Single-file Diffusion Research Articles

Harmonic chain far from equilibrium: Single-file diffusion, long-range order, and hyperuniformity

Harmonic chain far from equilibrium: Single-file diffusion, long-range order, and hyperuniformity

Uphill Drift in the Absence of Current in Single-File Diffusion

Uphill Drift in the Absence of Current in Single-File Diffusion

Single-file diffusion and its influence on membrane gas separation: A case study on UTSA-280

Gas permeation in metal-organic framework-based (MOF-based) membranes is often elucidated through the solution-diffusion model, where the adsorption and diffusion of gases play equally vital roles. This study draws attention to a unique phenomenon known as single-file diffusion (SFD) occurring within MOF membranes that possess ultramicropores with dimensions comparable to the gas molecules themselves. When SFD takes place, the separation performance becomes solely reliant on the adsorption quantities on the feed side of the membrane. As a proof of concept, we fabricated a UTSA-280 membrane and subjected it to testing using gas mixtures of CO2/N2 and CO2/CH4. Two crucial observations substantiate the occurrence of single-file diffusion. Firstly, in the gas mixtures, the diffusion coefficients of N2 or CH4 were observed to align closely with that of CO2, despite the intrinsic diffusion coefficients of CO2, N2, and CH4, as determined from single-gas permeation experiments, exhibiting differences. Secondly, the CO2 mole fractions within the adsorption phase closely mirrored those in the gas phase on the permeate side. Given the high adsorption selectivity of UTSA-280 for CO2, the UTSA-280 membrane delivers outstanding permeation selectivity for CO2/N2 (611) and CO2/CH4 (80.7). Our experimental findings are supported by mesoscale kinetic Monte Carlo simulations, which confirmed the relation between the CO2 compositions in the adsorption phase on the feed side and in the gas phase on the permeate side. Furthermore, density functional theory calculations revealed high energy barriers associated with CO2 surpassing its counterparts, rendering such processes unfavorable, thereby reinforcing our experimental findings regarding single-file diffusion.

Dynamical crossovers and correlations in a harmonic chain of active particles.

We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSDs) and space-time correlations through Green's function techniques and numerical simulations. Depending on chain characteristics, i.e., different time scales determined by interaction stiffness and persistence of activity, tagged-particle MSDs exhibit ballistic, diffusive, and single-file diffusion (SFD) scaling over time, with crossovers explained by our analytic expressions. Our results reveal transitions in bulk particle displacement distributions from an early-time bimodal to late-time Gaussian, passing through regimes of unimodal distributions with finite support and negative excess kurtosis and longer-tailed distributions with positive excess kurtosis. The distributions exhibit data collapse, aligning with ballistic, diffusive, and SFD scaling in the appropriate time regimes. However, at much longer times, the distributions become Gaussian. Finally, we derive analytic expressions for steady-state static and dynamic two-point displacement correlations. We verify these from simulations and highlight the differences from the equilibrium results.

Single-file diffusion in spatially inhomogeneous systems.

We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

Exact spatial correlations in single-file diffusion.

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behavior results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles. Despite their importance, these bath-tracer correlations have long remained elusive, because their determination is a complex many-body problem. Recently, we have shown that, for several paradigmatic models of single-file diffusion such as the simple exclusion process, these bath-tracer correlations obey a simple exact closed equation. In this paper, we provide the full derivation of this equation, as well as an extension to another model of single-file transport: the double exclusion process. We also make the connection between our results and the ones obtained very recently by several other groups and which rely on the exact solution of different models obtained by the inverse scattering method.

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.

Selective Uptake of Ethane/Ethylene Mixtures by UTSA-280 is Driven by Reversibly Coordinated Water Defects

The metal–organic framework (MOF) UTSA-280 has been shown previously to separate ethane/ethylene mixtures. We show that this separation is kinetic; if full equilibrium is reached, the MOF is not selective. The time scales associated with this kinetic separation are sufficient to make the material potentially interesting for practical separations. The observation of kinetic separation is surprising because the MOF’s one-dimensional (1D) channels are small enough that molecular motion along the channels would be expected to take place by single-file diffusion, which is not observed. We show using a combination of experimental and modeling techniques that diffusion of molecules between adjacent 1D channels through local defects associated with coordinated water molecules allows net mixing of molecules and, moreover, that this process is potentially responsible for the selective nature of the observed kinetic separation. We show how activation and regeneration conditions play an essential role in controlling the density of these local defects.

Dynamic molecular ordering in multiphasic nanoconfined ionic liquids detected with time-resolved diffusion NMR

Molecular motion in nanosized channels can be highly complicated. For example, water molecules in ultranarrow hydrophobic nanopores move rapidly and coherently in a single file, whereas by increasing the pore size they organize into coaxial tubes, displaying stratified diffusion. Interestingly, an analogous complex motion is predicted in viscous charged fluids, such as room temperature ionic liquids (RTILs) confined in nanoporous carbon or silica; however, experimental evidence is still pending. Here, by combining 1H NMR diffusion experiments in different relaxation windows with molecular dynamics simulations, we show that the imidazolium-based RTIL [BMIM]+[TCM]−, entrapped in the MCM-41 silica nanopores, exhibits an intricate dynamic molecular ordering; adsorbed RTIL molecules form a fluctuating charged layer near the pore walls, while in the bulk pore space they diffuse discretely in coaxial tubular shells, with molecular mean square displacement following a nearly ∼τ0.5 time dependence, characteristic of single file diffusion.

Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion.

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.

Duality relations in single-file diffusion

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems have been considered, such as the simple exclusion process, which has reached the status of a paradigmatic model. Several different models of single-file diffusion have been shown to be related by a duality relation, which holds either microscopically or only in the hydrodynamic limit of large time and large distances. Here, we show that, within the framework of fluctuating hydrodynamics, these relations are not specific to these models and that, in the hydrodynamic limit, every single-file system can be mapped onto a dual single-file system, which we characterise. This general duality relation allows us to obtain new results for different models, by exploiting the solutions that are available for their dual model.

Role of initial conditions in one-dimensional diffusive systems: Compressibility, hyperuniformity, and long-term memory.

We analyze the long-lasting effects of initial conditions on dynamical fluctuations in one-dimensional diffusive systems. We consider the mean-squared displacement of tracers in homogeneous systems with single-file diffusion, and current fluctuations for noninteracting diffusive particles. In each case we show analytically that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched cases studied previously, alongside a continuous family of other classes among which equilibrated (or annealed) initial conditions are but one member. We verify our predictions through extensive Monte Carlo simulations.

Full statistics of nonstationary heat transfer in the Kipnis–Marchioro–Presutti model

We investigate non-stationary heat transfer in the Kipnis–Marchioro–Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, u(x, t = 0) = Wδ(x). We characterize the process by the heat transferred to the right of a specified point x = X by time T, and study the full probability distribution . The particular case of X = 0 has been recently solved by Bettelheim et al (2022 Phys. Rev. Lett. 128 130602). At fixed J, the distribution as a function of X and T has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov–Shabat inverse scattering method. We also discuss asymptotics of which we extract from the exact solution and also obtain by applying two different perturbation methods directly to the MFT equations.

Exact closure and solution for spatial correlations in single-file diffusion.

In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.

Superions in the Narrow Nanopores with Multiple Occupancy

The general theory of the single-file multiparticle diffusion in narrow pores can be greatly simplified in the case of the inverted bell-like shape of a single-particle energy profile, which is often observed in biological ion channels. There is a narrow and deep groove in the energy landscape of multiple interacting ions in such profiles, which corresponds to the pre-defined optimal conduction pathway in the configurational space. If such a groove exists, the motion of multiple ions can be reduced to the motion of a single quasiparticle, called the superion, which moves in a one-dimensional effective potential. The concept of superions reduces the computational complexity of the problem and provides the very clear physical interpretation of conduction phenomena in narrow pores.

Insights into Sorption and Molecular Transport of Aqueous Glucose into Zeolite Nanopores.

Liquid-phase heterogeneous catalysis using zeolites is important for biomass conversion to fuels and chemicals. There is a substantial body of work on gas-phase sorption in zeolites with different topologies; however, studies investigating the diffusion of complex molecules in liquid medium into zeolitic nanopores are scarce. Here, we present a molecular dynamics study to understand the sorption and diffusion of aqueous β-d-glucose into β-zeolite silicate at T = 395 K and P = 1 bar. Through 2-μs-long molecular dynamics trajectories, we reveal the role of the solvent, the kinetics of the pore filling, and the effect of the water model on these properties. We find that the glucose and water loading is a function of the initial glucose concentration. Although the glucose concentration increases monotonically with the initial glucose concentration, the water loading exhibits a nonmonotonic behavior. At the highest initial concentration (∼20 wt %), we find that the equilibrium loading of glucose is approximately five molecules per unit cell and displays a weak dependence on the water model. Glucose molecules follow a single-file diffusion in the nanopores due to confinement. The dynamics of glucose and water molecules slows significantly at the interface. The average residence time for glucose molecules is an order of magnitude larger than that in the bulk solution, while it is about twice as large for the water molecules. Our simulations reveal critical molecular details of the glucose molecule's local environment inside the zeolite pore relevant to catalytic conversion of biomass to valuable chemicals.

Hydrodynamic couplings of colloidal ellipsoids diffusing in channels

The hydrodynamic interactions (HIs) of two colloidal spheres characterized by the translation–translation (T–T) couplings have been studied under various confinements, but little is known regarding the HIs of anisotropic particles and rotational motions, which are common in nature and industry. Here, we study the T–T, rotation–rotation (R–R) and translation–rotation (T–R) hydrodynamic couplings of two colloidal ellipsoids sediment on the bottoms of channels in experiment, theory and simulation. We find that the degree of confinement and the particle shape anisotropy are critical tuning factors resulting in anomalous hydrodynamic and diffusive behaviours. The negative R–R coupling reflects the tendency of opposite rotations of two neighbouring ellipsoids. The positive T–R coupling reflects that an ellipsoid rotates away from the channel axis as another ellipsoid approaches. As the channel width increases, the positive T–T coupling changes to an abnormal negative coupling, indicating that the single-file diffusion can exist even in wide channels. By contrast, only positive T–T couplings were observed for spheres in channels. The T–T coupling increases with the aspect ratiop. The R–R coupling is the maximum at a moderatep ~ 2.8. The T–R coupling is the maximum at a moderate degree of confinement. The spatial range of HIs is longer than that of spheres and increases withp. We propose a simple model which reproduces some coupling phenomena between two ellipsoids, and it is further confirmed by low-Reynolds-number hydrodynamic simulation. These findings shed new light on anisotropic particle diffusion in porous media, transport through membranes, microfluidics and microrheology.

Generalized Correlation Profiles in Single-File Systems.

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterize the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we determine the scaling form of the GCPs with space and time, and unveil a nonmonotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides several exact results for the GCPs for paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the symmetric exclusion process and the random average process. The range of applicability of our approach is further illustrated by considering (i)extensions to general interactions between particles, (ii)the out-of-equilibrium situation of an initial step of density, and (iii)beyond the hydrodynamic limit, the GCPs at arbitrary time in the dense limit.

Diffusive properties of colloidal charged particles in a quasi-one-dimensional confinement

Diffusive properties of colloidal crystals in a quasi-one-dimensional channel are studied using numerical simulations. In order to study the influence of the attractive interaction between particles, it was introduced as an artificial dimensionless parameter β in the attractive term of the interaction potential. Changing the value of β, we can tune the effect of attraction between particles. We show that charged particles can change their mobility and the diffusion exponent of a one-chain like system. Variation on exponent diffusion can be induced by tuning the attractive part of interaction potential, making possible the existence of diffusive regimes between single-file diffusion (SFD) and normal diffusion, without changing confinement strength. System stoichiometry was changed, imposing particles in different arrangements in small clusters, which varies the diffusive behaviour. If stoichiometry is different from 1:1, it is possible to have particles with equal charges but with different mobilities. Another important observation is that mean-square displacement (MSD) for different charges is different for different values.

Non-Fickian single-file pore transport.

Single-file diffusion exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short porelike channels using a symmetric exclusion process with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux 〈Φ〉∼1/L^{3}, where L is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with 〈Φ〉∼1/L. Longer systems are more often in a low-flux state, leading to the non-Fickian behavior.