The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation*

ABSTRACT

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.     

Development of a grand canonical-kinetic Monte Carlo scheme for simulation of mixtures

A rejection-free methodology-based kinetic Monte Carlo (kMC) method has been developed in the grand canonical ensemble to simulate fluid mixtures. It comprises two different moves: entropic displacement of a selected molecule (based on the Rosenbluth algorithm) in the volume space of the system, and exchange of molecules with the surroundings (insertion or deletion). These two moves are made sequentially with M displacement moves followed by one exchange. The displacement moves are treated as sub-NVT sequences within a grand canonical ensemble. The procedure for deletion or insertion of a molecule is either, based on the Rosenbluth algorithm, or on a direct comparison, in which the average activity of one component is compared with its specified activity. The components are chosen either with equal probability or with a probability proportional to their density. The implementation of rejection-free kMC is much simpler than the Metropolis importance sampling MC procedure, which requires three different types of move, all of which must be tested for acceptance or rejection. The new scheme has been evaluated by applying it to fluid argon and to an equimolar mixture of methane, ethane and propane.     

Monte Carlo Simulation of Binary Gas Adsorption in Zeolite Cavities

Abstract

Grand canonical Monte Carlo simulations have been performed for binary adsorption of Lennard-Jones molecules with point multipole moments in zeolite cavities of type X. Fluid-solid electrostatic interactions were taken into account. Phase diagrams and total coverage were calculated for three binaries and compared with experimental measurements. MC simulations gave good agreement with experiment for two mixtures (C₂H₄-CO₂ and CO₂-CH₄) but there were discrepancies between simulation and experiment for the system i-C₄H₁₀-C₂H₄. The dependence of excess Gibbs free energy on the composition and pressure was studied. Negative deviations from ideality are due to energetic heterogeneity and size effects. Unlike liquid-vapor equilibrium, deviations from the Lorentz-Berthelot mixing rules for the adsorbates have little effect upon the phase behavior. Density distributions show that the components compete for the high energy sites inside the cavity; depending on its relative strength of adsorption, one component may be excluded from such positions (CH₄ in CO₂-CH₄), or the two species may share sites inside the cavity (C₂H₄-CO₂).     

Adsorption of Binary Mixtures in a Zeolite Micropore

Abstract

We investigate the selective adsorption of xenon, argon, and methane in zeolite NaA by applying the grand canonical ensemble Monte Carlo simulation technique to an adsorbed binary mixture and to two reference systems: i) an adsorbed single component system and ii) a bulk mixture. We define and calculate selectivities and excess densities due to i) mixing and ii) adsorption in terms of differences between the binary adsorbed system and these reference systems. We observe that xenon selectively adsorbs in both xenon-argon and xenon-methane mixtures at low chemical potential (low pressure) due to its greater energetic interaction with the zeolite. However, a reversal in selectivity occurs at higher chemical potential in both of these mixtures. This is due in large part to the greater efficiency in which the smaller component “packs” in the pore as compared to the bulk. We show that the crossover in selectivity occurs at a lower chemical potential for a mixture where one component can occupy regions of the porespace inaccessible to the other. We suggest that this crossover in selectivity may be a general feature of microporous adsorption.     

A study of the adsorption of bacterial cells on porous materials

The paper presents experimental data on the adsorption of bacterial cells on porous materials.Translated from Mikrobiologiya, Vol. 73, No. 6, 2004, pp. 810–816.Original Russian Text Copyright © 2004 by Samonin, Elikova.     

Reconciliation of different simulation methods in the determination of the equilibrium branch for adsorption in pores

The recently proposed mid-density scheme [Liu Z, Herrera L, Nguyen VT, Do DD, Nicholson D. A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 2011; 37(11):932–939, Liu Z, Do DD, Nicholson D. A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 2012; 38(3):189–199] is tested against a method 2V-NVT (similar to the well-established gauge cell method) and the canonical ensemble (CE) method, using argon adsorption at 87 K in graphitic slit pores of infinite and finite length. In infinitely long pores, the equilibrium transition is vertical that is expected for an infinite system to have a first-order transition and this vertical transition was found to lie at the middle of the hysteresis loop and satisfies the well-known Maxwell rule of equal area. For pores of finite length, the equilibrium transitions are steep and are close to, but not exactly identical to, the desorption branch. This lends support to the conventional view that the desorption branch is nearest to equilibrium, although both adsorption and desorption branches are strictly speaking metastable; a view proposed originally by Everett [Everett DH. Capillary condensation and adsorption hysteresis. Berichte Der Bunsen-Gesellschaft [Phys Chem Chem Phys]. 1975; 79(9):732–734]. As a consequence, the Maxwell rule of equal area does not apply to finite systems. As the widely accepted CE and gauge cell methods do not falsify the mid-density scheme, this study lends strong support to the validity of this technique for the study of equilibria.     

Adsorption and diffusion of CO2 and CH4 in covalent organic frameworks: an MC/MD simulation study

Covalent organic frameworks (COFs) are a promising gas separation material which have been developed recently. In this work, we have used grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations to investigate the adsorption and diffusion properties of CO₂ and CH₄ in five recent synthesised COF materials. We have also considered the properties of amino-modified COFs by adding –NH₂ group to the five COFs. The adsorption isotherm, adsorption/diffusion selectivity, self/transport diffusion coefficients have been examined and discussed. All of the five COFs exhibit promising adsorption selectivity which is higher than common nanoporous materials. An S-shaped adsorption isotherm can be found for CO₂ instead of CH₄ adsorption. The introduction of –NH₂ group is effective at low pressure region (<200?kPa). The diffusion coefficients are similar for TS-COFs but increase with the pore size for PI-COFs, and the diffusion coefficients seem less dependent on the –NH₂ groups.     

Methane adsorption in several series of newly synthesised metal-organic frameworks: a molecular simulation study

In this work, the adsorption of methane in several newly synthesised metal-organic frameworks (MOFs) is studied using grand canonical Monte Carlo simulations. The factors influencing the adsorption behaviour of methane in different series of materials were investigated at low, moderate and high pressures, respectively. The simulation results show that the isosteric heat of adsorption at infinite dilute, the accessible surface area and the free volume of materials play important roles in methane adsorption, while the main factors are different in different ranges of pressure. These are consistent with the rules obtained from well-studied MOFs by the Snurr group and by Wang, proving that they are applicable to the newly synthesised MOFs. Based on these, the influencing factors were further discussed by classifying the MOFs through the pore topology, and it was found that the pore topology should not be ignored when performing efficient modifications of MOFs at moderate and high pressures. This work may provide useful information to design novel MOFs with high methane uptake in the future.     

Solvation studies of DMP323 and A76928 bound to HIV protease: analysis of water sites using grand canonical Monte Carlo simulations.

We examine the water solvation of the complex of the inhibitors DMP323 and A76928 bound to HIV-1 protease through grand canonical Monte Carlo simulations, and demonstrate the ability of this method to reproduce crystal waters and effectively predict water positions not seen in the DMP323 or A76928 structures. The simulation method is useful for identifying structurally important waters that may not be resolved in the crystal structures. It can also be used to identify water positions around a putative drug candidate docked into a binding pocket. Knowledge of these water positions may be useful in designing drugs to utilize them as bridging groups or displace them in the binding pocket. In addition, the method should be useful in finding water sites in homology models of enzymes for which crystal structures are unavailable.     

Monte Carlo Simulation Study of Adsorption Characteristics in Slit-Like Micropores Under Supercritical Conditions

Abstract

Adsorption characteristics of a solute diluted in supercritical fluids has been investigated by using the Monte Carlo simulation techniques. The Lennard-Jones potential function is used for describing interactions for a model system of CO₂ + benzene in slit-like micropores with infinite graphitic carbon walls. A modified μVT ensemble method with particle exchange proposed by Cracknell, Nicholson and Quirke (1993) is found to be much superior to the conventional μVT ensemble method especially for dense mixtures in a pore. Adsorption isotherms of CO₂ and benzene, in equilibrium with a dilute benzene mixture in CO₂ (mole fraction of benzene = 0.001), are computed by varying pressure, temperature, the benzene–surface interaction potential, and the slitwidth. Adsorption isotherm curve of CO₂ increases with an increase in pressure while that of benzene shows a maximum at a pressure far below the critical pressure of CO₂ and then it decreases with increasing pressure. The decrease in benzene adsorption with increasing pressure is attributable to both the enhanced solubility in supercritical CO₂ and the competitive adsorption of CO₂. The isotherm curves of each component at two temperatures, 313.2 K and 323.2 K, show to cross at a pressure near the critical pressure due to the “density effect” on the chemical potentials of a solute at supercritical fluid conditions. When the interaction between a solute and a surface increases, the adsorption isotherm increases. Narrowing the slitwidth results in the increase in the adsorption of solute since the external potential from two walls becomes deeper.     

Mixtures of Associating and Non-associating Chains on Activated Surfaces: A Monte Carlo Approach

Abstract

The behavior of mixtures of associating and non-associating chains confined in pores with activated surfaces is studied by means of molecular simulation. The fluid molecules are modeled as a chain of four tangent Lennard-Jones spheres. Some of the chains have an additional associating square-well site placed in an end sphere. The activated surfaces of the slit pore are modeled via an integrated Lennard-Jones (10-4-3) potential with specific association sites protruding from the surface. We present Gibbs ensemble Monte Carlo simulation results for the partitioning of mixtures of chains in the bulk and confined phases for this particular model. The chain-wall association governs the adsorption behavior of the system. The preferential adsorption of associating chains is seen to strongly depend on temperature and pore width. Selectivities obtained are in the range of those seen in experiments of alkane-alkanol mixtures.     

RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials

A new software package, RASPA, for simulating adsorption and diffusion of molecules in flexible nanoporous materials is presented. The code implements the latest state-of-the-art algorithms for molecular dynamics and Monte Carlo (MC) in various ensembles including symplectic/measure-preserving integrators, Ewald summation, configurational-bias MC, continuous fractional component MC, reactive MC and Baker's minimisation. We show example applications of RASPA in computing coexistence properties, adsorption isotherms for single and multiple components, self- and collective diffusivities, reaction systems and visualisation. The software is released under the GNU General Public License.     

Molecular simulations of physical and chemical adsorption under gas and liquid environments using force field- and quantum mechanics-based methods

Here we review our simulations of adsorption on metal–organic frameworks (MOFs) and platinum (Pt) catalysts, focusing on the modelling methods required to understand these two very different systems. MOFs are porous, crystalline materials with large surface areas, which are promising for a variety of adsorption applications. We review our simulations of gas uptake in PCN-53 (porous coordination network) as well as gas storage in MOFs functionalised with metal alkoxide sites. While fluid–solid interactions in both systems can be modelled quite well using algebraic force fields, the alkoxide sites in the functionalised MOFs require specialised versions, in order to describe the stronger adsorption energies. We discuss grand canonical Monte Carlo (GCMC) simulations of both systems. Pt is a common catalyst, and simulations have proven quite useful for providing molecular level details to understand its functionality. This involves understanding adsorption phenomena, which often requires quantum mechanical calculations. We describe our periodic boundary condition density functional theory (DFT) simulations of Pt-catalysed NO oxidation, focusing on adsorbate geometries and coverage effects. Finally, we describe one of the current ‘grand challenges’ in molecular simulations of adsorption, modelling catalytic activity in aqueous phase, which requires a combination of algebraic force fields, DFT and GCMC.     

A grand canonical Monte Carlo simulation study of argon and krypton confined inside weakly attractive slit pores

Grand canonical Monte Carlo simulations are performed to investigate the adsorption of argon and krypton inside weakly attractive slit pores. We examine the effects of confinement on these monoatomic fluids (modelled using the triangle-well potential) in a hard wall slit pore as also when the pore-fluid interactions are uniformly and weakly attractive. The effects of temperature and pressure on the adsorption isotherms of these confined fluids are found to be the same as those reported in literature. The equilibrium density profiles for argon and krypton exhibit both uniform distribution and layering under different conditions. In addition, for krypton, under specific conditions inside the narrow pores, we note the development of frustrated layering.     

Solvation Force and Confinement-Induced Phase Transitions of Model Ultra Thin Films

Abstract

The static (equilibrium) properties of atomically thin films confined between two surfaces are studied as a function of surface separation by Grand Canonical Monte Carlo and Molecular Dynamics simulations. A model was used, in which the fluid and wall species consist of two different Lennard-Jones rare gas atoms. This was designed to mimic the static SFA experiments in which it is known that epitaxy is not necessary for inducing an oscillatory solvation force in simple non polar liquids. We have been able to simulate, using this simple system, many aspects of the equilibrium properties observed in the experiments. The solvation force is an exponentially damped, periodic curve. All peaks of maximum amplitude in the solvation force correspond to solid-like structures. These structures melt in increasing the surface separation. A further increase in separation leads to the addition of a whole layer and the recrystallisation of the film. In addition this model displays an interesting phenomenon of confinement induced solid-solid phase transition. Two different stable packing (bcc and triclinic) can be observed in the bilayer film and a transition from one to the other occurs when the surface separation is changed. This phase change has been studied as a function of pressure and temperature. As compared to the simulations using a ‘commensurate’ model, in which the fluid and wall species are made of like atoms, the results obtained here are in much better agreement with experimental findings.     

Insulin adsorption into porous charged membranes: Effect of the electrostatic interaction

Insulin adsorption into a series of porous charged membranes was investigated by batch adsorption experiments, and the experimental results were analyzed by the homogeneous diffusion model. The membranes used in this study were prepared by pore‐surface modification of porous poly(acrylonitrile) (PAN) membranes by grafting with weak acidic and basic functional groups. The amount of insulin adsorbed into the membrane was determined from the material balance of insulin. The insulin partition coefficient K between the membrane and solution was estimated from the equilibrium adsorption amount, and the effective diffusion coefficient D was estimated by matching the model with the experimental data as a fitting parameter. The dependence of K and D on the charge properties of the insulin and membrane is observed and discussed. The partition coefficient K increased when the insulin and the membrane carried opposite charges, on the other hand, the effective diffusion coefficient D was reduced. These results indicate that the electrostatic interaction between the insulin and the membranes played an important role in the insulin adsorption. © 2009 American Institute of Chemical Engineers Biotechnol. Prog. 2009     

Modeling of adsorption in nanopores

Adsorption in nonporous materials has been studied using Grand Canonical Monte Carlo simulations. We discuss three types of materials: (a) a model of cylindrical pores with smooth walls, representing MCM-41 like materials, (b) a model of cylindrical pores with regular structured walls (model of carbon nanotubes) and (c) a material with crystalline wall structure (zeolites). Typical problems related to the stability of adsorbed layers have been analyzed. We have shown that the mechanism of adsorption is strongly dependent on the structure of the pore walls. In the case of amorphous walls it may lead to metastable configurations. In nanotubes, the ordered corrugation structure of walls determines the low temperature structure of the adsorbed system. In 3D ordered porous system, such as zeolites, the mechanism of adsorption is mostly determined by characteristic sites of adsorption.Figure Adsorbed atoms and energy fluctuations at the pressure of the first layer formation of krypton atoms: (a) instantaneous numbers of adsorbed atoms (per nm² of the pore wall) as a function of the time of simulation (Monte Carlo steps) observed in a relatively long run, (b) the bimodal distribution of the energy fluctuations is a consequence of the behavior of the systems as shown in (a).     

Advancing simulations of biological materials: applications of coarse-grained models on graphics processing unit hardware

The timescales of biological processes, primarily those inherent to the molecular mechanisms of disease, are long (>μs) and involve complex interactions of systems consisting of many atoms (>10⁶). Simulating these systems requires an advanced computational approach, and as such, coarse-grained (CG) models have been developed and highly optimised for accelerator hardware, primarily graphics processing units (GPUs). In this review, I discuss the implementation of CG models for biologically relevant systems, and show how such models can be optimised and perform well on GPU-accelerated hardware. Several examples of GPU implementations of CG models for both molecular dynamics and Monte Carlo simulations on purely GPU and hybrid CPU/GPU architectures are presented. Both the hardware and algorithmic limitations of various models, which depend greatly on the application of interest, are discussed.     

Methane and carbon dioxide adsorption and diffusion in amorphous,metal-decorated nanoporous silica

The adsorptive and diffusive behaviour of methane and carbon dioxide in amorphous nanoporous adsorbents composed of spherosilicate building blocks, in which isolated metal sites have been distributed, is examined. The adsorbent contains cubic silicate building blocks (spherosilicate units: Si₈O₂₀), which are cross linked by SiCl₂O₂ bridges and decorated with either –OTiCl₃ or –OSiMe₃ groups of the other cube corners. The model structures were generated to correspond to experimentally synthesised materials, matching physical properties including density, surface area and accessible volume. It is shown that both methane and carbon dioxide adsorb via physisorption only in the modelled materials. Adsorption isotherms and energies at 300 K for pressures up to 100 bar were generated via molecular simulation. The maximum gravimetric capacity of CH₄ is 16.9 wt%, occurring at 300 K and 97 bar. The maximum gravimetric capacity of CO₂ is 50.3 wt%, occurring at 300 K and 51.6 bar. The best performing adsorbent was a low-density (high accessible volume) material with no –OTiCl₃ groups. The presence of –OTiCl₃ did not enhance physisorption even on a volumetric basis, and the high molecular weight of –OTiCl₃ groups is a significant penalty on a gravimetric basis. Based on the pair correlation functions, the most favourable adsorption sites for both adsorbates are located in front of the faces of spherosilicate cubes. The self-diffusivity and activation energy for diffusion are also reported.