Concentration and Chainlength Dependence of the Diffusivity of Alkanes in Zeolites Studied with MD Simulations

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.

Hyperloop-like diffusion of long-chain molecules under confinement

The ultrafast transport of adsorbates in confined spaces is a goal pursued by scientists. However, diffusion will be generally slower in nano-channels, as confined spaces inhibit motion. Here we show that the movement of long-chain molecules increase with a decrease in pore size, indicating that confined spaces promote transport. Inspired by a hyperloop running on a railway, we established a superfast pathway for molecules in zeolites with nano-channels. Rapid diffusion is achieved when the long-chain molecules keep moving linearly, as well as when they run along the center of the channel, while this phenomenon do not exist for short-chain molecules. This hyperloop-like diffusion is unique for long-chain molecules in a confined space and is further verified by diffusion experiments. These results offer special insights into molecule diffusion under confinement, providing a reference for the selection of efficient catalysts with rapid transport in the industrial field.

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.

Topology-Dependent Alkane Diffusion in Zirconium Metal-Organic Frameworks

Metal-organic frameworks (MOFs) can be designed for chemical applications by modulating the size and shape of intracrystalline pores through selection of their nodes and linkers. Zirconium nodes with variable connectivity to organic linkers allow for a broad range of topological nets that have diverse pore structures even for a consistent set of linkers. Identifying an optimal pore structure for a given application, however, is complicated by the large material space of possible MOFs. In this work, molecular dynamics simulations were used to determine how a MOF's topology affects the diffusion of propane and isobutane over the full range of loadings and to understand how MOFs can be tuned to reduce transport limitations for applications in separations and catalysis. High-throughput simulation techniques were employed to efficiently calculate loading-dependent diffusivities in 38 MOFs. The results show that topologies with higher node connectivity have reduced alkane diffusivities compared to topologies with lower node connectivity. Molecular siting techniques were used to elucidate how the pore structures in different topologies affect adsorbate diffusivities.

Understanding the Loading Dependence of Adsorbate Diffusivities in Hierarchical Metal-Organic Frameworks

Using atomistic simulations, we studied the diffusion of n-hexane in a series of isoreticular hierarchical metal-organic frameworks (MOFs) NU-100x. Nonmonotonic diffusivity-loading relationships that depend on the pore sizes were observed, which can be explained by the spatial distribution of adsorbates at different loadings. For one of the MOFs in the series, NU-1000-M, the diffusivity-loading relationship is almost identical to the previously reported results of n-hexane diffusion in the hierarchical self-pillared pentasil (SPP) zeolite. Detailed analysis revealed that the similarity results from their similar micropore and window sizes, which was confirmed by free-energy mapping. The effects of temperature and adsorbate chain length on the diffusion were also studied, which supported our conclusion that the diffusivity in hierarchical nanoporous materials is primarily controlled by the sizes of the micropores and the connecting windows, particularly at relatively low loadings.

Molecular Dynamics Study of Hydrogen on Alkali-Earth Metal Cations Exchanged X Zeolites

The self-diffusion of hydrogen in Ca2+-, Mg2+- and Ba2+-exchanged X zeolites (Mg46X, Ca46X, and Ba46X) has been studied by molecular dynamics (MD) simulations for various temperatures and loadings. The results indicate that in the temperature range of 77–298 K and the loading range of 1–80 molecules/cell, the self-diffusion coefficients are found to range from1.2×10-9 m2·s−1to2.3×10-7 m2·s−1which are in good agreement with the experimental values from the quasielastic neutron scattering (QENS) and pulse field gradients nuclear magnetic resonance (PFG NMR) measurements. The self-diffusion coefficients decrease with loading due to packing of sorbate-sorbate molecules which causes frequent collusion among hydrogen molecules in pores and increases with increasing temperature because increasing the kinetic energy of the gas molecules enlarges the mean free path of gas molecule. The mechanism of diffusion of hydrogen molecules in these zeolites is transition diffusion. Knudsen diffusion occurs at low loading and the molecular bulk diffusion occurs at higher loading. For given temperature and loading, the self-diffusion coefficients decrease in the orderBa46X<Mg46X<Ca46X, due to the different sizes and locations of the divalent cations. Moreover, the effect of concentration of molecular hydrogen on self-diffusion coefficient also is analyzed using radial distribution function (RDF).

Molecular-Dynamics Simulation of Self-Diffusion of Molecular Hydrogen in X-Type Zeolite

The self-diffusion of hydrogen in NaX zeolite has been studied by molecular-dynamics simulations for various temperatures and pressures. The results indicate that in the temperature range of 77–293 K and the pressure range of 10–2700 kPa, the self-diffusion coefficients are found to range from 1.61 × 10−9 m2·s−1to 3.66 × 10−8 m2·s−1which are in good agreement with the experimental values from the quasielastic neutron scattering (QENS) and pulse field gradients nuclear magnetic resonance (PFG NMR) measurements. The self-diffusion coefficients decrease with increasing pressure due to packing of sorbate-sorbate molecules which causes frequent collusion among hydrogen molecules in pores and increase with increasing temperature because increasing the kinetic energy of the gas molecules enlarges the mean free path of gas molecule. The activated energy for hydrogen diffusion determined from the simulation is pressure-dependent.

Molecular modeling of chiral-modified zeolite HY employed in enantioselective separation

Insight into enantioselective separation utilizing chiral-modified zeolite HY could be useful in designing a chiral stationary phase for resolving pharmaceutical compounds. A model was employed to better understand the enantioseparation of valinol in zeolite HY that contains (+)-(1R;2R)-hydrobenzoin as a chiral modifier. This model incorporates the zeolite support and accounts for the flexible change. Results from grand canonical Monte Carlo and molecular dynamics simulations indicate that the associated diastereomeric complex consists of a single (+)-(1R;2R)-hydrobenzoin and a single valinol molecules located in the zeolite HY supercage. Supercage-based docking simulation predicted an enantioselectivity of 2.6 compared with that of 1.4 measured experimentally. Also, the supercage-based docking simulation demonstrated a single binding motif in the S complex, and two binding motifs in the R complex. The multiple binding modes in the R complex resulted in its lower stability. This is hypothesized to be the origin of the weaker binding between (-)-(R)-valinol and the chiral modifier, and explains why (+)-(R)-valinol is retained more in the chiral-modified zeolite system studied.

Molecular dynamics simulation of self- and mutual diffusion coefficients for confined mixtures

The self- and mutual diffusion coefficients for binary mixtures of Ar-Kr both in the bulk and in the nanopores were studied by molecular dynamics simulations. The composition dependences and the relationships between the self- and the mutual diffusion coefficients both in the bulk and in the nanopores were further discussed. It was found that the simulation results (D(c.m.)) are close to the calculated ones (D(s)) for the Ar-Kr system. Both self- and mutual diffusion coefficients in nanopores are much lower than that of the bulk, and they ever decrease as the pore width decreases. Nevertheless, the self- and mutual diffusion coefficients increase as the mole fraction of Ar increases, and as expected, increase as the temperature increases. The self-diffusion coefficients of mixtures both in the bulk and in the nanopores are predicted by the Carman model and by the molecular cluster model.

Insertion of Dipolar Molecules in Channels of a Centrosymmetric Organic Zeolite: Molecular Modeling and Experimental Investigations on Diffusion and Polarity Formation

The mechanism of insertion of p-nitroaniline (PNA) and its diffusion behavior in channels of the hexagonal host structure of tris(o-phenylenedioxy)cyclotriphosphazene (TPP) was investigated by means of molecular modeling tools. Strong preferential sites in the bulk were found to be due to pi-pi and NH-pi interactions between PNA and channel walls of TPP. MD simulations showed that diffusion can be characterized by jumps from one site to the next, occurring mainly because of the dynamic flexibility of the host structure. Calculations of host-guest interactions between the TPP surface and PNA approaching the entrance of channels with its terminal H2N-first or O2N-first revealed that the H2N-first insertion is clearly preferred. Preferential insertion of PNA is found to be the reason for polar effects, observed experimentally. Because of a distinct guest-host recognition at the surface, guest-guest interactions were found to have a minor influence on polarity.

Detailed Process of Adsorption of Alkanes and Alkenes on Zeolites

The adsorption of alkanes and alkenes on zeolites is investigated by comparing the adsorption characteristics for three types of zeolite: ferrierite, ZSM-5, and mordenite. The activation energy for the diffusion of propane and n-butane on ferrierite and the heat of adsorption of C(2)-C(4) alkanes and alkenes on zeolites and silica are estimated based on Fourier transform infrared spectroscopy, and the diffusion processes in the micropores are elucidated by comparing the results with previously reported activation energies for n-butene diffusion. The adsorption of 1-butene on mordenite is also examined. The structure and process of experimentally observable adsorption is found to differ depending on the type of zeolite and adsorbing molecule, reflecting differences in the sizes of molecules and pores. This differing behavior is utilized to interpret the elementary adsorption processes of alkanes and alkenes on zeolites.

Molecular simulations of the adsorption of cycloalkanes in MFI-type silica

A new force field for the simulation of the adsorption of cycloalkanes in nanoporous silica affords a significant improvement over any previously employed force field. The simulated isotherms reproduce the most salient features in the experimental isotherms extremely well. The study of cyclo-pentane, -hexane, and -heptane adsorption in MFI-type silica indicates an inflection for cyclopentane but not for cyclohexane at intermediate pressure. If corroborated by experiments, such an inflection point would afford an excellent calibration point for further force field developments. At low pressures, mixture isotherms of cyclohexane and n-hexane show a temperature dependence on the selectivity in accordance with recent results by J. P. Fox and S. P. Bates, J. Phys. Chem., 2004, 108, 17136. This dependence is caused by a difference in temperature dependence of the Henry coefficient for both molecules. At high pressures entropy effects due to packing always favor the sorption of n-hexane. Furthermore, the influence of the flexibility of the zeolite framework on the adsorption of these rather bulky molecules is investigated. It is found that this influence of the flexibility on the adsorption of cyclohexane is as small as with n-alkanes.

Computer simulations of adsorption and diffusion for binary mixtures of methane and hydrogen in titanosilicates

Equilibrium molecular dynamics (MD) simulations of equimolar mixtures of hydrogen and methane were performed in three different titanosilicates: naturally occurring zorite and two synthetic titanosilicates, ETS-4 and ETS-10. In addition, single-component MD simulations and adsorption isotherms generated using grand canonical Monte Carlo simulations were performed to support the mixture simulations. The goal of this study was to determine the best membrane material to carry out hydrogen/methane separations. ETS-10 has a three-dimensional pore network. ETS-4 and zorite have two-dimensional pore networks. The simulations carried out in this study show that the increased porosity of ETS-10 results in self-diffusion coefficients for both hydrogen and methane that are higher in ETS-10 than in either ETS-4 or zorite. Methane only showed appreciable displacement in ETS-10. The ability of the methane molecules to move in all three directions in ETS-10 was demonstrated by the high degree of isotropy shown in the values of the x, y, and z components of the self-diffusion coefficient for methane in ETS-10. From our simulations we conclude that ETS-10 would be better suited for fast industrial separations of hydrogen and methane. However, the separation would not result in a pure hydrogen stream. In contrast, ETS-4 and zorite would act as true molecular sieves for separations of hydrogen and methane, as the methane would not move through membranes made of these materials. This was indicated by the near-zero self-diffusion coefficient of methane in ETS-4 and zorite.

Incommensurate diffusion in confined systems

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate. Furthermore, the physical compatibility between the adsorbate and the adsorbent has a direct effect on the heat of adsorption, the Henry coefficients, the activation energy, and the frequency factors.

n-Pentane and isopentane in one-dimensional channels

Molecular dynamics studies of n-pentane and isopentane in one-dimensional channels of AlPO(4)-5 and a carbon nanotube are reported. Variation of the structure and energetics in AlPO(4)-5 along the channel axis of isopentane is similar to what has been found for other rigid molecular systems. In n-pentane, these properties exhibit more frequent undulations along the channel due to flexibility. The end-to-end distance of n-pentane is a function of its position along the channel in AlPO(4)-5, suggesting that n-pentane has to alternately stretch in the narrow part and destretch or coil in the broader part of the channel. n-Pentane lies flat instead of upright on the inner surface of the carbon nanotube. Both of the species exhibit diffusive motion in AlPO(4)-5, and the self-diffusivity is higher than that in bulk. Isopentane has a higher diffusivity than does n-pentane. This is attributed to the higher cross section of isopentane, which is closer to the void cross section. Further, the coupling of the translational motion with the slower dihedral angle reorientation in the case of n-pentane decreases its mobility. Superdiffusive motion is seen for both species in the carbon nanotube. These results can be understood in terms of the levitation effect.

Analytical results for the reactivity of a single-file system

We derive analytical expressions for the reactivity of a single-file system with fast diffusion and particles entering and leaving the system at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of particles entering and leaving the system. For large systems, the number of unconverted particles decreases exponentially with distance from the open end.

A periodic DFT study of intramolecular isomerization reactions of toluene and xylenes catalyzed by acidic mordenite

A periodic density functional theory (DFT) study of the isomerization reactions of toluene and xylene catalyzed by acidic mordenite is reported. Monomolecular isomerization reactions have been considered and analyzed. The different reaction pathways have been discussed in detail. The use of periodic structure calculations allows consideration and analysis of zeolite electrostatic contributions and steric constraints that occur within zeolite micropores. Major differences in the details of protonation reaction pathways are found when periodic structures are used rather than small cluster models of the Brønsted acidic site. Complex relationships are found between zeolite topology and reaction pathways.