Analysis by synchrotron X-ray scattering of the kinetics of formation of an Fe-based metal-organic framework with high CO₂ adsorption

Porous metal-organic framework (MOF) materials¹ are relevant to a range of applications including gas adsorption,² carbon capture and storage,³ catalysis,⁴ separations,⁵ chemical sensing,⁶ and proton conductivity.⁷ However, there is a significant disparity between the number of MOFs (nearly 70 000 in the Cambridge Structural Database)⁸ and a fundamental understanding of the mechanism of formation during hydrothermal and solvothermal reactions that are commonly used for their synthesis. This leads to barriers and uncertainties in large-scale syntheses, which often restrict the exploration of their properties beyond the laboratory scale. Developing an in-depth understanding of the mechanisms of formation will greatly improve our ability to design and synthesize materials to scale and in high purity. Indeed, a complete understanding of how MOFs form is essential for their potential implementation into practical processes.

Studies on the fundamental energetics of synthesis for a limited number of MOFs have been reported using a range of techniques, including in situ light scattering,^9–12 wide angle X-ray scattering (WAXS),¹³ and extended X-ray adsorption fine structure (EXAFS),¹⁴ with energy-dispersive X-ray powder diffraction (EDXRPD) also being developed.^15–18 More recent studies have also employed the use of monochromatic X-rays, allowing the identification of phase and kinetic information directly from in situ measurements.^19–23 Many of these investigations into the kinetics of formation of MOFs have used relatively small ligand systems (e.g., those containing a single phenyl ring), which limits the scope of applicability. Here, we describe the high CO₂ adsorption in highly robust MOF, MFM-300(Fe), based upon the biphenyl-3,3′,5,5′-tetracarboxylate linker, combined with direct visualization of the binding location and dynamics for adsorbed CO₂ molecules within the pores via in situ synchrotron X-ray diffraction and FTIR microspectroscopy. We also report an investigation of the formation of MFM-300(Fe) via time-resolved monochromatic synchrotron X-ray powder diffraction. We employed the classical Avrami-Erofe’ev (AE)^24–26 model in the form modified by Khanna and Taylor²⁷ as used by Finney and Finke²⁸ [Eq. (1)],

where α is the extent of crystal growth, k is the rate constant, t is the reaction time, and n is the crystal growth exponent. We then included a modified version of the two-step kinetic Finke-Watzky (FW) model [Eq. (2)]^28–31 to deconvolute the AE model into two discrete crystallization steps,

where α is the extent of crystal growth, k₁ is the rate constant for average nucleation, k₂ is the rate constant for average autocatalytic growth, and t is the reaction time. This converted form of the FW model allows expression of different parts of the solid-state kinetic reaction to be deconvoluted to extract physical meaning to the processes of crystallization.²⁸ The success of a 1000-fold scale-up of MFM-300(Fe) enabled evaluation of its ability in dynamic breakthrough separations of CO₂ from gas mixtures.

We sought to investigate the scale-up of the MFM-300 series of materials^32–35 and chose the Fe analog³⁶ for its excellent adsorption capacity and selectivity of CO₂ and because of the high relative abundance and low cost of iron. MFM-300(Fe) is constructed by extended [FeO₄(OH)₂]_∞ chains bridged by biphenyl-3,3′,5,5′-tetracarboxylate linkers to afford square-shaped channels that run along the c-axis and are decorated with hydroxyl groups (μ₂-OH) that bridge Fe(iii) centers [Figs. 1(a)–1(c)]. MFM-300(Fe) shows a total adsorption capacity of CO₂ of 9.55 mmol g⁻¹ at 293 K and 20 bar, demonstrating a 30% capacity increase and a higher value of heat of adsorption Q_st (28.4–37.4 kJ mol⁻¹) compared to MFM-300(Al)³² [Figs. 1(d) and 1(e)]. In addition, MFM-300(Fe) shows the potential for CO₂/CH₄ and CO₂/N₂ separations calculated from single component isotherms using the ideal adsorption solution theory (IAST) method with selectivities of 1.87 and 21.6, respectively, at 293 K and 1.0 bar [Fig. 1(f)]. Furthermore, MFM-300(Fe) is capable of methane storage with a packing density (0.304 g cm⁻³) greater than that of MFM-300(In) (0.231 g cm⁻³) under ambient conditions.³⁷ This makes MFM-300(Fe) an excellent candidate for potential applications in CO₂ capture and CH₄ storage.

The binding domains for adsorbed CO₂ molecules in MFM-300(Fe) were refined using the Rietveld method, employing a Fourier difference map that fitted the high resolution powder X-ray diffraction (PXRD) data (Fig. S10) against that of the activated MOF sample (Fig. S9). MFM-300(Fe) undergoes a slight unit cell expansion [a = 15.1227(2) Å, c = 12.0769(2) Å, V = 2761.9(1) ų] on loading with CO₂, and we observe a total occupancy of 1.0 CO₂ molecule per μ₂-OH functionality within the pore, in good agreement with the isothermal uptake (1.25 CO₂ molecules/μ₂-OH at 293 K and 1.0 bar). Two CO₂ sites (I, II) were observed, and both were modeled as a rigid body. The overall fitting indices for the refinement were 6.78%, 3.14%, and 2.16 for R_wp, R_exp, and goodness of fit (GOF), respectively, indicating a satisfactory overall fit. The CO₂ molecule at site I is adjacent to the μ₂-OH functionality and is situated at a distance of 2.6918(1) Å (μ₂-O⋯^ICO₂) over two positions of disorder, pivoting on the closest oxygen in plane with the hydroxy-chain at an occupancy of 0.79(1) [Fig. 2(a)]. CO₂ molecules at site II (occupancy = 0.208) form an intermolecular ^IICO₂⋯^IICO₂ (3.015 Å) helical chain that propagates through end-on T-shaped interactions in both directions parallel to the c axis. This helical chain is anchored in place by CO₂ molecules at site I at a distance of 3.667 Å (^ICO₂⋯^IICO₂) [Fig. 2(a)], thus stabilizing an overall intermolecular packing of adsorbed CO₂ molecules in the pore.

The host-guest interactions have also been studied by in situ synchrotron FTIR microspectroscopy.³³ The bare framework has a ν(OH) stretching mode at 3647 cm⁻¹ (peak II) [Fig. 2(c)]. Upon CO₂ loading, a red-shift of this peak to 3637 cm⁻¹ (peak III) is observed, indicating a strong host-guest binding, which is coupled with the depletion of the band assigned to the –OH stretch in the bare MOF [Figs. 2(c) and S11]. The ν(OH) stretching vibrations in the isostructural analogs MFM-300(In) and MFM-300(Al) occur at 3657 cm⁻¹ and 3693 cm⁻¹, respectively,^33,38 suggesting that the –OH bonds within these two materials are stronger than that of MFM-300(Fe), thus making the –OH group in MFM-300(Fe) more acidic and accessible to guest species. Furthermore, the In- and Al-analogs do not experience the same magnitude of red-shift of the ν(OH) stretch even when the MOFs are fully saturated with CO₂. In addition, the combination bands of adsorbed CO₂ molecules at 3695 cm⁻¹ (peak I) and 3590 cm⁻¹ (peak IV) increase as a function of partial pressure of CO₂ as expected [Figs. 2(c) and S11].

The IR spectra [Fig. 2(c)] were analyzed using the four peaks I–IV at 3695 cm⁻¹, 3647 cm⁻¹, 3637 cm⁻¹, and 3590 cm⁻¹, respectively, and the peak areas were analyzed as a function of the level of CO₂ loading. A significant transformation in the ν(OH) stretching vibrations was identified, with the almost complete depletion of band II with increasing loadings of CO₂ (Fig. S11). This suggests that the majority of the –OH sites are occupied by 1.0 bar, in excellent agreement with the observed locations of CO₂ within MFM-300(Fe). The growth of the new peak (III) has a similar profile to the shape of the isotherm, again supporting the interaction of CO₂ being primarily with the –OH functionality. The CO₂ combination bands 2v₂ + v₃ and v₁ + v₃ at 3695 cm⁻¹ and 3590 cm⁻¹, respectively (peaks I and IV), also confirm interaction of CO₂ with the OH functionality (Fig. S11). The small amount of adsorbed CO₂ molecules at site II are likely responsible for the slight increase in intensity at 3677 cm⁻¹ as a function of CO₂ loading.

We sought to gain a detailed understanding of the formation of MFM-300(Fe) via in situ time-resolved PXRD experiments. Two sets of reactions, each using the original and halved synthetic concentration (A and B, respectively) (see the supplementary material for details), were conducted at beamline I12 (λ = 0.2328 Å), Diamond Light Source, at 384.25 K, 401.85 K, and 417.55 K in V-shaped reactors to encourage formation of crystalline material within the X-ray beam. The resultant diffraction patterns were collected using a 2D area detector. The diffraction frames underwent a processing pipeline of detector calibration, threshold masking, background subtraction, Azimuthal integration, and a rolling baseline correction.³⁹ Upon commencement of the reaction, the complete dissolution of the reactants was observed confirming formation of crystalline material directly from solution.

Diffraction data as a function of time and extent of crystal growth for concentration A in reaction I are shown in Fig. 3 (other data are shown in the supplementary material). Due to the limited observed diffraction at low levels of crystallization, it was only possible to track the formation of two Bragg peaks [110] and [211] in all 6 samples (3 temperatures × 2 concentrations). The formation of MFM-300(Fe) in the I4₁22 phase has been confirmed in all 6 reactions (Figs. 3 and S2–S6), and no disallowed reflections were observed for the final product (Fig. S1). A notable feature during the reaction is the growth and subsequent decay of a notable Bragg peak at approximately 4.5° (d = 2.95 Å), which is not apparent in the final PXRD pattern of MFM-300(Fe). This was observed predominantly at higher concentration reactions (I, III, and V) and most noticeably at 384.25 K. This peak is tentatively attributed to a kinetic intermediate comprising an iron oxide chain, which are then linked subsequently by biphenyl-3,3′,5,5′-tetracarboxylate linker to form the MFM-300(Fe) framework (Figs. S15 and S16).

The classical solid-state chemistry approach to kinetic analysis is to employ the AE equation [Eq. (1)] as a means of quantifying reaction kinetics. In an effort to bring more physical understanding to the reaction, the kinetic analysis was supplemented by use of the adapted FW model [Eq. (2)]. Mathematical fittings were carried out using the lmfit⁴⁰ module within Python, and this offered a nonlinear least squares minimization and curve fitting allowing us to fit both the [110] and [211] peaks and calculate their amplitude growth as a function of time. The resultant plots [Figs. 4(a)–4(c)] were fitted using the two selected kinetic models (AE and FW). The two peaks that were fitted for kinetic analysis, [110] and [211], represent allowed reflections in the lattice of MFM-300(Fe) (Fig. S14). These two planes point approximately 34.1° in different directions to one another, and the subsequent fittings of extent of crystal growth vs time reveal the same or very similar rate constants (Table S1). This then allows us to conclude that during the formation process MFM-300(Fe) is propagating in at least two directions at the same rate. Much like the lithium meso-tartrates,²⁴ the exponent n from the AE equation (1) is not a fixed integer value in the formation of MFM-300(Fe) (Table S1). Fixed integer values are often suggestive of the dimensional nature of the particle growth; MFM-300(Fe) having a noninteger value implies that particle morphology plays no rate-limiting role during the synthesis.

As expected, the rates of formation increased with increasing temperature (Table S1). The average activation energy (E_a), the average energy of nucleation (⁠$Eak1$⁠), and the average energy of autocatalytic growth (⁠$Eak2$⁠) were calculated using the Arrhenius equation [Eq. (3) in the supplementary material] to be 50.9, 56.7, and 50.7 kJ mol⁻¹, respectively [Fig. 4(d)]. The fact that the energy of nucleation is larger than the energy for autocatalytic growth suggests that nucleation is the overall rate-determining step in the formation of MFM-300(Fe). The E_a of formation of CAU-1-NH₂ has been reported as 136.6 kJ mol⁻¹ under solvothermal conditions.¹⁷ In comparison, HKUST-1, MOF-14, CPO-27(Ni), CPO-27(Co), and MIL-100(Mn) all undergo a two-step kinetic model analysis producing E_a nucleation values of 71.6, 113.9, 83.6, 83.6, and 126.5 kJ mol⁻¹, respectively, and E_a growth values of 63.8, 82.8, 72.8, 48.4, and 98.9 kJ mol⁻¹, respectively.^16,18,19 This is a similar trend to that observed for MFM-300(Fe) with values for nucleation being larger than those for autocatalytic growth.

A 1000-fold scale-up of the synthesis of MFM-300(Fe) (from milligrams to tens of grams) has been achieved with the inclusion of vigorous stirring in the reaction to promote the nucleation by creating additional nucleation sites. This has enabled further evaluation of the CO₂ separation properties under dynamic flow conditions using a fixed-bed reactor packed with multigrams of MFM-300(Fe). Microbreakthrough experiments based upon milligrams of sample typically carry large uncertainties,³⁴ and, therefore, scale-up of MOF synthesis is of critical importance to evaluate their performance under practical conditions.

The selectivity that MFM-300(Fe) demonstrates toward CO₂ is corroborated by breakthrough experiments whereby single component N₂, CO₂, and CH₄ (Figs. S7 and S8) and dual component mixtures of CO₂/CH₄ and CO₂/N₂ (Fig. 5) were flowed through a fixed bed packed with MFM-300(Fe) under ambient conditions (298 K and 1 bar). Breakthrough experiments for CO₂/N₂ at 15:85 v/v diluted with He to a total flow rate of 30 ml min⁻¹ confirmed that N₂ elutes through the bed first (breakthrough dimensionless time = 1150, saturation dimensionless time = 4170) followed by CO₂, which starts to elute when C/C₀ N₂ = 0.65 (dimensionless time = 2340, saturated dimensionless time = 10 660). For a 50:50 v/v mixture of CO₂/N₂, complete saturation of N₂ occurs before CO₂ starts to breakthrough (N₂ breakthrough dimensionless time = 1180, CO₂ breakthrough dimensionless time = 2670), emphasizing the ability of this material to selectively retain CO₂ over N₂. This is entirely consistent with the calculated selectivity from IAST calculations. Similar results are obtained from CO₂/CH₄ breakthrough experiments where CH₄ breaks through first (breakthrough dimensionless time = 1460, saturated dimensionless time = 7340) followed by CO₂ (breakthrough dimensionless time = 2840, saturation dimensionless time = 11 440). However, the difference in breakthrough time for the two components here is smaller, owing to the stronger affinity of MFM-300(Fe) to CH₄ than N₂, again consistent with the IAST selectivities. Despite the higher uptake of CH₄ at 1 bar and 298 K than the other analogs of MFM-300(In),³⁷ MFM-300(Fe) still exhibits overall selectivity for CO₂.

In conclusion, we report the analysis of the kinetics of formation of MFM-300(Fe) with an overall activation energy of 50.9 kJ mol⁻¹. The additional use of the two-step kinetic Finke-Watzky (FW) model allowed deconvolution of the activation energy into two distinct parts that have a physical manifestation and have therefore more closely modeled the synthesis of this MOF. This calculation yielded two discrete activation energies for the average nucleation within the reaction (56.7 kJ mol⁻¹) and the activation energy for the average autocatalytic growth within the reaction (50.7 kJ mol⁻¹). These studies confirm that this approach can be used to study the kinetics of formation of complex MOF systems comprising larger linker ligands. MFM-300(Fe) displays high adsorption and selectivity for CO₂, and the binding domains and dynamics for adsorbed CO₂ molecules in MFM-300(Fe) have been determined from synchrotron X-ray scattering experiments. The performance of MFM-300(Fe) for CO₂ adsorption and separation has been studied under both static and dynamic conditions using the scaled-up materials, demonstrating its potential for further investigations for applications in carbon capture and storage.

See supplementary material containing details of synthesis, analysis of gas adsorption data, X-ray diffraction data, FTIR, and breakthrough experiments.

We thank EPSRC (Grant No. EP/I011870), ERC (Grant No. AdG 742041), and the Royal Society and University of Manchester for funding. We are grateful to Diamond Light Source for access to Beamline I12 (No. EE-11278), I11 and B22.

The authors declare no conflict of interest.