Diffusion in Porous Media: Phenomena and Mechanisms

Modeling Mass Transport Dynamics in Deformable Hydrogels during Evaporation

Hydrogels possess exceptional mechanical properties and biocompatibility, making them widely used in contemporary bioengineering. Specifically, in the development of wearable and implantable health monitoring devices as well as drug delivery systems, hydrogels are utilized to enable precise control over the transport of solutes. Nonetheless, predicting the distribution of substances within hydrogels still poses a significant challenge due to the complex interplay between the movement of water content, migration of solutes, and deformability of the hydrogel polymer network, which presents challenges to theoretical modeling. Our work introduces a numerical model that addresses the movement of water and solute within a flexible hydrogel, accounting for evaporation and/or moisture absorption at the boundary. The model solves for water saturation, solute concentration, and hydrogel deformation iteratively at each time step while computing the boundary movement velocity based on the transport process. By comparing the modeled results of geometry deformation and water and solute distributions during evaporation with our experiments, we demonstrate the accuracy and applicability of our proposed model. This capability to precisely analyze water and solute concentrations in deformable and nonuniform hydrogel environments paves the way for advancements in biosensing and drug delivery methods that rely on elastic porous materials.

Vibration mixing for enhanced paper-based recombinase polymerase amplification

Isothermal nucleic acid amplification tests (NAATs) are a vital tool for point-of-care (POC) diagnostics. These assays are well-suited for rapid, low-cost POC diagnostics for infectious diseases compared to traditional PCR tests conducted in central laboratories. There has been significant development of POC NAATs using paper-based diagnostic devices because they provide an affordable, user-friendly, and easy to store format; however, the difficulties in integrating separate liquid components, resuspending dried reagents, and achieving a low limit of detection hinder their use in commercial applications. Several studies report low assay efficiencies, poor detection output, and poorer limits of detection in porous membranes compared to traditional tube-based protocols. Recombinase polymerase amplification is a rapid, isothermal NAAT that is highly suited for POC applications, but requires viscous reaction conditions that has poor performance when amplifying in a porous paper membrane. In this work, we show that we can dramatically improve the performance of membrane-based recombinase polymerase amplification (RPA) of HIV-1 DNA and viral RNA by employing a coin cell-based vibration mixing platform. We achieve a limit of detection of 12 copies of DNA per reaction, nearly 50% reduction in time to threshold (from ∼10 minutes to ∼5 minutes), and an overall fluorescence output increase up to 16-fold when compared to unmixed experiments. This active mixing strategy enables reactions where the target and reaction cofactors are isolated from each other prior to the reaction. We also demonstrate amplification using a low-cost vibration motor for both temperature control and mixing, without the requirement of any additional heating components.

Insights into mechanism and modelling of dynamic moisture sorption in dual-porous insulation materials with micro- and nano-scale pores

HYPOTHESIS

Understanding moisture sorption in porous insulation materials is challenging due to the influence of multiscale pore structures on phase behavior and transport properties. Dynamic moisture sorption in dual-porous materials is likely co-determined by interior micro- and nano-scale pores, and an accurate physical model for predicting moisture evolution can be developed by clarifying the sorption mechanisms.

EXPERIMENTS

Moisture behavior during the dynamic sorption of dual-porous insulation material is measured by low-field nuclear magnetic resonance (NMR) experiments. The contributions of micro- and nano-scale pores to the adsorbed moisture are differentiated using NMR relaxometry, and the evolution of moisture morphology is quantitatively analyzed.

FINDINGS

Analysis of T2 evolution reveals that the moisture in nano-scale pores alters from adsorption layers to liquid with increasing relative humidity (RH), while minimal sorption occurs in micro-scale pores. Moisture is mainly transferred as vapor molecules at low RH levels, with the dynamic sorption enhanced by molecular diffusion in micro-scale pores. Capillary flow in nano-scale pores dominates moisture transport when RH rises above a threshold, leading to a significant increase in apparent moisture diffusivity. According to the elucidated mechanism, a physical model is further developed to predict moisture sorption inside dual-porous insulation materials, and it may serve as a basis for evaluating and optimizing the performance of dual-porous systems in different environments.

Development of alginate macroporous hydrogels using sacrificial CaCO3 particles for enhanced hemostasis

Polymeric hydrogels have increasingly garnered attention in the field of hemostasis. However, there remains a lack of targeted development and evaluation of non-dense polymeric hydrogels with physically incorporated pores to enhance hemostasis. Here, we present a facile route to macroporous alginate hydrogels using acid-induced CaCO3 dissolution to provide Ca2+ for alginate gelation and CO2 bubbles for subsequent macropore formation. The as-prepared pore structure in the hydrogels and its formation mechanisms were characterized through microscopic imaging and nitrogen adsorption/desorption tests. Functional analyses revealed that the macroporous hydrogels exhibited improved rheology, blood absorption, coagulation factor delivery, and platelet aggregation. Ultimately, the introduction of pores significantly enhanced the hemostatic effectiveness of alginate hydrogels in vivo, as demonstrated in rat tail amputation and liver injury models, leading to a reduction in blood loss of up to 77 % or a decrease in bleeding time of up to 88 %. Notably, hydrogels with higher porosity achieved with a CaCO3 to alginate ratio of 40 % outperformed those with lower porosity in the aforementioned properties. Furthermore, these improvements were found to be biocompatible and elicited minimal inflammation. Our findings underscore the potential of a simple porous hydrogel design to enhance hemostasis efficacy by physically incorporating macropores.

Quantifying the Influence of Electrolytes on the Kinetics of Spontaneous Emulsification

This study quantifies the influence of electrolytes on the kinetics of the spontaneous emulsification phenomenon (SEP) of heavy hydrocarbons in a nonionic surfactant solution. The rate of emulsifying hexadecane in Triton X-100, with the presence of sodium chloride and potassium chloride, has been measured using a technique of monitoring single oil droplet photography. The emulsion droplet size produced in the process was measured under the same conditions by using dynamic light scattering. The data obtained from the two experiments were employed to investigate the mass transfer coefficient of the surfactant molecules through the intermediate layer formed between hexadecane and the surfactant solution. It was found that the electrolytes in an aqueous solution increase the surfactant diffusion rate through the intermediate layer and reduce the emulsion droplet size. As a result, both electrolytes reduce the rate of spontaneous emulsification, with potassium chloride having a more substantial reduction. A model was developed to quantify the influence of electrolytes on the kinetics of the SEP. The data and modeling results verify the influence of ions on the kinetics of spontaneous emulsification. The results provide a significant foundation for predicting the solubilization of heavy hydrocarbons in an electrolyte solution.

Deep learning for diffusion in porous media

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk et al. in Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.

Combined effect of seawater and load on methacrylate adhesive

Although the shipbuilding industry is constantly demanding new advanced joining solutions, adhesive technology is not as developed in the marine as compared to other industries. The main reason is the lack of specific knowledge that guarantees the durability of the bonded joints in optimal conditions during the life cycle of a ship. This work simulates in the laboratory a marine-like environment by immersing an adhesive in seawater and subjecting it to constant loading. The objective is to characterize the seawater absorption behavior and its consequences on the mechanical, thermal, and chemical properties of the adhesive after this aging process. Seawater ingress was determined through gravimetric tests at several load conditions of the tensile strength of the adhesive. Besides, absorption process was studied using Fick's Law, determining the diffusion coefficients. The thermal behavior was monitored with differential scanning calorimetry (DSC) and the chemical degradation was analyzed using Fourier transform infrared spectroscopy (FTIR). Also, the mechanical properties were determined by tensile tests. The surface of the adhesive (dried) was studied by Scanning Electron Microscopy (SEM) technique and the porosity was measured by physisorption with a high-performance adsorption analyzer. A numerical simulation was developed using Darcy's Law combined with continuity equation. The results show that application of loads and immersion in seawater until full saturation of seawater improve the mechanical properties of the adhesive, but it affects negatively to the glass transition temperature. This should be considered when designing adhesive bonding joints on ships.

Modeling transport and filtration of nanoparticle suspensions in porous media

Recently membrane filters have gained in significance due to the need to provide protection against airborne pollution. A question of importance, and some controversy, is the efficiency of filters for small nanoparticles with diameters below 100 nm as these are considered particularly dangerous due to possible penetration into the lungs. The efficiency is measured by the number of particles blocked by the pore structure after passing though the filter. To study the penetration into pores by nanoparticles suspended in a fluid, a stochastic transport theory based on an atomistic model is used to calculate particle density and flow within the pores, resulting pressure gradient, and filter efficiency. The importance of pore size relative to particle diameter and of the parameters of the pore wall interactions are investigated. The theory is applied to aerosols in fibrous filters and found to reproduce common trends in measurements. As particles enter the initially empty pores on relaxation to the steady state the small penetration measured at the onset of filtration increases faster in time the smaller the nanoparticle diameter. Control of pollution by filtration is achieved by strong repulsion of pore walls for particle diameters greater than twice the effective pore width. For smaller nanoparticles the steady-state efficiency decreases as the pore wall interactions weaken. Effective efficiency is increased when the suspended nanoparticles inside the pores combine into clusters of sizes greater than the filter channel width.

Continuous Glucose Monitoring Enabled by Fluorescent Nanodiamond Boronic Hydrogel

Continuous monitoring of glucose allows diabetic patients to better maintain blood glucose level by altering insulin dosage or diet according to prevailing glucose values and thus to prevent potential hyperglycemia and hypoglycemia. However, current continuous glucose monitoring (CGM) relies mostly on enzyme electrodes or micro-dialysis probes, which suffer from insufficient stability, susceptibility to corrosion of electrodes, weak or inconsistent correlation, and inevitable interference. A fluorescence-based glucose sensor in the skin will likely be more stable, have improved sensitivity, and can resolve the issues of electrochemical interference from the tissue. This study develops a fluorescent nanodiamond boronic hydrogel system in porous microneedles for CGM. Fluorescent nanodiamond is one of the most photostable fluorophores with superior biocompatibility. When surface functionalized, the fluorescent nanodiamond can integrate with boronic polymer and form a hydrogel, which can produce fluorescent signals in response to environmental glucose concentration. In this proof-of-concept study, the strategy for building a miniatured device with fluorescent nanodiamond hydrogel is developed. The device demonstrates remarkable long-term photo and signal stability in vivo with both small and large animal models. This study presents a new strategy of fluorescence based CGM toward treatment and control of diabetes.

Porous Hydrogels: Present Challenges and Future Opportunities

In this feature article, we critically review the physical properties of porous hydrogels and their production methods. Our main focus is nondense hydrogels that have physical pores besides the space available between adjacent cross-links in the polymer network. After reviewing theories on the kinetics of swelling, equilibrium swelling, the structure-stiffness relationship, and solute diffusion in dense hydrogels, we propose future directions to develop models for porous hydrogels. The aim is to show how porous hydrogels can be designed and produced for studies leading to the modeling of physical properties. Additionally, different methods that are used for making hydrogels with physically incorporated pores are briefly reviewed while discussing the potentials, challenges, and future directions for each method. Among kinetic methods, we discuss bubble generation approaches including reactions, gas injection, phase separation, electrospinning, and freeze-drying. Templating approaches discussed are solid-phase, self-assembled amphiphiles, emulsion, and foam methods.

Bacterial mobility and motility in porous media mimicked by microspheres

Bacterial motion in porous media is essential for their survival, proper functioning, and various applications. Here we investigated the motion of Escherichia coli bacteria in microsphere-mimicked porous media. We observed reduced bacterial velocity and enhanced directional changes of bacteria as the density of microspheres increased, while such changes happened mostly around the microspheres and due to the collisions with the microspheres. More importantly, we established and quantified the correlation between the bacterial trapping in porous media and the geometric confinement imposed by the microspheres. In addition, numerical simulations showed that the active Brownian motion model in the presence of microspheres resulted in bacterial motion that are consistent with the experimental observations. Our study suggested that it is important to distinguish the ability of bacteria to move easily - bacterial mobility - from the ability of bacteria to move independently - bacteria motility. Our results showed that bacterial motility remains similar in porous media, but bacterial mobility was significantly affected by the pore-scale confinement.

Multiscale modeling of solute diffusion in triblock copolymer membranes

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model's predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

Perineuronal nets restrict transport near the neuron surface: A coarse-grained molecular dynamics study

Perineuronal nets (PNNs) are mesh-like extracellular matrix structures that wrap around certain neurons in the central nervous system. They are hypothesized to stabilize memories in the brain and act as a barrier between cell and extracellular space. As a means to study the impact of PNNs on diffusion, the nets were approximated by negatively charged polymer brushes and simulated by coarse-grained molecular dynamics. Diffusion constants of single neutral and single charged particles were obtained in directions parallel and perpendicular to the brush substrate. The results for the neutral particle were compared to different theories of diffusion in a heuristic manner. Diffusion was found to be considerably reduced for brush spacings smaller than 10 nm, with a pronounced anisotropy for dense brushes. The exact dynamics of the chains was found to have a negligible impact on particle diffusion. The resistance of the brush proved small compared to typical values of the membrane resistance of a neuron, indicating that PNNs likely contribute little to the total resistance of an enwrapped neuron.

Mixing in Porous Media: Concepts and Approaches Across Scales

This review provides an overview of concepts and approaches for the quantification of passive, non-reactive solute mixing in steady uniform porous media flows across scales. Mixing in porous media is the result of the interaction of spatial velocity fluctuations and diffusion or local-scale dispersion, which may lead to the homogenization of an initially segregated system. Velocity fluctuations are induced by spatial medium heterogeneities at the pore, Darcy or regional scales. Thus, mixing in porous media is a multiscale process, which depends on the medium structure and flow conditions. In the first part of the review, we discuss the interrelated processes of stirring, dispersion and mixing, and review approaches to quantify them that apply across scales. This implies concepts of hydrodynamic dispersion, approaches to quantify mixing state and mixing dynamics in terms of concentration statistics, and approaches to quantify the mechanisms of mixing. We review the characterization of stirring in terms of fluid deformation and folding and its relation with hydrodynamic dispersion. The integration of these dynamics to quantify the mechanisms of mixing is discussed in terms of lamellar mixing models. In the second part of this review, we discuss these concepts and approaches for the characterization of mixing in Poiseuille flow, and in porous media flows at the pore, Darcy and regional scales. Due to the fundamental nature of the mechanisms and processes of mixing, the concepts and approaches discussed in this review underpin the quantitative analysis of mixing phenomena in porous media flow systems in general.

Brownian motion on an out-of-thermal-equilibrium surface

The motion of colloidal species on an out-of-thermal equilibrium surface is studied experimentally by optical microscopy. Water droplets of size in the micrometer range, spontaneously formed at a spherical-like interface between water and oil, are the colloidal species. The interface appears as a convex meniscus when putting water on oil with an added nonionic surfactant. Since the water density is greater than that of oil, the interface is produced into the oil. The spontaneously formed water droplets move attached to the interface while still growing from submicrometer sizes to a few micrometers. Although the dynamic nature of the process, with both the interface and the particles still changing, produces heterogeneities in the system, anomalous diffusion was not observed. The motion of the droplets has a well-identified Brownian component with a Gaussian distribution of steps due to the thermal agitation of the media surrounding the droplets and a drift component due to the effect of gravity.

Investigation of Molecular Mean Free Path, Molecular Kinetic Energy, and Molecular Polarity Affecting Knudsen Diffusivity along Pore Channels

The effective purification of corrosive gases at the cathode air stream side is essential for proton exchange membrane fuel cells’ performance in real-world applications. Gas molecular diffusion depth along the pore channel is a sufficient parameter that determines the effectiveness of the porous purification media. The collision between gas molecules and pore surfaces is the crucial determinant of the diffusion depth. An analytical model was developed to predict the gas molecular diffusion depth in the pore channels. Two different crystal sizes of UiO-66 were synthesized to validate against the model result and empirically determine the diffusion depths. The parametric effects of the mean free path, molecular kinetic energy, and molecular polarity on molecular diffusivity were assessed. A smaller molecular mean free path and greater molecular kinetic energy were favorable for larger diffusion depth, owing to the fewer collisions and enhanced bounces after collisions. Greater molecular polarity led to shorter diffusion depth due to the enhanced van der Waals force between molecules and pore surfaces.

A multiparametric advection-diffusion reduced-order model for molecular transport in scaffolds for osteoinduction

Scaffolds are microporous biocompatible structures that serve as material support for cells to proliferate, differentiate and form functional tissue. In particular, in the field of bone regeneration, insertion of scaffolds in a proper physiological environment is known to favour bone formation by releasing calcium ions, among others, triggering differentiation of mesenchymal cells into osteoblasts. Computational simulation of molecular distributions through scaffolds is a potential tool to study the scaffolds’ performance or optimal designs, to analyse their impact on cell differentiation, and also to move towards reduction in animal experimentation. Unfortunately, the required numerical models are often highly complex and computationally too costly to develop parametric studies. In this context, we propose a computational parametric reduced-order model to obtain the distribution of calcium ions in the interstitial fluid flowing through scaffolds, depending on several physical parameters. We use the well-known Proper Orthogonal Decomposition (POD) with two different variations: local POD and POD with quadratic approximations. Computations are performed using two realistic geometries based on a foamed and a 3D-printed scaffolds. The location of regions with high concentration of calcium in the numerical simulations is in fair agreement with regions of bone formation shown in experimental observations reported in the literature. Besides, reduced-order solutions accurately approximate the reference finite element solutions, with a significant decrease in the number of degrees of freedom, thus avoiding computationally expensive simulations, especially when performing a parametric analysis. The proposed reduced-order model is a competitive tool to assist the design of scaffolds in osteoinduction research.

Kinetics of Sorption in Hygroscopic Hydrogels

Hygroscopic hydrogels hold significant promise for high-performance atmospheric water harvesting, passive cooling, and thermal management. However, a mechanistic understanding of the sorption kinetics of hygroscopic hydrogels remains elusive, impeding an optimized design and broad adoption. Here, we develop a generalized two-concentration model (TCM) to describe the sorption kinetics of hygroscopic hydrogels, where vapor transport in hydrogel micropores and liquid transport in polymer nanopores are coupled through the sorption at the interface. We show that the liquid transport due to the chemical potential gradient in the hydrogel plays an important role in the fast kinetics. The high water uptake is attributed to the expansion of hydrogel during liquid transport. Moreover, we identify key design parameters governing the kinetics, including the initial porosity, hydrogel thickness, and shear modulus. This work provides a generic framework of sorption kinetics, which bridges the knowledge gap between the fundamental transport and practical design of hygroscopic hydrogels.

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H2, CH4) or permanent (CO2, radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

Buffering by Transporters Can Spare Geometric Hindrance in Controlling Glutamate Escape

The surface of astrocyte processes that often surround excitatory synapses is packed with high-affinity glutamate transporters, largely preventing extrasynaptic glutamate escape. The shape and prevalence of perisynaptic astroglia vary among brain regions, in some cases providing a complete isolation of synaptic connections from the surrounding tissue. The perception has been that the geometry of perisynaptic environment is therefore essential to preventing extrasynaptic glutamate escape. To understand to what degree this notion holds, we modelled brain neuropil as a space filled with a scatter of randomly sized, overlapping spheres representing randomly shaped cellular elements and intercellular lumen. Simulating release and diffusion of glutamate molecules inside the interstitial gaps in this medium showed that high-affinity transporters would efficiently constrain extrasynaptic spread of glutamate even when diffusion passages are relatively open. We thus estimate that, in the hippocampal or cerebellar neuropil, the bulk of glutamate released by a synaptic vesicle is rapidly bound by transporters (or high-affinity target receptors) mainly in close proximity of the synaptic cleft, whether or not certain physiological or pathological events change local tissue geometry.

Three-Dimensional Membrane Imaging with X-ray Ptychography: Determination of Membrane Transport Properties for Membrane Distillation

Abstract

Membrane distillation (MD) is a desalination technique that uses a membrane to thermally separate potable water from sea or brackish water. The mass transport processes through the membrane are commonly described by the dusty gas model. These processes are modeled assuming uniform, ideally cylindrical capillaries and are adjusted for the membrane geometry by including porosity and tortuosity. The tortuosity is usually set to 2 or is used as an adjusting parameter to fit theoretical models to experimentally measured data. In this work, ptychographic X-ray computed tomography is employed to map the three-dimensional (3D) structure of three commercial state-of-the-art PTFE membranes in MD. The porosity, tortuosity and permeability (viscous flow coefficient) of the samples are computed using the lattice Boltzmann method. The intrinsic permeability is compared to the dusty gas model and an apparent permeability is proposed which is corrected for Knudsen slip effects at the membrane structure.

Article Highlights

Elucidation of Diffusivity of Hydrogen Isotopes in Flexible MOFs by Quasi-Elastic Neutron Scattering

Kinetic-quantum-sieving-assisted H₂ :D₂ separation in flexible porous materials is more effective than the currently used energy-intensive cryogenic distillation and girdle-sulfide processes for isotope separation. It is believed that material flexibility results in a pore-breathing phenomenon under the influence of external stimuli, which helps in adjusting the pore size and gives rise to the optimum quantum-sieving phenomenon at each stage of gas separation. However, only a few studies have investigated kinetic-quantum-sieving-assisted isotope separation using flexible porous materials. In addition, no reports are available on the microscopic observation of isotopic molecular transportation during the separation process under dynamic transition. Here, the experimental observation of a significantly faster diffusion of deuterium than hydrogen in a flexible pore structure, even at high temperatures, through quasi-elastic neutron scattering, is reported. Unlike rigid structures, the extracted diffusion dynamics of hydrogen isotopes within flexible frameworks show that the diffusion difference between the isotopes increases with an increase in temperature. Owing to this unique inverse trend, a new strategy is suggested for achieving higher operating temperatures for efficient isotope separation utilizing a flexible metal-organic framework system.

Diffusion of colloidal particles in model porous media

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.