417	−8.414
	MIL-88D	−0.110	0.016	−0.008	−0.007	−0.020	−0.026

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The charge density difference in Fig. 5 shows that the charge accumulation and donation clouds of the CO₂ molecule have a relationship with that of the Fe and O atoms of the MIL-88 series, while the C and H atoms of the MIL-88 series exhibit an ignorable role in the interaction with the CO₂ molecule as no significant charge clouds have been found on these atoms. Besides, we explored the nature of the CO₂@MIL-88s interaction at the electronic orbital level through the analysis of the orbital-projected density of states (PDOS), which was presented in Fig. 6. This figure revealed that the 1π_g, 2σ_u/1π_u, and 2σ_g peaks of the CO₂ molecule locate near −4.5, −8.0, and −9.5 eV, respectively.⁴⁷ The p_x, p_y, p_z, and s orbitals of the MIL-88 series distribute below −1.0 eV, while the d orbitals of the MIL-88s position around the Fermi level. Generally, the interaction between adsorbate and adsorbent stems from the attraction between occupied states of the isolated adsorbate with unoccupied states of the isolated adsorbent and vice versa. When the combined system is formed, the electronic states of the adsorbate and the adsorbent become completely overlapping to make the peak resonance. Therefore, the overlapping between the electronic states of the adsorbate and adsorbent becomes an indication of their interaction. We found in Fig. 6 that the peak resonance forms between the DOS peaks of the CO₂ molecule with mainly the C and O p_x, p_y, and p_z orbitals and weakly the Fe s and d_z² orbitals of the MIL-88 series for the energy below −1.0 eV. This observation and the charge density difference implied that the C and O p_x, p_y, and p_z orbitals of the organic linkers should be the dominant factors contributing to the CO₂@MIL-88s interaction.

Fig. 5 The charge density difference of the CO₂@MIL-88D system with the different adsorption configurations and sites. Negative charge accumulation (yellow) and donation (cyan). Similar features of the charge clouds have been shown for MIL-88A, B, and C in Fig. S4–S6 in the ESI.† Isosurface values (e⁻ bohr⁻³) for the charge density difference of the MIL-88D@CO₂ system at different sites are listed in Table S1.†

Fig. 6 The orbital-projected density of states of the CO₂@MIL-88 systems in the most favourable adsorption state: (a) end-on at the Fe metal of MIL-88A, (b) end-on at the Fe metal of MIL-88B, (c) end-on at the Fe metal of MIL-88C, and (d) side-on at the organic linker of MIL-88D. The Fermi level was set to 0 eV.

3.3. The CO₂ capture capacity of MIL-88 series

Using the force fields presented in the Computational techniques section, we calculated the CO₂ capture gravimetric and volumetric capacities of the MIL-88 series via the isotherms as a function of pressures at the temperature of 298 K. Fig. 7a displays the obtained isotherms in gravimetric uptake, i.e., the adsorbed amount per unit mass of adsorbent (wt%), and Fig. 7b is in volumetric uptakes, i.e., the adsorbed amount per unit volume (cm³ (STP) per cm³). Besides, the number of CO₂ molecules loading per unit cell of MIL-88A, MIL-88B, MIL-88C, and MIL-88D were also displayed in Fig. S8 in ESI.† We found that the total and excess isotherms rapidly increase at the low-pressure range and gradually enhance with the increase in pressure. Afterward, the excess isotherms approach their maximum value^48,49 and slowly decrease after passing by the maximum while the total isotherms continue developing up to 60 bar. Table 4 lists the maximal CO₂ uptakes for gravimetric and volumetric capacities, where maximum excess loading was achieved at 25 bar for MIL-88A and B, 20 bar for MIL-88C, and 30 bar for MIL-88D. The highest value of total uptake was achieved at 60 bar for MIL-88A, B, and D, while it reached the earlier pressure value, about 20 bar for MIL-88C because the isotherms become flat for pressures greater than 20 bar. Table 4 shows that both excess and total isotherms are in the order MIL-88A (FMA linker) > MIL-88D (BPDC linker) > MIL-88B (BDC linker) > MIL-88C (NDC linker) for the gravimetric CO₂ uptake (proportional to the adsorption energy tendency at the linker and hollow sites) and MIL-88A > MIL-88B > MIL-88D > MIL-88C (proportional to the adsorption energy tendency at the metal site) for the volumetric uptake. This finding implies that MIL-88A and MIL-88C would be the best and worst candidates for CO₂ capture, respectively. Also, the tendency of the gravimetric uptakes is in good agreement with that of the average adsorption energy obtained above, i.e., the stronger the adsorption energy, the higher the capture capacity.

Fig. 7 The excess (dashed line) and total (solid line) CO₂ adsorption isotherms of MIL-88A, B, C, and D at 298 K: (a) gravimetric capacity and (b) volumetric capacity.

Table 4 The maximum excess and absolute capture capacity of CO₂ in MIL-88A, B, C, and D at 298 K

Adsorbent	mmol g^−1		wt%		cm^3 (STP) per cm^3
	Total	Excess	Total	Excess	Total	Excess
MIL-88A	12.11	10.90	53.26	47.98	292.65	263.61
MIL-88B	9.61	8.51	42.29	37.45	234.44	207.60
MIL-88C	4.00	3.64	17.58	16.04	115.11	104.98
MIL-88D	11.74	10.18	51.66	44.79	228.35	197.97

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Next, we calculated the isosteric heat of the CO₂ adsorption, Q_st, in MIL-88s, as shown in Fig. 8. The average value of the curves exhibited Q_st in the order: MIL-88A (34.9 kJ mol⁻¹) > MIL-88B (32.5 kJ mol⁻¹) > MIL-88D (32.1 kJ mol⁻¹) > MIL-88C (31.8 kJ mol⁻¹). This tendency is consistent with the volumetric uptakes and the adsorption energy at the metal site, as mentioned above. Moreover, the value of Q_st represents the CO₂@MIL-88s interaction. The obtained values of Q_st are rather high compared to those of many other MOFs.⁵⁰

Fig. 8 The isosteric heat of the CO₂ adsorption in MIL-88 series at the low-pressure range and 298 K.

To elucidate the effect of moisture on the CO₂ adsorption capacity in the MIL-88 series, we calculated both gravimetric and volumetric amounts of CO₂ adsorption in the presence of H₂O. The results were described in Fig. S7 and Table S2 in ESI.† Compared to those without H₂O, the CO₂ adsorption capacities in MIL-88s insignificantly decreased in the presence of H₂O. The decrease was about 4–8% for the absolute uptakes at 40 bar and 2–6% for the maximum excess.

It is necessary to consider the influences of macroscopic parameters on the CO₂ capture capacity. Fig. 9 presents the dependence of the gravimetric uptakes of the CO₂ capture on the specific surface area and pore volume of the MIL-88 series. We found a simple relationship, i.e., adsorption capacity proportionally depends on the specific surface area (Fig. 9a) and the pore volume (Fig. 9b). Here, the specific surface area and pore volume data of the MIL-88 series were calculated theoretically by grand canonical Monte Carlo simulations with nitrogen gas utilized to obtain them.

Fig. 9 The relationship between the CO₂ uptakes with (a) specific surface area and (b) pore volume.

Substituting the organic linkers caused the effects on adsorption energy and uptakes, which were perhaps due to the following reasons: (1) geometric modification, i.e., the organic linkers led to the different SSA and pore volume of MIL-88s. The larger SSA and pore volume lead to higher CO₂ capacity. (2) Electronic property modification via the overlapping of wavefunctions²² between CO₂ and the organic linkers, even for the metal and hollow adsorption sites, see Fig. S9 in ESI.† We found that the wavefunctions of CO₂ and that of the C and O atoms of the organic linkers can overlap. The same or opposite direction oscillations of the wavefunctions cause constructive and destructive interferences, respectively. We can see that the wavefunction interaction of CO₂ with the organic linker shows more clearly for MIL-88A and D than for MIL-88B and C, which somehow shows a relationship to the obtained CO₂ uptakes.

Fig. 10 shows the excess gravimetric capacity of CO₂ versus temperature at a low pressure of 1 bar. The uptake decreases as the temperature increases, following the straight line for MIL-88C; however, the curves for MIL-88A, B, and D. The isotherms approach a convergent value as the temperature is high enough from the room temperature. Particularly, MIL-88A achieved the excess uptake of 4.00 mmol g⁻¹ at 303 K, which is in good agreement with the experimental value of 4.95 mmol g⁻¹ at 30 °C (303 K).²⁵ Moreover, the shape of the CO₂ adsorption curve on MIL-88A is consistent with that of the experiment in the temperature range from 293 to 333 K.²⁵

Fig. 10 The excess uptakes versus temperatures of MIL-88 series at 1 bar. The experimental data were obtained from ref. 25.

4 Conclusions

This work investigated the CO₂@MIL-88s interaction and the CO₂ capture capacity in the MIL-88 series using the vdW-DF density functional theory calculations and grand canonical Monte Carlo simulations. We found a proportional relationship between the adsorption energy with the gravimetric uptake FMA linker (MIL-88A) > BPDC linker (MIL-88D) > BDC linker (MIL-88B) > NDC linker (MIL-88C), proportional to the adsorption strength of CO₂ at the linker and hollow sites and the isosteric heat of CO₂ adsorption with the volumetric uptake FMA linker (MIL-88A) > BDC linker (MIL-88B) > BPDC linker (MIL-88D) > NDC linker (MIL-88C), proportional to the adsorption strength of CO₂ at the metal site). We have to emphasize that the replacement of the organic linkers is the only difference in the geometric structure of MIL-88A, B, C, and D. Therefore, the substitution of the linkers also influences the adsorption strength of CO₂ not only at the organic linkers but also at the metal and hollow sites. The gravimetric and volumetric uptakes indicated that MIL-88A (with fumarate linker) should be the best candidate among the MIL-88 series for CO₂ capture. Furthermore, the physical insights have been elucidated that the contributions of the MIL-88 series to the interaction with CO₂ are as follows: the C and O p orbitals (dominant) and the Fe s and d_z² orbitals (minor). The H atoms of the MIL-88 series played an ignorable role in the CO₂@MIL-88 interaction.

Author contributions

Conceptualization (DNS, VC), formal analysis (NTXH, DNS), investigation (NTXH, DNS), resources (DNS, VC), supervision (DNS), validation (NTXH, VC, DNS), visualization (NTXH, OKL, TPD), writing of original draft (DNS), reviewing and editing (VC, DNS).

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number VL2022-20-01.

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Footnote

† Electronic supplementary information (ESI) available: Theoretical investigation of CO₂ capture in the MIL-88 series: effects of organic linker modification. See DOI: https://doi.org/10.1039/d3ra01588b

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