Metal–organic frameworks (MOFs) are compounds consisting of metal ions or clusters coordinated to organic ligands to form one-, two-, or three-dimensional structures.  They are a subclass of coordination polymers, with the special feature that they are often porous. The organic ligands included are sometimes referred to as "struts", one example being 1,4-benzenedicarboxylic acid (BDC).
More formally, a metal–organic framework is a coordination network with organic ligands containing potential voids. A coordination network is a coordination compound extending, through repeating coordination entities, in one dimension, but with cross-links between two or more individual chains, loops, or spiro-links, or a coordination compound extending through repeating coordination entities in two or three dimensions; and finally a coordination polymer is a coordination compound with repeating coordination entities extending in one, two, or three dimensions.[1]
In some cases, the pores are stable during elimination of the guest molecules (often solvents) and could be refilled with other compounds.  Because of this property, MOFs are of interest for the storage of gases such as hydrogen and carbon dioxide. Other possible applications of MOFs are in gas purification, in gas separation, in catalysis, as conducting solids and as supercapacitors.[2]
The synthesis and properties of MOFs constitute the primary focus of the discipline called reticular chemistry (from Latin reticulum, "small net").[3] Differently from MOFs covalent organic framework (COFs) are made entirely from light elements (H, B, C, N, and O) with extended structures.[4]

Structure
MOFs are composed of two major components: a metal ion or cluster of metal ions and an organic molecule called a linker. For this reason, the materials are often referred to as hybrid organic–inorganic materials; however, this terminology has recently been explicitly discouraged.[1] The organic units are typically mono-, di-, tri-, or tetravalent ligands.[5] The choice of metal and linker dictates the structure and hence properties of the MOF. For example, the metal's coordination preference influences the size and shape of pores by dictating how many ligands can bind to the metal and in which orientation.

To describe and organize the structures of MOFs, a system of nomenclature has been developed. Subunits of a MOF, called secondary building units (SBU), can be described by topologies common to several structures. Each topology, also called a net, is assigned a symbol, consisting of three lower-case letters in bold. MOF-5, for example, has a pcu net. The database of net structures can be found at the .[7]
Attached to the SBUs are bridging ligands.  For MOF's, typical bridging ligands are  di- and tricarboxylic acids.  These ligands typically have rigid backbones.  Examples are benzene-1,4-dicarboxylic acid (BDC or teraphthalic acid, biphenyl-4,4'-dicarboxylic acid (BPDC), and the tricarboxylic acid trimesic acid.

Synthesis
General Synthesis
The study of MOFs developed from the study of zeolite. Except for the use of preformed ligands, MOFs and zeolites are produced almost exclusively by hydrothermal or solvothermal techniques, where crystals are slowly grown from a hot solution. In contrast with zeolites, MOFs are constructed from bridging organic ligands that remain intact throughout the synthesis.[8] Zeolite synthesis often makes use of a "template". Templates are ions that influence the structure of the growing inorganic framework.  Typical templating ions are quaternary ammonium cations, which are removed later. In MOFs, the framework is templated by the SBU (secondary building unit) and the organic ligands.[9][10] A templating approach that is useful for MOFs intended for gas storage is the use of metal-binding solvents such as N,N-diethylformamide and water. In these cases, metal sites are exposed when the solvent is evacuated, allowing hydrogen to bind at these sites.[11]
Since ligands in MOFs typically bind reversibly, the slow growth of crystals often allows defects to be redissolved, resulting in a material with millimeter-scale crystals and a near-equilibrium defect density. Solvothermal synthesis is useful for growing crystals suitable to structure determination, because crystals grow over the course of hours to days. However, the use of MOFs as storage materials for consumer products demands an immense scale-up of their synthesis. Scale-up of MOFs has not been widely studied, though several groups have demonstrated that microwaves can be used to nucleate MOF crystals rapidly from solution.[12][13] This technique, termed "microwave-assisted solvothermal synthesis", is widely used in the zeolite literature,[8] and produces micron-scale crystals in a matter of seconds to minutes,[12][13] in yields similar to the slow growth methods.
A solvent-free synthesis of a range of crystalline MOFs has been described.[14] Usually the metal acetate and the organic proligand are mixed and ground up with a ball mill. Cu3(BTC)2 can be quickly synthesised in this way in quantitative yield. In the case of Cu3(BTC)2 the morphology of the solvent free synthesised product was the same as the industrially made Basolite C300. It is thought that localised melting of the components due to the high collision energy in the ball mill may assist the reaction. The formation of acetic acid as a by-product in the reactions in the ball mill may also help in the reaction having a solvent effect[15] in the ball mill.
A recent advancement in the solvent-free preparation of MOF films and composites is their synthesis by chemical vapor deposition. This process, MOF-CVD,[16]
was first demonstrated for ZIF-8 and consist of two steps. In a first step, metal oxide precursor layers are deposited. In the second step, these precursor layers are exposed to sublimed ligand molecules, that induce a phase transformation to the MOF crystal lattice. Formation of water during this reaction plays a crucial role in directing the transformation.
Post-synthetic Modification
Although the three-dimensional structure and internal environment of the pores can be in theory controlled through proper selection of nodes and organic linking groups, the direct synthesis of such materials with the desired functionalities can be difficult due to the high sensitivity of MOF systems. Thermal and chemical sensitivity, as well as high reactivity of reaction materials, can make forming desired products challenging to achieve. The exchange of guest molecules and counter-ions and the removal of solvents allow for some additional functionality but are still limited to the integral parts of the framework.[17] The post-synthetic exchange of organic linkers and metal ions is an expanding area of the field and opens up possibilities for more complex structures, increased functionality, and greater system control.[17][18]
Ligand Exchange
Post-synthetic modification techniques can be used to exchange an existing organic linking group in a prefabricated MOF with a new linker by ligand exchange or partial ligand exchange.[18][19] This exchange allows for the pores and, in some cases the overall framework of MOFs, to be tailored for specific purposes. Some of these uses include fine-tuning the material for selective adsorption, gas storage, and catalysis.[18][11] To perform ligand exchange prefabricated MOF crystals are washed with solvent and then soaked in a solution of the new linker. The exchange often requires heat and occurs on the time scale of a few days.[19] Post-synthetic ligand exchange also enables the incorporation of functional groups into MOFs that otherwise would not survive MOF synthesis, due to temperature, pH, or other reaction conditions, or hinder the synthesis itself by competition with donor groups on the loaning ligand.[18]
Metal Exchange
Post-synthetic modification techniques can also be used to exchange an existing metal ion in a prefabricated MOF with a new metal ion by metal ion exchange . The complete metal metathesis from an integral part of the framework has been achieved without altering the framework or pore structure of the MOF. Similarly to post-synthetic ligand exchange post-synthetic metal exchange is performed by washing prefabricated MOF crystals with solvent and then soaking the crystal in a solution of the new metal.[20] Post-synthetic metal exchange allows for a simple route to the formation of MOFs with the same framework yet different metal ions.[17]
Stratified Synthesis
In addition to modifying the functionality of the ligands and metals themselves, post-synthetic modification can be used to expand upon the structure of the MOF. Using post-synthetic modification MOFs can be converted from a highly ordered crystalline material toward a heterogeneous porous material.[21] Using post-synthetic techniques, it is possible for the controlled installation of domains within a MOF crystal which exhibit unique structural and functional characteristics. Core-shell MOFs and other layered MOFs have been prepared where layers of have unique functionalization but in most cases are crystallographically compatible from layer to layer.[22]
Composite materials
Another approach to increasing adsorption in MOFs is to alter the system in such a way that chemisorption becomes possible. This functionality has been introduced by making a composite material, which contains a MOF and a complex of platinum with activated carbon. In an effect known as hydrogen spillover, H2 can bind to the platinum surface through a dissociative mechanism which cleaves the hydrogen molecule into two hydrogen atoms and enables them to travel down the activated carbon onto the surface of the MOF. This innovation produced a threefold increase in the room-temperature storage capacity of a MOF; however, desorption can take upwards of 12 hours, and reversible desorption is sometimes observed for only two cycles.[23][24] The relationship between hydrogen spillover and hydrogen storage properties in MOFs is not well understood but may prove relevant to hydrogen storage.
Hydrogen storage

Molecular hydrogen has the highest specific energy of any fuel. However unless the hydrogen gas is compressed, its volumetric energy density is very low, so the transportation and storage of hydrogen require energy-intensive compression and liquefaction processes.[25][26] Therefore, development of new hydrogen storage methods which decrease the concomitant pressure required for practical volumetric energy density is an active area of research.[25] MOFs attract attention as materials for adsorptive hydrogen storage because of their high specific surface areas and surface to volume ratios, as well as their chemically tunable structures.[23] Compared to an empty gas cylinder, a MOF-filled gas cylinder can store more hydrogen at a given pressure because hydrogen molecules adsorb to the surface of MOFs. Furthermore, MOFs are free of dead-volume, so there is almost no loss of storage capacity as a result of space-blocking by non-accessible volume.[5] Also, because the hydrogen uptake is based primarily on physisorption, many MOFs have a fully reversible uptake-and-release behavior. No large activation barriers are required when liberating the adsorbed hydrogen.[5] The storage capacity of a MOF is limited by the liquid-phase density of hydrogen because the benefits provided by MOFs can be realized only if the hydrogen is in its gaseous state.[5]
The extent to which a gas can adsorb to a MOF's surface depends on the temperature and pressure of the gas. In general, adsorption increases with decreasing temperature and increasing pressure (until a maximum is reached, typically 20-30 bar, after which the adsorption capacity decreases).[5][23] However, MOFs to be used for hydrogen storage in automotive fuel cells need to operate efficiently at ambient temperature and pressures between 1 and 100 bar, as these are the values that are deemed safe for automotive applications.[23]

The U.S. Department of Energy (DOE) has published a list of yearly technical system targets for on-board hydrogen storage for light-duty fuel cell vehicles which guide researchers in the field (5.5 wt %/40 g L−1 by 2017; 7.5 wt %/70 g L−1 ultimate).[27] Materials with high porosity and high surface area such as MOFs have been designed and synthesized in an effort to meet these targets. These adsorptive materials generally work via physical adsorption rather than chemisorption due to the large HOMO-LUMO gap and low HOMO energy level of molecular hydrogen. A benchmark material to this end is MOF-177 which was found to store hydrogen at 7.5 wt % with a volumetric capacity of 32 g L−1 at 77 K and 70 bar.[28] MOF-177 consists of [Zn4O]6+ clusters interconnected by 1,3,5-benzebetribenzoate organic linkers and has a measured BET surface area of 4630 m2 g−1. Another exemplary material is PCN-61 which exhibits a hydrogen uptake of 6.24 wt % and 42.5 g L−1 at 35 bar and 77 K and 2.25 wt % at atmospheric pressure.[29] PCN-61 consists of [Cu2]4+ paddle-wheel units connected through 5,5′,5′′-benzene-1,3,5-triyltris(1-ethynyl-2-isophthalate) organic linkers and has a measured BET surface area of 3000 m2 g−1. Despite these promising MOF examples, the classes of synthetic porous materials with the highest performance for practical hydrogen storage are activated carbon and covalent organic frameworks (COFs).[30]
Design principles
Practical applications of MOFs for hydrogen storage are met with several challenges. For hydrogen adsorption near room temperature, the hydrogen binding energy would need to be increased considerably.[23] Several classes of MOFs have been explored, including carboxylate-based MOFs, heterocyclic azolate-based MOFs, metal-cyanide MOFs, and covalent organic frameworks. Carboxylate-based MOFs have by far received the most attention because
they are either commercially available or easily synthesized,
they have high acidity (pKa ˜ 4) allowing for facile in situ deprotonation,
the metal-carboxylate bond formation is reversible, facilitating the formation of well-ordered crystalline MOFs, and
the bridging bidentate coordination ability of carboxylate groups favors the high degree of framework connectivity and strong metal-ligand bonds necessary to maintain MOF architecture under the conditions required to evacuate the solvent from the pores.[23]
The most common transition metals employed in carboxylate-based frameworks are Cu2+ and Zn2+. Lighter main group metal ions have also been explored. Be12(OH)12(BTB)4, the first successfully synthesized and structurally characterized MOF consisting of a light main group metal ion, shows high hydrogen storage capacity, but it is too toxic to be employed practically.[31] There is considerable effort being put forth in developing MOFs composed of other light main group metal ions, such as magnesium in Mg4(BDC)3.[23]
The following is a list of several MOFs that are considered to have the best properties for hydrogen storage as of May 2012 (in order of decreasing hydrogen storage capacity).[23] While each MOF described has its advantages, none of these MOFs reach all of the standards set by the U.S. DOE. Therefore, it is not yet known whether materials with high surface areas, small pores, or di- or trivalent metal clusters produce the most favorable MOFs for hydrogen storage.[5]

Zn4O(BTE)(BPDC), where BTE3−=4,4′,4″-[benzene-1,3,5-triyl-tris(ethyne-2,1-diyl)]tribenzoate and BPDC2−=biphenyl-4,4′-dicarboxylate (MOF-210) [32]
Hydrogen storage capacity (at 77 K): 8.6excess wt% (17.6 total wt%) at 77K and 80bar. 44 total g H2/L at 80 bar and 77 K.[32]
Hydrogen storage capacity (at 298 K): 2.90delivery wt% (1-100 bar) at 298K and 100bar.[33]Zn4O(BBC)2, where BBC3−=4,4′,4″-[benzene-1,3,5-triyl-tris(benzene-4,1-diyl)]tribenzoate (MOF-200) [32]

Hydrogen storage capacity (at 77 K): 7.4excess wt% (16.3 total wt%) at 77K and 80bar. 36 total g H2/L at 80 bar and 77 K.[32]

Hydrogen storage capacity (at 298 K): 3.24delivery wt% (1-100 bar) at 298K and 100bar.[33]Zn4O(BTB)2, where BTB3−=1,3,5-benzenetribenzoate (MOF-177) [34]

Structure: Tetrahedral [Zn4O]6+ units are linked by large, triangular tricarboxylate ligands. Six diamond-shaped channels (upper) with diameter of 10.8Å surround a pore containing eclipsed BTB3− moieties (lower).

Hydrogen storage capacity: 7.1wt% at 77K and 40bar; 11.4wt% at 78bar and 77K.

MOF-177 has larger pores, so hydrogen is compressed within holes rather than adsorbed to the surface. This leads to higher total gravimetric uptake but lower volumetric storage density compared to MOF-5.[23]Zn4O(BDC)3, where BDC2−=1,4-benzenedicarboxylate (MOF-5) [35]

Structure: Square openings are either 13.8 or 9.2Å depending on the orientation of the aromatic rings.

Hydrogen storage capacity: 7.1wt% at 77K and 40bar ; 10wt% at 100bar; volumetric storage density of 66g/L.

MOF-5 has received much attention from theorists because of the partial charges on the MOF surface, which provide a means of strengthening the binding hydrogen through dipole-induced intermolecular interactions; however, MOF-5 has poor performance at room temperature (9.1g/L at 100bar).[23]Mn3[(Mn4Cl)3(BTT)8]2, where H3BTT=benzene-1,3,5-tris(1<i>H-tetrazole) [36]

Structure: Consists of truncated octahedral cages that share square faces, leading to pores of about 10Å in diameter. Contains open Mn2+ coordination sites.

Hydrogen storage capacity: 60g/L at 77K and 90bar; 12.1g/L at 90bar and 298K.

This MOF is the first demonstration of open metal coordination sites increasing strength of hydrogen adsorption, which results in improved performance at 298K. It has relatively strong metal-hydrogen interactions, attributed to a spin state change upon binding or to a classical Coulombic attraction.[23]Cu3(BTC)2(H2O)3, where H3BTC=1,3,5-benzenetricarboxylic acid [37]

Structure: Consists of octahedral cages that share paddlewheel units to define pores of about 9.8Å in diameter.
High hydrogen uptake is attributed to overlapping attractive potentials from multiple copper paddle-wheel units: each Cu(II) center can potentially lose a terminal solvent ligand bound in the axial position, providing an open coordination site for hydrogen binding.[23]
Structural impacts on hydrogen storage capacity
To date, hydrogen storage in MOFs at room temperature is a battle between maximizing storage capacity and maintaining reasonable desorption rates, while conserving the integrity of the adsorbent framework (e.g. completely evacuating pores, preserving the MOF structure, etc.) over many cycles. There are two major strategies governing the design of MOFs for hydrogen storage:
1) to increase the theoretical storage capacity of the material, and
2) to bring the operating conditions closer to ambient temperature and pressure. Rowsell and Yaghi have identified several directions to these ends in some of the early papers.[38][39]
Surface area
The general trend in MOFs used for hydrogen storage is that the greater the surface area, the more hydrogen the MOF can store. High surface area materials tend to exhibit increased micropore volume and inherently low bulk density, allowing for more hydrogen adsorption to occur.[23]
Hydrogen adsorption enthalpy
High hydrogen adsorption enthalpy is also important. Theoretical studies have shown that 22-25kJ/mol interactions are ideal for hydrogen storage at room temperature, as they are strong enough to adsorb H2, but weak enough to allow for quick desorption.[40] The interaction between hydrogen and uncharged organic linkers is not this strong, and so a considerable amount of work has gone in synthesis of MOFs with exposed metal sites, to which hydrogen adsorbs with an enthalpy of 5-10kJ/mol. Synthetically, this may be achieved by using ligands whose geometries prevent the metal from being fully coordinated, by removing volatile metal-bound solvent molecules over the course of synthesis, and by post-synthetic impregnation with additional metal cations.[11][36] (C5H5)V(CO)3(H2) and Mo(CO)5(H2) are great examples of increased binding energy due to open metal coordination sites;[41] however, their high metal-hydrogen bond dissociation energies result in a tremendous release of heat upon loading with hydrogen, which is not favorable for fuel cells.[23] MOFs, therefore, should avoid orbital interactions that lead to such strong metal-hydrogen bonds and employ simple charge-induced dipole interactions, as demonstrated in Mn3[(Mn4Cl)3(BTT)8]2.
An association energy of 22-25kJ/mol is typical of charge-induced dipole interactions, and so there is interest in the use of charged linkers and metals.[23] The metal–hydrogen bond strength is diminished in MOFs, probably due to charge diffusion, so 2+ and 3+ metal ions are being studied to strengthen this interaction even further. A problem with this approach is that MOFs with exposed metal surfaces have lower concentrations of linkers; this makes them difficult to synthesize, as they are prone to framework collapse. This may diminish their useful lifetimes as well.[11][23] Most common strategies to increase this binding energy for MOFs and molecular hydrogen have been reviewed.[42]
Sensitivity to airborne moisture
MOFs are frequently sensitive to moisture in the air. In particular, IRMOF-1 degrades in the presence of small amounts of water at room temperature. Studies on metal analogues have unraveled the ability of metals other than Zn to stand higher water concentrations at high temperatures.[43][44]
To compensate for this, specially constructed storage containers are required, which can be costly. Strong metal-ligand bonds, such as in metal-imidazolate, -triazolate, and -pyrazolate frameworks, are known to decrease a MOF's sensitivity to air, reducing the expense of storage.[23]
Pore size
In a microporous material where physisorption and weak van der Waals forces dominate adsorption, the storage density is greatly dependent on the size of the pores. Calculations of idealized homogeneous materials, such as graphitic carbons and carbon nanotubes, predict that a microporous material with 7Å-wide pores will exhibit maximum hydrogen uptake at room temperature. At this width, exactly two layers of hydrogen molecules adsorb on opposing surfaces with no space left in between.[23]
[45]
10Å-wide pores are also of ideal size because at this width, exactly three layers of hydrogen can exist with no space in between.[23] (A hydrogen molecule has a bond length of 0.74Å with a van der Waals radius of 1.17Å for each atom; therefore, its effective van der Waals length is 3.08Å.) [46]
Structural defects
Structural defects also play an important role in the performance of MOFs. Room-temperature hydrogen uptake via bridged spillover is mainly governed by structural defects, which can have two effects:
1) a partially collapsed framework can block access to pores; thereby reducing hydrogen uptake, and
2) lattice defects can create an intricate array of new pores and channels causing increased hydrogen uptake.[47]
Structural defects can also leave metal-containing nodes incompletely coordinated. This enhances the performance of MOFs used for hydrogen storage by increasing the number of accessible metal centers.[48] Finally, structural defects can affect the transport of phonons, which affects the thermal conductivity of the MOF.[49]
Hydrogen adsorption
Adsorption is the process of trapping atoms or molecules that are incident on a surface; therefore the adsorption capacity of a material increases with its surface area. In three dimensions, the maximum surface area will be obtained by a structure which is highly porous, such that atoms and molecules can access internal surfaces. This simple qualitative argument suggests that the highly porous metal-organic frameworks (MOFs) should be excellent candidates for hydrogen storage devices.
Adsorption can be broadly classified as being one of two types: physisorption or chemisorption. Physisorption is characterized by weak van der Waals interactions, and bond enthalpies typically less than 20kJ/mol. Chemisorption, alternatively, is defined by stronger covalent and ionic bonds, with bond enthalpies between 250 and 500kJ/mol. In both cases, the adsorbate atoms or molecules (i.e. the particles which adhere to the surface) are attracted to the adsorbent (solid) surface because of the surface energy that results from unoccupied bonding locations at the surface. The degree of orbital overlap then determines if the interactions will be physisorptive or chemisorptive.[50]
Adsorption of molecular hydrogen in MOFs is physisorptive. Since molecular hydrogen only has two electrons, dispersion forces are weak, typically 4-7 kJ/mol, and are only sufficient for adsorption at temperatures below 298 K.[23]
A complete explanation of the H2 sorption mechanism in MOFs was achieved by statistical averaging in the grand canonical ensemble, exploring a wide range of pressures and temperatures.[51][52] Later work  revealed a pore filling mechanism as important in both COFs and MOFs.[33]
Determining hydrogen storage capacity
Two hydrogen-uptake measurement methods are used for the characterization of MOFs as hydrogen storage materials: gravimetric and volumetric. To obtain the total amount of hydrogen in the MOF, both the amount of hydrogen absorbed on its surface and the amount of hydrogen residing in its pores should be considered. To calculate the absolute absorbed amount (Nabs), the surface excess amount (Nex) is added to the product of the bulk density of hydrogen (ρbulk) and the pore volume of the MOF (Vpore), as shown in the following equation:[53]

N

a
b
s

=

N

e
x

+

ρ

b
u
l
k

V

p
o
r
e

{\displaystyle N_{\rm {abs}}=N_{\rm {ex}}+\rho _{\rm {bulk}}V_{\rm {pore}}}

Gravimetric method
The increased mass of the MOF due to the stored hydrogen is directly calculated by a highly sensitive microbalance.[53] Due to buoyancy, the detected mass of adsorbed hydrogen decreases again when a sufficiently high pressure is applied to the system because the density of the surrounding gaseous hydrogen becomes more and more important at higher pressures. Thus, this "weight loss" has to be corrected using the volume of the MOF's frame and the density of hydrogen.[54]
Volumetric method
The changing of amount of hydrogen stored in the MOF is measured by detecting the varied pressure of hydrogen at constant volume.[53] The volume of adsorbed hydrogen in the MOF is then calculated by subtracting the volume of hydrogen in free space from the total volume of dosed hydrogen.[55]
Other methods of hydrogen storage
There are six possible methods that can be used for the reversible storage of hydrogen with a high volumetric and gravimetric density, which are summarized in the following table, (where ρm is the gravimetric density, ρv is the volumetric density, T is the working temperature, and P is the working pressure):[56]

Of these, high-pressure gas cylinders and liquid hydrogen in cryogenic tanks are the least practical ways to store hydrogen for the purpose of fuel due to the extremely high pressure required for storing hydrogen gas or the extremely low temperature required for storing hydrogen liquid. The other methods are all being studied and developed extensively.[56]
Catalysis
MOFs have potential as heterogeneous catalysts, although applications have not been commercialized.[57]  Their high surface area, tunable porosity, diversity in metal and functional groups make them especially attractive for use as catalysts. Zeolites are extraordinarily useful in catalysis.[58] Zeolites are limited by the fixed tetrahedral coordination of the Si/Al connecting points and the two-coordinated oxide linkers.  Fewer than 200 zeolites are known.  In contrast with this limited scope, MOFs exhibit more diverse coordination geometries, polytopic linkers, and ancillary ligands (F−, OH−, H2O among others). It is also difficult to obtain zeolites with pore sizes larger than 1nm, which limits the catalytic applications of zeolites to relatively small organic molecules (typically no larger than xylenes). Furthermore, mild synthetic conditions typically employed for MOF synthesis allow direct incorporation of delicate functionalities into the framework structures. Such a process would not be possible with zeolites or other microporous crystalline oxide-based materials because of the harsh conditions typically used for their synthesis (e.g., calcination at high temperatures to remove organic templates).
Zeolites still cannot be obtained in enantiopure form, which precludes their applications in catalytic asymmetric synthesis, e.g., for the pharmaceutical, agrochemical, and fragrance industries. Enantiopure chiral ligands or their metal complexes have been incorporated into MOFs to lead to efficient asymmetric catalysts. Even some MOF materials may bridge the gap between zeolites and enzymes when they combine isolated polynuclear sites, dynamic host–guest responses, and a hydrophobic cavity environment. MOFs might be useful for making semi-conductors. Theoretical calculations show that MOFs are semiconductors or insulators with band gaps between 1.0 and 5.5 eV which can be altered by changing the degree of conjugation in the ligands indicating its possibility for being photocatalysts.
Design

Like other heterogeneous catalysts, MOFs may allow for easier post-reaction separation and recyclability than homogeneous catalysts. In some cases, they also give a highly enhanced catalyst stability. Additionally, they typically offer substrate-size selectivity. Nevertheless, while clearly important for reactions in living systems, selectivity on the basis of substrate size is of limited value in abiotic catalysis, as reasonably pure feedstocks are generally available.
Metal ions or metal clusters

Among the earliest reports of MOF-based catalysis was the cyanosilylation of aldehydes by a 2D MOF (layered square grids) of formula Cd(4,4’-bpy)2(NO3)2.[59] This investigation centered mainly on size- and shape-selective clathration.  A second set of examples was based on a two-dimensional, square-grid MOF containing single Pd(II) ions as nodes and 2-hydroxypyrimidinolates as struts.[60] Despite initial coordinative saturation, the palladium centers in this MOF catalyze alcohol oxidation, olefin hydrogenation, and Suzuki C–C coupling. At a minimum, these reactions necessarily entail redox oscillations of the metal nodes between Pd(II) and Pd(0) intermediates accompanying by drastic changes in coordination number, which would certainly lead to destabilization and potential destruction of the original framework if all the Pd centers are catalytically active. The observation of substrate shape- and size-selectivity implies that the catalytic reactions are heterogeneous and are indeed occurring within the MOF. Nevertheless, at least for hydrogenation, it is difficult to rule out the possibility that catalysis is occurring at the surface of MOF-encapsulated palladium clusters/nanoparticles (i.e., partial decomposition sites) or defect sites, rather than at transiently labile, but otherwise intact, single-atom MOF nodes.  "Opportunistic" MOF-based catalysis has been described for the cubic compound, MOF-5.[61] This material comprises coordinatively saturated Zn4O nodes and a fully complexed BDC struts (see above for abbreviation); yet it apparently catalyzes the Friedel–Crafts tert-butylation of both toluene and biphenyl. Furthermore, para alkylation is strongly favored over ortho alkylation, a behavior thought to reflect the encapsulation of reactants by the MOF.
Functional struts
The porous-framework material [Cu3(btc)2(H2O)3], also known as HKUST-1,[62] contains large cavities having windows of diameter ~6 Å. The coordinated water molecules are easily removed, leaving open Cu(II) sites. Kaskel and co-workers showed that these Lewis acid sites could catalyze the cyanosilylation of benzaldehyde or acetone.  The anhydrous version of HKUST-1 is an acid catalyst.[63] Compared to Brønsted vs. Lewis acid-catalyzed pathways, the product selectivity are distinctive for three reactions: isomerization of a-pinene oxide, cyclization of citronellal, and rearrangement of a-bromoacetals, indicating that indeed [Cu3(btc)2] functions primarily as a Lewis acid catalyst.
MIL-101, a large-cavity MOF having the formula [Cr3F(H2O)2O(BDC)3], is a cyanosilylation catalyst.[64] The coordinated water molecules in MIL-101 are easily removed to expose Cr(III) sites. As one might expect, given the greater Lewis acidity of Cr(III) vs. Cu(II), MIL-101 is much more active than HKUST-1 as a catalyst for the cyanosilylation of aldehydes. Additionally, the Kaskel group observed that the catalytic sites of MIL-101, in contrast to those of HKUST-1, are immune to unwanted reduction by benzaldehyde. The Lewis-acid-catalyzed cyanosilylation of aromatic aldehydes has also been carried out by Long and co-workers using a MOF of the formula Mn3[(Mn4Cl)3BTT8(CH3OH)10].[65] This material contains a three-dimensional pore structure, with the pore diameter equaling 10 Å. In principle, either of the two types of Mn(II) sites could function as a catalyst. Noteworthy features of this catalyst are high conversion yields (for small substrates) and good substrate-size-selectivity, consistent with channellocalized catalysis.
Encapsulated catalysts
The MOF encapsulation approach invites comparison to earlier studies of oxidative catalysis by zeolite-encapsulated Fe(porphyrin)[66] as well as Mn(porphyrin)[67] systems. The zeolite studies generally employed iodosylbenzene (PhIO), rather than TPHP as oxidant. The difference is likely mechanistically significant, thus complicating comparisons. Briefly, PhIO is a single oxygen atom donor, while TBHP is capable of more complex behavior. In addition, for the MOF-based system, it is conceivable that oxidation proceeds via both oxygen transfer from a manganese oxo intermediate as well as a manganese-initiated radical chain reaction pathway. Regardless of mechanism, the approach is a promising one for isolating and thereby stabilizing the porphyrins against both oxo-bridged dimer formation and oxidative degradation.[68]
Metal-free organic cavity modifiers
Most examples of MOF-based catalysis make use of metal ions or atoms as active sites. Among the few exceptions are two nickel- and two copper-containing MOFs synthesized by Rosseinsky and co-workers.[69] These compounds employ amino acids(L- or D-aspartate) together with dipyridyls as struts. The coordination chemistry is such that the amine group of the aspartate cannot be protonated by added HCl, but one of the aspartate carboxylates can. Thus, the framework-incorporated amino acid can exist in a form that is not accessible for the free amino acid. While the nickel-based compounds are marginally porous, on account of tiny channel dimensions, the copper versions are clearly porous.
The Rosseinsky group showed that the carboxylic acids behave as Brønsted acidic catalysts, facilitating (in the copper cases) the ring-opening methanolysis of a small, cavityaccessible epoxide at up to 65% yield. Superior homogeneous catalysts exist however.
Kitagawa and co-workers have reported the synthesis of a catalytic MOF having the formula [Cd(4-BTAPA)2(NO3)2].[70] The MOF is three-dimensional, consisting of an identical catenated pair of networks, yet still featuring pores of molecular dimensions. The nodes consist of single cadmium ions, octahedrally ligated by pyridyl nitrogens. From a catalysis standpoint, however, the most interesting feature of this material is the presence of guest-accessible amide functionalities. The amides are capable of base-catalyzing the Knoevenagel condensation of benzaldehyde with malononitrile. Reactions with larger nitriles, however, are only marginally accelerated, implying that catalysis takes place chiefly within the material's channels rather than on its exterior. A noteworthy finding is the lack of catalysis by the free strut in homogeneous solution, evidently due to intermolecular H-bonding between bptda molecules. Thus, the MOF architecture elicits catalytic activity not otherwise encountered.
In an interesting alternative approach, Férey and coworkers were able to modify the interior of MIL-101 via Cr(III) coordination of one of the two available nitrogen atoms of each of several ethylenediamine molecules.[71] The free non-coordinated ends of the ethylenediamines were then used as Brønsted basic catalysts, again for Knoevenagel condensation of benzaldehyde with nitriles.
A third approach has been described by Kim and coworkers.[72] Using a pyridine-functionalized derivative of tartaric acid and a Zn(II) source they were able to synthesize a 2D MOF termed POST-1. POST-1 possesses 1D channels whose cross sections are defined by six trinuclear zinc clusters and six struts. While three of the six pyridines are coordinated by zinc ions, the remaining three are protonated and directed toward the channel interior. When neutralized, the noncoordinated pyridyl groups are found to catalyze transesterification reactions, presumably by facilitating deprotonation of the reactant alcohol. The absence of significant catalysis when large alcohols are employed strongly suggests that the catalysis occurs within the channels of the MOF.
Achiral catalysis

Metals as catalytic sites
The metals in the MOF structure often act as Lewis acids. The metals in MOFs often coordinate to labile solvent molecules or counter ions which can be removed after activation of the framework. The Lewis acidic nature of such unsaturated metal centers can activate the coordinated organic substrates for subsequent organic transformations. The use of unsaturated metal centers was demonstrated in the cyanosilylation of aldehydes and imines by Fujita and coworkers in 2004.[73] They reported MOF of composition {[Cd(4,4′-bpy)2(H2O)2] • (NO3)2 • 4H2O} which was obtained by treating linear bridging ligand 4,4′-bipyridine (bpy) with Cd(NO3)2 . The Cd(II) centers in this MOF possesses a distorted octahedral geometry having four pyridines in the equatorial positions, and two water molecules in the axial positions to form a two-dimensional infinite network. On activation, two water molecules were removed leaving the metal centers unsaturated and Lewis acidic. The Lewis acidic character of metal center was tested on cyanosilylation reactions of imine where the imine gets attached to the Lewis-acidic metal centre resulting in higher electrophilicity of imines. For the cyanosilylation of imines, most of the reactions were complete within 1 h affording aminonitriles in quantitative yield. Kaskel and coworkers[74] carried out similar cyanosilylation reactions with coordinatively unsaturated metals in three-dimensional (3D) MOFs as heterogeneous catalysts. The 3D framework [Cu3(btc)2(H2O)3] (btc: Benzene-1,3,5- tricarboxylate) (HKUST-1) used in this study was first reported by Williams et al.[75] The open framework of [Cu3(btc)2(H2O)3] is built from dimeric cupric tetracarboxylate units (paddle-wheels) with aqua molecules coordinating to the axial positions and btc bridging ligands. The resulting framework after removal of two water molecules from axial positions possesses porous channel. This activated MOF catalyzes the trimethylcyanosilylation of benzaldehydes with a very low conversion (<5% in 24 h) at 293 K. As the reaction temperature was raised to 313 K, a good conversion of 57% with a selectivity of 89% was obtained after 72 h. In comparison, less than 10% conversion was observed for the background reaction (without MOF) under the same conditions. But this strategy suffers from some problems like 1) the decomposition of the framework with increase of the reaction temperature due to the reduction of Cu(II) to Cu(I) by aldehydes; 2) strong solvent inhibition effect; electron donating solvents such as THF competed with aldehydes for coordination to the Cu(II) sites, and no cyanosilylation product was observed in these solvents; 3) the framework instability in some organic solvents. Several other groups have also reported the use of metal centres in MOFs as catalysts[76][77] Again, electron-deficient nature of some metals and metal clusters makes the resulting MOFs efficient oxidation catalysts. Mori and coworkers[78] reported MOFs with Cu2 paddle wheel units as heterogeneous catalysts for the oxidation of alcohols. The catalytic activity of the resulting MOF was examined by carrying out alcohol oxidation with H2O2 as the oxidant. It also catalyzed the oxidation of primary alcohol, secondary alcohol and benzyl alcohols with high selectivity. Hill et al.[79] have demonstrated the sulfoxidation of thioethers using an MOF based on vanadium-oxo cluster V6O13 building units.
Functional linkers as catalytic sites
Functional linkers can be also utilized as catalytic sites. A 3D MOF {[Cd(4- BTAPA)2(NO3)2] • 6H2O • 2DMF} (4-BTAPA=1,3,5-benzene tricarboxylic acid tris [N-(4-pyridyl)amide], DMF=N,N-dimethylformamide) constructed by tridentate amide linkers and cadmium salt catalyzes the Knoevenagel condensation reaction.[80] The pyridine groups on the ligand 4-BTAPA act as ligands binding to the octahedral cadmium centers, while the amide groups can provide the functionality for interaction with the incoming substrates. Specifically, the – NH moiety of the amide group can act as electron acceptor whereas the C=O group can act as electron donor to activate organic substrates for subsequent reactions. Ferey et al.[81] reported a robust and highly porous MOF [Cr3(µ3-O)F(H2O)2(BDC)3] (BDC: Benzene-1,4- dicarboxylate) where instead of directly using the unsaturated Cr(III) centers as catalytic sites, the authors grafted ethylenediamine (ED) onto the Cr(III) sites. The uncoordinated ends of ED can act as base catalytic sites, ED-grafted MOF was investigated for Knoevenagel condensation reactions. A significant increase in conversion was observed for ED-grafted MOF compared to untreated framework (98% vs 36%).
Entrapment of catalytically active noble metal nanoparticles
The entrapment of catalytically active noble metals can be accomplished by grafting on functional groups to the unsaturated metal site on MOFs. Ethylenediamine (ED) has been shown to be grafted on the Cr metal sites and can be further modified to encapsulate noble metals such as Pd.[82] The entraped Pd has similar catalytic activity as Pd/C in the Heck reaction. Ruthenium nanoparticles have catalytic activity in a number of reactions when entrapped in the MOF-5 framework.[83] This Ru-encapsulated MOF catalyzes oxidation of benzyl alcohol to benzyaldehyde, although degradation of the MOF occurs.  The same catalyst was used in the hydrogenation of benzene to cyclohexane. In another example, Pd nanoparticles embedded within defective HKUST-1 framework enable the generation of tunable Lewis basic sites.[84] Therefore, this multifunctional Pd/MOF composite is able to perform stepwise benzyl alcohol oxidation and Knoevenagel condensation.
Reaction hosts with size selectivity
MOFs might prove useful for both photochemical and polymerization reactions due to the tuneability of the size and shape of their pores. A 3D MOF {[Co(bpdc)3(bpy)] • 4DMF • H2O} (bpdc: biphenyldicarboxylate, bpy: 4,4′-bipyridine) was synthesized by Li and coworkers.[85] Using this MOF photochemistry of o-methyl dibenzyl ketone (o-MeDBK) was extensively studied. This molecule was found to have a variety of photochemical reaction properties including the production of cyclopentanol. MOFs have been used to study polymerization in the confined space of MOF channels. Polymerization reactions in confined space might have different properties than polymerization in open space. Styrene, divinylbenzene, substituted acetylenes, methyl methacrylate, and vinyl acetate have all been studied by Kitagawa and coworkers as possible activated monomers for radical polymerization.[86][87] Due to the different linker size the MOF channel size could be tunable on the order of roughly 25 and 100 Å2. The channels were shown to stabilize propagating radicals and suppress termination reactions when used as radical polymerization sites.
Asymmetric catalysis
Several strategies exist for constructing homochiral MOFs. Crystallization of homochiral MOFs via self-resolution from achiral linker ligands is one of the way to accomplish such a goal. However, the resulting bulk samples contain both enantiomorphs and are racemic. Aoyama and coworkers[88] successfully obtained homochiral MOFs in the bulk from achiral ligands by carefully controlling nucleation in the crystal growth process. Zheng and coworkers[89] reported the synthesis of homochiral MOFs from achiral ligands by chemically manipulating the statistical fluctuation of the formation of enantiomeric pairs of crystals. Growing MOF crystals under chiral influences is another approach to obtain homochiral MOFs using achiral linker ligands. Rosseinsky and coworkers[90][91] have introduced a chiral coligand to direct the formation of homochiral MOFs by controlling the handedness of the helices during the crystal growth. Morris and coworkers[92] utilized ionic liquid with chiral cations as reaction media for synthesizing MOFs, and obtained homochiral MOFs. The most straightforward and rational strategy for synthesizing homochiral MOFs is, however, to use the readily available chiral linker ligands for their construction.
Homochiral MOFs with interesting functionalities and reagent-accessible channels
Homochiral MOFs have been made by Lin and coworkers using 2,2′-bis(diphenylphosphino)-1,1′-binaphthyl (BINAP), 1,1′-bi-2,2′-naphthol (BINOL) as a chiral ligands.[93] These ligands can coordinate with catalytically active metal sites to enhance the enantioselectivity. A variety of linking groups such as pyridine, phosphonic acid, and carboxylic acid can be selectively introduced to the 3,3′, 4,4′, and the 6,6′ positions of the 1,1'-binaphthyl moiety. Moreover, by changing the length of the linker ligands the porosity and framework structure of the MOF can be selectivily tuned.
Postmodification of homochiral MOFs
Lin and coworkers have shown that the postmodification of MOFs can be achieved to produce enantioselective homochiral MOFs for use as catalysts.[94] The resulting 3D homochiral MOF {[Cd3(L)3Cl6]• 4DMF • 6MeOH • 3H2O} (L=(R)-6,6'-dichloro-2,2'-dihydroxyl-1,1'-binaphthyl-bipyridine) synthesized by Lin was shown to have a similar catalytic efficiency for the diethylzinc addition reaction as compared to the homogeneous analogue when was pretreated by Ti(OiPr)4 to generate the grafted Ti- BINOLate species. The catalytic activity of MOFs can vary depending on the framework structure. Lin and others found that MOFs synthesized from the same materials could have drastically different catalytic activities depending on the framework structure present.[95]
Homochiral MOFs with precatalysts as building blocks
Another approach to construct catalytically active homochiral MOFs is to incorporate chiral metal complexes which are either active catalysts or precatalysts directly into the framework structures. For example, Hupp and coworkers[96] have combined a chiral ligand and bpdc (bpdc: biphenyldicarboxylate) with Zn(NO3)2 and obtained twofold interpenetrating 3D networks. The orientation of chiral ligand in the frameworks makes all Mn(III) sites accessible through the channels. The resulting open frameworks showed catalytic activity towards asymmetric olefin epoxidation reactions. No significant decrease of catalyst activity was observed during the reaction and the catalyst could be recycled and reused several times. Lin and coworkers[97] have reported zirconium phosphonate-derived Ru-BINAP systems. Zirconium phosphonate-based chiral porous hybrid materials containing the Ru(BINAP)(diamine)Cl2 precatalysts showed excellent enantioselectivity (up to 99.2% ee) in the asymmetric hydrogenation of aromatic ketones.
Biomimetic design and photocatalysis
Some MOF materials may resemble enzymes when they combine isolated polynuclear sites, dynamic host–guest responses, and hydrophobic cavity environment which are characteristics of an enzyme.[98] Some well-known examples of cooperative catalysis involving two metal ions in biological systems include: the diiron sites in methane monooxygenase, dicopper in cytochrome c oxidase, and tricopper oxidases which have analogy with polynuclear clusters found in the 0D coordination polymers, such as binuclear Cu2 paddlewheel units found in MOP-1[99][100] and [Cu3(btc)2] (btc=benzene-1,3,5-tricarboxylate) in HKUST-1 or trinuclear units such as {Fe3O(CO2)6} in MIL-88,[101] and IRMOP-51.[102] Thus, 0D MOFs have accessible biomimetic catalytic centers. In enzymatic systems, protein units show "molecular recognition", high affinity for specific substrates. It seems that molecular recognition effects are limited in zeolites by the rigid zeolite structure.[103] In contrast, dynamic features and guest-shape response make MOFs more similar to enzymes. Indeed, many hybrid frameworks contain organic parts that can rotate as a result of stimuli, such as light and heat.[104] The porous channels in MOF structures can be used as photocatalysis sites. In photocatalysis, the use of mononuclear complexes is usually limited either because they only undergo single- electron process or from the need for high-energy irradiation. In this case, binuclear systems have a number of attractive features for the development of photocatalysts.[105] For 0D MOF structures, polycationic nodes can act as semiconductor quantum dots which can be activated upon photostimuli with the linkers serving as photon antennae.[106] Theoretical calculations show that MOFs are semiconductors or insulators with band gaps between 1.0 and 5.5 eV which can be altered by changing the degree of conjugation in the ligands.[107] Experimental results show that the band gap of IRMOF-type samples can be tuned by varying the functionality of the linker.[108]
Additional potential applications
Biological imaging and sensing

A potential application for MOFs is biological imaging and sensing via photoluminescence. A large subset of luminescent MOFs use lanthanides in the metal clusters. Lanthanide photoluminescence has many unique properties that make them ideal for imaging applications, such as characteristically sharp and generally non-overlapping emission bands in the visible and near-infrared (NIR) regions of the spectrum, resistance to photobleaching or 'blinking', and long luminescence lifetimes.[109] However, lanthanide emissions are difficult to sensitize directly because they must undergo LaPorte forbidden f-f transitions. Indirect sensitization of lanthanide emission can be accomplished by employing the "antenna effect," where the organic linkers act as antennae and absorb the excitation energy, transfer the energy to the excited state of the lanthanide, and yield lanthanide luminescence upon relaxation.[110] A prime example of the antenna effect is demonstrated by MOF-76, which combines trivalent lanthanide ions and 1,3,5-benzenetricarboxylate (BTC) linkers to form infinite rod SBUs coordinated into a three dimensional lattice.[111] As demonstrated by multiple research groups, the BTC linker can effectively sensitize the lanthanide emission, resulting in a MOF with variable emission wavelengths depending on the lanthanide identity.[112][113] Additionally, the Yan group has shown that Eu3+- and Tb3+- MOF-76 can be used for selective detection of acetophenone from other volatile monoaromatic hydrocarbons. Upon acetophenone uptake, the MOF shows a very sharp decrease, or quenching, of the luminescence intensity.[114]
For use in biological imaging, however, two main obstacles must be overcome:
MOFs must be synthesized on the nanoscale so as not to affect the target's normal interactions or behavior
The absorbance and emission wavelengths must occur in regions with minimal overlap from sample autofluorescence, other absorbing species, and maximum tissue penetration.[115][116]
Regarding the first point, nanoscale MOF (NMOF) synthesis has been mentioned in an earlier section. The latter obstacle addresses the limitation of the antenna effect. Smaller linkers tend to improve MOF stability, but have higher energy absorptions, predominantly in the ultraviolet (UV) and high-energy visible regions. A design strategy for MOFs with redshifted absorption properties has been accomplished by using large, chromophoric linkers. These linkers are often composed of polyaromatic species, leading to large pore sizes and thus decreased stability. To circumvent the use of large linkers, other methods are required to redshift the absorbance of the MOF so lower energy excitation sources can be used. Post-synthetic modification (PSM) is one promising strategy. Luo et al. introduced a new family of lanthanide MOFs with functionalized organic linkers. The MOFs, deemed MOF-1114, MOF-1115, MOF-1130, and MOF-1131, are composed of octahedral SBUs bridged by amino functionalized dicarboxylate linkers. The amino groups on the linkers served as sites for covalent PSM reactions with either salicylaldehyde or 3-hydroxynaphthalene-2-carboxyaldehyde. Both of these reactions extend the π-conjugation of the linker, causing a redshift in the absorbance wavelength from 450nm to 650nm. The authors also propose that this technique could be adapted to similar MOF systems and, by increasing pore volumes with increasing linker lengths, larger pi-conjugated reactants can be used to further redshift the absorption wavelengths.[117] Biological imaging using MOFs has been realized by several groups, namely Foucault-Collet and co-workers. In 2013, they synthesized a NIR-emitting Yb3+-NMOF using phenylenevinylene dicarboxylate (PVDC) linkers. They were observed cellular uptake in both HeLa cells and NIH-3T3 cells using confocal, visible, and NIR spectroscopy.[118] Although low quantum yields persist in water and Hepes buffer solution, the luminescence intensity is still strong enough to image cellular uptake in both the visible and NIR regimes.
Drug delivery systems
The synthesis, characterization, and drug-related studies of low toxicity, biocompatible MOFs has shown that they have potential for medical applications. Many groups have synthesized various low toxicity MOFs and have studied their uses in loading and releasing various therapeutic drugs for potential medical applications. A variety of methods exist for inducing drug release, such as pH-response, magnetic-response, ion-response, temperature-response, and pressure response.[119]
In 2010 Smaldone et al., an international research group, synthesized a biocompatible MOF termed CD-MOF-1 from cheap edible natural products. CD-MOF-1 consists of repeating base units of 6 γ-cyclodextrin rings bound together by potassium ions. γ-cyclodextrin (γ-CD) is a symmetrical cyclic oligosaccharide that is mass-produced enzymatically from starch and consists of eight asymmetric α-1,4-linked D-glucopyranosyl residues.[120] The molecular structure of these glucose derivatives, which approximates a truncated cone, bucket, or torus, generates a hydrophilic exterior surface and a nonpolar interior cavity. Cyclodextrins can interact with appropriately sized drug molecules to yield an inclusion complex.[121] Smaldone's group proposed a cheap and simple synthesis of the CD-MOF-1 from natural products. They dissolved sugar (γ-cyclodextrin) and an alkali salt (KOH, KCl, potassium benzoate) in distilled bottled water and allowed 190 proof grain alcohol (Everclear) to vapor diffuse into the solution for a week. The synthesis resulted in a cubic (γ-CD)6 repeating motif with a pore size of approximately 1nm. Subsequently, in 2017 Hartlieb et al. at Northwestern did further research with CD-MOF-1 involving the encapsulation of ibuprofen. The group studied different methods of loading the MOF with ibuprofen as well as performing related bioavailability studies on the ibuprofen-loaded MOF. They investigated two different methods of loading CD-MOF-1 with ibuprofen; crystallization using the potassium salt of ibuprofen as the alkali cation source for production of the MOF, and absorption and deprotonation of the free-acid of ibuprofen into the MOF. From there the group performed in vitro and in vivo studies to determine the applicability of CD-MOF-1 as a viable delivery method for ibuprofen and other NSAIDs. In vitro studies showed no toxicity or effect on cell viability up to 100 μM. In vivo studies in mice showed the same rapid uptake of ibuprofen as the ibuprofen potassium salt control sample with a peak plasma concentration observed within 20 minutes, and the cocrystal has the added benefit of double the half-life in blood plasma samples.[122] The increase in half-life is due to CD-MOF-1 increasing the solubility of ibuprofen compared to the pure salt form.
Since these developments many groups have done further research into drug delivery with water-soluble, biocompatible MOFs involving common over-the-counter drugs. In March 2018 Sara Rojas and her team at Paris-Saclay University published their research on drug incorporation and delivery with various biocompatible MOFs other than CD-MOF-1 through simulated cutaneous administration. The group studied the loading and release of ibuprofen (hydrophobic) and aspirin (hydrophilic) in three biocompatible MOFs (MIL-100(Fe), UiO-66(Zr), and MIL-127(Fe)). Under simulated cutaneous conditions (aqueous media at 37°C) the six different combinations of drug-loaded MOFs fulfilled "the requirements to be used as topical drug-delivery systems, such as released payload between 1 and 7 days" and delivering a therapeutic concentration of the drug of choice without causing unwanted side effects.[123] The group discovered that the drug uptake is "governed by the hydrophilic/hydrophobic balance between cargo and matrix" and "the accessibility of the drug through the framework." The "controlled release under cutaneous conditions follows different kinetics profiles depending on: (i) the structure of the framework, with either a fast delivery from the very open structure MIL-100 or a slower drug release from the narrow 1D pore system of MIL-127 or (ii) the hydrophobic/hydrophilic nature of the cargo, with a fast (Aspirin) and slow (Ibuprofen) release from the UiO-66 matrix."
Recent research involving MOFs as a drug delivery method includes more than just the encapsulation of everyday drugs like ibuprofen and aspirin. In early 2018 Chen et al., from Zhejiang University in Hangzhou China, released an article in ACS's Applied Materials and Interfaces detailing their work on the use of MOF ZIF-8 (zeolitic imidazolate framework-8) in antitumor research "to control the release of an autophagy inhibitor, 3-methyladenine (3-MA), and prevent it from dissipating in a large quantity before reaching the target."[124] The group performed in vitro studies and determined that "the autophagy-related proteins and autophagy flux in HeLa cells treated with 3-MA@ZIF-8 NPs show that the autophagosome formation is significantly blocked, which reveals that the pH-sensitive dissociation increases the efficiency of autophagy inhibition at the equivalent concentration of 3-MA." This shows promise for future research and applicability with MOFs as drug delivery methods in the fight against cancer.
Methane storage
In October 2011, researchers at the California Institute of Technology synthesized 14 new Covalent-Organic Frameworks (COFs). Two of these COFs, COF-103-Eth-trans and COF-102-Ant, were found to exceed the DOE target of 180 v(STP)/v at 35 bar for methane storage.[125] They reported that using thin vinyl bridging groups aid performance by minimizing the interaction between methane and the COF at low pressure. It is believed that this method could be extended to MOFs due to the similarity between MOFs and COFs[125]
Semiconductors
In 2014 researchers proved that they can create electrically conductive thin films of MOFs (Cu3(BTC)2 (also known as HKUST-1; BTC, benzene-1,3,5-tricarboxylic acid) infiltrated with the molecule 7,7,8,8-tetracyanoquinododimethane) that could be used in applications including photovoltaics, sensors and electronic materials and a path towards creating semiconductors. The team demonstrated tunable, air-stable electrical conductivity with values as high as 7 siemens per meter, comparable to bronze.[126]
Ni
3(2,3,6,7,10,11-hexaiminotriphenylene)2 was shown to be a metal-organic graphene analogue that has a natural band gap, making it a semiconductor, and is able to self-assemble. It represents a family of similar compounds. Because of the symmetry and geometry in 2,3,6,7,10,11-hexaiminotriphenylene (HITP), the overall organometallic complex has an almost fractal nature that allows it to perfectly self-organize. By contrast, graphene must be doped to give it the properties of a semiconductor. Ni3(HITP)2 pellets had a conductivity of 2 S/cm, a record for a metal-organic compound.[127][128]
Bio-mimetic mineralization
Biomolecules can be incorporated during the MOF crystallization process. Biomolecules including proteins, DNA and antibodies could be encapsulated within ZIF-8. Enzymes encapsulated in this way were stable and active even after being exposed to harsh conditions (e.g. aggressive solvents and high temperature). ZIF-8, MIL-88A, HKUST-1, and several luminescent MOFs containing lanthanide metals were used for the biomimetic mineralization process.[129]
Carbon capture

Because of their small, tunable pore sizes and high void fractions, MOFs are a promising potential material for use as an adsorbent to capture CO2.  MOFs could provide a more efficient alternative to traditional amine solvent-based methods in CO2 capture from coal-fired power plants.[130]
MOFs could be employed in each of the main three carbon capture configurations for coal-fired power plants: pre-combustion, post-combusiton, and oxy-combustion.[131] However, since the post-combustion configuration is the only one that can be retrofitted to existing plants, it garners the most interest and research. In post-combustion carbon capture, the flue gas from the power plant would be fed through a MOF in a packed-bed reactor setup. Flue gas is generally 40 to 60°C with a partial pressure of CO2 at 0.13 - 0.16 bar. CO2 can bind to the MOF surface through either physisorption, which is caused by Van der Waals interactions, or  chemisorption, which is caused by covalent bond formation.[132] Once the MOF is saturated with CO2, the CO2 would be removed from the MOF through either a temperature swing or a pressure swing. This process is known as regeneration. In a temperature swing regeneration, the MOF would be heated until CO2 desorbs. To achieve working capacities comparable to the amine process, the MOF must be heated to around 200°C. In a pressure swing, the pressure would be decreased until CO2 desorbs.[133]
In addition to their tunable selectivities for different molecules, another property of MOFs that makes them a good candidate for carbon capture is their low heat capacities.  Monoethanolamine (MEA) solutions, the leading method for capturing CO2 from flue gas, have a heat capacity between 3-4 J/g K since they are mostly water.  This high heat capacity contributes to the energy penalty in the solvent regeneration step, i.e., when the adsorbed CO2 is removed from the MEA solution.  MOF-177, a MOF designed for CO2 capture, has a heat capacity of 0.5 J/g K at ambient temperature.[131]
In a collaborative project sponsored by the U.S. DOE, MOFs were shown to separate 90% of the CO2 from the flue gas stream using a vacuum pressure swing process. The MOF Mg(dobdc) has a 21.7 wt% CO2 loading capacity. Estimations showed that, if a similar system would be applied to a large scale power plant, the cost of energy would increase by 65%, while a U.S. NETL baseline amine-based system would cause an increase of 81% (the U.S. DOE goal is 35%). The cost of capturing CO2  would be $57 / ton CO2 captured, while for the amine system the cost is estimated to be $72 / ton CO2 captured. The project estimated that the total capital required to implement such project in a 580 MW power plant would be $354 million.[134]
Desalination/ion separation
MOF membranes can mimic substantial ion selectivity. This offers the potential for use in desalination and water treatment. As of 2018 reverse osmosis supplied more than half of global desalination capacity, and the last stage of most water treatment processes. Osmosis does not use dehydration of ions, or selective ion transport in biological channels and it is not energy efficient. The mining industry, uses membrane-based processes to reduce water pollution, and to recover metals. MOFs  could be used to extract metals such as lithium from seawater and waste streams.[135]
MOF membranes such as ZIF-8 and UiO-66 membranes with uniform subnanometer pores consisting of angstrom-scale windows and nanometer-scale cavities displayed ultrafast selective transport of alkali metal ions. The windows acted as ion selectivity filters for alkali metal ions, while the cavities functioned as pores for transport. The ZIF-8[136] and UiO-66[137] membranes showed a LiCl/RbCl selectivity of ~4.6 and ~1.8, respectively, much higher than the 0.6 to 0.8 selectivity in traditional membranes.[138]
Water vapor capture
A team of researchers at the Massachusetts Institute of Technology and University of California Berkeley have developed a prototype that captures water vapor from the air, and then releases it with the application of a smaller amount of heat compared to existing commercially available technologies.[139]
Ferroelectrics and Multiferroics
Some MOFs also exhibit spontaneous electric polarization, which occurs due to the ordering of electric dipoles (polar linkers or guest molecules) below a certain phase transition temperature.[140] If this long-range dipolar order can be controlled by the external electric field, a MOF is called ferroelectric.[141] Some ferroelectric MOFs also exhibit magnetic ordering making them single structural phase multiferroics. This material property is highly interesting for construction of memory devices with high information density.
Interaction with Gravitational forces
Gravitational force is considered as a tool for managing the MOFs' crystal size; in which high g‐force led to the formation of small MOF crystals, while low g‐force (g less than 1) produced rather bigger crystals, caused by the facet‐oriented crystal fusion. Hence, g‐force would be used to increase or decrease MOFs' size by changing their convection and sedimentation.[142]
See also

BET theory
Conjugated microporous polymer
Coordination chemistry
Coordination polymers
Cryogenics
Crystal nets (periodic graphs)
Hydrogen
Hydrogen economy
Liquid hydrogen
Macromolecular assembly
Omar M. Yaghi
Susumu Kitagawa
Gérard Férey
Organometallic chemistry
United States Department of Energy
X-ray Crystallography
Zeolitic imidazolate frameworks
Solid sorbents for carbon capture

What can we do with metal–organic frameworks?


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Glossary of field theory
Glossary of group theory
Glossary of linear algebra
Glossary of ring theory
List of cohomology theories
Calculus and analysis

Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis evolved from calculus.
List of complex analysis topics
List of functional analysis topics
List of vector spaces in mathematics
List of integration and measure theory topics
List of harmonic analysis topics
List of Fourier analysis topics
List of multivariable calculus topics
List of q-analogs
List of real analysis topics
List of variational topics
Glossary of tensor theory
List of mathematical series
See also Dynamical systems and differential equations section below.
Geometry and topology

Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
List of geometry topics
List of geometric shapes
List of curves topics
List of triangle topics
List of circle topics
List of topics related to pi
List of general topology topics
List of differential geometry topics
List of algebraic geometry topics
List of algebraic surfaces
List of algebraic topology topics
List of cohomology theories
List of geometric topology topics
List of knot theory topics
List of Lie group topics
Glossary of differential geometry and topology
Glossary of general topology
List of mathematical properties of points
Glossary of Riemannian and metric geometry
Glossary of scheme theory
Combinatorics
Combinatorics concerns the study of discrete (and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics).
Outline of combinatorics
List of graph theory topics
Glossary of graph theory
Logic

Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.
List of Boolean algebra topics
List of first-order theories
List of large cardinal properties
List of mathematical logic topics
Glossary of order theory
List of set theory topics
Number theory
Number theory studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.
List of algebraic number theory topics
List of number theory topics
List of recreational number theory topics
Glossary of arithmetic and Diophantine geometry
List of prime numbers—not just a table, but a list of various kinds of prime numbers (each with an accompanying table)
List of zeta functions
Applied mathematics
Dynamical systems and differential equations

A differential equation is an equation involving an unknown function and its derivatives.
In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
List of dynamical systems and differential equations topics
List of partial differential equation topics
List of nonlinear partial differential equations
Mathematical physics
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".1
List of mathematical topics in classical mechanics
List of mathematical topics in quantum theory
List of mathematical topics in relativity
List of string theory topics
Index of wave articles
Computation

The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science and engineering.
List of algorithm general topics
List of computability and complexity topics
Lists for computational topics in geometry and graphics
List of combinatorial computational geometry topics
List of computer graphics and descriptive geometry topics
List of numerical computational geometry topics
List of computer vision topics
List of formal language and literal string topics
List of numerical analysis topics
List of terms relating to algorithms and data structures
Information theory and signal processing
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data.
Signal processing is the analysis, interpretation, and manipulation of signals. Signals of interest include sound, images, biological signals such as ECG, radar signals, and many others. Processing of such signals includes filtering, storage and reconstruction, separation of information from noise, compression, and feature extraction.
List of information theory topics
List of algebraic coding theory topics
List of cryptography topics
Probability and statistics

Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. Statistics, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics).
List of probability topics
List of stochastic processes topics
List of probability distributions
Catalog of articles in probability theory
List of statistics topics
Outline of regression analysis
Game theory
Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics, evolutionary biology, political science, social psychology and military strategy.
Glossary of game theory
List of games in game theory
Operations research
Operations research is the study and use of mathematical models, statistics and algorithms to aid in decision-making, typically with the goal of improving or optimizing performance of real-world systems.
List of network theory topics
List of knapsack problems
Methodology
List of graphical methods
List of mathematics-based methods
List of rules of inference
Mathematical statements
A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.
List of algorithms
List of axioms
List of conjectures
List of conjectures by Paul Erdős
Combinatorial principles
List of equations
List of formulae involving pi
List of mathematical identities
List of inequalities
List of lemmas
List of mathematical proofs
General concepts
List of convexity topics
List of dualities
List of exceptional set concepts
List of exponential topics
List of factorial and binomial topics
List of fractal topics
List of logarithm topics
List of numeral system topics
List of order topics
List of partition topics
List of polynomial topics
List of properties of sets of reals
List of transforms
List of permutation topics
Mathematical objects
Among mathematical objects are numbers, functions, sets, a great variety of things called "spaces" of one kind or another, algebraic structures such as rings, groups, or fields, and many other things.
List of mathematical examples
List of curves
List of complex reflection groups
List of complexity classes
List of examples in general topology
List of finite simple groups
List of Fourier-related transforms
List of mathematical functions
List of mathematical knots and links
List of manifolds
List of mathematical shapes
List of matrices
List of numbers
List of polygons, polyhedra and polytopes
List of regular polytopes
List of simple Lie groups
List of small groups
List of special functions and eponyms
List of algebraic surfaces
List of surfaces
Table of Lie groups
Equations named after people
Scientific equations named after people
About mathematics
List of mathematical societies
List of letters used in mathematics and science
List of mathematics competitions
List of mathematics history topics
List of publications in mathematics
Mathematicians

Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical physics).
List of geometers
List of logicians
List of game theorists
List of mathematicians
List of mathematical probabilists
List of statisticians
Work of particular mathematicians

List of things named after Niels Henrik Abel
List of things named after Archimedes
List of things named after Emil Artin
List of things named after Thomas Bayes
List of things named after Élie Cartan
List of things named after Augustin-Louis Cauchy
List of things named after Arthur Cayley
List of things named after Richard Dedekind
List of things named after Pierre Deligne
List of things named after Peter Gustav Lejeune Dirichlet
List of things named after Albert Einstein
List of things named after Euclid
List of things named after Leonhard Euler
List of things named after Paul Erdős
List of things named after Fibonacci
List of things named after Ferdinand Georg Frobenius
List of things named after Carl Friedrich Gauss
List of things named after Évariste Galois
List of things named after Jacques Hadamard
List of things named after Erich Hecke
List of things named after Eduard Heine
List of things named after Charles Hermite
List of things named after W. V. D. Hodge
List of things named after Carl Gustav Jacob Jacobi
List of things named after Felix Klein
List of things named after Joseph-Louis Lagrange
List of things named after Pierre-Simon Laplace
List of things named after Adrien-Marie Legendre
List of things named after Gottfried Leibniz
List of things named after John Milnor
List of things named after Isaac Newton
List of things named after Henri Poincaré
List of things named after Siméon Denis Poisson
List of things named after Pythagoras
List of things named after Srinivasa Ramanujan
List of things named after Bernhard Riemann
List of things named after Jean-Pierre Serre
List of things named after James Joseph Sylvester
List of things named after Alfred Tarski
List of things named after Karl Weierstrass
List of things named after André Weil
List of things named after Hermann Weyl
List of things named after Ernst Witt
List of things named after John von Neumann
Reference tables
List of mathematical reference tables
List of moments of inertia
Table of derivatives
Integrals
In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions.
Lists of integrals
List of integrals of exponential functions
List of integrals of hyperbolic functions
List of integrals of inverse hyperbolic functions
List of integrals of inverse trigonometric functions
List of integrals of irrational functions
List of integrals of logarithmic functions
List of integrals of rational functions
List of integrals of trigonometric functions
Journals
List of mathematics journals
List of mathematics education journals
Category:History of science journals
Category:Philosophy of science literature
Meta-lists
List of important publications in mathematics
List of important publications in statistics
List of mathematical theories
List of mathematics categories
Table of mathematical symbols
Table of logic symbols
Others
Lists of unsolved problems in mathematics
List of topics related to π
List of order theory topics
Notes
:  Definition from the Journal of Mathematical Physics .
External links and references
 from the American Mathematical Society, a scheme authors find many mathematics research journals asking them to use to classify their submissions; those published then include these classifications.