Single-file Diffusion Research Articles

Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica.

The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the "passing propensity," P, of reactant and product species inside the pores. We find that P ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, P reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine P versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for P into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting P. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.

Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation.

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [h_{C1},h_{C2}]. We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits h_{C1} and h_{C2}, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.

Brownian Dynamics simulations of model colloids in channel geometries and external fields

We review the results of Brownian Dynamics simulations of colloidal particles in external fields confined in channels. Super-paramagnetic Brownian particles are well suited two- dimensional model systems for a variety of problems on different length scales, ranging from pedestrian walking through a bottleneck to ions passing ion-channels in living cells. In such systems confinement into channels can have a great influence on the diffusion and transport properties. Especially we will discuss the crossover from single file diffusion in a narrow channel to the diffusion in the extended two-dimensional system. Therefore a new algorithm for computing the mean square displacement (MSD) on logarithmic time scales is presented. In a different study interacting colloidal particles were dragged over a washboard potential and are additionally confined in a two-dimensional micro-channel. In this system kink and anti-kink solitons determine the depinning process of the particles from the periodic potential.

Some peculiarities of labile oxygen kinetics in underdoped single crystals of YBa2Cu3O7-x

We study the time dependence of the electrical conductivity of single-crystalline YBa2Cu3O7-x with varying oxygen content. We show that the accelerated transport of the oxygen ions in the initial stage of the process occurs along one-dimensional clusters of nonstoichiometric vacancies through the single-file diffusion mechanism. The final stage of the oxygen ion redistribution in the studied compound is described with a classical mechanism of bulk diffusion. At the same time, the degree of deviation from the oxygen stoichiometry significantly influences the change in duration of the time intervals corresponding to the mechanisms of single-file and bulk diffusion of the labile oxygen.

Enhancement of Brownian motion for a chain of particles in a periodic potential.

The transport of particles in very confined channels in which single file diffusion occurs has been largely studied in systems where the transverse confining potential is smooth. However, in actual physical systems, this potential may exhibit both static corrugations and time fluctuations. Some recent results suggest the important role played by this nonsmoothness of the confining potential. In particular, quite surprisingly, an enhancement of the Brownian motion of the particles has been evidenced in these kinds of systems. We show that this enhancement results from the commensurate effects induced by the underlying potential on the vibrational spectra of the chain of particles, and from the effective temperature associated with its time fluctuations. We will restrict our derivation to the case of low temperatures for which the mean squared displacement of the particles remains smaller than the potential period.

Single-file diffusion in oxygen underdoped ReBa2Cu3O7-x (Re=Y, Ho) single crystals

Single-file diffusion in oxygen underdoped ReBa2Cu3O7-x (Re=Y, Ho) single crystals

Effects of Cage-Breaking Events in Single-File Diffusion on Elongation Correlation

Collective motion of caged particles is studied by calculating correlations of elongations (i.e., excess distances between two tagged particles) in a one-dimensional colloidal system, with the focus on the effect of overtaking events by which particles can hop out of the cage. It is shown analytically and verified numerically that the effect of overtaking is more prominent in shorter lengthscales, and also that the two-time elongation correlation exhibits ageing behavior due to overtaking.

Confined Water: Structure, Dynamics, and Thermodynamics.

Understanding the properties of strongly confined water is important for a variety of applications such as fast flow and desalination devices, voltage generation, flow sensing, and nanofluidics. Confined water also plays an important role in many biological processes such as flow through ion channels. Water in the bulk exhibits many unusual properties that arise primarily from the presence of a network of hydrogen bonds. Strong confinement in structures such as carbon nanotubes (CNTs) substantially modifies the structural, thermodynamic, and dynamic (both translational and orientational) properties of water by changing the structure of the hydrogen bond network. In this Account, we provide an overview of the behavior of water molecules confined inside CNTs and slit pores between graphene and graphene oxide (GO) sheets. Water molecules confined in narrow CNTs are arranged in a single file and exhibit solidlike ordering at room temperature due to strong hydrogen bonding between nearest-neighbor molecules. Although molecules constrained to move along a line are expected to exhibit single-file diffusion in contrast to normal Fickian diffusion, we show, from a combination of molecular dynamics simulations and analytic calculations, that water molecules confined in short and narrow CNTs with open ends exhibit Fickian diffusion because of their collective motion as a single unit due to strong hydrogen bonding. Confinement leads to strong anisotropy in the orientational relaxation of water molecules. The time scale of relaxation of the dipolar correlations of water molecules arranged in a single file becomes ultraslow, of the order of several nanoseconds, compared with the value of 2.5 ps for bulk water. In contrast, the relaxation of the vector that joins the two hydrogens in a water molecule is much faster, with a time scale of about 150 fs, which is about 10 times shorter than the corresponding time scale for bulk water. This is a rare example of confinement leading to a speedup of orientational dynamics. The orientational relaxation of confined water molecules proceeds by angular jumps between two locally stable states, making the relaxation qualitatively different from that expected in the diffusive limit. The spontaneous entry of water inside the hydrophobic cavity of CNTs is primarily driven by an increase in the rotational entropy of water molecules inside the cavity, arising from a reduction in the average number of hydrogen bonds attached to a water molecule. From simulations using a variety of water models, we demonstrate that the relatively simple SPC/E water model yields results in close agreement with those obtained from polarizable water models. Finally, we provide an account of the structure and thermodynamics of water confined in the slit pore between two GO sheets with both oxidized and reduced parts. We show that the potential of mean force for the oxidized part of GO sheets in the presence of water exhibits two local minima, one corresponding to a dry cavity and the other corresponding to a fully hydrated cavity. The coexistence of these two regimes provides permeation pathways for water in GO membranes.

Dipeptides Embedded in a Lipid Bilayer Membrane as Synthetic Water Channels.

Water channels are essential to life sciences and many biological processes. We report a molecular simulation study on dipeptides embedded in a lipid (dipalmitoylphosphatidylcholine) membrane as synthetic water channels. Five dipeptides are examined including FF, FL, LF, and LL (with hydrophilic channels) and AV (with hydrophobic channel). It is found that AV is unstable in the lipid membrane due to incompatible interaction between the hydrophilic external surface of AV and the hydrophobic lipid tails; whereas FF, FL, LF, and LL with hydrophobic external surface exhibit good stability. In the four hydrophilic channels FF, FL, LF, and LL, water chains are formed; the number of chains ranges from multiple, two to one depending on channel diameter; moreover, water undergoes single-file diffusion and the mobility is enhanced with increasing channel diameter. The permeation rate of water in the FF channel is 9.20/ns, about three times that in aquaporin; however, the rate in FL, LF, and LL is much slower. Intriguingly, the rate can be tuned by a lateral stress/strain on the lipid membrane. The simulation study provides fundamental understanding on the stability of dipeptide channels embedded in a lipid membrane, quantitatively characterizing water structure, dynamics, and permeation in the channels. These microscopic insights are useful for the development of new water channels.

Molecular simulation study of water transport through aquaporin-inspired pore geometry

Water permeation dynamics through hourglass-shaped nanopore is addressed by using Molecular dynamics (MD) simulations. The objective of this research is to understand the variation of the length on water transport in hourglass-shaped pore. We found that the water flow decreases with length due to the hydrodynamic resistance at the entrances, that has large contribution on water flow. Moreover, it was shown that water flux decreases as the length increases, which is consistent with the experimental study. The fluctuations of the density profiles at the center of the pore reduce as the length increases, which is an indication of fast local permeability through highly continuous motion. The pore surface becomes highly frictionless with increasing the length due to the low water-wall interaction. On the other hand, the hydrodynamic resistance (viscos dissipation) at the center of the pore decreases as the length increases, whereas the entrance effect can be highlighted. The MSD curve indicates a Fickian diffusion with increasing the length, even though a Single-file diffusion is expected. It can be found that the changing the cone angle affects on flow rate enhancement through hourglass-shaped nanochannels.

Tagged particle in single-file diffusion with arbitrary initial conditions

We compute the full probability distribution of the positions of a tagged particle exactly for the given arbitrary initial positions of the particles, and for general single-particle propagators. We consider the thermodynamic limit of our exact expressions in quenched and annealed settings. For a particular class of single-particle propagators, the exact formula is expressed in a simple integral form in the quenched case whereas in the annealed case, it is expressed as a simple combination of Bessel functions. In particular, we focus on the step and the power-law initial configurations. In the former case, a drift is induced even when the one-particle propagators are symmetric. On the other hand, in the later case the scaling of the cumulants of the position of the tracer differs from the uniform case. We provide numerical verifications of our results.

Numerical study of the diffusion of binary hydrocarbon blends in ZSM-12 zeolites

The experimental results for the simultaneous diffusion of toluene and ethylene in one dimensional channels of the ZSM-12 zeolite which have been reported in a previous publication are fitted with an original finite difference numerical simulation model. This system is mimicking the single file diffusion of hydrocarbons in the zeolite passive hydrocarbon trap installed at the exhaust of an internal combustion engine, prior to the catalytic muffler, to solve the hydrocarbon cold start emission problem. The study encompasses the effects of Na+, H+ and Ag+ counterions and temperature ramp on the temperature programmed desorption of the binary mixture. A simple lattice gas model is proposed to simulate the binary gas diffusion in a one dimensional pore lattice. Numerical simulations show that taking into account an Arrhenius dependence of the binary gas diffusion coefficient on temperature yielded a good fit of these experimental results, explaining many significant features of the temperature programmed desorption profile observed experimentally.

Anomalous and nonanomalous behaviors of single-file dynamics

We study the dynamics of a tagged particle that undergoes single-file diffusion in an environment of point Brownian particles. Specifically, we examine the effect of the particle density on the well-known anomalous sub-diffusion behavior of the tagged particle. We compare two single-file systems; the first maintains a fixed average particle density and the second experiences a dilution with time. Both our analytical predictions and computational results, that study the time evolution of the mean square displacement per particle for both systems, show that the behavior of the tagged particle transforms from anomalous sub-diffusive (if the average particle density is kept fixed) to normal if a reduction in the average particle density takes place during the diffusion. Our computational results are based on a discrete Monte-Carlo technique that captures perfectly the dynamics of the continuum formulation of single-file systems.

Effects of Antisite Defects on Li Diffusion in LiFePO4 Revealed by Li Isotope Exchange

Li–Fe antisite defects are commonly found in LiFePO4 particles and can impede or block Li diffusion in the single-file Li diffusion channels. However, due to their low concentration (∼1%), the effect of antisite defects on Li diffusion has only been systematically investigated by theoretical approaches. In this work, the exchange between Li in solid LiFePO4 (92.5% enriched with 6Li) and Li in the liquid Li electrolyte solution (containing natural abundance Li, 7.6% 6Li and 92.4% 7Li) was measured as a function of time by both ex situ and in situ solid-state nuclear magnetic resonance experiments. The experimental data reveal that the time dependence of the isotope exchange cannot be modeled by a simple single-file diffusion process and that defects must play a role in the mobility of ions in the LiFePO4 particles. By performing kinetic Monte Carlo simulations that explicitly consider antisite defects, which allow Li to cross over between adjacent channels, we show that the observed tracer exchange behavio...

Relaxation of the electric resistance in YBa2Cu3O7−x single crystals at room temperature

In this paper, the relaxation of the electrical resistance of a YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text] single crystal that is kept for a long time at room temperature in air atmosphere is investigated. It is shown that with increasing time of keeping, relaxation of the electrical resistivity at room temperature is observed, controlled by a single channel and the classical oxygen ion diffusion mechanisms. The faster transport of oxygen ions in the initial stage of the implantation process can take place along one-dimensional nonstoichiometric vacancies in a single-file diffusion mode. The final stage of oxygen transport in this compound is described by an ordinary classical diffusion mechanism.

Possible role of molecular clustering in single-file diffusion of mixed and pure gases in dipeptide nanochannels

Single-file diffusion (SFD) of CO, CO2, and CH4 gas molecules confined in L-Ala-L-Val nanochannels as both pure and binary mixtures is investigated using pulsed field gradient (PFG) NMR at the high field of 17.6 T. A unique SFD mobility is observed for each of the sorbates as pure gases. As binary mixtures, both sorbates exhibit identical SFD mobilities. The mixture mobilities were observed to be larger than those of the slowest-diffusing component in its pure form under the conditions when the total concentration of sorbate molecules in the channels was the same or comparable. It is proposed that molecular clustering in the studied channels is responsible for the relationship experimentally observed between the one-component and mixture mobilities. It is demonstrated that molecular clustering can also explain the lack of the experimental observation of a transition from the SFD mechanism to the center-of-mass diffusion mechanism, viz. diffusion mechanism characterized by correlated movements of all molecules in any particular channel.

Complementary mode analyses between sub- and superdiffusion.

Several subdiffusive stochastic processes in nature, e.g., the motion of a tagged monomer in polymers, the height fluctuation of interfaces, particle dynamics in single-file diffusion, etc., can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating superdiffusion, which is paired with or complementary to subdiffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergo sub- and superdiffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness of looking at the force fluctuation in experiments, where a polymer is driven by a constant velocity.

Computing osmotic permeabilities of aquaporins AQP4, AQP5, and GlpF from near-equilibrium simulations

Measuring or computing the single-channel permeability of aquaporins/aquaglyceroporins (AQPs) has long been a challenge. The measured values scatter over an order of magnitude but the corresponding Arrhenius activation energies converge in the current literature. Osmotic flux through an AQP was simulated as water current forced through the channel by kilobar hydraulic pressure or theoretically approximated as single-file diffusion. In this paper, we report large scale simulations of osmotic current under sub M gradient through three AQPs (water channels AQP4 and AQP5 and glycerol-water channel GlpF) using the mature particle mesh Ewald technique (PME) for which the established force fields have been optimized with known accuracy. These simulations were implemented with hybrid periodic boundary conditions devised to avoid the artifactitious mixing across the membrane in a regular PME simulation. The computed single-channel permeabilities at 5°C and 25°C are in agreement with recently refined experiments on GlpF. The Arrhenius activation energies extracted from our simulations for all the three AQPs agree with the in vitro measurements. The single-file diffusion approximations from our large-scale simulations are consistent with the current literature on smaller systems. From these unambiguous agreements among the in vitro and in silico studies, we observe the quantitative accuracy of the all-atom force fields of the current literature for water-channel biology. We also observe that AQP4, that is particularly rich in the central nervous system, is more efficient in water conduction and more temperature-sensitive than other water-only channels (excluding glycerol channels that also conduct water when not inhibited by glycerol).

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times.

Particles confined to a single file, in a narrow quasi-one-dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two-dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs' case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.

Different diffusion mechanisms of oxygen in ReBa2Cu3O7−x (Re = Y, Ho) single crystals

In the present study, the time dependencies of the resistivity of ReBa2Cu3O7−x (Re=Y, Ho) single crystals with varying degree of deviation from oxygen stoichiometry was investigated. It was shown that the accelerated transport of oxygen ions in the initial stage of the process can be carried out along the one-dimensional non-stoichiometric vacancies’ accumulation by the single file diffusion mechanism. The final phase redistribution of oxygen ions in ReBa2Cu3O7−x (Re=Y, Ho) is described by the classical mechanism of volume diffusion. The substitution of yttrium by holmium significantly affects the charge redistribution and changes the efficient interaction of ions in CuO-planes, thereby modifying the mass transfer diffusion mechanisms in the oxygen sublattice. Thus, a significant length change of the time intervals occurs, corresponding to the oxygen ions’ single file and volume diffusion mechanisms.