Adsorption of Carbon Dioxide, Methane, and Nitrogen on Zn(dcpa) Metal-Organic Framework

Abstract

Adsorption-based processes using metal-organic frameworks (MOFs) are a promising option for carbon dioxide (CO₂) capture from flue gases and biogas upgrading to biomethane. Here, the adsorption of CO₂, methane (CH₄), and nitrogen (N₂) on Zn(dcpa) MOF (dcpa (2,6-dichlorophenylacetate)) is reported. The characterization of the MOF by powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), and N₂ physisorption at 77 K shows that it is stable up to 650 K, and confirms previous observations suggesting framework flexibility upon exposure to guest molecules. The adsorption equilibrium isotherms of the pure components (CO₂, CH₄, and N₂), measured at 273–323 K, and up to 35 bar, are Langmuirian, except for that of CO₂ at 273 K, which exhibits a stepwise shape with hysteresis. The latter is accurately interpreted in terms of the osmotic thermodynamic theory, with further refinement by assuming that the free energy difference between the two metastable structures of Zn(dcpa) is a normally distributed variable due to the existence of different crystal sizes and defects in a real sample. The ideal selectivities of the equimolar mixtures of CO₂/N₂ and CO₂/CH₄ at 1 bar and 303 K are 12.8 and 2.9, respectively, which are large enough for Zn(dcpa) to be usable in pressure swing adsorption.

1. Introduction

Metal-organic frameworks (MOFs) are being touted as the next generation materials for several adsorptive separation and purification processes [1,2]. MOFs are porous crystalline materials consisting of metal centers connected by organic moieties [3]. An unlimited amount of MOF structures can be envisioned and perhaps synthesized; furthermore, the materials can be tailored for specific applications through pore size tuning and functionalization [4]. These features place MOFs as a very diverse class of materials with potential applications in nearly all fields of chemical engineering [5,6,7,8,9,10,11,12].

Among the available portfolio of MOFs, there are several structures that present structural flexibility, which can be triggered by exposure to specific guest species, changes in temperature or mechanical pressure, or interactions with light or electric fields [13,14]. Framework flexibility generally manifest itself through breathing or gate-opening effects [13]. A comprehensive review regarding MOF flexibility was published by Schneemann et al. [14], in which it is stated that, so far, less than a hundred MOFs have shown important breathing effects. The authors classified the type of flexibility into “breathing”, “swelling”, “linker rotation”, and “subnetwork displacement”. The most well-known cases of MOF flexibility are the breathing behavior of MIL-53 [15,16,17] and the gate-opening of ZIF-8 [18,19].

The MIL-53 family of MOFs consists of trivalent metal (e.g., Al [20], Cr [17], Fe [21], and Sc [22]) terephthalates, which can switch between large-pore (lp) and narrow-pore (np) forms [15,16,17], with unit cell volume variation of up to 40% [23]. The conformational change can be triggered by different stimuli, for example temperature changes [22,24], application of mechanical pressure [25,26], and adsorption of guest molecules (such as H₂O, CO₂, and other gases) [20,22,26,27]. Interestingly, the synthesis route and solvents employed critically impact the breathing properties of MIL-53 [28], and several authors have observed the absence of the breathing effect in the commercial MIL-53(Al) synthesized by BASF (Basolite©A100) when exposed to CO₂ [29,30,31].

Another type of MOF flexibility is related to linker rotation [32], of which the most well-known example occurs in ZIF-8, which presents a gate-opening effect [18,19]. The linker rotation triggers a window opening that allows for the adsorption of larger molecules than expected [18].

Recently, MOFs with step-shaped isotherms typical of flexible MOFs have been considered as potential adsorbents for CO₂ capture by temperature swing adsorption (TSA), as they permit decreasing the energy consumption of the process when compared with traditional zeolite 13X systems [33].

Zn(dcpa) is a poorly studied microporous MOF that reportedly exhibits dynamic behavior and stepwise adsorption. Zn(dcpa) is based on paddle-wheel Zn₂ units and unsymmetrical pyridyl dicarboxylate, which give rise to a three-dimensional intersecting pore network with a pore opening of 6.3 × 12.2 Ų [34]. The Zn(dcpa) framework structure is shown in Figure 1. Liu et al. [34] observed the dynamic behavior of Zn(dcpa) upon exposure to N₂ and CO₂ at 77 K and 195 K, respectively. However, they did not observe the MOF’s flexible behavior when adsorbing CO₂ at 273 and 293 K and N₂ at 293 K, up to 1 bar.

In this work, the potential of Zn(dcpa) for application in the separation/purification of gaseous streams containing CO₂, CH₄, and N₂, namely post-combustion CO₂ capture and biogas upgrading, is evaluated. For this purpose, the single-component adsorption equilibria of CO₂, CH₄, and N₂ have been measured at 273−323 K up to 35 bar, and the isosteric heat of adsorption and ideal CO₂/CH₄ and CO₂/N₂ equilibrium selectivities evaluated. Furthermore, the MOF has been characterized regarding its textural properties and thermal stability. The uncommon stepwise adsorption and hysteretic desorption behavior for CO₂ at 273 K has been interpreted in terms of the osmotic thermodynamic theory. The data reported here add important knowledge about the adsorption properties of Zn(dcpa), as prior studies about this MOF are limited to a few publications [34,35].

2. Materials and Methods

2.1. Materials

The Zn(dcpa) MOF sample employed was synthesized at the Materials Center at Technical University Dresden (Germany). After its synthesis, the sample was washed with DMF and, subsequently, activated at 453 K under vacuum for 24 h. The gases employed in the measurements were provided by Air Liquide and Praxair (Portugal) with purities of 99.998% (CO₂), 99.95% (CH₄), 99.99% (N₂), and 99.999% (He).

2.2. Zn(dcpa) Characterization

The sample was characterized using powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), N₂ physisorption at 77 K, and helium porosimetry. The N₂ adsorption isotherm at 77 K and PXRD were determined by the supplier upon request. TGA analysis was performed using a LABSYS Evo TGA-DTA/DSC from SETARAM Instrumentation, under an argon flow at a heating rate of 3 K/min (up to 1130 K). Helium picnometry was performed at 323 K, in a gravimetric apparatus (described in the next section), to determine the skeletal density of the MOF (ρ_s).

2.3. Single-Component Adsorption Equilibrium

Single-component adsorption equilibrium isotherms of CO₂, CH₄, and N₂ at 273 K, 303 K, and 323 K, between 0 and 35 bar, were determined using the standard static gravimetric method [31,36,37]. The measurements were performed in a high-pressure magnetic-suspension balance ISOSORP 2000 (Rubotherm GmbH, Germany) using approximately 600 mg of Zn(dcpa) powder. Both the adsorption and desorption data were recorded to evaluate the hysteretic effects. The sample was received from the supplier already activated and stored in an argon atmosphere, which is why the pre-treatment performed before measuring the adsorption equilibrium isotherms was limited to overnight vacuum. The experimental setup and procedure are detailed elsewhere [31,37].

The excess amount adsorbed, $q_{\mathrm{exc}}$, is determined as follows

$$q_{\mathrm{exc}}=\frac{w-m_{\mathrm{s}}-m_{\mathrm{h}}+V_{\mathrm{h}}{\rho }_{\mathrm{g}}}{m_{\mathrm{s}}}+v_{\mathrm{s}}{\rho }_{\mathrm{g}}$$

(1)

where $w$ is the apparent mass weighted; $m_{\mathrm{s}}$ is the mass of MOF; $V_{\mathrm{h}}$ and $m_{\mathrm{h}}$ correspond to the volume and mass of the measuring cell, respectively, which contribute to the buoyancy effects; ${\rho }_{\mathrm{g}}$ is the density of the bulk gas at the experimental conditions; and $v_{\mathrm{s}}$ is the specific volume of the solid matrix of the MOF ($v_{\mathrm{s}}=1/{\rho }_{\mathrm{s}}$, where ${\rho }_{\mathrm{s}}$ is the skeletal density of the adsorbent). $v_{\mathrm{s}}$ was determined by helium pycnometry performed at 323 K in the gravimetric apparatus. This was determined assuming that He penetrates the MOF pore volume without being adsorbed.

The absolute amount adsorbed, $q$, can be determined from the excess amount adsorbed, using the following

$$q =q_{\mathrm{exc}}\left(\frac{{\rho }_{\mathrm{l}}}{{\rho }_{\mathrm{l}}-{\rho }_{\mathrm{g}}}\right)$$

(2)

assuming that the adsorbed phase density corresponds to the density of the liquid at its boiling point at 1 atm (${\rho }_{\mathrm{l}}$) [38].

3. Results and Discussion

3.1. Zn(dcpa) Characterization

The PXRD patterns obtained are displayed in Figure 2, showing that the position of the reflexes changed during activation. This effect was also observed by Liu et al. [34], who associated it with framework shrinkage upon removal of the guest molecules. The authors also observed the reversibility of this phenomenon when readsorbing the solvent.

The thermal stability of the sample was also characterized by TGA; the recorded sample mass as a function of the heating temperature is shown in Figure 3. The results show an initial mass decrease (~10%) from room temperature up to around 400 K, due to the removal of pre-adsorbed impurities and humidity, due to MOF exposure to the indoor atmosphere just prior to the analysis. MOF was stable up to 650 K, after which a steep decrease in the mass was observed, reaching a mass decrease of 50%, similar to the behavior observed by Liu et al. [34]. Above 750 K, the Zn(dcpa) mass decreased more smoothly until reaching the remaining experimental amount of ca. 25% at 1130 K.

The Zn(dcpa) porosity was evaluated by N₂ adsorption at 77 K. The obtained isotherm is plotted in Figure 4, showing an initial step followed by a smoother increase until $p/p_0=0.06$; then, another steep increase is observed before reaching a nearly constant plateau with only a small increase between $p/p_0=0.2$ (274 cm³/g) and $p/p_0=0.97$ (303 cm³/g). Note that $p$ and $p_0$ are the equilibrium and saturation pressures of the adsorbate at 77 K, respectively. The same behavior was observed by Liu et al. [34] who attributed the first step of the isotherm to the Zn(dcpa) structure with shrunken pores, and the second step to an expanded structure. In our work, the expanded structure had a specific pore volume of 0.47 cm³/g, determined at a relative pressure of $p/p_0=0.97$, assuming the pores were filled with condensed liquid N₂ at its normal boiling point. The desorption branch showed hysteresis at $p/p_0<0.2$, which is also in accordance with a previous report, although in our case, the hysteresis loop seemed to close at lower pressures—which corresponds to a return to the shrunken pore conformation—as opposed to the observation of Liu et al. [34].

3.2. Single-Component Adsorption Equilibrium

Prior to the adsorption of CO₂, CH₄, and N₂, the skeletal density of Zn(dcpa) was determined by helium picnometry at 323 K, obtaining a ${\rho }_{\mathrm{s}}=1.74 \mathrm{g}/{\mathrm{cm}}^3$ ($v_{\mathrm{s}}=1/{\rho }_s=0.575$ cm³/g). For a purely crystalline porous material with a regular lattice, $v_{\mathsf{\mu }}+v_{\mathrm{s}}$ is equal to the specific volume of the unit cell of the lattice. The particle density determined, ${\rho }_{\mathrm{p}}=1/\left(v_s+v_{\mu }\right)=0.957$ g/cm³, is in excellent agreement with the value obtained from the crystallographic data (${\rho }_{\mathrm{p}}=0.961$ g/cm³) by Liu et al. [34].

The adsorption equilibria of CO₂, CH₄, and N₂ on the Zn(dcpa) MOF were measured at 273, 303, and 323 K over the pressure range of 0 to 35 bar. The CO₂, CH₄, and N₂ absolute adsorption equilibrium isotherms obtained are reported in Figure 5, Figure 6 and Figure 7, respectively. The CO₂ adsorption isotherms were quite steep in the Henry region, showing a high adsorption capacity at a low pressure, an important feature for use in post-combustion CO₂ capture applications. On the other hand, the N₂ adsorption isotherms were much more linear and had lower adsorption capacity; the CH₄ adsorption isotherms were intermediate between those of CO₂ and N₂.

An interesting feature of the CO₂ adsorption equilibrium isotherms can be observed in Figure 5. At 273 K, the adsorption branch of the isotherm follows a typical Langmuir-type shape up to approximately 22 bar, where a step in the isotherm is observed. This behaviour is similar to that observed by Liu et al. [34] for CO₂ adsorption at 195 K, which the authors related to the transition between a shrunken-pore phase and an expanded-pore one. The desorption branch then follows a different path than the adsorption one, showing a hysteresis loop that closes at 7 bar. The reproducibility of this behaviour was checked by repeating the measurements. The stepwise CO₂ adsorption observed is an interesting feature of Zn(dcpa) that can be explored for gas separation or storage applications. It can enhance the working capacity of the solid material upon mild pressure or temperature swings [33]. Despite the observation of the MOF flexibility for CO₂ adsorption at 273 K, the same behaviour was not observed for any of the other temperatures nor for the adsorbate species tested (CH₄ and N₂).

3.3. Osmotic Thermodynamic Theory

Some materials present clear transitions between different metastable framework structures. Zn(dcpa) is an example of such materials. In these cases, an “osmotic subensemble” [15,39,40,41,42] can be employed to describe the equilibrium between host structures when exposed to gaseous adsorbates. Alternatively, Ghysels et al. [42] proposed another free energy model able to describe the thermodynamics of breathing phenomena in flexible materials. In this work, we interpreted our data using the former approach.

The osmotic potential [43] of the solid−adsorbate system for the ith structure of Zn(dcpa), either shrunken-pore (SP) or expanded-pore (EP), is

$$\begin{array}{c}{\mathsf{\Omega }}_{\mathrm{os}}^{\left(i\right)}\left(P,T\right)=F_{\mathrm{host}}^{\left(i\right)}\left(T\right)+P{v}_{\mathrm{p}}^{\left(i\right)}-{{\displaystyle \int }}_0^P{q}^{\left(i\right)}\left(P,T\right)v_{\mathrm{g}}\left(P,T\right) dP\\ =F_{\mathrm{host}}^{\left(i\right)}\left(T\right)+P{v}_{\mathrm{p}}^{\left(i\right)}-RT{{\displaystyle \int }}_0^P{q}^{\left(i\right)}\left(P,T\right)Z\left(P,T\right) d\ln P\end{array}$$

(3)

where $F_{\mathrm{host}}^{\left(i\right)}\left(T\right)$ corresponds to the empty structure’s free energy at temperature $T$ and $v_{\mathrm{p}}^{\left(i\right)}$ to its apparent specific volume (i.e., to the sum of its skeletal, $v_{\mathrm{s}}$, and porous, $v_{\mu }^{\left(i\right)}$, volumes); $q^{\left(i\right)}\left(P,T\right)$ corresponds to the adsorption isotherm considering a rigid framework in its ith structural form; and $v_{\mathrm{g}}=1/n_{\mathrm{g}}$ and $P$ are the molar volume and compressibility factor of the adsorptive. The difference in the osmotic potential between both of the structures considered (EP and SP), $∆{\mathsf{\Omega }}_{\mathrm{os}}\left(P,T\right)={ \mathsf{\Omega }}_{\mathrm{os}}^{\left(\mathrm{EP}\right)}\left(P,T\right)-{\mathsf{\Omega }}_{\mathrm{os}}^{\left(\mathrm{SP}\right)}\left(P,T\right)$, is thus

$$∆{\mathsf{\Omega }}_{\mathrm{os}}\left(P,T\right)=∆F_{\mathrm{host}}\left(T\right)+P∆v_{\mathrm{p}}-RT{{\displaystyle \int }}_0^P∆q\left(P,T\right)Z\left(P,T\right) d\ln P$$

(4)

where $∆\varphi \equiv {\varphi }^{\left(\mathrm{EP}\right)}-{\varphi }^{\left(\mathrm{SP}\right)}$ is the difference in the value of property $\varphi$ between the EP and SP structures at temperature $T$. If $∆{\mathsf{\Omega }}_{\mathrm{os}}>0$, the SP structure will be more stable than EP; if $∆{\mathsf{\Omega }}_{\mathrm{os}}<0$, the reverse will be true. For Zn(dcpa), $v_{\mu }^{\left(\mathrm{EP}\right)}=0.47$ cm³/g and $v_{\mu }^{\left(\mathrm{SP}\right)}=0.14$ cm³/g; hence $∆v_{\mathrm{p}}={\left(v_{\mathrm{s}}+v_{\mu }\right)}^{\left(\mathrm{EP}\right)}-{\left(v_{\mathrm{s}}+v_{\mu }\right)}^{\left(\mathrm{SP}\right)}\approx v_{\mu }^{\left(\mathrm{EP}\right)}-v_{\mu }^{\left(\mathrm{SP}\right)}=0.33$ cm³/g. Assuming ideal gas behavior ($Z\approx 1$), the previous equation can be simplified to

$$∆{\mathsf{\Omega }}_{\mathrm{os}}\left(P,T\right)\approx ∆F_{\mathrm{host}}\left(T\right)+P∆v_{\mathrm{p}}-RT{{\displaystyle \int }}_0^P∆q\left(P,T\right) d\ln P.$$

(5)

If $∆F_{\mathrm{host}}$ and $∆q\left(P\right)$ are known at a given temperature $T$, putting $∆{\mathsf{\Omega }}_{\mathrm{os}}=0$ in Equation (4) (or Equation (5)) and solving it for $P$ gives the pressure at which the phase transition occurs at $T$. However, in real scenarios, the MOF crystals have defects and the sample has a distribution of crystal sizes, both contributing to smoothing the structural transitions between the two metastable framework structures. Here, we extend the osmotic thermodynamic theory to account for this diffuse effect. It is assumed that for a real sample, $∆F_{\mathrm{host}}$ is normally (Gaussian) distributed around the corresponding value for a perfect crystal with a probability density function

$$f\left(∆F_{\mathrm{host}}\right)=\frac{1}{{\sigma }_{∆F}\sqrt{2\pi }}\exp \left(-\frac{1}{2}\frac{{\left(∆F_{\mathrm{host}}-∆F_{\mu }\right)}^2}{{\sigma }_{∆F}^2}\right),$$

(6)

where $∆F_{\mu }$ is the mean or expectation of the distribution (i.e., the value of $∆F_{\mathrm{host}}$ for a perfect crystal) and ${\sigma }_{∆F}$ is its standard deviation. Given that in the case under study, the structural transition is triggered by exposure to a specific guest species, the previous hypothesis is almost equivalent to considering that the adsorptive pressure, $P$, that triggers the structural transition at a fixed temperature is also a normally distribute variable and, therefore, that its cumulative distribution function, $\Phi \left(P\right)$, at a fixed temperature is

$$\Phi \left(P\right)\equiv {\displaystyle \int }f\left(P\right)dP=\frac{1}{2}\left[1+\mathrm{erf}\left(\frac{P-P_{\mu }}{{\sigma }_P\sqrt{2}}\right)\right]$$

(7)

where $P_{\mu }$ is the mean or expectation of the distribution (i.e., the transition pressure for a perfect crystal) and ${\sigma }_P$ is its standard deviation. Note that $\Phi \left(x\right)=\mathrm{prob}\left(P \le x\right)$, where the right-hand side represents the probability that $P$ takes on a value less than or equal to $x$. Therefore, the macroscopically observed adsorption branch of the isotherm for a real sample is given by

$$\begin{array}{c}{q}_{\mathrm{ads}}\left(P\right)=\left[1-{\Phi }_{\mathrm{ads}}\left(P\right)\right]q^{\left(\mathrm{SP}\right)}\left(P\right)+{\Phi }_{\mathrm{ads}}\left(P\right)q^{\left(\mathrm{EP}\right)}\left(P\right)\\ q_{\mathrm{des}}\left(P\right)=\left[1-{\Phi }_{\mathrm{des}}\left(P\right)\right]q^{\left(\mathrm{SP}\right)}\left(P\right)+{\Phi }_{\mathrm{des}}\left(P\right)q^{\left(\mathrm{EP}\right)}\left(P\right)\end{array}\hspace{1em}\hspace{1em}(\mathrm{fixed} T)$$

(8)

where $q^{\left(i\right)}\left(P,T\right)$ is the adsorption isotherm considering a rigid framework constrained to its ith form.

This model was fitted to our experimental data, assuming the adsorption isotherms for the metastable forms of the framework are Langmuirian, i.e.,

$$q^{\left(i\right)}\left(P\right)=\frac{q_{\infty }^{\left(i\right)}{b}^{\left(i\right)}P}{1+b^{\left(i\right)}P}$$

(9)

where $q_{\infty }^{\left(i\right)}$ and $b^{\left(i\right)}$ are the saturation capacity and equilibrium constant for the ith form, respectively, in which case Equation (5) reduces to

$$∆{\mathsf{\Omega }}_{\mathrm{os}}\left(P,T\right)=∆F_{\mathrm{host}}\left(T\right)+P∆v_{\mathrm{p}}-RT\left[q_{\infty }^{\left(\mathrm{EP}\right)}\ln \left(1+b^{\left(\mathrm{EP}\right)}P\right)-q_{\infty }^{\left(\mathrm{SP}\right)}\ln \left(1+b^{\left(\mathrm{SP}\right)}P\right)\right]$$

(10)

Table 1. Fitted parameters of the osmotic thermodynamic theory to the adsorption (Ads) and desorption (Des) branches of the experimental CO2 isotherm at 273 K. $∆F_{\mathrm{host}}\equiv F_{\mathrm{host}}^{\left(\mathrm{EP}\right)}-F_{\mathrm{host}}^{\left(\mathrm{SP}\right)}$.

	${\mathit{q}}_{\mathit{\infty }}$	$\mathit{b}$		${\mathit{P}}_{\mathit{\mu }}$	${\mathit{\sigma }}_{\mathit{P}}$	$\mathbf{∆}{\mathit{F}}_{\mathbf{h}\mathbf{o}\mathbf{s}\mathbf{t}}$
	(mol/kg)	(atm −1)		(atm)	(atm)	(J/g)
SP	5.65	1.30	Ads	23.0	1.3	−4.45
EP	12.2	0.143	Des	7.0	0.5	−10.7

lists the parameter values resulting from the model fitting to the experimental data, saturation capacity and Langmuir equilibrium constant ($q_{\infty }^{\left(i\right)}$ and $b^{\left(i\right)}$) for CO₂ adsorption at 273 K in the SP and EP metastable structures of Zn(dcpa), mean and standard deviation ($P_{\mu }$ and ${\sigma }_{\mu }$,) of the Gaussian distribution of adsorptive pressure that triggers the phase transition along the adsorption and desorption branches of the isotherm, and the corresponding free energy changes of the empty structure ($∆F_{\mathrm{host}}$).

Figure 8 compares the experimental adsorption data and the fitted osmotic thermodynamic model, and shows that excellent agreement with the experimental results has been reached using the proposed procedure, substantiated by the fact that the plotted adsorption and desorption curves accurately reproduce the experimental data.

The first two numeric columns of

Table 2. Fitting of the Langmuir adsorption isotherm model to the CH₄ and N₂ experimental adsorption data at 273 K. The parameters for the EP form are estimated as $q_{i,\infty }^{\left(\mathrm{EP}\right)}=q_{i,\infty }^{\left(\mathrm{SP}\right)}{q}_{{\mathrm{CO}}_2,\infty }^{\left(\mathrm{EP}\right)}/q_{{\mathrm{CO}}_2,\infty }^{\left(\mathrm{SP}\right)}$ and $b_i^{\left(\mathrm{EP}\right)}=b_i^{\left(\mathrm{SP}\right)}{b}_{{\mathrm{CO}}_2}^{\left(\mathrm{EP}\right)}/b_{{\mathrm{CO}}_2}^{\left(\mathrm{SP}\right)}$.

	${\mathit{q}}_{\mathit{\infty }}^{\left(\mathbf{SP}\right)}$	${\mathit{b}}^{\left(\mathbf{SP}\right)}$	${\mathit{q}}_{\mathit{\infty }}^{\left(\mathbf{EP}\right)}$	${\mathit{b}}^{\left(\mathbf{EP}\right)}$
	(mol/kg)	(atm −1)	(mol/kg)	(atm −1)
${\mathrm{N}}_2$	3.681	0.089	7.948	0.010
${\mathrm{CH}}_4$	4.328	0.411	9.346	0.045

list the parameter values of the Langmuir adsorption isotherm model that best fit the CH₄ and N₂ experimental adsorption data at 273 K (Figure 9); these values apply when the framework is in its SP form. The last two columns of Table 2 list the corresponding values if the framework were hypothetically in EP form; given the absence of experimental data, the Langmuir parameters were estimated using the following scaling rules:

$$q_{i,\infty }^{\left(\mathrm{EP}\right)}=q_{i,\infty }^{\left(\mathrm{SP}\right)}\frac{q_{{\mathrm{CO}}_2,\infty }^{\left(\mathrm{EP}\right)}}{q_{{\mathrm{CO}}_2,\infty }^{\left(\mathrm{SP}\right)}} \mathrm{and} b_i^{\left(\mathrm{EP}\right)}=b_i^{\left(\mathrm{SP}\right)}\frac{b_{{\mathrm{CO}}_2}^{\left(\mathrm{EP}\right)}}{b_{{\mathrm{CO}}_2}^{\left(\mathrm{SP}\right)}}$$

(11)

Although these rules are rather crude and their application cannot be considered quantitatively precise, they allow us to explain why the adsorption isotherms of CH₄ and N₂ do not point to a phase transition between the SP and EP structures (and no hysteresis) in the pressure range tested experimentally by us. The reason is that in the case of CH₄ or N₂ adsorption, the pressure must be increased considerably, well above the maximum experimental value tested by us, for the term $RT{\int }_0^P∆q\left(P,T\right) d\ln P$ to change the sign of $∆{\mathsf{\Omega }}_{\mathrm{os}}$. A similar reasoning explains why the CO₂ adsorption isotherms at 303 K and 323 K do not hint at a phase transition between the SP and EP structures.

3.4. Potential of Zn(dcpa) for CO₂/N₂ and CO₂/CH₄ Separation

To assess the potential use of Zn(dcpa) for the adsorptive separation of CO₂/N₂ and CO₂/CH₄, we first compared the single-component equilibrium isotherms and the obtained selectivities. Figure 10a compares the isotherms obtained at 303 K for the three gases. The ideal selectivity for an equimolar mixture, ${\alpha }_{\mathrm{A}/\mathrm{B}}=q_{\mathrm{A}}/q_{\mathrm{B}}$, was calculated using the single-component adsorption capacity ratio; the obtained results are reported in Figure 10b,c for the CO₂/N₂ and CO₂/CH₄ selectivities, respectively. Both the CO₂/N₂ and CO₂/CH₄ selectivities decreased with the increasing pressure, ranging from 12.8 (at 1 bar) to 6.7 (6 bar) for CO₂/N₂, and from 2.9 (at 1 bar) to 2.1 (6 bar) for CO₂/CH₄. The CO₂/N₂ selectivity was significantly higher than that of CO₂/CH₄, especially at a lower pressure. Although the reported equilibrium selectivity did not take into account the influence of adsorption kinetics or the impact of a real gas mixture, these results serve as a first evaluation of the good potential of Zn(dcpa) for CO₂ separation from CO₂/N₂ and CO₂/CH₄ mixtures. Comparing the selectivity of Zn(dcpa) for CO₂/N₂ with those of the commercial MOFs MIL-53(Al) [31], ZIF-8, [44], and Fe-BTC [45] (Figure 10b,c), it is concluded that the former outperformed the others at a lower pressure. For example, at 1 bar, the order of selectivities was 12.8 (Zn(dcpa)) > 10.5 (Fe-BTC) > 9.6 (MIL-53(Al)) > 5.9 (ZIF-8). The same can be said about the CO₂/CH₄ selectivity trend: 2.9 (Zn(dcpa)) > 2.7 (MIL-53(Al)) > 2.6 (ZIF-8), although in this case, ZIF-8 surpassed Zn(dcpa) at pressures above 2.4 bar.

The isosteric heat of adsorption, $Q_{\mathrm{st}}$, was determined from the experimental data via the Clausius−Clapeyron equation: ${\left(\log P\right)}_q=\mathrm{const}-Q_{\mathrm{st}}/RT$ [46] Using this approach, the plot of $\log P$ versus $-1/RT$, at constant loading, should give a straight line from which the slope of $Q_{\mathrm{st}}$ can be obtained. The plots in Figure 11 of $Q_{\mathrm{st}}$ for CO₂, CH₄, and N₂ on Zn(dcpa) as a function of loading show that for CH₄, their values were approximately constant within the loading range studied, while for CO₂ and N₂, a linear increase was observed. It should be noted that in the case of CO₂, $Q_{\mathrm{st}}$ was plotted for loadings lower than the MOF’s conformational change observed at 273 K, i.e., less than 4 mol/kg. The isosteric heat of the adsorption was higher for CO₂ (23–28 kJ/mol), which is in accordance with the values reported in the literature [34], followed by that for CH₄ (~19.5 kJ/mol) and N₂ (13–15 kJ/mol).

4. Conclusions

Zn(dcpa) MOF was characterized through PXRD, thermogravimetric analysis, and N₂ adsorption at 77 K. In line with the XRD and N₂ data reported by Liu et al. [34], our results indicate that the framework conformation changes (pore shrinkage/pore expansion) upon removal/loading of guest molecules. The TGA results demonstrate that the MOF is stable up to 650 K.

The adsorption equilibrium isotherms of CO₂, CH₄, and N₂ on Zn(dcpa) at 273 K, 303 K, and 323 K are reported up to 35 bar. The obtained data highlight the interesting behavior of CO₂ adsorption at 273 K, which exhibits a stepped isotherm related to the transition between shrunken- and expanded-pore phases at around 22 bar. When observing the desorption branch of the isotherm, a hysteresis loop is present, closing at 7 bar. Although the same behavior is observed for CO₂ adsorption at 195 K [34], this is the first report of this effect at 273 K. None of the remaining CO₂ (303 K and 323 K), CH₄, or N₂ isotherms show the same behavior.

The CO₂ adsorption equilibrium at 273 K is accurately interpreted using the osmotic thermodynamic theory, which is further refined by considering that the free energy difference between the two metastable structures of Zn(dcpa) is a normally distributed variable due to the distribution of crystal sizes and the defects in a real MOF sample.

Regarding the uptake amounts, Zn(dcpa) can adsorb higher amounts of CO₂, followed by CH₄ and N₂. The CO₂/N₂ and CO₂/CH₄ ideal equilibrium selectivities of Zn(dcpa) at 303 K are evaluated for equimolar mixtures, resulting in 12.8 and 2.9, respectively, for a total pressure of 1 bar.

The reported data are essential for the modelling of adsorption-based processes, namely pressure swing adsorption (PSA) and temperature swing adsorption (TSA), for the separation of mixtures containing the studied gases, e.g., biogas upgrading and CO₂ capture from flue gases.