Electrically Conductive Metal–Organic Frameworks

Abstract

Metal–organic frameworks (MOFs) are intrinsically porous extended solids formed by coordination bonding between organic ligands and metal ions or clusters. High electrical conductivity is rare in MOFs, yet it allows for diverse applications in electrocatalysis, charge storage, and chemiresistive sensing, among others. In this Review, we discuss the efforts undertaken so far to achieve efficient charge transport in MOFs. We focus on four common strategies that have been harnessed toward high conductivities. In the “through-bond” approach, continuous chains of coordination bonds between the metal centers and ligands’ functional groups create charge transport pathways. In the “extended conjugation” approach, the metals and entire ligands form large delocalized systems. The “through-space” approach harnesses the π–π stacking interactions between organic moieties. The “guest-promoted” approach utilizes the inherent porosity of MOFs and host–guest interactions. Studies utilizing less defined transport pathways are also evaluated. For each approach, we give a systematic overview of the structures and transport properties of relevant materials. We consider the benefits and limitations of strategies developed thus far and provide an overview of outstanding challenges in conductive MOFs.

1. Introduction

Metal–organic frameworks (MOFs) are a class of porous materials with high surface areas consisting of inorganic nodes connected by organic linkers.¹⁻³ Since the inception of the field in the late 1990s and early 2000s, these materials have been investigated extensively for applications, such as gas storage,⁴⁻⁷ separations,⁸⁻¹¹ and catalysis,¹²⁻¹⁵ because of their high porosity and chemical tunability. In contrast, the electronic properties of MOFs have received comparatively little attention until recently, and the potential of this class of materials as electrically conductive porous materials has only begun to be realized. Despite the relative youth of this research area, many advances in designing, synthesizing, and characterizing electrically conductive MOFs have been made, and the field has experienced considerable expansion in just the last five years, the focus period for this Review (Figure 1)

Figure 1.

Histogram showing cumulative number of papers focusing on aspects of electrical conductivity in MOFs from 2008 to 2019, grouped according to the design strategy employed.

Electrically conductive MOFs are of considerable interest from many perspectives. They are relevant as active materials for many applications, including electrocatalysis,¹⁶⁻²⁰ chemiresistive sensing,²¹⁻²⁶ and energy storage technologies.²⁷⁻³⁰ Their fundamental transport properties merit further study, as certain conductive MOFs have been predicted to host topologically nontrivial electronic structures.³¹⁻³⁶ Additionally, they may contain arrangements of inorganic or organic moieties that are unprecedented in other materials, potentially giving rise to new physical phenomena.^37,38 They also present exciting new avenues for creativity in ligand design, self-assembly, and crystal engineering.

This Review covers recent advances in the chemistry of this class of materials, with emphasis on design principles, experimental materials discovery, and characterization of transport properties. We focus the majority of our discussion on crystalline coordination networks with potential voids³⁹ with two- and three-dimensional connectivities for which electrical conductivity values are reported. Where appropriate, we also review chemically related materials (as demonstrated by compositional and structural characterization) that do not exhibit permanent porosity. While it is important to understand the mechanisms underlying the transport properties of the most conductive MOFs, we believe it can be equally instructive to examine structure–property relationships among materials that may not exhibit record conductivity values. In an effort to capture the granularity necessary to establish broader trends, the conductivities of the materials included in this Review span more than 17 orders of magnitude.

Many other reviews pertaining to electrically conductive MOFs have appeared in recent years. Sun et al. first provided an overview of porous conductive MOFs in 2016,⁴⁰ and Medina et al. provided an update to this work.⁴¹ Several other perspectives on conductive MOFs, their applications, and outlooks have been written.⁴²⁻⁴⁶ Ko et al.,⁴⁷ Zheng et al.,⁴⁸ and Solomos et al.⁴⁹ have focused on two-dimensional (2D) conductive MOFs, and Murase et al. analyzed mixed valency in conductive MOFs.⁵⁰ Application-focused reviews have covered electrocatalysis⁵¹ and chemiresistive sensing.⁵²⁻⁵⁴ Stassen et al. reviewed MOF integration into electronic devices.⁵⁵ Sun et al. described techniques for measuring the conductivity of MOFs.⁵⁶ For a critical review of mostly nonporous conductive coordination polymers, we direct readers to the work of Givaja et al.⁵⁷

1.1. Design Strategies and Mechanisms

Electrical conductivity is a characteristic of a material that quantifies the efficacy of the transport of electrical charge. It is a convolution of the charge carrier concentration, n, and the carrier mobility, μ.⁵⁸ Control over either of these quantities is nontrivial and requires deep understanding of the electronic structure of the material, as well as the mechanisms underlying charge transport.

From a fundamental perspective, charge transport in solids can be described by one of two general mechanisms: hopping transport and ballistic (or band-like) transport (Figure 2).⁴⁰ In the former, the charges transfer between discrete, nonbonded sites, where the charge carriers are localized. This mechanism is common to disordered materials, glasses, and organic semiconductors. In the latter, strong interactions between the sites allow for formation of continuous energy bands with delocalized charge carriers. This mechanism is often found in crystalline inorganic materials.

Figure 2.

Schematic representations of (a) ballistic band-like charge transport and (b) hopping charge transport. In both modes of transport, electrons move from high to low electric potential energy (denoted as E). In band-like transport, movement of electrons proceeds along a smooth energy landscape, while in hopping transport, movement of electrons is gated by activation barriers (denoted as E_a).

In chemical terms, an analogy can be made between these two mechanisms and the Robin–Day classification of mixed-valence compounds.⁵⁹ In a material with strong covalent bonding, where we would expect band-like transport, the electrons are delocalized between the different states—similar to that of a class III mixed-valence compound. In contrast, charge transport in more ionic materials is better described by the hopping mechanism. In these cases, distinct sites with differing valences exist, and additional energy has to be applied to transfer the electron between them–similar to a class II mixed-valence compound. (Insulating materials with very low conductivities are analogous to class I mixed-valence compounds, in which the valences are trapped and even hopping is inaccessible.)

The key difference in observable parameters for the two mechanisms lies in the temperature dependence of conductivity. Hopping-type conductivity is always thermally activated: higher temperatures lead to higher conductivities. This dependence follows an exponential law and is described by σ = σ₀ exp[−(T₀/T)^1/d], where σ is the conductivity, T is the temperature, T₀ and σ₀ are constants specific to the material, and d is the dimensionality of the sample.^60,61

In contrast to hopping, band-like transport can be both thermally activated and deactivated. In metallic materials with sufficiently high carrier concentrations, the conductivity is limited by various scattering processes, which are enhanced at higher temperatures, leading to less efficient transport. In semiconductors, the conductivity is generally limited by the charge carrier concentration. At higher temperatures, more free holes or electrons are generated, giving higher conductivities. Because very few MOFs are metallic, the specific temperature dependences for metals will not be discussed. The conductivity of semiconductors often follows an Arrhenius dependence, σ = σ₀ exp[−(E_a/kT)], where E_a is the activation energy. The value of E_a is tied to the width of the band gap, as well as the energy levels of dopants.⁵⁸

The generalized electronic band structures of an insulator, semiconductor, and metal are illustrated in Figure 3. Generally, an insulator is defined by a large band gap (E_g), usually in excess of ∼4 eV, which results in very low population of the conduction band. A semiconductor has an intermediate E_g that allows promotion of free charge carriers to the conduction band (e.g., by thermal or optical excitation). A metal contains at least one band crossing the Fermi level (E_F), resulting in a continuum of allowed electronic states that leads to high conductivities.

Figure 3.

Electronic structures of a generic insulator, semiconductor, and metal, where E_g is the band gap and E_F is the Fermi level.

In practice, many factors complicate the determination of charge transport mechanisms. Specifically for conductive MOFs, two key issues are involved. First, most measurements in the literature have been carried out on polycrystalline pellets, and not on single crystals. This adds an inherent thermally activated contribution to the resistance from hopping between different grains of the material.⁶² Second, significant disorder or defects can lead to creation of trap states, where charge carriers will be localized and would need to hop between.^60,61 It is also easy to imagine, for instance, how a missing linker defect could break up a charge transport pathway and create a barrier to charge transport; other types of defects would have similar effects.⁶³

Ultimately, a decisive determination of the charge transport mechanism in a material would involve a combination of variable temperature single-crystal conductivity studies, electronic structure calculations, and optical spectroscopy, at the minimum. Few studies, however, provide such in-depth investigation of charge transport in MOFs, making the actual underlying mechanisms difficult to discuss in the context of this Review. Therefore, we have opted to discuss the approaches that researchers have applied to designing conductive MOFs and how successful these strategies have been.

Much of the early work on electrical transport in MOFs took inspiration from similar work on coordination polymers,⁶⁴ covalent organic frameworks (COFs),³⁷ and molecular conductors.⁶⁵ In fact, conductive MOFs can be thought of as porous molecular conductors, given that they are indeed composed of molecular building blocks. The general approaches taken toward achieving high conductivities in MOFs also originate from these more established fields. Two key strategies in particular are the so-called through-bond and through-space approaches. The former focuses on improving bonding between the metal and the ligands to achieve stronger charge delocalization; the latter targets noncovalent interactions between organic fragments, particularly π–π stacking, to introduce continuous charge transport pathways. We anticipate that the nature of the transport pathways may affect the transport properties in MOFs, coordination polymers, COFs, and other conductors in similar ways despite other differences in the nature of these materials.

A number of unique characteristics of MOFs, however, tend to limit direct applications of these strategies. In particular, the inherent porosity of MOFs precludes close intermolecular contacts in many structural types, particularly in isotropic structures (i.e., high-symmetry structures where charge transport pathways are identical in all three crystallographic directions). In addition, the majority of MOFs are formed with carboxylate linkers, which usually form relatively ionic bonds with the metals, leading to large energy gaps and trapped valences/confined electronic states. That said, the chemical and structural tunability of MOFs, as well as their unique host–guest chemistry, have allowed for these approaches to evolve and produce materials with a variety of motifs favorable for conductivity (encompassing inorganic and organic components). Below, we give a broad overview of the current form of these approaches toward achieving electrical conductivity in MOFs (Figure 4).

Figure 4.

Orbital representations of potential charge transport pathways operative in MOFs. (a) The through-bond pathway involves orbitals from the metal and ligand functional groups. (b) The extended conjugation pathway also involves π–d conjugation including the ligand core (both are shown here for M = a transition metal). (c) The through-space pathway involves π–π stacking of organic moieties (E = S for tetrathiafulvalene, a common component in MOFs).

1.1.1. Through-Bond Pathways

Networks of coordination bonds in MOFs can form continuous routes for charge delocalization. In this work, we refer to bonding motifs involving metals and the ligand functional group (but not the organic core) as through-bond pathways. MOFs with continuous SBUs comprising metals and ligand moieties with well-matched energy levels and good orbital overlap can result in small band gaps and high charge mobilities, both of which are favorable for conductivity. Examples of 1D (most common)⁶⁶⁻⁷⁰ and 3D pathways (much rarer)^68,71,72 have both been reported.

Many reports in this category focus on softer, more electropositive linkers, with sulfur or nitrogen coordinating to the metals, in which the energy matching and metal–ligand orbital overlap are improved.⁶⁶⁻⁶⁸ Fe-based MOFs, particularly those with azolate ligands containing mixed-valent Fe^II/III centers, exhibit the highest conductivities in this class of materials.^68−70,72 These directions follow principles previously demonstrated for inorganic chalcogenide chains,⁷³ as well as conducting metallopolymers.⁷⁴

1.1.2. Extended Conjugation

Pairing transition metals with ligands containing chelating functional groups (e.g., ortho-diols, diamines, and dithiols) that are conjugated with the organic core results in frameworks with extended conjugation encompassing both the organic and inorganic components. Some of these MOFs with 2D structures have been proposed to be metal–organic analogs of graphene, referring to the similarity between their extended π–d conjugation within the ab plane, and the sp² hybridization of graphene. This π–d conjugation allows for efficient delocalization of charge carriers within the plane, with such frameworks exhibiting the highest conductivities for MOFs.^{21,30,75−79}

The organic linkers found in MOFs with extended conjugation include dihydroxybenzoquinone, chloranilic acid, and hexa-substituted triphenylenes and benzenes. The redox-active nature of these aromatic cores is also important for enhancing conductivity: many of these ligands are partially oxidized during solvothermal growth, introducing charge carriers into the as-synthesized frameworks.

For the majority of the 2D-connected frameworks, charge transport within the π–d conjugated planes has been invoked to be the dominant mechanism behind conductivity. We note, however, that π–π interlayer interactions in the bulk structures may also be important for contributing to charge delocalization.

1.1.3. Through-Space Pathways

Organic components participating in π–π interactions with one another can form through-space charge transport pathways. For organic semiconductors, it is well-established that the spatial separation is inversely correlated with the magnitude of the transfer integral and hence the charge mobility.⁸⁰ In an analogous way, linkers that have a high propensity for π–π interactions can yield MOFs with high conductivities originating from the organic components. Work in this direction can be seen as extension of prior research on dense coordination polymers based on tetracyanoquinodimethane (TCNQ), which show electrical conductivities above 0.1 S/cm.⁸¹⁻⁸³

Several well-known building blocks in organic electronics have been incorporated into conductive MOFs with through-space charge pathways. For example, MOFs with ligands based on tetrathiafulvalene (TTF), an electron-rich organosulfur molecule, exhibit conductivities varying systematically with the stacking distance between the ligands.⁸⁴⁻⁸⁸ Conductive naphthalene-, anthracene-, and naphthalenediimide-based MOFs also exhibit π–π stacking.^38,89−91

For conductive 2D MOFs that are fully conjugated within the ab plane, the role of through-space conductivity (i.e., transport along the c direction) remains to be fully elucidated. However, recent studies on triphenylene-based MOFs suggest charge transport through π–π stacking indeed contributes to the high bulk conductivities observed.^79,92

1.1.4. Redox Hopping

In practice, it is difficult to unambiguously distinguish between the two general mechanisms through which charge transport in MOFs can proceed (i.e., band-like transport and charge hopping transport). Even in structures with ostensible high-mobility transport pathways, real defect concentrations are unknown, and grain boundary resistances in polycrystalline samples may obfuscate the intrinsic behavior. Hence, hopping conduction cannot be ruled out, especially at lower temperatures. However, for frameworks in which no crystallographic pathways that could facilitate band-like transport can be identified, it is reasonable to assume that conductivity proceeds via a hopping mechanism (Figure 5). In such materials, the presence of redox-active metals or linkers, as well as small spatial separation between these components, can promote charge hopping.

Figure 5.

Schematic representations of electron transport via (a) a redox hopping mechanism between organic linkers and (b) a guest-promoted pathway involving host–guest interactions between the inorganic framework nodes and guest molecules.

1.1.5. Guest-Promoted Transport

The porosity of MOFs can present both a challenge and an opportunity with respect to conductivity. Many researchers have exploited the porosity of MOFs to induce conductivity by postsynthetically loading electroactive guest molecules into the framework. These guests then form charge transport pathways throughout the material through guest–guest or guest–framework interactions. A diverse set of approaches to introducing conductivity pathways into such materials exist, encompassing both the aforementioned strategies translated to host–guest interactions, as well as entirely new directions, such as incorporation of extended solid state or polymeric materials within the pores. In all cases involving this strategy, it should be noted that porosity is either significantly reduced or even completely eliminated, as may be expected by occupying the pores with bulky guests.

1.2. Electronic Structures of MOFs

Electronic energy levels in MOFs, like other extended solids, are conveniently represented as band structures, where the energies of orbitals are plotted versus k-space (the crystal momentum).⁹³ Although experimental band structures and densities of states (defined as the number of energy levels versus energy) can be probed using photoemission spectroscopies, in practice, these techniques have only rarely been applied to MOFs.^94,77 Therefore, the vast majority of band structures for MOFs are computed using density functional theory (DFT) calculations. They are commonly referenced to the electrostatic potential inside a pore.⁹⁶

The calculated band structures for representative MOFs with insulating, semiconducting, and metallic electronic structures are shown in Figure 6. Zn₄O(BDC)₃ (BDC = benzene-1,4-dicarboxylate), or MOF-5, has a band gap of 4.6 eV, indicating that it is an insulator.⁴⁵ The majority of reported MOFs are expected to be insulators as well due to large energy gaps between their frontier orbitals. The computed band gap of Zn₂(TTFTB) (TTFTB = tetrathiafulvalene tetrabenzoate) is approximately 1.75 eV,⁸⁴ a typical value for a semiconductor. We note that, in the case of Zn₂(TTFTB), the computed electronic band gap and the optical band gap from a Tauc plot (2.0 eV) are in reasonable agreement.⁹⁷ However, in the absence of transport measurements, optical band gaps alone are not sufficient to determine that a compound is a semiconductor. Finally, the calculated band structure of Ni₃(HIB)₂ (HIB = hexaiminobenzene) contains bands crossing the Fermi level, suggesting metallic character.⁷⁷ Ultraviolet photoemission spectroscopy showed a nonzero density of states at the Fermi level, consistent with metallicity. Although temperature-dependent conductivity for polycrystalline samples of this compound indicated thermally activated transport, in seeming contradiction with the metallic nature predicted by computations, the authors proposed that scattering at grain boundaries dominated transport, which is otherwise metallic within each particle. The accuracy of a computed electronic band structure is necessarily determined by the quality of the input crystal structure and the functional used. Significant structural disorder and large unit cells in many MOFs can introduce considerable challenges for band structure calculations. The relevance of computed band structures to the real transport properties of a MOF should, therefore, always be considered in relation to the structural integrity of the model and practical constraints on computational resources.

Figure 6.

Calculated electronic band structures and densities of states for an insulating MOF, Zn₄O(BDC)₃ (MOF-5);⁴⁵ a semiconducting MOF, Zn₂(TTFTB);⁸⁴ and a metallic MOF, Ni₃(HIB)₂.⁷⁷

1.3. Practical Considerations

To achieve fundamental understanding of charge transport in MOFs, it is necessary to deconvolute carrier concentration and mobility. Mobility can be obtained directly with noncontact measurements such as time-resolved terahertz spectroscopy (TRTS) or flash-photolysis time-resolved microwave conductivity (FP-TRMC). Hall effect measurements and field-effect transistors (FET) also allow determination of carrier mobility and identity (i.e., whether electrons or holes are the majority carriers). However, all of these measurements are challenging and have steep requirements for sample quality and preparation and, thus, have been rarely undertaken in MOFs. Furthermore, results obtained from one technique are not easily compared with those from other techniques. For instance, whereas FP-TRMC reports intrinsic mobility values, these are alternating current mobility values that cannot and should not be compared on a one-to-one basis with mobility values obtained from FET devices, which normally operate under direct current. As a result of all these factors, the majority of publications in this area simply report conductivity values without attempting to probe mobility or carrier concentration. Ideally, mobility values from contact (Hall or FET) measurements are preferable to supplement conductivity values because they provide additional insight into transport properties.

A number of previous reports described in detail the various methods of measuring electrical conductivity on MOFs and other coordination polymers.^56,57 Briefly, conductivity can be measured on either single crystals or on polycrystalline samples in the form of films or powders. Although clearly more technically challenging, single-crystal measurements are preferred because they eliminate contributions from grain boundary resistance, sample anisotropy, and other factors apart from the intrinsic conductivity of the material. In practice, however, because of particle size considerations and the considerable skill and effort required to produce single-crystal devices for many samples, powder or film measurements are used instead. Powders are generally pressed into compact pellets, while films are usually grown on or transferred onto insulating substrates to ensure that only the MOF material contributes to the measured conductivity.

Conductivity measurements—regardless of whether they are carried out on powders, films, or single crystals—are typically performed in either a two-probe or four-probe configuration. The former (Figure 7a) is simpler and involves simply contacting the material with two wires. In the conventional implementation, a known voltage is supplied to the sample, and the current that passes through it is measured to obtain the resistance through Ohm’s law. Significant issues may arise when the contact between the wires and the sample is poor, as this configuration does not compensate for contact resistance. The use of the four-probe configuration, in which four wires are attached to the sample, eliminates contributions from contact resistance from the values measured. In the most common linear four-probe configuration, the outer two wires are used to supply a known current, and the inner two wires are used to measure the potential drop caused by the applied current. This method allows for precise determination of the intrinsic resistance of the sample and elimination of contact effects, so long as all contacts are identical and the geometry of the sample is rigorously determined. Other specific configurations for four-probe measurements exist, depending on the morphology of the studied material: for example, the van der Pauw method uses four wires placed around the outer perimeter of a sample.

Figure 7.

Measurement techniques commonly used for measuring electrical conductivity of MOFs.⁵⁶I and V denote current and voltage, respectively, and L, w, and t denote the length, width, and thickness of the samples, respectively. s denotes the spacing between contacts. R_AB and R_AC are the resistances measured between contacts A and B and A and C, respectively. F₁ and F₂ are correction factors depending on the geometry of the sample and the values of R_AB and R_AC, respectively.

When four-probe measurements are executed on single crystals, typically the four-contact configuration is used (Figure 7b). In this method, two sets of wires are attached to the material along the direction where the conductivity is being evaluated. It is important that the contacts cover the full width of the crystal in the orthogonal direction to allow good estimates of the cross-section area through which current is passed. Here, the resistance of the device, R, is the numerical derivative of the measured voltage drop with respect to the applied current, in accordance with Ohm’s law. The resistivity can be estimated using the formula , where L is the distance between the two inner contacts, w is the width, and t is the thickness of the sample.

On extended films and pellets, contact resistance can be analogously minimized with the four-point measurement (Figure 7c). In this case, four small contacts are attached to the surface, equally spaced along a line. The conductivity can be calculated from , where s is the spacing between the contacts and F₁ is a correction factor dependent on the geometry of the sample.

The van der Pauw method (Figure 7d) is generally less sensitive to the shape of the sample and should be preferred to the linear four-probe configuration when working with non-rectangular samples. For van der Pauw measurements, four small contacts are attached to four corners of the sample. Then, two resistances are estimated, with current applied along one side, and voltage measured along the opposite. Then, the conductivity of the sample is estimated with , where t is the thickness of the sample, R_AB and R_AC are the resistances along two orthogonal sides, and F₂ is a correction factor dependent on the two resistances.

The contacts are usually made of precious metals, such as Au, Ag, or Cu, and are attached with conductive adhesive, including carbon, gold, or silver paint, or by depositing a thin layer of metal on the surface of the sample to attach the wires to it. Generally, contact resistances can be minimized by matching the work functions of the sample of interest and the contact materials.

Accurate and precise determination of the conductivities of MOFs is the first step toward evaluating their utility in a range of applications.⁵¹⁻⁵³ For example, electrode materials in energy storage applications, such as supercapacitors or batteries, typically require relatively high conductivities on the order of 0.1 S/cm or higher.²⁷⁻³⁰ High electrical conductivity alone is not sufficient, however, as ionic conductivity is crucial to enable operation at application-relevant currents.^27,29 Engineering composites that incorporate less conductive MOFs may also be a promising approach for energy storage applications.⁹⁸⁻¹⁰⁰ For chemiresistive sensing, the requirements for conductivity are more flexible, as the electronics and device design can be tailored to accommodate different conductivities. MOFs showing promise as chemiresistive sensors have conductivities ranging from 10^–4 to 8 S/cm.^25,101 Generally, the change in conductivity upon interaction with an analyte is more important than the absolute conductivity itself.⁵²⁻⁵⁴ For electrocatalysis, conductivity requirements are likely to vary significantly depending on the rate of the reaction being studied. The higher the rate of the electrochemical reaction, the more stringent the requirements on the MOF conductivity, because electron transport within the electrode (here, the MOF) should not be the rate limiting step in an electrochemical system. MOFs with conductivities between 10^–5 to 60 S/cm have been explored for different reactions, including oxygen reduction,^17,20 hydrogen evolution,¹⁶ and carbon dioxide reduction.¹⁰²

2. Through-Bond Pathways

The through-bond approach focuses on investigating frameworks with continuous coordination/covalent pathways that can promote efficient charge transport. A number of studies report control over both the carrier concentration and mobility and, thus, the electrical conductivity, owing to the intrinsic tunability of MOFs (Table 1).

Table 1. Selected Properties for MOFs with Through-Bond Pathways for Charge Transport.

materiala	description	σ (S/cm)b	σ method	Ea (eV)c	BET SA (m2/g)d	μ (cm2 V–1 s –1)	ref
DOBDC MOFs
Co2(DOBDC)(DMF)2	desolv.	1.5 × 10–13	2-probe pellet	0.58			(68)
		6 × 10–13	vdP pellet				(114)
Cu2(DOBDC)(DMF)2	desolv.	1.4 × 10–14	2-probe pellet	0.69			(68)
Fe2(DOBDC)(DMF)2	solv.	3.2 × 10–7	2-probe pellet	0.42	248		(67)
Fe2(DOBDC)(DMF)2	desolv.	4.8 × 10–8	2-probe pellet		241		(67)
Mg2(DOBDC)(DMF)2	desolv.	2.1 × 10–14	2-probe pellet	0.64			(68)
		6 × 10–13	vdP pellet				(114)
Mn2(DOBDC)(DMF)2	solv.	3.9 × 10–13	2-probe pellet		287		(67)
Mn2(DOBDC)(DMF)2	desolv.	3.0 × 10–13	2-probe pellet	0.55			(67)
		4 × 10–13	vdP pellet				(114)
Ni2(DOBDC)(DMF)2	desolv.	2.8 × 10–14	2-probe pellet	0.62			(68)
		6 × 10–13	vdP pellet				(114)
Zn2(DOBDC)(DMF)2	desolv.	3.3 × 10–14	2-probe pellet	0.54			(68)
		6 × 10–12	vdP pellet				(114)
DSBDC MOFs
Fe2(DSBDC)(DMF)2	solv.	3.9 × 10–6	2-probe pellet		54		(67)
Fe2(DSBDC)(DMF)2	desolv.	5.8 × 10–7	2-probe pellet	0.27	83		(67)
Fe2(DSBDC)	act.	1.5 × 10–9	2-probe pellet				(115)
Mn2(DSBDC)(DMF)2	solv.	2.5 × 10–12	2-probe pellet		232	0.02 (FP-TRMC)e	(66,67)
Mn2(DSBDC)(DMF)2	desolv.	1.2 × 10–12	2-probe pellet	0.81		0.01 (FP-TRMC)	(66,67)
AnBHB MOFs
Co2(AnBHB)		4 × 10–8	vdP pellet		1213		(114)
Mg2(AnBHB)		5 × 10–9	vdP pellet		1137		(114)
Mn2(AnBHB)		3 × 10–8	vdP pellet		1748		(114)
Ni2(AnBHB)		4 × 10–7	vdP pellet		1352		(114)
Zn2(AnBHB)		6 × 10–8	vdP pellet		1124		(114)
Fe–azolate MOFs
Fe(1,2,3-triazolate)2		7 × 10–9	2-probe pellet (AC)		370		(72)
Fe(1,2,3-triazolate)2(BF4)0.33	ox. (Th•+BF4–)	0.3(1)	2-probe pellet	0.0571f	50		(72)
Fe(1,2,3-triazolate)2	ox. (air)	3.0 × 10–6	2-probe pellet	0.39	443		(68)
		7.7 × 10–5	4-probe pellet		450		(71)
Fe(1,2,3-triazolate)2	ox. (I2)	1.0 × 10–3	4-probe pellet				(71)
Fe2(BDP)3		9.6 × 10–3	4-probe sc			0.02 (FP-TRMC)	(69)
K0.8Fe2(BDP)3	red. (K+[C10H8]•–)					0.29 (FP-TRMC)	(69)
K0.98Fe2(BDP)3	red. (K+[C10H8]•–)	0.025	2-probe sc (FET)			0.84 (e, FET)	(69)
Fe2(BDT)3	ox. (air)	1.2(4)	2-probe sc	0.16	614		(70)
Fe2Cl2(BTDD)		1.1 × 10–7	2-probe pellet	0.39	365		(68)
other azolate MOFs
Cd(1,2,3-triazolate)2		1.4 × 10–13	2-probe pellet	0.75			(68)
Co(1,2,3-triazolate)2		5.1 × 10–14	2-probe pellet	0.64			(68)
Cu(1,2,3-triazolate)2		3.2 × 10–14	2-probe pellet	0.59			(68)
Mg(1,2,3-triazolate)2		9.9 × 10–15	2-probe pellet	0.74			(68)
Mn(1,2,3-triazolate)2		8.2 × 10–14	2-probe pellet	0.59			(68)
Zn(1,2,3-triazolate)2		1.2 × 10–14	2-probe pellet	0.77			(68)
Co2Cl2(BTDD)		3.7 × 10–13	2-probe pellet	0.86			(68)
Mn2Cl2(BTDD)		1.3 × 10–14	2-probe pellet	0.89			(68)
Ni2Cl2(BTDD)		2.8 × 10–13	2-probe pellet	0.84			(68)
other through-bond pathways
[Cu2(Hmna)(mn)][NH4]		10.96	4-probe sc	0.006			(130)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or 296 K.

^cDerived from Arrhenius model unless otherwise indicated. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^dCalculated from N₂ adsorption isotherms.

^eMeasured for methanol-exchanged Mn₂(DSBDC).

^fDerived from polaronic nearest-neighbor hopping.

In most cases, this approach is realized in frameworks with 1D inorganic SBUs, also known as rod-based MOFs.¹⁰³ The majority of such materials employ carboxylate linkers and (−M–O−)_∞ chains. The relatively ionic bonding between transition metals and carboxylates generally leads to poor orbital overlap and low band dispersion−metal and ligand energy levels are relatively localized, leading to low conductivity.

The more successful studies have attempted to solve this issue by increasing the metal–ligand covalency. The general approach so far has been to work with softer ligands, in which the metal-binding atoms are sulfur and nitrogen rather than oxygen. One clear illustration of this concept is substitution of (−M–O−)_∞ chains for (−M–S−)_∞ SBUs in MOF-74/CPO-27 analogs, which led to increased conductivities and mobilities and decreased band gaps.^66,67

As in most other approaches, the carrier concentration is generally controlled through introduction of mixed-valent species, although it is rarely precisely quantified. Specifically, in pyrazolate, triazolate, and tetrazolate MOFs, Fe^II/III mixed valency has resulted in high conductivity values that were tunable and correlated with the concentration of charge carriers.⁶⁹⁻⁷² Interestingly, the abundance of detailed and systematic structure–function relationship studies for through-bond materials allows us to speculate that the limiting factor for electrical conductivity in many of these MOFs is indeed the carrier concentration: the mixed-valence Fe^II/III materials show vastly higher conductivities than those with other d-metals, and the conductivities correlate strongly with the extent of mixed valency.

Although the majority of studies investigate rod MOFs with 1D conductivity pathways, select examples with isotropic 3D pathways exist, most notably the framework Fe(1,2,3-triazolate)₂.^68,71,72 That said, the vast majority of MOFs containing 1D rod SBUs or other continuous inorganic coordination motifs have not yet been studied for electronic transport, even though stable mixed valency has been demonstrated in some of these other 1D SBUs.^104−106 Applying principles to increase conductivity in through-bond pathways to these unexplored materials is likely to yield new conductive MOFs with even more structural diversity and tunability.

2.1. MOF-74-Type Frameworks

The family of M₂(DOBDC) (M = divalent metal; DOBDC = 2,5-dioxidobenzene-1,4-dicarboxylate) frameworks,^{103,107−113} colloquially known as MOF-74 or CPO-27, exhibit 1D hexagonal channels and infinite SBUs consisting of (−M–O−)_∞ chains (Figure 8). In the as-synthesized frameworks, which have the formula M₂(DOBDC)(DMF)₂, the metal ions occupy a pseudo-octahedral environment, with one DMF molecule coordinated to each metal center. Removal of this DMF molecule through activation allows for direct modification of the metals’ coordination geometry, as well as access to coordinatively unsaturated metal sites.

Figure 8.

Structure of Fe₂(DSBDC), showing (a) the proposed through-bond conduction pathway comprising (−Fe–S−)_∞ chains, as well as bridging ligand carboxylates and oxygens from coordinated DMF molecules, and (b) hexagonal 1D pores.⁶⁷

In a comparative study of different structural families of rod MOFs, Sun et al. reported the conductivities of seven different M^II₂(DOBDC)(DMF)₂ materials (M = Mg, Mn, Fe, Co, Ni, Cu, Zn).⁶⁸ The conductivities of the Mg, Mn, Co, Ni, Cu, and Zn materials were very low, between 1.4 × 10^–14 S/cm for Cu₂(DOBDC)(DMF)₂ and 3.0 × 10^–13 S/cm for Mn₂(DOBDC)(DMF)₂. (Similar conductivity values for these materials were also reported by Scheurle et al.¹¹⁴)

Sun et al. hypothesized that replacing the hydroxy group of the linker with a thiol group would increase the conductivity of the resulting frameworks due to better energy matching between the frontier orbitals of the thiolate and the metal. Indeed, the framework Mn₂(DSBDC)(DMF)₂ (DSBDC = 2,5-disulfidobenzene-1,4-dicarboxylate) exhibited a higher conductivity by about 1 order of magnitude (2.5 × 10^–12 S/cm) than Mn₂(DOBDC) (3.9 × 10^–13 S/cm).^66,67 The conductivities of the Fe analogs were approximately 6 orders of magnitude higher than those of the Mn materials, with the DSBDC MOF again being more conductive than the DOBDC MOF (3.9 × 10^–6 S/cm for Fe₂(DSBDC), and 3.2 × 10^–7 S/cm for Fe₂(DOBDC)).⁶⁷ The charge mobilities of methanol-exchanged and activated Mn₂(DSBDC), as measured by FP-TRMC, were 0.02 and 0.01 cm² V^–1 s^–1.⁶⁷

These results suggest that replacing (−M–O−)_∞ chains with (−M–S−)_∞ chains creates a more efficient pathway for intrachain charge transport. The authors attributed the dramatically higher conductivities of the Fe MOFs to the loosely bound electrons in the β-spin d band of Fe^II (the analogous state is empty for high-spin Mn^II), effectively lowering the band gap for the Fe materials compared to the Mn analogs. Although these original studies did not detect Fe^III by Mössbauer spectroscopy, oxidation of a small fraction of framework Fe^II centers to Fe^III may also explain these differences in conductivity.⁶⁸

A similar effect was observed in the M₂(DOBDC)(DMF)₂ materials, where the conductivity of Fe₂(DOBDC)(DMF)₂ was significantly higher than for the other metals, at 4.8 × 10^–8 S/cm.⁶⁸ Oxidation of some Fe^II centers to Fe^III because of the low reduction potential of the Fe^II/III couple was deemed likely from electron paramagnetic resonance (EPR) spectroscopy studies, despite the handling of Fe₂(DOBDC)(DMF)₂ under inert conditions. For these materials, the authors attributed the higher conductivity of the Fe^II MOF to the relatively higher energy valence orbitals of the high-spin Fe^II compared to other metals, leading to a smaller band gap.

Sun et al. also investigated the effects of pore guest DMF molecules on the electrical conductivities of M₂(DOBDC)(DMF)₂ and M₂(DSBDC)(DMF)₂ (M = Fe^II, Mn^II).⁶⁷ Guest-free Mn and Fe DOBDC and DSBDC frameworks each exhibited lower conductivities by about 1 order of magnitude compared to the as-synthesized materials. This difference was hypothesized to be the result of defects introduced by the solvent exchange and evacuation process. Removal of coordinated DMF in Fe₂(DSBDC) was found to further reduce¹¹⁵ the conductivity by an additional 2 orders of magnitude to 1.5 × 10^–9 S/cm. DFT calculations indicated that coordinated DMF accepts electron density from Fe centers, effectively hole-doping the material and increasing charge density. Studying different solvation conditions for other MOFs with coordinated solvents may reveal broader trends related to the effect of solvents on their conductivities. For example, a rhodium iodide coordination polymer showed reversible conductivity changes of up to 5 orders of magnitude on removal of water solvent.¹¹⁶

Scheurle et al. incorporated anthracene into the MOF-74 structure by reacting the 4,4′-(anthracene-9,10-diyl)bis(2-hydroxybenzoate) linker with divalent Mg, Mn, Co, Ni, and Zn.¹¹⁴ The anthracene moieties are separated by the relatively long distance of 5.7 Å, thus making the charge transport through π–π stacking unlikely. Despite this, all of these MOFs were several orders of magnitude more conductive (between 5 × 10^–9 S/cm for Mg and 4 × 10^–7 S/cm for Ni) than their DOBDC analogs. This increase in conductivity was attributed to the presence of the electron-rich anthracene core, which likely affects the charge density of the material. Also of note is the high porosity of these materials, with Brunauer−Emmett−Teller (BET) surface areas above 1100 m²/g.

2.2. Azolate Frameworks

MOFs with pyrazolate, triazolate, and tetrazolate linkers tend to exhibit pronounced electronic coupling between the metals and the linkers by virtue of the strong σ-donating and π-accepting character of azolates.¹¹⁷ In such structures, 1D chain SBUs with bridging azolates are a common motif.¹¹⁸ The short bridging lengths of azolates, along with their covalent bonding to the metal, are responsible for notable cooperative electronic properties. For example, many 1D coordination polymers containing (−Fe–N–N−)_∞ motifs based on triazolate and tetrazolate ligands are spin-crossover materials.^119−121 Cooperative binding events in metal–triazolate MOFs also trigger spin-state transitions¹²² and reversible charge transfer events¹²³ at the metal centers. These electronic considerations motivated the initial studies of the transport properties of such materials.

High conductivities have been reported in Fe–azolate frameworks with Fe^II/III mixed valency, which effectively introduces mobile charge carriers into the (−Fe–N–N−)_∞ chains (Figure 9). Intervalence charge transfer (IVCT) processes in these MOFs are expected to resemble those in molecular mixed-valence complexes of d⁵–d⁶ metal centers with π-acid bridging linkers.¹²⁴ The accessibility of metal-centered mixed valency likely results from the low reduction potential of Fe^III coupled with small reorganization energies of the coordination spheres, which in turn lead to faster electron transfer rates compared to other transition metals.⁵⁹ In other words, both thermodynamic and kinetic factors can be expected to play a role in enabling facile charge transport.

Figure 9.

Structures of Fe–azolate MOFs. (a–c) SBUs of Fe(1,2,3-triazolate)₂,⁷² Fe₂(BDT)₃,¹²⁶ and Fe₂(BDP)₃,²⁷² respectively, showing continuous (−Fe–N–N−)_∞ chains. (d) Connectivity of Fe(1,2,3-triazolate)₂, showing continuous 3D diamondoid network of Fe–N bonds. (e and f) Connectivities of Fe₂(BDT)₃ and Fe₂(BDP)₃, respectively, showing 1D channels.

In their report of the M^II(1,2,3-triazolate)₂ series of isostructural MOFs (M = Mg, Fe, Co, Cu, Zn, and Cd),¹²⁵ Gándara et al. indicated that the Fe(1,2,3-triazolate)₂ material was conductive (7.7 × 10^–5 S/cm) in its as-synthesized form.⁷¹ In this structure, each triazolate linker bridges three octahedrally coordinated Fe^II centers, forming a 3D network with diamond topology containing (−Fe–N–N−)_∞ chains (Figure 9a,d). The material is permanently porous, with a BET surface area of 450 m²/g. Sun et al. later reported that the Mg, Mn, Co, Cu, Zn, and Cd MOFs with 1,2,3-triazolate are insulating (conductivities <2 × 10^–13 S/cm) and measured a conductivity value of 3.0 × 10^–6 S/cm for Fe(1,2,3-triazolate)₂, similar to the original study.⁶⁸

In these reports, Fe(1,2,3-triazolate)₂ was handled in ambient atmosphere because no changes in powder X-ray diffraction (PXRD) patterns were observed after several weeks of air exposure (suggesting stability to these conditions). However, several pieces of evidence suggested that oxidation of the Fe^II centers is accessible and contributes to the conductivity. Gándara et al. found that the conductivity increased to 1.0 × 10^–3 S/cm after exposure to I₂ vapor with retention of the structure. They surmised that some Fe^II sites were oxidized to Fe^III, enabling IVCT. Sun et al. showed that the room temperature EPR spectrum contained signals at g ≈ 2.0 and 4.2, consistent with the presence of high-spin Fe^III centers. DFT electronic band structure calculations of Fe(1,2,3-triazolate)₂ with Fe^III defects revealed unoccupied Fe^III midgap states that could facilitate the formation of mobile valence band holes. Moreover, the calculated spin density distribution also indicated partial delocalization of unpaired electrons among Fe sites.

Definitive evidence of the importance of mixed valency on the conductivity of Fe(1,2,3-triazolate)₂ was shown by Park et al. via the systematic postsynthetic introduction of Fe^III sites.⁷² By handling all reagents under rigorously air-free conditions, they obtained the Fe(1,2,3-triazolate)₂ material with a pink color, in contrast to the orange or brown powders reported previously. The material contained only low-spin Fe^II by Mössbauer spectroscopy, and its electrical conductivity was only <7 × 10^–9 S/cm, about 3 orders of magnitude lower than previous reports.

Upon oxidation with stoichiometric amounts of thianthrene tetrafluoroborate, materials with the formula Fe(1,2,3-triazolate)₂(BF₄)_x were obtained, in which BF₄^– counteranions charge-balance the Fe^III centers introduced into the framework. Critically, increasing the BF₄^– content (and hence the Fe^III concentration) increased the conductivities, which in the study was explained by a polaronic hopping model. The maximum achieved BF₄^– loading of x = 0.33 corresponds to one anion per pore; accordingly, Fe(1,2,3-triazolate)₂(BF₄)_0.33 showed a very low BET surface area of 50 m²/g. The conductivity of Fe(1,2,3-triazolate)₂(BF₄)_0.33, 0.3(1) S/cm, is among the highest reported for 3D frameworks, and represents an increase of nearly 8 orders of magnitude over the starting material. In addition, detailed Mössbauer spectroscopy measurements revealed that charges were delocalized between Fe^II and Fe^III on the measurement time scale (∼10^–8 s) at 290 K.

Correlation between introduction of Fe^II/III mixed valency into (−Fe–N–N−)_∞ chains and increased conductivity was also demonstrated for an Fe^II framework with benzene-1,4-ditetrazolate (BDT).⁷⁰ This material, Fe₂(BDT)₃ (Figure 9b,e), was initially reported as an all-Fe^II compound with mixed spin states and a black color.¹²⁶ Xie et al. found that crystals synthesized under anaerobic conditions were orange-red in color, gradually darkening to black after several days in ambient atmosphere with no changes in the PXRD patterns. The air-exposed material remained porous, with a BET surface area of 614 m²/g. The single-crystal conductivities measured along the direction of the (−Fe–N–N−)_∞ direction increased from 6(2) × 10^–5 S/cm for the as-synthesized material to 1.8 S/cm after 30 days in air. UV–vis–NIR spectroscopy and DFT band structure calculations further confirmed IVCT between Fe^II and Fe^III centers as the likely mode of charge transport in this material. The method of oxidation and results observed in this work are similar to a study of a porous vanadyl analog of Prussian blue.¹²⁷

The Fe^II framework with bis[1,2,3-triazolo[4,5-b],[4′,5′-i])dibenzo[1,4]dioxin (BTDD), Fe₂Cl₂(BTDD), also contains (−Fe–N–N−)_∞ chains as part of the rod SBUs in a hexagonal structure similar to MOF-74. Sun et al. reported the conductivity of this material to be 1.1 × 10^–7 S/cm,⁶⁸ almost 6 orders of magnitude higher than the Mn^II, Co^II, and Ni^II isostructural materials.¹²⁸ Unintentional doping with Fe^III was again invoked to explain the higher conductivity.

Achieving Fe^II/III mixed valency with an all-Fe^III starting material was demonstrated by Aubrey et al. with the framework Fe₂(BDP)₃ (BDP = benzene-1,4-dipyrazolate) (Figure 9c,f).⁶⁹ Reduction of Fe₂(BDP)₃ with potassium naphthalenide afforded materials with the formula K_xFe₂(BDP)₃ (0 < x ≤ 2.0). Single crystals were incorporated into FET devices by depositing platinum/carbon contacts between the MOF and prepatterned electrodes. The highest conductivity measured for one such device was 0.025 S/cm for K_0.98Fe₂(BDP)₃ (corresponding to about half of the Fe^III centers reduced to Fe^II). The electron mobility from the same device was 0.84 cm² V^–1 s^–1. In comparison, a device of the original Fe₂(BDP)₃ material exhibited a conductivity of 3.5 × 10^–7 S/cm and electron mobility of 2 × 10^–3 cm² V⁻¹ s⁻¹. The authors suspected that the true intrinsic conductivity of the material was underestimated because of contact resistance in the two-probe configuration. Indeed, a four-probe device of Fe₂(BDP)₃ showed a significantly higher conductivity of 9.6 × 10^–3 S/cm, suggesting that the values for the reduced material may also be underestimated to some extent.

In many of the cases presented above, electronic structure calculations have shown significant band dispersion, confirming the strong coupling between Fe d orbitals and azolate π-orbitals.⁶⁸⁻⁷⁰ This feature, however, appears to not be unique to iron-based materials. Indeed, the calculated band structures of M(1,2,3-triazolate)₂ frameworks with other metals suggest that they may also exhibit mobile charge transport pathways and relatively small band gaps.⁶⁸ If free carriers can be introduced into MOFs with related structural motifs, they will likely comprise additional platforms for conductivity. We note also that triazolate and pyrazolate frameworks generally exhibit high chemical stability because of the strong donating ability of these ligands, and therefore may be of interest for applications in which stability and conductivity are both important.¹²⁹

Pathak et al. attempted¹³⁰ to extend the through-bond approach to two dimensions by incorporating extended 2D Cu–S sheets in [Cu₂(Hmna)(mna)][NH₄] (Hmna = 6-mercaptonicotinic acid). Although this framework is completely nonporous and cannot be strictly called a MOF, it showed some of the highest conductivities reported to date for coordination polymer single crystals, up to ∼11 S/cm. The material behaved as a semiconductor with a low E_a of ∼6 meV, noticeably lower than the calculated bandgap (1.2 eV) or observed optical bandgap (1.34 eV).

3. Extended Conjugation

The discovery of free-standing graphene¹³¹ in 2004 precipitated an avalanche of interest in the electronic properties of 2D materials.^132−137 In addition to the “top-down” methods commonly used for the preparation of these nanoscale compounds, the possibility of creating synthetic 2D materials via “bottom-up” approaches has also been explored.^135−139 Conductive 2D MOFs made via solvothermal self-assembly have emerged as 2D materials with promising transport properties. Calculated band structures suggest that they may host exotic electronic properties, including topologically protected surface states.^{31,32,34−36} Members of this class exhibit the highest conductivities for porous, crystalline framework materials.

The MOFs in this section feature linkers based on conjugated organic cores and redox-noninnocent chelating groups such as ortho-diols (catechols), -diamines, and -dithiols (Figure 10). The oxidation states for a catechol fragment, hydroquinone, semiquinone, and quinone, can also be accessed in the nitrogen- and sulfur-containing analogs. In most cases, the ligands are partially oxidized during synthesis, which favors deprotonation and subsequent framework formation. The resulting MOFs contain mixed-valent linkers—potentially leading to high carrier densities—with some examples of charge states that can be tuned postsynthetically. Although 2D frameworks have received the most attention and constitute the vast majority of examples, we also discuss several frameworks with 3D structures showing extended metal–linker conjugation and high conductivities.

Figure 10.

Redox series of 2–, 1–, and 0 charge states for a deprotonated catecholoid fragment, a common motif in conductive MOFs with extended conjugation.

The metal–organic linkages in these MOFs are analogous to motifs known to promote charge delocalization in inorganic complexes. For example, the redox-noninnocent ligands in metal–dithiolene complexes facilitate electron delocalization between the metal and linker.^140,141 Such compounds are components in many molecular conductors (and even superconductors).¹⁴² Ligand radical character in the bis(o-diiminobenzosemiquinonate) Ni^II complex is known to be stabilized by the metal binding.^143−145 Dihydroxybenzoquinone-type linkers also demonstrate strong electronic and magnetic coupling in transition metal complexes, especially in their oxidized radical forms.^146−148

We note that the structures of these materials are considered to be 2D in the sense that covalent bonds extend only within the ab plane. However, to date, mono- or few-layer samples of 2D MOFs displaying extended conjugation have not been studied in detail. Moreover, only one study on single crystals contacted along the conjugation direction has been reported.⁷⁹ Hence, interlayer effects are expected to influence the reported bulk properties. Molecular metal–dithiolene and diiminobenzosemiquinonate complexes exhibit semiconducting or metallic behavior with the highest conductivities along the stacking direction,^142,144 suggesting that transport facilitated by noncovalent c direction interactions may also contribute to the conductivities measured in powder samples of 2D MOFs. This intuition is supported by existing cross-plane conductivity measurements^79,149 and transport studies of related MOFs with no π–d conjugation.⁹²

3.1. Frameworks with Ditopic Redox Noninnocent Linkers

A number of materials built with tetraoxolene ligands, such as dihydroxybenzoquinonate (dhbq) and chloranilate (Cl₂dhbq), show high electrical conductivity concurrent with intrinsic porosity (Table 2). Although this class of materials is quite expansive,¹⁴⁶ charge transport studies have focused on a family of layered honeycomb anionic frameworks, [M₃(X₂dhbq)₂]ⁿ⁻ (X = H, Cl, Br)^150−153 and structurally related 3D phases,^154,155 discussed in detail below.

Table 2. Selected Properties for MOFs with dhbq and Related Ligands.

materiala	description	σ (S/cm)b	σ methodc	Ea (eV)d	BET SA (m2/g)e	ref
[Cr2(dbhq)3][(H2NMe2)1.5]		1.2(1) × 10–4	2-probe pellet	0.44	collapse	(153)
[Fe2(dhbq)3][(Bu4N)2] (3D)		0.16(1)	2-probe pellet		dense	(154)
[Fe2(dhbq)3][Na0.9(Bu4N)1.8] (3D)	red. (Na+[C10H8]•–)	6.2(1) × 10–3	2-probe pellet		dense	(154)
[Fe2(Cl2dhbq)3][(Me2NH2)2]	solv.	0.014	2-probe pellet			(150)
[Fe2(Cl2dhbq)3][(Me2NH2)2]	act.	1.0(3) × 10–3	2-probe pellet		1175	(150)
[Fe2(Cl2dhbq)3][(Cp2Co)1.43(Me2NH2)1.57]	red. (Cp2Co)	5.1(3) × 10–4	2-probe pellet			(150)
[Fe2(Cl2dhbq)3][(H3O)(phz)3]		0.031(8)	2-probe sc (∥)			(152)
		1.0(9) × 10–4	2-probe sc (⊥)			(152)
		4 × 10–5	2-probe pellet	0.16		(157)
[Fe2(Br2dhbq)3][(H3O)(phz)3]		3(1) × 10–3	2-probe sc (∥)			(152)
		6(2) × 10–6	2-probe sc (⊥)			(152)
[Mn2(Cl2dhbq)3][(Me4N)2]		1.14(3) × 10–13	2-probe pellet	0.74		(151)
[Mn2(Cl2dhbq)3][Na3(Me4N)2]	red. (Na+[C10H8]•– and [C12H10]•–)	2.27(1) × 10–8	2-probe pellet	0.489		(151)
[Mn2(Cl2dhbq)3][Na(Me4N)]	ox.	1.45(2) × 10–13	2-probe pellet			(151)
[Ti2(Cl2dhbq)3][(H2NMe2)2]		2.7(2) × 10–3	2-probe pellet	0.27f	collapse	(153)
[V2(Cl2dhbq)3][(H2NMe2)2]		0.45(3)	2-probe pellet	0.064g	collapse	(153)
[Zn2(Cl2dhbq)3][(H2NMe2)2]		1.5(3) × 10–9	2-probe pellet			(150)
CrCl2(pyz)2		3.2 × 10–2	2-probe pellet			(158)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or between 295 and 300 K under N₂ or Ar atmosphere.

^c∥ denotes device contacted in-plane/parallel to 2D layers; ⊥ denotes device contacted cross-plane/perpendicular to 2D layers.

^dDerived from Arrhenius model unless otherwise indicated. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^eCalculated from N₂ adsorption isotherms.

^fDerived from polaronic nearest-neighbor hopping.

^gDerived from Efros-Shklovskii variable-range hopping.

The easily accessible redox couples of these ligands and their resulting ability to form stable radicals form the origin of strong magnetic coupling in a number of magnetic molecular complexes.^146−148 The incorporation of these ligands into MOFs harnessed these features to produce materials with permanent porosity, high electrical conductivity, and magnetic ordering. Notably, the Fe^II/III-based materials display some of the highest conductivities and magnetic ordering temperatures in MOFs.

The mechanism of conductivity in these materials is up for debate: while most works propose hopping between either redox-active metal sites or radical organic linkers to be responsible for charge transport, many of these MOFs display high degrees of electron delocalization between the linker and the metal. As a result, they show similarities to the materials in the following section, which exhibit extended conjugation between the metal and ligand.

3.1.1. Two-Dimensional Layered Frameworks with Ditopic Linkers

This structure type, which was initially reported for Mn^II and Cd^II chloranilates,¹⁵⁶ consists of hexagonal layered structures with solvent-accessible pores of ∼1.5 nm in diameter. The metal atoms are each octahedrally coordinated by three ligands (Figure 11). The frameworks are all anionic, with charge-balancing cations located either within the pore or between the layers. For simplicity, most of the following observations will discuss only the anionic framework.

Figure 11.

Structure of [Fe₂(Cl₂dhbq)₃]^2–, showing a honeycomb arrangement of Fe^II/III and Cl₂dbhq^2– within a single 2D layer (charge-balancing [Me₂NH]⁺ cations occupying pore volume not shown).¹⁵⁰

The Harris group reported¹⁵⁰ early studies of electrical conductivity in chloranilate frameworks, focusing initially on the Fe^III and Zn^II materials. The materials were produced through the reaction of the corresponding divalent metal salt and chloranilic acid and are charge-balanced by dimethylammonium ions that reside in the pores of the framework. The low barrier to oxidation of Fe^II results in electron transfer from the Fe^II ions to the ligands, converting two-thirds of these to the 3– radical state (Cl₂dhbq^3–•), and leaving the remaining third in the closed-shell Cl₂dhbq^2– state (Figure 12). This ligand-based mixed valency resulted in the high conductivity of 1.4(7) × 10^–2 S/cm. When desolvated, the conductivity decreased to 1.0(3) × 10^–3 S/cm, attributed to slight framework distortions. Chemical reduction of the MOF by excess Cp₂Co led to full conversion of the ligands to the Cl₂dhbq^3–• radical state, which caused a further decrease in conductivity to 5.1(3) × 10^–4 S/cm. The lower conductivity upon the loss of mixed valency is consistent with charge transport facilitated by electron transfer between Cl₂dhbq^3–• and Cl₂dhbq^2– in the as-synthesized material. The temperature dependence of conductivity for the different states of [Fe₂(Cl₂dhbq)₃]ⁿ⁻ showed similar semiconductor-type behavior with Arrhenius activation energies of ∼0.3 eV.

Figure 12.

Redox series of 4–, 3–, and 2– charge states for linkers based on dihydroxybenzoquinone (dhbq).

The presence of strong coupling between metal centers via radical bridging ligands was further corroborated by the magnetic behavior of [Fe₂(Cl₂dhbq)₃]^2–. Solvated [Fe₂(Cl₂dhbq)₃]^2– ordered ferromagnetically at 80 K, whereas the desolvated (and less conductive) material ordered at 22 K, suggesting weaker coupling. The reduced material ordered at a higher temperature of 105 K, as would be expected for more Fe^III ions being bridged by radical-containing ligands in the reduced material.

In the Zn–chloranilate framework, the oxidation of Zn^II by Cl₂dhbq^2– is not thermodynamically accessible, resulting in the full ligand population of [Zn₂(Cl₂dhbq)₃]^2– remaining in the closed-shell Cl₂dhbq^2– states. Accordingly, the conductivity of this material was relatively low (1.5(3) × 10^–9 S/cm). The authors proposed that the closed-shell configuration of Zn^II with filled d orbitals introduces a barrier to charge transport between the ligands, leading to lower conductivity. The relative influence of the d shell filling vs the ligand oxidation states could be probed via reduction of the zinc material to a similar mixed-valence state as in the Fe analog.

An isostructural Mn^II-based system, [Mn₂(Cl₂dhbq)₃]^2–, showed an increase in conductivity upon reduction.¹⁵¹ The conductivity value rose from 1.14(3) × 10^–13 S/cm for the fully oxidized version with Cl₂dhbq^2– diamagnetic linkers, to 2.27(1) × 10^–8 S/cm for the reduced version, [Mn₂(Cl₂dhbq)₃]^5–, containing Cl₂dhbq^3–• radical linkers. To explain the difference in conductivities between the Mn^II and Fe^II materials, the authors proposed a poorer energetic match between the Mn atoms and the linker compared to Fe. This mismatch may have also led to noticeably higher activation energies of 0.489(8) eV for the reduced and 0.74(3) eV for the oxidized Mn frameworks. The change in conductivity was fully reversible upon chemical oxidation to the initial state [Mn₂(Cl₂dhbq)₃]^2–. Notably, like the Fe^III-based framework, [Mn₂(Cl₂dhbq)₃]^5– displayed a ferromagnetic transition, albeit with a lower T_c of 41 K.

The charge transport behavior of chloranilate frameworks with the same overall honeycomb structure and mixed-valent Fe^II/III was also studied. The first report, by Shilov et al.,¹⁵⁷ discussed the structure and electronic properties of [Fe^IIFe^III(Cl₂dhbq^2–)₂(Cl₂dhbq^3–•)]^2–. Unlike the aforementioned [Fe^III₂(Cl₂dhbq)₃]^2– system, in which the charge balancing (Me₂NH)⁺ ions are located mainly inside the pores, the framework charge in the mixed-valent Fe^II/III framework is balanced by hydrogen-bonded layers of [(H₃O)₂(phenazine)]²⁺. Shilov et al. were unable to isolate single crystals of this material, and conducted a thorough investigation of its electronic properties on polycrystalline powder samples. Mössbauer spectroscopy combined with magnetometry revealed the mixed-valent nature of the material, with the Fe atoms present both in pure 2+ and 3+ states, as well as in the mixed-charge 2.5+ state, with relative concentrations dependent on the temperature. The material showed a relatively high conductivity of 4 × 10^–5 S/cm (polycrystalline pellet) and an Arrhenius E_a of 0.16 eV.

A later study reported single-crystal measurements on a material with the same nominal formula, [Fe^IIFe^III(Cl₂dhbq^2–)₃]⁻, assigned to different charge states (with all the ligands in their closed-shell Cl₂dhbq^2– configurations, and no organic radicals).¹⁵² Despite the lack of organic radicals, the MOF showed a high conductivity of 0.031(8) S/cm from single-crystal measurements parallel to the layers, and 1.0(9) × 10^–4 S/cm orthogonal to the layers. Similar conductivities, 3(1) × 10^–3 S/cm (parallel) and 6(2) × 10^–6 S/cm (orthogonal), were obtained for the isostructural framework containing bromanilate instead of chloranilate. The high anisotropy of the conductivity confirmed that charge transport is mainly limited within the ab plane. Though these values were from single-crystal measurements (vs powder pellet values for [Fe^III₂(Cl₂dhbq)₃]^2–), it is remarkable that the conductivities were of the same magnitude. This result demonstrates that ligand mixed valency and metal mixed valency can both enable charge transport in these systems, consistent with strong electronic coupling between metals and ligands.

A series of structurally related frameworks based on early first row transition metals, [V₂(Cl₂dhbq)₃]^2–, [Ti₂(Cl₂dhbq)₃]^2–, and [Cr₂(dhbq)₃]^1.5– showed similarly high conductivities.¹⁵³ Precursors containing the highly reducing divalent early 3d transition metal ions Ti^II, V^II, and Cr^II were combined with Cl₂dhbq^2– and dhbq^2–, reducing the linkers to the corresponding radical anions. The more diffuse orbitals of the early transition metals (as compared to the later Ni, Co, or Cu) were hypothesized to allow for orbital overlap with the ligand and thus more efficient charge delocalization. This approach proved successful, producing materials with conductivities of 2.7(2) × 10^–3 S/cm for [Ti₂(Cl₂dhbq)₃]^2–, 0.45(3) S/cm for [V₂(Cl₂dhbq)₃]^2–, and 1.2(1) × 10^–4 S/cm for [Cr₂(dhbq)₃]^1.5–. The observed conductivities followed the same trend as the degree of electronic delocalization observed by optical spectroscopy, where the Ti and Cr-based materials can be classified as Robin–Day class II and the V-based material as class III, indicating much stronger charge delocalization in the latter.

The charge states of both the ligands and the metals in these three materials differed. From elemental analysis, optical spectroscopy, and magnetization measurements, the three materials had the following assignments: [Ti^IV₂(Cl₂dhbq^3–)₂(Cl₂dhbq^4–)]^2–, [V^III₂(Cl₂dhbq^2–)(Cl₂dhbq^3–)₂]^2– (assigned putatively, as electronic delocalization did not allow full resolution of the metal/ligand charge states), and [Cr^III₂(dhbq^2–)_1.5(dhbq^3–)_1.5]^1.5–. The stronger charge delocalization and significantly higher conductivity in the V-based materials are explained by a better energy match between the ligand orbitals and the metal 3d shell. Interestingly, [Ti₂(Cl₂dhbq)₃]^2– displayed strong antiferromagnetic coupling between the organic radical spins, with a Curie–Weiss temperature of −223 K, although no ordering was observed in it or the other two materials. Variable temperature conductivity measurements revealed semiconducting behavior fitting well with either polaronic nearest-neighbor hopping (Ti- and Cr-based materials) or the Efros–Shklovskii variable range hopping (VRH) model (V-based material). These mechanisms differed from the Fe-based materials, perhaps as a result of the wider temperature range fitted (a narrower region may yield an Arrhenius-type dependence).

A similar approach was later applied¹⁵⁸ to dense pyrazine-based square lattice coordination polymers, in which the reaction of a Cr^II salt with pyrazine led to the formation of a highly conductive nonporous framework. As in the dhbq materials, the conductivity originated from the reduction of pyrazine to its radical anion form, which led to improved ligand π-system–metal d-orbital overlap, as well as introduction of mobile charge carriers. The material, CrCl₂(pyz)₂ (pyz = pyrazine), showed a relatively high conductivity of 3.2 × 10^–2 S/cm for a pressed pellet, along with a semiconductor-type temperature dependence, which could be fitted to the Mott law for two dimensions.

3.1.2. Three-Dimensional Frameworks Based on dhbq

Dihydroxybenzoquinone also forms 3D frameworks with many late transition¹⁵⁹ and rare-earth metals.¹⁶⁰ The charge transport properties of the Fe material have been evaluated in detail.¹⁵⁴ [Fe₂(dhbq)₃]^2– is a cubic interpenetrated 3D framework with octahedral Fe^III sites containing radical dhbq^3–• anions, with the as-synthesized formula [Fe^III₂(dhbq^3–•)₂(dhbq^2–)]^2– (Figure 13a). The two component sublattices are enantiomeric and fully independent from each other (Figure 13b). Due to the bulky tetrabutylammonium ions compensating the charge, the material is essentially nonporous (though a high theoretical surface area of 5070 m²/g was calculated for the fully oxidized material with charge-balancing cations removed from the pores). The as-synthesized material showed an impressive electrical conductivity of 0.16(1) S/cm from a 2-probe pellet measurement. This is one of the highest values reported to date for a 3D material with likely isotropic charge transport. The authors proposed that the high conductivity arises from charge hopping between dhbq^3–• and dhbq^2– centers. This agrees with the lower conductivity (6.2(1) × 10^–3 S/cm) observed upon reduction of the material by an average of 0.7 e^– per ligand to [Fe^III₂(dhbq)₃]^2.7–, which effectively lessened the extent of ligand-based mixed valency and hence the concentration of available charge hopping sites. Interestingly, both the as made and the reduced materials displayed a very low-energy absorption edge suggestive of Robin–Day type-II/III mixed valency originating from the dhbq^2–/3–• couple. This assignment implies that the charges are significantly delocalized and that description of the charge transport from a band-like perspective may be appropriate.

Figure 13.

Structure of [Fe₂(dhbq)₃]^2–, showing (a) a single sublattice illustrating local coordination environments of Fe^III and dhbq^2–/3–•, and (b) two interpenetrated nets (charge-balancing Bu₄N⁺ cations not shown).¹⁵⁴

A Tb^III-based chloranilate MOF with a three-dimensional structure has been reported to have an electrical conductivity of 6.25 × 10^–4 S/cm.¹⁵⁵ This lower value compared to transition metal chloranilate MOFs is likely due to the strongly ionic bonding character between the ligand and the lanthanide.

3.2. Frameworks with Flat, Multitopic, Conjugated Linkers

Layered two-dimensional frameworks based on flat, fully conjugated ligands with trigonal geometries constitute one of the most prominent classes of conductive MOFs (see Tables 3–5). To the best of our knowledge, these materials show the highest conductivities observed for ordered microporous materials. The clear and consistent strategy underlying these high conductivities, which are usually thought to originate from the strong electron delocalization within the 2D layers, also contributes to the broad appeal of these materials. The high conductivity values and straightforward design principles drive the growing number of studies on these materials.

Table 3. Selected Properties for MOFs Based on O-Functionalized Flat, Conjugated Linkers.

materiala	description	σ (S/cm)b	σ methodc	Ea (eV)d	BET SA (m2/g)e	μ (cm2 V–1 s –1)	ref
triphenylene-based MOFs
Co9(HOTP)4		0.1	4-probe pellet				(164)
		0.032	vdP pellet		465		(162)
		3.3 × 10–3	vdP film				(162)
		2 × 10–3	2-probe pellet				(20)
Cu3(HOTP)2		1.5	4-probe sc (⊥)				(79)
		0.5	2-probe sc (∥)				(79)
	vac.	0.29	4-probe film	0.13			(170)
	vac.	0.21	4-probe sc				(149)
	Ar	0.045	vdP pellet		512		(161)
		0.027	vdP pellet		306		(162)
		0.02	2-probe pellet	0.16			(163)
		0.02	4-probe pellet				(164)
		0.02	2-probe film	0.16			(163)
		0.01	2-probe pellet				(168)
		7.6(3) × 10–3	4-probe pellet				(165)
		3 × 10–3	2-probe pellet		540		(166)
		2 × 10–3	2-probe pellet				(22)
		1 × 10–4	4-probe film	0.24			(167)
Fe3(HOTP)2	amorphous	3 × 10–3	4-probe pellet				(164)
Ni9(HOTP)4		0.010(3)	4-probe pellet				(165)
		0.01	4-probe pellet				(169)
		6.8 × 10–3	vdP pellet		430		(162)
		6 × 10–3	2-probe pellet				(20)
		1.1 × 10–3	vdP film				(162)
		1.6(2) × 10–4	2-probe film				(23)
		2.7 × 10–6	4-probe pellet				(164)
La1+x(HOTP)	N2	8.2 × 10–4	2-probe pellet	0.26	325		(92)
Nd1+x(HOTP)	N2	8.0 × 10–4	2-probe pellet	0.24	513		(92)
Ho1+x(HOTP)	N2	0.053	2-probe pellet	0.25	208		(92)
Yb1+x(HOTP)	N2	0.010	2-probe pellet	0.25	452		(92)
MOFs based on other linkers
Cu3(HOB)2	N2	7.3 × 10–8	vdP pellet	0.5	158		(171)
Cu3(HOTP)(THQ)	Ar	2.35 × 10–5	2-probe pellet	0.3	441		(172)
Cu2[Cu(OPc)]		∼1 × 10–7	2-probe pellet		358		(173)
Cu2[Ni(ONPc)]		0.0313	4-probe pellet		267		(25)
Cu2[Ni(OPc)]		0.0143	4-probe pellet		284		(25)
K3Fe2[Fe(OPc)]		∼1 × 10–5	vdP pellet	0.261	206	4.35 (h, pellet Hall) 15(2) (TRTS)	(174)
Ni2[Ni(ONPc)]		0.0178	4-probe pellet		174		(25)
Ni2[Ni(OPc)]		7.22 × 10–4	4-probe pellet		101		(25)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or between 295 and 302 K.

^c∥ denotes device contacted in-plane/parallel to 2D layers; ⊥ denotes device contacted cross-plane/perpendicular to 2D layers.

^dDerived from Arrhenius model. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^eCalculated from N₂ adsorption isotherms.

Table 5. Selected Properties for MOFs Based on N-Functionalized Flat, Conjugated Linkers.

materiala	description	σ (S/cm)b	σ method	Ea (eV)c	BET SA (m2/g)d	μ (cm2 V–1 s –1)	ref
triphenylene-based MOFs
Co3(HITP)2		8 × 10–4	4-probe pellet		340		(192)
Co2.14Ni0.86(HITP)2		5 × 10–3	4-probe pellet				(192)
Co1.27Ni1.73(HITP)2		0.024	4-probe pellet				(192)
Co0.73Ni2.27(HITP)2		0.032	4-probe pellet				(192)
Cu3(HITP)2		0.2	2-probe pellet				(21)
		0.2	2-probe pellet				(22)
Ni3(HITP)2	vac.	150	4-probe sc (∥)e				(79)
	vac.	50	vdP pellet		63017		(27)
		40	vdP film				(75)
	vac.	2	2-probe pellet				(75)
		2	2-probe pellet				(22)
		1.9	4-probe pellet		282		(192)
		0.228	2-probe film				(190)
	amorphous	2.6(3) × 10–3	2-probe film				(23)
						48.6 (h, FET)	(191)
						45.4 (h, FET)	(198)
benzene-based MOFs
Co3(HIB)2	vac.	1.57	4-probe pellet		240		(28)
Cu3(HIB)2	vac.	13	vdP pellet	0.608	114		(77)
Fe3(HIB)2		149.2	vdP pellet				(30)
Mn3(HIB)2		107.7	vdP pellet				(30)
(Mn/Fe)3(HIB)2		359	vdP pellet		2298		(30)
Ni3(HIB)2	vac.	8	vdP pellet		151		(77)
	vac.	0.7(15)	4-probe pellet				(29)
	vac.	0.11(3)	4-probe pellet		353		(29)
MOFs based on other linkers
Ni2[Ni(IPc)]	He	0.2	4-probe film	0.11	593		(194)
Ni3(HITP)2 (annulated)	ox. (I2)	0.01	4-probe pellet		47		(195)
		insulating	4-probe pellet				(195)
Ni3(TABTT)2	ox.	0.1	vdP pellet	0.041			(196)
	Ar or N2	3 × 10–6	vdP pellet				(197)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified), 298 K, or 300 K.

^cDerived from the Arrhenius model. For materials exhibiting more than one distinct activation region, E_a at 300 K is given.

^dCalculated from N₂ adsorption isotherms.

^e∥ denotes device contacted in-plane/parallel to 2D layers.

The strong delocalization is produced by covalent bonding between the metal and the linker to form an extended π-conjugated framework (Figure 14). Three key features of the ligands enable this electronic structure. First of all, the catecholoid linkers are highly susceptible to oxidation, producing organic radicals in the MOF. Second, full conjugation within the linker, which consists of one large π-system, facilitates the delocalization and stabilization of said radicals. Finally, good energy matching between the linker and the metal frontier orbitals allows the conjugated system to extend throughout the full layer. The overall geometry of the material is also important for the extended conjugation of the π-systems, as coplanar linkers form flat 2D layers.

Figure 14.

Representations of the structures of 2D honeycomb sheets in porous MOFs exhibiting extended conjugation with (a) triphenylene-based linkers and (b) benzene-based linkers, both with various functional groups (X) and framework metals (M).

Materials in this class can be divided into three broad categories, based on the linker used: semiquinoid-based materials with oxygen-based linkers, iminosemiquinoid-based materials with nitrogen-based linkers, and dithiolene-based materials with sulfur-based linkers. With the exception of several recent reports, each category consists of two families: one with larger hexa-substituted triphenylene linkers, and one with smaller hexa-substituted benzene linkers, with the former being more porous, and the latter typically being dense. Overall, increasing the bond strength between the metal and the ligand (i.e., moving from oxygen-based to nitrogen- to sulfur-based linkers) and increasing the framework density (moving from a triphenylene core to a benzene core) both appear to result in higher conductivities.

Despite these challenges for accurate, consistent structural and compositional characterization of 2D conductive MOFs, their high conductivities have attracted significant interest from applied studies in electrocatalysis,¹⁶⁻²⁰ chemiresistive sensing,²¹⁻²⁵ and energy storage technologies.²⁷⁻³⁰ An excellent overview of potential applications of these materials is provided in ref (47).

3.2.1. Semiquinoid Linker-Based Materials

3.2.1.1. Hexahydroxytriphenylene MOFs

In 2012, the Yaghi group reported the first materials of this family with Co^II, Ni^II, and Cu^II, which crystallize in two different structures.¹⁴⁹ On the basis of synchrotron PXRD and transmission electron microscopy (TEM), they found that Cu^II and 2,3,6,7,10,11-hexahydroxytriphenylene (H₆HOTP) form a layered honeycomb framework with each metal coordinated by two linkers in a square planar environment, resulting in an overall formula of Cu₃(HOTP)₂. Co^II and Ni^II produced MOFs with similar honeycomb layers, but with the metal sites in octahedral environments with two terminal aqua ligands. Additionally, the framework layers in the Co and Ni MOFs are interleaved with layers of molecular [(H₂O)₄M]₃HOTP clusters, which contribute to an overall formula M₉(HOTP)₄ (discounting solvent molecules) (Figure 15). Both the Cu and the Co/Ni structure types have a near-eclipsed arrangement of the layers, resulting in permanent microporosity, with surface areas in the range of 400–500 m²/g.

Figure 15.

Structure of Co₉(HOTP)₄, showing (a) view of 2D honeycomb layers with octahedrally coordinated Co centers bridging triphenylene-based linkers, alternating with layers of trinuclear molecular clusters, and (b) stacking arrangement of the extended and molecular layers in the material.¹⁴⁹

As implied by their distinct formulas, these two structure types also contain different ligand charge states (HOTP is assumed to be fully deprotonated in both cases). In Cu₃(HOTP)₂, all linkers are HOTP^3–, (i.e., oxidized by 3 electrons). In Co₉(HOTP)₄ and Ni₉(HOTP)₄, the average charge state is HOTP^4.5–. Hmadeh et al. proposed that the framework layers retain the same M^II₃HOTP^3–₂ configuration, while the molecular clusters have the neutral [(H₂O)₅M^II]₃HOTP^6– assignment. However, we note that HOTP and M–O bond lengths in the clusters and in the framework are nearly identical, differing by <0.01 Å. Therefore, a model with homogeneous ligand oxidation states, in which the anionic [M^II_1.5HOTP^4.5–]^1.5– framework layers are charge-balanced by the cationic {[(H₂O)₄M^II]₃HOTP^4.5–}^1.5+ layers, should also be considered.

Although the authors of the initial report focused on the structural aspects of the materials, they also measured the electrical conductivity of Cu₃(HOTP)₂ to be 0.1 S/cm in a single-crystal device contacted along the c axis—the highest value at the time for a porous MOF. Similar values have been reported for Cu₃(HOTP)₂ powders and films (from 0.02 to 0.2 S/cm).^22,161−168 Although the initial report did not include conductivity data for Co₉(HOTP)₄ and Ni₉(HOTP)₄, later studies^{20,23,162,164,165,169} provided pressed powder pellet values in the range from 3 × 10^–3 to 0.1 S/cm for Ni₉(HOTP)₄ and from 3 × 10^–6 S/cm to 3 × 10^–3 S/cm for Co₉(HOTP)₄ (see Table 3). Although an Fe-based HOTP material has also been reported, showing a conductivity of 3 × 10^–3 S/cm, it appeared to be completely amorphous by PXRD.¹⁶⁴

Recently, Song et al. synthesized thin films of Cu₃(HOTP)₂ with preferential orientation of the ab plane parallel to the substrate surface via a layer-by-layer method.¹⁷⁰ Four-probe measurements across the surface of the film (i.e., comprising predominantly in-plane contributions) showed a high conductivity of 0.29 S/cm. Variable-temperature measurements revealed an Arrhenius E_a of 0.13 eV above 240 K, with Mott VRH behavior below 200 K. The thin films were investigated as potential spin-valve materials in the same study.

In a recent report, Day et al. optimized the synthesis of Cu₃(HOTP)₂ to produce micron-sized crystals.⁷⁹ A detailed TEM and PXRD investigation showed that the layers in Cu₃(HOTP)₂ are in fact stacked in a slightly offset fashion with a continuous shift along the c direction, creating a tilted stack, as opposed to the straight stack of Co₉(HOTP)₄ (Figure 16). The authors also achieved synthetic control over the morphology of the crystallites, obtaining both needle-shaped crystals with the long axis aligned with the stacking direction, as well as shorter prism-shaped crystals with nearly isotropic dimensions. Sonication-assisted liquid-phase exfoliation of the prism-shaped crystals produced thinner hexagonal flakes. The authors used electron-beam lithography to fabricate four-point probe devices measuring conductivity both perpendicular to the MOF layers (“cross-plane”; measured on the needle crystals), and within the MOF layers (“in-plane”; measured on the exfoliated flakes). Surprisingly, the measured values of 1.5 S/cm for cross-plane devices and 0.5 S/cm for in-plane devices were within the same order of magnitude. This result challenges the view that conductivity in these materials is primarily due to intralayer transport; the most likely explanation to the high cross-plane conductivity values is interlayer charge transport mediated by close stacking and interactions between the π-systems of neighboring layers.

Figure 16.

Structure of Cu₃(HOTP)₂, showing (a) 2D honeycomb layers with square planar Cu centers bridging triphenylene-based linkers and (b) continuous slipped stacking arrangement of layers.⁷⁹

The significance of π–π stacking with respect to the charge transport of 2D layered MOFs showing intralayer extended conjugation remains an open question. The single-crystal studies by Day et al.⁷⁹ suggest significant π–π stacking contributions, as equally high conductivities were found for in-plane and cross-plane devices for Cu₃(HOTP)₂. More focus was put toward π–π stacking in this class of MOFs in a study by Skorupskii et al. investigating a series of Ln_1+x(HOTP) (Ln = La^III, Nd^III, Ho^III, Yb^III) materials.⁹² In contrast with the structure of Cu₃(HOTP)₂, the lanthanides are not located in the same plane as the linkers, but rather in-between the linker layers, connecting them into a 3D framework (Figure 17). In this structure, the HOTP linkers form continuous stacks with extremely close π–π interactions of 3.0–3.1 Å. In addition, the precise π–π stacking distances were found to correlate directly with the sizes of the lanthanide cations. The authors found that despite the lack of conjugation in the layers, these materials displayed high conductivities of up to 0.05 S/cm (for Ho_1+x(HOTP)). Importantly, the conductivity decreased with longer stacking distances separating the linkers: the conductivity of La_1+x(HOTP) was 1 × 10^–3 S/cm, which was attributed to the larger La^III pushing the layers farther apart. DFT calculations of the band structure of Ln_1+x(HOTP) showed high band spread and metallicity in the cross-plane direction, with negligible contribution of Ln^III to the frontier bands—indicating that the transport occurs primarily through π–π interactions of organic linkers and not Ln–O chains. Taken together, these findings demonstrated the importance of the cross-plane charge transport in these materials.

Figure 17.

Structure of Nd_1+x(HOTP),⁹² showing (a) Nd coordination environment and close π–π stacking distances among triphenylene linkers and (b) 1D channels along the ligand stacking direction.

3.2.1.2. Other Semiquinoid Linkers

Cu₃(HOB)₂, a material based on the smaller hexahydroxybenzene (H₆HOB) linker and Cu^II, was also investigated for its charge transport properties.¹⁷¹ The structure of the material resembles Cu₃(HOTP)₂ but with smaller pores due to the smaller ligand core. Despite the similarities, the material showed a significantly lower conductivity of 7.3 × 10^–8 S/cm in a two-probe pellet configuration at room temperature. The temperature dependence of the conductivity was fitted to give an Arrhenius E_a of 0.45 eV, similar to many other materials in this class. A curious feature of Cu₃(HOB)₂ is the extremely close stacking of its layers, which are separated by only 2.96 Å, which may lead to a more significant contribution of cross-plane charge transport to the electrical conductivity.

A hybrid of Cu₃(HOTP)₂ and Cu₃(HOB)₂ was recently reported by Yao et al.¹⁷² In Cu₃(HOTP)(HOB), the two linkers alternate within the layer, forming an ordered layered trigonal network. The layers stack in an eclipsed fashion, forming continuous 1D channels, similar to Cu₃(HOTP)₂. This structure resulted in high intrinsic porosity, with a BET surface area of 441.2 m²/g. Two-probe pressed pellet measurements revealed a conductivity of 2.53 × 10^–5 S/cm, considerably lower than that of Cu₃(HOTP)₂ (up to 0.2 S/cm), but higher than Cu₃(HOB)₂ (7.3 × 10^–8 S/cm). The temperature dependence of the conductivity similarly showed an E_a of 0.30 eV—in-between those of Cu₃(HOTP)₂ and Cu₃(HOB)₂. This work served as another demonstration of the tunability of MOFs.

A number of semiquinoid linkers with metallophthalocyanine (M′(OPc))^25,173 and metallonaphthalocyanine (M′(ONPc))²⁵ cores were also used to synthesize conductive MOFs. The resulting frameworks have the formulas M₂[M′(OPc)] and M₂[M′(OPc)], respectively, where M is the framework metal and M′ is the central (Pc) metal. From simulations based on PXRD patterns, Cu₂[Cu(OPc)] consists of 2D square grids of Cu(OPc) linkers connected by Cu^II atoms in a square-planar environment, similar to Cu₃(HOTP)₂ (Figure 18). The authors proposed an eclipsed stacking model for the materials with square channels of ∼15 Å in diameter. Permanent porosity was confirmed by N₂ adsorption, which revealed a BET surface area of 358 m²/g. The electrical conductivity of pressed pellets ranged between 10^–8 S/cm and 10^–6 S/cm, significantly lower than for HOTP-based materials. A later study reported Ni^II and Cu^II-based Ni(OPc) and Ni(ONPc) MOFs, which were found to be isostructural to Cu₂[Cu(OPc)].²⁵ These materials showed considerably higher conductivities, ranging from 10^–4 to 10^–2 S/cm, with the Cu^II-based materials showing higher values compared to Ni^II (the authors did not propose an explanation for this difference).

Figure 18.

Representation of the structure of square 2D sheets in MOFs based on phthalocyanine (Pc) linkers with various functional groups (X) and framework and central Pc metals (M and M′, respectively).

Feng and co-workers also reported an all-Fe phthalocyanine-based framework with the formula K₃Fe₂[Fe(OPc)].¹⁷⁴ X-ray photoelectron spectroscopy (XPS) indicated a mixture of Fe^II and Fe^III in the samples (the authors were not able to distinguish between the framework and central Pc Fe sites). The relatively low BET surface area, 206 m²/g, was attributed to the K⁺ counterions in the pores. The conductivity of a van der Pauw pellet was ∼1 × 10^–5 S/cm at 300 K, with a high-temperature E_a of 0.26 eV. Hall measurements revealed p-type behavior with a hole concentration of ∼2.4 × 10^–14 cm^–3 and mobility of ∼0.1 cm² V^–1 s^–1. Noncontact TRTS measurements estimated a higher mobility of 15(2) cm² V^–1 s^–1 for photogenerated carriers. Ferromagnetic ordering up to 350 K in this material was also observed through magnetometry.

3.2.2. Thiolate Linker-Based Materials

3.2.2.1. Triphenylenehexathiolate MOFs

Initial work on MOFs with thiol-functionalized triphenylenes¹⁷⁵ and benzenes⁶⁵ was largely inspired by the nickel bis(dithiolene) motif in molecular complexes.¹⁷⁶ This fragment exhibits strong charge delocalization and planar geometry, which are enabled by the redox noninnocence of the ligand. Nickel bis(dithiolene) complexes are also redox-active, exhibiting several reversibly accessible states. These features led researchers to believe that extending the motif into a coordination polymer would allow for the formation of an extended π-conjugated sheet akin to graphene.

The framework Pt₃(THT)₂ (THT = 2,3,6,7,10,11-triphenylenehexathiolate), reported in 2014 by Xu and Cui,¹⁷⁵ exhibited both permanent porosity (300–400 m²/g) and electrical conductivity (1.4 × 10^–6 S/cm). The as-made material was anionic but could be oxidized into an almost neutral framework with I₂. No significant impact of oxidation on the conductivity was observed. As expected from the very strong and covalent bonding between Pt and thiol ligands, the material was not highly crystalline, with only broad peaks present in the PXRD pattern. Nevertheless, the unit cell dimensions agreed with a structure containing the ligands connected by square-planar Pt^II ions into a hexagonal net.

Materials with similar structures were also isolated with Co^II and Fe^III.^78,177 Co₃(THT)₂ shows somewhat improved crystallinity compared to Pt₃(THT)₂ and was first investigated as an electrocatalyst for H₂ evolution.¹⁶ The material was porous (370 m²/g) and exhibited a conductivity of 1.4 × 10^–3 S/cm at 300 K in a van der Pauw geometry, considerably higher than the Pt analog. The temperature dependence of the conductivity was complex and warrants further investigation: the authors saw an increase in resistivity with decreasing temperature (as would be expected for a semiconductor) for temperatures close to room temperature, and the opposite (as would be seen for a metal) in the low-temperature regime (below ∼180 K). We caution that similar behavior can be interpreted as phase artifacts in alternating current measurements of resistive samples. Interestingly, from the theoretical computations, the authors concluded that despite the highly covalent bonding in the sheet, the main mechanism for charge transport is expected to be along the c (stacking) direction. Also of note is the mixed valency of the metal ions: magnetometry results suggested that the correct charge assignment for the material is [Co^III₂Co^II(THT)₂]^3–.

Fe₃(THT)₂ displayed the highest conductivity to date among THT materials, reaching 3.4 × 10^–2 S/cm at 300 K in a four-probe device.⁷⁸ This material was permanently porous, with a BET surface area of 526 m²/g. Although the PXRD patterns were not of sufficiently high quality to resolve the exact stacking sequence, both PXRD and high-resolution TEM measurements proved the overall layered honeycomb structure, similar to Pt₃(THT)₂ and Co₃(THT)₂. The study reported Hall effect and THz spectroscopy measurements to extract a charge mobility value of ∼200 cm² V^–1 s^–1, depending on the measurement. We note that discussions of the material as both heavily doped semiconductor (in the main text) and as an intrinsic semiconductor (in the Supplementary Information) are present in ref (78). The overall semiconducting behavior, however, was conclusively proven by variable temperature conductivity measurements. Optical absorption data suggested a direct band gap of 0.245 eV, matching well with the DFT calculated value of 0.350 eV. Interestingly, although the authors started with Fe^II salts and allowed no exposure to oxidants during the reaction, the metal charge state in the final material is Fe^III. As metal-based mixed valency provides an excellent way to introduce free carriers, a more rigorously air-free synthesis could allow access to a Fe^II/III mixed material. A later work¹⁷⁸ proposed different Fe oxidation states and reported unusual maxima in variable temperature conductivity behavior (as with the report on the Co analog of this material,¹⁷⁷ we caution that similar behavior can be interpreted as phase artifacts). Clearly, this is a material that warrants further investigation and that could benefit from a systematic variation of synthetic conditions, as well as additional transport measurements.

The Feng group also reported a related material with Fe^III, Fe₃(PTC) (PTC = perthiolated coronene).¹⁷⁹ This framework was essentially nonporous: the type II N₂ adsorption isotherm revealed a (primarily external) surface area of 210 m²/g. The simulated structures contained acetylacetonate-like coordination modes of the thiols to the metal, unlike the typical catechol-like mode observed in Pt₃(THT)₂. Although the authors discussed several potential layer stacking sequences, they did not elaborate on the assignment of this particular Fe–S coordination mode. Similar to Fe₃(THT)₂, despite using an Fe^II salt in oxidant-free conditions, the metal charge state in the material was assigned unambiguously to Fe^III. The material displayed very high conductivities of up to 10 S/cm for pressed pellets in van der Pauw geometries. The conductivity increased with decreasing temperature with an Arrhenius E_a of 0.2 eV, similar to most MOFs discussed in this section. Importantly, this material was also ferromagnetic below ∼20 K and is the only material in this class with reported magnetic ordering.

THT materials with Ni^II and Cu^II have also been reported,¹⁸⁰ but the structural analysis was based on PXRD patterns with essentially no discrete peaks, and thus no definite conclusions on the structures can be made.

3.2.2.2. Benzenehexathiolate MOFs

In a foundational work in 2013, Kambe et al. incorporated the nickel bis(dithiolene) motif into a π-conjugated 2D material, the Ni₃(BHT)₂ (BHT = benzenehexathiolate) framework.⁶⁵ The as-synthesized material, which was characterized as a thin black film, showed a two-probe pressed pellet conductivity value of 0.15 S/cm and a four-probe conductivity of 2.8 S/cm (reported in a later work by the same group).⁹⁴ The higher four-probe value is likely the result of eliminating contact resistance.

These authors also probed the charge states of nickel bis(dithiolene) fragments in the MOF, and the dependence of conductivity on the redox assignments. Infrared (IR) spectroscopy and XPS studies showed that the as-synthesized material contained mixed-valence 0 and –1 charge states, with an average charge of −3/4. Both the pure 0 and −1 states were accessible through electrochemical means and chemical oxidation/reduction (in contrast with molecular species, only the 0/–1 couple appeared to be reversible). Compared to the as-synthesized mixed-valent MOF (2.8 S/cm), the fully reduced material in the −1 state showed a lower conductivity of 6.7 × 10^–3 S/cm. The oxidized material in the 0 state showed the highest conductivity of 160 S/cm.

DFT calculations and photoelectron spectroscopy (PES) suggested that both the as-made and the reduced materials were metallic in nature. However, the temperature dependence of the conductivity showed thermally activated behavior characteristic for a narrow-gap semiconductor. The authors proposed that the discrepancy could be a result of structural disorder in the real materials.

A palladium coordination polymer of BHT was later reported by the same group¹⁸¹ and was proposed to have a similar structure to Ni₃(BHT)₂ based on TEM data. However, PXRD analysis revealed no discrete peaks, and the electron diffraction data were of poor quality, prohibiting detailed structural characterization. Initial synthetic attempts led to coprecipitation of Pd⁰ nanoparticles, along with the proposed MOF. Addition of an oxidizing buffer in the form of K₃[Fe(CN)₆] allowed the authors to generate pure Pd₃(BHT)₂, as evidenced by TEM. The material exhibited a similar charge state to Pd₃(BHT)₂, with the palladium bis(dithiolene) fragment present in mixed-valence 0/–1 states. The average charge state was found to be −0.19, which was higher than seen in as-made Ni₃(BHT)₂, likely because of the oxidizing buffer added to prevent formation of Pd⁰ nanoparticles. The electrical conductivity of the pure Pd₃(BHT)₂ material was reported to be of similar magnitude to the Pd⁰-contaminated material (2.8 × 10^–2 S/cm), though the precise value was not specified. This conductivity is noticeably lower than that of Ni₃(BHT)₂, although the sample quality of Pd₃(BHT)₂ was significantly worse as well, prohibiting any definite conclusions.

The dense coordination polymer Cu₃(BHT) reported by Huang et al. in 2015 holds the record for the highest conductivity in MOFs with low or minimal porosity (Table 4).⁷⁶ Although the material is nonporous, its structure and composition are related to other materials in this family, meriting inclusion in this Review. In contrast to Ni₃(BHT)₂, in which the BHT linker acts as a tritopic ligand, in Cu₃(BHT) the ligand bonds to six Cu^II ions, thus increasing the framework density (Figure 19). The conductivities of Cu₃(BHT) are the highest values reported for coordination polymers. Initial four-probe measurements on thin films revealed a value of 1580 S/cm at room temperature. In later studies by the same group on more crystalline samples,¹⁸² the conductivities reached 2500 S/cm for a similar configuration. Interestingly, while the initial work reported a 3D Mott VRH dependence of electrical conductivity, which is characteristic for semiconductors, the later study showed a metallic dependence. As the authors noted, this is likely due to the drastically improved crystallinity of the material in the later study. Field-effect transistors based on Cu₃(BHT) films⁷⁶ displayed very high (∼100 cm² V^–1 s^–1) electron and hole mobilities, along with low (∼10) on/off ratios, which the authors likened to the behavior of gapless graphene. The very low on/off ratios are in good agreement with the metallic temperature dependence shown in the later study. Importantly, Cu₃(BHT) was also reported to transition into a superconducting state (exhibiting zero electrical resistance) below 0.25 K, marking the first such observation for a coordination polymer or MOF.¹⁸² The components of this structure responsible for the superconductivity—or even the metallic transport—in this material remain to be definitively identified. More efficient stacking, higher framework density, or stronger Cu–S bonds all potentially play a role.

Table 4. Selected Properties for MOFs Based on S-Functionalized Flat, Conjugated Linkers.

materiala	description	σ (S/cm)b	σ method	Ea (eV)c	BET SA (m2/g)d	μ (cm2 V–1 s –1)	ref
triphenylene-based MOFs
Co3(THT)2	He	1.39(14) × 10–3	4-probe pellet		370		(177)
Fe3(THT)2(NH4)3	vac.	0.034	4-probe film		526	125(9) (TRTS)	(78)
						211(7) (TRTS)
						229(33) (film Hall)
Pt3(THT)2		3.86 × 10–4	2-probe pellet				(175)
	act.	2.47 × 10–4	2-probe pellet		329		(175)
	ox. (I2)	1.09 × 10–4	2-probe pellet		391		(175)
benzene-based MOFs
Ag3(BHT)2	He	363	4-probe film		dense		(186)
Ag5(BHT)	He	250	4-probe film	0.0163	dense		(185)
	He	50	4-probe pellet		dense		(185)
	red. (LiBHEt3)	0.073	4-probe pellet		dense		(185)
Au3(BHT)2		1.12 × 10–4	4-probe film				(186)
Cu3(BHT)		2500	4-probe film		dense		(187)
	He	1580	4-probe film	0.002	dense	116 (e), 99 (h) (FET)	(76)
		280	4-probe pellet		dense		(188)
		48	4-probe pellet		dense		(188)
Ni3(BHT)2	ox., vac.	160	4-probe film	0.010			(94)
	vac.	2.80	4-probe film	0.026			(94)
		0.15	2-probe pellet				(65)
	red.	6.7 × 10–3	2-probe pellet				(65)
Pb3(BHT)		2 × 10–6	2-probe pellet	0.37	dense		(184)
Pb2.96Tl0.04(BHT)	doped (Tl+)	1 × 10–4	2-probe pellet		dense		(184)
Pd3(BHT)2		2.8 × 10–2	4-probe film				(181)
MOFs based on other linkers
Cu3(BHSe)		110	4-probe pellet		dense		(183)
Fe3(PTC)	vac.	10	vdP pellet		210		(179)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or between 295 and 300 K.

^cDerived from Arrhenius model. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^dCalculated from N₂ adsorption isotherms.

Figure 19.

Representation of the structure of a 2D layer of the coordination polymer Cu₃(BHT), showing dense coordination of square planar Cu centers by benzenehexathiolate linkers.

The Zhu group also reported the selenolate analog of Cu₃(BHT), denoted as Cu₃(BHSe).¹⁸³ The conductivity of a pressed pellet of this dense coordination polymer was 110 S/cm, similar to that of Cu₃(BHT). Although thermally activated conductivity was observed, the authors proposed that Cu₃(BHSe) may also be metallic due to weak temperature dependence and strong absorption throughout the IR region, with semiconductor-like behavior induced by grain boundaries.

Another dense phase structurally related to Cu₃(BHT) was reported in 2008 by Turner et al.¹⁸⁴ This framework, Pb₃(BHT), has the same overall placement of linkers in layers but contains larger Pb^II atoms sitting in between the layers and binding them into a 3D solid. The material showed only low conductivities of 2 × 10^–6 S/cm for a two-probe pressed pellet. The conductivity nevertheless increased by 2 orders of magnitude to 0.1 × 10^–3 S/cm after doping with Tl^I.

A well-characterized dense Ag^I BHT polymer was also reported,¹⁸⁵ with a structure unrelated to Cu₃(BHT) or Ni₃(BHT)₂. The material showed high conductivity values of up to 250 S/cm. Its structure contains many potential pathways for conductivity, including infinite Ag–Ag and Ag–S–Ag chains, and the origin of charge transport is likely different from that in Cu₃(BHT) and Ni₃(BHT)₂. Another work reported Ag^I and Au^I coordination polymers based on BHT, which were inferred to be dense phases isostructural to Cu₃(BHT).¹⁸⁶ However, the reported PXRD patterns bear little resemblance to those of the Cu analog, and no attempts at fitting were shown. The materials showed high conductivities of up to 363 S/cm for Ag₃(BHT), and up to 1.12 × 10^–4 S/cm for Au₃(BHT).

3.2.3. Iminosemiquinoid Linker-Based Materials

3.2.3.1. Hexaiminotriphenylene MOFs

The highest conductivity in a porous MOF to date belongs to Ni₃(HITP)₂ (HITP = 2,3,6,7,10,11-hexaiminotriphenylene), first reported by Sheberla et al.⁷⁵ Just like Ni₃(BHT)₂ is inspired by metal dithiolene complexes, the design of Ni₃(HITP)₂ is based on the Ni(isq)₂ complex, which has a fully conjugated biradical ground state.¹⁸⁹ As was initially proposed based on DFT calculations and later confirmed in a detailed TEM study,⁷⁹ Ni₃(HITP)₂ forms a structure similar to Cu₃(HOTP)₂, where the honeycomb layers stack in a slipped but near-eclipsed fashion, creating micropores of ∼1.6 nm in diameter (Figure 20). Unlike Cu₃(HOTP)₂, the offset direction in Ni₃(HITP)₂ alternates every layer (ABAB), creating a straight rather than a tilted stack. The initial paper reported four-probe film and pressed pellet conductivities of 40 and 10 S/cm, respectively, which were the highest values shown by a porous material at the time. The temperature dependence of the conductivity was thermally activated and linear over an unusually large temperature range. Although consistent with semiconductor-type behavior, this behavior did not fit to a specific transport model. The material showed intrinsic microporosity with a relatively high surface area of 630 m²/g.¹⁷ A number of later studies reported conductivities ranging from 2.6(3) × 10^–3 to 150 S/cm for Ni₃(HITP)₂.^{22,23,27,79,190}

Figure 20.

Structure of Ni₃(HITP)₂, showing (a) 2D honeycomb layers with square planar Ni centers bridging triphenylene-based linkers, and (b) ABAB stacking arrangement of layers.^75,79

High quality thin films of this landmark material were later reported by Wu et al., who fabricated field-effect transistors¹⁹¹ from Ni₃(HITP)₂. These devices revealed p-type semiconducting behavior with a high hole mobility of ∼40 cm² V^–1 s^–1. This mobility is higher than for most organic semiconductors and is likely responsible for the high electrical conductivity of the material. The depletion-mode behavior of the FETs indicated that the as-made material possessed a sufficiently high carrier concentration. The FETs exhibited high on/off ratios of up to 1000.

The excellent bulk transport properties align well with what chemical intuition would predict based on the structure of Ni₃(HITP)₂. Strong in-plane bonding between the iminosemiquinone HITP^3– linker and Ni^II and close (3.35 Å) near-eclipsed stacking of the π-conjugated layers both contribute to charge delocalization and high mobility. Further oxidation of the iminosemiquinone linkers leads to removal of electrons—formation of excess holes—in the material, producing a p-type semiconductor. These results, taken together with the temperature dependence, are consistent with Ni₃(HITP)₂ being a semiconductor.

Surprisingly, in a later study, Day et al. fabricated single-crystal four-probe devices of Ni₃(HITP)₂, which revealed higher conductivities (up to 100 S/cm) and, more importantly, a nonzero conductivity at temperatures approaching 0 K.⁷⁹ Day et al. proposed that this behavior can be explained by metallic charge transport in the material.⁷⁹ This apparent disagreement between the FET study and the single-crystal study can perhaps be resolved by a computational investigation by Foster et al.,⁶³ which showed that disorder and defects in Ni₃(HITP)₂ can lead to the opening of a band gap in the otherwise metallic material.

A Cu^II-based HITP material has also been reported, with a structure apparently similar to Ni₃(HITP)₂. Cu₃(HITP)₂ showed conductivities as high as 0.2 S/cm for two-probe pressed pellet measurements.²¹ Poor air stability of the material precluded further investigations.

Recently, Lian et al. reported the novel Co₃(HITP)₂ MOF, as well as mixed-metal Co_xNi_3–x(HITP)₂ MOFs.¹⁹² However, the crystallinity of the Co₃(HITP)₂ samples was very poor and may be at least partially responsible for the relatively low bulk conductivity of 8 × 10^–4 S/cm, several orders of magnitude lower than that of pure Ni₃(HITP)₂ synthesized via similar methods (0.19 S/cm). The mixed-metal Co/Ni MOFs showed increasing conductivities with increasing Ni content. Because of the lack of structural data, it remains to be determined whether the lower conductivity of Co₃(HITP)₂ compared to Ni₃(HITP)₂ is a result of different electron counts, structural distortions, layer stacking patterns, or other factors.

3.2.3.2. Hexaiminobenzene MOFs

A number of materials based on hexaiminobenzene (HIB), the nitrogen-containing analog of benzenehexathiol and hexahydroxybenzene, have also been made. The first report of a coordination polymer based on this linker was in 2017 by Lahiri et al.¹⁹³ The study showed synthesis of thin films of HIB materials based on Cu^II, Ni^II, and Co^II. Although little experimental evidence was provided in support of structural claims, the materials showed hexagonal symmetry based on electron diffraction patterns. No conductivity values were reported, although FET devices were fabricated, demonstrating semiconducting behavior.

Two later reports discussed the Cu^II and Ni^II-based frameworks in more detail, showing that their structures were both similar to that of Ni₃(BHT)₂.^29,77 In Ni₃(HIB)₂ and Cu₃(HIB)₂, however, the hexagonal honeycomb layers stacked in a slipped-parallel fashion, as opposed to the eclipsed arrangement in Ni₃(BHT)₂. The reported conductivities varied between the different reports, ranging from 0.7 S/cm to 10 S/cm for Ni₃(HIB)₂ and from 0.11 S/cm to 0.7 S/cm for Cu₃(HIB)₂. Ultraviolet photoemission spectroscopy for both materials showed a nonzero charge density at the Fermi level—similar to Ni₃(BHT)₂—indicating metallicity. However, the temperature dependence of the electrical conductivity of both Ni₃(HIB)₂ and Cu₃(HIB)₂ again showed a semiconductor-type dependence and was attributed to intergrain contributions dominating charge transport that is otherwise intrinsically metallic (i.e., metallic transport within a single-crystal particle but temperature-activated transport between particles). Ni₃(HIB)₂ and Cu₃(HIB)₂ showed BET surface areas of 100–150 m²/g with type II N₂ adsorption isotherms, indicating mostly external surface adsorption—unsurprising given the extremely small particle size (∼10 nm) and small pore diameter (<1 nm).

A Co^II-based material with a structure similar to that of Ni₃(HIB)₂ was reported by Park et al., who proposed an eclipsed arrangement of the layers in the Co analog (unlike the Cu and Ni materials).²⁸ This stacking mode led to permanent microporosity with a BET surface area of 240 m²/g. The electrical conductivity of the material, as determined from two-probe pressed pellet measurements, ranged from ∼0.1 to 1.57 S/cm, similar to the Cu^II and Ni^II materials.

Nanoparticulate Fe₃(HIB)₂ and Mn₃(HIB)₂ showed some of the highest conductivities observed in MOFs,³⁰ reaching 100–360 S/cm at 300 K for pressed pellets. The authors attributed the transport properties to high crystallinity of their materials: the PXRD patterns appear to be better resolved than for other M₃(HIB)₂ materials. PXRD and TEM suggested that the materials have an eclipsed arrangement of the 2D layers, which may also have contributed to the higher conductivities. Interestingly, the materials were obtained as multishelled hollow sphere hierarchical structures, which led to very high surface areas of over 2300 m²/g.

3.2.3.3. Other Iminosemiquinoid Linkers

Jia et al. reported an octaiminophthalocyanine (IPc)-based Ni^II MOF, similar in structure to M₂[M′(OPc)] materials mentioned above.¹⁹⁴ Consistent with the general trend of imino-functionalized linkers engendering higher conductivities than their oxy-functionalized counterparts, Ni₂[Ni(IPc)] showed a significantly higher conductivity as compared to Ni₂[Ni(OPc)], with values as high as 0.2 S/cm reported for four-probe pellet measurements.

In a recent report, Jiang et al. studied a material based on Ni₃(HITP)₂ in which the [NiN₄] sites were capped with propylene fragments, forming macrocyclic tetraaza[14]annulene linkages.¹⁹⁵ This framework exhibited the same honeycomb structure as Ni₃(HITP)₂ and was calculated to favor a similar slipped-parallel stacking. The as-made material, synthesized in air-free conditions, was fully insulating, but oxidation with I₂ led to a drastic increase in conductivity to 0.01 S/cm. While technically the material could be considered a covalent organic framework beyond the scope of this Review, this work showcases the structurally tunable nature of conductive MOFs. Further work is necessary to determine the origin of the substantial differences in charge transport behavior of this material and Ni₃(HITP)₂.

The group of Nishihara, which originally reported Ni₃(BHT)₂, later reported a Ni^II coordination polymer based on 1,3,5-triaminobenzene-2,4,6-trithiol, which can be thought of as a hybrid of benzenehexathiol and hexaaminobenzene. Both an oxidized¹⁹⁶ and a reduced form of this material have been reported.¹⁹⁷ The reduced form showed sharp PXRD peaks ascribed to the staggered arrangement of the hexagonal conjugated layers, similar to Ni₃(BHT)₂. The oxidized form presumably has a similar structure. The reduced material exhibited a low conductivity of 3 × 10^–6 S/cm, which increased to 0.3 S/cm upon oxidation, as indicated by pressed pellet measurements. This change is unsurprising given that the reduced form is unlikely to possess a significant number of free carriers, which typically originate from the oxidation of the amino moieties into their radical iminosemiquinonate form. The relative conductivities are also consistent with a DFT study of the material, which indicated the oxidized form to be metallic, and the reduced form to be a semiconductor with a band gap >1.0 eV. The two forms of the material were interconvertible by solution-phase oxidation with ferrocenium tetrafluouroborate or reduction with decamethylcobaltocene.

4. Through-Space Pathways

Unlike the previous two strategies, the through-space approach focuses on intermolecular interactions of organic linkers instead of covalent metal–ligand bonds. Largely inspired by organic semiconductors and charge-transfer salts, this approach utilizes the high propensity of planar conjugated organic ligands to form structures containing π–π stacking in the solid state. The intrinsic tunability of MOFs can allow for fine control over the stacking sequence and distance to a degree that is difficult to achieve in classical polymeric and molecular materials. As is the case for the other approaches, mixed valency plays a crucial role: partial oxidation of organic ligands^37,85,200 provides charge carriers and potentially even biases the system toward the formation of π–π interactions during synthesis.²⁰¹

Frameworks based on tetrathiafulvalene (TTF), an archetypal organic semiconductor building block, constitute a large portion of MOFs designed with this approach in mind. Some of the most detailed studies correlating π–π stacking configuration and conductivity were performed on materials made from TTF-based ligands. In particular, these studies demonstrate how varying parameters such as metal size⁸⁴ and solvent ratios⁸⁵ can result in structural changes that allow control over transport properties. That said, studies of these materials are not limited to TTF-based MOFs, and π–π stacking between a diverse set of other organic cores, including anthracene,³⁸ naphthalene,⁸⁹ and napthalenediimide,^90,91 has so far enabled efficient charge transport (Table 6). Clearly, given the vast arsenal of organic molecules that have been employed in organic semiconductors with π–π stacking in mind, we expect that this approach will become much more popular in the future.

Table 6. Selected Properties of MOFs with Through-Space Pathways for Charge Transport.

materiala	description	σ (S/cm)b	σ methodc	Ea (eV)d	BET SA (m2/g)e	μ (cm2 V–1 s –1)	ref
tetrathiafulvalene tetrabenzoate-based MOFs
Cd2(TTFTB)		2.9(5) × 10–4	2-probe sc		559		(84)
		2.5(5) × 10–4	2-probe sc	0.293			(56)
		1.91 × 10–4	4-probe sc				(56)
		4.39 × 10–6	4-probe pellet				(56)
		2.7 × 10–6	vdP pellet				(56)
		2.1(1) × 10–6	2-probe pellet				(56)
		2.4(7) × 10–7	2-probe sc (⊥)f				(56)
Co2(TTFTB)		1.5(3) × 10–5	2-probe sc		665		(84)
Mn2(TTFTB)		9(1) × 10–5	2-probe sc		594		(84)
Zn2(TTFTB)		5.0 × 10–4	TRTS				(208)
		4.0(6) × 10–6	2-probe sc		662	0.2 (FP-TRMC)	(37, 84)
	ox. (I2)	2.5(2) × 10–10	EIS				(200)
La4(TTFTB)4		2.5(7) × 10–6	2-probe pellet	0.28	596		(85)
La(TTFTB)		9.0(4) × 10–7	2-probe pellet	0.20	454		(85)
La4(TTFTB)3		1.0(5) × 10–9	2-probe pellet	0.44	362		(85)
Gd3(TTFTB)2(OAc)(OH)		2.0 × 10–7	4-probe pellet				(86)
Tb3(TTFTB)2(OAc)(OH)		1.5 × 10–6	4-probe pellet				(86)
Dy3(TTFTB)2(OAc)(OH)		3.9 × 10–7	4-probe pellet				(86)
Ho3(TTFTB)2(OAc)(OH)		6.7 × 10–6	4-probe pellet				(86)
Er3(TTFTB)2(OAc)(OH)		7.4 × 10–6	4-probe pellet				(86)
Er4(TTFTB)3(I3)2	ox. (I2)	2 × 10–8	2-probe pellet				(87)
Er4(TTFTB)3		1 × 10–9	2-probe pellet				(87)
Tb4(TTFTB)3(I3)2	ox. (I2)	4 × 10–8	2-probe pellet				(87)
Tb4(TTFTB)3		1 × 10–8	2-probe pellet				(87)
Dy4(TTFTB)3(I3)2	ox. (I2)	1 × 10–8	2-probe pellet				(87)
Dy4(TTFTB)3		7 × 10–9	2-probe pellet				(87)
Ho4(TTFTB)3(I3)2	ox. (I2)	8 × 10–9	2-probe pellet				(87)
Ho4(TTFTB)3		1 × 10–9	2-probe pellet				(87)
Dy(TTFTB)		3 × 10–7	4-probe pellet				(86)
Yb6(TTFTB)5		9(7) × 10–7	2-probe pellet				(88)
Lu6(TTFTB)5		3(2) × 10–7	2-probe pellet				(88)
tetrathiafulvalene tetrapyridyl-based MOFs
Fe(dca)[TTF(py)4](ClO4)		1.2 × 10–7	2-probe pellet				(209)
	ox. (I2)	7.6 × 10–5	2-probe pellet				(209)
Fe(dca)2[TTF(py)4]0.5		4.1 × 10–9	2-probe pellet				(209)
	ox. (I2)	1.3 × 10–6	2-probe pellet				(209)
Mn(dca)2[TTF(py)4]0.5		6.3 × 10–9	2-probe pellet				(210)
Mn(N3)[TTF(py)4](ClO4)		1.5 × 10–9	2-probe pellet				(210)
MnCl2[TTF(py)4]		2 × 10–10	2-probe pellet				(210)
MOFs based on other linkers
ZnNa2(AnBEB)2		1.3(5) × 10–3	2-probe sc		collapse		(38)
Cd(DPNDI)		0.033	2-probe sc				(90)
		7.6 × 10–6	2-probe pellet				(90)
	act.	0.037	2-probe pellet				(90)
Cu(DPNDI)2		1.2 × 10–5	2-probe sc				(91)
Cd2.39(TPDAP)3		1 × 10–6	2-probe sc				(212)
Cd2(TPDAP)2		insulating	2-probe sc				(212)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or between 293 and 300 K.

^cSingle-crystal devices are contacted parallel to the π–π stacking direction unless otherwise indicated.

^dDerived from Arrhenius model. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^eCalculated from N₂ adsorption isotherms.

^fContacted perpendicular to π–π stacking direction.

In most of the existing examples, π–π stacking between ligands results in the formation of 1D conduction pathways. However, more unusual and complex arrangements, such as zigzag chains and orthogonal orientations, have also been reported.^38,88 Many 2D extended conjugation MOFs also exhibit significant π–π stacking among the covalently bonded layers, and as previously discussed, this stacking may in fact contribute as much to the conductivity as the in-plane conjugation. Therefore, charge transfer between organic components is a pervasive motif in conductive MOFs regardless of their categorization.

4.1. Tetrathiafulvalene-Based Frameworks

TTF is an organosulfur compound that is an excellent electron donor.²⁰² The stability of its radical cation form has made it a popular component in conducting charge-transfer salts, in which π–π stacking and close intermolecular contacts in oxidized TTF stacks facilitate charge transport.²⁰³ Functionalized TTF derivatives are also used in supramolecular chemistry because of their redox activity and participation in noncovalent interactions.^204,205 As a result of their electroactive nature and π–π stacking propensity, ligands based on TTF form conductive MOFs with a diverse range of structures. We note that conductive, nonporous coordination polymers containing TTF-based linkers, such as TTF tetracarboxylate,²⁰⁶ have been reported and reviewed.²⁰⁷

The isostructural series of M^II₂(TTFTB) frameworks (M = Mn, Co, Zn, and Cd; TTFTB = tetrathiafulvalene tetrabenzoate) reported by Narayan et al.³⁷ and Park et al.⁸⁴ contain infinite 1D helical stacks of TTF (Figure 21). They are permanently porous, with BET surface areas between 559 and 665 m²/g. The single-crystal structures of these MOFs showed that the TTF moieties within the stacks have a single close S···S contact distance of <3.8 Å. As the size of the M^II cation increases, the stack effectively becomes pinched, shortening the S···S distance from 3.773(3) Å for Co^II to 3.654(2) Å for Cd^II.

Figure 21.

Structure of Cd₂(TTFTB) showing (a) infinite 1D helical stacking of tetrathiafulvalene cores with a continuous close S···S contact of 3.654(2) Å and (b) 1D channels parallel to the stacking direction.⁸⁴

The single-crystal conductivities measured along the stacking direction for the M₂(TTFTB) frameworks showed a striking correlation with the S···S distances, with average values of 2.9(5) × 10^–4 S/cm for Cd₂(TTFTB), 9(1) × 10^–5 S/cm for Mn₂(TTFTB), 1.5(3) × 10^–5 S/cm for Co₂(TTFTB), and 4.0(6) × 10^–6 S/cm for Zn₂(TTFTB). DFT band structure calculations indicated that the valence band comprises S and C orbitals from the ligand TTF core, and has a large dispersion of 400 meV. Increasing the size of the metal cation and contracting the stacking distance increases the overlap of S p_z orbitals and, thus, the charge mobility along the TTF stacks. Detailed investigations of the electrochemical and spectroscopic properties of these MOFs further confirmed the central role of the TTF core, showing that ligand-based IVCT mediates the charge transport.²⁰⁰ The large band dispersion leads to high charge mobilities in these frameworks: FP-TRMC and TRTS studies of Zn₂(TTFTB) revealed a mobility value³⁷ of 0.2 cm² V^–1 s^–1, and photoconductivity (with 400 nm pump-pulses) of 5 × 10^–4 S/cm.²⁰⁸

The large (up to 1 mm in length), high-quality single crystals that can be obtained for these M₂(TTFTB) phases have enabled thorough characterization of their properties: for example, Cd₂(TTFTB) was used as a model system for a comparative study of techniques to measure conductivity in MOFs.⁵⁶

Several different TTFTB MOFs based on lanthanides show diverse structures, while retaining the general trend of conductivities correlating inversely with S···S contact distances. Xie et al. reported three TTFTB MOFs with La^III which crystallize with 1D stacks of TTFTB ligands and rectangular pores.⁸⁵ Notably, the H₂O to DMF ratio used in their synthesis appeared to play a role in determining the extent of π–π stacking. The two more conductive phases showed average conductivity values of 2.5(7) × 10^–6 and 9(4) × 10^–7 S/cm, respectively, with longest S···S contacts of 3.640(4) and 4.083(3) Å. The third phase was significantly less conductive (1.0(5) × 10^–9 S/cm) and has a much longer S···S contact of 7.072(7) Å. The BET surface areas of these polymorphs ranged between 362 and 596 m²/g.

TTFTB-based MOFs with middle and late lanthanides also showed polymorphism dependent on the synthesis conditions (Figure 22). Castells-Gil et al. reported⁸⁶ two structure types of TTFTB frameworks with Gd^III, Tb^III, Dy^III, Ho^III, and Er^III. M₃(TTFTB)₂(OAc)(OH), featuring continuous π–π stacking with S···S contact distances of <4 Å, showed consistently higher conductivities, with the highest value of 1.5 × 10^–5 S/cm measured in the Tb^III material. A different family of frameworks with Tb^III, Dy^III, Ho^III, and Er^III reported by Su et al. do not have close or continuous π–π stacking and consistently exhibited relatively low conductivities between 10^–9 and 10^–8 S/cm, with marginal increases upon doping with I₂.⁸⁷ The smallest lanthanides, Tm^III, Yb^III, and Lu^III, form TTFTB MOFs with unusual 2D structures and showed conductivities up to 2.6 × 10^–6 S/cm.⁸⁸ In contrast with the 1D TTF stacks in most other phases with this ligand, these MOFs contain one ligand oriented orthogonally to the others.

Figure 22.

Structures of (a) La₄(TTFTB)₄, (b) Tb₃(TTFTB)₂(OAc)(OH), (c) Tb₄(TTFTB)₃, and (d) La₄(TTFTB)₃ with the longest S···S contact distances indicated.⁸⁵⁻⁸⁷

Assuming that electron transfer between TTF cores dominates charge transport in TTFTB MOFs, the longest S···S contact in 1D ligand stacks should limit the overall rate of charge transfer in the stack. Hence, the value of the shortest S···S contact between each pair of adjacent ligands, denoted as (S···S)_min, should be correlated with the conductivity. Indeed, plotting the conductivities of these materials vs the longest crystallographic (S···S)_min contacts in each structure shows an inverse correlation between these parameters (Figure 23).⁸⁵ This general trend suggests that intermolecular TTF distances determine the bulk conductivities of these MOFs across different structures and compositions. Similar trends should be observed for other MOFs where the dominant transport pathway is through close ligand···ligand π-based interactions.

Figure 23.

Pressed pellet conductivities of MOFs with the TTFTB ligand⁸⁵ and different metals plotted versus the longest crystallographic S···S contact distance between two neighboring ligands.

For instance, other TTF-containing frameworks have been synthesized with the tetrathiafulvalene tetrapyridyl (TTF(py)₄) ligand. Wang et al. reported two polymorphic Fe^II materials, Fe(dca)₂[TTF(py)₄]_0.5 and Fe(dca)[TTF(py)₄](ClO₄).²⁰⁹ They lack continuous π–π stacking pathways and have conductivities on the order of 10^–9 S/cm in their as-synthesized forms. Upon treatment with I₂, their conductivities increased to 1.3 × 10^–6 and 7.6 × 10^–5 S/cm because of the oxidation of the TTF cores to their radical cation state. Notably, the incorporation of I₃^– proceeded via a single crystal-to-single crystal transformation in the latter MOF. Yu et al. reported three Mn^II frameworks with TTF(py)₄ with similar conductivities as the undoped Fe^II analogs (between 2.0 × 10^–10 and 6.3 × 10^–9 S/cm) because of the absence of close-stacking interactions in their structures.²¹⁰

Wang et al. also combined the TTF(py)₄ ligand with TCNQ as both a second ligand and an interstitial guest in MOFs with Zn^II and Cd^II.²¹¹ Though the combination of donor–acceptor systems in a single MOF framework is appealing for increasing conductivity, the conductivities of these frameworks were relatively low (∼10^–8 S/cm). After treatment with I₂, the conductivity of the Cd^II framework increased slightly to 2.16 × 10^–7 S/cm, but no evidence of additional TTF(py)₄ oxidation was apparent (the interstitial TCNQ^•– was replaced with I₃^–). The modest conductivity values were attributed to large separation between the redox-active moieties and the orthogonality of TTF and TCNQ.

In most of these reports, EPR and optical absorption spectroscopy studies on TTF-based frameworks have generally indicated that they contain some TTF^•+ species in their as-synthesized forms. Therefore, IVCT between partially oxidized TTF cores appears to be the general mechanism responsible for conductivity in these materials.

4.2. Other π–π Stacked Frameworks

A number of other planar organic cores have been used to make electrically conductive MOFs, including anthracene, naphthalenediimide, and naphthalene. The resulting materials have generally been studied in isolated reports, and unifying or comparative studies have yet to be carried out. Nonetheless, some of the highest conductivity values for the through-space approach have been achieved in these MOFs. Hence, more systematic investigations into non-TTF π–π stacked frameworks and their conductivities will accelerate development in this area and point out worthy synthetic targets for new linkers.

Chen et al. reported a mixed-metal MOF with the formula ZnNa₂(AnBEB)₂ (AnBEB = 4,4′-(anthracene-9,10-diylbis(ethyne-2,1-diyl))dibenzoate) containing unusual zigzag packing of the anthracene moieties, with an interplanar distance of approximately 3.4 Å between neighboring ligands.³⁸ The conductivity from single-crystal measurements was 1.3(5) × 10^–3 S/cm. This high value was attributed to the relatively close stacking distances and the zigzag packing motif. In contrast to other MOFs in this category, there was no evidence of ligand-based mixed valency for this framework. After activation, crystallinity and porosity were lost due to structural collapse from removal of coordinated solvents.

Another study reported a porous Cd^II material with the N,N′-di(4-pyridyl)-1,4,5,8-naphthalenetetracarboxdiimide (DPNDI) linker.⁹⁰ The structure is a π–π stacked assembly of linear [Cd(OH₂)₄(DPNDI)] polymers, which arrange into a hexagonal framework. The interlayer stacking distance is remarkably short, at only 3.18 Å (compared to typical distances of ∼3.3 Å for napthalenediimide (NDI)-based molecules). This close stacking, along with the ability of the NDI core to form stable radical anions, led to high conductivities up to 3.3 × 10^–3 S/cm measured on single crystals along the stacking axis. Measurements on pressed pellets yielded much lower values up to 7.6 × 10^–6 S/cm, perhaps due to the considerable anisotropy of the material. Unexpectedly, the desolvated form showed a higher conductivity than either of the above (3.7 × 10^–2 S/cm). However, the material exhibited a structural transition upon solvent removal, and its final structure was not fully determined.

Kuang et al. studied Cu^I(DPNDI)₂, an NDI-based framework with considerably further stacking distances than in the Cd^II material, with closest contacts of ∼3.7 A.⁹¹ The NDIs are also offset horizontally, leading to reduced overlap of their π-systems. Despite this, the MOF demonstrated a relatively high conductivity of 1.2 × 10^–5 S/cm, as determined from single-crystal measurements.

Another Cd^II-pyridyl-based framework, with the redox-active conjugated linker 2,5,8-tri(4-pyridyl)1,3-diazaphenalene, showed single-crystal conductivities of ∼1 × 10^–6 S/cm.²¹² The intrinsically porous structure consists of continuous columns of the linkers, with a relatively short stacking distance of 3.3 Å. The same linker was also found to form a different framework with Cd^II without continuous stacking, which was insulating. The different transport properties between these two MOFs demonstrate the importance of a continuous charge transport pathway.

Dense naphthalene-based MOFs with π–π stacking have also been reported to be conductive. Haider et al. obtained a dense Sr^II framework with 1,4,5,8-naphthalenetetracarboxylate that exhibited white-light emission.⁸⁹ This structure contains 2D sheets with Sr–carboxylate chains and closely stacked naphthalene cores separated by ∼3.4 Å and showed a conductivity of ∼10^–4 S/cm.

Panda and Banerjee fabricated field-effect transistors based on a series of indium isophthalate frameworks.²¹³ Out of the three materials investigated, only one featured close π–π stacking and showed a hole mobility of 4.6 × 10^–3 cm² V^–1 s^–1. Electrical conductivity of the material was not reported.

5. Redox Hopping

In this section, we summarize the transport properties of MOFs that do not conform to the above-mentioned design strategies. In general, these materials do not contain well-defined crystallographic pathways that could allow for band-like charge transport. Although many of these MOFs do contain redox-active components, they are separated by distances long enough to preclude direct orbital overlap. Therefore, charge hopping is the likely mechanism of conduction in these materials.

On average, the greater separation between hopping sites in these materials can be expected to coincide with lower charge mobilities compared to other classes of conductive MOFs. Consistent with this expectation, the highest conductivities for MOFs in this category^26,214,215 are lower than those falling under other design strategies. However, the wide range of conductivity values reported (Table 7) suggest that the factors limiting charge transport may vary widely among different materials (e.g., carrier concentration, carrier mobility, or grain boundary resistance), and can be difficult to predict from structural and compositional information alone.

Table 7. Selected Properties of MOFs Exhibiting Conduction Based on Redox Hopping Mechanisms.

materiala	description	σ (S/cm)b	σ method	Ea (eV)c	BET SA (m2/g)d	ref
metal-based hopping
Cu[Cu(pdt)2]		6 × 10–4	(not reported)	0.193	collapse	(64,216)
Cu[Ni(pdt)2]		2.6 × 10–3	2-probe pellet			(26)
		1 × 10–8	2-probe film	0.49	385	(216)
	ox. (I2)	1 × 10–4	2-probe film	0.18		(216)
Cu2.4Co0.6(BTC)2		1.4 × 10–8	2-probe pellet			(222)
U1.23Th4.77O4(OH)4(NO3)2(Me2BPDC)5		7 × 10–10	2-probe pellet			(224)
U1.23Th4.77Co3O4(OH)4(NO3)2(Me2BPDC)5	CoII on nodes	1.4 × 10–7	2-probe pellet			(224)
linker-based hopping
Zn2(BPDC)2(BPMTC)		6.4(9) × 10–7	2-probe pellet		dense	(215)
	irrad.	1.7(3) × 10–6	2-probe pellet		dense	(215)
Zn2(SDC)2(BPMTC)		9.5(21) × 10–7	2-probe pellet		dense	(215)
	irrad.	2.9(7) × 10–6	2-probe pellet		dense	(215)
Zn4O(NDC)3		0.0398	4-probe film			(227)
Zr6O4(OH)8(Me2BPDC)4	with BCMTC	1.3(3) × 10–5	2-probe pellet			(215)
	with BCMTC, irrad.	2.3(2) × 10–5	2-probe pellet			(215)
Zr6(OH)16(TBAPy)2 (NU-1000)	electrophoretic film	1.3 × 10–9	thin film EIS (1.6 V vs Ag/AgCl)			(225)
	solvothermal film	1.2 × 10–7	thin film EIS (1.6 V vs Ag/AgCl)			(225)
mixed metal- and linker-based hopping
Cd(3-bpd)(SCN)2		4.53 × 10–7	2-probe film diode		dense	(220)
Cd(4-bpd)(SCN)2		2.9 × 10–6	2-probe film diode		dense	(221)
Cd(azbpy)(mglu)		1.29 × 10–5	2-probe film diode		dense	(219)
Cd(azbpy)(msuc)		2.64 × 10–5	2-probe film diode		dense	(219)
Cd(azbpy)(suc)		3.20 × 10–5	2-probe film diode		dense	(219)
Cd1.5(azbpy)2(glu)(NO3)		2.07 × 10–5	2-probe film diode		dense	(219)
Cd2(azbpy)2(HIP)2		1.86	2-probe film diode		dense	(214)
Zn(azbpy)(HIP)		1.1 × 10–4	2-probe film diode		dense	(218)
Zn(azbpy)0.5(HIP)		2.5 × 10–5	2-probe film diode		106	(218)
Co3[Co(TCPP)]2		3.62 × 10–8	2-probe film (EIS)			(229)
Mg3Fe2[Co(OPc)]	ox. (I2)	1 × 10–5	2-probe sc		1481	(102)
Ni/Fe(NDC)	nanosheets	1.0(2) × 10–5	4-probe film		dense	(231)
Ni/Fe(NDC)	bulk	1.0(5) × 10–8	4-probe film		dense	(231)
Na3Pb6(THT)2(OH)		1.1 × 10–6	2-probe pellet			(228)
Sm2(BHC)		1.46 × 10–5	2-probe pellet		dense	(234)
Sr(1,2,4-BTC)		6 × 10–6	2-probe pellet	0.17	dense	(232)
Sr(ntca)		1 × 10–4	diode		dense	(89)
[Zn(SIP)][EMIM]		4.35 × 10–11 (373 K)	2-probe pellet (AC)	1.17	dense	(233)
Co-DAPV	no structure	0.035	4-probe film			(235)
Cu-BTC	no structure	8.3 × 10–8 to 5.3 × 10–11	2-probe pellet		dense–850	(236)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or 300 K unless otherwise indicated.

^cDerived from Arrhenius model. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^dCalculated from N₂ adsorption isotherms.

In general, higher conductivities in this category appear to correlate with the presence of redox-active components in the MOFs (e.g., linkers featuring metal–dithiolene units,^26,64,216 conjugated organic cores,^215,217 and azo groups^{214,218−221}). Excitation of mobile carriers from these motifs presumably facilitates conductivity.

5.1. Metal-Based Hopping

In 2009, Takaishi et al. reported Cu[Cu(pdt)₂] (pdt = pyrazine-2,3-dithiolate], which exhibited a conductivity of 6 × 10^–4 S/cm.⁶⁴ The authors hypothesized that linking the known electron acceptor [Cu^III(pdt)]⁻ with donating Cu^I ions could lead to the formation of an electrically conductive MOF. The authors obtained a 3D porous framework with Cu centers in a square-planar geometry (Figure 24) upon reaction of Na[Cu(pdt)₂]·2H₂O and CuI. Analysis of the bond lengths and angles from the X-ray crystal structure indicated that electron transfer had occurred between the donating and accepting fragments of the MOF, bringing both copper sites to a formal oxidation state of Cu^II. This oxidation state assignment was further corroborated by the paramagnetic behavior of the compound. The authors attributed the relatively high conductivity of the MOF to redox hopping among the Cu centers, perhaps facilitated by the charge bistability of Cu^I[Cu^III(pdt)₂] and Cu^II[Cu^II(pdt)₂] units.

Figure 24.

Structure of Cu[Cu(pdt)₂] showing square channels formed by pyrazine-linked Cu centers and redox-active [Cu(pdt)₂]^2– units.⁶⁴

While the crystal structure of Cu[Cu(pdt)₂] contains 1D square channels filled with disordered solvent, Kobayashi et al. reported that the compound amorphized and collapsed upon desolvation.²¹⁶ They were able to synthesize the structural analog Cu[Ni(pdt)₂], with Ni replacing Cu in the dithiolene-coordinated site. This mixed-metal MOF retained crystallinity and microporosity after activation, exhibiting a BET surface area of 385 m²/g. The conductivity of as-synthesized Cu[Ni(pdt)₂] was reported to be 1 × 10^–8 S/cm in the original study and 2.6 × 10^–6 S/cm in a later study.²⁶ Upon exposure to I₂ vapor, the conductivity increased to 1 × 10^–4 S/cm without measurable incorporation of iodine species into the framework. Analogous to the case of Cu[Cu(pdt)₂], redox hopping among partially oxidized nickel-dithiolene units is the likely mechanism of conduction. These results constitute the first example of a permanently microporous MOF with conductivity tunable over several orders of magnitude through doping.

Dolgopolova et al. studied the influence of exchanging Co^II into Cu₃(BTC)₂ (BTC = benzene-1,3,5-tricarboxylate) on its conductivity.²²² The particular choice of Co^II was motivated by an earlier computational study, which investigated the effects of partial metal substitution in MOF-5 on its electronic structure.²²³ Cu_2.4Co_0.6(BTC)₂ was found to be somewhat more conductive than monometallic Cu₃(BTC)₂, with the conductivity increasing from 2.0 × 10^–10 S/cm to 1.4 × 10^–8 S/cm with the introduction of Co^II. In the same study, Dolgopolova et al. also provided a microwave conductivity investigation of the materials, showing that the effective conductivity of the exchanged material was approximately one order of magnitude higher than that of the original. This difference was attributed to the presence of Co^II midgap states, which can lower the energetic barrier to charge hopping.

An analogous strategy was employed by the same group to increase the conductivity of a bimetallic actinide framework U_1.23Th_4.77O₄(OH)₄(NO₃)₂(Me₂BPDC)₅ (Me₂BPDC^2– = 2,2′-dimethylbiphenyl-4,4′-dicarboxylate).²²⁴ Introduction of Co^II ions into the framework led to the extension of the hexanuclear cluster node to give the formula U_1.23Th_4.77Co₃O₄(OH)₄(NO₃)₂(Me₂BPDC)₅ and resulted in enhancement of the electrical conductivity from 7.0 × 10^–10 S/cm to 1.4 × 10^–7 S/cm. DFT calculations showed narrowing of the bandgap upon addition of Co^II due to the addition of midgap Co–O-based states. This result is similar to what was observed in the previous Cu₃(BTC)₂ study and is most likely responsible for the improved charge transport.

5.2. Linker-Based Hopping

Dolgopolova et al. also investigated ways of controlling charge transport in photoresponsive MOFs using linker isomerization.²¹⁵ The authors synthesized a set of mixed-linker frameworks with photoactive spiropyran and diarylethene fragments in the linkers. The spiropyran fragments isomerize on exposure to UV light to form merocyanine zwitterions. Similarly, diarylethene moieties form more extended conjugated (closed) systems under UV-irradiation, which break up (open) following exposure to visible light at 590 nm (Figure 25a). The authors used these two transformations as switches for charge transport, hypothesizing that the different charge distribution and size of the conjugated system between the nonisomerized and isomerized linkers would affect the energetic and spatial separation between hopping sites, thus allowing control over the conductivity. They found that a spiropyran-containing MOF exhibited a reversible increase in the conductance of single crystals upon UV irradiation. Reverse isomerization of merocyanine at ambient conditions complicated the study, so the authors focused on photoactive systems using diarylethene (Figure 25b). Both in situ and ex situ conductivity and diffuse reflectance measurements on three different Zn^II- and Zr^IV-based frameworks containing diarylethene motifs showed small but statistically significant (p < 0.05) three- to four-fold increases in conductivity upon isomerization of the linker into its “closed” form (Table 7). This study demonstrated the first realization of photoswitchable charge transport in MOFs.

Figure 25.

(a) Scheme showing photoswitchable isomerization of “open” and “closed” forms of diarylethene derivatives and (b) structure of Zn₂(SDC)₂(BPMTC) with the “open” form of the diarylethene linker.²¹⁵

Goswami et al. studied the conductivity of Zr₆(OH)₁₆(TBAPy)₂ (NU-1000; TBAPy = tetrakis(p-benzoate) pyrene) thin films at 1.6 V vs Ag/AgCl using EIS.²²⁵ At this potential, the TBAPy linker is expected to be present in both its closed-shell TBAPy^4– and radical trianion TBAPy^•3– forms. They discovered higher conductivities for films with preferential orientation along the c direction than those oriented along the ab direction, which is consistent with closer redox hopping distances along the c direction. As expected from the generation of more charge carriers (i.e., radical ligand species), the conductivity values obtained by this method (up to 1.2 × 10^–7 S/cm) were significantly higher than those reported for NU-1000 without an applied potential (9.1 × 10^–12 S/cm).²²⁶

Dawood et al. fabricated thin film devices of interpenetrated Zn₄O(NDC)₃ (NDC = 2,6-naphthalenedicarboxylate) using electron beam deposition of copper electrodes.²²⁷ Surprisingly, these devices exhibited high conductivities up to 3.98 × 10^–2 S/cm despite relatively discontinuous stacking in the structure of the MOF. The authors hypothesized that the interpenetrated arrangement of naphthalene cores allows for charge hopping.

5.3. Mixed Metal- and Linker-Based Hopping

Ghoshal and co-workers have reported several Zn^II and Cd^II frameworks with the 4,4′-azobispyridine linker and other carboxylate ligands, including 5-hydroxyisophthlate,^214,218 methylsuccinate, methylglutarate, and glutarate.²¹⁹ Their conductivities ranged from 1.29 × 10^–5 S/cm²¹⁹ to 1.86 S/cm.²¹⁴ Roy and co-workers made Cd^II frameworks with an extended azo-based linker, 1,4-bis(3-pyridyl)-2,3-diaza-1,3-butadiene, with conductivities of 4.53 × 10^–7 S/cm²²⁰ and 2.90 × 10^–6 S/cm.²²¹ All of these azo materials also exhibited Schottky diode-like behavior in thin film devices, with some increases in conductivity upon photoillumination. They were dense except for one Zn^II framework with 4,4′-azobispyridine and 5-hydroxyisophthlate, which displayed a BET surface area of 105.8 m²/g.²¹⁸ Redox-hopping among metal centers and π–π interactions among the linkers were both proposed to contribute to the observed conductivity.

Huang et al. combined the triphenylenehexathiol (THT) ligand with Pb^II in order to obtain a framework with the formula [Pb₆(THT)₂(OH)]^3– (charge-balanced by Na⁺ in the pores).²²⁸ While other MOFs with the THT ligands exhibit extended conjugation in 2D structures, the reaction conditions used in this study (using in situ deprotection of the linker to slow down crystallization) appeared to favor the formation of a 3D framework without close π–π interactions or continuous through-bond pathways. The conductivity of this MOF (1.1 × 10^–6 S/cm) was accordingly lower compared to other THT-based materials.

The charge transport and electrochemical properties of a porphyrin-based framework, Co₃[Co(TCPP)]₂ (TCPP = 5,10,15,20-(4-carboxyphenyl)porphyrin), was investigated by Ahrenholtz et al.²²⁹ The conductivity measured by EIS on a thin film grown on FTO was 3.62 × 10^–8 S/cm. Charge diffusion parameters from cyclic voltammetry and spectroelectrochemical analysis combined with the relatively low conductivity value were deemed consistent with a redox hopping mechanism of conduction between framework Co centers and the linker porphyrins. Another study reported the charge mobilities obtained by FP-TRMC measurements of two porphyrin-based MOF films, Zn[Pd(DPPDB)] and Zn[(H₂DPPDB)] (Pd(DPPDB) = palladium(II) 4,4′-(10,20-diphenylporphyrin-5,15-diyl)dibenzoate, and (H₂DPPDB) its free base porphyrin analog). These films, grown on conductive fluorine-doped tin oxide, showed mobilities of 0.002 cm² V^–1 s^–1 for Zn[Pd(DPPDB)] and 0.003–0.004 cm² V^–1 s^–1 for Zn[(H₂DPPDB)].²³⁰

Matheu et al. recently reported a 3D framework based on Co^II phthalocyanine with the OPc linker and Fe^III as the framework metal with the formula Mg₃Fe₂[Co(OPc)].¹⁰² Unlike other OPc frameworks, which form 2D sheets with extended metal–linker conjugation, this MOF contains no π–π stacking, with all ligands being separated by more than 13 Å. The octahedral coordination of Co^II centers in the Pc units (with two axial aquo ligands) and the formation of Fe₃(−C₂O₂−)₆(OH₂)₂ SBUs likely both favor this more porous structure. Despite the long separation distance, the single-crystal conductivity (measured along the c direction, which contains continuous SBU–OPc linkages) was ∼10^–5 S/cm. The relatively high value was attributed to charge hopping between redox-active Pc molecules and SBUs.

Duan et al. synthesized thin nanosheets of the dense 2D mixed-metal MOF (Ni/Fe)(NDC) for electrocatalytic water splitting.²³¹ The nanostructured MOF was significantly more conductive (1.0(2) × 10^–5 S/cm) than the bulk MOF (1.0(5) × 10^–8 S/cm), which was attributed to defects and vacancies induced by nanostructuring. The mixed-metal approach may also have introduced free charge carriers into the framework.

The conductivities of several dense frameworks with benzene-based carboxylate linkers without open-shell transition metals have been studied.^232−234 These values range from 10^–11 to 10^–5 S/cm. Hopping between the ligands or carboxylate-coordinated metal centers is likely to be responsible for the transport behaviors observed.

6. Guest-Promoted Transport

Using host–guest interactions to increase conductivity is perhaps the strategy most specific to MOFs. By leveraging the intrinsic microporosity of MOFs, high loadings of electroactive molecules can be introduced into the pores to increase electrical conductivity (Table 8). In contrast with charge doping, which increases the number of charge carriers by reacting the material with (usually small quantities of) oxidizing or reducing species, guest-mediated conductivity commonly involves the introduction of stoichiometric amounts of new species into the MOF. These relatively high loadings of guests are usually necessary to form continuous charge transport pathways (and hence obtain high mobilities). Guests with extended structures, including conductive polymers and inorganic oxides, have also been introduced. In most cases, charge transfer between the framework and the guest appears to be important for increasing conductivity, presumably as a mechanism for generating free charge carriers.

Table 8. Selected Properties of MOFs with Guest-Mediated Charge Transport Pathways.

materiala	description, guests	σ (S/cm)b	σ methodc	Ea (eV)d	BET SA (m2/g)e	ref
iodine and polyiodides
Co3(BDC)3(bpz)2	I2	1.56 × 10–6 (2.59 × 10–9)	2-probe pellet			(244)
Co3(lac)2(pybz)2	I2	7 × 10–6	2-probe pellet			(247)
Co3(NDC)2	I2	1.88 × 10–6	Hall bar film			(252)
Cu6(pybz)8(OH)2	I5–, I7–	8.11 × 10–7 (8.4 × 10–9)	2-probe film			(243)
Eu4(BPT)4	I2	8.27 × 10–7	2-probe pellet (EIS)	0.602	69.6	(250)
Tb(Cu4I4)(PCA)3	I2	2.16 × 10–4 (5.72 × 10–11)	2-probe sc			(248)
V2(OH)2(BPTC)	I2, I3–	1.2 × 10–4 (1.7 × 10–10)	2-probe pellet (AC)			(249)
Zn3(lac)2(pybz)2	I2	3.42 × 10–3	2-probe sc (∥)			(246)
	I2	1.65 × 10–4	2-probe sc (⊥)			(246)
organic and organometallic molecules
Cd(TTF(py)4)(TCNQ•–)0.5(NO3)	TCNQ•–	2.63 × 10–8	2-probe pellet			(211)
Cd(TTF(py)4)(TCNQ2–)0.5(NO3)0.5	TCNQ•– (air)	4.77 × 10–8	2-probe pellet			(211)
Cd(TTF(py)4)(TCNQ2–)0.5(NO3)0.5	TCNQ•– (air, I2-treated)	5.97 × 10–8	2-probe pellet			(211)
Cd(TTF(py)4)(TCNQ•–)0.5(NO3)0.5	I3–	2.16 × 10–7	2-probe pellet			(211)
Cd(TTF(py)4)(TCNQ2–)0.5(NO3)	pristine	(1.05 × 10–8)	2-probe pellet			(211)
Zn(TTF(py)4)(TCNQ•–)0.5(NO3)	TCNQ•–	2.48 × 10–8	2-probe pellet			(211)
Cu(TPyP)Cu2(OAc)4	TCNQ	1 × 10–6 (1 × 10–9)	4-probe film			(260)
Cu2(TATAB)3	TCNQ	2.67 × 10–7 (9.75 × 10–12)	2-probe pellet			(258)
Cu3(BTC)2 (HKUST-1)	TCNQ	0.07	2-probe film	0.041	214	(237)
	TCNQ	3 × 10–3	2-probe film			(255)
	TCNQ	1.5 × 10–4	2-probe pellet		573.7	(245)
	TCNQ	1.92 × 10–10	2-probe Hg drop film			(254)
	ferrocene	3.57 × 10–15	2-probe Hg drop film			(261)
	pristine	(2 × 10–9)	2-probe film			(222)
Zn2(TCPB)(BPDPNDI)	MV2+	2.3(3) × 10–3	4-probe film			(242)
	DFDNB	3.5(6) × 10–4	4-probe film			(242)
	DNT	1.5(2) × 10–4	4-probe film			(242)
	C60	4.0(6) × 10–5	4-probe film			(242)
	pristine	(5.8 × 10–5)	4-probe film			(242)
Fe3O(TTFTB)3 (MUV-2)	C60	4.7 × 10–9 (3.7 × 10–11)	2-probe pellet		1040	(239)
Zn(TPP)	C60	1.5 × 10–11 (2 × 10–13)	2-probe film			(262)
Zr6(OH)16(TBAPy)2 (NU-1000)	Ni(IV) bis(dicarbollide)	4.3 × 10–9 (9.1 × 10–12)	2-probe pellet		1260	(226)
Zr6(OH)16(TBAPy)2 (NU-901)	C60	1 × 10–3 (<10–14)	2-probe pellet		1550	(238)
conductive polymers and oxides
Cd2(NDC)(PCA)2	polypyrrole	1 × 10–3	4-probe pellet		dense	(266)
	polypyrrole	0.2	Hall bar pellet		dense	(266)
	I2 (control)	2.9 × 10–7	4-probe pellet			(266)
	pristine	(1 × 10–12)	4-probe pellet			(266)
Cr(OH)(BDC) (Cr-MIL-53)	PEDOT	1.1 × 10–3 (<10–11)	2-probe pellet (EIS)		803	(240)
La(BTC)	PEDOT	2.3 × 10–8	2-probe pellet (EIS)			(240)
Zn3(lac)2(pybz)2	polypyrrole	0.01	2-probe sc		135	(263)
Al(OH)(BDC) (Al-MIL-53)	S	1.2 × 10–10	2-probe pellet			(217)
	polypyrrole + S	2.71	4-probe pellet			(217)
	pristine	(1.39 × 10–7)	4-probe pellet		1370	(217)
Cr3OF(BDC)3 (Cr-MIL-101)	S	4.91 × 10–9	2-probe pellet			(217)
	polypyrrole + S	0.472	4-probe pellet			(217)
	pristine	(4.42 × 10–7)	2-probe pellet		3250	(217)
[Zr6(OH)16]2(TCPP)3 (PCN-224)	S	1.2 × 10–10	2-probe pellet			(217)
	polypyrrole + S	0.113	4-probe pellet			(217)
	pristine	(5.74 × 10–7)	2-probe pellet		2660	(217)
Zr6(OH)16(TBAPy)2 (NU-1000)	SnO	1.8 × 10–7 (9.1 × 10–12)	2-probe film		680	(241)

^aSee Abbreviations.

^bMeasured at room temperature (exact temperature unspecified) or 298 K. Value given in parentheses corresponds to pristine guest-free material.

^c∥ denotes device contacted parallel to guest-filled channels; ⊥ denotes device contacted perpendicular to channels.

^dDerived from Arrhenius model. For materials exhibiting more than one distinct activation regions, E_a at 300 K is given.

^eCalculated from N₂ adsorption isotherms.

The advantages of this strategy lie chiefly with the possibility of tuning the guest and framework properties in a synergistic fashion. Materials with highly tunable conductivities can be realized,²³⁷ and conductivity modulation across 11 orders of magnitude have been demonstrated.²³⁸ In addition, by selecting starting frameworks with high porosities and different pore sizes, the resulting guest@MOFs can retain high surface areas.^{226,238−241} For frameworks that are less porous in their original state, partial loading of guests can potentially allow for the optimization of conductivity versus surface area. Matching the reduction potentials of the framework and guest,²³⁸ as well as the sizes of the guest and pores,²⁴² are promising routes toward further customization of transport properties in this class of materials.

Although examples of crystallographically resolved guests exist,^226,243,244 the inclusion of guests and the formation of conductive pathways are often inferred from spectroscopic data that do not provide atomistic resolution. Finally, growth of conductive side products during guest infiltration can further complicate the attribution of increased conductivity to the guest@MOF assembly.²⁴⁵ Detailed compositional and crystallographic studies, therefore, can clarify the mechanisms behind conductivity enhancement achieved through this strategy.

6.1. Iodine and Polyiodides

Although iodine loading into MOFs has been explored predominantly in the context of doping—with the charge transport happening through pathways intrinsic to the framework—conductivity mediated by encapsulated channels of iodide species has also been demonstrated. Zeng et al. found that a double-walled MOF Zn₃(lac)₂(pybz)₂ (pybz = 4-(pyridin-4-yl)benzoate, lac = dl-lactate) with 1D square channels incorporated I₂ upon soaking in a cyclohexane solution.²⁴⁶ Conductivity measurements on single monoliths (loss of crystallinity was observed upon reaction with I₂) revealed a value of 3.42 × 10^–3 S/cm along the direction of the channels. The Co^II analog incorporated a similar amount of I₂ but exhibited a lower pellet conductivity of 7 × 10^–6 S/cm.²⁴⁷ The authors of these studies proposed that charge transfer between iodide species and pybz π-electrons led to these relatively high conductivities (we note that the conductivities of the guest-free frameworks were not reported). However, loss of crystallinity upon I₂ incorporation made mechanistic interpretation challenging.

Yin et al. uncovered more definitive evidence of the role of polyiodide inclusion in a related system.²⁴³ By including I₂ in the solvothermal reaction with Cu^II and pybz, they obtained Cu₆(pybz)₈(OH)₂·I₅^–·I₇^– with crystallographically resolved polyiodide anions incorporated into the channels. The conductivity of a thin film of the material was 8.11 × 10^–7 S/cm. Soaking in methanol removed I₂ from the polyiodides to afford Cu₆(pybz)₈(OH)₂(I^–)₂ and lowered the conductivity by 2 orders of magnitude (8.04 × 10^–9 S/cm). We note that, while these pybz materials were porous in their original forms, with BET surface areas up to 800 m²/g for Co₃(dl-lac)₂(pybz)₂, their porosities were likely not maintained after iodide inclusion. No adsorption measurements were attempted for any of these iodine-treated materials.

Hu et al. combined thorough crystallographic and physical characterization to explain the enhancement of transport properties in Tb(Cu₄I₄)(PCA)₃ (PCA = 4-pyridinecarboxylate) upon uptake of I₂.²⁴⁸ The single-crystal conductivity of the parent material, which included framework iodide anions, was 5.72 × 10^–11 S/cm. After I₂ inclusion, the conductivity increased by 7 orders of magnitude to reach 2.16 × 10^–4 S/cm. This dramatic change was attributed to the extended {Cu₄I₅} layer formed by strong I^–···I₂···I^– interactions, as seen from single-crystal X-ray diffraction (Figure 26). Notably, this work demonstrated reversible adsorption/desorption of I₂ and associated modulation of the conductivity.

Figure 26.

Structure of Tb(Cu₄I₄)(PCA)₃²⁴⁸ containing crystallographically resolved I₂ guests with close I^–···I₂···I^– contacts highlighted.

Another example of crystallographically resolved iodine inclusion is Co₃(BDC)₃(bpz)₂·0.5 I₂ (BDC = benzene-1,4-dicarboxylate, bpz = 3,3′,5,5′-tetramethyl-4,4′-bipyrazole), which contained I₂ in the channels.²⁴⁴ While no evidence of the reduction of I₂ to iodide species by the framework was found, the conductivity nevertheless increased by 3 orders of magnitude to 1.56 × 10^–6 S/cm upon introduction of I₂.

Zhang et al. found that iodine adsorption in the V₂(OH)₂(BPTC) framework resulted in oxidation of about 30% of the native V^III centers to V^IV.²⁴⁹ Powder and single-crystal X-ray diffraction analyses revealed the presence of both I₂ and I₃^– in the channels, forming a helical chain. The conductivity of the iodine-containing MOF increased to 1.2 × 10^–4 S/cm from an original value of 1.7 × 10^–10 S/cm. The authors attributed conductivity to both mixed-valent V centers and charge hopping along the iodine chains.

Other instances of iodine incorporation resulting in electrical conductivity have also been reported. Encapsulation of ∼17% iodine by weight into Eu₄(BPT)₄ (BPT = biphenyl-3,4′,5-tricarboxylate) yielded a conductivity of 8.27 × 10^–7 S/cm (the conductivity of the parent material was not reported).²⁵⁰ Uptake of I₂ and I₃^– by Co₃(NDC)₃ (NDC = 2,6-naphthalenedicarboxylate)²⁵¹ resulted in a conductivity of 1.88 × 10^–6 S/cm for a thin film device.²⁵² Hall effect measurements were also carried out, yielding a hole mobility of 21.2 cm² V^–1 s^–1 and a carrier concentration of 5 × 10¹¹ cm^–3. Hall effect measurements on films of CoBDC and CoNDC grown on TiO₂ and doped with I₂ showed similar mobility values of 21.2 and 87.6 cm² V^–1 s^–1, respectively.²⁵³

Finally, stoichiometric polyiodide incorporation also increased the conductivity of several tetrathiafulvalene-based MOFs, as discussed in more detail above.^{87,200,209,211} In most cases, these changes were attributed to oxidation of the ligand core, although we note that transport through iodide channels may also play a role.

6.2. Organic and Organometallic Molecules

The guest-promoted approach is not limited to smaller inorganic species, as large organic molecules have also been incorporated in MOFs to increase their conductivity. Talin et al. reported that soaking thin films of Cu₃(BTC)₂ (or HKUST-1; BTC = benzene-1,3,5-tricarboxylate) in a saturated solution of TCNQ, an electron acceptor, increased its conductivity 6 orders of magnitude from 10^–8 to 0.07 S/cm after 72 h.²³⁷ The decrease in the BET surface area from 1844 to 214 m²/g indicated that TCNQ was incorporated into the pores. The conductivities increased with longer exposure times in good agreement with percolation theory, leading the authors to propose that conducting regions were formed in the MOF by TCNQ bridging the copper paddlewheel SBUs (Figure 27). Vibrational and UV–vis spectroscopic data were consistent with partially reduced TCNQ, implying charge transfer between the framework and TCNQ.

Figure 27.

Predicted structure of TCNQ@Cu₃(BTC)₂ with TCNQ bridging the Cu^II paddlewheel clusters of the MOF to form a continuous charge transport pathway.^237,245

Higher conductivities in TCNQ@Cu₃(BTC)₂ compared to the pristine MOF were corroborated by other reports.^245,254,255 However, Schneider et al.²⁴⁵ and Thürmer et al.²⁵⁶ showed that partial or full conversion of Cu₃(BTC)₂ into the dense coordination polymer Cu(TCNQ) (σ ∼ 0.1 S/cm^82,257) upon exposure to TCNQ proceeded under certain conditions. These works highlighted the importance of verifying the phase composition of MOFs after treatment with redox-active species and raise the question of whether the formation of a highly conductive parasitic phase contributes to the improved conductivity. Hence, additional investigation into the mechanism of conductivity enhancement in this system remains important.

TCNQ incorporation led to a 10⁴-fold improvement in conductivity in Cu₂(TATAB)₃ (TATAB = 4,4′,4″-((1,3,5-triazine-2,4,6-triyl)tris(azanediyl)) tribenzoate), a denser MOF-based on the same copper paddlewheel SBU.²⁵⁸ Although the overall structure and metal environment in Cu₂(TATAB)₃ is similar to Cu₃(BTC)₂, the larger size of the linker leads to formation of an interpenetrated framework, with reduced porosity compared to Cu₃(BTC)₂. When reacted with a methanolic solution of TCNQ, Cu₂(TATAB)₃ darkened in color, and its conductivity increased from 9.75  ×  10^–12 to 2.67  ×  10^–7 S/cm, as determined from two-probe pressed pellet measurements. No discussion of the exact mechanism of TCNQ interactions with the framework was provided; however, the denser arrangement of the copper paddlewheels in the material makes it difficult to envision a bridging binding mode for the TCNQ, as was proposed for Cu₃(BTC)₂.

TCNQ incorporation was also reported to increase the conductance of thin-film MOF devices via charge transfer between TCNQ and the framework for both Co₂(DOBDC)²⁵⁹ and a 2D MOF constructed of Cu^II acetate paddlewheels and a tetrapyridyl porphyrin linker.²⁶⁰

The effects of ferrocene doping on the conductivity of thin films of Cu₃(BTC)₂ have also been investigated.²⁶¹ Activated thin films of the MOF were exposed to ferrocene vapors, which led to a slight improvement of the electrical conductivity, from 1.47 × 10^–15 to 3.57 × 10^–15 S/cm. From the thickness dependence of the current density in the films, the authors concluded that the conduction mechanism was not tunneling through the films but rather hopping-type.

Guo et al. demonstrated that soaking films of a pillared paddlewheel MOF with an electron-rich pyridyl- and dipyrrolidyl-substituted naphthalene diimide (NDI) ligand in a solution of methyl viologen dication (MV²⁺) increased the conductivity from 6 × 10^–7 to 2 × 10^–5 S/cm.²⁴² Soaking in solutions of the weaker π-acids dinitrotoluene and 1,5-difluoro-2,4-dinitrobenzene also improved the conductivity, though by less than one order of magnitude. In contrast, treatment with a solution of C₆₀ resulted in unchanged conductivity, which was attributed to size exclusion by the MOF pores. The authors proposed that donor–acceptor interactions between the π-acid guests and the electron-rich ligand introduced charge carriers and potentially also increased the charge mobility via π–π interactions.

Yet larger redox-active guests have been incorporated in more porous frameworks. Goswami et al. reported that C₆₀ uptake dramatically increased the conductivity of Zr₆(OH)₁₆(TBAPy)₂ (NU-901; TBAPy = tetrakis(p-benzoate) pyrene).²³⁸ The conductivity of C₆₀@NU-901 was on the order of 10^–3 S/cm, ∼10¹¹ times higher than guest-free NU-901 (<10^–14 S/cm). A related study by Kung et al. reported the incorporation of an electron-deficient metallacarborane, nickel(IV) bis(dicarbollide) (NiCB), into a different polymorph of Zr₆(OH)₁₆(TBAPy)₂ known as NU-1000.²²⁶ EIS yielded an estimated conductivity of 2.7 × 10^–7 S/cm for NiCB@NU-1000. The value from a more conventional two-probe pressed pellet measurement was lower (4.3 × 10^–9 S/cm) but still exceeded that of pristine NU-1000 (9.1 × 10^–12 S/cm) by several orders of magnitude. UV–vis spectroscopy data for both of these guest@MOFs revealed charge transfer bands corresponding to donor–acceptor interactions between the guests and pyrene-based linkers, which ostensibly enhanced the conductivities. Notably, both NiCB@NU-1000 and C₆₀@NU-901 retained significant porosity, with BET surface areas of 1260 and 1550 m²/g, respectively.

Souto et al. encapsulated C₆₀ in a similarly mesoporous MOF with the formula Fe₃O(TTFTB)₃ (MUV-2) with a redox-active TTF-based ligand.²³⁹ Similar to the pyrene-based MOFs, a charge transfer band in the UV–vis spectroscopy data indicated donor–acceptor interactions between C₆₀ and the TTF core. While DFT calculations predicted favorable ligand-to-guest charge transfer and a lowered bandgap in the C₆₀-encapsulated material, the conductivity increase was modest (from 3.7 × 10^–11 S/cm for MUV-2 to 4.7 × 10^–9 S/cm for C₆₀@MUV-2). The authors attributed the relatively low conductivity value to low C₆₀ loading (C₆₀@MUV-2 remained highly porous, with a BET surface area of 1040 m²/g) and long distances separating the ligand TTF moieties.

C₆₀ incorporation into thin films of surface-mounted metal–organic frameworks (SURMOFs) has also been demonstrated to increase their conductivities. Deposition of C₆₀@Cu(BPDC) (BPDC = biphenyl-4,4′-dicarboxylate) and C₆₀@Zn(TPP) (TPP = 5,15-bis(3,4,5-trimethoxyphenyl)-10,20-bis(4-carboxyphenyl)porphyrin) SURMOFs was carried out by spin-coating alternating layers of solutions of the metal salt, linker, and C₆₀.²⁶² The conductivities of the C₆₀-containing frameworks (∼10^–11 S/cm) were at least 2 orders of magnitude higher than the pristine SURMOFs (<2 × 10^–13 S/cm). For C₆₀@Zn(TPP), a C₆₀ loading of about 0.9 molecules per unit cell was assigned based on UV–vis spectroscopy and mass spectrometry. C₆₀@Zn(TPP) also exhibited photoconductivity, reaching a maximum conductivity of 1.3 × 10^–9 S/cm when irradiated with 455 nm light. No surface area measurements were carried out on these materials.

6.3. Conductive Polymers and Oxides

Conductive extended solids—both organic and inorganic—have been encapsulated in MOFs. For polymer⊃MOF assemblies, conductivities higher than either of the pristine components have been reported. Enhanced transport properties in polymer⊃MOF materials have been generally attributed to charge transfer interactions between polymer chains surrounded by π-donor ligands, as well as high degrees of order and orientation in the polymers. In situ hole doping of the polymers by I₂ during the polymerization process are also likely to play a role.

Polymer chains have been incorporated into MOFs by loading monomers into the channels and then reacting the material with I₂ to induce polymerization. Wang et al. first demonstrated this approach with polypyrrole (PPy) and Zn₃(lac)₂(pybz)₂,²⁶³ likely inspired by an earlier work,²⁶⁴ in which well-ordered polypyrrole was grown inside a layered coordination polymer. The resulting PPy⊃Zn₃(lac)₂(pybz)₂ material (Figure 28) reached a conductivity of 1.0 × 10^–2 S/cm, higher than both I₂@Zn₃(lac)₂(pybz)₂ (3.42 × 10^–3 S/cm),²⁴⁶ and bulk PPy synthesized by the same group in similar conditions to the MOF loading procedure (∼10^–5 S/cm). (Much higher values for the conductivity of PPy have been obtained with different synthetic procedures.²⁶⁵) Interestingly, PPy extracted from the MOF showed significantly higher conductivity compared to the bulk powder. Dhara et al. obtained PPy⊃Cd₂(NDC)(PCA)₂ (NDC = 2,6-napthalenedicarboxylate, PCA = 4-pyridinecarboxylate) using the same strategy,²⁶⁶ resulting in a 10⁹-fold increase in conductivity to ∼10^–3 S/cm (via I–V measurements). From Hall effect measurements, a higher conductivity of 0.2 S/cm was estimated, along with an electron mobility of 8.15 cm² V⁻¹ s⁻¹ and electron density of 1.50 × 10¹⁷ cm^–3.

Figure 28.

Illustration of a chain of polypyrrole occupying the pore volume of Zn₃(lac)₂(pybz)₂.^246,263

Jiang et al. investigated co-incorporation of both PPy and elemental sulfur into a number of highly porous MOFs for potential applications in lithium–sulfur batteries.²¹⁷ The MOFs Cr₃OF(BDC)₃ (Cr-MIL-101), Al(OH)(BDC) (Al-MIL-53), and [Zr₆(OH)₁₆]₂(TCPP)₃ (PCN-224; TCPP = 5,10,15,20-(4-carboxyphenyl)porphyrin) were first loaded with sulfur by heating the activated materials in a sealed tube together with powdered sulfur. Then, the sulfur-loaded frameworks were put into a solution of pyrrole to which Fe^III was added to induce polymerization. This resulted in overall compositions of roughly 1:1:1 S:PPy:MOF for Cr-MIL-101 and Al-MIL-53, and roughly 2:1:1 S:PPy:MOF. While loading with sulfur slightly decreased the electrical conductivities of the three MOFs (from ∼10^–7 to ∼10^–9 S/cm), incorporation of polypyrrole caused dramatic increases in conductivity (0.113–2.71 S/cm). That said, these values are similar to polypyrrole grown on sulfur in the same study (1.73 S/cm).

Le Ouay et al. incorporated poly(3,4-ethylenedioxythiophene) (PEDOT) into Cr-MIL-101.²⁴⁰ The conductivity of the PEDOT⊃Cr-MIL-101 material with 57% polymer loading by weight was 1.1 × 10^–3 S/cm (compared to <10^–11 S/cm for Cr-MIL-101 alone). This material had a BET surface area of 803 m²/g, partially retaining the high porosity of the Cr-MIL-101 host. The mass fraction of PEDOT in Cr-MIL-101 was found to correlate directly with the conductivity and inversely with the surface area. Interestingly, when PEDOT was incorporated into La(BTC), a MOF with 1D channels, the composite showed a much smaller increase in conductivity than PEDOT⊃Cr-MIL-101, reaching only 2.3 × 10^–8 S/cm. The authors hypothesized that the 3D architecture of Cr-MIL-101 may enable higher conductivity by allowing for more PEDOT interchain interactions.

Motivated by the ubiquitous conductive tin oxide glasses, Kung et al. investigated the modification of Zr₆(OH)₁₆(TBAPy)₂ (NU-1000) with postsynthetically installed tetratin(IV) oxy clusters.²⁴¹ The activated MOF was immersed in a solution of a tin precursor, which readily hydrolyzed at the hydroxyl and aqua sites of the Zr cluster. The material was then subjected to a steam treatment, and this whole process was repeated several times. The authors found that the unmodified MOF, as well as the same MOF after one or two cycles of the installation process (in which the concentration of the installed clusters was low enough to give isolated tin(IV) oxy clusters), were both insulating. However, after three cycles, the clusters formed continuous strands of tin(IV) oxide, leading to a significant improvement in conductivity, with values as high as 1.8 × 10^–7 S/cm. Despite the considerable amount of tin(IV) oxide in the material, it was still porous, with BET surface areas of 680 m²/g. This study demonstrated that conductive MOFs can be attained through the guest-promoted design strategy using extended inorganic solids, in addition to the more commonly utilized organic and organometallic molecules and polymers.

7. Conclusions and Outlook

Recent years have witnessed a broad diversification of strategies used to imbue MOFs with mobile charge carriers and pathways for charge transport. These strategies have centered upon various intrinsic structural components of MOFs, including the inorganic SBU, extended bonding between the metal and linker, and noncovalent interactions among linkers. Additionally, the porosity of MOFs has been leveraged to introduce extrinsic guests that mediate conductivity. Across these distinct approaches, we summarize unifying characteristics among the materials we have discussed:

• (1)The ubiquity of mixed-valence motifs. Mixed valency among metal centers or linkers can both introduce charge carriers into MOFs. For example, frameworks containing Fe^II/III in chain SBUs are more conductive than those containing only divalent metals. Semiquinonate MOFs (and their imino- and thio-analogs) contain both radical and closed-shell oxidation states of the linkers in the solid state. Conductive MOFs based on tetrathiafulvalene and other conjugated organic molecules also contain a mixture of the radical cation and neutral forms of the organic cores. Some of these materials are grown with a mixture of ligand oxidation states (often with the presence of atmospheric oxygen serving as an in situ oxidant) and contain intrinsic mixed-valency in their as-synthesized forms. In other cases, mixed-valent motifs are postsynthetically introduced (e.g., deliberate oxidation of Fe^II centers to Fe^III, reduction of Fe^III to Fe^II, or partial oxidation of tetrathiafulvalene to its radical cation form using I₂). Materials in which the concentration of different charge states can be tuned have generally exhibited conductivities correlating with the extent of mixed-valency.
• (2)The presence of continuous charge transport pathways. Regardless of whether conduction proceeds by charge hopping or band conduction mechanisms, close proximity of the sites that charges can occupy correlates with conductivity. Moreover, continuous arrangement of these sites throughout the structure of the material is important to enable long-range charge transport. Continuous 1D, 2D, and 3D covalently bonded motifs have been demonstrated to facilitate conductivity in MOFs. In addition, in frameworks containing extensive π–π stacking, closer contact distances throughout the stack are correlated with higher conductivities.
• (3)The inherent chemical tunability of MOFs and resulting control over transport properties. Harnessing the modular nature of MOFs, comparative studies have begun to systematically change the identities of the metal and ligands to compare their effects on the resulting transport properties. Additional framework compositions are accessible through a combination of de novo synthesis and postsynthetic modification strategies. Routes to control π–π stacking motifs, as well as the connectivity and dimensionality of the frameworks, have also been demonstrated to correlate with conductivities. Finally, harnessing the inherent porosity of MOFs toward guest-promoted conductivity opens up the door to near-endless host–guest combinations with different properties.

This field has seen immense growth and progress in the past five years, allowing for the relationships among structure, composition, and physical properties discussed in this Review to be established from existing studies. Nevertheless, many worthwhile directions remain to be pursued in terms of both fundamental studies and potential applications of conductive MOFs. We highlight some of the most intriguing questions and pressing challenges:

• (1)Disentangling the properties of charge carriers in MOFs. Only a handful of charge mobility values have been reported for MOFs (Table 9), and many of these studies have used noncontact methods, such as FP-TRMC and TRTS. Hall effect measurements and FET devices using high-quality thin films or ideally single crystals of MOFs can determine the nature of the charge carriers (i.e., electrons or holes), as well as the carrier concentration and mobility. In general, deeper investigations into the mechanisms underlying high conductivities will yield more useful insights than a race toward record conductivity values. Additionally, computational studies (e.g., band structure calculations) will be important in corroborating experimental findings in this area.
• (2)Realizing more examples of isotropic conduction pathways in MOFs. The majority of conductive MOFs have anisotropic structures. For most MOFs with through-bond and through-space conduction pathways, charge transport dominates in a single crystallographic direction. For MOFs displaying extended conjugation, even though both in-plane and out-of-plane directions are expected to contribute to conductivity, different relative contributions may still result in anisotropic character in the bulk transport. Only isolated examples of conductive MOFs with isotropic structures and crystallographically resolved transport pathways have been reported.^68,71,72,154 The problem of installing charge carriers in close proximity to one another in an isotropic, porous network presents an intriguing intellectual and synthetic challenge. On the practical side, isotropic materials should offer some advantages for integration into devices on account of their orientation-independent properties.
• (3)Conductivity in mixed-metal and mixed-linker systems. Apart from mixed-valent motifs, targeting MOFs with more than one metal or ligand can be a strategy to dope these materials and increase their conductivities. Such systems could conceivably be realized through either direct synthesis or postsynthetic cation- or ligand-exchange.^267,268 Preliminary examples of mixed-metal approaches^{192,222,231,269} portend promising capabilities to further tune the conductivity of MOFs through compositional variation.
• (4)Further elucidation of transport mechanisms responsible for excellent bulk conductivities in selected 2D MOFs, especially Ni₃(HITP)₂. Very recent single-crystal transport studies on materials with triphenylene-based linkers (namely, Ni₃(HITP)₂ and Cu₃(HOTP)₂) have indicated that the in-plane conductivities are similar in magnitude to the cross-plane conductivities.⁷⁹ These findings suggest that π–π stacking interactions between the layers may play an important role in determining the bulk transport properties of these materials. In addition to more characterization of high-quality single crystals, unambiguously determining the crystal structures, stacking motifs, and metal and linker oxidation states in these materials can address this question. Finally, studies that systematically vary the identities of the metal and ligand and examine the resulting conductivities may offer further insights.
• (5)Isolation and characterization of single layers of 2D MOFs. Several theoretical works have predicted monolayers of 2D MOFs with extended conjugation to be materials with topologically nontrivial electronic states.³¹⁻³⁶ Although exfoliation down to single layers has been demonstrated for nonporous 2D coordination polymers that are conductive,²⁷⁰ the transport properties of isolated mono- or few-layer samples of 2D MOFs with extended π–d conjugation have not been reported in detail. The realization of such materials could reveal new platforms for studying transport phenomena at the forefront of experimental physics research. On a related note, further dimensional reduction of the motifs that facilitate charge transport in MOFs to 1D and 0D structures can shed light on specific coupling mechanisms.²⁷¹
• (6)Expanding the library of ligands for MOFs featuring through-space charge transport pathways. To date, most conductive MOFs with transport pathways comprising π–π stacking are made with TTF-based ligands. Though a large variety of different donor and acceptor molecules are utilized in organic electronics, most of these have not yet been incorporated into MOFs. Clever ligand designs that overcome synthetic hurdles that may be encountered in using such molecules can lead to new MOFs with through-space charge transport pathways and potentially notable photophysical properties.
• (7)More detailed structural investigations of host–guest interactions in MOFs. In MOFs with guest-promoted conductivities, the locations of most guest species within the pores of the MOF have not been crystallographically resolved. Determining the nature of charge-transfer interactions that increase conductivity in such systems would benefit from crystallographic investigation. Additionally, side reactivity between the guest and framework decomposition products is a potential concern in some of these systems. More in-depth structural studies (e.g., Rietveld refinement for crystalline powders, pair distribution function analysis for less crystalline materials) can also allow for more definitive assignment of enhanced transport properties to the host–guest composite versus conductive side products.
• (8)Influence of environment and atmosphere on MOF conductivity values. The successful application of conductive MOFs to chemiresistive sensing is a consequence of the sensitivity of the electronic properties of these materials to the atmosphere in which they are measured. Both reversible and irreversible changes in conductivity of MOFs may be observed upon exposure to different atmosphere (e.g., oxygen, moisture, volatile organic compounds, corrosive vapors). While such responses have been productively harnessed toward tunable conductivities and sensing applications, unmonitored atmospheric effects may also influence reported conductivity values. Hence, controlling and purposefully studying the impact of environmental effects can lead to more reproducible values in the literature and new materials for chemiresistive sensing.
• (9)Best practices for materials preparation and measurement techniques. As a corollary to the previous point, depending on the material and use case, the standard (or ideal) conditions under which to measure the transport characteristics of a MOF may vary. In addition, the same material (nominally, in terms of structure and composition) prepared under different conditions or measured in different form factors may exhibit conductivity values varying over several orders of magnitude. To maintain clarity in this growing field and ensure reproducibility, we believe it is increasingly important for researchers to document their sample and device preparation procedures, as well as the details of the measurement conditions (e.g., temperature, atmosphere, illumination, nature of the electrical contacts, as well as details on the measurement apparatus).⁵⁶ In addition, reporting the temperature dependence of the conductivity (from which an activation energy and transport mechanism can be extracted) is more instructive than the room temperature value alone.

Table 9. Charge Mobility Values of Metal–Organic Frameworks.

materiala	description	μ (cm2 V–1 s–1)	method	carrier type	ref
through-bond
Fe2(BDP)3		0.02	FP-TRMC		(69)
K0.8Fe2(BDP)3	red. (K+[C10H8]•–)	0.29	FP-TRMC		(69)
K0.98Fe2(BDP)3	red. (K+[C10H8]•–)	0.84	FET	e	(69)
Mn2(DSBDC)	MeOH-exchanged	0.02	FP-TRMC		(67)
	act.	0.01	FP-TRMC		(67)
extended conjugation
Cu3(BHT)		99	FET	h	(76)
		116	FET	e	(76)
Fe3(THT)2(NH4)3		125(9)	TRTS		(78)
		211(7)	TRTS		(78)
		229(33)	Hall		(78)
Ni3(HITP)2		48.6	FET	h	(191)
		45.4	FET	h	(198)
through-space
[In(isophthalate)2]		4.6 × 10–3	FET		(213)
Zn2(TTFTB)		0.2	FP-TRMC		(37)
hopping
Zn(H2DPPDB)		3–4 × 10–3	FP-TRMC		(230)
Zn[Pd(DPPDB)]		2 × 10–3	FP-TRMC		(230)
guest-promoted
Co(BDC)	I2-doped	21.2	Hall (film on TiO2/FTO)	h	(253)
Co3(NDC)3	I2-doped	87.6	Hall (film on TiO2/FTO)	h	(253)
Co3(NDC)3	I2-doped	21.2	Hall (film on TiO2/FTO)	h	(252)

^aSee Abbreviations.

We note in closing that conductivity values relevant to real-world applications have already been attained in MOFs. Inventive synthetic approaches, optimized growth techniques, and improved device fabrication can (and should) all continue to raise the ceiling of the transport properties attainable in porous, crystalline framework materials. However, equally important are the continuing refinement of design principles and more detailed mechanistic investigations into charge transport in MOFs. Future work along these lines will undoubtedly reveal novel fundamental properties and opportunities for application for this versatile class of materials.

Glossary

Abbreviations

1,2,4-BTC

benzene-1,2,4-tricarboxylate

1D

one-dimensional

2D

two-dimensional

3-bpd

1,4-bis(3-pyridyl)-2,3-diaza-1,3-butadiene

3D

three-dimensional

4-bpd

1,4-bis(4-pyridyl)-2,3-diaza-1,3-butadiene

act.

activated (all solvent removed)

AnBEB

4,4′-(anthracene-9,10-diylbis(ethyne-2,1-diyl))dibenzoate

AnBHB

4,4′-(anthracene-9,10-diyl)bis(2-hydroxybenzoate)

azbpy

trans-4,4′-azobispyridine

BCMTC

4,4′-(cyclopent-1-ene-1,2-diyl)bis(5-methylthiophene-2-carboxylate)

BDC

benzene-1,4-dicarboxylate

BDP

benzene-1,4-dipyrazolate

BDT

benzene-1,4-ditetrazolate

BET (SA)

Brunauer–Emmett–Teller (surface area)

BHC

benzenehexacarboxylate

BHSe

benzenehexaselenolate

BHT

benzenehexathiolate

BPDC

biphenyl-4,4′-dicarboxylate

BPDPNDI

N,N′-bis(4-pyridyl)-2,6-dipyrrolidyl-1,4,5,8-naphthalenetetracarboxydiimide

BPMTC

bis(5-pyridyl-2-methyl-3-thienyl)cyclopentane

BPT

biphenyl-3,4′,5-tricarboxylate

BPTC

biphenyl-3,3′,5,5′-tetracarboxylate

bpz

3,3′,5,5′-tetramethyl-4,4′-bipyrazole

Br₂dhbq

2,5-dibromo-3,6-dihydroxo-1,4-benzoquinone

BTC

benzene-1,3,5-tricarboxylate

BTDD

bis(1H-1,2,3-triazolo[4,5-b],[4,′5′-i]dibenzo[1,4]dioxin

Cl₂dhbq

2,5-dichloro-3,6-dihydroxo-1,4-benzoquinone

Cp₂Co

cobaltocene

DAPV

di(3-diaminopropyl)-viologen

dca

dicyanamide

desolv.

desolvated (pore solvents removed)

DFDNB

1,5-difluoro-2,4-dinitrobenzene

DFT

density functional theory

dhbq

2,5-dihydroxy-1,4-benzoquinone

DNT

dinitrotoluene

DOBDC

2,5-dioxybenzene-1,4-dicarboxylate

DPNDI

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

DSBDC

2,5-disulfidobenzene-1,4-dicarboxylate

E_a

activation energy

EIS

electrochemical impedance spectroscopy

EMIM

1-ethyl-3-methylimidazolium

EPR

electron paramagnetic resonance

FET

field-effect transistor

FP-TRMC

flash photolysis time-resolved microwave conductivity

glu

glutarate

H₂DPPDB

free base 4,4′-(10,20-diphenylporphyrin-5,15-diyl)dibenzoate

HIB

hexaiminobenzene

HIP

5-hydroxyisophthalate

HITP

2,3,6,7,10,11-hexaiminotriphenylene

Hmna

6-mercaptonicotinic acid

HOB

hexaoxybenzene

HOTP

2,3,6,7,10,11-hexaoxytriphenylene

IPc

2,3,9,10,16,17,23,24-octaiminophthalocyanine

IR

infrared

lac

lactate

Me₂BPDC

2,2′-dimethylbiphenyl-4,4′-dicarboxylate

mglu

methylglutarate

MOF

metal–organic framework

msuc

methylsuccinate

MV²⁺

methyl viologen (1,1′-dimethyl-4,4′-bipyridinium)

NDC

2,6-naphthalenedicarboxylate

NiCB

nickel(IV) bis(dicarbollide)

ntca

1,4,5,8-naphthalenetetracarboxylate

ONPc

3,4,12,13,21,22,30,31-octaoxynaphthalocyanine

OPc

2,3,9,10,16,17,23,24-octaoxyphthalocyanine

ox.

oxidized

PCA

4-pyridinecarboxylate

pdt

2,3-pyrazinedithiolene

PEDOT

poly(3,4-ethylenedioxythiophene)

PES

photoelectron spectroscopy

phz

phenazine

PTC

perthiolated coronene

PXRD

powder X-ray diffraction

pybz

4-(pyridin-4-yl)benzoate

pyz

pyrazine

red.

reduced

sc

single crystal

SDC

stilbene-4,4′-dicarboxylate

SEM

scanning electron microscopy

SIP

5-sulfoisophthalate

solv.

solvated

suc

succinate

TABTT

1,3,5-triaminobenzene-2,4,6-trithiol

TATAB

4,4′,4″-((1,3,5-triazine-2,4,6-triyl)tris(azane diyl)) tribenzoate

TBAPy

tetrakis(p-benzoate) pyrene

TCNQ

tetracyanoquinodimethane

TCPB

1,2,4,5-tetrakis(4-carboxyphenyl)benzene

TCPP

5,10,15,20-(4-carboxyphenyl)porphyrin

TEM

transmission electron microscopy

Th^•+BF₄^–

thianthrene tetrafluoroborate

THQ

tetrahydroxy-1,4-quinone

THT

triphenylene-2,3,6,7,10,11-hexathiolate

TPDAP

2,5,8-tri(4-pyridyl)1,3-diazaphenalene

TPP

5,15-bis(3,4,5-trimethoxyphenyl)-10,20-bis(4-carboxyphenyl)porphyrin

TPyP

5,10,15,20-tetra-4-pyridyl-porphyrin

TRTS

time-resolved terahertz spectroscopy

TTF

tetrathiafulvalene

TTF(py)₄

tetrathiafulvalene tetrapyridyl

TTFTB

tetrathiafulvalene tetrabenzoate

UV–vis

ultraviolet–visible

vac.

under vacuum

vdP

van der Pauw

VRH

variable range hopping

XPS

X-ray photoelectron spectroscopy

μ

carrier mobility (e = electron mobility, h = hole mobility)

σ

conductivity

Biographies

Lilia S. Xie is a Ph.D. student and an NSF Graduate Research Fellow in Mircea Dincă’s group at MIT. Her current research focuses on electrically conductive metal–organic frameworks with through-space charge transport pathways. She received her A.B. in chemistry in 2014 from Princeton University, where she worked with Robert Cava on the crystal growth of topological semimetals and superconductors.

Grigorii Skorupskii is a Ph.D. student in Mircea Dincă’s group at MIT. His research focuses on charge transport in metal–organic frameworks with extended conjugation conductivity pathways. He received his B.Sc. in materials science in 2015 from Moscow State University where he worked on metal-ion battery electrode materials.

Mircea Dincă is a Professor in the Department of Chemistry at MIT. His group’s research is broadly focused on understanding and changing materials’ physical and chemical properties through means that are not typically applicable to solids. He also gets excited about making new materials that combine canonically antithetical properties, such as porosity and electrical transport, to yield something that is greater than the sum of its parts. Educated at Princeton University (A.B. in Chemistry, 2003) and UC Berkeley (PhD in Inorganic Chemistry, 2008), he aspires to one day create and control (chemical) disorder.

Author Contributions

^† L.S.X. and G.S. contributed equally to this work.

The authors declare no competing financial interest.