Diffusion of Alkane Mixtures in Zeolites: Validating the Maxwell−Stefan Formulation Using MD Simulations

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.

Modeling the transport of CO2, N2, and their binary mixtures through highly permeable silicalite-1 membranes using Maxwell-Stefan equations

Carbon dioxide (CO₂) is the main contributor to global warming; therefore, research efforts aim at its capture. Membranes, in particular, zeolite membranes offer a promising approach for CO₂ separation and capture. Membranes are typically characterized by their selectivity and permeance that are highly dependent on the operating conditions namely, total feed pressure and composition. Therefore, more reliable characterization parameters are required such as Maxwell- Stefan exchange diffusivities. In this work, a model based on Maxwell-Stefan equations and Extended Langmuir isotherm was developed to investigate the transport of binary mixtures of CO₂ and N₂ through thin silicalite-1 membranes. The exchange diffusivities, D₁₂ and D₂₁, of CO₂ and N₂ were determined at different total feed pressures and feed compositions. All gas separation tests were conducted at stage cut not exceeding 5%. The single component diffusivities of CO₂ and N₂ required by the model were found experimentally using the results of the respective single gas permeation tests. The results displayed that as CO₂ concentration in the feed increased from 15% to 85%, the values of D₁₂ and D₂₁ decreased from 2.8 × 10^-10 to 1.1 × 10^-10 m²/s and 2.8 × 10^-10 to 1.3 × 10^-10 m²/s, respectively, while the N₂ permeance decreased by about one order of magnitude from 2.7 × 10^-7 to 2.4 × 10^-8 mol/m².s.Pa. Consequently, the exchange diffusivities showed considerably smaller dependence on the operating conditions compared to the permselectivity and permeance. Hence, they are more appropriate in describing the intrinsic transport characteristics of silicalite-1 membranes.

Simultaneous interlayer and intralayer space control in two-dimensional metal-organic frameworks for acetylene/ethylene separation

Three-dimensional metal−organic frameworks (MOFs) are cutting-edge materials in the adsorptive removal of trace gases due to the availability of abundant pores with specific chemistry. However, the development of ideal adsorbents combining high adsorption capacity with high selectivity and stability remains challenging. Here we demonstrate a strategy to design adsorbents that utilizes the tunability of interlayer and intralayer space of two-dimensional fluorinated MOFs for capturing acetylene from ethylene. Validated by X-ray diffraction and modeling, a systematic variation of linker atom oxidation state enables fine regulation of layer stacking pattern and linker conformation, which affords a strong interlayer trapping of molecules along with cooperative intralayer binding. The resultant robust materials (ZUL-100 and ZUL-200) exhibit benchmark capacity in the pressure range of 0.001–0.05 bar with high selectivity. Their efficiency in acetylene/ethylene separation is confirmed by breakthrough experiments, giving excellent ethylene productivities (121 mmol/g from 1/99 mixture, 99.9999%), even when cycled under moist conditions.

Designing efficient adsorbents for trace gas removal remains a serious challenge. Here, the authors show promise in layered 2D metal−organic frameworks, often overlooked in favor of 3D frameworks, for separating trace acetylene from ethylene with enhanced performance and high stability.

Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials

The Maxwell-Stefan (M-S) formulation, that is grounded in the theory of irreversible thermodynamics, is widely used for describing mixture diffusion in microporous crystalline materials such as zeolites and metal-organic frameworks (MOFs). Binary mixture diffusion is characterized by a set of three M-S diffusivities: Đ ₁, Đ ₂, and Đ ₁₂. The M-S diffusivities Đ ₁ and Đ ₂ characterize interactions of guest molecules with pore walls. The exchange coefficient Đ ₁₂ quantifies correlation effects that result in slowing-down of the more mobile species due to correlated molecular jumps with tardier partners. The primary objective of this article is to develop a methodology for estimating Đ ₁, Đ ₂, and Đ ₁₂ using input data for the constituent unary systems. The dependence of the unary diffusivities Đ ₁ and Đ ₂ on the pore occupancy, θ, is quantified using the quasi-chemical theory that accounts for repulsive, or attractive, forces experienced by a guest molecule with the nearest neighbors. For binary mixtures, the same occupancy dependence of Đ ₁ and Đ ₂ is assumed to hold; in this case, the occupancy, θ, is calculated using the ideal adsorbed solution theory. The exchange coefficient Đ ₁₂ is estimated from the data on unary self-diffusivities. The developed estimation methodology is validated using a large data set of M-S diffusivities determined from molecular dynamics simulations for a wide variety of binary mixtures (H₂/CO₂, Ne/CO₂, CH₄/CO₂, CO₂/N₂, H₂/CH₄, H₂/Ar, CH₄/Ar, Ne/Ar, CH₄/C₂H₆, CH₄/C₃H₈, and C₂H₆/C₃H₈) in zeolites (MFI, BEA, ISV, FAU, NaY, NaX, LTA, CHA, and DDR) and MOFs (IRMOF-1, CuBTC, and MgMOF-74).

A Facile Way to Prolong Service Life of Double Base Propellant

The safe storage time for double base propellant (DBP or DB propellant) with stabilizers could usually be calculated to be greater than 40 years. However, the actual service life is far below that, which is largely caused by the decline of propellant mechanical performance. In this work polytetrafluoroethylene (PTFE) was introduced into the double base propellant formula as an additive. The tensile properties of this propellant before and after artificial aging were determined. The evaporation and diffusion characteristics of nitroglycerin (NG) in propellant were evaluated by thermogravimetry analysis (TGA). The results showed that mechanical properties of propellant were improved due to PTFE, especially for elongation at −40 °C, which was greatly increased by 115%. Moreover, the results of TGA showed that NG migration was reduced due to PTFE, which delayed the decline of propellant mechanical performance during aging. The reduction in elongation at −40 °C caused by aging was decreased by 68.5% for PTFE modified DBP. Enhanced mechanical properties and reduced NG migration could potentially prolong propellant service life.

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.

Commensurate-incommensurate adsorption and diffusion in ordered crystalline microporous materials

For homologous series of linear chain molecules, there could be either a match, or mismatch, between the characteristic periodicity of the host structure and the characteristic length of the guest molecules. The major objective of this article is to highlight the influence of commensurateness, or incommensurateness, on both the adsorption and diffusion characteristics. Published experimental data, backed by molecular simulation results, are used to highlight the attendant non-monotonicity in adsorption strengths and diffusivities. We demonstrate the possibility of separating mixtures of n-alkanes, n-alcohols, and hydrocarbon isomers by appropriate and judicious choice of the dimensions, topology, and connectivity of the crystalline host material. Of particular practical interest are entropy-based separations that manifest at pore saturation conditions, relying on differences in the saturation capacities of the constituent species; the exploiting of such entropy effects is discussed with the aid of several examples.

Self-diffusivity, M-S and Fick diffusivity of CO2 in Na-clay: The influences of concentration and temperature

Storing CO₂ in underground saline aquifers is an important way to reduce CO₂ emission in atmosphere, where gas/fluid diffusion in clay plays a key role in CO₂ leakage and migration. Various diffusivities, self-diffusivity, Maxwell–Stefan (M–S) diffusivity and Fick diffusivity, in clay interlayer are investigated by molecular dynamics (MD). Self-diffusivity varies with CO₂ concentration, and reaches the maximum value at 2 molecules/unit-cell. High fluid concentration leads to clay swelling, thereby increasing self-diffusivity. However, the fractional free volume of clay explains the trend of CO₂ self-diffusivity, which does not decrease with CO₂ concentration monotonously but reaches the maximum when CO₂ concentration reaches 2. Displacement distribution of CO₂ molecules is analysed to explore the microscopic diffusion mechanism, which is characterised by logarithmic normal distribution. The mean value of such distribution further explains the self-diffusivity dependence on CO₂ concentration. M–S and Fick diffusivities of CO₂ are calculated by MD for the first time, both of which increase with increasing CO₂ and H₂O concentration and temperature. Based on self-diffusivity and M–S diffusivity, a quantity representing the coupling strength between CO₂ molecules is presented; it increases firstly with CO₂ concentration but begins to decrease when CO₂ concentration is beyond 2.

Uphill diffusion and overshooting in the adsorption of binary mixtures in nanoporous solids

Under certain conditions, during binary mixture adsorption in nanoporous hosts, the concentration of one component may temporarily exceed its equilibrium value. This implies that, in contrast to Fick's Law, molecules must diffuse in the direction of increasing rather than decreasing concentration. Although this phenomenon of ‘overshooting' has been observed previously, it is only recently, using microimaging techniques, that diffusive fluxes in the interior of nanoporous materials have become accessible to direct observation. Here we report the application of interference microscopy to monitor ‘uphill' fluxes, covering the entire period of overshooting from initiation until final equilibration. It is shown that the evolution of the profiles can be adequately predicted from the single-component diffusivities together with the binary adsorption equilibrium data. The guest molecules studied (carbon dioxide, ethane and propene) and the host material (ZSM-58 or DDR) are of practical interest in relation to the development of kinetically selective adsorption separation processes.

During the transient adsorption of a binary mixture in a nanoporous host, the concentration of one component may temporarily exceed its equilibrium value, with molecules diffusing in the direction of increasing concentration. Here, the authors use microimaging to examine this process in a real system.

A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO2 in microporous materials

We applied a method based on a block cellular automaton (BCA) algorithm to the study of diffusion of various binary mixtures adsorbed in a model microporous material, such as zeolite ZK4. Our aim was to test the capability of our model to cope with systems in which more than one species is present, using a set of parameters based on heuristic considerations from the molecular dynamics (MD) results present in the literature. A rigorous methodology for the assignment of suitable adsorption energies and diffusion activation barriers for our BCA has not been developed yet, nonetheless the results were quite interesting at this stage and we obtained a good qualitative agreement with MD data in the literature. The mixtures we investigated contain CO(2), which causes the so-called segregation-effect, a strong suppression of self-diffusivity of co-adsorbed species. This effect gives rise to relevant problems in the application of some well established and robust methods, while our model proved to be able to reproduce both the common features and the segregation anomaly in the trends of diffusion.

Thermophysical properties of undercooled alloys: an overview of the molecular simulation approaches

We review the studies on the thermophysical properties of undercooled metals and alloys by molecular simulations in recent years. The simulation methods of melting temperature, enthalpy, specific heat, surface tension, diffusion coefficient and viscosity are introduced and the simulated results are summarized. By comparing the experimental results and various theoretical models, the temperature and the composition dependences of the thermophysical properties in undercooled regime are discussed.

Hydrogen bonding effects in adsorption of water-alcohol mixtures in zeolites and the consequences for the characteristics of the Maxwell-Stefan diffusivities

This work highlights a variety of peculiar characteristics of adsorption and diffusion of polar molecules such as water, methanol and ethanol in zeolites. These peculiarities are investigated with the aid of configurational-bias Monte Carlo (CBMC) simulations of adsorption isotherms, and molecular dynamics (MD) simulations of diffusivities in FAU, MFI, DDR, and LTA zeolites. Because of strong hydrogen bonding, significant clustering of the guest molecules occurs in all investigated structures. Because of molecular clustering, the inverse thermodynamic factor 1/Gamma(i) identical with (d[ln c(i)])/(d[ln f(i)]) exceeds unity for a range molar concentrations c(i) within the micropores. The degree of clustering is lowered as the temperature is increased. For the concentration ranges for which 1/Gamma(i) > 1, the Fick diffusivity, D(i), for unary diffusion is often lower than both the Maxwell-Stefan, D(i), and the self-diffusivity, D(i,self). For water-alcohol mixtures, the hydrogen bonding between water and alcohol molecules is much more predominant than for water-water, and alcohol-alcohol molecule pairs. Consequently, the adsorption of water-alcohol mixtures shows significant deviations from the predictions of the ideal adsorbed solution theory (IAST). The water-alcohol bonding also leaves its imprint on the mixture diffusion characteristics. The Maxwell-Stefan diffusivity, D(i), of either component in water-alcohol mixtures is lower than the corresponding values of the pure components; this behavior is distinctly different from that for mixtures of nonpolar guest molecules. The binary exchange coefficient D(12) for water-alcohol mixtures is also significantly lower than either self-exchange coefficients D(11) and D(22) of the constituent species. This implies that correlation effects are significantly stronger in water-alcohol mixtures than for the constituent species. Correlation effects are found to be significant for water-alcohol mixture diffusion in DDR and LTA zeolites, even though such effects are negligible for the pure constituents. The major conclusion to emerge from this investigation is that, unlike mixtures of nonpolar molecules, it is not possible to estimate water-alcohol mixture adsorption and diffusion characteristics on the basis of pure component data.

Modeling pure gas permeation in nanoporous materials and membranes

The low-pressure transport of simple fluids in nanopores and in disordered nanoporous networks is analyzed, using a recent oscillator model theory from the author's laboratory, considering the trajectories of molecules moving in the potential energy field of the fluid-pore wall interaction. The scaling behavior of the single-pore theory is discussed, and it is shown that the Knudsen model provides an upper bound to the diffusivity scaled with the pore radius. The single-pore theory is shown to apply well to ordered materials and successfully interprets recent literature data on the variation of permeability with diffusant molecular size for a DDR zeolite membrane. A peak in permeability is seen at a pore-size-dependent molecular size because of the opposing effects of equilibrium and transport. Application to disordered pore networks is also presented on the basis of a hybrid correlated random walk effective medium theory imbedding the oscillator model at the single-pore level, and a rigorous expression for the tortuosity is derived from the theory. A rich variety of behavior is predicted for the tortuosity, which can increase or decrease with increasing extent of pore size nonuniformity as well as with changes in temperature because the diffusing species preferentially flows through more conducting pores. Weakly adsorbing gases such as helium are seen to have a higher tortuosity than more strongly adsorbing ones. The predicted values of tortuosity are shown to be in line with those obtained from the interpretation of recent experimental mesoporous membrane transport data and are in the range of 5-10 whereas those extracted using the Knudsen model are unrealistically high, in the range of 10-20.

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.