Hydrocarbon Sorption in Flexible MOFs-Part II: Understanding Adsorption Kinetics

Abstract

The rate of sorption of n-butane on the structurally flexible metal-organic framework [Cu₂(H-Me-trz-ia)₂], including its complete structural transition between a narrow-pore phase and a large-pore phase, was studied by sorption gravimetry, IR spectroscopy, and powder X-ray diffraction at close to ambient temperature (283, 298, and 313 K). The uptake curves reveal complex interactions of adsorption on the outer surface of MOF particles, structural transition, of which the overall rate depends on several factors, including pressure step, temperature, as well as particle size, and the subsequent diffusion into newly opened pores. With the aid of a kinetic model based on the linear driving force (LDF) approach, both rates of diffusion and structural transition were studied independently of each other. It is shown that temperature and applied pressure steps have a strong effect on the rate of structural transition and thus, the overall velocity of gas uptake. For pressure steps close to the upper boundary of the gate-opening, the rate of structural transition is drastically reduced. This feature enables a fine-tuning of the overall velocity of sorption, which can even turn into anti-Arrhenius behavior.

Keywords: flexible materials; kinetic analysis; metal–organic frameworks.

Figure 1

Adsorption isotherms for the system n-butane on 1 at 283, 298, 313, and 328 K in a logarithmic pressure scale (left) and the resulting Dubinin plot using the corresponding states theory for all temperatures, including the GOS- and GOE-points (right).

Figure 2

Time-dependent X-ray powder diffraction (Cu-K_α1 radiation, stationary Dectris Pilatus detector) patterns for the uptake of n-butane on 1 at 298 K for a pressure step of 0 → 10 kPa in a glass capillary. The grey bars emphasize the two areas (2θ ≈ 11° and 13°) with the most significant change regarding the phase transition.

Figure 3

Particle size distribution for 1 after different numbers of adsorption-desorption cycles plotted as the derivative dN/dX.

Figure 4

Transport diffusivities of n-butane on 1 in dependence of the loading. The grey area marks the loading range between gate-opening start (GOS) and gate-opening end (GOE). The arrows indicate much higher diffusivities in the regions of very low and very high pressures, which were not measurable under the experimental conditions.

Figure 5

Gravimetric uptake of n-butane on 1 at 298 K after a pressure step 0 → 10 kPa, the fitted model presented in this work and the uptake as derived from PXRD data measured under the same conditions, representing the state of structural transition in dependence of time.

Figure 6

Schematic representation of the governing processes during adsorption of n-butane on 1 and their respective rate constants.

Figure 7

Uptake of n-butane on 1 at 283, 298, 313, and 328 K for a pressure step 0 → 0.04 p $p_0^{-1}$ and their corresponding fits for the whole process (left) and zoomed-in for the first 50 s (right).

Figure 8

Dubinin plot of n-butane adsorption on 1 at 283, 298, 313, and 328 K. The position of GOE (A_GOE = 10,600 J mol⁻¹) and of the uptake equilibria for dA_GO = 4100 J mol⁻¹ (S1: A = 6500 J mol⁻¹) and dA_GO = 5700 J mol⁻¹ (S2: A = 4900 J mol⁻¹) with respect to GOE are shown as dotted lines.

Figure 9

Gas uptake curves for n-butane on 1 at 283, 298, 313, and 328 K for changes in adsorption potential of dA = 4100 J mol⁻¹ (left) and dA=5700 J mol⁻¹ (right) with respect to A_GOE.

Figure 10

Two uptakes with the same sorption rate coefficient, although the black curve shows the relative uptake at a lower temperature and a smaller pressure step.