Transport Phenomena in Nanoporous Materials

Measuring Mass Transfer of n-Hexane and 2-Chloroethyl Ethyl Sulfide in Sorbent/Polymer Fiber Composites Using a Volumetric Adsorption Apparatus

The integration of metal-organic frameworks (MOFs) into composite systems serves as an effective strategy to increase the processability of these materials. Notably, MOF/fiber composites have shown much promise as protective equipment for the capture and remediation of chemical warfare agents. However, the practical application of these composites requires an understanding of their mass transport properties, as both mass transfer resistance at the surface and diffusion within the materials can impact the efficacy of these materials. In this work, we synthesized composite fibers of MOF-808 and amidoxime-functionalized polymers of intrinsic microporosity (PIM-1-AX) and measured the adsorption and mass transport behavior of n-hexane and 2-chloroethyl ethyl sulfide (CEES), a sulfur mustard simulant. We developed a new Fickian diffusion model for cylindrical shapes to fit the dynamic adsorption data obtained from a commercial volumetric adsorption apparatus and found that mass transport behavior in composite fibers closely resembled that in the pure PIM fibers, regardless of MOF loading. Moreover, we found that n-hexane adsorption mirrors that of CEES, indicating that it could be used as a structural mimic for future adsorption studies of the sulfur mustard simulant. These preliminary insights and the new model introduced in this work lay the groundwork for the design of next-generation composite materials for practical applications.

Structures and Dynamics of Complex Guest Molecules in Confinement, Revealed by Solid-State NMR, Molecular Dynamics, and Calorimetry

This review gives an overview of current trends in the investigation of confined molecules such as water, small and higher alcohols, carbonic acids, ethylene glycol, and non-ionic surfactants, such as polyethylene glycol or Triton-X, as guest molecules in neat and functionalized mesoporous silica materials employing solid-state NMR spectroscopy, supported by calorimetry and molecular dynamics simulations. The combination of steric interactions, hydrogen bonds, and hydrophobic and hydrophilic interactions results in a fascinating phase behavior in the confinement. Combining solid-state NMR and relaxometry, DNP hyperpolarization, molecular dynamics simulations, and general physicochemical techniques, it is possible to monitor these confined molecules and gain deep insights into this phase behavior and the underlying molecular arrangements. In many cases, the competition between hydrogen bonding and electrostatic interactions between polar and non-polar moieties of the guests and the host leads to the formation of ordered structures, despite the cramped surroundings inside the pores.

Molecular Diffusion in Nanoreactors' Pore Channel System: Measurement Techniques, Structural Regulation, and Catalytic Effects

Nanoreactors, as a new class of materials with highly enriched and ordered pore channel structures, can achieve special catalytic effects by precisely identifying and controlling the molecular diffusion behavior within the ordered pore channel system. Nanoreactors-driven molecular diffusion within the ordered pore channels can be highly dependent on the local microenvironment in the nanoreactors' pore channel system. Although the diffusion process of molecules within the ordered pore channels of nanoreactors is crucial for the regulation of catalytic behaviors, it has not yet been as clearly elucidated as it deserves to be in this study. In this review, fundamental theory and measurement techniques for molecular diffusion in the pore channel system of nanoreactors are presented, structural regulation strategies of pore channel parameters for controlling molecular diffusion are discussed, and the effects of molecular diffusion in the pore channel system on catalytic reactivity and selectivity are further analyzed. This article attempts to further develop the underlying theory of molecular diffusion within the theoretical framework of nanoreactor-driven catalysis, and the proposed perspectives may contribute to the rational design of advanced catalytic materials and the precise control of complex catalytic kinetics.

Scaling laws for single-file diffusion of adhesive particles

Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

Two-Dimensional Ultrathin Silica Films

Two-dimensional (2D) ultrathin silica films have the potential to reach technological importance in electronics and catalysis. Several well-defined 2D-silica structures have been synthesized so far. The silica bilayer represents a 2D material with SiO₂ stoichiometry. It consists of precisely two layers of tetrahedral [SiO₄] building blocks, corner connected via oxygen bridges, thus forming a self-saturated silicon dioxide sheet with a thickness of ∼0.5 nm. Inspired by recent successful preparations and characterizations of these 2D-silica model systems, scientists now can forge novel concepts for realistic systems, particularly by atomic-scale studies with the most powerful and advanced surface science techniques and density functional theory calculations. This Review provides a solid introduction to these recent developments, breakthroughs, and implications on ultrathin 2D-silica films, including their atomic/electronic structures, chemical modifications, atom/molecule adsorptions, and catalytic reactivity properties, which can help to stimulate further investigations and understandings of these fundamentally important 2D materials.

X-ray diffraction for probing free energy profiles and self-diffusivity of gases in metal–organic frameworks

This paper presents a novel methodology for measuring the free energy profiles and the self-diffusivity of gases in crystalline microporous materials.

Solid-state NMR studies of non-ionic surfactants confined in mesoporous silica

This review gives an overview of current trends in the investigation of confined molecules such as higher alcohols, ethylene glycol and polyethylene glycol as guest molecules in neat and functionalized mesoporous silica materials. All these molecules have both hydrophobic and hydrophilic parts. They are characteristic role-models for the investigation of confined surfactants. Their properties are studied by a combination of solid-state NMR and relaxometry with other physicochemical techniques and molecular dynamics techniques. It is shown that this combination delivers unique insights into the structure, arrangement, dynamical properties and the guest-host interactions inside the confinement.

Transport Diffusion of Linear Alkanes (C5-C16) through Thin Films of ZIF-8 as Assessed by Quartz Crystal Microgravimetry

We report uptake capacities and transport diffusivities, D, for each of eight linear alkanes (ranging from C₅ to C₁₆) in quartz crystal-supported films of solvent-evacuated ZIF-8. Analyses of the alkane uptake profiles revealed that the transport dynamics are governed by guest diffusion through metal-organic framework (MOF) (ZIF-8) crystallites rather than by rates of entry into films at the MOF/vapor interface. The obtained diffusivities range from just over 10^-18 m²/s to just under 10^-14 m²/s. Notably, minimum cross-sectional widths for all guests exceed the crystallographically measured width of ZIF-8's largest apertures and imply consistently with previous experimental and computational studies that apertures expand to accommodate guest uptake. On average, each additional carbon decreases the transport diffusivity of an alkane by twofold. Closer examination, however, reveals an odd-even effect such that linear alkanes having even numbers of carbons diffuse more rapidly than alkanes featuring one more or one less carbon atom. Thus, ZIF-8's differentiation of transport diffusivities for pairs of alkanes differing in length by only one carbon atom can be significantly greater than the aforementioned factor of 2. Elucidation of the microscopic basis for the odd-even behavior, however, awaits the outcome of molecular dynamics calculations that are beyond the scope of the present study. For compact, solvothermally prepared films, guest transport is dominated by 1D diffusion from the film/vapor interface and toward the underlying quartz crystal. For much lower density, electrophoretically deposited (EPD) films, crystallites behave nearly independently, and guest transport can be adequately modeled by assuming rapid permeation of macroscopic voids between crystallites, followed by entry and rate-limiting radial diffusion into isolated crystallites. One consequence is that EPD films can be much more rapidly infiltrated by molecular guests than can compact, solvothermally grown films. The combined results have potentially favorable implications for the development of kinetic separation schemes for closely related analytes.

Effect of External Surface Diffusion Barriers on Platinum/Beta-Catalyzed Isomerization of n-Pentane

We have developed a generalizable strategy to quantify the effect of surface barriers on zeolite catalysis. Isomerization of n‐pentane, catalyzed by Pt/Beta, is taken as a model reaction system. Firstly, the surface modification by chemical liquid deposition of SiO₂ was carried out to control the surface barriers on zeolite Beta crystals. The deposition of SiO₂ leads to a very slight change in the physical properties of Beta crystals, but an obvious reduction in Brønsted acid sites. Diffusion measurements by the zero‐length column (ZLC) method show that the apparent diffusivity of n‐pentane can be more than doubled after SiO₂ deposition, indicating that the surface barriers have been weakened. Catalytic performance was tested in a fixed‐bed reactor, showing that the apparent catalytic activity improved by 51–131 % after SiO₂ deposition. These results provide direct proof that reducing surface barriers can be an effective route to improve zeolite catalyst performance deteriorated by transport limitations.

Diffusion of confined fluids in microporous zeolites and clay materials

Fluids exhibit remarkable variation in their structural and dynamic properties when they are confined at the nanoscopic scale. Various factors, including geometric restriction, the size and shape of the guest molecules, the topology of the host, and guest-host interactions, are responsible for the alterations in these properties. Due to their porous structures, aluminosilicates provide a suitable host system for studying the diffusion of sorbates in confinement. Zeolites and clays are two classes of the aluminosilicate family, comprising very ordered porous or layered structures. Zeolitic materials are important due to their high catalytic activity and molecular sieving properties. Guest molecules adsorbed by zeolites display many interesting features including unidimensional diffusion, non-isotropic rotation, preferred orientation and levitation effects, depending on the guest and host characteristics. These are useful for the separation of hydrocarbons which commonly exist as mixtures in nature. Similarly, clay materials have found application in catalysis, desalination, enhanced oil recovery, and isolation barriers used in radioactive waste disposal. It has been shown that the bonding interactions, level of hydration, interlayer spacing, and number of charge-balancing cations are the important factors that determine the nature of diffusion of water molecules in clays. Here, we present a review of the current status of the diffusion mechanisms of various adsorbed species in different microporous zeolites and clays, as investigated using quasielastic neutron scattering and classical molecular dynamics simulation techniques. It is impossible to write an exhaustive review of the subject matter, as it has been explored over several decades and involves many research topics. However, an effort is made to cover the relevant issues specific to the dynamics of different molecules in microporous zeolites and clay materials and to highlight a variety of interesting features that are important for both practical applications and fundamental aspects.

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

Diffusion and reaction in pore hierarchies by the two-region model

The two-region (“Kärger”) model of diffusion in complex pore spaces is exploited for quantitating mass transfer in hierarchically organized nanoporous materials, consisting of a continuous microporous bulk phase permeated by a network of transport pores. With the implications that the diffusivity in the transport pores significantly exceeds the diffusivity in the micropores and that the relative population of the transport pores is far below that of the micropores, overall transport depends on only three independent parameters. Depending on their interrelation, enhancement of the overall mass transfer is found to be ensured by two fundamentally different mechanisms. They are referred to as the limiting cases of fast and slow exchange, with the respective time constants of molecular uptake being controlled by different parameters. Complemented with reaction terms, the two-region model may equally successfully be applied to the quantitation of the combined effect of diffusion and reaction in terms of the effectiveness factor. Generalization of the classical Thiele concept is shown to provide an excellent estimate of the effectiveness factor of a chemical reaction in hierarchically porous materials, solely based on the intrinsic reaction rate and the time constant of molecular uptake relevant to the given conditions.

Application of microimaging to diffusion studies in nanoporous materials

Microimaging on the basis of, respectively, interference microscopy and IR microscopy permit the observation of the distribution of guest molecules in nanoporous solids and their variation with time. Thus attainable knowledge of both concentration gradients and diffusion fluxes provides direct access to the underlying diffusion phenomena. This includes, in particular, the measurement of transport diffusion under transient, i. e. under non-equilibrium conditions, and of self- or tracer diffusion on considering the rate of tracer exchange. Correlating the difference in guest concentration close to the external surface to its equilibrium value with the influx into the nanoporous solid, microimaging does as well allow the direct determination of surface resistances. Examples illustrating the variety of information thus attainable include the comparison of mass transfer under equilibrium and non-equilibrium conditions, single- and multicomponent diffusion and chemical reactions. They, finally, introduce into the potentials of microimaging for an in-depth study of mass transfer in mixed-matrix membranes. This tutorial review may serve as first introduction into the topic. Further references are linked for the interested reader.

Diffusion in nanopores: inspecting the grounds

This paper provides a general overview of the phenomenon of guest diffusion in nanoporous materials. It introduces the different types of diffusion measurement that can be performed under both equilibrium and non-equilibrium conditions in either single- or multicomponent systems. In the technological application of nanoporous materials for mass separation and catalytic conversion diffusion often has a significant impact on the overall rate of the process and is quite commonly rate controlling. Diffusion enhancement is therefore often a major goal in the manufacture of catalysts and adsorbents.

Investigating the Process and Mechanism of Molecular Transport within a Representative Solvent-Filled Metal-Organic Framework

Effective permeation into, and diffusive mass transport within, solvent-filled metal-organic frameworks (MOFs) is critical in applications such as MOF-based chemical catalysis of condensed-phase reactions. In this work, we studied the entry from solution of a luminescent probe molecule, 1,3,5,7-tetramethyl-4,4-difluoroboradiazaindacene (BODIPY), into the 1D channel-type, zirconium-based MOF NU-1008 and subsequent transport of the probe through the MOF. Measurements were accomplished via in situ confocal fluorescence microscopy of individual crystallites, where the evolution of the fluorescence response from the crystallite was followed as functions of both time and location within the crystallite. From the confocal data, intracrystalline transport of BODIPY is well-described by one-dimensional diffusion along the channel direction. Varying the chemical identity of the solvent revealed an inverse dependence of probe-molecule diffusivity on bulk-solvent viscosity, qualitatively consistent with expectations from the Stokes-Einstein equation for molecular diffusion. At a more quantitative level, however, measured diffusion coefficients are about 100-fold smaller than expected from Stokes-Einstein, pointing to substantial channel-confinement effects. Evaluation of the confocal data also reveals a non-negligible mass transport resistance, i.e., surface barrier, associated with the probe molecule leaving the solution and permeating the exterior surface of the MOF. Permeation by the probe entails displacement of solvent from the MOF channels. The magnitude of the resistance increases with the size of the solvent molecule. This work draws attention to the importance of MOF structure, external-surface barriers, and solvent molecule identity to the overall transport process in MOFs, which should assist in understanding the performance of MOFs in applications such as condensed-phase heterogeneous catalysis.

Small Molecules, Non-Covalent Interactions, and Confinement

This review gives an overview of current trends in the investigation of small guest molecules, confined in neat and functionalized mesoporous silica materials by a combination of solid-state NMR and relaxometry with other physico-chemical techniques. The reported guest molecules are water, small alcohols, and carbonic acids, small aromatic and heteroaromatic molecules, ionic liquids, and surfactants. They are taken as characteristic role-models, which are representatives for the typical classes of organic molecules. It is shown that this combination delivers unique insights into the structure, arrangement, dynamics, guest-host interactions, and the binding sites in these confined systems, and is probably the most powerful analytical technique to probe these systems.

Transport Phenomena in Zeolites in View of Graph Theory and Pseudo-Phase Transition

Transport phenomena play an essential role in catalysis. While zeolite catalysis is widely applied in industrial chemical processes, its efficiency is often limited by the transport rate in the micropores of the zeolite. Experimental and theoretical methods are useful for understanding the transport phenomena on multiscale levels. Traditional diffusion models usually use a linear driving force and an isotropic continuum medium, such that transport in a hierarchical catalyst structure and the occurrence of nonlinear deactivation cannot be well understood. Due to the presence of spatial confinement and an ordered structure, some aspects of the transport in a zeolite cannot be regarded as continuum phenomena and discrete models are being developed to explain these. Graph theory and small-world networks are powerful tools that have allowed pseudo-phase transition phenomena and other nontrivial relationships to be clearly revealed. Discrete models that include graph theory can build a bridge between microscopic quantum physics and macroscopic catalyst engineering in both the space and time scales. For a fuller understanding of transport phenomena in diverse fields, several theoretical methods need to be combined for a comprehensive multiscale analysis.

Mapping diffusivity of narrow channels into one dimension

The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, a molecular-dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks confined to long, narrow, structureless channels with hard walls in the no-passing regime. We show that the diffusion coefficient obtained from the mean-squared displacement can be mapped onto the exact results for the diffusion of the strictly-one-dimensional hard rod system through an effective occupied volume fraction obtained from either the equation of state or a geometric projection of the particle interaction diameters.

Static field gradient NMR studies of water diffusion in mesoporous silica

NMR diffusometry is used to ascertain the pore-size dependent water diffusion in MCM-41 and SBA-15 silica over broad temperature ranges. Detailed analysis of 1H and 2H NMR stimulated-echo decays reveals that fast water motion through voids between different silica particles impairs such studies in the general case. However, water diffusion inside single pores is probed in the present approach, which applies high static field gradients to enhance the spatial resolution of the experiment and uses excess water in combination with subzero temperatures to embed the silica particles in an ice matrix and, thus, to suppress interparticle water motion. It is found that the diffusion of confined water slows down by almost two orders of magnitude when the pore diameter is reduced from 5.4 nm to 2.1 nm at weak cooling. In the narrower silica pores, the temperature dependence of the self-diffusion coefficient of water is well described by an Arrhenius law with an activation energy of Ea = 0.40 eV. The Arrhenius behavior extends over a broad temperature range of at least 207-270 K, providing evidence against a fragile-to-strong crossover in response to a proposed liquid-liquid phase transition near 225 K. In the wider silica pores, partial crystallization results in a discontinuous temperature dependence. Explicitly, the diffusion coefficients drop when cooling through the pore-size dependent melting temperatures Tm of confined water. This finding can be rationalized by the fact that water can explore the whole pore volumes above Tm, but is restricted to narrow interfacial layers sandwiched between silica walls and ice crystallites below this temperature. Comparing our findings for water diffusion with previous results for water reorientation, we find significantly different temperature dependencies, indicating that the Stokes-Einstein-Debye relation is not obeyed.

PFG-NMR as a Tool for Determining Self-Diffusivities of Various Probe Molecules through H-ZSM-5 Zeolites

The understanding of major zeolite applications is partially based on diffusion of molecules inside or outside microporous networks. However, it is still a challenge to measure such phenomena. The diffusion ordered nuclear magnetic resonance spectroscopy (DOSY) technique has been reported to measure a probe molecule's diffusion inside porous solids. Pulsed-field gradient (PFG)-NMR has been used herein to measure the self-diffusivity of different probe molecules, such as neopentane, benzene, toluene and 1-dodecene with increasing dynamic diameter, respectively, on a series of H-ZSM-5 zeolites. The latter materials exhibit different crystal sizes, Si/Al ratios and the presence (or absence) of crystalline defects. In addition, shaped zeolite bodies representing industrial catalysts were compared with the afore-mentioned samples.

The effect of soft repulsive interactions on the diffusion of particles in quasi-one-dimensional channels: A hopping time approach

Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping events are rare, the diffusion coefficient in the long time limit can be related to a hopping time that measures the average time it takes for a particle to escape the local cage formed by its neighbors. In this work, we show that a transition state theory (TST) that calculates the free energy barrier for two particles attempting to pass each other in the small system isobaric ensemble is able to quantitatively predict the hopping time in a system of two-dimensional soft repulsive disks [U(r_ij)=(σ/r_ij)^α] confined to a hard walled channel over a range of channel radii and degrees of particle softness measured in terms of 1/α. The free energy barrier exhibits a maximum at intermediate values of α that moves to smaller values of 1/α (harder particles) as the channel becomes narrower. However, the presence of the maximum is only observed in the hopping times for wide channels because the interaction potential dependence of the kinetic prefactor plays an increasingly important role for narrower channels. We also begin to explore how our TST approach can be used to optimize and control dynamics in confined quasi-one-dimensional fluids.

NMR relaxation in porous materials at zero and ultralow magnetic fields

NMR detection in the ultralow-field regime (below 10 μT) was used to measure the nuclear spin relaxation rates of liquids imbibed into silica pellets with mean pore diameters in the 10-50 nm range. Heptane, formic acid and acetic acid were studied and relaxation rate data were compared with a conventional field-cycling NMR technique. Detection of ¹H-¹³C spin coupling NMR signals at zero field (∼0.1 nT) allowed spectroscopic identification of molecules inside the porous material and unambiguous measurements of the chemistry-specific relaxation rates in liquid mixtures. In the case of molecules that contain ¹H and ¹³C, spin-singlet state relaxation can provide additional information about the dynamics. Applications and future improvements to the methodology are discussed.

Diffusion processes in a poly-crystalline zeolitic material: A molecular dynamics study

Extensive molecular dynamics simulations of xenon in two classes of zeolite crystal systems, one consisting of purely intra-crystalline space and the other with both intra- and inter-crystalline space are reported. The latter mimics a typical poly-crystalline sample of zeolite. Comparison of results from these two systems provides insights into the structure and dynamics in the presence of inter-crystalline space. The temperature, as well as the distance between the crystallites, has been varied. The density distribution and diffusivities calculated inside the poly-crystalline system show that the interfacial region between the crystal and the inter-crystalline region acts as a bottleneck for diffusion through the system. At lower temperatures, the particles are trapped at the interface due to the pronounced energy minima present in that region. With the increase in temperature, the particles are able to overcome this barrier frequently, and the transport across the inter-crystalline region is increased. A ballistic or superdiffusive motion is seen in the inter-crystalline region along all the axes except along the axis which has the inter-crystalline space. The transition time for ballistic to diffusive motion increases with the increase in the length of the inter-crystalline space. Velocity auto- and cross correlation functions exhibit strong oscillations and exchange of kinetic energy along directions perpendicular to the direction of the inter-crystalline space. These results explain why uptake and PFG-NMR measurements exhibit lower values for diffusivity for the same system when compared to Quasi-Elastic Neutron Scattering. Thus, using molecular dynamics simulations, we were able to correlate the difference of diffusivity values measured using various experimental methods where these inter-crystalline regions are common.

Molecular Modelling for Reactor Design

Chemical reactor modelling based on insights and data on a molecular level has become reality over the last few years. Multiscale models describing elementary reaction steps and full microkinetic schemes, pore structures, multicomponent adsorption and diffusion inside pores, and entire reactors have been presented. Quantum mechanical (QM) approaches, molecular simulations (Monte Carlo and molecular dynamics), and continuum equations have been employed for this purpose. Some recent developments in these approaches are presented, in particular time-dependent QM methods, calculation of van der Waals forces, new approaches for force field generation, automatic setup of reaction schemes, and pore modelling. Multiscale simulations are discussed. Applications of these approaches to heterogeneous catalysis are demonstrated for examples that have found growing interest over the last few years, such as metal-support interactions, influence of pore geometry on reactions, noncovalent bonding, reaction dynamics, dynamic changes in catalyst nanoparticle structure, electrocatalysis, solvent effects in catalysis, and multiscale modelling.

On the parallelism between the mechanisms behind chromatography and drug delivery: the role of interactions with a stationary phase

A huge number of studies and work in the drug delivery literature are focused on understanding and modeling transport phenomena, the pivotal point for a good device design. The rationalization of all phenomena involved is fundamental, but several concerns arise leaving many issues unsolved. In order to change the point of view we decided to focus our attention on the parallelisms between two fields that seem to be very far from each other: chromatography and drug release. Taking advantages of the studies conducted by many researchers using chromatographic columns we decided to explain all the phenomena involved in drug delivery considering sodium ibuprofen (IP) molecules as analytes and hydrogel as a stationary phase. In particular, we considered not only diffusion, but also drug-polymer interactions as adsorption on the stationary phase and drug-drug interactions as aggregation of analytes. The hydrogel investigated is a promising formulation made of agarose and carbomer 974p (AC) loaded with IP, a non-steroidal common anti-inflammatory drug. The self-diffusion coefficient of IP in AC formulations was measured by using an innovative method based on a magic angle spinning NMR spectroscopic technique to produce high resolution (liquid-like) spectra. This method (HR-MAS NMR) is used in combination with pulsed field gradient spin echo (PGSE) liquid-state techniques. The model predictions satisfactorily match with the experimental data obtained in water and the gel environment, indicating that the model presented here, despite its simplicity, is able to describe the key phenomena governing the device behavior and could be used to rationalize the experimental activity.

Supramolecular Organization in Confined Nanospaces

Empty spaces are abhorred by nature, which immediately rushes in to fill the void. Humans have learnt pretty well how to make ordered empty nanocontainers, and to get useful products out of them. When such an order is imparted to molecules, new properties may appear, often yielding advanced applications. This review illustrates how the organized void space inherently present in various materials: zeolites, clathrates, mesoporous silica/organosilica, and metal organic frameworks (MOF), for example, can be exploited to create confined, organized, and self-assembled supramolecular structures of low dimensionality. Features of the confining matrices relevant to organization are presented with special focus on molecular-level aspects. Selected examples of confined supramolecular assemblies - from small molecules to quantum dots or luminescent species - are aimed to show the complexity and potential of this approach. Natural confinement (minerals) and hyperconfinement (high pressure) provide further opportunities to understand and master the atomistic-level interactions governing supramolecular organization under nanospace restrictions.

Anomaly in the Chain Length Dependence of n-Alkane Diffusion in ZIF-4 Metal-Organic Frameworks

Molecular diffusion is commonly found to slow down with increasing molecular size. Deviations from this pattern occur in some host materials with pore sizes approaching the diameters of the guest molecules. A variety of theoretical models have been suggested to explain deviations from this pattern, but robust experimental data are scarcely available. Here, we present such data, obtained by monitoring the chain length dependence of the uptake of n-alkanes in the zeolitic imidazolate framework ZIF-4. A monotonic decrease in diffusivity from ethane to n-butane was observed, followed by an increase for n-pentane, and another decrease for n-hexane. This observation was confirmed by uptake measurements with n-butane/n-pentane mixtures, which yield faster uptake of n-pentane. Further evidence is provided by the observation of overshooting effects, i.e., by transient n-pentane concentrations exceeding the (eventually attained) equilibrium value. Accompanying grand canonical Monte Carlo simulations reveal, for the larger n-alkanes, significant differences between the adsorbed and gas phase molecular configurations, indicating strong confinement effects within ZIF-4, which, with increasing chain length, may be expected to give rise to configurational shifts facilitating molecular propagation at particular chain lengths.

Anomalous molecular infiltration in graphene laminates

Molecular transport in graphene laminated coatings exhibits anomalous character: penetrant infiltration occurs through molecular-sized nano-channels having distributed path lengths.

Proton-Exchange-Induced Configuration Rearrangement in a Poly(ionic liquid) Solution: A NMR Study

Polymeric ionic liquids have emerged recently as a promising alternative to traditional polymers as the polymer electrolyte membrane materials of choice because of their strongly decoupled dynamics between the polymer backbone and the counterions. Knowledge of proton exchange and transport mechanism in such materials is critical to the design and development of new poly(ionic liquid) materials with improved electrochemical properties. Our NMR results show that the proton exchange between the labile proton of the diethylmethylammonium (NH122) cation and H₂O molecules is accompanied by a concerted configuration rearrangement of the ammonium. Through a combination of PFG-NMR and proton relaxation (line width) analysis, we demonstrate that at lower temperatures the labile proton diffuses along with the NH122 ammonium cation as an integral unit, whereas at higher temperatures the NH/H₂O proton exchange sets in gradually, and the PFG-NMR measured diffusion coefficient is a population-averaged value between the two exchanging sites.

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs' case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.

Diffusion of single dye molecules in hydrated TiO2 mesoporous films

Fluorescence correlation spectroscopy (FCS) shows how the pore dimensions of thin and hydrated TiO₂ mesoporous calcined films modulate the diffusion of molecules across the pore network.

Association and Diffusion of Li(+) in Carboxymethylcellulose Solutions for Environmentally Friendly Li-ion Batteries

Carboxymethylcellulose (CMC) has been proposed as a polymeric binder for electrodes in environmentally friendly Li-ion batteries. Its physical properties and interaction with Li(+) ions in water are interesting not only from the point of view of electrode preparation-processability in water is one of the main reasons for its environmental friendliness-but also for its possible application in aqueous Li-ion batteries. We combine molecular dynamics simulations and variable-time pulsed field gradient spin-echo (PFGSE) NMR spectroscopy to investigate Li(+) transport in CMC-based solutions. Both the simulations and experimental results show that, at concentrations at which Li-CMC has a gel-like consistency, the Li(+) diffusion coefficient is still very close to that in water. These Li(+) ions interact preferentially with the carboxylate groups of CMC, giving rise to a rich variety of coordination patterns. However, the diffusion of Li(+) in these systems is essentially unrestricted, with a fast, nanosecond-scale exchange of the ions between CMC and the aqueous environment.

Thermodynamic Resistance to Matter Flow at The Interface of a Porous Membrane

Nanoporous materials are important in industrial separation, but their application is subject to strong interfacial barriers to the entry and transport of fluids. At certain conditions the fluid inside and outside the nanoporous material can be viewed as a two-phase system, with an interface between them, which poses an excess resistance to matter flow. We show that there exist two kinds of phenomena which influence the interfacial resistance: hydrodynamic effects and thermodynamic effects, which are independent of each other. Here, we investigate the role of the thermodynamic effects in carbon nanotubes (CNTs) and slit pores and compare the associated thermodynmic resistance with that due to hydrodynamic effects traditionally modeled by the established Sampson expression. Using CH4 and CO2 as model fluids, we show that the thermodynamic resistance is especially important for moderate to high pressures, at which the fluid within the CNT or slit pore is in the condensed state. Further, we show that at such pressures the thermodynamic resistance becomes comparable with the internal resistance to fluid transport at length scales typical of membranes used in fuel cells, and of importance in membrane-based separation, and nanofluidics in general.