Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model

Probing Self-Diffusion of Guest Molecules in a Covalent Organic Framework: Simulation and Experiment

Covalent organic frameworks (COFs) are a class of porous materials whose sorption properties have so far been studied primarily by physisorption. Quantifying the self-diffusion of guest molecules inside their nanometer-sized pores allows for a better understanding of confinement effects or transport limitations and is thus essential for various applications ranging from molecular separation to catalysis. Using a combination of pulsed field gradient nuclear magnetic resonance measurements and molecular dynamics simulations, we have studied the self-diffusion of acetonitrile and chloroform in the 1D pore channels of two imine-linked COFs (PI-3-COF) with different levels of crystallinity and porosity. The higher crystallinity and porosity sample exhibited anisotropic diffusion for MeCN parallel to the pore direction, with a diffusion coefficient of Dpar = 6.1(3) × 10-10 m2 s-1 at 300 K, indicating 1D transport and a 7.4-fold reduction in self-diffusion compared to the bulk liquid. This finding aligns with molecular dynamics simulations predicting 5.4-fold reduction, assuming an offset-stacked COF layer arrangement. In the low-porosity sample, more frequent diffusion barriers result in isotropic, yet significantly reduced diffusivities (DB = 1.4(1) × 10-11 m2 s-1). Diffusion coefficients for chloroform at 300 K in the pores of the high- (Dpar = 1.1(2) × 10-10 m2 s-1) and low-porosity (DB = 4.5(1) × 10-12 m2 s-1) samples reproduce these trends. Our multimodal study thus highlights the significant influence of real structure effects such as stacking faults and grain boundaries on the long-range diffusivity of molecular guest species while suggesting efficient intracrystalline transport at short diffusion times.

Features of Self-Diffusion of Tridecane Molecules in a Porous Medium of Kaolinite Used as a Model of a Chemically Inert Membrane

The present work focused on the experimental study of the specific features of self-diffusion of tridecane molecules in macroporous kaolinite, which is used as a raw material for the production of chemically inert membranes. The measurements of self-diffusion coefficients by pulsed magnetic field gradient nuclear magnetic resonance (PMFG NMR) revealed an increased translational mobility of tridecane molecules in kaolinite with incomplete filling of the pore space. This effect was accompanied by a sharp change in the slope of the Arrhenius plot of the self-diffusion coefficients of tridecane molecules in kaolinite. An analysis of the diffusion spin echo decay in the tridecane-kaolinite system revealed a discrepancy between the experimental data and the theoretical predictions, considering the effect of the geometry of porous space on molecular mobility. It was shown that the experimental results could be interpreted in terms of a model of two phases of tridecane molecules in the pores of kaolinite, in the gaseous and adsorbed state, coexisting under the fast-exchange conditions. Within the framework of the model, the activation energies of self-diffusion were calculated, which agreed satisfactorily with the experimental data. Additionally, the effects of the internal magnetic field gradients arising in a porous medium loaded with a gas or liquid on the data of the PFG NMR measurements were calculated. It was shown that the effect of magnetic field inhomogeneities on the measured self-diffusion coefficients of tridecane in kaolinite is small and could be neglected.

Boosting molecular diffusion following the generalized Murray's Law by constructing hierarchical zeolites for maximized catalytic activity

Diffusion is an extremely critical step in zeolite catalysis that determines the catalytic performance, in particular for the conversion of bulky molecules. Introducing interconnected mesopores and macropores into a single microporous zeolite with the rationalized pore size at each level is an effective strategy to suppress the diffusion limitations, but remains highly challenging due to the lack of rational design principles. Herein, we demonstrate the first example of boosting molecular diffusion by constructing hierarchical Murray zeolites with a highly ordered and fully interconnected macro-meso-microporous structure on the basis of the generalized Murray's Law. Such a hierarchical Murray zeolite with a refined quantitative relationship between the pore size at each length scale exhibited 9 and 5 times higher effective diffusion rates, leading to 2.5 and 1.5 times higher catalytic performance in the bulky 1,3,5-triisopropylbenzene cracking reaction than those of microporous ZSM-5 and ZSM-5 nanocrystals, respectively. The concept of hierarchical Murray zeolites with optimized structural features and their design principles could be applied to other catalytic reactions for maximized performance.

Quantitating Diffusion Enhancement in Pore Hierarchies

A microporous continuum traversed by a set of mutually perpendicular channels is considered to be a model for a hierarchically porous system of the mesoporous zeolite type. Transient profiles of molecular uptake as determined by kinetic Monte Carlo (kMC) simulation are found to be in excellent agreement with the result attained by the application of the two-region model (the Kärger model) of molecular diffusion. In particular, it is found that, in the two limiting cases referred to as fast exchange and slow exchange, there exist two simple analytical expressions for the rate of molecular uptake and hence for the quantification of transport enhancement in comparison with the purely microporous adsorbent. In the general case, transport enhancement is simply recognized by the reciprocal addition of the expressions in the two limiting cases.

Understanding Oxygen Release from Nanoporous Perovskite Oxides and Its Effect on the Catalytic Oxidation of CH4 and CO

The design of nanoporous perovskite oxides is considered an efficient strategy to develop performing, sustainable catalysts for the conversion of methane. The dependency of nanoporosity on the oxygen defect chemistry and the catalytic activity of perovskite oxides toward CH₄ and CO oxidation was studied here. A novel colloidal synthesis route for nanoporous, high-temperature stable SrTi_0.65Fe_0.35O_3-δ with specific surface areas (SSA) ranging from 45 to 80 m²/g and pore sizes from 10 to 100 nm was developed. High-temperature investigations by in situ synchrotron X-ray diffraction (XRD) and TG-MS combined with H₂-TPR and Mössbauer spectroscopy showed that the porosity improved the release of surface oxygen and the oxygen diffusion, whereas the release of lattice oxygen depended more on the state of the iron species and strain effects in the materials. Regarding catalysis, light-off tests showed that low-temperature CO oxidation significantly benefitted from the enhancement of the SSA, whereas high-temperature CH₄ oxidation is influenced more by the dioxygen release. During isothermal long-term catalysis tests, however, the continuous oxygen release from large SSA materials promoted both CO and CH₄ conversion. Hence, if SSA maximization turned out to efficiently improve low-temperature and long-term catalysis applications, the role of both reducible metal center concentration and crystal structure cannot be completely ignored, as they also contribute to the perovskite oxygen release properties.

Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials

Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.

Pulsed field gradient NMR diffusion measurement in nanoporous materials

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

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.

Mesoporous silica-encapsulated gold core–shell nanoparticles for active solvent-free benzyl alcohol oxidation

Silica-encapsulated gold core@shell nanoparticles (Au@SiO₂ CSNPs) were synthesized via a tunable bottom-up procedure to catalyze the aerobic oxidation of benzyl alcohol.

Diffusion of methyl oleate in hierarchical micro-/mesoporous TS-1-based catalysts probed by PFG NMR spectroscopy

Pulsed field gradient (PFG) NMR is successfully applied to trace the diffusion of methyl oleate (MO) inside the mesopores of hierarchically structured titanium silicalite-1 (TS-1)-based catalysts. Introduction of mesoporosity by post-synthetic treatment of initially microporous TS-1 provides additional active surface to improve catalytic activity in the epoxidation of MO. The present study provides experimental evidence of the accessibility of mesopores for MO resulting from alkaline treatment of TS-1. The self-diffusion coefficients of MO inside the pores of hierarchically structured TS-1 catalysts are up to two orders of magnitude lower compared to the values in the bulk liquid phase. Additionally, the methodological capability of PFG NMR for measuring self-diffusion coefficients of long-chain hydrocarbons (up to C19) confined to narrow mesopores of catalytically active is demonstrated for the first time.

Direct assessment of methyl oleate diffusion confined to nanopores of TS-1-based catalysts by means of pulsed field gradient NMR.

Free Energy Landscape of Cellulose as a Driving Factor in the Mobility of Adsorbed Water

The diffusion coefficient of water adsorbed in hydrophilic porous materials, such as noncrystalline cellulose, depends on water activity. Faster diffusion at higher water concentrations is observed in experimental and modeling studies. In this paper, two asymptotic water concentrations, near-vacuum and fully saturated, are investigated at the surface of crystalline cellulose with molecular dynamics simulations. An increasing water concentration leads to significant changes in the free energy landscape due to perturbation of local electrostatic potential. Smoothening of strong energy minima, corresponding to sorption sites, and formation of layered structure facilitates water transport in the vicinity of cellulose. The determined transition probabilities and hydrogen bond stability reflect the changes in the energy landscape. As a result of a concentration increase, the emerging basins of attraction and spreading out of those existing in the diluted state lead to an increase in water entropy. Thermal fluctuations of cellulose are demonstrated to rearrange the landscape in the diluted limit, increase adsorbed water entropy, and decrease the water-cellulose H-bond lifetime.

1H NMR Investigations of Activated Carbon Loaded with Volatile Organic Compounds: Quantification, Mechanisms, and Diffusivity Determination

Three volatile organic compounds (VOCs), benzene, cyclohexane, and dichloromethane, were adsorbed onto activated carbon fiber cloth. ¹H (magic-angle spinning (MAS) and pulsed field gradient (PFG)) NMR techniques were carried out, and the signals were analyzed in terms of peak surface areas and shifts. These techniques were shown to be very useful for determining (i) the intrinsic quantification of adsorbed molecules (VOCs and/or water) in the porosity of the materials (the adsorption capacities ranged from 0.2 to 4 mol·kg^-1); (ii) the mechanisms of interactions between adsorbed organic molecules and the carbon walls (illustrations of positions of the molecule inside the pore volume are proposed; the proton-wall distance was less than 0.15 nm); and (iii) the diffusivities (surface diffusion coefficients (D_S) were estimated at ≈4.10^-12 m²·s^-1 for cyclohexane, ≈1.10^-11 m²·s^-1 for benzene, and ≈4.10^-11 m²·s^-1 for dichloromethane).

Noninvasive Experimental Evidence of the Linear Pore Size Dependence of Water Diffusion in Nanoconfinement

We show that nuclear magnetic relaxation experiments at variable magnetic fields (NMRD) provide noninvasive means for probing the spatial dependence of liquid diffusion close to solid interfaces. These experiments performed on samples of cylindrical and spherical nanopore geometries demonstrate that the average diffusion coefficient parallel to the interface is proportional to the pore radii in different dynamics regimes. A master curve method allows extraction of gradients of diffusion coefficients in proximity of the pore surfaces, indicative of the efficiency of coupling between liquid layers. Due to their selectivity in frequency, NMRD experiments are able to differentiate the different water dynamical events induced by heterogeneous surfaces or composed dynamical processes. This analysis relevant in physical and biological confinements highlights the interplay between the molecular and continuous description of fluid dynamics near interfaces.

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.

Diffusion in nanoporous materials: fundamental principles, insights and challenges

The increasing complexity of nanoporous catalysts and adsorbents presents a challenge to both the experimental measurement and theoretical modeling of transport behavior.

Transport properties of hierarchical micro–mesoporous materials

This work provides an overview of different experimental techniques of diffusion measurements in porous materials and discusses transport properties of several classes of hierarchically organized micro-mesoporous materials.

Water diffusion in amorphous hydrophilic systems: a stop and go process

The diffusion of H2O in three amorphous polymer-H2O systems is studied as a function of H2O content using molecular dynamics. A picture of H2O molecule motion comprising alternating steps of being bound at an adsorption site ("stop") and moving ("go") emerges. This picture is made quantitative. The bound time, frequency of stop-go steps, and tortuosity all decrease with H2O content. Fourier analysis of particle motion during bound time segments provides a measure of an attempt frequency that is connected quantitatively to the bound time and an activation energy of a hydrogen bond. For increasing H2O content, the polymer-H2O systems swell, leading to an increase in the diffusion coefficient and porosity and a decrease in activation energy.

Recent NMR developments applied to organic-inorganic materials

In this contribution, the latest developments in solid state NMR are presented in the field of organic-inorganic (O/I) materials (or hybrid materials). Such materials involve mineral and organic (including polymeric and biological) components, and can exhibit complex O/I interfaces. Hybrids are currently a major topic of research in nanoscience, and solid state NMR is obviously a pertinent spectroscopic tool of investigation. Its versatility allows the detailed description of the structure and texture of such complex materials. The article is divided in two main parts: in the first one, recent NMR methodological/instrumental developments are presented in connection with hybrid materials. In the second part, an exhaustive overview of the major classes of O/I materials and their NMR characterization is presented.

Heterogeneous catalysis for sustainable biodiesel productionviaesterification and transesterification

Low temperature catalytic conversion of triglycerides and fatty acids sourced from renewable feedstocks represents a key enabling technology for the sustainable production of biodiesel through energy efficient, intensified processes.

Diffusion Study by IR Micro-Imaging of Molecular Uptake and Release on Mesoporous Zeolites of Structure Type CHA and LTA

The presence of mesopores in the interior of microporous particles may significantly improve their transport properties. Complementing previous macroscopic transient sorption experiments and pulsed field gradient NMR self-diffusion studies with such materials, the present study is dedicated to an in-depth study of molecular uptake and release on the individual particles of mesoporous zeolitic specimens, notably with samples of the narrow-pore structure types, CHA and LTA. The investigations are focused on determining the time constants and functional dependences of uptake and release. They include a systematic variation of the architecture of the mesopores and of the guest molecules under study as well as a comparison of transient uptake with blocked and un-blocked mesopores. In addition to accelerating intracrystalline mass transfer, transport enhancement by mesopores is found to be, possibly, also caused by a reduction of transport resistances on the particle surfaces.