Pushing the Limits of Heat Conduction in Covalent Organic Frameworks Through High-Throughput Screening of Their Thermal Conductivity

Tailor-made materials featuring large tunability in their thermal transport properties are highly sought-after for diverse applications. However, achieving `user-defined' thermal transport in a single class of material system with tunability across a wide range of thermal conductivity values requires a thorough understanding of the structure-property relationships, which has proven to be challenging. Herein, large-scale computational screening of covalent organic frameworks (COFs) for thermal conductivity is performed, providing a comprehensive understanding of their structure-property relationships by leveraging systematic atomistic simulations of 10,750 COFs with 651 distinct organic linkers. Through the data-driven approach, it is shown that by strategic modulation of their chemical and structural features, the thermal conductivity can be tuned from ultralow (≈0.02 W m-1 K-1) to exceptionally high (≈50 W m-1 K-1) values. It is revealed that achieving high thermal conductivity in COFs requires their assembly through carbon-carbon linkages with densities greater than 500 kg m-3, nominal void fractions (in the range of ≈0.6-0.9) and highly aligned polymeric chains along the heat flow direction. Following these criteria, it is shown that these flexible polymeric materials can possess exceptionally high thermal conductivities, on par with several fully dense inorganic materials. As such, the work reveals that COFs mark a new regime of materials design that combines high thermal conductivities with low densities.

An automated protocol to construct flexibility parameters for classical forcefields: applications to metal-organic frameworks

In this work, forcefield flexibility parameters were constructed and validated for more than 100 metal-organic frameworks (MOFs). We used atom typing to identify bond types, angle types, and dihedral types associated with bond stretches, angle bends, dihedral torsions, and other flexibility interactions. Our work used Manz's angle-bending and dihedral-torsion model potentials. For a crystal structure containing N atoms in its unit cell, the number of independent flexibility interactions is 3(N atoms - 1). Because the number of bonds, angles, and dihedrals is normally much larger than 3(N atoms - 1), these internal coordinates are redundant. To reduce (but not eliminate) this redundancy, our protocol prunes dihedral types in a way that preserves symmetry equivalency. Next, each dihedral type is classified as non-rotatable, hindered, rotatable, or linear. We introduce a smart selection method that identifies which particular torsion modes are important for each rotatable dihedral type. Then, we computed the force constants for all flexibility interactions together via LASSO regression (i.e., regularized linear least-squares fitting) of the training dataset. LASSO automatically identifies and removes unimportant forcefield interactions. For each MOF, the reference dataset was quantum-mechanically-computed in VASP via DFT with dispersion and included: (i) finite-displacement calculations along every independent atom translation mode, (ii) geometries randomly sampled via ab initio molecular dynamics (AIMD), (iii) the optimized ground-state geometry using experimental lattice parameters, and (iv) rigid torsion scans for each rotatable dihedral type. After training, the flexibility model was validated across geometries that were not part of the training dataset. For each MOF, we computed the goodness of fit (R-squared value) and the root-mean-squared error (RMSE) separately for the training and validation datasets. We compared flexibility models with and without bond-bond cross terms. Even without cross terms, the model yielded R-squared values of 0.910 (avg across all MOFs) ± 0.018 (st. dev.) for atom-in-material forces in the validation datasets. Our SAVESTEPS protocol should find widespread applications to parameterize flexible forcefields for material datasets. We performed molecular dynamics simulations using these flexibility parameters to compute heat capacities and thermal expansion coefficients for two MOFs.

Reversible and high-contrast thermal conductivity switching in a flexible covalent organic framework possessing negative Poisson's ratio

The ability to dynamically and reversibly control thermal transport in solid-state systems can redefine and propel a plethora of technologies including thermal switches, diodes, and rectifiers. Current material systems, however, do not possess the swift and large changes in thermal conductivity required for such practical applications. For instance, stimuli responsive materials, that can reversibly switch between a high thermal conductivity state and a low thermal conductivity state, are mostly limited to thermal switching ratios in the range of 1.5 to 4. Here, we demonstrate reversible thermal conductivity switching with an unprecedented 18× change in thermal transport in a highly flexible covalent organic framework with revolving imine bonds. The pedal motion of the imine bonds is capable of reversible transformations of the framework from an expanded (low thermal conductivity) to a contracted (high thermal conductivity) phase, which can be triggered through external stimuli such as exposure to guest adsorption and desorption or mechanical strain. We also show that the dynamic imine linkages endow the material with a negative Poisson's ratio, thus marking a regime of materials design that combines low densities with exceptional thermal and mechanical properties.

Reversible Thermal Conductivity Switching Using Flexible Metal-Organic Frameworks

The ability to control thermal transport is critical for the design of thermal rectifiers, logic gates, and transistors, although it remains a challenge to design materials that exhibit large changes in thermal conductivity with switching ratios suitable for practical applications. Here, we propose the use of flexible metal-organic frameworks, which can undergo significant structural changes in response to various stimuli, to achieve tunable switchable thermal conductivity. In particular, we use molecular dynamics simulations to show that the thermal conductivity of the flexible framework Fe(bdp) (bdp2- = 1,4-benzenedipyrazolate) becomes highly anisotropic upon transitioning from the expanded to the collapsed phase, with the conductivity decreasing by nearly an order of magnitude along the direction of compression. Our results add to a small but growing number of studies investigating metal-organic frameworks for thermal transport.

Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations

Metal-organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Thermally Conductive Self-Healing Nanoporous Materials Based on Hydrogen-Bonded Organic Frameworks

Hydrogen-bonded organic frameworks (HOFs) are a class of nanoporous crystalline materials formed by the assembly of organic building blocks that are held together by a network of hydrogen-bonding interactions. Herein, we show that the dynamic and responsive nature of these hydrogen-bonding interactions endows HOFs with a host of unique physical properties that combine ultraflexibility, high thermal conductivities, and the ability to "self-heal". Our systematic atomistic simulations reveal that their unique mechanical properties arise from the ability of the hydrogen-bond arrays to absorb and dissipate energy during deformation. Moreover, we also show that these materials demonstrate relatively high thermal conductivities for porous crystals with low mass densities due to their extended periodic framework structure that is comprised of light atoms. Our results reveal that HOFs mark a new regime of material design combining multifunctional properties that make them ideal candidates for gas storage and separation, flexible electronics, and thermal switching applications.

Exploring the Impact of the Linker Length on Heat Transport in Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are a highly versatile group of porous materials suitable for a broad range of applications, which often crucially depend on the MOFs’ heat transport properties. Nevertheless, detailed relationships between the chemical structure of MOFs and their thermal conductivities are still largely missing. To lay the foundations for developing such relationships, we performed non-equilibrium molecular dynamics simulations to analyze heat transport in a selected set of materials. In particular, we focus on the impact of organic linkers, the inorganic nodes and the interfaces between them. To obtain reliable data, great care was taken to generate and thoroughly benchmark system-specific force fields building on ab-initio-based reference data. To systematically separate the different factors arising from the complex structures of MOF, we also studied a series of suitably designed model systems. Notably, besides the expected trend that longer linkers lead to a reduction in thermal conductivity due to an increase in porosity, they also cause an increase in the interface resistance between the different building blocks of the MOFs. This is relevant insofar as the interface resistance dominates the total thermal resistance of the MOF. Employing suitably designed model systems, it can be shown that this dominance of the interface resistance is not the consequence of the specific, potentially weak, chemical interactions between nodes and linkers. Rather, it is inherent to the framework structures of the MOFs. These findings improve our understanding of heat transport in MOFs and will help in tailoring the thermal conductivities of MOFs for specific applications.

Pore Size Dictates Anisotropic Thermal Conductivity of Two-Dimensional Covalent Organic Frameworks with Adsorbed Gases

Two-dimensional covalent organic frameworks (2D COFs) are a class of modular polymeric crystals with high porosities and large surface areas, which position them as ideal candidates for applications in gas storage and separation technologies. In this work, we study the influence of pore geometry on the anisotropic heat transfer mechanisms in 2D COFs through systematic atomistic simulations. More specifically, by studying COFs with varying pore sizes and gas densities, we demonstrate that the cross-plane thermal conductivity along the direction of the laminar pores can either be decreased due to solid-gas scattering (for COFs with relatively smaller pores that are ≲2 nm) or increased due to additional heat transfer pathways introduced by the gas adsorbates (for COFs with relatively larger pores). Our simulations on COF/methane systems reveal the intricate relationship among gas diffusivities, pore geometries, and solid-gas interactions dictating the modular thermal conductivities in these materials. Along with the understanding of the fundamental nature of gas diffusion and heat conduction in the porous framework crystals, our results can also help guide the design of efficient 2D polymeric crystals for applications with improved gas storage, catalysis, and separation capabilities.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

Molecular Insights into the Correlation between Microstructure and Thermal Conductivity of Zeolitic Imidazolate Frameworks

The thermal conductivity of metal-organic frameworks (MOFs) imposes significant impacts on the thermal transfer performance of related adsorption systems in engineering applications. However, how the structural properties of MOFs affect their thermal conductivities has yet to be unraveled. In this work, the thermal conductivities of 18 zeolitic imidazolate frameworks (ZIFs) were calculated by equilibrium molecular dynamics (MD) simulations. It was revealed that the thermal conductivities of ZIFs were not directly correlated with the commonly investigated structural properties. Thus, two parameters including alignment tensor (A_i) and pathway factor (P_f) were proposed to quantitatively evaluate the orientation and distribution of heat transfer pathways within frameworks, which was demonstrated to correlate better with the thermal conductivities of ZIFs. This study provides new insights into the thermal transfer mechanism within framework-based nanoporous materials, which may also facilitate fundamental understanding and guide the rational design of porous crystals with the thermal conductivity of interest.