Coupling Structural and Adsorption Properties of Metal–Organic Frameworks: From Pore Size Distribution to Pore Type Distribution

Metal–organic frameworks (MOFs) attract a rapidly growing attention across the disciplines due to their multifarious pore structures and unique ability to selectively adsorb, store, and release various guest molecules. Pore structure characterization and coupling of adsorption and structural properties are imperative for rational design of advanced MOF materials and their applications. The pore structure of MOFs represents a three-dimensional network comprised of several types of pore compartments: interconnected cages and channels distinguished by their size, shape, and chemistry. Here, we propose a novel methodology for pore structure characterization of MOF materials based on matching of the experimental adsorption isotherms to in silico-generated fingerprint isotherms of adsorption in individual pore compartments of the ideal crystal. The proposed approach couples structural and adsorption properties, determines the contributions of different types of pores into the total adsorption, and estimates to what extent the pore structure of the sample under investigation is different from the ideal crystal. The MOF pore structure is characterized by the pore type distribution (PTD), which is more informative than the traditional pore size distribution that is based on oversimplistic pore models. The method is illustrated on the example of Ar adsorption at 87 K on hydrated and dehydrated structures of Cu-BTC, one of the most well-known MOF materials. The PTD determined from the experimental isotherm provides an estimate of the crystal fraction in the sample and the accessibility and degree of hydration of different types of pore compartments. In addition, the PTD determined from the experimental adsorption isotherm is used to predict the isosteric heat of adsorption that provides important information on the specifics of adsorption interactions. The results are found to be in excellent agreement with experimental data. Such detailed information about the pore structure and adsorption properties of practical MOF samples cannot be obtained with currently available methods of adsorption characterization

Pore Structure Compartmentalization for Advanced Characterization of Metal–Organic Framework Materials

Metal–organic frameworks (MOFs) are nanoporous crystals which are widely used as selective adsorbents, separation membranes, catalysts, gas and energy storage media, and drug delivery vehicles. The unique adsorption and transport properties of MOFs are determined by their complex three-dimensional (3D) networks of pores, cages, and channels that differ in size, shape, and chemical composition. While the morphological structure of MOF crystals is known, practical MOF materials are rarely ideal crystals. They contain secondary phases, binders, residual chemicals, and various types of defects. It is of paramount importance to evaluate the degree of crystallinity and accessibility of different pore compartments to adsorb guest molecules. To this end, we recently suggested the method of fingerprint isotherms based on the comparison of the experimentally measured adsorption isotherms and theoretical isotherms on ideal MOF crystals produced by Monte Carlo (MC) simulations and decomposed with respect to different pore compartments [Parashar, S.ACS Appl. Nano Mater. 2021, 4, 5531–5540 and Dantas, S.; Neimark, A. V. ACS Appl. Mater. Interfaces 2020, 12, 15595–15605]. In this work, we develop an automated algorithm for pore network compartmentalization that is a prerequisite for calculations of the fingerprint isotherms. The proposed algorithm partitions the unit cell into realistically shaped compartments based on the geometric pore size distribution. The proposed method is demonstrated on several characteristic systems, including Cu-BTC, IRMOF-1, UiO-66, PCN-224, ZIF-412, and 56 structures from the CoRE MOF database

Adsorption-Induced Deformation of Mesoporous Solids

The Derjaguin−Broekhoff−de Boer theory of capillary condensation is employed to describe deformation of mesoporous solids in the course of adsorption−desorption hysteretic cycles. We suggest a thermodynamic model, which relates the mechanical stress induced by the adsorbed phase to the adsorption isotherm. Analytical expressions are derived for the dependence of the solvation pressure on the vapor pressure. The proposed method provides a description of nonmonotonic hysteretic deformation during capillary condensation without invoking any adjustable parameters. The method is showcased drawing on the examples of literature experimental data on adsorption deformation of porous glass and SBA-15 silica

Self-Assembly in Nafion Membranes upon Hydration: Water Mobility and Adsorption Isotherms

By means of dissipative particle dynamics (DPD) and Monte Carlo (MC) simulations, we explored geometrical, transport, and sorption properties of hydrated Nafion-type polyelectrolyte membranes. Composed of a perfluorinated backbone with sulfonate side chains, Nafion self-assembles upon hydration and segregates into interpenetrating hydrophilic and hydrophobic subphases. This segregated morphology determines the transport properties of Nafion membranes that are widely used as compartment separators in fuel cells and other electrochemical devices, as well as permselective diffusion barriers in protective fabrics. We introduced a coarse-grained model of Nafion, which accounts explicitly for polymer rigidity and electrostatic interactions between anionic side chains and hydrated metal cations. In a series of DPD simulations with increasing content of water, a classical percolation transition from a system of isolated water clusters to a 3D network of hydrophilic channels was observed. The hydrophilic subphase connectivity and water diffusion were studied by constructing digitized replicas of self-assembled morphologies and performing random walk simulations. A non-monotonic dependence of the tracer diffusivity on the water content was found. This unexpected behavior was explained by the formation of large and mostly isolated water domains detected at high water content and high equivalent polymer weight. Using MC simulations, we calculated the chemical potential of water in the hydrated polymer and constructed the water sorption isotherms, which extended to the oversaturated conditions. We determined that the maximum diffusivity and the onset of formation of large water domains corresponded to the saturation conditions at 100% humidity. The oversaturated membrane morphologies generated in the canonical ensemble DPD simulations correspond to the metastable and unstable states of Nafion membrane that are not realized in the experiments

Coupling Structural and Adsorption Properties of Metal–Organic Frameworks: From Pore Size Distribution to Pore Type Distribution

Metal–organic frameworks (MOFs) attract a rapidly growing attention across the disciplines due to their multifarious pore structures and unique ability to selectively adsorb, store, and release various guest molecules. Pore structure characterization and coupling of adsorption and structural properties are imperative for rational design of advanced MOF materials and their applications. The pore structure of MOFs represents a three-dimensional network comprised of several types of pore compartments: interconnected cages and channels distinguished by their size, shape, and chemistry. Here, we propose a novel methodology for pore structure characterization of MOF materials based on matching of the experimental adsorption isotherms to in silico-generated fingerprint isotherms of adsorption in individual pore compartments of the ideal crystal. The proposed approach couples structural and adsorption properties, determines the contributions of different types of pores into the total adsorption, and estimates to what extent the pore structure of the sample under investigation is different from the ideal crystal. The MOF pore structure is characterized by the pore type distribution (PTD), which is more informative than the traditional pore size distribution that is based on oversimplistic pore models. The method is illustrated on the example of Ar adsorption at 87 K on hydrated and dehydrated structures of Cu-BTC, one of the most well-known MOF materials. The PTD determined from the experimental isotherm provides an estimate of the crystal fraction in the sample and the accessibility and degree of hydration of different types of pore compartments. In addition, the PTD determined from the experimental adsorption isotherm is used to predict the isosteric heat of adsorption that provides important information on the specifics of adsorption interactions. The results are found to be in excellent agreement with experimental data. Such detailed information about the pore structure and adsorption properties of practical MOF samples cannot be obtained with currently available methods of adsorption characterization

Molecular Model of Dimethylmethylphosphonate and Its Interactions with Water

We propose a simple united-atom second-order potential model for dimethylmethylphosphonate (DMMP) designed to reproduce molecular conformations and physical properties, such as the liquid density, heat of evaporation, and thermal expansion coefficient of the pure liquid. By use of the model, we explore molecular structure, thermodynamic characteristics, and dynamic properties of liquid DMMP and its aqueous solutions by molecular dynamics simulations. It is shown that accurate choice of partial atomic charges is of crucial importance for a correct description of phase behavior and physical properties of aqueous solutions of alkylphosphonates. The excess volume and the enthalpy of mixing in a DMMP−water system were found negative with a minimum presumably located within the concentration range between 33 and 50% volume. On average, one DMMP molecule forms two hydrogen bonds with surrounding water via the oxygen atom that forms a double bond to phosphorus. The average lifetime of hydrogen bonds does not exceed rotation correlation time of individual water molecule, thus indicating that there are no long-living DMMP·H2O complexes in the aqueous solutions

Vapor-to-Droplet Transition in a Lennard-Jones Fluid: Simulation Study of Nucleation Barriers Using the Ghost Field Method

We report a comprehensive Monte Carlo (MC) simulation study of the vapor-to-droplet transition in Lennard-Jones fluid confined to a spherical container with repulsive walls, which is a case study system to investigate homogeneous nucleation. The focus is made on the application of a modified version of the ghost field method (Vishnyakov, A.; Neimark, A. V. J. Chem. Phys. 2003, 119, 9755) to calculate the nucleation barrier. This method allows one to build up a continuous trajectory of equilibrium states stabilized by the ghost field potential, which connects a reference droplet with a reference vapor state. Two computation schemes are employed for free energy calculations, direct thermodynamic integration along the constructed trajectory and umbrella sampling. The nucleation barriers and the size dependence of the surface tension are reported for droplets containing from 260 to 2000 molecules. The MC simulation study is complemented by a review of the simulation methods applied to computing the nucleation barriers and a detailed analysis of the vapor-to-droplet transition by means of the classical nucleation theory

Pore Structure Compartmentalization for Advanced Characterization of Metal–Organic Framework Materials

Metal–organic frameworks (MOFs) are nanoporous crystals which are widely used as selective adsorbents, separation membranes, catalysts, gas and energy storage media, and drug delivery vehicles. The unique adsorption and transport properties of MOFs are determined by their complex three-dimensional (3D) networks of pores, cages, and channels that differ in size, shape, and chemical composition. While the morphological structure of MOF crystals is known, practical MOF materials are rarely ideal crystals. They contain secondary phases, binders, residual chemicals, and various types of defects. It is of paramount importance to evaluate the degree of crystallinity and accessibility of different pore compartments to adsorb guest molecules. To this end, we recently suggested the method of fingerprint isotherms based on the comparison of the experimentally measured adsorption isotherms and theoretical isotherms on ideal MOF crystals produced by Monte Carlo (MC) simulations and decomposed with respect to different pore compartments [Parashar, S.ACS Appl. Nano Mater. 2021, 4, 5531–5540 and Dantas, S.; Neimark, A. V. ACS Appl. Mater. Interfaces 2020, 12, 15595–15605]. In this work, we develop an automated algorithm for pore network compartmentalization that is a prerequisite for calculations of the fingerprint isotherms. The proposed algorithm partitions the unit cell into realistically shaped compartments based on the geometric pore size distribution. The proposed method is demonstrated on several characteristic systems, including Cu-BTC, IRMOF-1, UiO-66, PCN-224, ZIF-412, and 56 structures from the CoRE MOF database

Adsorption-Induced Deformation of Microporous Carbons: Pore Size Distribution Effect

We present a thermodynamic model of adsorption-induced deformation of microporous carbons. The model represents the carbon structure as a macroscopically isotropic disordered three-dimensional medium composed of stacks of slit-shaped pores of different sizes embedded in an incompressible amorphous matrix. Adsorption stress in pores is calculated by means of Monte Carlo simulations. The proposed model reproduces qualitatively the experimental nonmonotonic dilatometric deformation curve for argon adsorption on carbide-derived activated carbon at 243 K and pressure up to 1.2 MPa. The elastic deformation (contraction at low pressures and swelling at higher pressures) results from the adsorption stress that depends strongly on the pore size. The pore size distribution determines the shape of the deformation curve, whereas the bulk modulus controls the extent of the sample deformation