Diffusion in nanopores: inspecting the grounds

Methanol diffusion and dynamics in zeolite H-ZSM-5 probed by quasi-elastic neutron scattering and classical molecular dynamics simulations

Zeolite ZSM-5 is a key catalyst in commercially relevant processes including the widely studied methanol to hydrocarbon reaction, and molecular diffusion in zeolite pores is known to be a crucial factor in controlling catalytic reactions. Here, we present critical analyses of recent quasi-elastic neutron scattering (QENS) data and complementary molecular dynamics (MD) simulations. The QENS experiments show that the nature of methanol diffusion dynamics in ZSM-5 pores is dependent both on the Si/Al ratio (11, 25, 36, 40 and 140), which determines the Brønsted acid site density of the zeolite, and that the nature of the type of motion observed may vary qualitatively over a relatively small temperature range. At 373 K, on increasing the ratio from 11 to 140, the observed mobile methanol fraction increases and the nature of methanol dynamics changes from rotational (in ZSM-5 with Si/Al of 11) to translational diffusion. The latter is either confined localized diffusion within a pore in zeolites with ratios up to 40 or non-localized, longer-range diffusion in zeolite samples with the ratio of 140. The complementary MD simulations conducted over long time scales (1 ns), which are longer than those measured in the present study by QENS (≈1-440 ps), at 373 K predict the occurrence of long-range translational diffusion of methanol in ZSM-5, independent of the Si/Al ratios (15, 47, 95, 191 and siliceous MFI). The rate of diffusion increases slightly by increasing the ratio from 15 to 95 and thereafter does not depend on zeolite composition. Discrepancies in the observed mobile methanol fraction between the MD simulations (100% methanol mobility in ZSM-5 pores across all Si/Al ratios) and QENS experiments (for example, ≈80% immobile methanol in ZSM-5 with Si/Al of 11) are attributed to the differences in time resolutions of the techniques. This perspective provides comprehensive information on the effect of acid site density on methanol dynamics in ZSM-5 pores and highlights the complementarity of QENS and MD, and their advantages and limitations. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 2)'.

Geometry and Chemistry: Influence of Pore Functionalization on Molecular Transport and Diffusion in Solvent-Filled Zirconium Metal-Organic Frameworks

Postsynthetic modification (PSM) of metal-organic frameworks (MOFs) enables incorporation of diverse functionalities in pores for chemical separations, drug delivery, and heterogeneous catalysis. However, the effect of PSM on molecular transport, which is essential for most applications of MOFs, has been rarely studied. In this paper, we used perfluoroalkane-functionalized Zr-MOF NU-1008 as a platform to systematically interrogate transport processes and mechanisms in solvated pores. We anchored perfluoroalkanes onto NU-1008 nodes by solvent-assisted ligand incorporation (SALI-n, with n = 3, 5, 7, and 9 denoting the number of fluorinated carbons). Transport of a luminescent molecule, BODIPY, through individual crystallites of four versions of methanol-filled SALI-n was monitored by confocal fluorescence microscopy as a function of time and location. In comparison with the parent NU-1008, the diffusivity of the probe molecules within SALI-n declined by 2- to 7-fold depending on chain length and loading, presumably due to the reduction in pore diameter or adsorptive interactions with perfluoroalkyl chains. Atomistic simulations were performed to uncover the microscopic behavior of the BODIPY diffusion in SALI-n. The perfluoroalkyl chains are observed to stay close to the pore walls, instead of extending toward the pore center. BODIPY molecules, which preferably interact with linkers, were pushed to the interior of the channels as the chain length increased, resulting in solvated diffusion and minor differences in the short-time mobility of BODIPY in SALI-n. This suggested that the observed decline of transport diffusivity in SALI-n mainly stemmed from the reduction in the pore size when these flexible chains are present. We anticipate that this proof of concept will assist in understanding how pore functionalization can physically and chemically affect mass transport in MOFs and will be useful in further guiding the design of PSM to realize the optimal performance of MOFs for various applications.

Diffusion coefficients and MSD measurements on curved membranes and porous media

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

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.

Confinement Effects on Distribution and Transport of Neutral Solutes in a Small Hydrophobic Nanopore

Molecular dynamics simulations are used to study confinement effects in small cylindrical silica pores with extended hydrophobic surface functionalization as realized, for example, in reversed-phase liquid chromatography (RPLC) columns. In particular, we use a 6 nm cylindrical and a 10 nm slit pore bearing the same C₁₈ stationary phase to compare the conditions inside the smaller-than-average pores within an RPLC column to column-averaged properties. Two small, neutral, apolar to moderately polar solutes are used to assess the consequences of spatial confinement for typical RPLC analytes with water (W)-acetonitrile (ACN) mobile phases at W/ACN ratios between 70/30 and 10/90 (v/v). The simulated data show that true bulk liquid behavior, as observed over an extended center region in the 10 nm slit pore, is not recovered within the 6 nm cylindrical pore. Instead, the ACN-enriched solvent layer around the C₁₈ chain ends (the ACN ditch), a general feature of hydrophobic interfaces equilibrated with aqueous-organic liquids, extends over the entire pore lumen of the small cylindrical pore. This renders the entire pore a highly hydrophobic environment, where, contrary to column-averaged behavior, neither the local nor the pore-averaged sorption and diffusion of analytes scales directly with the W/ACN ratio of the mobile phase. Additionally, the solute polarity-related discrimination between analytes is enhanced. The consequences of local ACN ditch overlap in RPLC columns are reminiscent of ion transport in porous media with charged surfaces, where electrical double-layer overlap occurring locally in smaller pores leads to discrimination between co- and counterionic species.

Diffusion coefficients in nanoporous solids derived from membrane permeation measurements

Based on the molecular understanding of the interplay of diffusion and adsorption, new membrane materials can be developed and the operational conditions of gas separation membranes can be optimized. Therefore, numerous diffusion and adsorption studies are conducted to optimize membrane materials. However, in an opposite way, transport or Fickian diffusion coefficients DT can be derived from membrane permeation studies with surprising accuracy. From measuring the gas transport through nanoporous supported thin-layer membranes or through mixed matrix membranes with nanoporous fillers in a polymer matrix, the transport diffusion coefficients DT of gases in novel nanoporous materials such as zeolites, MOFs, COFs… can be estimated.