*2.3. Gas Uptake*

#### Equilibrium and Kinetic Breakthrough Gas Adsorption Studies

To establish the maximum and equilibrium uptake capacity of the solids towards C3H4/C3H6 gases, Micromeritics ASAP 2420 (Germany) was used. Samples of around 100 mg were outgassed for at least 12 h under vacuum at 338 K before the adsorption/desorption experiments. Tests were conducted at a range of temperatures between 300–360 K (controlled via water (300–320 K) or oil (340–360 K) jacket) and pressures from 0–100 KPa. An in-house simple setup was used to test the breakthrough experiments (dynamic tests). The setup consisted mainly of a small quartz adsorption column (I.D 4 mm, height: 160 mm), gas flow controllers and gas analyzer. The required amount of adsorbent was used in the columns and then activated inside the column at 338 K for a couple of hours using helium (He) gas to ensure that any unwanted inert gases had been fully purged from the column. To eliminate any errors in the use of the gas mixtures, a (10/90 *v*/*v*) C3H4/C3H6 gas mixture cylinder was purchased (Buzwair gas Inc. Qatar) and used in the experiments. A total flow rate of 5 mL (STP min−1) was used in all experiments. The flow rate was found to offer the best optimum conditions without having to fluidize the bed. The beds were regenerated ahead of a new gas breakthrough cycle using He (99.99 purity) for 30 min at 298 K and a flow rate of 5 mL min−1. The same sample of solid MOF sorbent was used for up to eight successive breakthrough cycles in order to study the stability of the adsorbent during multiple cycle operations of sorption and desorption. The experimental procedure for each cycle was identical to that described above.

### **3. Theoretical Modeling**

#### *3.1. Isotherm and Kinetic Models*

The adsorption isotherms of the pure compounds on the NbOFFOVE-1-Ni, SIFSIX-3- Ni were determined. Many models are reported in the literature to describe the adsorbent capacity for a certain species. The most commonly used in the case of gas-solid adsorption system are Langmuir, Freundlich, Sips and Toth isotherms [10]. The first two are known as the two parameter models, while the latter models are a hybrid combination of the two parameter models.

The Langmuir model is one of the most widely used isotherms in many applications including solid-gas and solid-liquid separations. The model is based on the assumption of monolayer interaction between the adsorbent and adsorbate with the assumption that all adsorption sites have similar adsorption energy requirements. Equation (1) represents one of the simplest forms to describe the Langmuir isotherm, where the maximum or saturation adsorption capacity is related to the system pressure and Langmuir constant, as shown in Equation (1):

$$\mathbf{Q} = \mathbf{q}\_{\rm sat} \frac{\mathbf{k} \mathbf{P}}{1 + \mathbf{k}\_{\rm l} \mathbf{P}} \tag{1}$$

where Q (mmol g<sup>−</sup>1) is the adsorption capacity, qsat (mmol g<sup>−</sup>1) is the equilibrium uptake capacity of the gas species, P is the system pressure (kPa), and kl: isotherm constant related to the energy of adsorption

The two main factors of Equation (1) were estimated from experimental data and used to establish the model fit of the data to the isotherm. The applicability of the isotherm is typically related to another factor that is associated with the Langmuir model, as described in Equation (2):

$$\mathbf{R}\_{\rm l} = \frac{1}{1 + \mathbf{k}\_{\rm l} \mathbf{P}} \tag{2}$$

The value of the separation factor Rl is indicative of the ability of the model to fit the experimental data.

The Freundlich isotherm, on the other hand, is based on the assumption of multilayer adsorption with various adsorption energies [35]. In this model (Equation (3)), the increase in the pressure of the system increases the uptake capacity of the adsorbent.

$$\mathbf{Q} = \, \mathbf{k}\_{\mathbf{f}} \mathbf{P}^{\mathbf{h}} \tag{3}$$

where kf is the Freundlich constant and n is a constant. A value of n lower than 1 is indicative of chemisorption rather than physisorption.

Although both models are widely used in many applications, their ability to fit the experimental data in a wide range of applications is limited in systems related to adsorption of many hydrocarbons. Accordingly, hybrid multiconstant models that are based on the two models have been used with better representation of the adsorption of hydrocarbons on solid materials.

The Sips model is an isotherm derived from both Langmuir and Freundlich isotherms and is presented in Equation (4) [10]:

$$\mathbf{Q} = \ \mathbf{q}\_{\rm sat} (\mathbf{k}\_{\rm s} \mathbf{P})^{1/\rm m} / (1 + \mathbf{k}\_{\rm s} \mathbf{P})^{1/\rm m} \tag{4}$$

where ks is Sips constant and m is a constant that represents deviation from ideal heterogeneity of the adsorption system and is typically considered as intensity factor with values above 1 indicative of a heterogeneous adsorption. Equation (4) reduces to its Langmuir form (Equation (1)) in cases when m equals unity. The Sips model is known to be best applied in cases where the system operates at higher-pressure conditions. The Toth isotherm [36] (Equation (5)), on the other hand, is another hybrid combination of the Langmuir and Freundlich isotherm that is reported to have better data fitting in applications at a wider variety of pressures compared to the Sips model.

$$\mathbf{Q} = \mathbf{q}\_{\text{sat}} \left\{ \left( \frac{(\mathbf{k}\_t \mathbf{P})^n}{\left(1 + \mathbf{k}\_t\right)^n} \right) \right\}^{\frac{1}{n}} \tag{5}$$

where kt and n are Toth constants specific for adsorbate-adsorbent pairs, while n indicates the affinity of the adsorption. A value of n close to 1 is an indication of the system heterogeneity. As with the Sips model, a value of 1 reduced the Toth equation back into Langmuir isotherm. The applicability of this model in a good range of system pressure application resulted in its wider application in gas solid adsorption systems.

Statistical analyses were used to evaluate the fit of the experimental data to the various models. The most reported parameter used is based on the average absolute relative deviation (AARD), coefficient of determination (R2) (Equations (6) and (7), respectively).

$$\text{AARD}(100\%) = \frac{100}{\text{N}} \sum\_{i=1}^{\text{N}} \left| \frac{\text{Q}\_{\text{exp}} - \text{Q}\_{\text{pred}}}{\text{Q}\_{\text{exp}}} \right| \tag{6}$$

$$\mathbf{R}^2 = 1 - \frac{\sum\_{i=1}^{N} \left( \mathbf{Q}\_{\text{pred}} - \mathbf{Q}\_{\text{exp}\text{i}} \right)^2}{\sum\_{i=1}^{N} \left( \mathbf{Q}\_{\text{pred}-\text{i}} - \overline{\mathbf{Q}}\_{\text{exp}} \right)^2} \tag{7}$$

where Qpred is the predicted amounts, Qexp is the values of Q obtained experimentally, and N is the number of the experimental data points used in the isotherm fit.

#### *3.2. Isosteric Heats of Adsorption, IAST Selectivity and Adsorption Kinetics*

The isosteric heat of adsorption makes it possible to characterize the surface properties of adsorbents, catalysts, and other materials, and provides information on the homogeneity and heterogeneity of surface. The calculation of the isosteric heats of adsorption (Qst (kJ mol−1)) is essential for an understanding of the strength of the interactions between the solid surface and the adsorbate in addition to any energetic heterogeneity in the solid surface. The calculations are typically based on the fundamental Clausius-Clapeyron equation:

$$\mathbf{Q}\_{\rm st} = \mathbf{R} \mathbf{T}^2 \left( \frac{\partial \ln \mathbf{P}}{\partial \mathbf{T}} \right)\_{\rm qsat} \tag{8}$$

where P and T are the system pressure and temperatures and qsat is the saturated equilibrium uptake amount (mmol g<sup>−</sup>1).

To assess the selectivity and feasibility of the separation, the IAST selectivity was considered for C3H4/C3H6 gases on the two metal organic frameworks employed in this study. The IAST calculations facilitate the study of the selectivity in binary gas mixtures. A full mathematical description is available elsewhere [6,10,37,38].

Adsorption kinetics is fundamental for engineering evaluation of adsorption systems. Typically, models derived from Fick's law of micropore diffusion are employed to model adsorption uptake curves via the calculation of the intercystalline diffusivity (Dc) [10]. An analytical solution of the equation based on the assumption of approximate cylindrical geometry of the solids is given as:

$$\frac{\mathbf{q}}{\mathbf{q}\_{\infty}} = 1 - \sum\_{\mathbf{n}=1}^{\infty} \frac{4\alpha (1+\alpha)}{4 + 4\alpha + \alpha^2 \beta\_{\mathbf{n}}^2 \exp\left(-\frac{\mathbf{D}\_{\tilde{\mathbf{c}}}}{\mathbf{r}\_{\tilde{\mathbf{c}}}^2} \beta\_{\mathbf{n}}^2 \mathbf{t}\right)}\tag{9}$$

where q∞ is the equilibrium adsorbed amount (mmol g<sup>−</sup>1), t is the time (s), and constants α and β are calculated as detailed in [10].

#### **4. Results and Discussion**

#### *4.1. Adsorbent Characterization*

The SIFSIX and NbOFFIVE metal organic frameworks were synthesized and characterized as described in our earlier work [34]. Figure 2 offers some of the main characteristics obtained, including SEM, FTIR, N2 adsorption desorption, and TGA analysis. In addition, Table 1 presents the estimated surface area and pore volumes. Thermal stability is essential for proper application of microporous materials in separation processes. The stability of the prepared materials was tested in a harsh temperature environment, i.e., up to 750 ◦C, by thermogravimetric analysis in the presence of nitrogen gas. The TGA isotherms are given in Figure 2i for both sorbents and represent the change in the weight of the material at elevated temperatures. A steep change in the mass of the adsorbent indicates a less stable structure and the possibility of material deterioration at higher temperature settings. At 280–300 ◦C, both materials underwent between 10–15% decrease in mass. The decrease was much steeper in the case of SIFSIX compared to NbOFFIVE at temperatures above 300 ◦C. The results of TGA obtained in our study were in good agreemen<sup>t</sup> with those reported in Bhatt [39] and Kumar [40]. The initial loss of mass is usually due to the evaporation of free water and other volatile compounds. A large drop in mass at elevated temperatures, as is the case in SIFSIX, may result in the decomposition of the material and the loss of wall and structural integrity [30,35]. The interactions between the different functional groups in a material can clarify the gas uptake. FTIR spectroscopy (Figure 2ii) was recorded in the range of 400–4000 cm<sup>−</sup>1. For NbOFFIVE-1-Ni, the peaks at 3221, 1615, 1402, and 465 cm<sup>−</sup><sup>1</sup> most likely correspond to the characteristic nickel O–H stretching. A SEM micrographs for the two prepared materials (Figure 2iv) showed multisized agglomerations in both materials with the pore size in the range of 100–600 nm. Voids are clearly present between the uniform particles. The porous nature of the materials was tested using N2 adsorption.

A significant difference in pore size and volume (Figure 2iii) was found between the SIFSIX and NbOFFIVE; both were higher for SIFSIX. The pore size for this compound was nearly 2.6 times higher than that recorded for the Nb MOF (Table 1), indicating a more enhanced surface area and porosity, and the formation of a well-defined structure [17]. The shape of the adsorption and desorption isotherms (depicted in Figure 2iii) clearly indicated a reversible Type-I isotherm in accordance with IUPAC categorization. This type indicated the formation of uniform narrow mesopores and a wider distribution of the pores [10,36,41]. The initial steep rise in the N2 adsorption–desorption isotherm at a low relative pressure (P/Po less than 0.001) is typically associated with the formation of microporosity. The high-adsorbed volume values (Figure 2iii) at relative pressures higher than 0.8 have been attributed to the N2 capillary condensation in the antiparticle pores, and may indicate expandable pores and a flexible structure which may lead to what is known as gate-opening effect [35]. The N2 adsorption–desorption isotherms did not indicate the presence of a clear hysteresis loop at low P/Po ratio. A slight hysteresis effect was present at higher P/Po ratio.

**Figure 2.** Characterization results for SIFSIX-3-Ni and NbOFFIVE-1-Ni; (**i**) TGA; (**ii**) FTIR; (**iii**) N2 adsorption/desorption; (**iv**) SEM images (**a**) NbOFFIVE-1-Ni, (**b**) SIFSIX-3-Ni.

It has been reported that the separation of C3H6/C3H8, for example, is dominated by size selection separation [1]. It is hence expected that the separation of C3H4/C3H6 will follow a similar mechanism as in both cases of fluorinated metal organic frameworks (NbOFFIVE and SIFSIX were deployed under similar experimental conditions). The restrictive pore size of the metal organic frameworks due to the prevention of the pyrazine moieties (Figure 1) affects the size selection between gas species. From the N2 adsorption data, BET areas were estimated to be 248 and 368 m<sup>2</sup> g<sup>−</sup><sup>1</sup> for NbOFFIVE and SIFSIX, respectively (Table 1). The experimentally obtained total pore volumes were 0.095 and 0.167 cm<sup>3</sup> g<sup>−</sup><sup>1</sup> for NbOFFIVE and SIFSIX, respectively.

#### *4.2. C3H4/C3H6 Uptake and Separation*

The potential of using the microporous metal organic frameworks for the selective adsorption–desorption and molecular interactions and binding nature of propyne over propylene at low pressure ranges (up to 100 kPa) and various temperatures was investigated. The results are presented in Figures 3 and 4. Figure 3a,b depicts an example of adsorption and desorption gas uptake for both adsorbents at a range of pressures up to 100 kPa. The figure shows the adsorption at 300 K as an example. Similar trends were obtained at different temperatures. The figure clearly reveals that different uptake values can be obtained in the case of propyne and propylene, indicating an effective separation due to the differences in the uptake values and steepness of the isotherms obtained. Both figures clearly show that propyne is adsorbed in a larger amount at a given pressure in comparison to propylene. A maximum uptake value of 3.28 and 2.99 mmol g<sup>−</sup><sup>1</sup> was obtained for propyne on SIFSIX-3-Ni and NbOFFIVE, respectively at 300 K. The maximum absorbed values for propyne were lower than those for propyne on both adsorbents, as can be seen from Figure 3a,b. Values of 2.9 and 2.39 mmol g<sup>−</sup><sup>1</sup> were obtained for propylene on SIFSIX and NbOFFIVE, respectively. The C3H6 and C3H4 values on the SIFSIX were higher than those recorded for the NbOFFIVE-1-Ni for the entire pressure range at a given temperature. It is also evident that the difference in the adsorption of C3H4 and C3H6 on SIFSIX was wider (Figure 3a) than that obtained on the NbOFFIVE MOF (Figure 3b). This indicated that the separation of propyne from C3H6 on the SIFSIX was more effective than that on the NbOFFIVE based MOF, and provides evidence of the potential for C3H4/C3H6 separation applications. A value of 2.85 mmol g<sup>−</sup><sup>1</sup> was reported for SIFSIX-3-Ni at 298 K for propylene [42]. The anion pillar NbOF5 2− is bulkier than SiF6 2− and has longer F-Nb bond length (1.89 compared to 1.68 Å for SIFSIX), resulting in a thinner and longer pore space (4.66 × 7.88) which leads to lower propyne capacity [18]. This led us to conclude that small changes to the pore structure can have a major influence on the selectivity and absorbability of the adsorbate on the selected MOFs.

In addition, study of the adsorption–desorption behavior for propyne and propylene for both adsorbents (Figure 3) was important to establish the reversibility (regeneration ability) for the adsorbents. It is clear that both adsorbent isotherms show reversibility upon uptake of propyne and C3H6 gases. It is also evident that the hysteresis effect is more pronounced in propyne adsorption for both sorbents compared to that for C3H6. This indicated a strong affinity and molecular interactions between C3H4 molecules and the structure of the sorbents. A less defined hysteresis effect is realized in the case of propylene adsorption on both solids. A similar effect was reported in a recent study by Lin et al. [42]. Li et al. [4] reported that some metal organic frameworks such as SIFSX-1-Cu, SIFSIX-2- Cu-i, ELM-12 have a strong interaction with C3H4 at pressures less than 20 kPa. These interactions were exhibited in a steep adsorption uptake isotherm at a fixed temperature over propylene with the reported benchmark uptake values [4]. One issue related to the aforementioned materials is that their pore sizes were large, allowing the passage of both gases, and hence reducing their potential selectivity.

The effect of temperature on the adsorption of C3H4 and C3H6 on both MOFs is given in Figure 4. Temperatures in the range of 300–360 K were used for pressures up to 1 kPa. It can be seen from Figure 4a–c that the temperature has a profound impact on the removal and uptake rate for all adsorbents. It is clearly shown that the uptake of the gases is lowered by the elevation in temperature. Other adsorption systems such as C3H6 and C3H8, as reported in studies, showed similar trends with respect to uptake values vs. temperature [10]. No other studies have shown the full experimental isotherm results for propyne and C3H6 systems. In all cases, the adsorption of C3H4 is higher than that for propylene at all temperature ranges and in both adsorbents. In addition, SIFSIX outperformed NbOFFIVE for the selectivity of C3H4. It can also be noted that a steep increase in the adsorption capacity at the lower pressure range is more apparent in the case of C3H4 and SIFSIX combination at all temperature ranges in comparison with the other adsorbent/adsorbate systems (Figure 4a). A similar result was reported, but

in the C3H6 and C3H8 systems on different metal organic frameworks [10]. To facilitate a good comparison, Figure 4c also shows experimental uptake isotherms at a selected temperature for both adsorbents and adsorbate systems. The superior uptake capacity of SIFSIX for propyne is evident, especially at low-pressure ranges (<20 kPa), indicating a strong interaction between the SIFSIX and C3H4. Comparisons between the uptake capacity and those published in the literature are presented in Table 2. This higher affinity and uptake values may also be related to the better BET surface area and pore structure of the SIFSIX compared to NbOFFIVE metal organic frameworks (Table 1). Figure 4c shows that the gap between the two isotherms for C3H4 and C3H6 are larger in SIFSIX compared to that in NbOFFIVE. A marked gap means that the separation is feasible for this system, and will be further studied via IAST analysis. The kinetic diameter of the molecule will have a major effect on the selectivity of one gas over another. Propyne is a linear molecule (4.16 × 4.01 × 6.51 Å), while C3H6 is a larger molecule which is typically curve-shaped with 4.64 × 4.16 × 6.44 Å [4]. Irrespective of the linear shape, the existence of the methyl group in both gases makes their kinetic diameters quite close (4.2 and 4.6 Å for C3H4 and C3H6, respectively). This small difference is one of the main reasons for the difficulty and energy intensity of their separation. SIFSIX and NbOFFIVE have a range of reported dimensions, depending on methods of preparation, post-treatment and experimental conditions, (Table 1), which clearly indicates that SIFSIX is more suited for the adsorption of C3H4 from C3H6. A micropore analysis of the SIFSIX and kinetic diameter (average 4.2) will allow both C3H4 and C3H6 to enter the pores. Nonetheless, it seems that a large number of anions (SiF6<sup>2</sup>−) in the pores and channels of the framework [4] provides a better binding ability for alkynes, as compared to alkenes, creating a preferred sieving effect towards propyne. This results in the excellent selectivity and separation ability of SIFSIX compared to NbOFFIVE. The maximum equilibrium adsorption value reported here for the SIFSIX MOF was higher than that reported for the same material and C3H4 separation (1.87 mmol g<sup>−</sup>1) [4]. The difference may be attributed to the different *v*/*v*% ratios used in the reported study. In addition, the value recorded in our work is similar to the benchmark uptake value reported for UTSA-200 ([Cu(azpy)2(SiF6)]n; azpy = 4,4-azopyridine) in a recent work by Li et al. (4). The main reason for the good reported selectivity is the small aperture size of the UTSA-200 (3.4 Å), meaning that size exclusion is the only dominating mechanism in this case, compared to stronger interactions between SIFSIX and the C3H4 gas. Yang et al. [18] reported that the precise tuning of the size of the inorganic anion hybrid ultramicroporous materials based on SiF6<sup>2</sup>− and NbOF5<sup>2</sup>− serves as a single molecule trap for propyne.

**Figure 3.** (**a**) adsorption/ desorption of C3H4 on SIFSIX-3-Ni at 300 K and (**b**) adsorption/ desorption of C3H6 on NbOFFIVE-1-Ni at 300 K.

**Figure 4.** Full experimental isotherms at different temperatures (300–360 K) (**a**) C3H4 and SIFSIX-3-Ni (**b**) C3H6 and SIFSIX-3-Ni (**c**) C3H4 and NbOFFIVE-1-Ni (**d**) C3H6 and NbOFFIVE-1-Ni.


**Table 2.** Uptake adsorption values reported in the literature.

#### *4.3. IAST Selectivity and Isosteric Heats of Adsorption*

Figure 5a shows the isosteric heats of sorption (Qst) as a function of uptake amounts of propyne and propylene. The trends in Figure 5a clearly indicate that the Qst of C3H4 is higher than that for C3H6 for both SIFSIX and NBOFFIVE metal organic frameworks. A higher Qst value is indicative of strong affinity and interactions between the solid pore structure and the gas being adsorbed. At zero uptake, the maximum value of Qst is attained. For SIFSIX and C3H4 system, the Qst zero was around 45 kJ Kmol−<sup>1</sup> and for propylene system, the maximum value was around 30 kJ Kmol−1. Similar trend was observed in the case of NbOFFIVE with the gas systems where isosteric heats of adsorption at zero uptakes were 38 and 30 kJ Kmol−1, respectively, for propyne and propylene systems. In both cases, the values of Qst at zero coverage were higher for C3H4 than for C3H6, indicating a stronger affinity and interactions between the C3H4 molecules and the MOF structures. In addition, the value for propyne for the SIFSIX is higher than that obtained for NbOFFIVE, also indicating the stronger affiliation and intermolecular interactions between the SIF and propyne gas. In addition, the general trend for all cases is that Qst decreases gradually with the increase in uptake rate of the gases on the pore structure of the solids. The continuous decrease at a similar rate indicates the homogeneity of the pore environment. Typically, as Qst increases with higher uptake rates, heterogeneity of the surface is usually present [10]. In addition, the differences between the propyne and propylene for both solids is a good indication of the separation possibilities of the two gases.

**Figure 5.** (**a**) Isosteric heats of sorption for SIFSIX and NbOFFIVE metal organic frameworks for both C3H4 and C3H6 as a function of adsorption uptake, (**b**) IAST selectivity for C3H4/C3H6 system on both adsorbents at 300 K.

To assess the separation ability of the two compounds, the selectivity (a key factor and application index for industry) of the ideal adsorbed solution theory (IAST) were calculated and are presented in Figure 5b for 10/90 *v*/*v* binary gas mixtures of C3H4 and C3H6 at 300 K. The IAST is typically employed, as the isotherms for binary systems of gases are difficult to measure. In the IAST estimations, it was assumed that the gas species had formed an idea mixture. This approximation has been used in many studies of metal organic frameworks and different gas species. Full details on the and mathematical treatment of Raoult's law are given elsewhere [10]. As indicated in Figure 5b, the selectivity of propyne over propylene for both metal organic frameworks was higher at lower pressure operations compared to pressures above 20 kPa. In some studies using different flexible structures, metal organic framework trends for propane/propylene adsorption, for example, showed higher selectivity at pressures above 60 kPa, indicating increased adsorption due to the "gate opening" effect of the MOF structures used [10]. The trend observed in this investigation led us to the conclusion that the structure of the used metal organic frameworks did not change with an increase of pressure in the range used in this study. In addition, the SIFSIX showed a higher selectivity between the two gases compared to those found for NbOFFIVE. As there is no published data on the selectivity of the gases and MOF combinations used, it is difficult to draw comparisons with other works. However, the trends reported here lean towards the conclusion of the size sieving effect and strong interactions between the propyne and SIFSIX at low pressure range. A Qst value of 68 kJ mol−<sup>1</sup> at 0.003 bar was reported by Yang et al. [18] for SIFSIX, and was attributed to the effect of single-molecule trap and the strong interaction between the MOF and the gas molecules.

#### *4.4. Modeling of the Equilibrium and Kinetic Adsorption for C3H4/C3H6 on Metal Organic Frameworks*

Experimental data were fitted to isotherms in an effort to help predict the general behavior of the adsorbent adsorbate interactions and uptake values. Isotherms were divided into one-parameter isotherms, such as Langmuir and Freundlich, or a multicontent hybrid combination of the two models such as the Sips and Toth models, as explained in an earlier section. The affinity of the system for adsorption was indicated by the value of the calculated constants. In the case of Langmuir and Freundlich, the linearized form of the Equations (1) and (3) is used to estimate the equilibrium adsorption uptake amount (qsat) under a given pressure and temperature system. It is also related to the maximum adsorbed amount Q. The experimental results obtained for both metal organic frameworks and the two gases were analyzed by regression analyses, and all model fits are represented in Figure 6. In the Freundlich model, a value of 1/n close to zero indicates a heterogeneous surface, while a value of n greater than 1 indicates strong affinity [41]. From the trends shown in Figure 6a,b, it can be seen that the two linearized models did not represent the adsorption data well, as reflected by the lowered AARD (Table 3) for the range of pressures for the SIFSIX and propyne systems. Having said that, both the Freundlich and Langmuir models represented the data between the other adsorbent adsorbate combinations. This may have been due to stronger monolayer type interactions between the propyne and SIFSIX compared to the NbOFFIVE gas system. Even in the case of propylene and SIFSIX, both isotherms managed to represent the data in a more accurate manner. It can also be seen that both models underestimated the experimental uptake data in most cases. This was more apparent at higher pressure regions, especially in the Nb gas adsorbent-adsorbate systems. Apart from SIFSIX/propyne, the isotherm models represented the data at lower pressure ranges. The Sips (combined Langmuir and Freundlich isotherm) and the Toth model regression fitting are given in Figure 6c,d. Both models offered a better fit of the experimental data over the entire range of pressures. Again, it can be seen that in the case of the SIFSIX and propyne combination, the Sips model was less accurate compared to the Toth model.

In addition to equilibrium and selectivity studies, information related to the adsorption system kinetics is key in designing of adsorption systems. The most reliable method of addressing the transient uptake curves is to use micropores diffusion models that are based on Fick's law of diffusion (Equation (9)). The modeled data are given in Figure 7, where the fractional uptake ratio is expressed as a function of time (solid lines are model-estimated values). It can be seen that the model fit the adsorption uptake data well at all combinations of metal organic frameworks and gases, indicating a diffusion based process. It can also be seen that the model fits the propyne and SIFSIX combination best. This was expected, given the availability of passage through the SIFSIX structure due to the suitability of the kinetic size of both the adsorbent and adsorbate. From Equation (9) and upon fitting of the experimental data, the values of Dc/rc 2 were calculated and are reported in Table 3. It can be seen from Figure 7 that the value of the time constant of micropore diffusion Dc/rc 2 increased with increase in temperature. In addition, the propyne time constant was smaller than that of propylene for both adsorbents owing to the ease of diffusion due to the size acceptance of propyne compared to that of propylene.

**Figure 6.** Fitted adsorption isotherms at temperatures of 300 K (**a**) Freundlich, (**b**) Langmuir, (**c**) Sips, (**d**) Toth.

**Figure 7.** Fractional adsorption rate for C3H4/C3H6 on SIFSIX-3-Ni and NbOFFIVE-1-Ni.

#### *4.5. Breakthrough and Cyclic Breakthrough Experiments*

To confirm the validity of the kinetic effect and the ability and extent of the separation on the SIFSIX and NBOFFIVE metal organic frameworks, studies on binary mixtures of C3H4/C3H6 (10/90 *v*/*v*) were conducted. It can be clearly seen from the trends in Figure 8a that the heavier propylene molecules were eluted first from the column, in contrast to the lighter propyne molecules, upon adsorption on SIFSIS-3-Ni. Similar trends were found for the Nb gas combination (not shown). This also confirms earlier findings about the stronger bindings and affinities found between propyne and the SIFSIX adsorbent. The trends (Figure 8a) show that the breakthrough for propylene occurs after nearly 4–5 min and yields a 99.98% purity gas, while propyne was slowly eluted and becomes detectable in the outgas after nearly 16 min. This confirms the suitability of SIFSIX for the appropriate separation of C3H6/C3H4 systems. Accordingly, high purity propylene gas can be effectively separated and collected within the 10-min gap between the breakthrough of propyne and propylene from the column confirming the potential application of SIFSIX-3-Ni for the separation. Effective durability and recyclability are very important parameters in the selection and operation of adsorbent in gas separations. Eight cycles of adsorption and regeneration were conducted in order to examine the recyclability of the adsorbents and its effectiveness in repeated application. After each breakthrough test, the experimental breakthrough column was simply heated to around 423 K for 20 min [44] to allow the desorption of the gas adsorbed in the solid. Figure 8b shows the uptake ratios for eight consecutive cycles using the same experimental condition and adsorbent-adsorbate combinations. As can be seen, the adsorption capacity of the solids was not accepted with repeated use, confirming the suitability of solids for potential C3H4/C3H6application.

**Figure 8.** (**a**) Dynamic breakthrough curves for the SIFSIX and NbOFFIVE and C3H4/C3H6 systems at 300 K (4 cycles are shown); (**b**) uptake amounts of C3H4/C3H6after 8 adsorption cycles at 300 K.


**Table 3.** Modeling isotherm statistical parameters, isosteric heats of adsorption and micropores diffusion time constants for MOFs and C3H4/ C3H6 at 300 K.
