Chapter 1: Structure, Design and Synthesis

abdc

2-aminobenzene-1,4-dicarboxylate

ad

adipate

aip

5-aminoisophthalate

Amal

allylmaloate

AzDC

4,4′-azobenzene dicarboxylate

azpy

azopyridine

BBCDC

9,9′-([1,1′-biphenyl]-4,4′-diyl)bis(9H-carbazole-3,6-dicarboxylate)

1,4-bdc or bdc

1,4-benzene dicarboxylate

bdp

1,4-benzenedipyrazolate

benztb

N,N,N′,N′-benzidine tetrabenzoate

BME-bdc

2,5-bis(2-methoxyethoxy)-1,4-benzenedicarboxylate

bpa

1,2-bis(4-pyridyl)acetylene

4,4′-bpdc

4,4′-biphenyl dicarboxylate

bpe

1,2-(bis(4-pyridyl)ethylene)

bpee

bipyridine ethylene

BPnDC

benzophenone-4,4′-dicarboxylate

bpp

1,3-bis(4-pyridyl)-propane

bpt

3,6-bis(4-pyridyl)-1,2,4,5-tetrazine

BPT

biphenyl-3,4′,5-tricarboxylate

bpy

4,4′-bipyridine

1_st-Br₂

bistable switch 4-(2,7-dibromo-9H-fluoren-9-ylidene)-3-methyl-1,2,3,4-tetrahydrophenanthrene

bza

benzoate

CAU

Christian-Albrechts-Universität zu Kiel

cdc

trans-1,4-cyclohexanedicarboxylate

3-CH₃-spy

3-methylstyrylpyridine

CID

coordination polymer with interdigitated structure

dabco

1,4-diazabicyclo[2.2.2]octane

dhbc

2,5-dihydroxybenzoate

dpe

1,2-di(4-pyridyl)ethylene

dpNDI

N,N′-di(4-pyridyl)-1,4,5,8-naphthalenetetracarboxdiimide

dps

4,4′-dipyridylsulfide

dpt

3-(2-pyridyl)-5-(4-pyridyl)-1,2,4-triazolate

DUT

Dresden University of Technology

ELM

elastic layer structured metal–organic framework

etz

3,5-diethyl-1,2,4-triazolate

FcDC

1,1′-ferrocenedicarboxylate

FTR

frustrated trigonal-symmetry rotator

fu-bdc

functionalised 1,4-benzene dicarboxylate

fum

fumarate

Hdhbc

2,5-dihydroxybenzoate

ip

isophthalate

L0

bis(pyridyl)dithienylethene

L2

4,4′-((4-(tert-butyl)-1,2-phenylene)bis(oxy))dibenzoate

L3

2,3-difluoro-1,4-bis(4-pyridyl)benzene

L4

1,2,4,5-benzenetetracarboxylate

L5

2,2′-(1,3,5,7-tetraoxo-5,7-dihydropyrrolo[3,4-f]isoindole-2,6(1H,3H)-diyl)dipropionate

L6

5-(tert-butyl)-N1,N3-di(pyridin-4-yl)isophthalamide

miba

4-(1H-2-methylimidazol-1-yl)benzoate

MIL

Materials Institut Lavoisier

MIP

Materials of the Institute of Porous Materials from Paris

ndc

naphthalene dicarboxylate

3-pia

N-(3-pyridyl)isonicotinamide

pcu

primitive cubic

ppt

3-(2-pyrazinyl)-5-(4-pyridyl)-1,2,4-triazolate

PXRD

powder X-ray diffraction

pyrdc

pyridine-2,3-dicarboxylate

pytpy

2,4,6-tris(4-pyridyl)pyridine

pzdc

pyrazine-2,3-dicarboxylate

SCXRD

single-crystal X-ray diffraction

SHF

Sheffield framework

SNU

Seoul National University

2-stp

2-sulfoterephthalate

SU

Stockholm University

tci

tris(2-carboxyethyl)isocyanurate

UTSA

University of Texas at San Antonio

VTTF

2,2′-[1,2-bis(4-benzoic acid)-1,2-ethanediylidene]bis-1,3-benzodithiole

Soft porous crystals have received increasing attention owing to their attractive features as structurally dynamic functional solids.¹ These materials form the 3rd generation of porous coordination polymers (PCPs)/metal–organic frameworks (MOFs) that reversibly transform with at least one of the bi-/multi-stable phases bearing porosity. This transition between different states is driven by external stimuli or by the presence of certain species in the voids. Apart from developing these materials for specific applications,^2,3 there is growing interested in the community to understand the structural factors that cause softness, and thereby potentially predicting or designing novel flexible materials.^4,5 Structural response in MOFs is broadly divided into the following types—breathing, swelling, linker rotation and network movement.⁶ These responses are usually observed in their guest adsorption–desorption profiles, with a signature gate-opening adsorption and desorption with hysteresis. Apart from solvent/guest inclusion or release, the transformations can also be triggered by a physical stimulus, such as temperature, light or mechanical pressure.⁷ While breathing and swelling modes involve discernible changes in cell volume,⁸ some other modes such as linker rotation offer dynamic response without any or negligible change in the overall framework.

Flexibility, in general, can be linked to supramolecular interactions and the stability of the framework in the transformed state. The metal–ligand coordination bond is one of the vital factors that governs the structure and its stability, not only at the local level, but also can impact the overall packing and consequent properties in MOFs. The constituents—metal and linker—also have a role at their individual level in bestowing softness to the system. Likewise, the intraframework interactions influence dynamicity, especially in compounds featuring integrated self-assembly of coordination nets. Guest molecules that occupy the void spaces of MOFs during synthesis, often drive framework flexibility due to strong interactions with the framework backbone. MOFs are typically synthesised at high temperatures and/or pressures from solution. It is seen that using the same building units, varying structures, and topologies are obtained. Pertinent to the discussion of this chapter, in certain examples a flexible structure is the product obtained only under specific reaction conditions.⁹ Additionally, the non-structural reagents—guest molecules—can also direct the self-assembly to a particular conformation by functioning as the template.¹⁰ Another route of inclusion of guest molecules is by binding to the metal centre and being a part of the coordination sphere.

There are different approaches to analysing the library of flexible compounds; in this chapter, we view flexibility from the perspective of (a) framework building blocks and (b) topological level. It is worth noting, that softness in a multi-component system is essentially a combination of different factors working simultaneously, and a strict distinction is inappropriate. However, based on a wider pool of compounds certain trends are drawn and a dominating factor in every case can be identified. The examples listed in the subsequent sections are not exhaustive but mainly aim to demonstrate a flavour of different structural aspects from the literature on flexible MOFs.

In general, flexibility in frameworks and especially with non-interpenetrated structures, is typically ascribed to either the building units and/or guest molecules. The release/inclusion of guests in such systems often leads to different structural responses, such as sliding, swelling or pore contraction (Figure 1.1). The broader context of structural softness can be narrowed down to the choice and character of the building blocks. It is expected that the use of certain metal cations with variable coordination numbers in conjunction with linkers having suitable donor groups offer a dynamic coordination node, and lead to the formation of non-rigid frameworks. In certain cases, the presence of a hemilabile coordination bond may also render local flexibility.^11,12 Ligands with flexible bonds are known to impart flexibility, but not necessarily lead to formation of flexible MOFs.¹³ Another subset involves ligands with functional groups at their core that respond dramatically to an external stimulus. This motion can in turn alter the coordination environment and impart structural dynamicity.

Guest molecules also play a major part in the flexibility of MOFs. Owing to accessible binding sites within the pore walls, with ligand or metal, the host–guest interaction can be stronger than the coordination sphere rigidity to afford a breathing behaviour. However, guest molecules that bind to the framework component may also lead to a flexible response upon their release. This chapter describes several examples of flexibility that are seen as an outcome of either the ligands, metals or guest molecules.

The ligand in MOFs is typically functionalised for application-specific demands. However, the addition of substituents on the organic linker is seen to have a profound effect on the dynamic nature of flexible MOFs. This was demonstrated in a comprehensive study of MIL-88: [Fe₃O(L)₃(H₂O)₂(OH)] (where L = 1,4-bdc (88B), 4,4′-bpdc (88D)), which represents one of the prominent series of flexible MOFs, whose breathing behaviour is driven by host–guest interactions (described in Section 1.4).¹⁴ By functionalising the linkers in two MOFs of the series—MIL-88B and MIL-88D—with a range of groups, such as Cl, Br, CH₃, OH, NH₂, NO₂, CF₃ and F, the swelling properties were studied. In addition, the number of functional groups per ligand varied between 1, 2 and 4. The swelling properties for the MOF were seen to have a direct correlation to the size, number and nature of the secondary functional group. For instance, the amplitude of swelling was reported to be lower as the number of the CH₃ groups per linker were increased from two to four, in both MIL-88B and MIL-88D. This also led to the formation of permanent porosity in certain cases. Additionally, changes in the host–guest and intraframework interactions brought about by the nature of functional groups led to lowering the barrier for the initial diffusion of guests, which facilitated the inclusion of non-polar solvents that could otherwise not cause framework swelling in the non-functionalised compounds. Another MOF that breathes reversibly (discussed in Section 1.4) is MIL-53: [Mⁱⁱⁱ(OH)(bdc)]; MIL-53(Al)-NH₂ represents an extension of the parent MOF with a secondary pendant group.¹⁵ Although ligand functionalisation is usually seen to influence guest binding properties, it was reported that the amine group mainly contributed to the flexibility of the system by interacting with the AlO₄(OH)₂ chains.¹⁶ The presence of the functional group led to the formation of a distinct large pore (lp) phase during methane adsorption at very high pressures, that is absent for MIL-53(Al).¹⁷ On these lines, the breathing behaviours for MIL-53(Al)-OH and MIL-53(Al)-(OH)₂ were reported by testing their ability for methane adsorption (298 K).¹⁸ As in the case with the amine, the hydroxy group also interacted with the metal chain and noticeable differences were seen for gate-opening pressures for the two MOFs. This was attributed to the extent of hydrogen bond interactions between the hydroxy groups with the inorganic chain, with the MOF with a higher density of functional groups opening the pore at higher pressures. As a control, when the hydroxy group was replaced with methoxy i.e., MIL-53(Al)-OCH₃, it was found that MOF no longer exhibited breathing behaviour and presented a type-I adsorption profile with no hysteresis, corresponding to a rigid structure. This reinforced the role of hydrogen bonding involving the substituent group regarding the flexibility of the framework.

Co(bdp) represents another well-studied MOF in the literature.¹⁹ The structure of the pristine phase comprises Co²⁺ in tetrahedral coordination to N-atoms of the deprotonated bdp²⁻ ligands. The nitrogen adsorption isotherms at low temperatures (77 and 87 K) for the desolvated compound showed uncommon multistep filling, which was ascribed to a combination of adsorbate–adsorbent interactions and structural transformations. The gate-opening behaviour along with a strong hysteresis was also seen in the case of hydrogen adsorption, that exhibited strong temperature and pressure dependence. In a subsequent study involving a combination of in situ experiments, it was revealed that the desolvated structure underwent a stepwise structural reorganisation during pore opening from the closed form.²⁰ From a Co²⁺ centre in a square-planar geometry for the guest-free phase, the opening of the pore involved a transition to a tetrahedral conformation. This was also accompanied by the reorientation of the benzene rings in the ligand along with a change in dihedral angles of the coordinated pyrazolate rings.

This characteristic behaviour was further examined by adding substituents to the benzene ring in a series of MOFs: Co(F-bdp), Co(p-F₂-bdp), Co(o-F₂-bdp), Co(bdp-d₄) and Co(p-Me₂-bdp).²¹ All the compounds exhibited a stepwise N₂ adsorption, with subtle changes, except for Co(p-Me₂-bdp) that had a discernible profile. Using methane as a probe adsorbate, larger differences in pore opening pressures were noted (Figure 1.2). Structural characterisation suggested the presence of edge-to-face π–π interactions in the guest-free phase stabilised the compound (Figure 1.2(a)). It was seen that the methyl substituent led to greater stability of the closed pore, while fluoro substituents weakened the non-covalent interaction. Pillar-layered MOFs such as [Zn₂(bdc)₂(dabco)]_n, were reported to exhibit some degree of breathing behaviour.^22,23 The addition of a functional group to the ligand, such as amino or alkoxy, was seen to enhance the degree of breathing.^24,25 Also, carrying out post-synthetic modification on an –NH₂ functional MOF, with linear alkyl anhydrides (O[CO(CH₂)_nCH₃]₂, n = 0 to 5), led to modulation of the breathing behaviour.²⁴ It was found that the nature of the organic substituent stabilised either the large or narrow pore form. Subsequently, in an extensive study on Zn(ii)-based MOFs viz. [Zn₂(fu-bdc)₂(dabco)]_n, the dangling groups covalently bound to the phenyl ring were systematically varied.²⁶ It was observed that the addition of long substituents led to a greater degree of breathing in such systems. This behaviour was reasoned to the interaction of the dangling groups with the framework backbone, and with the incoming guests. Instead of using aliphatic substituents, the effect of using aromatic substituents was demonstrated in modulating the flexibility at the local level, and consequently that of the overall structure in two isostructural 3D MOFs: [Zn₂(bdc-R)₂(bpy)](solvent)]_n (where R = NO₂ or H).²⁷ Owing to the presence of nitro groups in the dangling side chain, strong π–π interactions with the ligand core were observed. For the other MOF, no such interactions were possible, and the pendant groups were arranged in a way that led to the expansion of the void volume (∼34%) and instead had CH–π interactions with the central phenyl ring. The activated phase for both compounds obtained by heating under vacuum reversibly regenerated the pristine structure when exposed to DMF. It was found that activation of the nitro-containing MOF by supercritical CO₂ drying led to the slightly different guest-free structure. The product obtained from both activation methods had the interlayers locked by the strong interaction between the nitroaromatic group and central phenyl ring. The differences in the structure based on the method of activation were found to be due to the stress caused by the pressure of liquid CO₂, which was reflected in a change in the Zn-paddlewheel unit, with one Zn–O clipped after desolvation. This result reinforced the impact of pressure and temperature in soft porous crystals.¹ The same compound was also explored for its ability to screen xylene isomers as the guests participate in π–π interactions with the functional components.²⁸ It was observed that o-xylene (oX) was adsorbed preferentially from a mixture of isomers, as it had the most cooperative interaction with the compound. Although secondary functional sites offer a wider range of possibilities for tuning flexibility, it was also noted that in certain structures, changing the atomic composition of the ligand alters structural softness.²⁹ Two isostructural MOFs—[Fe(ppt)₂] and [Fe(dpt)₂]—were examined for their adsorption properties. [Fe(ppt)₂] exhibited flexibility, while [Fe(dpt)₂] retained a rigid framework. The differences were suggested to arise from the varying coordination ability of the linker’s constitution, with Hppt having pK_b = 0.65, while Hdpt had pK_b = 8.8. Consequently, rigidity and flexibility were seen having a direct correlation with the softness of the coordination bond.

Apart from substitution of the organic linker, another type of post-synthetic modification arises from functional sites within the core of the ligands. One of the more studied functions in MOFs is that of photodimerisation reactions that lead to the rearrangement of bonds in a coordination polymer/MOF and subsequently alter the pore chemistries. In this regard a flexible Mn(ii)-based MOF—[Mn(bdc)(dpe)]—was reported to exhibit guest-dependent gate-opening behaviour.³⁰ The metal centre (Mn(ii)) had a distorted coordination environment in the pristine phase, while the guest-free phase led to shrinkage of the narrow pore. The distance between the olefinic groups was 4.02 Å, which satisfied Schimdt’s criterion for photodimerisation (<4.2 Å). Unlike the use of secondary functional groups, the orientation of the pore wall was deemed to distinguish between the two gases that were used in the study, CO₂ and C₂H₂. The pore opening from the desolvated phase involved an end-on interaction for CO₂, whereas for C₂H₂ the CH–π interaction required pore expansion and undergo gate-opening adsorption. Subsequently, a photoinduced [2 + 2] cycloaddition reaction was carried out (Figure 1.3). The resulting framework after light irradiation showed a distinct colour change on account of loss of conjugation, and a significantly different orientation of the phenylene rings was obtained. Not only was the total adsorption reduced, but the selectivity for the two gases was absent. This resulted from the merging of narrow pore pockets into a single channel pore and unfavourable configuration of the phenylene rings for interaction with the guest.

The idea of cross-photodimerisation has also been investigated in a few other MOFs, for instance, the [2 + 2] cycloaddition reaction in a 3D, Zn(ii)-based MOF: [Zn₂(H₂O)₂(Amal)₂(bpe)].³¹ The pristine MOF crystallised in ins topology, which upon irradiation underwent photoreaction resulting in the formation of a cyclobutane ring and the resulting structure had a new topology. This was seen as a broader strategy to prepare unsymmetrical ligands based on an unsaturated backbone. It is worth noting that this approach of photochemical [2 + 2] reactions using functional ligands in CPs and MOFs has been increasingly applied and found suitable for a range of structural transformations and applications.^32–34 

In another report, an uncommon example of a material showing photoinduced non-linear contraction (PINC) in a 2D Zn(ii)-MOF—[Zn₂(bdc)₂(3-CH₃-spy)₂]·H₂O—was noted.³⁵ The parent compound showed anisotropic positive thermal expansion (PTE). The photochemical reaction led to the formation of a 3D structure, by virtue of cyclobutane rings between the interdigitated layers. Interestingly, when the reaction was carried out by varying the wavelength of irradiation, it was found that the lattice parameter along a-axis and unit cell volume shrunk most at λ = 385 nm. It was found that apart from the reaction in the linker, the Zn-paddle wheel unit also underwent distortion.

A common theme with photochemical reactions is the large stress and strain inflicted on the polymeric structure. To be able to accommodate the structural changes accompanying photoinduced reactions, an approach of using linkers with active groups in flexible structure was proposed.³⁶ The dithienylethene (DTE) moieties are known for the photoresponsiveness, and it was included as the linker core in the Zn(ii)-based interpenetrated MOF [Zn₄(bdc)₄(L₀)₂·4DMF·H₂O]_n. The DTE could undergo a reversible transition from open to closed form upon irradiation of UV radiation in several solvents, and also in the solid-state. The flexible nature of the MOF was ascribed to enable an effective reaction, as the changes in the bonds caused significant structural changes. Similarly, the photoisomerisation of azo bonds from trans to cis upon UV irradiation offers an attractive pathway to bestow local flexibility in MOFs. Such a study was reported in a Zn(ii)-based, interpenetrated MOF bearing potentially two linkers with photoactive sites, Zn(AzDC)(BPE)_0.5.³⁷ A dynamic photoinduced isomerisation was observed, which caused remarkable differences in guest (CO₂) uptake, with release of CO₂ being observed when the compound was exposed to radiation during adsorption. This was caused due to the increase in surface energy caused by trans–cis isomerisation and consequent weakening of intermolecular interactions with the adsorbate. These results further reinforce the efficacy of soft porous crystals for photo responsiveness.

Ligands based on flexible bonds, either as donor groups or part of the core, are attractive candidates to bestow structural dynamicity. An example of a guest-induced structural transformation in a MOF with soft coordination bonds was reported in the Co(II)-based MOF-Co(VTTF).³⁸ The desolvated phase led to the formation of a non-porous structure that included a bond between the S-atom of the linker with Co(ii) centres. During the adsorption of ethylene gas, the structure underwent a two-step opening with the interaction between the π-rich guest with Co(ii) displacing the bond with the S-atoms of the ligand. The inherent lability of the coordination bond allowed the structure to open up completely with increasing pressures and led to a Co(ii)–C₂H₄ interaction at all sites. As a control, when adsorption with ethane (C₂H₆) was recorded, the structure did not open even at higher pressures. The hemilabile bond-assisted, guest-dependent structural transformation was termed as a gate-locking/unlocking mechanism. Among early reports of complete structural characterisation by single-crystal-to-single-crystal studies in the domain of flexible MOFs, a reversible transformation in a 2D MOF—{[Cu(pyrdc)(bpp)]·(5H₂O)}_n—having a highly flexible pillar (bpp) was observed.³⁹ The pristine phase comprised five-coordinate Cu(ii) bonded to four independent ligands. However, when the compound was heated, the colour of the compound changed to dark blue, and the guest water was lost leading to the shirking of the pores. Structural information suggested the breaking of a coordination bond at one Cu-centre with the N-atom of the pyridyl group (Figure 1.4). This transition was accompanied by a large change in the orientation and bonding direction of the flexible pillar ligand. Upon resolvation, the original phase was recovered, and the guest-free phase exhibited gate-opening adsorption towards CO₂ (195 K) and vapours of polar solvents, e.g., methanol and ethanol (298 K). The same group also presented such behaviour in a 3D MOF—{[Ln(tci)(H₂O)]·4H₂O}_n (where Ln = Ce or Gd)—that showed a dynamic and reversible structural behaviour upon partial loss of water molecules.⁴⁰ The resulting phase was stable and had a change in its pore shape that exhibited the typical gate-opening behaviour towards water adsorption at 298 K. The flexibility and stability of the partially evacuated compound after heating was ascribed to the flexible –CH₂–CH₂– linkages in the ligand.

Another case of a dynamic MOF is {[Zn₄O(L2)₃(DMF)₂]·xG}_n (G = guest) – referred to as DynaMOF-100 – in which the linker contains flexible ether linkers.⁴¹ The pristine phase of the compound underwent significant squeezing upon desolvation (void volume reduction from ∼3441 ų to ∼916 ų), resulting from the loss of guest and coordinated solvent molecules (Figure 1.5). This was accompanied by slippage of the 2D layers to result in an overall non-porous structure. Additionally, the pristine structure having a secondary building unit (SBU)—{Zn₄O(O₂C⁻)₆(DMF)₂}—with mixed tetrahedral and octahedral coordinating Zn(ii) cations transformed to a non-porous phase [Zn₄O(L2)₃]_n with all Zn(ii) centres in tetrahedral coordination. This porous to non-porous transition was found to be fully reversible. The flexible nature of the compound was ascribed to a combination of accommodative ether linkages in the ligand and the stability of Zn(ii) in varying coordination environments. Based on low-temperature CO₂ adsorption (195 K) on the desolvated MOF, the effective pore diameter was estimated to be 5.1 Å. When single-component adsorption for xylene isomers (kinetic diameter ∼0.6 nm) was performed at 298 K, it was found that only p-xylene could open the framework, while its isomers were unable to enter the pores. A re-solvated phase of p-xylene in presence of DMF was obtained, which suggested the pore opening was a combination of guest fitting and favourable π–π bonding interactions with the linker, facilitated by the flexible ether bonds.

DynaMOF-100 was also able to distinguish the industrially relevant C8-mixture (styrene and ethyl benzene) by accommodating styrene and remaining in the closed pore form for ethyl benzene.⁴² Like the previous study, styrene was found to have multiple non-covalent interactions with the MOF, that stabilised the included guest molecules. Another set of 2D Zn(ii)-based flexible MOFs was reported, that contracted upon desolvation and expanded for vapours of various solvents, chiefly being able to separate C8-isomers.⁴³ Two MOFs with different pillar linkers—[Zn₂(aip)₂(pillar)]·2DMF (pillar = bpy or bpe)—had roughly the same breathing behaviour, except the MOF with bpe showed higher dynamic character due to the presence of flexible core in the linker. When the activated MOFs were exposed to different guests—small organic solvents and C8 hydrocarbons—it was noted that the extent of pore expansion had a correlation with the size of the adsorbate. Similar to the ether links described above, the flexible sp²-hybridised N-nodes in DUT-13 ⁴⁴—Zn₄O(benztb)_1.5—can drive the linker from a staggered conformation in the open-pore form to an eclipsed orientation in the closed-pore phase.⁴⁵ This breathing behaviour was triggered by the adsorption of the guests and was found to be fully reversible.

An early example of a flexible MOF came using an aliphatic linker in a 3D MOF: {[La₂(ad)₃(H₂O)₄]·6H₂O}_n.⁴⁶ It was suggested that the presence of an aliphatic linker could absorb any structural distortions and prevent collapse upon removal of the guest solvent. This was realised when the MOF was heated at 115 °C, which led to complete removal of free water and partial loss of coordinated water. The addition and removal of water from the system was reported to be a reversible process, that highlighted the role of an aliphatic backbone. Another example of such flexibility induced by bulky guests, e.g., xylenes, was reported in a system, structurally related to MIL-53.⁴⁷ The Al-MOF—[Al(OH)(cdc)]·H₂O (referred as CAU-13)—comprised of the linkers in a 1 : 1 ratio of a,a- and e,e-conformations that exhibited slight breathing in response to water and CO₂.⁴⁸ In both the cases, the primary mode of interaction was with the bridging µ₂-OH groups in the MOF. However, although π–π interactions with framework pore walls were absent, when vapour adsorption for xylenes was carried out, the structure was able to fully open with all the linkers in e,e-configuration (Figure 1.6). The effective cell volume increase in response to xylene inclusion was ∼25%. Such behaviour was also observed for the Ga(iii)-analogue,⁴⁹ however the In(iii) and Cr(iii)-MOFs did not exhibit breathing.^50,51 Although generally non-aromatic linkers are expected to bestow higher flexibility, it was found that using fumaric acid as the linker in a MIL-53(Al) analogue led to formation of an almost robust structure.⁵² However, using a fully saturated ligand—adipic acid (H₂ADP)—gave rise to a flexible variant MIL-53-ADP,⁵³ which displayed breathing behaviour upon hydration and removal of water. The linker was seen to change its conformation and shorten its length, from 5.79 and 5.90 Å to 5.43 and 5.70 Å in the hydrated forms. Also, the framework expanded by ∼10% with the inclusion of water. The flexibility directed by the adaptability of the backbone further reiterated the utility of aliphatic linkers.

Zr(iv)-Based MOFs have received increasing attention, owing to the thermal and chemical stability bestowed by the strong coordination bonds in such systems. Consequently, these compounds are commonly seen to be topologically rigid. In an interesting study, the role of linker backbone and substituents in a series of isostructural MOFs based on 10-connected Zr₆ SBU [Zr₆(µ₃-O)₄(µ₃-OH)₄] and C4-ligands was examined.⁵⁴ The selection of ligands—fumaric acid (F), succinic acid (S) and malic acid (M)—comprised variation in degrees of freedom and in the case of malic acid an additional hydroxy substituent. The resulting MOFs—MIP-203-F, MIP-203-S and MIP-203-M, respectively, —exhibited structural flexibility with varying degrees. Upon desolvation, all the compounds showed an opening of the pore when exposed to different polar solvents. Similarly, when the compounds were tested for gas adsorption, differences were noted in terms of pore opening. MIP-203-F exhibited a swelling response, while MIP-203-S, having the highest degree of freedom, was found to have linker rotation to accommodate guests. MIP-203-M having a secondary functional group exhibited the highest selectivity for CO₂/N₂ separation.

The flexibility of coordination bonds in MOFs also provides scope for breathing behaviour, and strongly depends upon the nature and size of the cation. Such coordination softness-induced transformation was observed in a Cd(ii)-based MOF built from a mixed N- and O-donor ligand, miba.⁵⁵ The pristine MOF showed six-coordinate Cd(ii), binding with four O-atoms of the carboxylates and two N-atoms from the imidazolyl units. Upon desolvation, the linker rotated, and the coordination of the metal nodes changed to five-coordinate, hexahedral. The closed-pore structure obtained after desolvation could be opened after the application of high-pressure CO₂ gas. DFT calculations revealed that the coordination bonds for Cd(ii) are flexible, which allows linker rotation during desolvation, to convert the system into a low-energy, non-porous state. Similar flexibility, driven by the dynamic nature of the coordination bonds, was noted in a doubly interpenetrated, pillar-layered framework: [Zn₂(BPnDC)₂(bpy)] (referred to as SNU-9).⁵⁶ The synthesis of the MOF and its stepwise gas adsorption behaviour was previously studied,⁵⁷ when it was observed that the cell volume shrunk by ∼28% upon loss of guest molecules. However, unlike typical flexibility reported in interpenetrated MOFs, the breathing behaviour in SNU-9 was attributed to the change in the coordination environment of Zn(ii). The coordination for one of the Zn(ii) centres changed from distorted octahedral in the pristine phase to distorted square-pyramidal (Figure 1.7). This was also reflected in reorientation of one of the BPnDC²⁻ ligands. It is worth noting, that the concept of soft SBU was previously introduced using another Zn(ii)-based interpenetrated, pillar-layered MOF: {[Zn₂(bdc)₂(L3)]·2.5DMF·0.5H₂O}_n.⁵⁸ The pristine structure with a regular paddle-wheel coordination environment (square pyramidal geometry) underwent transformation to a tetrahedrally coordinated Zn(ii)-based structure upon heating. This was accompanied by a drastic reduction of the cell volume of ∼28%. Also, it was reported that this transition was gradual with the coexistance of multiple phases at the intermediate temperatures.

Generally, Zn(ii) is expected to exhibit dynamic coordination environments for most MOFs because of its stability in different coordination geometries. In an interesting finding, such flexibility was seen in a Bi(iii)-MOF constructed using a tripodal ligand: [Bi(BPT)·2MeOH] (referred to as SU-100).⁵⁹ The Bi(iii) ions having coordination number seven, exhibited an inorganic building unit of Bi₂O₁₂ dimers, with two O-atoms bridging the Bi(iii) cations. When the compound was exposed to different polar solvents such as methanol, DMF and DEF, the structure expanded with up to 10% change in unit cell volume corresponding to the inclusion of DEF. A mechanistic investigation suggested the flexibility of the Bi₂O₁₂ unit in modulating the framework breathing. The Bi–O–Bi bond angles were observed to change from 121.1(5)° in the as-synthesised phase to 110.5(3)° in the DEF-included structure, and the bridging carboxylates were seen to move apart from each other during expansion.

In a broader context, the choice of the metal ion has an immense impact on the flexible nature of MOFs. Among the more studied dynamic MOFs in the literature, DUT-49—[Cu₂(BBCDC)]⁶⁰—which is composed of a tetratopic ligand, has shown structural contraction during gas adsorption.⁶¹ It was found that the compound showed an abrupt decrease in gas uptake (CH₄ adsorption at 111 K) at a certain pressure, forming a metastable phase. Detailed in situ studies revealed that filling of the mesopores led to a sudden buckling of the ligand leading to the conversion of the open pore form to the closed pore form, termed as negative gas adsorption (NGA). Structurally, this step was accompanied by rotation of the linker along the biphenyl backbone. DUT-49 sustained the NGA profiles for adsorptions at different temperatures and even for other hydrocarbons such as n-butane. Also, this behaviour was observed for high-pressure CO₂ adsorption in DUT-49, and also with other systems constructed with different carbazole connecting groups: phenyl (DUT-48), triphenyl (DUT-50) and naphthyl (DUT-46).⁶² Subsequently, the role of metal ions in directing the flexibility of frameworks was examined by the same group.⁶³ By post-synthetically exchanging metal ions in DUT-49(Cu) with Mn(ii), Fe(ii), Ni(ii), Zn(ii), Co(ii) and Cd(ii), a series of MOFs was prepared. It was found that the Cu(ii)-MOF was the most flexible and had the highest porosity, while the Ni(ii)-analogue exhibited moderate flexibility. MOFs with other metal ions were unstable upon activation and did not retain porous properties. These trends were ascribed to the role of M–M bonds in the structure, with Cu (2.634 Å) and Ni (2.720 Å) having short distances. Although rarely found, Mn–Mn and Cd–Cd paddle-wheel moieties were observed in the structures although, they were inadequate to sustain stability during the activation procedure.

A study on similar lines was reported by varying the metal ions in a series of 2D MOF viz. MCID-1 [M(ip)(bpy)]_n (M = Co, Ni, Cu and Zn) and their response towards guest (water) molecule inclusion was monitored.⁶⁴ The structure formed hydrophobic pores upon desolvation for all the M-ions, which then opened up for guest inclusion in the gaps of the 2D layers. However, significant differences were noted for water uptake, which was correlated to the distortion of the coordination environment. CuCID-1 displayed an early onset (P/P₀ = 0.33) for guest inclusion, which was attributed to the Jahn–Teller effect maintaining coordination distortion even after desolvation of the parent phase. ZnCID-1 had an overall similar uptake, with a much higher gate pressure (P/P₀ = 0.6), while NiCID-1 and CoCID-1 did not have any considerable guest inclusion over the entire pressure range. This observation was consistent in mixed-metal MOFs, wherein the presence of Cu(ii) or Zn(ii) allowed the compounds to open up for water adsorption. This influence of the metal-ion character was also observed in the changing structural dynamics of UTSA-300—[Zn(dps)₂(SiF₆)]_n—by replacing Zn(ii) with Cu(ii) (denoted as NCU-100; UTSA-300-Cu).⁶⁵ The structure comprising octahedrally coordinated metal ions exhibited a difference in the M–F bond length (Cu–F: 2.27 Å vs. Zn–F: 2.09 Å), owing to the Jahn–Teller distortion. The parent Zn-MOF underwent interlayer space shrinkage but had a narrow pore structure (3.5 × 3.9 × 4.1 ų and 4.3 × 4.3 × 4.1 ų) that opened during guest inclusion. However, the Cu-MOF maintained an open pore structure (3.6 × 4.3 × 4.2 ų and 4.7 × 4.5 × 4.2 ų), despite a similar interlayer shrinkage. These subtle structural differences were seen to have a profound effect on the application, with the Cu-MOF showing higher uptake of C₂H₂ even at lower pressures.

MIL-53 represents an important type of flexible MOF that exhibits guest-induced breathing behaviour. However, the breathing phenomenon is also strongly dependent upon the choice of the metal centre, as observed in MIL-53(Fe).⁶⁷ Likewise other metal ions such as In(iii),⁶⁸ Ga(iii)⁶⁶ and Sc(iii),^69,70 are seen to have a significant impact on the pore dynamics. The varying evolution of the structures and corresponding thermal stabilities were suggested to be an outcome of the difference in ionic radius of the metal cation in octahedral coordination, and their electronic configuration (Figure 1.8).⁶⁶ The implications of these differences in breathing behaviour are discussed in more detail in Section 1.4. Such differences in rigidity vs. flexibility based on metal ions were also reported for linkers with bulky backbones—MIL-53-FcDC—where the Ga-MOF showed breathing behaviour towards heavy guests such as iodine and pyrazine, while the Al- and In-analogues did not exhibit breathing.^9,71,72 In addition to exploring various metal cations, mixed-metal and mixed valence approaches have also been tested for MIL-53 structures, including linkers with secondary functional groups such as amino (–NH₂).^73–77 

As described in previous section, MOFs having ligands with pendant alkyl chains are seen to present a highly dynamic response. For instance, it was seen that the Zn(ii)-compound—[Zn₂(BME-bdc)₂(dabco)]_n—exhibited multiple phases during CO₂ adsorption, with a discernible intermediate phase between the narrow pores in a desolvated state and the open pore form after CO₂ inclusion.⁷⁸ Apart from the non-covalent interactions between the pendant groups with the linker backbone, the distortion of the coordination environment was suggested to drive this flexibility. The study on this system was further expanded by preparing a series of isostructural MOFs—[M₂(BME-bdc)₂(dabco)]—with varying metal centres (M = Zn(ii), Cu(ii), Ni(ii) and Co(ii)).⁷⁹ During desolvation, the extent of pore contraction was seen to alter with the metal node: Co(ii) exhibiting the maximum, while Cu(ii) with a more rigid coordination environment demonstrated the least (Figure 1.9). These differences were ascribed to the electronic effects of the metal ions in destabilising the square pyramidal geometry of the large pore phase. Again, during CO₂ adsorption, a similar pattern for Zn(ii) and Cu(ii)-MOFs was observed with distinct gate pressures and identification of three states: narrow pore, intermediate and large pore. However, for Ni(ii) and Co(ii), there was gradual inclusion of the gas before complete conversion to large pore phases at higher pressures. Another study compared the same set of metal cations in DUT-8: [Ni₂(2,6-ndc)₂(dabco)].⁸⁰ DUT-8(Ni) was earlier seen to exhibit breathing behaviour, and the Co(ii)-analog was found to exhibit a similar nature. Interestingly, the Zn(ii)-MOF transitioned into a non-porous phase and did not open up. DUT-8(Cu) was seen to maintain an open pore structure upon evacuation.

Apart from transition metals, lanthanides are also seen to impart different features. Owing to higher coordination numbers, typically MOFs constructed from such metal ions have dense packing. This facet was explored by preparing a series of rare-earth (RE) metal ion-based MOFs from a tripodal ligand with acylamide moieties.⁸¹ Compounds prepared from Y(iii), Ce(iii), Nd(iii), Eu(iii), Tb(iii), Dy(iii), Ho(iii), and Tm(iii) yielded rigid porous structures, with the metal-ions having a coordination number of eight. However, the compound obtained with La(iii) exhibited structural differences, with the metal ion having a coordination number of nine, and flexibility upon desolvation. This was also reflected in the adsorption for the La-MOF that exhibited gate-opening with a large hysteresis for the low-temperature (195 K) CO₂ isotherm.

Another type of flexibility in MOFs is seen by triggering redox reactions at the metal centre. Among the early studies aimed at using MOFs for charge storage, a partially fluorine-doped MIL-53—[Fe(OH)_0.8(F)_0.2(bdc)]·H₂O—was reported as a candidate for reversible insertion of Li⁺ ions.⁸² The MOF was cycled against lithium metal as a counter electrode between 1.5 and 3.5 V. It was found that a mixed-valence Fe³⁺/Fe²⁺ state could be achieved reversibly during lithiation with the insertion of ∼0.6 lithium ions. Apart from the redox reaction, the structural evolution suggested swelling of the MOF during exposure to the electrolyte: ethylene carbonate and dimethyl carbonate (1 : 1). The cell parameters were also found to alter during Li-ion insertion or removal. A gravimetric capacity of 75 mA h g⁻¹ was reported for the material at a low discharge rate of C/40.

The response of including a redox-active guest molecule (hydroquinone = H₂Q) in a vanadium-based flexible MOF—MIL-47(V)—was later examined.⁸³ The breathing behaviour of this compound is discussed further in Section 1.5. The as-prepared MOF, [V^III(OH)(bdc)] underwent oxidative loss of guest species upon heating in air to have the metal centre oxidised to +4, resulting in the overall framework of [V(O)(bdc)].⁸⁴ The redox-active guest was included in the activated MOF either by heating under ambient air or treatment under anhydrous conditions (Figure 1.10). When heated in air, the guest underwent oxidation to release a proton and electron that reduced the metal centre and converted the bridging oxygen to µ-OH. The resulting p-benzoquinone formed a charge-transfer complex with excess hydroquinone, which was loaded in the pores of the MOF. The change in the oxidation state of the metal in MIL-47(V) to +3 is seen to make the system more flexible in developing a strategy to activate the MOF.⁸⁵ However, heating activated MIL-47(V) with hydroquinone under inert conditions led to a drastically different outcome. Hydroquinone is known to thermally degrade above 250 °C, and led to stepwise conversion to p-benzoquinone with p-semiquinone radical and p-semiquinone radical anion as intermediates. It was suggested that the formation of the radical led to the reduction of V(iv) and protonation of the bridging O-atom. Subsequently, formation of the radical anion would further protonate the µ₂-OH and the radical anion stabilised the inorganic chain, with the loss of a water molecule.

In an early report in this regard, guest-induced structural transformations were observed in a 2D Co(ii)-based MOF: {[Co(NCS)₂(3-pia)₂]·2EtOH·11H₂O}_n.⁸⁶ The pristine structure upon heating transformed to an amorphous phase, that exhibited formation of guest-included crystalline phases upon exposure to Me₂CO, THF or water to form {[Co(NCS)₂(3-pia)₂]·4Me₂CO}_n, {[Co(NCS)₂(3-pia)₂]·4THF}_n or {[Co(NCS)₂(3-pia)₂](H₂O)₂}_n. Both acetone and THF included phases upon heating underwent a transition to the crystalline phase, accompanied by a naked eye colour change from pink to violet. As an important finding, this structure could revert to the THF or acetone-included phase reversibly. It was also suggested that the presence of the amide groups in the ligand stabilised the guest-free phases by hydrogen bonding between the layers, and those interactions directed the sliding of the 2D sheets during structural transformations. Among other early compounds in the domain of flexible MOFs, MIL-47 (V)⁸⁴ and MIL-53 (Cr)^87,88 were regarded as important findings. Both MOFs are constructed from bdc²⁻ ligands MIL-47: [VO(bdc)]; MIL-53ht: [Cr(OH)(bdc)] and exhibited expansion of the pore upon desolvation. MIL-47 could revert to the as-synthesised phase upon treatment with trimethylbenzene and 2-methyl-1-propanol. In the case of MIL-53, once the unreacted linker was removed from the structure, a reversible transition between the closed and open pores was observed. However, unlike MIL-47 which led to the formation of a hydrophobic pore, the closed-pore form in MIL-53 included water. This was ascribed to the presence of hydroxyl groups in the metal chains that could interact with the water molecule. In a following study of the hydration behaviour in the aluminium analogue of MIL-53(Cr), it was found that the presence of hydrogen bonding interactions between the guest water and frameworks O-atoms were responsible for the breathing behaviour and stability of the narrow pore configuration.⁸⁹ These differences in the pore chemistry for the two MOFs were further observed when gas adsorption studies were performed using CO₂ and CH₄.⁹⁰ While the CH₄ adsorption isotherm for MIL-53 (Al or Cr) showed a characteristic profile for a nanoporous solid, the response to CO₂ was significantly different. The isotherm had a step at ∼6 bar, which was seen for both MIL-53(Cr) and MIL-53(Al). However, when MIL-47 was tested for CO₂ adsorption, it did not show any steps during adsorption and the total amount adsorbed above 10 bar was similar for both sets of MOFs. A more detailed study of the adsorption of CO₂ by MIL-47(V) was later reported.⁹¹ This difference in behaviour was reasoned to be CO₂ having a permanent quadrupole, that led to MIL-53 undergoing shrinkage of the pore in the first instance and opening subsequently, like the observation for water. A set of investigations were later reported that reinforced the active role of the hydroxy (–OH) group during adsorption of CO₂. Specifically, it was found that both O and H-atoms are involved in strong non-covalent interactions with the guest CO₂, which leads to the breathing behaviour for MIL-53.^92–95 

The understanding was further expanded by studying the adsorption of C1–C4 hydrocarbons in MIL-53(Cr).⁹⁶ As reported earlier, no closing of the pore was observed for CH₄. However, in the case of other hydrocarbons, the concurrent presence of the large pore and narrow pore forms was observed, and the extent of breathing was found to depend upon the size of the adsorbate. In terms of energetics, it was found that an initial enthalpy of −20 kJ mol⁻¹ was required to initiate the transition from large-to-narrow pores. Interestingly, when this study was expanded for other alkanes (C5–C9),⁹⁷ it was found that for all hydrocarbons there was a discernible sub-step, suggesting narrow pore formation as an intermediate. As expected, the total adsorbed amounts lowered with the increasing size of the adsorbate. However, when a different metal centre (MIL-53(Al)) was tried, it was found that the position of the step differentiated noticeably from MIL-53(Cr). Apart from hydrocarbons, this system (MIL-53(Cr)) was also explored for adsorption of polar solvent vapours, e.g., water, methanol and ethanol.⁹⁸ It was found that all the three guests squeezed the large pore, but for the alcohols the pore closing was partial. Also, in the case of water, the MOF did not open at any pressure step after closing, whereas for the alcohols the transition to large pore form happened after P/P₀ ∼0.2. For all the three guests, the mechanism was proposed to have hydrogen bond interactions between protons of the hydroxy group and O-atoms of the guest, and between protons of the guest and O-atoms of the hydroxy of the inorganic chain. Also, adsorption for ethanol was reported to be most energetic as with a longer alkyl chain, it could simultaneously interact with two metal-chains of the structures. In another study on MIL-53(Al), it was observed that during vapour adsorption of C8-alkyl aromatic compounds (xylene isomers and ethylbenzene), the MOF exhibited contraction of the pore at lower pressures.⁹⁹ Following corresponding gate-opening pressures, a separation between the guest molecules was seen along with reopening of the pore. The differences in uptake at higher pressures was correlated to the differential packing of the guests, accompanied with interactions between the methyl groups and carboxylate of the framework. Several groups subsequently reported the synthesis and breathing behaviour of MIL-53(Al) MOFs by addition of secondary functional groups to the ligand, and also by the testing post-synthetic modification in such MOFs.^100–104 The influence of linker rotation and the effect of host–guest interactions with pendant secondary groups towards guest inclusion of liquids was later probed in a series of MIL-53(Al)-X MOFs (X = H, CH₃, NH₂, NO₂ and OH) using NMR spectroscopy.¹⁰⁵ The impact on linker rotation upon the flexibility of MOFs is discussed in more details in Section 1.6. While interaction with guest and linker rotation are key drivers for structural changes in MIL-53 compounds, it was found that mechanical pressure could also be used to control the pore motions.¹⁰⁶ It was proposed to use external pressure to constrain the MOF to a narrow pore (np) form and use that phase for gas adsorption and separation. After adsorption the pressure would be released, that drives the MOF back to the large pore form. This was suggested as a better control for enhancing the regeneration process of the adsorbent.

MIL-53(Fe) is similar to the Cr and Al versions but exhibits different flexibility.⁶⁷ The as-synthesised structure consists of water molecules in its pores. Upon desolvation, unlike the Al(iii) and Cr(iii)-MOFs that undergo pore opening, MIL-53(Fe) exhibits a reversible pore contraction with an intermediate dehydrated structure that has very narrow pores. This difference was ascribed to differences in the M–O–M inorganic chains and the orientation of the ligand. Interestingly, MIL-53(Ga) exhibited a breathing behaviour that lies between the Al and Fe analogues.⁶⁶ While the structure opened up completely upon dehydration like Al-MOF, the intermediate step followed the Fe-MOF where a very narrow pore structure was formed. Unlike the Fe-MOF, the intermediate structure had high thermal stability (60–220 °C), before opening the pores completely. MIL-53(Sc) exhibited the formation of a closed pore form upon desolvation, which showed the smallest volume among all analogs of the MIL-53 series.¹⁰⁷ This was attributed to greater flexibility owing to the larger ionic radius for Sc(iii). Interestingly, hydration at room temperature to the desolvated structure gave rise to an intermediate that had water molecules included in alternate channels (Figure 1.11).

These structural differences with different metal cations are seen to have a significant impact on the breathing behaviour. Although MIL-53(Fe) does not have a permanent porosity in its evacuated state, it was observed that treatment with a range of liquids gave rise to pore opening to the large pore forms with the inclusion of guest molecules.¹⁰⁸ This process was seen to be rapid and the swelling of the structure was seen to be influenced by the interactions or lack of it with the hydroxy groups in the inorganic chains. Further investigation on this MOF was carried out for its ability to adsorb light alkanes (C1–C4) at 303 K. Unlike Al or Cr-MOFs, MIL-53(Fe) exhibited complex stepwise adsorption for all the hydrocarbons.¹⁰⁹ The structure opened from the very narrow pore (vnp) form to an intermediate np. The steps in the adsorption profiles varied with the size of the adsorbate, and the pore opening process was attributed to a combination of host–guest interactions and the size of the pore for corresponding guest inclusion. However, MIL-53(Sc) exhibited different behaviour for CO₂ adsorption (196 K) which had a two-step process leading to the complete opening of the pore with the presence of a closed pore intermediate from the vnp in the evacuated state.¹⁰⁷ As described in Section 1.3 the presence of secondary functional groups has a significant impact on the breathing behaviour of flexible MOFs. When the linker was functionalised with the –NO₂ group, the compound directly opened to the lp form, and the step was at a much lower pressure compared to the non-functionalised MOF. This was ascribed to the steric hindrance caused by the bulky group. Likewise, it was noted that when the linker in MIL-53(Fe) was functionalised with groups of varying characters, such as –Cl, –Br, –CF₃, –CH₃, –NH₂, –OH, –CO₂H, the breathing patterns with respect to the non-functionalised MOF were altered.¹¹⁰ Although in all the cases the compounds retained their flexibility, the breathing nature was complex and was dependent upon the host–guest interactions as more sites were available for guest interactions. In addition, factors like steric hindrance caused by the pendant groups and intraframework interactions were seen to influence the ability of the compound to breathe.

Another set of MOFs—MIL-88—was found to present a very high degree of breathing. Initially reported using fumaric acid as ligand, the MOF was prepared as a second step after the formation of a trimeric SBU.¹¹¹ The resulting MOF—[Fe₃O(CH₃OH)₃(fum)₃·(CH₃CO₂)·(CH₃OH)_4.5] (referred to as MIL-88A)—underwent structure shrinkage when heated and desolvated. However, a very large swelling behaviour was observed with ∼85% change in cell volume from the fully evacuated state and upon hydration.¹¹² The guest inclusion was also seen for other polar molecules, e.g., methanol, ethanol and butanol, and the extent of swelling was found to be inversely correlated to the size of the guest. More importantly, this swelling was fully reversible over multiple cycles. The swelling was proposed as a combination of rotation of the metal trimeric SBU and the free rotation of the linker based on single bonds. This system was further expanded into a series of isoreticular MOFs MIL88B (1,4-bdc), MIL-88C (2,6-ndc) and MIL-88D (4,4′-bpdc), that were prepared using a similar synthetic protocol as described initially.¹¹³ Interestingly, all the compounds of this series exhibited large breathing, and the extent of swelling was also found to vary with the nature of the ligand.¹¹⁴ A detailed study using a number of organic solvents, e.g., pyridine, DMF, DEF, DMC, DMSO, toluene, hexane, lutidine, water and alcohols, suggested that in principle the host–guest interactions drove the swelling behaviour. Broadly, these interactions could be classified into the affinity of polar liquids with the SBU and weak non-covalent (van der Waals, π–π, CH–π) interactions for all solvents with the linkers. Also, for these solvents, the swelling was found to be reversible in all the MOFs.

Similar to the MIL-series MOFs, solvent-dependent breathing was also seen in a In(iii)-based MOF: (Me₂NH₂)[In(abdc)₂] (referred to as SHF-61).¹¹⁵ The compound had a two-fold interpenetrated 3D structure that comprised of uncoordinated cations and occluded solvent molecules.¹¹⁶ The adsorption properties for the solvent evacuated phase were found to be strongly dependent upon the solvent used for pre-activation treatment. When treated with CHCl₃, the structure adopted an open pore form that remained unaltered during adsorption. However, when the pristine phase was heated directly, a continuous breathing phenomenon corresponding to the desolvation of the solvents (DMF and water) was noted. This continuous structural change was found to be fully reversible and was linked to the strong interaction of the solvent molecules with the framework.

The synthesis of MOFs typically leads to inclusion of water or other solvents in the framework, either as coordinated molecules or free guests within the pore. In certain cases, use of bulky solvents functions as a templating agent that leads to formation of porous architectures. Among the different structures, 2D MOFs are seen to offer higher degree of flexibility in such cases during guest removal. Flexibility of the linker and/or variable coordinating tendency of the metal ions are further seen to facilitate softness in such systems. This was observed in the first instance of gate-opening adsorption in MOFs.¹¹⁷ The synthesised pre-ELM-11 phase {[Cu(BF₄)₂(bpy)(H₂O)₂](bpy)}_n, exhibited 2D Cu(bpy)₂ layers that were bound by non-covalent interactions. When the compound was activated at different temperatures (348–423 K), differences in N₂ (77 K), Ar (77 K) and CO₂ (273 K) adsorption profiles were seen which could be linked to partial or complete loss of coordinated water molecule. In a following study, it was revealed that the adsorption of the fully dehydrated phase proceeded by clathrate formation of the adsorbates within the layers of the compound.^118,119 This was validated by observations of change in volume of the sample upon CO₂ gas inclusion. Subsequently, several groups tried to elucidate the detailed understanding about the flexible nature of ELM-11.^120,121

This study was followed by a series of compounds that could possess dynamic behaviour, for instance in a Cu(ii)-based 2D MOF: {[Cu₂(tci)(OH)(H₂O)₃]1.5H₂O}_n.¹²² Upon guest removal—both free and coordinated water molecules—the 2D sheets in the structure were seen to slide and contract the pores. The desolvated phase had Cu(ii) ion in square-planar geometry (deep blue colour) from an octahedral arrangement (greenish blue) in the pristine phase. This presence of a coordinatively unsaturated site (CUS) in the activated phase was seen to aid the adsorption of water molecules and revert to the pristine structure. The same group had also observed such structural changes in another set of 2D MOFs—{[Ce(tci)(H₂O)₂]·2H₂O}_n and {[Pr(tci)(H₂O)₂]·2H₂O}_n—based on a ligand with flexible aliphatic arms.¹²³ The compounds having central metal ion in a distorted square-antiprismatic geometry with coordinated water, underwent conversion to a 3D phase upon heating accompanied with loss of bound and free water. This phase change was observed to be reversible and seen to occur for both the compounds. Such sliding of 2D MOFs with coordinated water is also seen for several other MOFs as well.¹²⁴ Similar flexibility in a 3D Al(iii)-MOF having coordinated water [Al₂(OH)₂(H₂O)₂(L4)] (referred to as MIL-118A) was subsequently observed.¹²⁵ The compound upon heating lost the coordinated water molecules and transformed to [Al₂(OH)₂(L4)] (MIL-118B). This transition involved the non-bonded carboxylate in the pristine phase participating in coordination to the metal centre instead. Upon hydration of MIL-118B, it was observed that water could now enter the pores and the inorganic layer adjusted to form a rectangular pore shape. The rehydrated phase (MIL-118C) could reversibly transform back to MIL-118B upon dehydration (Figure 1.12).

Likewise, other polar solvents used in the reaction medium often bind to the metal centres, and some compounds exhibit flexible responses upon desolvation. This was seen in a Zn(ii)-based 3D MOF [Zn₂L5₂(DMF)₂]_n, that could squeeze its pores upon loss of coordinated DMF molecules.¹²⁶ While the guest-free structure could reversibly return to its pristine form after exposure to DMF, the desolvated phase when left in air adopted a different phase, owing to the coordination of water molecule. Low-temperature CO₂ and CH₄ adsorption exhibited gate-opening behaviour, and due to the presence of CUS, the compound also showed uptake for polar adsorbate such as tetrahydrofuran and dioxane. The same group later observed flexibility in Cu(ii)-based MOF constructed from neutral N-donor ligands and using bulky o-xylene as a pore template: {[Cu(L6)₂(NO₃)₂]·(oX)·(DMF)}_n.¹²⁷ The pristine phase with a 1D coordination polymer structure, underwent conversion to a non-porous 2D MOF upon desolvation. This transition was accompanied by the bending of the ligand in the presence of Cu(ii) allowing structural softness. As a side note, typically for MOFs constructed from neutral N-donor ligands, the anions used in the reaction function as the charge-balancing species in such frameworks.^128,129 Depending upon their coordinating ability, the ions either bind to the metal centres or are present as uncoordinated species in the pores.¹³⁰ Not only do these direct functional characters of these system but also tap into the possibility of framework flexibility as the metal–ligand coordination bond is relatively softer compared to the conventionally used carboxylates or azolates.^131–133 In the above example, when NO₃⁻ anions were exchanged with strongly coordinating SCN⁻ ions, the equatorial bond lengths for Cu(ii) changed, which was accompanied with a noticeable colour change from blue to green and change in structural packing. Previously, a broader case for such MOFs to function as anion sensors was reported. The parent MOF based on Cu(i)—{[Cu(pytpy)](NO₃)(CH₃OH)}_n—could readily exchange the guest methanol with water and the resulting phase was able to distinguish a range of anions, e.g., F⁻, Cl⁻, Br⁻, N₃⁻, SCN⁻, CO₃²⁻ and I⁻, based on the change in colours.¹³⁴ While most of the exchanged products appeared to remain like the water-included structure, subtle changes brought about by the guest (anion) were observed. It is worth noting this subset of MOFs (ionic-MOFs) has evolved considerably since they were initially proposed and are finding avenues in multiple domains, especially on account of their structural softness.

Pillared-layer structures are witnessing increasing attention in the domain of MOFs, as they tend to offer a higher degree of opportunity to tune and modulate structural features in a controlled manner. In an early report in this regard, expansion or contraction of the pore was observed, depending upon the pillar used in the preparation of two similar 3D MOFs: {[Cd(pzdc)(azpy)]·2H₂O}_n and {[Cd(pzdc)(bpee)]·1.5H₂O}_n.¹³⁵ In both the structures water molecules occupied the pores and the protruded carboxylate moiety of the linker had hydrogen-bonding interactions. Upon desolvation, the MOF with ethylene linker exhibited shrinking owing to favourable H-bond interactions with the carboxylate group. However, the MOF with an azo-bonded linker expanded as proximity with carboxylates was unfavoured. It is worth noting that in certain cases the loss of uncoordinated guest molecules from the framework may lead to irreversible phase transitions that are either crystalline or amorphous.¹³⁶ 

Highly porous coordination framework always tends to maximise their packing efficiency, in which the empty spaces are usually occupied by molecules used in the synthesis (e.g., starting materials, solvents, counter ions, etc.), or additional coordination networks. These nets are not connected by coordination bonds but cannot be split without any bond breakage and thus termed as ‘interpenetration’.¹³⁷ The interpenetrated networks can be identified as n-fold (n ≥ 2) frameworks according to the number of the entangled networks in overall packing structures, such as from two to eight, and even up to 54-fold interpenetrated structures.^138,139

Generally, the increase in the degree of the interpenetration will reduce void space of frameworks, but can enhance structural stability and flexibility, the latter of which can be shown as displacement between the interpenetrated networks.⁶ This dynamic structural transformation behaviour usually stems from the distortion of the single net as well as the sliding action between multiple networks, which always serves as the key factors to regulate and control the property/functionality of the flexible interpenetrated frameworks.^1,140

As early as 2002, a two-fold interpenetrated pcu network of [Cu₂(bdc)₂(bpy)] was constructed by paddle-wheel Cu₂(RCOO)₄(py)₂ cluster and mixed linear linkers of terephthalate (bdc²⁻) and 4,4′-bipyridine (bpy) (Figure 1.13).^141,168,172 All of the neighbouring layer structures of [Cu₂(bpy)₂] are bridged by the bpy linkers to form a single pcu net of the 3D pillared-layer type framework (Figure 1.13(a)). This MOF was demonstrated to present dynamic gate-opening behaviours upon gas (N₂, CH₄) and vapour (methanol) sorption, as evidenced by PXRD (Figure 1.13(b)). SCXRD confirmed that the guest removal can allow the layers to be shifted to each other and the pillared ligand (bpy) will be tilted.¹⁴³ The distortion of the pillars and slippage of the layers is topologically accompanied by the displacement of interpenetrated networks regarding each other, finally forming a nonporous closed phase. The dry structure can expand to the guest-included open phase accordingly with the above-mentioned gate-type dynamic sorption behaviours.

The displacement of interpenetrated coordination frameworks can be controlled by counter anions with steric hindrance/electric attraction to regulate the pore size for sorption behaviours. For instance, a counter anion-controlled dynamic structure and sorption property was observed based on two-fold interpenetrated framework of [Ni(bpe)₂(N(CN)₂)]·N(CN)₂·5H₂O (Figure 1.14).¹⁴⁴ The single crystal diffraction analysis showed that its as-synthesised form has two types of channels. The smaller rectangular one (2.81 × 0.61 Ų) contains the counter anions of N(CN)₂, while the larger hexagonal one (6.50 × 4.74 Ų) accommodates many H₂O molecules. After exchanging the bent N(CN)₂ by linear N₃ molecules, the difference in pore size increases because the smaller N₃ allows the two-fold entangled structures to get much closer to each other, as confirmed by PXRD. As a result, CO₂ adsorption isotherms (195 K) showed a 25% increase in uptake after the anion exchange.

Most of the luminescent MOF sensors can detect a single target molecule in a mixture,¹⁴⁵ while cannot differentiate multiple targets from one another simultaneously (Figure 1.15(a)).¹⁴² For example, a two-fold, interpenetrated, naphthalenediimide-based MOF of [Zn₂(bdc)₂(dpNDI)]·4DMF was synthesised, showing structural typical dynamics based on the dislocation of two entangled networks upon guest removal/inclusion. This flexible interpenetrated MOF can accommodate a class of aromatic volatile organic compounds (VOCs) with an intense turn-on emission over the entire visible region (benzonitrile: 421 nm, benzene: 439 nm, toluene: 476 nm, o-xylene: 496 nm, m-xylene: 503 nm, p-xylene: 518 nm, and anisole: 592 nm), offering changed luminescent colours detectable by the naked eye (Figure 1.15(b) and 1.15(c)). The unique chemoresponsive, multicolour luminescence should be attributed to the different naphthalenediimide–aromatic guest interaction by induced-fit structural transformation within the interpenetrated framework.

Control over the degree of interpenetration to construct the CPs with desired structures and functionalities remains a great challenge because of a number of factors including temperature, concentration, solvent, time, pH and modulator.^138,146 Here we will focus on summarising recent advances in regulating the degree of interpenetration regarding flexible frameworks and the influence on the resulting properties.

One of the most successful design approaches to control interpenetration behaviours on flexible MOFs is to use metal ions/clusters with different organic ligands to build interpenetrated networks. A two-fold interpenetrated pcu network of [Zn₂(bdc)₂(bpy)] (void = 27.7%) was carefully explored for its guest-induced transformation.¹⁴⁷ After guest removal, its guest-free structure retained the original framework connectivity but finally transformed into a closed phase (void = 16.7%), which should be ascribed to the significantly distorted Zn₂ clusters and bent bpy ligands. Additionally, without any steric hindrance of guests, this coordination network slid to a stable position, resulting in a higher symmetry. By virtue of the reversible guest-induced flexibility, the closed phase can expand to an open state and show a hysteretic sorption behaviour upon gases (N₂, H₂, and CO₂).

To further understand the effect of ligand length on flexibility of framework, by using the well-defined Zn₂(RCOO)₄(py)₂ cluster with different linear ligands, a series of two-fold interpenetrated mixed-ligand MOFs were constructed: [Zn₂(bdc)₂(bpy)], [Zn₂(fm)₂(bpe)], [Zn₂(fm)₂(bpa)] and [Zn₂(fm)₂(bpy)].¹⁴⁹ The interpenetration here can provide flexibility to pillared-layer type frameworks whose tunable porous properties and sizes can be achieved and demonstrated by the dynamic adsorption behaviours of ethylene and ethane. By using the longer ligands,^150,151 a highly flexible three-fold interpenetrated [Zn₂(4,4′-biphenyldicarboxylate)₂(4,4′-bis(4-pyridyl)biphenyl)] was synthesised (Figure 1.16(a)).¹⁴⁸ This MOF exhibits six distinct phases and four types of structural transformation in response to various stimuli, which correspond to many observed dynamic structural transformations, including breathing, structural isomerism, shape memory effect, and change in the level of interpenetration (Figure 1.16(b)). Noted that structural flexibility of the interpenetrated frameworks can be finely tuned by the weak interactions (cooperation of local and global motility) from modified ligand substitutions.^27,152

Although interpenetration has been considered an effective strategy to introduce framework flexibility but increasing the number of interpenetrations is not always a good choice, because it will reduce the necessary space for dynamic behaviours. Significantly different framework flexibilities between two-fold and three-fold interpenetrated isomers of pillared-layer type [Zn₂(btdc)₂(bpy)] were observed.¹⁵³ CO₂ sorption supports that the three-fold interpenetrated one exhibits a type-I isotherm (total uptake of 55 cm³ g⁻¹ at 195 K), while the two-fold interpenetrated isomer shows a gate-opening-type behaviour (up to 201 cm³ g⁻¹). Parallel PXRD–adsorption measurements confirmed the structural rigidness of the three-fold interpenetrated isomer and revealed the structural transition from a square to a rhombus-shaped pore for the two-fold interpenetrated one. Obviously, the higher porosity plays an important role in the framework distortion. It should be noted that, besides the interpenetration number, interpenetration direction can also significantly influence framework dynamism.¹⁵⁴ 

When compared with the various types of fully interpenetrated frameworks, partial interpenetration is another exciting development to study structural flexibility. A tunable change of the interpenetration degrees was carried out by solvent-mediated grinding/stirring on a pcu network of [Zn₄O(dpdc)₃] (MUF-9).¹⁵⁵ By employing different solvents and/or heating times, MUF-9 can be constructed with non-, partial, and two-fold interpenetration. Besides, the similar partial interpenetration was also observed in another two-fold dia-type MOF (dia = diamondoid), (Me₂NH₂)_1.75[In(bptc)]_1.75·12DMF·10H₂O (NOTT-202) (Figure 1.17).¹⁵⁶ Interestingly, this MOF consists of two independent networks, one of which is partially formed with a crystallographic occupancy of 0.75. After desolvation, the interpenetrated framework showed sliding behaviours, resulting in a large expansion of pore sizes from 5.0 × 5.0 to 9.0 × 9.0 Ų as confirmed by in situ SCXRD. This partially interpenetrated framework showed three-step CO₂ adsorption (195 K) behaviour, which should be attributed to the reversible structural sliding transitions during the guest removal/induction. Note that higher temperature synthesis can yield fully interpenetrated rigid dia frameworks with a dramatically decreased porosity of <4%.

The flexibility of interpenetrated structures relies on not only the chemical compositions and local/long-range connectivity but also crystal size.¹⁵⁷ For example, the downsizing effect was observed upon the crystals of a flexible porous interpenetrated framework of [Cu₂(bdc)₂(bpy)] (void = 35%) (Figure 1.18).¹⁴³ A series of crystals with different sizes (methanol as a guest) were synthesised. After guest removal at room temperature, the crystals with 300 × 300 × 30 nm³ or larger size will shrink to a narrow-pore phase (void = 20%). Surprisingly, smaller nanocrystals can completely (50 × 50 × 20 to 60 × 60 × 20 nm³) or partially (110 × 110 × 23 to 160 × 160 × 25 nm³) retain the original open form as observed in the as-synthesised crystals. Their size-dependent flexibility will be different after heating at 200 °C, that is, all samples with different sizes can shrink. Further, methanol sorption (303 K) for the nanocrystals (50 × 50 × 20 nm³) exhibited a gate-opening isotherm upon the closed-state sample, but an ordinary type-I adsorption behaviour for the open-state sample. By comparison, this similar size-dependent structural flexibility was also experimentally demonstrated in an analogous MOF of [Cu₂(bdc)₂(bpe)]. This shape memory effect of size-dependent flexibility has been also observed in other flexible frameworks,^{140,158–160} and should be attributed to the different degrees of defects in the crystal, which greatly accelerate the phase transition. Obviously, they are unique platform frameworks to study macro- and micro-sized structures, which possess important guiding significance for the function/property modulation of MOFs.

Flexible coordination frameworks can undergo structural transformation only upon external stimuli. Among the various physical forces,^161,162 light irradiation can provide high energy to achieve the structural transformation. To realise light-controlled flexible coordination networks, employing photodynamic compounds as the skeleton of the bridging ligands is one of the most effective strategies. Based on these considerations, an approach through design and synthesis of a two-fold interpenetrated diarylethene-containing pillared-layer framework of [Zn₄(bdc)₄(L₀)₂·(G)] was developed.³⁶ Ligand L₀ serves as the pillar between a non-photochromic layer network of [Zn(bdc)], which accommodates changes in linker geometry after photoisomerisation without framework collapse confirmed by SCXRD. In addition, linker photoisomerisation was also well explored by spectroscopic studies and reversibly photo-modulated CO₂ sorption measurements, showing the possibility to tune the flexibility of the interpenetrated frameworks.¹⁶³ 

Interdigitation refers to polythreading of the digited motifs with finite length (usually coordinated ligand moieties) that can project into the accessible voids of adjacent layers in a face-to-face manner. Interdigitation is distinctly different from interpenetration because it did not have any structural penetration.¹⁶⁴ 

Up to now, a variety of 1D/2D interdigitated CPs have been successfully designed and constructed. Many of them exhibit high flexibility governed by the regulable weak interactions between interdigitated structures upon guest inclusion and removal.

In 2002, a representative 1D interdigitated CP of [Rh^II₂(benzoate)₄(pyrazine)] was constructed by linking the paddle-wheel Rh₂(benzoate)₄ cluster with the bridging ligand of pyrazine in a linear geometry (Figure 1.19(a)).¹⁶⁶ Tight stacking between the benzene and pyrazine rings along the eventual sliding chains enables the high-density packing to reduce the void space of skeletons without any solvents. While this CP was observed to adsorb N₂ with a type I adsorption isotherm (BET surface: ca. 350 m² g⁻¹) (Figure 1.19(b)). SCXRD analysis showed that, to accommodate the N₂ molecular, the linear chains undergo a significant shift along the c-axis (from C2/c to P1̄, void = 17.4%) (Figure 1.19(c)).¹⁶⁷ This indicates the underlying dynamic nature of 1D interdigitated CPs, in which the guest inclusion enables the chains to rearrange with each other to become porous structures. Based on this consideration, this kind of CPs have been intensely investigated for sorption of different small molecules, including CO₂, N₂O, NO, CH₄, SO₂, etc.^{165,168–171}

When compared with the 1D frameworks, 2D interdigitated CPs have been investigated more extensively for structure design and property evaluation. A series of 2D interdigitated frameworks based on linear bipyridyl and carboxylate ligands for sorption properties have been illustrated.^172,173 For example, a layer CP of [Cu₂(dhbc)₂(bpy)] has an interdigitation by π–π stacking interactions between benzene rings of the dhbc, which serves as the pillars between adjacent layers (Figure 1.20(a)). This π–π stacking offers moderate interaction to stabilise the structure, and its sliding motion gives an open framework when guests are adsorbed. This structural transformation will be accompanied by the shrinkage of layer distance after guest release. The compound exhibits hysteretic adsorption isotherms for CH₄, CO₂, N₂ and O₂ at 298 K (Figure 1.20(b)).

One of the most efficient approaches for the design and construction of interdigitated networks is to vary organic ligands to control interdigitation between layered structures to tune the pore sizes and shapes.^174,175 For example, based on the typical interdigitated CP of [Cu₂(dhbc)₂(bpy)], V-shaped dicarboxylate of ip was employed to replace the dhbc ligand to construct a similar interdigitated structure of [Zn₂(ip)₂(bpy)₂] (CID-1).¹⁷⁶ The Zn(ii) centre is linked by an isophthalate ligand to create 1D double-chains, which are connected by bpy linkers to give a 2D layer. The layers are interdigitated together to form 3D flexible frameworks with linear non-intersecting arrays of cavities with narrow connecting windows, which respond for its highly selective guest sorption behaviours. Following the guest-responsive flexibility of CID-1, there have already been extensive investigations of ligand design for the isoreticular interdigitated frameworks. Then longer ligands were employed in the construction of a series of similar flexible structures, including V-shaped dicarboxylate ligands for [Zn(ndc)(bpy)] (CID-3) and [Cd(bpndc)(bpy)] (CID-4),^177–179 and dipyridyl linkers for [Zn(ip)(bpb)] (CID-21), [Zn(ip)(bpt)] (CID-22) and [Zn(ip)(bpa)] (CID-23).¹⁸⁰ When compared with the CID-1 (12.2% of void), the replacement of substituent groups of the dicarboxylate/dipyridyl linkers can effectively increase their porosities and modulate the pore sizes and shapes (25.8% for CID-3, 29.4% for CID-4, 26.8% for CID-21 and CID-22, and 27.4% for CID-23). Interestingly, these isoreticular interdigitated frameworks showed highly size-dependent selective gas adsorption properties accompanied by reversible structure transformations.

The structural flexibility of the interdigitated networks can be finely tuned by the interchain interactions from varying ligand substitutions.^{168,169,181–183} For the 1D interdigitated CP of [Cu₂(benzoate)₄(pyrazine)], the para-substituent X groups (X = Cl, Br, I and OCH₃) on the benzoate (BA) ligands were utilised to construct a series of interdigitated CPs: [Cu^II₂(p-XBA)₄(pyrazine)].¹⁸⁴ Interestingly, although all of them were non-porous, gate-opening gas sorption behaviour for CO₂ (195 K) and N₂ (77 K) was observed with structural phase transitions. SCXRD analysis confirmed that the magnitude of interchain van der Waals interactions, including halogen⋯π, π⋯π, and C–H⋯π contacts should be associated with the gate-opening sorption pressure and hysteresis behaviours. Importantly, coupled with Hirshfeld surface analysis to evaluate the interactions for the type and magnitude, the structural flexibility would decrease as the larger halogen groups were included. However, the structural transformation and phase transition of the 1D interdigitated CPs can be also altered by the substitutions of the pyrazine. For example, owing to the steric hindrance of alkyl (X) groups from pyrazine derivatives (X-pyz), 1D chains of [Rh₂(bza)₄(X-pyz)] (X = 2-methyl, 2,3-dimethyl, or 2-ethyl-3-methyl) were able to switch from the zig-zag to straight upon CO₂ sorption.^168,169

Different from fine regulation of the flexibility on 1D CPs, judicious choice of substituent groups turns on the flexibility of 2D interdigitated CPs.^181,182 For example, a series of four open frameworks of [Fe(ip)(bpy)] (FeCID-1), [Fe(3,5-pyridinedicarboxylate)(bpy)] (FeCID-2), [Fe(5-NO₂-isophthalate)(bpy)] (FeCID-5), and [Fe(5-MeO-isophthalate)(bpy)] (FeCID-6) were reported. CO₂ sorption (195 K) revealed that all these CIDs were isoreticular networks, while only FeCID-5 exhibited structural flexibility, which should be attributed to the different influences of electronic properties or shapes of substituent groups on the overall packing layered structures.¹⁸¹ 

Metal centres in isostructural flexible interdigitated CPs may exhibit different coordination environments, which can affect the flexibility of whole frameworks.⁶⁴ For example, four isostructural CID-1s (M = Co, Ni, Cu, and Zn) were synthesised, where coordination geometries around the metal ions of Co and NiCID-1 were symmetric ideal octahedron with uniform coordination bond lengths (2.0–2.2 Å). However, CuCID-1⊃H₂O and ZnCID-1⊃H₂O showed distorted octahedral geometry (Jahn–Teller effect) revealed by one longer bond length (2.6 Å) between the metal centre and one oxygen atom compared to other coordination bonds. Interestingly, this series of interdigitated frameworks show different dynamic water-adsorption behaviours. The onset pressures (P/P₀) for CuCID-1 and ZnCID-1 were approximately 0.60 and 0.33, while CoCID-1 and NiCID-1 showed almost no water uptake below P/P₀ = 0.9. Crystal structure of CuCID-1⊃H₂O suggested that water molecules in channels form hydrogen bonds with oxygen atoms of the carboxylate ligand, which seemingly leads to the coordination distortion, thus resulting in the gate-opening structural transition for water sorption.

Crystal downsizing can also control the structural transformation of flexible interdigitated CPs.¹⁵⁸ For bulk CID-1 crystals guest removal at 130 °C under vacuum resulted in slight framework shrinkage as demonstrated by the shifting of PXRD peak higher 2θ values. When its crystal size was downsized to the nanoscale (30 × 100 × 500 nm³), the guest-removal-induced structural shrinkage would reduce significantly, possibly owing to the change in size or surface structure (covered with surfactant) of the crystals. SCXRD and synchrotron PXRD analyses exhibited that bulk- and nano-CID-1 underwent 3.2% and 2.1% reductions in their unit-cell volume after guest removal, respectively.¹⁵⁹ 

The structural flexibility of interdigitated frameworks can be also controlled by downsizing bulk crystals to a thin film at the nanoscale, endowed with dynamic gate-opening behaviour. A 2D Hofmann-type CP of Fe(pyridine)₂[Pt(CN)₄] thin film on the Au/Cr/Si substrate via a layer-by-layer (LbL) growth was fabricated.¹⁶⁰ The layered structure consists of [Pt(CN)₄]²⁻ and cyanide-bridged Fe(ii) ions coordinated by pyridine molecules, which formed π–π stacking with the adjacent pyridine rings to form a 3D interdigitated framework. Although this CP in bulk showed no uptake of guest molecules because of the densely packed layers, when fabricated as thin film with downsizing to 16 nm thick, the nanoscale thin film exhibited significant gate-opening behaviours for the vapours of water, methanol, ethanol and acetonitrile (Figure 1.21(a)). In situ PXRD studies revealed that the vertical interlayer space was expanded by 1.6% after ethanol adsorption to allow ethanol molecules to diffuse (Figure 1.21(b)). The dynamic structures in thin films should contribute to the lowering of potential barrier height in the gate-opening-type guest uptake, which resulted in specific response for guests and sorption kinetics that differs from the bulk crystals.¹⁸⁵ 

Apparently, inclusion of guest molecules into 2D interdigitated CPs will significantly affect or weaken the interlayer interdigitation between adjacent layers, which have been widely used to result in the breakage of bulk layered crystals to form nanosheets, usually called ‘solvent-induced exfoliation’.^186,187 For example, water molecules were introduced into the interlayer pockets of bulk crystals of [CuCl(dipyrimidinedisulfide)]·nH₂O to produce ultrathin nanosheets (<2 nm in thickness).¹⁸⁶ Besides, the spontaneous exfoliation of a bulk-layered Cu(ii)-MOF by use of tetrahydrofuran (THF) with significant interlayer expansion was demonstrated, and then further delamination of the expanded bulk-layered framework into the bilayer and even monolayer nanosheets in 2-methyltetrahydrofuran (MeTHF) and dioxane, respectively (Figure 1.22).¹⁸⁷ 

Due to the high porosity and structural flexibility around the coordination bonds of MOFs, the ligands in the structure exhibit movements such as rotation and vibration. For example, the rotation of the benzene ring of the ligand upon adsorption and desorption of the guest has been found from X-ray structural analysis (Figure 1.23).¹⁸⁸ Zn₄O(NTB)₂ has a 3D structure and the benzene ring of the NTB ligand rotates upon adsorption and desorption of the guest. Since the structure obtained by X-ray structure analysis is an average structure, it is not possible to quantitatively determine the frequency at which the ligands rotate.

In 2006, a report was published in which the protons of the MOF ligand were deuterated and the rotational frequency was quantitatively observed by solid-state ²H NMR spectroscopy.¹⁸⁹ [CdNa(2-stp)(pyz)_0.5(H₂O)] is a 3D structure in which the layered structure is bridged by the pillar pyrazine (Figure 1.24(a)). Solid-state ²H NMR spectroscopy was performed on [CdNa(2-stp)(pyz-d₄)_0.5(H₂O)], in which the four protons of pyrazine were deuterated, in the temperature range of 193 to 293 K. The characteristic Pake-doublet patterns were observed (Figure 1.24(b)). The pattern fitting was performed by simulating the rotational motion of pyrazine around the C2 axis (Figure 1.24(c)). Each fitting showed good agreement, and the rotational frequency was found to vary in the range of 2 × 10⁴ Hz (193 K) to 1 × 10⁵ Hz (293 K). From the Arrhenius plot, the activation energy of rotation was found to be as low as 7.7 kJ mol⁻¹. Considering that the typical energy of an O–H⋯O hydrogen bond is about 20 kJ mol⁻¹, the energy barrier of the ligand rotation is quite small. In this work, similar experiments were carried out for Zn₂(1,4-ndc-d₆)₂(dabco). This is a 3D pillared-layer type structure composed of a Zn²⁺ dinuclear paddle-wheel cluster. The rotation frequency of the ligand was 3 × 10⁶ Hz (203 K) to 5 × 10⁷ Hz (223 K). The activation energy of rotation was 53 kJ mol⁻¹. When benzene was introduced as a guest into this MOF, the rotation was found to stop.

A similar investigation was carried out for [Zn₄O(bdc)] (Figure 1.25(a), MOF-5). Cubic Zn₄O(bdc-d₄) was prepared by use of deuterated 1,4-benzenedicarboxylate (bdc-d₄), and solid-state ²H NMR measurements were carried out in the range of 300 to 435 K (Figure 1.25(a)).¹⁹⁰ The motion of bdc is mainly a two-site π-flip of the benzene ring, and its activation energy was 47 kJ mol⁻¹. The high activation energy of rotation of the carboxylates compared with N-donor ligands found in [CdNa(2-stp)(pyz)_0.5(H₂O)] is due to their electronic conjugation. Spectroscopy suggested that the rotation of the ligands incorporated into MOFs could be manifested in a variety of ways and could be controlled by external stimuli. Solid-state ²H NMR measurements of [V(OH)(bdc-d₄)] (MIL-47) and [Cr(OH)(bdc-d₄)] (MIL-53), which consist of paramagnetic metals, have also been reported (Figure 1.25(b)).¹⁹¹ Although the Pake doublet patterns are distorted by the paramagnetic metal ions, pattern simulation is successful. [Cr(OH)(bdc-d₄)] has a flexible structure with two phases, a narrow pore, and a large pore, while [V(OH)(bdc-d₄)] has a rigid structure and one phase exists. Both compounds show π-flipping of benzene rings of bdc-d₄ ligands, and the activation energies are 45 kJ mol⁻¹ for [V(OH)(bdc-d₄)] and 41 kJ mol⁻¹ for [Cr(OH)(bdc-d₄)]. The activation energies of both ligands are comparable to that of Zn₄O(bdc-d₄) (47 kJ mol⁻¹), but the rotational frequencies are more than an order of magnitude lower. This difference could reflect the constrained local environment for the phenylene ring in a 1D pore system when compared to a 3D one for [Zn₄O(bdc-4)]. Ring rotation in [Zr₆O₄(OH)₄(bdc-4)₆] (UiO-66) is also studied by the same procedure.¹⁹² 

Preservation of high molecular rotation dynamics, even at low temperatures, is a major challenge. Zn-FTR and Zr-FTR are constructed from bicyclo[1.1.1]pentane-1,3-dicarboxylic acid with Zn²⁺ and Zr⁴⁺ ions, respectively (Figure 1.26(a)).¹⁹³ In both of structures, the carboxylate groups, anchored on metal clusters, serve as the axle while allowing the bicyclic unit to freely rotate. The planes of carboxylate groups are perpendicular to another one (crossed arrangement), while those of Zr-FTR stay in a common plane (in-plane arrangement) (Figure 1.26(b)). Through the potential energy (MP2) scans, the researchers found that the crossed model shows a lower energy barrier than the in-plane conformation (Figures 1.26(c) and (d)). Solid-state NMR analysis gave a low rotation barrier for Zn-FTR to be 6.2 kcal mol⁻¹, with rotors showing the high-frequency motion of 10¹⁰ Hz (Figure 1.26(e)), even at a temperature below 2 K. The symmetry mismatch between the bicyclopentane rotator (three-fold trigonal) and the carboxylate struts (four-fold orthogonal) in Zn-FTR is the key factor for the hyper fast dynamics at cryogenic temperatures.

Even with the same crystal structure, changing the crystallite size can change the molecules’ packing state and the ligands’ rotational motion. [Zn(ip)(bpy)] (CID-1, Figure 1.27(a)) has a 2D layered interdigitation structure.¹⁹⁴ The average size of the crystals prepared by the conventional solvothermal synthesis is 5 µm × 20 µm. When anionic surfactant (AOT, dioctyl sulfosuccinate sodium salt) is used during crystal formation, nanocrystals of [Zn(ip)(bpy)] (NCID-1) can be synthesised. Due to the flexible structure, the cell parameters change upon crystal downsizing (Figure 1.15(a)). Deuterated 4,4-bipyridine (bpy-d₈) was used to prepare samples of two [Zn(ip)(bpy-d₈)] having different crystal sizes, and solid-state ²H NMR spectra were recorded (Figure 1.27(b)). For the bulk crystals, the rotational frequency was about 4 MHz at 298 K. For the nanocrystals, it was more than 10 MHz at 298 K.

Attempts have been made to control the rotational frequency of the ligands continuously.¹⁹⁵ One approach is to use a ligand-based solid solution. [Zn(5-nitroisophthalate)_x(5-methoxyisophthalate)_1−x(bpy-d₈)], a flexible structure with interdigitated 2D layers can be prepared (Figure 1.28(a)). Crystal cell parameters and bpy-d₈ ligand rotation depend on x (Figure 1.28(b)) and bpy-d₈ ligand rotation varies depending on x. The four-flip/two-flip rotational frequency exhibited by bpy-d₈ varies continuously in the range of 10³–10⁸ Hz at 298 K depending on the value of x. This is because the cell parameters of crystal structures change gradually depending on x. The cell volume also changes continuously depending on x, and the rotation barrier of bpy-d₈ also changes continuously.

Fe(pyrazine)[Pt-(CN)₄] is classified as a Hofmann clathrate, a 3D structure consisting of a 2D layer of [FePt(CN)₄] bridged by pyrazine, which is known to exhibit Fe²⁺-derived spin crossover behaviour (Figure 1.29(a)).¹⁹⁶ The transition temperatures are 285 K (heating) and 309 K (cooling). The connection between the rotational motion of pyrazine and the spin crossover has been studied by quasi-elastic neutron scattering (QENS) and solid-state ²H NMR spectroscopy. In the high-spin state at 300 K, the rotational frequency of the pyrazine rings is more than 10⁸ Hz, while in the low-spin state at 260 K, it decreases significantly to 3 × 10⁵ Hz (Figure 1.29(b)). The change in the Fe–N distance from 2.22 to 1.96 Å upon spin crossover results in a larger rotational barrier. Interestingly, the rotating pyrazine rings can be stopped after guest inclusion at room temperature.¹⁹⁷ Upon the sorption of six-/five-membered aromatic molecules, the framework expands to a larger cell volume with stabilisation of the high-spin state, while in the case of CS₂ sorption, restriction of network freedom by framework shrinkage results in stabilisation of the low-spin state. In other words, the spin crossover can be well controlled by changing the degree of dynamic motion of pyrazine.

As an example of basic molecular switches and machines, the dynamics of mechanically interlocked molecules (MIMs) have been studied in solution, but in this medium, the molecules are randomly dispersed, and their motions are incoherent. As a strategy to achieve a higher level of molecular organisation, several MIM-based MOFs have been prepared, such as these that contain a mechanically interlocked molecule as the pillaring strut between two periodic Zn²⁺-carboxylate layers (Figure 1.30(a)).¹⁹⁸ The MIM linker is a [2]rotaxane with a 24-crown-6 (24C6) macrocycle and an aniline-based axle with terminal pyridine donor groups. The single-crystal X-ray structures of MOFs UWDM-2 (1,4-diazophenyl-dicarboxylate) and UWDM-3 (1,4-biphenyl-dicarboxylate) show that both frameworks are large enough to contain the free volume required for rotation of the interlocked 24C6 macrocycle, but the frameworks are interpenetrated (UWDM-2 is three-fold, and UWDM-3 is two-fold). For UWDM-3 the 24C6 rings of the pillaring MIM are positioned directly inside the square openings of neighbouring Zn²⁺ dicarboxylate layers. Variable temperature (VT) ²H SSNMR spectroscopy (Figure 1.30(b)) demonstrated that the 24C6 macrocycles in UWDM-2 and UWDM-3 only undergo restricted motions related to ring flexibility or partial rotation but are incapable of undergoing free rotation. Variable-temperature studies showed that upon activation of UWDM-3 by removing the solvent, a phase change occurs. The new β-phase of UWDM-3 retained crystallinity, and ²H SSNMR spectroscopy demonstrated that the 24C6 macrocyclic ring of the pillared MIM strut is now free enough to undergo full rotation. The phase change is reversible; the β version of the MOF can be reverted to the original α state by re-solvation.

Incorporation of light-driven molecular rotors (photo-switchable molecules) into solid holds great promise to fabricate responsive materials. Researchers synthesised porous switchable frameworks (PSFs) by a Yamamoto cross-coupling between the tetra-p-bromo-phenylmethane (TPM-Br₄) and overcrowded alkene (1_st-Br₂, usually used as chiroptical switch) (Figure 1.31(a)).¹⁹⁹ Solid-state NMR, Raman and diffuse-reflectance UV-vis spectroscopies confirmed that the switchable rotor embedded in the porous framework maintains the quantitative photo-function and undergoes reversible wavelength-dependent isomerisation upon irradiation by light or heating (Figure 1.31(b)). As a result, they demonstrated photo-modulation for the gas adsorption capacity by striking reduction of the pore volume between irradiated and pristine states, specifically, 20% uptake change of N₂ (77 K) and CO₂ (195 K) at the relative pressure (P/P₀) of 0.6 bar (Figure 1.31(c)–(e)).

Motions such as ligand rotation depend on temperatures and affect gas adsorption behaviour. [Cu(etz)] is a 3D structure that exhibits a crystal structure similar to that of NbO²⁰⁰ and has pore openings with ethyl groups protruding from them. At low temperatures, such as 77 K, the ethyl groups have stopped moving and block the pores, so no gas is introduced. At 195 K, however, the ethyl groups are mobile, and gas is introduced as diffusion is enhanced. As a result, a reversal of the temperature dependence of gas adsorption, called ‘kinetically controlled flexibility’, is observed.

The change in ligand motion and pore size with temperature has a significant effect on gas sorption (Figure 1.32).²⁰¹ For the material CID-Me, as the temperature increased, the rotors exhibited rotational modes; such rotations dynamically expanded the size of the windows, leading to CO₂ adsorption. The ²H solid-state NMR and in situ ¹³C MASNMR spectra revealed that [Zn(5-methylisophthalate)(bpy-d₈)] shows both rotation motion of bpy ligands and wobbling motion of 5-methylisophthalate ligands (Figure 1.32(a)). The rotational frequencies of the rotors (k ∼ 10⁻⁶ s) and correlation times of adsorbed CO₂ (τ ∼ 10⁻⁸ s) were elucidated via solid-state NMR studies, which suggest that the slow rotation of the ligand rotors sterically restricts CO₂ diffusion in the pores. This restriction results in an unusually slow CO₂ mobility close to that in the solid state (τ ≥ 10⁻⁸ s). Once adsorbed at room temperature, CO₂ is robustly stored in the structure under vacuum at 195–233 K because of the steric hindrance of the ligand rotors. This mechanism was also applied to the storage of CH₄ (Figure 1.32(b)).

Although the effective pore size of [Zn(2-methylimidazolate)₂] (ZIF-8) is suitable for propylene/propane separation, the imidazolate linker shows some degree of framework flexibility, which severely deteriorates the separation factor of the separation, especially under high pressure and high-temperature conditions.²⁰² Therefore, inhibition of linker rotation is feasible for providing sharp molecular sieving and improving the separation factor (Figure 1.33). ZIF-8 with space group I4̄3m (denoted as ZIF_I4̄3m) undergoes structural transitions within the electric field (500 V mm⁻¹) (Figure 1.33(a)). The symmetry is reduced to the monoclinic space group Cm (ZIF_Cm), and the symmetry switches further to R3m (ZIF_ R3m) at higher electric fields (Figure 1.33(b)).²⁰³ ZIF_Cm bears a stiffened linker, exhibits a rigid pore size of 3.6 Å, and molecular sieve effects were observed for various gas pairs, including propylene/propane. In the recent work reported by the same research group,²⁰⁴ a direct current was utilised during membrane growth. The applied current induced the assembly of ZIF precursors into innately distorted ZIF_8-Cm, providing a ZIF-8 membrane with a stiffer framework (Figure 1.33(c)). The resulting membrane with enhanced molecular sieving ability showed a propylene/propane separation factor of up to 300. The hardening of the lattice and the thickening of the ZIF-8 membrane (up to 200 nm) also limited the permeability of propylene to only 1.74 × 10⁻⁸ mol m⁻² Pa⁻¹ s⁻¹.

Flip-flop molecular motion is a dynamic perturbation controlled by thermal energy in bent molecules such as phenothiazine.²⁰⁵ [Cu(OPTz)] is a Cu-based MOF with a butterfly-type ligand comprising isophthalic acid and phenothiazine-5,5-dioxide (OPTz) moieties (OPTz-ipa), which encodes an unprecedented mechanism of diffusion regulation by kinetic gate functionality enabling efficient gas separation and storage. [Cu(OPTz)] shows a temperature-responsive adsorption behaviour where the maximum uptake is observed at more than 100 K above the boiling point of the adsorbate. The adsorbate molecules are differentiated by each gate-admission temperature, facilitating kinetics-based gas separations of oxygen/argon and ethylene/ethane with high selectivities of ∼350 and ∼75 at high temperatures, which was previously unattainable by conventional static adsorption-based separation. The long-lasting physical encapsulation of ethylene at ambient conditions is demonstrated, owing to strongly impeded diffusion in distinctive nanochannels.

Undoubtedly, the structural variation and pronounced dynamic behaviour are unique features of MOFs (compared to other types of porous materials) and are extremely important for properties. As mentioned above, the flexibility of MOFs can be designed/modified through controlling structural components (ligand, metal and guest molecules) and network topologies (interpenetration, interdigitation and ligand rotation, and vibrations). These factors not only help to understand the structure–property relationships of flexible MOFs but also is a new dimension for developing MOF materials with excellent properties.

The structural changes of MOFs can be experimentally shown at the molecular level by virtue of available crystallographic techniques. Crystallographic techniques, especially SCXRD, can directly observe the structural changes of flexible MOFs. However, in addition to the initial and final thermodynamic equilibrium states in crystalline form, MOFs can show nonperiodic inhomogeneous and/or extremely complex superstructures, especially during thermodynamically nonequilibrium states of guest diffusion, chemical reactions and physical stimuli. To study these dynamic behaviours, various characterisation and simulation methods should be used, and better combined. Computational simulations are very helpful to validate and visualise the results obtained by chemical/physical measurements. With a better understanding of the relationships between dynamic behaviour, molecular building blocks and topologies, and external stimuli, one may rationally design and construct new flexible MOFs and control their dynamics to achieve the desired properties and functions.