A review of the features and applications of ZIF-8 and its derivatives for separating CO 2 and isomers of C 3 - and C 4 - hydrocarbons

frameworks-8


Introduction
In recent years, zeolitic imidazolate frameworks (ZIFs) have developed rapidly.Their structures are generated according to tetrahedral units where every metal ion (M) attaches to four organic imidazolate (Im) linkers (M− Im− M).Indeed, ZIFs are considered as a sub-family of MOFs, and their topology has been similar to that of zeolites (Song et al., 2012).ZIFs combine the advantages of both MOFs and zeolites since they have properties of these two materials such as crystallinity, porosity, and enthralling chemical and thermal stability (Sankar et al., 2019;Zou et al., 2018a).Moreover, ZIFs are considered as attractive candidates for several applications in gas separation by adsorption or in membranes, in sensing and in catalysis (Chen and Wang, 2020;Matsuoka et al., 2018;Samadi-Maybodi et al., 2015;Awadallah-F et al., 2019a).This advantage was ascribed to their excellent properties, including their high surface areas, microporous structures, chemical and thermal stabilities (Park et al., 2006); and synthesis controllability due to their structural flexibility, which leads to a sensible design of both their pore sizes and surface functionality.Therefore, special properties and applications of the ZIF family are under heavy research, where zeolitic imidazolate framework-8 (ZIF-8) is the most popular and classic member of this family.An advantage of ZIF-8 nanoparticles is their excellent stability that enabled long term operation (Yuan et al., 2017).
Zeolitic imidazolate framework-8 (ZIF-8) (Zn(mIm) 2 , where mIm is the 2-methylimidazolate) displays a solidate (SOD) topology (Fig. 1) that features a space group of interconnected six membered ring windows with an accessible diameter and pore width of 3.4 Å and 11.6 Å, respectively (Park et al., 2006;Banerjee et al., 2008;Sze Lai et al., 2014a).ZIF-8 contains 276 atoms in each unit cell.It crystallizes in cubic space group I43m with a lattice constant of 16.992 Å (Awadallah-F et al., 2019a;Huang et al., 2006).ZIF8 and its derivatives have a highly stable structure and play an important role in promising membranes for gas separation processes.Due to its robustness and good separation ability, many researchers have conducted further studies on it.(Song et al., 2012;Awadallah-F et al., 2019a;Awadallah-F et al., 2019b;Awadallah-F et al., 2019c).
Recent advancements in the chemical and petrochemical industries led to the development of various methods and technologies for gas separation.Due to its widespread use, the global demand for high-purity gas is growing rapidly.Gas separation has a potential impact on the chemical processing industry.Therefore, many separation processes and techniques have been used for gas separation.Table 1 summarizes the most important methods and points out their advantages and disadvantages.The innovation of gas separation through adsorption technology is related to the discovery of new adsorbents, such as organometallic frameworks (MOFs), especially zeolite imidazole frameworks (ZIFs), which have excellent thermal and chemical stability, and have microporous voids, leading to the large-scale industrial application of ZIFs (Wang et al., 2016;Neelakanda et al., 2016;Melgar et al., 2015;Bernardo et al., 2009;Pullumbi et al., 2019;Wankat, 1991).
Understanding how ZIF-8 interacts with alkanes is vital for its further development and commercialization in a wide range of applications.Applications of ZIF-8 materials are emerging due to their high porosity and stability, adjustable compositions and structural flexibility (Ma and Liu, 2019;Zou et al., 2018b).Both pristine ZIF-8 and its derivatives were developed as multifunctional materials making them attractive candidates for various applications such as environment protection (Pillai et al., 2019;Chen et al., 2019;Yoo et al., 2020), separations (Matsuoka et al., 2018); (Awadallah-F et al., 2019a;Awadallah-F et al., 2019b;Awadallah-F et al., 2019c), catalysis (Chen and Wang, 2020;Payra et al., 2020), sensing (Samadi-Maybodi et al., 2015), electronics (Aboraia et al., 2020) and drug delivery (Chen et al., 2018).In this section, attention will be focused on the gas separation.Indeed, ZIF-8 materials have a high potential in gas separation due to their highly porous structure.Moreover, gas separation can be affected by several factors such as ZIF-8 nanoparticle characteristics; including pore sizes, chemical modification, loading percentage and structure and fabrication conditions (such as method, temperature, time, …etc.) (Gong et al., 2017).
In this review, we analyze and summarize the recent research developments of ZIF-8 materials and its derivatives as well as their applications, especially for CO 2 gas separation.This review consists of different aspects including synthesis procedures to generate ZIF-8 nanomaterials, common characterization techniques and a summary of their main applications in several significant areas.Finally, it gives the latest research on the hydrocarbon adsorption by ZIF-8 and doped ZIF-8, along with new correlations of their corresponding adsorption isotherms.The notion of gate-opening pressure (P 0 ) of ZIF-8 and its derivatives for the adsorption and separation of various gases was well discussed and evaluated basing on statistical physics approach.Indeed, the present review focuses not only on the experimental point of view of ZIF-8 and its derivatives as proved by other review works (Feng et al., 2021;Li et al., 2021;Chen et al., 2014;Sze Lai et al., 2014b), but it also highlights the theoretical approach applied to ZIFs.To the best of our knowledge, the statistical physics theoretical approach was applied for the first time on Zeolitic Imidazolate Framework (ZIF) membranes applications while attempting to consider the effect of nanogate opening pressures.

Separation method/ technology
Advantages Disadvantages

Absorption by Solvents
High recovery rate of separation     framework (ZIF) requires complicated and long steps (Park et al., 2006).Generally speaking, smaller and uniform crystals with a thinner size distribution have been discovered by microwave-assisted methods, which are very desirable for some useful applications (Lucero et al., 2019).Bao et al. (2013) shows that the samples produced by the hydrothermal method have irregular shapes and variable particle sizes.However, a homogeneous sample having a hexagonal shape and an average particle diameter of about 0.350 μm was obtained by the microwave radiation synthesis method.On the other hand, the average particle size is affected by other synthesis conditions, such as Zn:2MeIm molar ratio, solvent, reaction temperature, irradiation time, precursor concentration, pressure, and mixed metal content (Fu et al., 2018;Muñoz-Gil and Figueiredo, 2019;Dunne et al., 2015).

Common characterization techniques
Various techniques were used to characterize the synthesized ZIF8 material in the goal to study the structure, morphology, physicochemical properties and thermal stability of the material.

Crystal structure prediction
The crystal structure and purity of ZIF8 can be demonstrated by characterization experiments using single crystal X-ray diffraction (XRD) methods.The high crystallinity of the produced ZIF8 material originates from the (001) very sharp peak at 2θ = 7.36 • (Samadi- Maybodi et al., 2015;Li et al., 2019;Duan et al., 2020).Moreover, from the XRD pattern, the particle size distribution could be estimated based on Scherrer Equation (Lai et al., 2016).Fig. 3 (A) shows an X-ray diffraction analysis of ZIF-8 that was synthesized with methanol and dimethylformamide solvents as denoted, respectively, by Z-A(MeOH) and Z-B (DMF) (Du et al., 2019).Indeed, high crystallinity of both samples was deduced from the diffraction peak (011) at 2θ = 7.36 • .However, Z-B (DMF) has higher symmetric planes since its diffraction peaks intensity is higher compared to those of Z-A(MeOH), which indicates the effect of solvent in ZIF-8 synthesis.On the other hand, Lai et al. (2016) have studied the temperature effect from 80 • C to 140 • C, where XRD characterization leads to detecting the higher crystallinity of ZIF-8 synthesized at 120 • C and 140 • C (Fig. 3 (B)).Indeed, to generate a supersaturation condition for the formation of ZIF-8 during a small period time (0.5 h), a lower temperature of 100 • C is insufficient, which led to the absence of its characteristic peak.

Size and morphology-controlled nanocrystals
Scanning electron microscope SEM imaging was used to study the morphology and crystal size distribution as a function of synthesis conditions.Indeed, as shown in Fig. 4, the development of ZIF-8 crystals was established by time progressing from cubes displaying 6 {100} faces to rhombic dodecahedra displaying 12 {110} faces.Probably, the latter is being the most stable ZIF-8 equilibrium morphology (Schejn et al., 2014;Jing et al., 2020).Jian et al. (2015a) investigated the development of ZIF-8 crystals depending on synthesis time (Fig. 5 (A)).Bumpy spherical particle surfaces are detected at 5 min.The period that presents the metastable phase for ZIF-8 growth was achieved when time increasing to 20-60 min.Thereafter, crystals with heterogeneous hexagonal facets begin to display.Homogeneous surfaces with little defects were established for ZIF-8 crystals at 4 h.By increasing time up to 8 h, the formation of various little ZIF-8 crystallites was attained, whereas the quantity turned into trivial at 16 h.The mechanism of Ostwald ripening (Challa et al., 2011) allows to describe this phenomenon.The well-known typical morphology of ZIF-8 given by rhombic dodecahedron shape with 12 {011} surfaces was attended at 24 h.After 3 days, this equilibrium shape is preserved.Jing et al. (2020) showed that the morphology and the average particle size changed with molar ratio of Ag/AgCl co-doped ZIF-8 as shown in Fig. 5 (B).Indeed, an average size of 600 ± 24 nm was found after 24 h of reaction time for ZIF-8 nanoparticles with a rhombic dodecahedron shape (Fig. 5a (B)).A reduction of the ZIF-8 particle size to 550 nm was detected by the addition of 5 mmol of AgNO 3 with a well-defined truncated rhombic dodecahedral crystals (Fig. 5b (B)).When 10 mmol of AgNO 3 is added, ZIF-8 average particle size decreased to 400 ± 18 nm.Thereafter, little Ag/AgCl nanoparticles are created in ZIF-8 nanomaterials (Fig. 5c (B)).For a 15 mmol of AgNO3, the average size decreased to 300 ± 22 nm with a well-defined shrunken cubic crystals (Fig. 5d (B)).Finally, when adding 20 mmol of AgNO 3 , ZIF-8 particle size decreased to 200 ± 20 nm (Fig. 5e (B)).This same decrease of particle size has been also detected by Awadallah et al. (Awadallah-F et al., 2019a) in the case of Cu/ZIF-8, where the obtained nanocrystal size decreases following the increase of Cu 2+ percentage (Fig. 5 (C)).
In addition, it has been observed that by changing the molar ratio of 2-methylimidazole (Hmim)/zinc nitrate hexahydrate (Zn), the morphology and average size can also be changed (Jian et al., 2015a;Kida et al., 2013;Tanaka et al., 2012).Zhang et al. (2018) shows that ZIF-8 synthesized with a Hmim/Zn molar ratio of 1 has a cubic shape with particles sizes of 0.4 μm and 0.8 μm.When the Hmim/Zn molar ratios are greater than unity, the morphology of all samples changes to truncated rhombic dodecahedron or rhombic dodecahedron shapes.Furthermore, a decrease of average particle size from 1.0 μm to 0.1 μm was detected by increasing the Hmim/Zn molar ratio from 4 to 16, respectively (Zhang et al., 2018).

Chemical characterizations
Functional groups: The presence of an imidazole group and a Zn-N interaction was confirmed by Fourier-transform infrared (FT-IR) spectra of ZIF-8, which confirms that the synthesis of ZIF-8 crystals was succeeded (Samadi-Maybodi et al., 2015;Du et al., 2019;Binaeian et al., 2019).Indeed, for pure ZIF-8, peaks at 2920-3180 cm − 1 show the stretching of aliphatic and aromatic C-H of imidazole ring, respectively.The peaks for out-of-plane and in-plane bending of imidazole ring are below 800 cm − 1 and in the region of 900-1350 cm − 1 , respectively.The peak around 1600 cm − 1 is due to the C--N stretch mode, while the sharp peaks at around 1300-1500 cm − 1 were attributed to the stretching of the entire ring.Finally, the peak at 420 cm − 1 shows the stretching of Zn-N bond when the zinc atoms in ZIF-8 connect to the nitrogen atoms of 2-methylimidazole linker during ZIF-8 synthesis (Samadi-Maybodi  et al., 2015;Binaeian et al., 2019;Xu et al., 2019).

Physical properties through gas adsorption
Using surface area and porosimetry analyzers that involve N 2 adsorption-desorption isotherm measurement at 77 K, along with possibly built-in density functional theory (DFT) calculations, is an effective characterization method that can provide details on the physical properties of ZIF-8 such as its surface area, micropore volume, total pore volume, and pore size distributions.The nitrogen adsorptiondesorption isotherms of ZIF-8 show, generally, a type I isotherm as reported in several studies (Lai et al., 2016;Du et al., 2019;Zhang et al., 2019;Pan et al., 2011), representing a microporous structure.Fig. 8 (a) shows an example that represents this last behavior.Indeed, a microporous structure was confirmed by a rise in the adsorbed volume at very small relative pressures (Jian et al., 2015b).
Typical type-I isotherms were also obtained for samples ZIF-8, Zn/ Co-ZIF-8, and Cu/ZIF-8 (Fig. 8 (b)), which indicates the presence of almost full microporosity (Awadallah-F et al., 2019d).However, behavior variation of isotherms to type-IV was achieved for P/P 0 values above 0.95.This could be attributed to the intra-aggregate voids that cause the presence of some large pores (Awadallah-F et al., 2019d).
The physical properties were affected by the synthesis conditions.For example, the specific surface areas presented in   In the Raman spectra of ZIF-8 and Cu/ZIF-8 (Fig. 6(ii)), standard peaks for ZIF-8 material were observed (Awadallah-F et al., 2019a).Indeed, the shift of some peaks compared to the 2-methylimidazole molecule confirms the formation of the final product.reduction of the Hmim/Zn molar ratio from 70 to 10 leads to decreasing the BET surface area and the total pore volume of particles from 1126 m 2 g -1 to 0.57 cm 3 g − 1 to 31.9 m 2 g -1 and 0.15 cm 3 g -1 , respectively.This decrease was caused by the greater particle size distributions at little Hmim/Zn molar ratio.Khan et al. (2018) have confirmed that smaller particles have larger BET surface areas, higher micropore volumes, and larger external surface areas.
On the other hand, the effect of synthesis of ZIFs with pure or mixed metal and/or pure or mixed ligand on the physical properties has been reported in several studies (Awadallah-F et al., 2019b;Chen et al., 2018;Kaur et al., 2016;Botas et al., 2010;Caskey et al., 2008;Zhang et al., 2019;Liao et al., 2015).Synthesis of Cu 2+ /ZIF-8 nanomaterials with various doping percentages (1%, 5%, 10% and 25%) was studied by Schejn et al. (2015).Indeed, the physical properties of pure ZIF-8 (S BET = 1700 m 2 g -1 , V micro = 0.662cm 3 g -1 ) are shown to decrease only at a high doping percentage (25% of Cu 2+ ); whereas the pore size distribution is centered around 1.2 nm for all doping percentages of Cu, which agrees with that of the ZIF-8 (Jian et al., 2015a;Challa et al., 2011;Kida et al., 2013;Tanaka et al., 2012;Zhang et al., 2018;Binaeian et al., 2019;Xu et al., 2019;Schejn et al., 2015).Moreover, the decrease of both the specific surface area and pore volume when ZIF-8 is loaded with Ag/AgCl nanoparticles is probably associated to diverse catalytic extents of ZIF-8 as explained by Jing et al. (2020).Similarly, the ZIF-8 pore size did not change by Ag/AgCl loading since these nanoparticles were just inlaid in the body of ZIF-8 (Jing et al., 2020).
The temperature also has an effect onto the physical properties of ZIF-8 as described by Lai et al. (2016) for temperatures ranging from 80 • C to 140 • C. A successful synthesis of highly crystalline ZIF-8 was achieved at 120 • C with BET surface areas of up to 690.75 m 2 g -1 and micropore volumes of up to 0.32 cm 3 g -1 .

Separation of carbon dioxide (CO 2 ) gas
Effective CO 2 separation from other gases by adsorption or membranes is one of ZIF-8 advantages (Gong et al., 2017).Chi et al. (2015) investigated the CO 2 /CH 4 separation using mixed matrix membranes (MMMs) generated from poly(styrene-block-ethylene-ranbutylene-bloc k-styrene) (SEBS) with different particle sizes of ZIF-8 and a fixed loading of 30 wt%.This is the ideal ZIF-8 concentration that leads to a good gas separation performance as reported in the literature (Chi et al., 2015;Zornoza et al., 2011).Indeed, the selectivity of CO 2 /CH 4 separation is nearly independent of ZIF-8 particle sizes since the surface areas of particles remain constant; whereas the selectivity can be enhanced from 4.3 to 5.4 when adding ZIF-8 to the membrane (SEBS/ZIF-8 MMMS) compared to the neat polymer membrane (SEBS) (Chi et al., 2015).However, in a previous work (Zornoza et al., 2011) it is reported that ZIF-8 particle sizes could affect CO 2 /CH 4 selectivity since ZIF-8 adsorbents have different surface areas with different sizes.Furthermore, a theoretical investigation of H 2 separation from CO 2 was presented by Bayati et al. ( 2019) using a ZIF-8 materials.The ZIF-8 nanomaterials exhibited a high tendency for CO 2 adsorption, while the diffusion coefficient of H 2 was much higher than that of CO 2 .From a theoretical point of view, the obtained results prove that ZIF-8 has a H 2 /CO 2 permselectivity greater than 30 at relatively low pressures (below 300 kPa), and it decreases at higher pressures.This result was interpreted by the progressive decrease of CO 2 adsorption contribution at lower pressures.
A novel approach was developed recently for the gas separation of isomers that are typically challenging to separate (e.g., propane vs. propylene and n-butane vs. isobutane) based on the concept of their distinguished threshold of nanogate-opening pressure (P 0 ).After this pressure threshold, long-chained molecules (e.g., C 3 and C 4 hydrocarbons) start to adsorb onto ZIFs as studied by Awadallah et al. (Awadallah-F et al., 2019a;Awadallah-F et al., 2019c).Indeed, ZIF-8 (Awadallah-F et al., 2019a;Awadallah-F et al., 2019c) and Cu/ZIF-8 (Awadallah-F et al., 2019a) and Co/ZIF-8 (Awadallah-F et al., 2019c) samples seem to widen the opening of their nanogates (meaning six-membered rings) at different threshold pressures during adsorption of diverse long-chain gases (such as propane, propylene, isobutane and n-butane) to a point that enables each of these molecules to be adsorbed (Awadallah-F et al., 2019a).Adsorption of such hydrocarbons will not occur at any pressures below this threshold.Consequently, P 0 has an important role in gas separation phenomenon on ZIFs where its value differs for each gas on the same ZIF.As a result, the separation of isomers using ZIF-8 materials can be highly facilitated at intermediate pressure values between the P 0 values for the corresponding component.At such intermediate pressure (P), the component that has a P 0 value lower than P will be adsorbed, while that with a P 0 value higher than P will remain in the gas phase.
The values of P 0 were evaluated for each ZIF versus each gas by Awadallah et al. (Awadallah-F et al., 2019a) through fitting equilibrium adsorption data toward an empirical adsorption isotherm model that was modified from the Langmuir adsorption isotherm model to account for starting the adsorption process at such threshold pressures.On this basis, we seek in the next section to evaluate the P 0 value, with an understanding of framework responses and adsorption energetics against other theoretical adsorption isotherm models founded on a statistical physics approach, while respecting the author's permission (Awadallah-F et al., 2019a).Indeed, to the best of our knowledge, statistical physics theoretical approach was applied here for the first time on Zeolitic Imidazolate Framework (ZIF) membranes applications while attempting to consider the effect of nanogate opening pressures.

Correlation of adsorption data on ZIFs with nanogate opening pressures
An important number of investigations on ZIF-8 focused extensively on understanding how to correlate their experimental adsorption properties to theoretical methods such as molecular simulations (Krokidas et al., 2018), conventional molecular dynamics (Krokidas et al., 2017), DFT simulations (Hobday et al., 2018;Zheng et al., 2017), theoretical modeling (Awadallah-F et al., 2019a;Awadallah-F et al., 2019b;Awadallah-F et al., 2019c;Autie-Castro et al., 2017) … etc.The modeling of adsorption isotherms in gas or liquid phase adsorption is a powerful method for surface characterization (Al-Ghouti and Da'ana, 2020).Therefore, the fitting of experimental data by either theoretical or empirical models is necessary to investigate adsorption systems.Here, as an illustration, we present a combined experimental and computational approach to study the adsorption of small-to-medium sized molecules, especially of natural hydrocarbon gases by ZIF-8 (Awadallah-F et al., 2019a).
Table 4 shows theoretical models developed by our research group to account for the nanogate opening pressures for the adsorption of longchained molecules on ZIFs.These models include the Modified Langmuir Model (MLM), Modified Ideal Monolayer Model (MIMM) and the Modified Real Monolayer Model (MRMM) presented in Equations ( 1)-(3), respectively.The last two models (MIMM and MRMM) are based on a statistical physics approach.Indeed, the statistical physics approach gives a physical meaning to the model's parameters and allows to describe phenomena outside the realm of traditional physics (Khalfaoui et al., 2003(Khalfaoui et al., , 2015)).The main advantage of the MRMM with respect to the MIMM is that it takes into account lateral interactions between adsorbed molecules (Khalfaoui et al., 2015) and thus describes a closer reality.These two theoretical models (MIMM and MRMM) will be compared to the semi-empirical one (MLM, Equation ( 1)).Indeed, P 0 in Equation ( 1) is a novel parameter presented into Langmuir model (Langmuir, 1916(Langmuir, , 1918) ) by Awadallah et al. (Awadallah-F et al., 2019a;Awadallah-F et al., 2019c).This parameter is hypothetically introduced to represent the pressure threshold at which the ZIF crystal can adsorb the corresponding gas molecule where it is understood to widen its nanogate opening.According to this hypothesis, the same principle was applied to our two theoretical models (Equations ( 2) and ( 3)) by introducing the new parameter P 0 .
The determination of the models' parameters is performed by nonlinear regression based on minimising the sum of squared errors, which corresponds to the least sum of squared errors (LSSE), between

Table 4
Theoretical adsorption models developed to account for nanogate opening pressures.

Theoretical models
Equations Parameters References

Modified Langmuir Model (MLM)
Qa(mole /kg) is the adsorbed amount, P(Mpa) is the exposure pressure, mL is the monolayer adsorption capacity, bL is the adsorption affinity, P0(Mpa) is the gate-opening pressure, (Awadallah-F et al., 2019a)

Modified Ideal Monolayer Model (MIMM)
n is the number of adsorbed molecule(s) per site, Nm is the receptor sites density(mol/kg), α is defined as: α = p 1/2 − P0, where p 1/2 (MPa) is the half-saturation pressure, Khalfaoui et al. (2003) Modified Real Monolayer Model (MRMM) (3) b (MPa − 1 ) represents the covolume of the adsorbate molecule, a(J /MPa) is the corresponding molecular pressure cohesion, β is expressed as (1/kBT), where kB is the Boltzmann's constant and T the experimental temperature, w is the characteristic concentration which was related to the energetic parameter as: where pvs(MPa) is the saturated vapor pressure, R(J /K.mol) is the ideal gas constant, ΔE a (kJ /mol) is the adsorption energy and Zgtr is the translational partition function of an ideal gas molecule per volume unit,
the experimental and correlated data using the Solver add-in of Microsoft Excel (Microsoft Corporation, 2016).The LSSE is defined by where Q calc is the correlated adsorbed amount (theoretical isotherm), Q meas is the measured adsorbed amount, i is the data point number and j is the total number of data points.The corresponding errors were calculated based on the absolute relative error (ARE) (Kapoor and Yang, 1989):

Experimental adsorption isotherms
Experimental adsorption isotherm data of n-butane, isobutane, propane, and propylene onto pure and Cu/ZIF-8 nanomaterials at 25 • C are presented in Fig. 9 (Awadallah-F et al., 2019a).It is observed from this figure that all gases exhibit no adsorption where the pressure increases up to an intermediate value that is specific for each gas on each adsorbent, which is defined by P 0 .Indeed, when P is less than P 0 , the opening nanogate of the ZIF crystal is considered to be insufficient for the free passage of molecules which hinders their adsorption, and thus the adsorbed quantity is zero.After this intermediate pressure, the behaviour of the adsorption isotherms exhibit a type-I behaviour according to the IUPAC classification (Awadallah-F et al., 2019a;Sing, 1985) where a plateau was reached.This behaviour was attributed to a surface saturation condition, which indicates that mesopores are filled as proved by Boudjema et al. (2020).The different aspects detected for n-butane, isobutane, propane, and propylene adsorption were attributed to the stereochemistry of each gas (Awadallah-F et al., 2019a).
The values of nanogate opening pressures (P 0 ) for each gas is distinct on each adsorbent.Differences between P 0 values become more obvious for the Cu/ZIF-8, especially on Cu 30% /ZIF-8.Consequently, coper-doped zeolitic imidazolate framework-8 showed an interesting tool for gas separation (Awadallah-F et al., 2019a;Goyal et al., 2018) based on the differences between the P 0 values of different components on the same adsorbent.For instance, if the operation pressure is set between the P 0 values of two components, the component with the lower P 0 value will be adsorbed whereas that with a higher P 0 value will not be adsorbed.

Theoretical fitting
All fitting parameters retrievable by MLM, MIMM and MRMM models are illustrated in Table 5.They are analyzed to investigate the adsorption systems more deeply.Hence, the best fitting model assessment was based firstly on minimizing SSE error function and then evaluated based on the magnitude of the ARE values.The lowest ARE values were obtained using the MRMM model (Table 5), leading to select it as the best fitting model.Fig. 10 shows an example of experimental adsorption isotherm correlation of propylene onto Cu 10% /ZIF-8 using the three adsorption isotherm models (Equations ( 1)-( 3)).The best correlation between experimental isotherm and theoretical one is observed from MRMM.The better presentation of the MRMM model for experimental adsorption data exhibiting nanogate opening pressures can also be evidenced by its lower ARE values.Furthermore, the superiority of the MRMM model can be attributed to its ability to describe an intermediate adsorption process among the neighboring adsorbed molecules.Indeed, adsorbed molecules can establish attraction or repulsion force with the neighboring molecules, subsequently, adsorbate-adsorbate interactions cannot be neglected (Khalfaoui et al., 2015).Hence, the adsorbent surface chemistry plays an important role in the interactions kind involved in the adsorption process (Lin et al., 2015;Nakhli et al., 2020).As a result, in the next paragraph, we try to interpret some parameters related to the MRMM fitting of the studied systems.
Fig. 11 shows the evolutions of w and b parameters with P 0 of nbutane, isobutane, propane and propylene gases onto ZIF-8 and Cu/ZIF-8.Indeed, w is the characteristic concentration that varies inversely with the energetic parameter as presented by Equation (4) (Table 4), and b represents the covolume of the adsorbate molecule.It can be noticed that the same evolution behavior has been detected for both w and b parameters with P 0 .Moreover, the same evolution was also detected following the values of w and molecular pressure cohesion (a) parameters with P 0 (Table 5).Consequently, it can be concluded that the higher covolume of adsorbate molecule and the higher molecular pressure cohesion led to the lower adsorption energy.Indeed, the change of parameters b and a could be attributed to the stereochemistry of each gas (Awadallah-F et al., 2019a) that affect the adsorption energy.
The adsorption energy is an important parameter that leads to a better understanding of the results obtained by Awadallah et al.Awadallah-F et al., 2019a).These authors have shown the importance of P 0 parameter in relation with gas separation performances.Indeed, P 0 values were found to be the same for both n-butane and isobutane couple in the case of ZIF-8 adsorbent since they have the same chemical formula (C 4 H 10 ), and hence the stereochemistry of each gas can explain the difference in adsorption capacity (Awadallah-F et al., 2019a).Indeed, n-butane molecule can easy penetrate the nanogate with less difficulty compared to the branched isobutane molecule (Awadallah-F et al., 2019a) and this is due to the linearity of the first one.Then, there is a difficulty to separate these molecules on ZIF-8 due to the approaching values of P 0 .The same reflection was observed for propane and propylene in the case of ZIF-8 adsorbent (Awadallah-F et al., 2019a).
Thereafter, the P 0 values were changed for each couple following the increases of Cu/ZIF-8 percentage.Therefore, it was concluded that Cu 30% /ZIF-8 adsorbent is more adequate than Cu 10% /ZIF-8 and ZIF-8 adsorbents for gases separation on the basis of differences between their P 0 values (Awadallah-F et al., 2019a).As a result, the conclusion about adsorption energy parameter deduced from w supports well these results.Indeed, as presented in Table 6, the variations of adsorption energy (estimated from Δw) and of P 0 increase follow the increase of Cu/ZIF-8 percentage for each couple of n-butane/isobutene and propane/propylene.Then, it can be deduced that the increase of copper percentage doped in ZIF-8 affects as well the adsorption energy, and then the variation of P 0 values for each pair of isomers.Consequently, the importance of P 0 parameter in relation with gas separation performances detected by Awadallah et al. (Awadallah-F et al., 2019a) could be related to the importance of the adsorption energy for each gas following the increase of copper percentage doped into ZIF-8.On the other hand, the difference in adsorption capacity from one gas to another by changing the copper percentage doped in ZIF-8 does not follow the same order.This point was attributed to several factors, as the stereochemistry and the polarity of each gas.

Conclusions
This review focuses on the latest synthesis methods of ZIF-8 and its derivatives; in addition to their common characterization techniques and their corresponding applications.Light was shed on the potential application of ZIF-8 in gas separation and the theoretical modeling of their adsorption isotherms was discussed.A statistical physics approach was applied in this review to correlate the experimental adsorption isotherms of some gases by ZIF-8 and its derivatives.As a state of the art, we treated the case of n-butane, isobutane, propane and propylene gases separations using ZIF-8 and Cu/ZIF-8 nanomaterials (Awadallah-F et al., 2019a).Some specific properties such as "gate opening" mechanism, is systematically described and discussed based on the statistical physics approach.As main conclusions, by increasing the Cu/ZIF-8 percentage, the values of the gate opening pressure (P 0 ) were changed for each isomer pair of n-butane/isobutane and propane/propylene, which enhances the performances of gas separation at pressures between their corresponding P 0 values.Consequently, Cu 30% /ZIF-8 adsorbent is more suitable than Cu 10% /ZIF-8 and ZIF-8 adsorbents for gas separations thanks to the exhibited differences in P 0 values.This point was confirmed by the adsorption energy parameter derived from statistical physics approach.Indeed, the importance of gate opening pressure could be related to the importance of the adsorption energy for each gas following the increases of Cu/ZIF-8 percentage.From this, we can infer that the specific characteristics of ZIF-8 and its derivatives will allow for various important applications ranging from sensing and electronic devices to drug delivery, and therefore offers a promising research field to be explored.In view of the great interest of several research groups, new concepts and techniques for the synthesis of ZIF are being adopted.In addition, the rapid growth of new applications and new opportunities for further exploration of ZIF materials will continue to emerge in the future.In fact, due to the lack of functional groups in natural ZIF8 particles, they are not suitable for many applications.For this, functional groups were necessary through the use of, e.g., amino reactive imidazole derivatives and doped ZIFs materials.Moreover, computational methods are important nowadays to complement experimental measurements.

Table 6
Values of P 0 , ΔP 0 , w and Δw fitting parameters for the isomer pairs of n-butane/ isobutane and propane/propylene as calculated from MRMM model at 25

M
.Bergaoui et al.

Fig. 11 .
Fig. 11.Evolutions of w and b parameters with P 0 values for each gas with different Cu/ZIF-8 percentages.

Table 2
State-of-the-art synthesis approaches and properties of ZIF-8 and its derivatives.

Table 5
Fitting parameters of MLM, MIMM and MRMM models for the adsorption at 25 • C.