How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory.

Mixed matrix membranes (MMMs), incorporating graphene and graphene oxide structural fragments, have emerged as promising materials for challenging gas separation processes. What remains unclear is the actual molecular mechanism responsible for the enhanced permeability and perm-selectivity of these materials. With the fully atomistic models still unable to handle the required time and length scales, here, we employ a simple qualitative model based on the lattice representation of the physical system and dynamic mean field theory. We demonstrate that the performance enhancement results from the flux-regularization impact of the 2D nanoflakes and that this effect sensitively depends on the orientation of the nanoflakes and the properties of the interface between the nanoflakes and the polymer.

Simple lattice model explains equilibrium separation phenomena in glassy polymers.

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes.

CRAFTED: An exploratory database of simulated adsorption isotherms of metal-organic frameworks.

Grand Canonical Monte Carlo is an important method for performing molecular-level simulations and assisting the study and development of nanoporous materials for gas capture applications. These simulations are based on the use of force fields and partial charges to model the interaction between the adsorbent molecules and the solid framework. The choice of the force field parameters and partial charges can significantly impact the results obtained, however, there are very few databases available to support a comprehensive impact evaluation. Here, we present a database of simulations of CO2 and N2 adsorption isotherms on 690 metal-organic frameworks taken from the CoRE MOF 2014 database. We performed simulations with two force fields (UFF and DREIDING), six partial charge schemes (no charges, Qeq, EQeq, MPNN, PACMOF, and DDEC), and three temperatures (273, 298, 323 K). The resulting isotherms compose the Charge-dependent, Reproducible, Accessible, Forcefield-dependent, and Temperature-dependent Exploratory Database (CRAFTED) of adsorption isotherms.

A data-science approach to predict the heat capacity of nanoporous materials.

The heat capacity of a material is a fundamental property of great practical importance. For example, in a carbon capture process, the heat required to regenerate a solid sorbent is directly related to the heat capacity of the material. However, for most materials suitable for carbon capture applications, the heat capacity is not known, and thus the standard procedure is to assume the same value for all materials. In this work, we developed a machine learning approach, trained on density functional theory simulations, to accurately predict the heat capacity of these materials, that is, zeolites, metal-organic frameworks and covalent-organic frameworks. The accuracy of our prediction is confirmed with experimental data. Finally, for a temperature swing adsorption process that captures carbon from the flue gas of a coal-fired power plant, we show that for some materials, the heat requirement is reduced by as much as a factor of two using the correct heat capacity.

Application of the dynamic mean field theory to fluid transport in slit pores.

We explore the applicability of the lattice model and dynamic mean field theory as a computationally efficient tool to study transport across heterogeneous porous media, such as mixed matrix membranes. As a starting point and to establish some basic definitions of properties analogous to those in the off-lattice systems, we consider transport across simple models of porous materials represented by a slit pore in a chemical potential gradient. Using this simple model, we investigate the distribution of density and flux under steady state conditions, define the permeability across the system, and explore how this property depends on the length of the pore and the solid-fluid interactions. Among other effects, we observe that the flux in the system goes through a maximum as the solid-fluid interaction is varied from weak to strong. This effect is dominated by the behavior of the fluid near the walls and is also confirmed by off-lattice molecular dynamics simulations. We further extend this study to explore transport across heterogeneous slit pore channels composed of two solids with different values of solid-fluid interaction strengths. We demonstrate that the lattice models and dynamic mean field theory provide a useful framework to pose questions on the accuracy and applicability of the classical theories of transport across heterogeneous porous systems.

Performance-Based Screening of Porous Materials for Carbon Capture.

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

Structure and dynamics of water in molecular models of hydrated polyvinylamine membranes.

Facilitated transport membranes (FTMs) constitute an emerging class of polymer materials with promising properties for carbon capture applications. The key feature of these membranes is the presence of chemical groups which, in the presence of water, engage in a reaction with dissolved carbon dioxide, thus enhancing the permeability and selectivity of the membrane. Currently, little is known about the organization of these membranes on a molecular level, reaction mechanisms and detailed chemical balance, transport of water, ion species and dissolved gas molecules. The nature of the actual facilitation mechanism and the factors responsible for this effect remain unclear. Here, we use a case of polyvinylamine (PVAm), one of the most studied fixed carrier material for FTMs, to propose molecular models of the hydrated polymers. We aim to understand how transport of water is governed by structural properties of the membrane, such as the free volume, pore limiting diameter, and degree of protonation. We observe that even at the highest experimentally used hydration level, the mobility of water in PVAm matrices is significantly lower than that in bulk water; unlike in bulk systems, chloride ions exhibit much slower diffusion in confined water; this, in turn, affects the diffusion of water, which also diminishes in the presence of chloride ions.

Exploring the thermodynamic criteria for responsive adsorption processes.

We describe a general model to explore responsive adsorption processes in flexible porous materials. This model combines mean field formalism of the osmotic potential, classical density functional theory of adsorption in slit pore models and generic potential functions which represent the Helmholtz free energy landscape of a porous system. Using this model, we focus on recreating flexible adsorption phenomena observed in prototypical metal-organic frameworks, especially the recently discovered effect of negative gas adsorption (NGA). We identify the key characteristics required for the model to generate unusual adsorption processes and subsequently employ an extensive parametric study to outline conditions under which gate-opening and NGA are observed. This powerful approach will guide the design of responsive porous materials and the discovery of entirely new adsorption processes.

Deciphering the Relations between Pore Structure and Adsorption Behavior in Metal-Organic Frameworks: Unexpected Lessons from Argon Adsorption on Copper-Benzene-1,3,5-tricarboxylate.

Consistent adsorption characterization of metal-organic frameworks (MOFs) is imperative for their wider adoption in industry and practical applications. Current approaches are based on the conventional intuitive representation of MOF pore space as a regular network of pore compartments (cages and channels), adsorption in which occurs independently according to their geometric dimensions. Here, we demonstrate that this conventional approach is unable to describe even qualitatively the shape of Ar adsorption isotherms on hydrated and dehydrated Cu-BTC structures, one of the most well-known MOF materials. A combination of geometric characterization of MOF crystallographic structure, molecular simulation, and virtual visualization of the adsorption process reveals that the filling of the adjacent pore compartments proceeds in parallel in a complex cooperative fashion. The proposed synergistic approach helps us to understand the relations between pore structure geometric and chemical features and adsorption behavior, laying down a foundation for improved methods for MOF characterization.

Improving the Mechanical Stability of Metal-Organic Frameworks Using Chemical Caryatids.

Metal-organic frameworks (MOFs) have emerged as versatile materials for applications ranging from gas separation and storage, catalysis, and sensing. The attractive feature of MOFs is that, by changing the ligand and/or metal, they can be chemically tuned to perform optimally for a given application. In most, if not all, of these applications one also needs a material that has a sufficient mechanical stability, but our understanding of how changes in the chemical structure influence mechanical stability is limited. In this work, we rationalize how the mechanical properties of MOFs are related to framework bonding topology and ligand structure. We illustrate that the functional groups on the organic ligands can either enhance the mechanical stability through formation of a secondary network of nonbonded interactions or soften the material by destabilizing the bonded network of a MOF. In addition, we show that synergistic effect of the bonding network of the material and the secondary network is required to achieve optimal mechanical stability of a MOF. The developed molecular insights in this work can be used for systematic improvement of the mechanical stability of the materials by careful selection of the functional groups.

Nanomaterial interactions with biomembranes: Bridging the gap between soft matter models and biological context.

Synthetic polymers, nanoparticles, and carbon-based materials have great potential in applications including drug delivery, gene transfection, in vitro and in vivo imaging, and the alteration of biological function. Nature and humans use different design strategies to create nanomaterials: biological objects have emerged from billions of years of evolution and from adaptation to their environment resulting in high levels of structural complexity; in contrast, synthetic nanomaterials result from minimalistic but controlled design options limited by the authors' current understanding of the biological world. This conceptual mismatch makes it challenging to create synthetic nanomaterials that possess desired functions in biological media. In many biologically relevant applications, nanomaterials must enter the cell interior to perform their functions. An essential transport barrier is the cell-protecting plasma membrane and hence the understanding of its interaction with nanomaterials is a fundamental task in biotechnology. The authors present open questions in the field of nanomaterial interactions with biological membranes, including: how physical mechanisms and molecular forces acting at the nanoscale restrict or inspire design options; which levels of complexity to include next in computational and experimental models to describe how nanomaterials cross barriers via passive or active processes; and how the biological media and protein corona interfere with nanomaterial functionality. In this Perspective, the authors address these questions with the aim of offering guidelines for the development of next-generation nanomaterials that function in biological media.

Self-assembly of anionic, ligand-coated nanoparticles in lipid membranes.

Ligand-functionalized nanoparticles (NPs) are a promising platform for imaging and drug delivery applications. A number of recent molecular simulation and theoretical studies explored how these NPs interact with model lipid membranes. However, interactions between ligand-coated NPs leading to possible cooperative effects and association have not been investigated. In this coarse-grained molecular dynamics study, we focus on a specific case of several anionic, ligand-coated NPs embedded in a lipid membrane. Several new effects are observed. Specifically, in the presence of cholesterol in the membrane, NPs tend to form linear clusters, or chains. Analysis of the driving forces for this association reveals an important role of the recently discovered orderphobic effect, although we acknowledge that a combination of factors must be at play. At the same time, we argue that the specific linear shape of the clusters is a result of a subtle balance between the forces that stabilize a NP in the membrane and the forces that drive the NP-NP association processes. These effects, observed for the first time in the NP-membrane systems, have also direct correspondence to similar effects in protein-membrane systems and these links between the two realms should be explored further.

Net, excess and absolute adsorption and adsorption of helium.

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.

Membrane partitioning of anionic, ligand-coated nanoparticles is accompanied by ligand snorkeling, local disordering, and cholesterol depletion.

Intracellular uptake of nanoparticles (NPs) may induce phase transitions, restructuring, stretching, or even complete disruption of the cell membrane. Therefore, NP cytotoxicity assessment requires a thorough understanding of the mechanisms by which these engineered nanostructures interact with the cell membrane. In this study, extensive Coarse-Grained Molecular Dynamics (MD) simulations are performed to investigate the partitioning of an anionic, ligand-decorated NP in model membranes containing dipalmitoylphosphatidylcholine (DPPC) phospholipids and different concentrations of cholesterol. Spontaneous fusion and translocation of the anionic NP is not observed in any of the 10-µs unbiased MD simulations, indicating that longer timescales may be required for such phenomena to occur. This picture is supported by the free energy analysis, revealing a considerable free energy barrier for NP translocation across the lipid bilayer. 5-µs unbiased MD simulations with the NP inserted in the bilayer core reveal that the hydrophobic and hydrophilic ligands of the NP surface rearrange to form optimal contacts with the lipid bilayer, leading to the so-called snorkeling effect. Inside cholesterol-containing bilayers, the NP induces rearrangement of the structure of the lipid bilayer in its vicinity from the liquid-ordered to the liquid phase spanning a distance almost twice its core radius (8-10 nm). Based on the physical insights obtained in this study, we propose a mechanism of cellular anionic NP partitioning, which requires structural rearrangements of both the NP and the bilayer, and conclude that the translocation of anionic NPs through cholesterol-rich membranes must be accompanied by formation of cholesterol-lean regions in the proximity of NPs.

On the flexibility of metal-organic frameworks.

Occasional, large amplitude flexibility in metal-organic frameworks (MOFs) is one of the most intriguing recent discoveries in chemistry and material science. Yet, there is at present no theoretical framework that permits the identification of flexible structures in the rapidly expanding universe of MOFs. Here, we propose a simple method to predict whether a MOF is flexible, based on treating it as a system of rigid elements, connected by hinges. This proposition is correct in application to MOFs based on rigid carboxylate linkers. We validate the method by correctly classifying known experimental MOFs into rigid and flexible groups. Applied to hypothetical MOFs, the method reveals an abundance of flexibility phenomena, and this seems to be at odds with the proportion of flexible structures among experimentally known MOFs. We speculate that the flexibility of a MOF may constitute an intrinsic impediment on its experimental realization. This highlights the importance of systematic prediction of large amplitude flexibility regimes in MOFs.

Homogeneous Hydrophobic-Hydrophilic Surface Patterns Enhance Permeation of Nanoparticles through Lipid Membranes.

We employ coarse-grained molecular dynamics simulations to understand why certain interaction patterns on the surface of a nanoparticle promote its translocation through a lipid membrane. We demonstrate that switching from a random, heterogeneous distribution of hydrophobic and hydrophilic areas on the surface of a nanoparticle to even, homogeneous patterns substantially flattens the translocation free-energy profile and dramatically enhances permeation. We then proceed to construct a more detailed coarse-grained model of a nanoparticle with flexible hydrophobic and hydrophilic ligands arranged into striped domains. Molecular dynamics simulations of these nanoparticles show that the terminal groups of the ligands tend to arrange themselves into homogeneous patterns, despite the underlying striped domains. These observations are linked to recent experimental studies.

Calculation and visualization of free energy barriers for several VOCs and TNT in HKUST-1.

A simple protocol based on a lattice representation of the porous space is proposed to locate and characterize the free energy bottle-necks in rigid metal organic frameworks. As an illustration we apply this method to HKUST-1 to demonstrate that there are impassable free energy barriers for molecules of trinitrotoluene in this structure.

Molecular recognition effects in atomistic models of imprinted polymers.

In this article we present a model for molecularly imprinted polymers, which considers both complexation processes in the pre-polymerization mixture and adsorption in the imprinted structures within a single consistent framework. As a case study we investigate MAA/EGDMA polymers imprinted with pyrazine and pyrimidine. A polymer imprinted with pyrazine shows substantial selectivity towards pyrazine over pyrimidine, thus exhibiting molecular recognition, whereas the pyrimidine imprinted structure shows no preferential adsorption of the template. Binding sites responsible for the molecular recognition of pyrazine involve one MAA molecule and one EGDMA molecule, forming associations with the two functional groups of the pyrazine molecule. Presence of these specific sites in the pyrazine imprinted system and lack of the analogous sites in the pyrimidine imprinted system is directly linked to the complexation processes in the pre-polymerization solution. These processes are quite different for pyrazine and pyrimidine as a result of both enthalpic and entropic effects.