## Introduction

Metal-organic frameworks (MOFs) are a class of porous crystals with extremely high surface areas that have been heralded as promising materials for a wide range of gas storage and separations applications1,2,3. In particular, three major energy applications stand to be improved with appropriately tailored MOFs: (1) hydrogen storage4,5,6,7, (2) natural gas storage8,9, and (3) carbon capture10,11,12,13. The predominant focus of previous MOF studies has been on the density of the adsorbed gas (usually the higher the better) or the relative difference in adsorbed densities between two or more gas species for separations applications (e.g., high CO2 adsorption relative to N2 and H2O adsorption for carbon capture). However, a critical property for the practical implementation of MOFs for gas adsorption applications has been mostly overlooked: thermal conductivity (k).

To fulfill their promise as practical industrial gas adsorbents, MOFs need to have both optimal gas adsorption and thermal transport properties. Relative to gas adsorption, however, little is understood about how to tune thermal conductivity in MOFs. Broadly, MOFs are thermal insulators, with thermal conductivities typically <2 W m−1 K−1 at room-temperature16,17,18. Moreover, it has been an open question as to how adsorbates influence MOF thermal conductivity. This particular question is critical to evaluating MOFs for potential use in gas storage and separations. If adsorbates facilitate thermal transport, then the challenges associated with rapid filling are mitigated, but if they impede thermal transport, the problems are exacerbated.

Studies of thermal transport in MOFs are limited16,19,20,21,22,23,24,25,26,27. A subset have considered the influence of adsorbates, yet drew conflicting conclusions21,23,24. Three of the authors of this article previously suggested, on the basis of molecular simulations, that the presence of an adsorbed gas reduces the thermal conductivity of MOFs due to additional scattering of framework phonons caused by gas-framework collisions23,28. Yet another molecular simulation-based study suggested that thermal conductivity increases upon gas adsorption due to additional heat transfer channels24. These contrasting descriptions of the adsorbate effect are depicted in Fig. 1 as “new heat pathways” and “extra phonon scattering”.

Experimental evidence regarding the effect of adsorbates on thermal conductivity in MOFs has also been inconclusive17,21,29. Schlemminger et al. 29 measured the thermal conductivity of MOF-5 powders30, compressed into pellets, in the presence of N2, He, Ar, and H2 gas at various pressures (0.25–15 MPa for H2). For higher H2 gas loadings, they observed an increase in the system thermal conductivity that was nevertheless lower than the pristine MOF-5 single crystal thermal conductivity. Although thermal transport in powders and pellets, where microcrystalline MOF granules are separated by significant void space, can be representative of behavior in practical adsorbent technologies, these systems provide little insight into the intrinsic nanoscale heat transfer mechanisms taking place within the MOF crystalline phase. Besides powders, thermal transport in the presence of adsorbates has been measured in MOF thin films. Cui et al.21 considered N2 and C6F14 adsorption at ambient pressures in thin films of the MOF ZIF-831 and found no significant change in the thermal conductivity. Erickson et al.17 measured thermal conductivity in TNCQ-loaded HKUST-132 thin films, but without experimental comparison to the unloaded (i.e., pristine) case.

What has so far been lacking are measurements of thermal conductivity changes within a MOF crystal caused by adsorption. In this article, we report experimental and theoretical investigations of the effect of different adsorbates, including water, methanol, and ethanol, on the thermal conductivity of the MOF HKUST-1 in both single crystal and thin film forms. The experimental measurements were performed independently by labs at Carnegie Mellon University (CMU) and at the University of Virginia (UVA) using two different optical methods: frequency-domain thermoreflectance (FDTR)33 and time-domain thermoreflectance (TDTR)34, respectively. FDTR measurements were carried out on single crystals synthesized at Northwestern University (NU). TDTR measurements were conducted on thin films prepared at the Karlsruhe Institute of Technology (KIT). The theoretical evaluation was performed using classical molecular dynamics (MD) modeling and the Green–Kubo method for predicting thermal conductivity23,28. Both our simulation and experimental results show that the thermal conductivity of HKUST˗1 decreases upon loading with different adsorbate molecules. These results demonstrate that the additional phonon scattering induced by adsorption can dominate the thermal conductivity change by overcoming the creation of additional heat transfer pathways.

## Results

### Methodological overview

Although a driving motivation for this research revolves around the adsorption of gases, we opted to focus the experimental work on liquid adsorbates for two reasons. Firstly, in lieu of performing challenging in situ thermal conductivity measurements at extremely high pressures, pores filled with liquid adsorbates have similar densities to pores with gaseous adsorbates at saturation loading. Secondly, our molecular modeling predictions were insensitive to whether the adsorbate belonged in a liquid or gas phase outside of the MOF (see Supplementary Fig. 1.1). Therefore, if the experiments validated the modeling predictions for liquid adsorbates, the results would provide support for our predictions on gas adsorbates at high pressures. Nevertheless, there may be differences between gas and liquid adsorption in MOFs that are not captured by our molecular models, and assessing the significance of these discrepancies would ultimately require in situ thermal conductivity measurements at high gas pressures.

Equilibrium MD simulations were run at a temperature of 300 K using the large-scale atomic/molecular massively parallel simulator (LAMMPS)35 to model HKUST-1 in vacuum and in the presence of liquid water, methanol, and ethanol. The Green–Kubo method36 was used to predict the thermal conductivity of each structure (see Supplementary Note 1 and Eq. (S1.1)). We showed in prior work23,28 that the trend of adsorption-induced reduction in the thermal conductivity of porous crystals was insensitive to the choice of force field and its parameterization. As such, the objective of our molecular-modeling predictions was to investigate changes in thermal conductivity relative to the pristine case rather than to predict absolute values.

### Experimental setup

Our parallel experimental measurements on HKUST-1 single crystals and thin films are summarized in Fig. 2. HKUST-1 single crystals, typically ~200 μm in size, were mounted onto a silicon carrier wafer and an Au/Pt transducer layer was sputtered onto them to facilitate thermoreflectance measurements (Fig. 2a). To ensure that liquid adsorbates could enter the crystal freely without being impeded by the Au/Pt transducer layer, ~20% of the area was blocked with a strip of Kapton tape, which was then removed after the transducer layer was sputtered. The partially coated HKUST-1 single crystals were thermally activated, then immersed in methanol, ethanol, or water (see “Methods” section). After removing from the liquid and inspecting optically for signs of degradation (Fig. 2c), each crystal was briefly dried with N2 and then measured using FDTR to determine its thermal conductivity. (See Supplementary Note 3 for HKUST-1 crystal synthesis details and Supplementary Note 5 for additional FTDR measurement details.) Separately, polycrystalline HKUST-1 surface-anchored MOF (SURMOF) thin films were self-assembled onto the metal side of Al/silica glass and Au/silica glass substrates using layer-by-layer liquid phase epitaxy37 (see Fig. 2b, d and Supplementary Note 2 for SURMOF fabrication details). Powder X-ray diffraction (PXRD) measurements confirmed the same crystal structure on the films as the ~200 μm single crystals (Fig. 2e). The SURMOFs were cut into four sections, three of which were infiltrated with either methanol, ethanol, or water. Only the SURMOF assembled on Au was submerged in water so as to reduce the effects of oxidation likely to occur with the Al in the Al/silica substrates. The thermal conductivities of the pristine and infiltrated HKUST-1 thin films, for a range of film thicknesses, were then measured using TDTR17,38,39. See Supplementary Note 4 for TDTR measurement details.

### Thermoreflectance measurements and simulation results

For the pristine HKUST-1 case (i.e., no adsorbates), measured thermal conductivities ranged between 0.44 and 0.73 W m−1 K−1 across all thin film samples, with the single crystals at the higher end of that range at 0.69 ± 0.05 W m−1 K−1. These values are in the typical range of other room temperature MOF thermal conductivity measurements, such as IRMOF-1 (0.32 W m−1 K−1)16, ZIF-8 (0.32 W m−1 K−1)21, and perovskite-like MOF-1 (1.3 W m−1 K−1)18. Our single crystal value for HKUST-1 is higher than previously reported by Chae et al. (0.26 W m−1 K−1)22. One possible explanation for this discrepancy is that our HKUST-1 samples were thermally activated for a longer period of time and at higher temperatures (see “Methods” section) than that prior study. If their samples contained residual solvent molecules, a reduced thermal conductivity would be consistent with our observations.

Both FTDR measurements on HKUST-1 single crystals and TDTR measurements on HKUST-1 thin films followed the same trend as our MD-based predictions: the presence of the selected adsorbates reduced thermal conductivity (Fig. 3a). The reductions ranged from 40% to 80% depending on the adsorbate and methodology. Moreover, the relevant timescale associated with heat dissipation in rapid adsorption applications is inversely proportional to thermal diffusivity (k/ρc, where ρ is density and c is heat capacity), which is even more greatly impacted than thermal conductivity by the presence of these adsorbates (Fig. 3b). In the case of adsorbed water, for example, a threefold thermal conductivity reduction, coupled with a sixfold increase in volumetric heat capacity (ρc), leads to an 18-fold reduction in thermal diffusivity. This sensitivity suggests that it may be important to carefully choose MOFs with appropriate thermal properties for rapid gas adsorption applications. As an illustration of the potential impact of this phenomenon, consider the idealized (worst) case where (1) a monolithic single-crystal MOF takes up the entire volume of a natural gas fuel tank (as opposed to the more common form factor of a tightly packed powder), and (2) that gaseous adsorbates at high pressure like methane yield similar thermal conductivity reductions to the liquid adsorbates we measured (as indicated by our simulations, see Supplementary Fig. 1.1b). In this case, if the thermal diffusivity reduction was not taken into account, then adsorption-induced effects would result in filling times more than an order-of-magnitude greater than expected.

These observations support our earlier simulation-based findings that gaseous adsorbates reduce thermal conductivity in porous crystals of varying pore size and shape23,28. It appears that the presence of adsorbates in certain MOFs, despite creating more pathways for heat conduction, primarily acts to disrupt thermal transport in the crystalline framework. Our earlier work suggests that the mechanism of this disruption is increased phonon scattering due to adsorbate-framework collisions23.

### Origins of adsorbate-induced thermal conductivity reduction

In the context of discovering MOFs for rapid adsorption/desorption applications, the adsorbate is typically a given, and the MOF being sought must have, among other properties, high intrinsic thermal conductivity. In such contexts, especially when the adsorbates are gases (which are poor heat conductors), it is likely that MOFs will experience thermal conductivity reductions during adsorption similar to what we observed in this study.

### Thermal conductivity reduction in the adsorbate phase

Surprisingly, our measured thermal conductivity of HKUST-1 with adsorbed water (0.21 ± 0.08 W m−1 K−1) was not only less than that of pristine HKUST-1 (0.69 ± 0.05 W m−1 K−1), but was also less than would be expected for bulk liquid water occupying the same contiguous void space (0.6 W m−1 K−1 × 68% void fraction [ϕ] = 0.41 W m−1 K−1). Thus, not only does the adsorbate reduce the adsorbent MOF’s intrinsic thermal conductivity, but confinement in the MOF pore geometry also reduces the effective thermal conductivity of the adsorbate itself. This finding highlights the inability of effective medium approximations (EMAs) to account for thermal transport in MOF–adsorbate systems. Since MOF–adsorbate composites form bi-continuous structures, any EMA will predict a composite thermal conductivity that is in between that of the MOF (scaled to an equivalent fully dense value: $$k_{{\mathrm{fully - dense}}} = k_{{\mathrm{bulk}}} \times \left( {1 - \phi } \right)^{ - 1}$$) and the pure phase of the adsorbate47. Indeed, even applying a simple rule-of-mixtures (i.e., $$k_{{\mathrm{MOF + adsorbate}}} = k_{{\mathrm{MOF,pristine}}} + \phi \times k_{{\mathrm{adsorbate,bulk}}}$$) significantly overpredicts the thermal conductivities of HKUST-1 with all tested adsorbates (Fig. 5a).

Further MD simulations suggest that the water inside HKUST-1 has a lower thermal conductivity than bulk liquid water even at the saturation density (Fig. 5b, c). Here we estimated the contribution of water to the thermal conductivity of the MOF–adsorbate composite by considering a system with a rigid MOF (i.e., MOF atoms are frozen and unable to vibrate). In this case, the system thermal conductivity has only contributions from the water phase, since the rigid MOF cannot transfer heat. Subsequently, the intrinsic thermal conductivity of the MOF was obtained by subtracting those contributions of water from the MOF–adsorbate composite thermal conductivity. This procedure indicated that although the thermal conductivity of water inside the MOF increased with adsorption density, even at saturation its thermal conductivity (0.30 W m−1 K−1) was lower than what would be expected from pure water occupying the same space (the MD-based bulk water thermal conductivity is 0.87 W m−1 K−1, for which a rule-of-mixtures approach would suggest a value of 0.59 W m−1 K−1 at a 68% void fraction).

We considered two possible causes of the observed thermal conductivity reduction in the adsorbate phase for water: (1) low connectivity, due to small pore apertures, between the volumes of water contained in neighboring pores of the MOF, and (2) framework-induced disruption of the natural hydrogen-bonding network. Calculations of radial distribution functions (see Supplementary Fig. 1.2) did not show any meaningful change in the water structure in the adsorbed versus pure phases, suggesting that framework-induced disruption of the natural hydrogen-bonding network is an unlikely origin of the reduced thermal conductivity. Hypothetically, if the aperture sizes between the pores of HKUST-1 were reduced to zero, the pockets of water in the pores would be disconnected and unable to transfer heat directly between each other. For the small but non-zero aperture sizes in HKUST-1, the transport of water between pores is restricted in a way that decreases thermal transport in the adsorbed water phase (see Supplementary Note 6 for further details).

Finally, we note that the MD modeling predicts that the thermal conductivity of HKUST-1 drops sharply after only a small amount of water is loaded, with gradual further reductions as the water density increases (see Fig. 5c). This sharp drop suggests that even a small amount of adsorbate loading can, in some cases, contribute significantly to phonon scattering in the framework. At low adsorbate densities, this reduction is likely to depend on the specific nature of the adsorbate–adsorbent interaction (e.g., weakly interacting adsorbates at low densities may not significantly perturb MOF thermal conductivity). This result suggests that optimizing thermal transport may require carefully matching MOF–adsorbate pairs that mitigate such sharp drops in thermal conductivity.

## Discussion

It is important to distinguish these observations of thermal transport within a crystalline MOF from prior, seemingly contradictory, observations of MOF powders29, which show an increase in thermal conductivity upon infiltration with gas. Powder thermal resistances are typically dominated by contact between particles, so that the introduction of a gas helps heat to transfer from one particle to another, exemplified by those systems’ pressure-dependent thermal conductivities48. Also distinct from MOFs are porous amorphous materials, such as aerogels, which show an increased thermal conductivity with gas pressure49. Aerogels have significantly higher porosities compared to MOFs ($$\phi \, > \, 99\%$$). As such, their pristine thermal conductivities are very low (≈0.01 W m−1 K−1). Furthermore, unlike MOFs, their large pores are comparable to, or larger, than the bulk gas molecule mean free paths50. As such, the molecules of a gas that have infiltrated an aerogel scatter with the solid infrequently and can have a significant thermal conductivity of their own.

As a broad material class, the generality of adsorbate-induced thermal conductivity reduction in MOFs is still to be determined; it is possible that a MOF with a sufficiently low thermal conductivity in combination with highly conductive adsorbate may behave in an opposite way. However, our experimental observations of HKUST-1 with liquid adsorbates are the first direct evidence of this phenomenon and our molecular simulations suggest that certain gaseous adsorbates at high pressure would have a similar impact on thermal conductivity.

## Methods

### MD modeling

Equilibrium MD simulations were run at a temperature of 300 K using the LAMMPS35 to model HKUST-1 in vacuum and in the presence of liquid water, methanol, and ethanol, as well as high-pressure hydrogen and methane gases (see Supplementary Fig. 1.1). The Green–Kubo method36 was used to predict the thermal conductivity of each structure (see Supplementary Note 1 and Eq. (S1.1)). To obtain the adsorbate densities, grand canonical Monte Carlo (GCMC) simulations were performed using the RASPA software package51 at a pressure of 1 bar for liquid adsorbates and 35 and 100 bar for methane and hydrogen, respectively. For both MD and GCMC, force fields were used without any parameter fitting specific to this work; all parameters were developed by others (see more details in the Supplementary Note 1). We showed in prior work23,28 that the trend of adsorption-induced reduction in the thermal conductivity of porous crystals was insensitive to the choice of force field and its parameterization. As such, our objective was to apply molecular modeling to investigate changes in thermal conductivity relative to the pristine case, rather than to predict absolute values.

### Single crystal HKUST-1 measurements using FDTR

HKUST-1 single crystals were synthesized, activated under vacuum at 150 °C, and characterized at NU (see Supplementary Note 3 for synthesis details). Crystals from the same batch were also sent in non-activated form to CMU and activated using the same procedure. The samples, typically ~200 μm in size, were mounted onto a silicon carrier wafer and a Au/Pt transducer layer was sputtered over them to facilitate thermoreflectance measurements (Fig. 3a). To ensure that liquid adsorbates could enter the crystal freely without being impeded by the Au/Pt transducer layer, ~20% of the area was blocked with a strip of Kapton tape, which was then removed after the transducer layer was sputtered. To measure how the thermal conductivity changed with liquid adsorption, the partially coated HKUST-1 single crystals were immersed in methanol or ethanol for 1 h, or in water for 20 min, immediately following the thermal activation process. These immersion times were found to yield full (i.e., saturation) adsorption in a prior study52. After removing each crystal sample from the liquid, inspecting optically for signs of degradation (Fig. 3c), and briefly drying their surface with N2, FDTR measurements were conducted at room temperature to determine their thermal conductivities. The FDTR lasers were scanned across the crystal until a spot was identified that was sufficiently smooth and flat for the required optical reflectance. (See Supplementary Note 5 for more FTDR measurement details.)

### Thin film HKUST-1 measurements using TDTR

Polycrystalline HKUST-1 SURMOF thin films were self-assembled onto the metal side of Al/silica glass and Au/silica glass substrates using layer-by layer liquid phase epitaxy37 (see Fig. 3b and Supplementary Note 2 for SURMOF fabrication details). PXRD measurements confirmed the same crystal structure on the films as the ~200 μm single crystals synthesized at NU (Fig. 3e). At UVa, the pristine HKUST-1 SURMOF samples were activated52,53 by vacuum thermal annealing at a pressure of 4.5 × 10-6 mbar and a temperature of 150 °C for 12 h. The activated SURMOFs were cut into four sections. Each section was separately infiltrated with methanol, ethanol, and water. As with the single-crystal samples used for FTDR measurements, the SURMOF films were fully submerged for an hour in each of the polar organic solvents and for 20 min in water. Only the SURMOF assembled on Au was submerged in deionized water, so as to reduce the effects of oxidation likely to occur with the Al in the Al/SiO2 substrates. The thermal conductivities of the HKUST-1 thin films in activated pristine form and loaded with different solvents for a range of film thicknesses were then measured using TDTR17,38,39 (Fig. 3g). (See Supplementary Note 4 for more TDTR measurement details.)