Adsorption deformation of microporous composites

Modelling of framework materials at multiple scales: current practices and open questions

The last decade has seen an explosion of the family of framework materials and their study, from both the experimental and computational points of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of material databases and the growing use of machine learning for the prediction of properties. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Metal-organic framework crystal-glass composites

The majority of research into metal-organic frameworks (MOFs) focuses on their crystalline nature. Recent research has revealed solid-liquid transitions within the family, which we use here to create a class of functional, stable and porous composite materials. Described herein is the design, synthesis, and characterisation of MOF crystal-glass composites, formed by dispersing crystalline MOFs within a MOF-glass matrix. The coordinative bonding and chemical structure of a MIL-53 crystalline phase are preserved within the ZIF-62 glass matrix. Whilst separated phases, the interfacial interactions between the closely contacted microdomains improve the mechanical properties of the composite glass. More significantly, the high temperature open pore phase of MIL-53, which spontaneously transforms to a narrow pore upon cooling in the presence of water, is stabilised at room temperature in the crystal-glass composite. This leads to a significant improvement of CO₂ adsorption capacity.

The formation of composite materials has been widely exploited to alter the chemical and physical properties of their components. Here the authors form metal–organic framework (MOF) crystal–glass composites in which a MOF glass matrix stabilises the open pore structure of MIL-53, leading to enhanced CO₂ adsorption.

Effects of Enhanced Flexibility and Pore Size Distribution on Adsorption-Induced Deformation of Mesoporous Materials

Here, we present a new model of adsorption-induced deformation of mesoporous solids. The model is based on a simplified version of local density functional theory in the framework of solvation free energy. Instead of density, which is treated as constant here, we used film thickness and pore radius as order parameters. This allows us to obtain a self-consistent system of equations describing simultaneously the processes of gas adsorption and adsorbent deformation, as well as conditions for capillary condensation and evaporation. In the limit of infinitely rigid pore walls, when the film becomes several monolayers thick, the model reduces to the well-known Derjaguin-Broekhoff-de Boer theory for pores with cylindrical geometry. We have investigated the effects of enhanced flexibility of the solid as well as the influence of pore size distribution on the adsorption/deformation process. The formulation of the theory allows to determine the average pore size and its width from the desorption branch of the strain isotherm only. The model reproduces the nonmonotonic behavior of the strain isotherm at low relative pressure. Furthermore, we discuss the effect of rigidity of the adsorbent on the pore size distribution, showing qualitatively different results of the adsorption isotherms for rigid and highly flexible materials, in particular, the shift of evaporation pressure to lower values and the absence of a limiting value of the loading at high relative pressure. We also discuss the results of the theory with respect to experimental data obtained from the literature.

Controlling relative polymorph stability in soft porous crystals with a barostat

We use Monte Carlo simulations to investigate the thermodynamic behavior of soft porous crystal (SPC) adsorbents under the influence of an external barostat. We consider SPCs that naturally exhibit polymorphism between crystal forms of two distinct pore sizes. In the absence of barostatting, these crystals may be naturally divided into two categories depending on their response to stress applied by the adsorbate fluid: those which macroscopically deform and change the volume of their unit cell ("breathing") and those which instead undergo internal rearrangements that change the adsorbate-accessible volume without modifying the unit cell volume ("gate-opening"). When breathing SPCs have a constant external pressure applied, in addition to the thermodynamic pressure of the adsorbate fluid, we find that the free energy difference between the crystal polymorphs is shifted by a constant amount over the entire course of adsorption. Thus, their relative stability may be easily controlled by the barostat. However, when the crystal is held at a fixed overall pressure, changes to the relative stability of the polymorphs tend to be more complex. We demonstrate a thermodynamic analogy between breathing SPCs held at a fixed pressure and macroscopically rigid gate-opening ones which explains this behavior. Furthermore, we illustrate how this implies that external mechanical forces may be employed to tune the effective free energy profile of an empty SPC, which may open new avenues to engineer the thermodynamic properties of these polymorphic adsorbents, such as selectivity.

Relationship between Pore-size Distribution and Flexibility of Adsorbent Materials: Statistical Mechanics and Future Material Characterization Techniques

Measurement of the pore-size distribution (PSD) via gas adsorption and the so-called "kernel method" is a widely used characterization technique for rigid adsorbents. Yet, standard techniques and analytical equipment are not appropriate to characterize the emerging class of flexible adsorbents that deform in response to the stress imparted by an adsorbate gas, as the PSD is a characteristic of the material that varies with the gas pressure and any other external stresses. Here, we derive the PSD for a flexible adsorbent using statistical mechanics in the osmotic ensemble to draw analogy to the kernel method for rigid materials. The resultant PSD is a function of the ensemble constraints including all imposed stresses and, most importantly, the deformation free energy of the adsorbent material. Consequently, a pressure-dependent PSD is a descriptor of the deformation characteristics of an adsorbent and may be the basis of future material characterization techniques. We discuss how, given a technique for resolving pressure-dependent PSDs, the present statistical mechanical theory could enable a new generation of analytical tools that measure and characterize certain intrinsic material properties of flexible adsorbents via otherwise simple adsorption experiments.

Macroscopic Simulation of Deformation in Soft Microporous Composites

Soft microporous materials exhibit properties, such as gated adsorption and breathing, which are highly desirable for many applications. These properties are largely studied for single crystals; however, many potential applications expect to construct structured or composite systems, examples of which include monoliths and mixed-matrix membranes. Herein, we use finite element methods to predict the macroscopic mechanical response of composite microporous materials. This implementation connects the microscopic treatment of crystalline structures to the response of a macroscopic sample. Our simulations reveal the bulk modulus of an embedded adsorbent within a composite is affected by the thickness and properties of the encapsulating layer. Subsequently, we employ this methodology to examine mixed-matrix membranes and materials of negative linear compressibility. This application of finite element methods allows for unprecedented insight into the mechanical properties of real-world systems and supports the development of composites containing mechanically anomalous porous materials.

Recent advances in the computational chemistry of soft porous crystals

We highlight recent progress in the field of computational chemistry of nanoporous materials, focusing on methods and studies that address the extraordinary dynamic nature of these systems: the high flexibility of their frameworks, the large-scale structural changes upon external physical or chemical stimulation, and the presence of defects and disorder.

Conformation-controlled hydrogen storage in the CAU-1 metal–organic framework

Adsorption induced changes in the CAU-1 structure and guest–guest interactions lead to rearrangements of H₂molecules and enhance hydrogen intake.