Organised chaos: entropy in hybrid inorganic-organic systems and other materials

Entropically driven melting of Cu-based 1D coordination polymers

We investigated the melting behavior of four CPs with one-dimensional structures from a thermodynamic point-of-view. The difference in melting points depending on the crystal structures is observed. The interactions within the crystals were analyzed using DFT calculations. These analyses suggest that entropic terms dominate the melting points.

Functional metal-organic liquids

For decades, the study of coordination polymers (CPs) and metal-organic frameworks (MOFs) has been limited primarily to their behavior as crystalline solids. In recent years, there has been increasing evidence that they can undergo reversible crystal-to-liquid transitions. However, their "liquid" states have primarily been considered intermediate states, and their diverse properties and applications of the liquid itself have been overlooked. As we learn from organic polymers, ceramics, and metals, understanding the structures and properties of liquid states is essential for exploring new properties and functions that are not achievable in their crystalline state. This review presents state-of-the-art research on the liquid states of CPs and MOFs while discussing the fundamental concepts involved in controlling them. We consider the different types of crystal-to-liquid transitions found in CPs and MOFs while extending the interpretation toward other functional metal-organic liquids, such as metal-containing ionic liquids and porous liquids, and try to suggest the unique features of CP/MOF liquids. We highlight their potential applications and present an outlook for future opportunities.

Two-dimensional lead halide perovskite lateral homojunctions enabled by phase pinning

Two-dimensional organic-inorganic hybrid halide perovskites possess diverse structural polymorphs with versatile physical properties, which can be controlled by order-disorder transition of the spacer cation, making them attractive for constructing semiconductor homojunctions. Here, we demonstrate a space-cation-dopant-induced phase stabilization approach to creating a lateral homojunction composed of ordered and disordered phases within a two-dimensional perovskite. By doping a small quantity of pentylammonium into (butylammonium)2PbI4 or vice versa, we effectively suppress the ordering transition of the spacer cation and the associated out-of-plane octahedral tilting in the inorganic framework, resulting in phase pining of the disordered phase when decreasing temperature or increasing pressure. This enables epitaxial growth of a two-dimensional perovskite homojunction with tunable optical properties under temperature and pressure stimuli, as well as directional exciton diffusion across the interface. Our results demonstrate a previously unexplored strategy for constructing two-dimensional perovskite heterostructures by thermodynamic tuning and spacer cation doping.

Rational Design of 2D Metal Halide Perovskites with Low Congruent Melting Temperature and Large Melt-Processable Window

Metal halide perovskites (MHPs) have garnered significant attention due to their distinctive optical and electronic properties, coupled with excellent processability. However, the thermal characteristics of these materials are often overlooked, which can be harnessed to cater to diverse application scenarios. We showcase the efficacy of lowering the congruent melting temperature (Tm) of layered 2D MHPs by employing a strategy that involves the modification of flexible alkylammonium through N-methylation and I-substitution. Structural-property analysis reveals that the N-methylation and I-substitution play pivotal roles in reducing hydrogen bond interactions between the organic components and inorganic parts, lowering the rotational symmetry number of the cation and restricting the residual motion of the cations. Additional I···I interactions enhance intermolecular interactions and lead to improved molten stability, as evidenced by a higher viscosity. The 2D MHPs discussed in this study exhibit low Tm and wide melt-processable windows, e.g., (DMIPA)2PbI4 showcasing a low Tm of 98 °C and large melt-processable window of 145 °C. The efficacy of the strategy was further validated when applied to bromine-substituted 2D MHPs. Lowering the Tm and enhancing the molten stability of the MHPs hold great promise for various applications, including glass formation, preparation of high-quality films for photodetection, and fabrication of flexible devices.

Natural Exponential and Three-Dimensional Chaotic System

Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.

Dynamics in the ordered and disordered phases of barocaloric adamantane

High-entropy order-disorder phase transitions can be used for efficient and eco-friendly barocaloric solid-state cooling. Here the barocaloric effect is reported in an archetypal plastic crystal, adamantane. Adamantane has a colossal isothermally reversible entropy change of 106 J K^-1 kg^-1. Extremely low hysteresis means that this can be accessed at pressure differences less than 200 bar. Configurational entropy can only account for about 40% of the total entropy change; the remainder is due to vibrational effects. Using neutron spectroscopy and supercell lattice dynamics calculations, it is found that this vibrational entropy change is mainly caused by softening in the high-entropy phase of acoustic modes that correspond to molecular rotations. We attribute this difference in the dynamics to the contrast between an 'interlocked' state in the low-entropy phase and sphere-like behaviour in the high-entropy phase. Although adamantane is a simple van der Waals solid with near-spherical molecules, this approach can be leveraged for the design of more complex barocaloric molecular crystals. Moreover, this study shows that supercell lattice dynamics calculations can accurately map the effect of orientational disorder on the phonon spectrum, paving the way for studying the vibrational entropy, thermal conductivity, and other thermodynamic effects in more complex materials.

Origin of Ferroelectricity in Two Prototypical Hybrid Organic-Inorganic Perovskites

Hybrid organic-inorganic perovskite (HOIP) ferroelectrics are attracting considerable interest because of their high performance, ease of synthesis, and lightweight. However, the intrinsic thermodynamic origins of their ferroelectric transitions remain insufficiently understood. Here, we identify the nature of the ferroelectric phase transitions in displacive [(CH₃)₂NH₂][Mn(N₃)₃] and order-disorder type [(CH₃)₂NH₂][Mn(HCOO)₃] via spatially resolved structural analysis and ab initio lattice dynamics calculations. Our results demonstrate that the vibrational entropy change of the extended perovskite lattice drives the ferroelectric transition in the former and also contributes importantly to that of the latter along with the rotational entropy change of the A-site. This finding not only reveals the delicate atomic dynamics in ferroelectric HOIPs but also highlights that both the local and extended fluctuation of the hybrid perovskite lattice can be manipulated for creating ferroelectricity by taking advantages of their abundant atomic, electronic, and phononic degrees of freedom.

The micromechanical model to computationally investigate cooperative and correlated phenomena in metal-organic frameworks

Computational insight into the impact of cooperative phenomena and correlated spatial disorder on the macroscopic behaviour of metal-organic frameworks (MOFs) is essential in order to consciously engineer these phenomena for targeted applications. However, the spatial extent of these effects, ranging over hundreds of nanometres, limits the applicability of current state-of-the-art computational tools in this field. To obtain a fundamental understanding of these long-range effects, the micromechanical model is introduced here. This model overcomes the challenges associated with conventional coarse-graining techniques by exploiting the natural partitioning of a MOF material into unit cells. By adopting the elastic deformation energy as the central quantity, the micromechanical model hierarchically builds on experimentally accessible input parameters that are obtained from atomistic quantum mechanical or force field simulations. As a result, the here derived micromechanical equations of motion can be adopted to shed light on the effect of long-range cooperative phenomena and correlated spatial disorder on the performance of mesoscale MOF materials.

Structural flexibility in crystalline coordination polymers: a journey along the underlying free energy landscape

In this perspective, we discuss structural flexibility in crystalline coordination polymers. We identify that the underlying free energy landscape unites scientific disciplines, and discuss key areas to advanced the field.

Correlated disorder in metal–organic frameworks

Metal–organic frameworks host many types of compositional and structural disorder. In this Highlight article we explore cases where this disorder is correlated, rather than random.

Unraveling the thermodynamic criteria for size-dependent spontaneous phase separation in soft porous crystals

Soft porous crystals (SPCs) harbor a great potential as functional nanoporous materials owing to their stimuli-induced and tuneable morphing between different crystalline phases. These large-amplitude phase transitions are often assumed to occur cooperatively throughout the whole material, which thereby retains its perfect crystalline order. Here, we disprove this paradigm through mesoscale first-principles based molecular dynamics simulations, demonstrating that morphological transitions do induce spatial disorder under the form of interfacial defects and give rise to yet unidentified phase coexistence within a given sample. We hypothesize that this phase coexistence can be stabilized by carefully tuning the experimental control variables through, e.g., temperature or pressure quenching. The observed spatial disorder helps to rationalize yet elusive phenomena in SPCs, such as the impact of crystal downsizing on their flexible nature, thereby identifying the crystal size as a crucial design parameter for stimuli-responsive devices based on SPC nanoparticles and thin films.

Soft porous crystals hold big promise as functional nanoporous materials due to their stimuli responsive flexibility. Here, molecular dynamics simulations reveal a new type of spatial disorder in mesoscale crystals that helps to understand the size-dependency of their phase transition behavior.

Entropy of Simulated Liquids Using Multiscale Cell Correlation

Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K - 1 mol - 1 for GAFF and 9.8 J K - 1 mol - 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.

Defective Metal-Organic Frameworks

The targeted incorporation of defects into crystalline matter allows for the manipulation of many properties and has led to relevant discoveries for optimized and even novel technological applications of materials. It is therefore exciting to see that defects are now recognized to be similarly useful in tailoring properties of metal-organic frameworks (MOFs). For instance, heterogeneous catalysis crucially depends on the number of active catalytic sites as well as on diffusion limitations. By the incorporation of missing linker and missing node defects into MOFs, both parameters can be accessed, improving the catalytic properties. Furthermore, the creation of defects allows for adding properties such as electronic conductivity, which are inherently absent in the parent MOFs. Herein, progress of the rapidly evolving field of the past two years is overviewed, putting a focus on properties that are altered by the incorporation and even tailoring of defects in MOFs. A brief account is also given on the emerging quantitative understanding of defects and heterogeneity in MOFs based on scale-bridging computational modeling and simulations.

Stimuli-triggered reversible switching mechanism between H- and J-type supramolecular assemblies of cationic porphyrins adsorbed on tungsten(VI) oxide surface

Supramolecular organic dye–inorganic semiconductor nanocrystal assemblies are potentially useful in a broad range of technologies and applications, including photovoltaic systems, but the molecular basis of the adsorption of dye molecules onto the semiconductor surfaces remains poorly understood. Herein, we investigated the pH-dependent adsorption and conformational change of two cationic porphyrin stereoisomers [5,10-diphenyl-15,20-di([Formula: see text]-methyl-4-pyridyl)porphyrin (cis-DMPyP) and 5,15-diphenyl-10,20-di([Formula: see text]-methyl-4-pyridyl)porphyrin (trans-DMPyP)] on the tungsten(VI) oxide (WO[Formula: see text] colloid nanoparticle in aqueous media by means of UV-vis absorption spectroscopy. In accordance with the combination of a modified Langmuir adsorption model and Kasha’s exciton coupling model, the molecular orientation and stacking arrangement of DMPyP derivatives on the WO[Formula: see text] colloid surface are discussed in detail. In the trans-DMPyP/WO[Formula: see text] aqueous system, trans-DMPyP molecules adopted flat-on orientation with respect to the WO[Formula: see text] colloid surface and eventually formed head-to-tail [Formula: see text]-dimers regardless of pH conditions. cis-DMPyP molecules in the acidic system also lay flat-on and mainly formed [Formula: see text]-dimers on the WO[Formula: see text] colloid surface, whereas ones in the neutral system exhibited a dominant edge-on orientation and had a higher tendency to form face-to-face [Formula: see text]-dimers. Additionally, we have also convincingly demonstrated the pH-triggered switchable [Formula: see text]-stacking geometry of cis-DMPyP molecules from [Formula: see text]- to [Formula: see text]-dimer and vice versa on the WO[Formula: see text] colloid surface. Such findings will undoubtedly provide a pertinent guideline for the rational design of stimuli-responsive organic-inorganic materials.

How Strong Is the Hydrogen Bond in Hybrid Perovskites?

Hybrid organic-inorganic perovskites represent a special class of metal-organic framework where a molecular cation is encased in an anionic cage. The molecule-cage interaction influences phase stability, phase transformations, and the molecular dynamics. We examine the hydrogen bonding in four AmBX₃ formate perovskites: [Am]Zn(HCOO)₃, with Am⁺ = hydrazinium (NH₂NH₃⁺), guanidinium (C(NH₂)₃⁺), dimethylammonium (CH₃)₂NH₂⁺, and azetidinium (CH₂)₃NH₂⁺. We develop a scheme to quantify the strength of hydrogen bonding in these systems from first-principles, which separates the electrostatic interactions between the amine (Am⁺) and the BX₃^- cage. The hydrogen-bonding strengths of formate perovskites range from 0.36 to 1.40 eV/cation (8-32 kcalmol^-1). Complementary solid-state nuclear magnetic resonance spectroscopy confirms that strong hydrogen bonding hinders cation mobility. Application of the procedure to hybrid lead halide perovskites (X = Cl, Br, I, Am⁺ = CH₃NH₃⁺, CH(NH₂)₂⁺) shows that these compounds have significantly weaker hydrogen-bonding energies of 0.09 to 0.27 eV/cation (2-6 kcalmol^-1), correlating with lower order-disorder transition temperatures.

Detecting Molecular Rotational Dynamics Complementing the Low-Frequency Terahertz Vibrations in a Zirconium-Based Metal-Organic Framework

We show clear experimental evidence of cooperative terahertz (THz) dynamics observed below 3 THz (∼100  cm^{-1}), for a low-symmetry Zr-based metal-organic framework structure, termed MIL-140A [ZrO(O_{2}C-C_{6}H_{4}-CO_{2})]. Utilizing a combination of high-resolution inelastic neutron scattering and synchrotron radiation far-infrared spectroscopy, we measured low-energy vibrations originating from the hindered rotations of organic linkers, whose energy barriers and detailed dynamics have been elucidated via ab initio density functional theory calculations. The complex pore architecture caused by the THz rotations has been characterized. We discovered an array of soft modes with trampolinelike motions, which could potentially be the source of anomalous mechanical phenomena such as negative thermal expansion. Our results demonstrate coordinated shear dynamics (2.47 THz), a mechanism which we have shown to destabilize the framework structure, in the exact crystallographic direction of the minimum shear modulus (G_{min}).

Giant barocaloric effect in the ferroic organic-inorganic hybrid [TPrA][Mn(dca)3] perovskite under easily accessible pressures

The fast growing family of organic-inorganic hybrid compounds has recently been attracting increased attention owing to the remarkable functional properties (magnetic, multiferroic, optoelectronic, photovoltaic) displayed by some of its members. Here we show that these compounds can also have great potential in the until now unexplored field of solid-state cooling by presenting giant barocaloric effects near room temperature already under easily accessible pressures in the hybrid perovskite [TPrA][Mn(dca)3] (TPrA: tetrapropylammonium, dca: dicyanamide). Moreover, we propose that this will not be an isolated example for such an extraordinary behaviour as many other organic-inorganic hybrids (metal-organic frameworks and coordination polymers) exhibit the basic ingredients to display large caloric effects which can be very sensitive to pressure and other external stimuli. These findings open up new horizons and great opportunities for both organic-inorganic hybrids and for solid-state cooling technologies.

Electroactive Nanoporous Metal Oxides and Chalcogenides by Chemical Design

The archetypal silica- and aluminosilicate-based zeolite-type materials are renowned for wide-ranging applications in heterogeneous catalysis, gas-separation and ion-exchange. Their compositional space can be expanded to include nanoporous metal chalcogenides, exemplified by germanium and tin sulfides and selenides. By comparison with the properties of bulk metal dichalcogenides and their 2D derivatives, these open-framework analogues may be viewed as three-dimensional semiconductors filled with nanometer voids. Applications exist in a range of molecule size and shape discriminating devices. However, what is the electronic structure of nanoporous metal chalcogenides? Herein, materials modeling is used to describe the properties of a homologous series of nanoporous metal chalcogenides denoted np-MX₂, where M = Si, Ge, Sn, Pb, and X = O, S, Se, Te, with Sodalite, LTA and aluminum chromium phosphate-1 structure types. Depending on the choice of metal and anion their properties can be tuned from insulators to semiconductors to metals with additional modification achieved through doping, solid solutions, and inclusion (with fullerene, quantum dots, and hole transport materials). These systems form the basis of a new branch of semiconductor nanochemistry in three dimensions.

Entropic contributions enhance polarity compensation for CeO2(100) surfaces

Surface structure controls the physical and chemical response of materials. Surface polar terminations are appealing because of their unusual properties but they are intrinsically unstable. Several mechanisms, namely metallization, adsorption, and ordered reconstructions, can remove thermodynamic penalties rendering polar surfaces partially stable. Here, for CeO₂(100), we report a complementary stabilization mechanism based on surface disorder that has been unravelled through theoretical simulations that: account for surface energies and configurational entropies; show the importance of the ion distribution degeneracy; and identify low diffusion barriers between conformations that ensure equilibration. Disordered configurations in oxides might also be further stabilized by preferential adsorption of water. The entropic stabilization term will appear for surfaces with a high number of empty sites, typically achieved when removing part of the ions in a polar termination to make the layer charge zero. Assessing the impact of surface disorder when establishing new structure-activity relationships remains a challenge.

Variable temperature and high-pressure crystal chemistry of perovskite formamidinium lead iodide: a single crystal X-ray diffraction and computational study

Single crystals of [(NH₂)₂CH]PbI₃ undergo a cubic-to-tetragonal phase transition at low temperature and high pressure.

Designing porous electronic thin-film devices: band offsets and heteroepitaxy

Increasing numbers of electrically active porous framework materials are being reported, with conductivities that make them attractive for technological applications. As design strategies for efficient carrier transport emerge, the next challenge is to incorporate the materials into a functioning device. In thin-film devices interface effects are of critical importance to overall function. In this article we present a method to identify compatible materials combinations to achieve mechanically robust, electronically optimal pairings. The computational screening is based on a two-step procedure: (i) matching of lattice constants to ensure interfaces with minimal epitaxial strain and therefore maximal mechanical and chemical stability; (ii) matching of absolute electron energies to construct energy-band-alignment diagrams, which can be used to screen for particular electronic applications. We apply the methodology to search for zeolitic imidazolate framework (ZIF) type materials that are compatible with native metal electrodes. The procedure allows us to predict simple routes for electrochemical deposition of ZIFs for application as conductive porous electrodes.

Self-Healing Behavior in a Thermo-Mechanically Responsive Cocrystal during a Reversible Phase Transition

The molecular-level motions of a coronene-based supramolecular rotator are amplified into macroscopic changes of crystals by co-assembly of coronene and TCNB (1,2,4,5-tetracyanobenzene) into a charge-transfer complex. The as-prepared cocrystals show remarkable self-healing behavior and thermo-mechanical responses during thermally-induced reversible single-crystal-to-single-crystal (SCSC) phase transitions. Comprehensive analysis of the microscopic observations as well as differential scanning calorimetry (DSC) measurements and crystal habits reveal that a thermally-reduced-rate-dependent dynamic character exists in the phase transition. The crystallographic studies show that the global similarity of the packing patterns of both phases with local differences, such as molecular stacking sequence and orientations, should be the origin of the self-healing behavior of these crystals.

Phase transitions and chromium(iii) luminescence in perovskite-type [C2H5NH3][Na0.5CrxAl0.5−x(HCOO)3] (x = 0, 0.025, 0.5), correlated with structural, dielectric and phonon properties

We report the synthesis, crystal structure, dielectric, vibrational and emission spectra of heterometallic MOFs, [C₂H₅NH₃][Na_0.5Cr_xAl_0.5−x(HCOO)₃] (x = 0, 0.025, 0.5).

Magnetic coupling in a hybrid Mn(ii) acetylene dicarboxylate

The design of ligands that mediate through-bond long range super-exchange in metal–organic hybrid materials would expand chemical space beyond the commonly observed short range, low temperature magnetic ordering.