Exploration of molecular dynamics during transient sorption of fluids in mesoporous materials

Microimaging of transient guest profiles to monitor mass transfer in nanoporous materials

The intense interactions of guest molecules with the pore walls of nanoporous materials is the subject of continued fundamental research. Stimulated by their thermal energy, the guest molecules in these materials are subject to a continuous, irregular motion, referred to as diffusion. Diffusion, which is omnipresent in nature, influences the efficacy of nanoporous materials in reaction and separation processes. The recently introduced techniques of microimaging by interference and infrared microscopy provide us with a wealth of information on diffusion, hitherto inaccessible from commonly used techniques. Examples include the determination of surface barriers and the sticking coefficient's analogue, namely the probability that, on colliding with the particle surface, a molecule may continue its diffusion path into the interior. Microimaging is further seen to open new vistas in multicomponent guest diffusion (including the detection of a reversal in the preferred diffusion pathways), in guest-induced phase transitions in nanoporous materials and in matching the results of diffusion studies under equilibrium and non-equilibrium conditions.

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.

Designed synthesis of CO2-promoted copper(ii) coordination polymers: synthesis, structural and spectroscopic characterization, and studies of versatile functional properties

A series of CO₂-promoted Cu(ii) coordination polymers in different coordination environments has been synthesized.

SAXS characterization of polymer-embedded hollow nanoparticles and of their shell porosity

Size parameters of SiO2/TiO2hollow nanoparticles (HNPs) of 25–100 nm in diameter were characterized by small-angle X-ray scattering (SAXS). On the basis of the decoupling and the Percus–Yevick approximations, and using a hollow sphere model, size information on HNPs was extracted, including average outer diameter, average inner diameter and polydispersity. Application of an alternative form factor based on hollow ellipsoids, and of a sticky hard sphere structure factor, did not improve the fit significantly. The shell porosity of the HNPs and the size of the pores in the HNP shell were further characterized by combining SAXS with gas adsorption methods. The above HNPs were then supported on a porous poly(ethylene oxide) scaffold by freeze drying from aqueous solution. To characterize the product, a multishell model was applied to fit the experimental SAXS curves and extract the following morphological information: distribution of HNPs between the surface and interior of the polymer, thickness of the polymer layers lining the outer and inner surfaces of HNPs, and densities of the outer and inner polymer layers. The work demonstrates the versatility of SAXS in obtaining key information on dissolved and polymer-supported HNPs in applications such as drug delivery and catalysis.

Elastic properties of liquid and solid argon in nanopores

We have measured sorption isotherms and determined the intrinsic longitudinal elastic modulus β(Ar,ads) of nanoconfined material via ultrasonic measurements combined with a special effective medium analysis. In the liquid regime the adsorbate only contributes to the measured effective properties when the pores are completely filled and the modulus is bulklike. At partial fillings its contribution is cancelled out by the high compressibility of the vapour phase. In contrast, at lower temperatures frozen argon as well as underlying liquid surface layers cause a linear increase of the effective longitudinal modulus upon filling. During sorption the contribution of the liquid surface layers near the pore wall β(Ar,surf) increases with the thickness of the solid layers reaching the bulk value β(Ar,liquid) only in the limit of complete pore filling. We interpret this effect as due to the gradual stiffening of the solid argon membrane. The measurements and their analysis show that longitudinal ultrasonic waves are well suited to the study of the elastic properties and liquid-solid phase transitions in porous systems. This method should also help to detect the influence of nanoconfinement on elastic properties in further research.

Sorption equilibrium, mechanism and thermodynamics studies of 1,3-propanediol on beta zeolite from an aqueous solution

To identify the adsorption characteristics of 1,3-propanediol on beta zeolite, the effects of temperature, zeolite dose, and 1,3-propanediol concentration were studied through batch experiments. The results showed that the pseudo-second order model expressed the kinetic data better. The experimental and theoretical adsorption capacities were 116.2 and 119.0 mg/g at 293 K, respectively. The adsorption equilibrium data were observed to satisfy the Freundlich isotherm model. Based on the Boyd plot, intraparticle diffusion primarily governed the uptake process. Moreover, thermodynamic parameters, such as changes in standard free energy (ΔG(0)), standard enthalpy (ΔH(0)), and standard entropy, were estimated. The negative values of ΔG(0) and ΔH(0) (-9.4 kJ/mol) indicated that the adsorption process was spontaneous, exothermic, and feasible. Finally, the activation energy derived from the Arrhenius equation suggested that the interaction mainly constitute physical adsorption.

Rapid, conformal gas-phase formation of silica (SiO2) nanotubes from water condensates

An innovative atomic layer deposition (ALD) concept, with which nanostructures of water condensates with high aspect ratio at equilibrium in cylindrical nanopores can be transformed uniformly into silica (SiO2) at near room temperature and ambient pressure, has been demonstrated for the first time. As a challenging model system, we first prove the conversion of cylindrical water condensates in porous alumina membranes to silica nanotubes (NTs) by introducing SiCl4 as a metal reactant without involving any catalytic reaction. Surprisingly, the water NTs reproducibly transformed into silica NTs, where the wall thickness of the silica NTs deposited per cycle was found to be limited by the amount of condensed water, and it was on the orders of ten nanometers per cycle (i.e., over 50 times faster than that of conventional ALD). More remarkably, the reactions only took place for 10-20 minutes or less without vacuum-related equipment. The thickness of initially adsorbed water layers in cylindrical nanopores was indirectly estimated from the thickness of formed SiO2 layers. With systematic experimental designs, we tackle the classical Kelvin equation in the nanosized pores, and the role of van der Waals forces in the nanoscale wetting phenomena, which is a long-standing issue lacking experimental insight. Moreover, we show that the present strategy is likely generalized to other oxide systems such as TiO2. Our approach opens up a new avenue for ultra-simple preparation of porous oxides and allows for the room temperature formation of dielectric layers toward organic electronic and photovoltaic applications.

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.

Capillary condensation in one-dimensional irregular confinement

A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.

Estimation of pore size distribution using concentric double pulsed-field gradient NMR

Estimation of pore size distribution of well calibrated phantoms using NMR is demonstrated here for the first time. Porous materials are a central constituent in fields as diverse as biology, geology, and oil drilling. Noninvasive characterization of monodisperse porous samples using conventional pulsed-field gradient (PFG) NMR is a well-established method. However, estimation of pore size distribution of heterogeneous polydisperse systems, which comprise most of the materials found in nature, remains extremely challenging. Concentric double pulsed-field gradient (CDPFG) is a 2-D technique where both q (the amplitude of the diffusion gradient) and φ (the relative angle between the gradient pairs) are varied. A recent prediction indicates this method should produce a more accurate and robust estimation of pore size distribution than its conventional 1-D versions. Five well defined size distribution phantoms, consisting of 1-5 different pore sizes in the range of 5-25 μm were used. The estimated pore size distributions were all in good agreement with the known theoretical size distributions, and were obtained without any a priori assumption on the size distribution model. These findings support that in addition to its theoretical benefits, the CDPFG method is experimentally reliable. Furthermore, by adding the angle parameter, sensitivity to small compartment sizes is increased without the use of strong gradients, thus making CDPFG safe for biological applications.

Characterizing size and porosity of hollow nanoparticles: SAXS, SANS, TEM, DLS, and adsorption isotherms compared

A combination of experimental methods, including transmission and grazing incidence small-angle X-ray scattering (SAXS and GISAXS), small-angle neutron scattering (SANS), transmission electron microscopy (TEM), dynamic light scattering (DLS), and N(2) adsorption-desorption isotherms, was used to characterize SiO(2)/TiO(2) hollow nanoparticles (HNPs) of sizes between 25 and 100 nm. In the analysis of SAXS, SANS, and GISAXS data, the decoupling approximation and the Percus-Yevick structure factor approximation were used. Brunauer-Emmett-Teller, t-plot, and a spherical pore model based on Kelvin equation were applied in the treatment of N(2) isotherms. Extracted parameters from the scattering and TEM methods are the average outer and inner diameters and polydispersity. Good agreement was achieved between different methods for these extracted parameters. Merits, advantages, and disadvantages of the different methods are discussed. Furthermore, the combination of these methods provided us with information on the porosity of the shells of HNPs and the size of intrawall pores, which are critical to the applications of HNPs as drug delivery vehicles and catalyst supports.

Silica monoliths with hierarchical porosity obtained from porous glasses

This review deals with "classical" porous glasses which are prepared by physical phase separation of alkali borosilicate glasses of suitable composition in combination with selective leaching. The resulting materials are characterized by a controllable pore size in the nanometer range, high mechanical, thermal and chemical stability and an adjustable macroscopic shape, which enables manufacturing of glass monoliths with various geometries. As a result of their formation, porous glasses obtained from physical phase separation exhibit a monomodal pore structure. There are only a few examples in the literature for the synthesis of hierarchically porous glasses. This review covers several synthesis strategies for the introduction of hierarchy into "classical" porous glass monoliths, including sintering and fusion of alkali borosilicate initial glasses as well as partial or complete pseudomorphic transformation of porous glasses into zeolites or ordered mesoporous materials.

Controlling the role of nanopore morphology in capillary condensation

The effect of pore morphology on capillary condensation and evaporation in nanoporous silicon is studied experimentally. A variety of cooperative and local effects are observed in tailored nanopores with well-defined regions by directly probing gas adsorption in each region using optical interferometry. All observations are ascribed to the ability of the nanopore region to access the gas reservoir directly and the nucleation of liquid bridges at local heterogeneities within the nanopore region. These assumptions, consistent with recent simulations, can be extended to any real nanoporous system.

Exploring Mass Transfer in Mesoporous Zeolites by NMR Diffusometry

With the advent of mesoporous zeolites, the exploration of their transport properties has become a task of primary importance for the auspicious application of such materials in separation technology and heterogeneous catalysis. After reviewing the potential of the pulsed field gradient method of NMR (PFG NMR) for this purpose in general, in a case study using a specially prepared mesoporous zeolite NaCaA as a host system and propane as a guest molecule, examples of the attainable information are provided.

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

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.

Magnetic resonance imaging by synergistic diffusion-diffraction patterns

Inferring on the geometry of an object from its frequency spectrum is highly appealing since the object could then be imaged noninvasively or from a distance (as famously put by Kac, "can one hear the shape of a drum?"). In nuclear magnetic resonance of porous systems, the shape of the drum is represented by the pore density function that bears all the information on the collective pore microstructure. So far, conventional magnetic resonance imaging (MRI) could only detect the pore autocorrelation function, which inherently obscures fine details on the pore structure. Here, for the first time, we report on a unique imaging mechanism arising from synergistic diffusion-diffractions that directly yields the pore density function. This mechanism offers substantially higher spatial resolution compared to conventional MRI while retaining all fine details on the collective pore morphology. Thus, using these unique synergistic diffusion-diffractions, the "shape of the drum" can be inferred.

Capillary condensation of adsorbates in porous materials

Hysteresis in capillary condensation is important for the fundamental study and application of porous materials, and yet experiments on porous materials are sometimes difficult to interpret because of the many interactions and complex solid structures involved in the condensation and evaporation processes. Here we make an overview of the significant progress in understanding capillary condensation and hysteresis phenomena in mesopores that have followed from experiment and simulation applied to highly ordered mesoporous materials such as MCM-41 and SBA-15 over the last few decades.

Cavitation and pore blocking in nanoporous glasses

In gas adsorption studies, porous glasses are frequently referred to as model materials for highly disordered mesopore systems. Numerous works suggest that an accurate interpretation of physisorption isotherms requires a complete understanding of network effects upon adsorption and desorption, respectively. The present article deals with nitrogen and argon adsorption at different temperatures (77 and 87 K) performed on a series of novel nanoporous glasses (NPG) with different mean pore widths. NPG samples contain smaller mesopores and significantly higher microporosity than porous Vycor glass or controlled pore glass. Since the mean pore width of NPG can be tuned sensitively, the evolution of adsorption characteristics with respect to a broadening pore network can be investigated starting from the narrowest nanopore width. With an increasing mean pore width, a H2-type hysteresis develops gradually which finally transforms into a H1-type. In this connection, a transition from a cavitation-induced desorption toward desorption controlled by pore blocking can be observed. Furthermore, we find concrete hints for a pore size dependence of the relative pressure of cavitation in highly disordered pore systems. By comparing nitrogen and argon adsorption, a comprehensive insight into adsorption mechanisms in novel disordered materials is provided.

On the cavitation and pore blocking in slit-shaped ink-bottle pores

We present GCMC simulations of argon adsorption in slit pores of different channel geometry. We show that the isotherm for an ink-bottle pore can be reconstructed as a linear combination of the local isotherms of appropriately chosen independent unit cells. Second, depending on the system parameters and operating conditions, the phenomena of cavitation and pore blocking can occur for a given configuration of the ink-bottle pore by varying the geometrical aspect ratio. Although it has been argued in the literature that the geometrical aspects of the system govern the evaporation mechanism (either cavitation or pore blocking), we here put forward an argument that the local compressibility in different parts of the ink-bottle pore is the deciding factor for evaporation. When the fluid in the small neck is strongly bound, cavitation is the governing process, and molecules in the cavity evaporate to the surrounding bulk gas via a mass transfer mechanism through the pore neck. When the pore neck is sufficiently large, the system of neck and cavity evaporates at the same pressure, which is a consequence of the comparable compressibility between the fluid in the neck and that in the cavity. This suggests that local compressibility is the measure of cohesiveness of the fluid prior to evaporation. One consequence that we derive from the analysis of isotherms of a number of connected pores is that by analyzing the adsorption branch or the desorption branch of an experimental isotherm may not lead to the correct pore sizes and the correct pore volume distribution.

Probing microscopic architecture of opaque heterogeneous systems using double-pulsed-field-gradient NMR

Microarchitectural features of opaque porous media and biological tissues are of great importance in many scientific disciplines ranging from chemistry, material sciences, and geology to biology and medicine. Noninvasive characterization of coherently organized pores is rather straightforward since conventional diffusion magnetic resonance methods can detect anisotropy on a macroscopic scale; however, it remains extremely challenging to directly infer on microarchitectural features on the microscopic scale in heterogeneous porous media and biological cells that are comprised of randomly oriented compartments, a scenario widely encountered in Nature. Here, we show that the angular bipolar double-pulsed-field-gradient (bp-d-PFG) methodology is capable of reporting on unique microarchitectural features of highly heterogeneous systems. This was demonstrated on a toluene-in-water emulsion system, quartz sand, and even biological specimens such as yeast cells and isolated gray matter. We find that in the emulsion and yeast cells systems, the angular bp-d-PFG methodology uniquely revealed nearly an image of the pore space, since it conveyed direct microarchitectural information such as compartment shape and size. In two different quartz sand specimens, the angular bp-d-PFG experiments demonstrated the presence of randomly oriented anisotropic compartments. We also obtained unequivocal evidence that diffusion in interconnected interstices is restricted and therefore non-Gaussian. In biological contexts, the angular bp-d-PFG experiments could uniquely differentiate between spherical cells and randomly oriented compartments in gray matter tissue, information that could not be obtained by conventional NMR methods. The angular bp-d-PFG methodology also performs very well even when severe background gradients are present, as is often encountered in realistic systems. We conclude that this method seems to be the method of choice for characterizing the microstructure of porous media and biological cells noninvasively.

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

In situ study on molecular diffusion phenomena in nanoporous catalytic solids

As an omnipresent phenomenon in nature, diffusion is among the rate-determining processes in many technological processes. This is in particular true for catalytic conversion in nanoporous materials. We provide a critical review of the possibilities of exploring diffusion phenomena over microscopic dimensions in such media by direct experimental observation. By monitoring the probability distribution of molecular displacements as a function of time, the pulsed field gradient technique of NMR (PFG NMR) records the rate of molecular re-distribution. By varying the observation time, PFG NMR is thus able to trace even hierarchies of transport resistances as occurring, e.g., in catalyst particles in the form of binder-compacted assemblages of zeolite crystallites. Alternatively, and complementary to this information, interference microscopy (IFM) and IR microscopy (IRM) are able to follow the evolution of intracrystalline concentration profiles during uptake and release. This allows, in particular, an accurate quantification of the transport resistances on the surface of the individual crystallites and of the probability that reactant molecules from the gas phase, upon colliding with the external surface, are able to penetrate through such "surface barriers" into the crystal bulk phase. Being able to distinguish between different molecular species, IRM is able to record the evolution of intracrystalline concentration profiles even during multi-component adsorption and catalytic reactions (169 references).

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

Capillary condensation and evaporation in alumina nanopores with controlled modulations

Capillary condensation in nanoporous anodic aluminum oxide presenting not interconnected pores with controlled modulations is studied using adsorption experiments and molecular simulations. Both the experimental and simulation data show that capillary condensation and evaporation are driven by the smallest size of the nanopore (constriction). The adsorption isotherms for the open and closed pores are almost identical if constrictions are added to the system. The latter result implies that the type of pore ending does not matter in modulated pores. Thus, the presence of hysteresis loops observed in adsorption isotherms measured in straight nanopores with closed bottom ends can be explained in terms of geometrical inhomogeneities along the pore axis. More generally, these results provide a general picture of capillary condensation and evaporation in constricted or modulated pores that can be used for the interpretation of adsorption in disordered porous materials.

Liquid-solid transition of confined water in silica-based mesopores

Cooling and heating curves of water confined in partially filled Vycor porous glass were measured for both adsorption and desorption processes. One endothermic and two exothermic peaks were observed for almost all cases. The peak temperature and the enthalpy of the exothermic peak located below 232 K increased initially and then decreased with further increases in the filling factor. These abnormal changes were analyzed based on the liquid-solid transition of nanoconfined water using a core/shell model, and the initial adsorption process of water in this typical mesoporous material with disordered pores is discussed. In addition, an interesting observation is that different peak temperatures for the endothermic peak and an almost constant peak temperature for the exothermic peak were observed at the same filling factor obtained under different sample preparation conditions, that is, adsorption and desorption processes. To compare with the liquid-solid transition temperatures of confined water in fully filled silica-based mesopores of different pore radius, a parameter of the ratio of pore inner surface area to confined liquid volume is proposed in this paper. Referring to this parameter, the core part of confined water in silica-based nanopores has the same liquid-solid transition temperatures. This suggestion is valid for the freezing process of water confined in either fully filled ordered or fully or partially filled disordered pores. For the melting process, different linear changes of melting temperature with the ratio of pore inner surface area to liquid volume were observed for water in disordered and ordered pores.

Microscopic theory of hysteretic hydrogen adsorption in nanoporous materials

Understanding gas adsorption confined in nanoscale pores is a fundamental issue with broad applications in catalysis and gas storage. Recently, hysteretic H(2) adsorption was observed in several nanoporous metal-organic frameworks (MOFs). Here, using first-principles calculations and simulated adsorption/desorption isotherms, we present a microscopic theory of the enhanced adsorption hysteresis of H(2) molecules using the MOF Co(1,4-benzenedipyrazolate) [Co(BDP)] as a model system. Using activated H(2) diffusion along the small-pore channels as a dominant equilibration process, we demonstrate that the system shows hysteretic H(2) adsorption under changes of external pressure. For a small increase of temperature, the pressure width of the hysteresis, as well as the adsorption/desorption pressure, dramatically increases. The sensitivity of gas adsorption to temperature changes is explained by the simple thermodynamics of the gas reservoir. Detailed analysis of transient adsorption dynamics reveals that the hysteretic H(2) adsorption is an intrinsic adsorption characteristic in the diffusion-controlled small-pore systems.

Mass transfer in a nanoscale material enhanced by an opposing flux

Diffusion is known to be quantified by measuring the rate of molecular fluxes in the direction of falling concentration. In contrast with intuition, considering methanol diffusion in a novel type of nanoporous material (MOF ZIF-8), this rate has now been found to be enhanced rather than slowed down by an opposing flux of labeled molecules. In terms of the key quantities of random particle movement, this result means that the self-diffusivity exceeds the transport diffusivity. It is rationalized by considering the strong intermolecular interaction and the dominating role of intercage hopping in mass transfer in the systems under study.