Small Diffusion Coefficient Research Articles

Design of Functional Gyroid Minimal Surfaces Transporting Proton Based Solely on Surface Hopping Conduction Mechanism.

Surface proton hopping conduction (SPHC) mechanisms is an important proton conduction mechanism in conventional polymer electrolytes, along with the Grotthuss and vehicle mechanisms. Due to the small diffusion coefficient of protons in the SPHC mechanism, few studies have focused on the SPHC mechanism. Recently, it has been found that a dense alignment of SO3 - groups significantly lowers the activation energy in the SPHC mechanism, enabling fast proton conduction. In this study, a series of polymerizable amphiphilic-zwitterions is prepared, forming bicontinuous cubic liquid-crystalline assemblies with gyroid symmetry in the presence of suitable amounts of bis(trifluoromethanesulfonyl) imide (HTf2N) and water. In situ polymerization of these compounds yields gyroid-nanostructured polymer films, as confirmed by synchrotron small-angle X-ray scattering experiments. The high proton conductivity of the films on the order of 10-2 S cm-1 at 40 °C and relative humidity of 90% is based solely on the SPHC mechanism.

Cosmic-Ray Feedback on Bistable Interstellar Medium Turbulence

While cosmic rays (E ≳ 1 GeV) are well coupled to a galaxy’s interstellar medium (ISM) at scales of L > 100 pc, adjusting stratification and driving outflows, their impact on small scales is less clear. Based on calculations of the cosmic-ray diffusion coefficient from observations of the grammage in the Milky Way, cosmic rays have little time to dynamically impact the ISM on those small scales. Using numerical simulations, we explore how more complex cosmic-ray transport could allow cosmic rays to couple to the ISM on small scales. We create a two-zone model of cosmic-ray transport, with the cosmic-ray diffusion coefficient set at the estimated Milky Way value in cold gas but smaller in warm gas. We compare this model to simulations with a constant diffusion coefficient. Quicker diffusion through cold gas allows more cold gas to form compared to a simulation with a constant, small diffusion coefficient. However, slower diffusion in warm gas allows cosmic rays to take energy from the turbulent cascade anisotropically. This cosmic-ray energization comes at the expense of turbulent energy which would otherwise be lost during radiative cooling. Finally, we show our two-zone model is capable of matching observational estimates of the grammage for some transport paths through the simulation.

Elucidating the separation role of C3N slit-pore on N2/CH4 in coalbed methane

A hybrid approach integrating molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulations was employed to investigate the separation efficacy of N2/CH4 across various C3N slit apertures. MD simulations enabled the determination of separation selectivity and diffusion coefficients of N2/CH4, thereby aiding in the elucidation of the separation mechanism. On the other hand, GCMC simulations provided insights into the adsorption isotherms and isosteric heats of N2 and CH4 within the C3N slit. These findings reveal that the highest selectivity of N2 over CH4 occurs at the zigzag-edge C3N with a pore size of 6.2 Å. However, this selectivity is accompanied by the smallest diffusion coefficient, attributable to size sieving effects. As the pore diameter increases, more gas molecules can permeate into the pores, leading to a rise in both the maximum adsorption capacity and the isosteric heat of methane adsorption. With increasing pressure, gas molecules tend to reach saturation at higher pressure levels. Our study primarily centers on examining the separation of N2/CH4 across various C3N slit-pores, encompassing both adsorption and diffusion phenomena. These findings offer theoretical insights and comprehension for the experimental separation of coalbed methane utilizing cheaper carbon-based materials.

Si/Graphite@C Composite Fabricated by Electrostatic Self-Assembly and Following Thermal Treatment as an Anode Material for Lithium-Ion Battery.

Commercial graphite anode has advantages such as low potential platform, high electronic conductivity, and abundant reserves. However, its theoretical capacity is only 372 mA h g-1. High-energy lithium-ion batteries have been a research hotspot. The Si anode has an extremely high specific capacity, but its application is hindered by defects such as large volume changes, poor electronic conductivity, and a small lithium-ion diffusion coefficient. Here, the Si/thermally reduced graphite oxide@carbon (Si/RGtO@C) composite was fabricated by electrostatic self-assembly followed by thermal treatment. The RGtO synergistic carbon coating layer can effectively compensate for the low electronic conductivity and buffer the volume expansion effect of the Si nanoparticles during charge/discharge cycles. The Si/RGtO@C anode demonstrated a significantly increased capacity compared to the RGtO. After 300 cycles, Si/RGtO@C kept a discharged capacity of 367.6 mA h g-1 at a high current density of 1.0 A g-1. The Si/RGtO@C anode shows an application potential for commercial high-energy lithium-ion batteries.

Molecular Dynamics Simulation of Hydrogen Barrier Performance of Modified Polyamide 6 Lining of IV Hydrogen Storage Tank with Graphene.

The polymer liner of the hydrogen storage cylinder was studied to investigate better hydrogen storage capacity in Type-IV cylinders. Molecular dynamics methods were used to simulate the adsorption and diffusion processes of hydrogen in a graphene-filled polyamide 6 (PA6) system. The solubility and diffusion characteristics of hydrogen in PA6 systems filled with different filler ratios (3 wt%, 4 wt%, 5 wt%, 6 wt%, and 7 wt%) were studied under working pressures (0.1 MPa, 35 MPa, 52 MPa, and 70 MPa). The effects of filler ratio, temperature, and pressure on hydrogen diffusion were analyzed. The results show that at atmospheric pressure when the graphene content reaches 5 wt%, its permeability coefficient is as low as 2.44 × 10-13 cm3·cm/(cm2·s·Pa), which is a 54.6% reduction compared to PA6. At 358 K and 70 MPa, the diffusion coefficient of the 5 wt% graphene/PA6 composite system is 138% higher than that at 298 K and 70 MPa. With increasing pressure, the diffusion coefficients of all materials generally decrease linearly. Among them, pure PA6 has the largest diffusion coefficient, while the 4 wt% graphene/PA6 composite system has the smallest diffusion coefficient. Additionally, the impact of FFV (free volume fraction) on the barrier properties of the material was studied, and the movement trajectory of H2 in the composite system was analyzed.

Liquid-Phase Exfoliation of Arsenic Trisulfide (As2S3) Nanosheets and Their Use as Anodes in Potassium-Ion Batteries.

Here, we demonstrate the production of 2D nanosheets of arsenic disulfide (As2S3) via liquid-phase exfoliation of the naturally occurring mineral, orpiment. The resultant nanosheets had mean lateral dimensions and thicknesses of 400 and 10 nm, and had structures indistinguishable from the bulk. The nanosheets were solution mixed with carbon nanotubes and cast into nanocomposite films for use as anodes in potassium-ion batteries. These anodes exhibited outstanding electrochemical performance, demonstrating an impressive discharge capacity of 619 mAh/g at a current density of 50 mA/g. Even after 1000 cycles at 500 mA/g, the anodes retained an impressive 94% of their capacity. Quantitative analysis of the rate performance yielded a capacity at a very low rate of 838 mAh/g, about two-thirds of the theoretical capacity of As2S3 (1305 mAh/g). However, this analysis also implied As2S3 to have a very small solid-state diffusion coefficient (∼10-17 m2/s), somewhat limiting its potential for high-rate applications.

Influence of Grain Size and Film Formation Potential on the Diffusivity of Point Defects in the Passive Film of Pure Aluminum in NaCl Solution

The influence of grain size on the corrosion behavior of pure aluminum and the defect density and diffusion coefficient of surface passive films were investigated using electron backscatter diffraction (EBSD) and electrochemical testing techniques, based on the point defect model (PDM). Samples with three different grain sizes (23 ± 11, 134 ± 52, and 462 ± 203 μm) were obtained by annealing at different temperatures and times. The polarization curves and electrochemical impedance spectroscopy results for the pure aluminum in the 3.5% NaCl solution showed that with decreasing grain size, the corrosion current (icorr) decreased monotonously, giving rise to a noble corrosion potential and a large polarization resistance. The Motte–Schottky results showed that the passive films that formed on pure aluminum with fine grains of 23 ± 11 μm had a low density (3.82 × 1020 cm−3) of point defects, such as oxygen vacancies and/or metal interstitials, and a small diffusion coefficient (1.94 × 10−17 cm2/s). The influence of grain size on corrosion resistance was discussed. This work demonstrated that grain refinement could be an effective approach to achieving high corrosion resistance of passive metals.

Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes

A theoretical analysis is conducted on the electrochemical behaviour of micro disk electrodes coated with thin coatings of electroactive polymers. The main focus of efforts to characterize the planar diffusion chemical reaction within polymer-modified ultra-microelectrodes is the creation of a theoretical model that explicitly takes into account the potential for the polymer film to cover the inlaid micro disc support surface. Approximate formulae for the steady-state amperometric response and formulation of the boundary value problem are given. The impact of substrate concentration, mediator concentration and current responsiveness in the solution besides the polymer film is also investigated. Akbari-Ganji method (AGM) and differential transformation method (DTM), two adequate and widely available analytical methods, were utilized to determine the steady-state non-linear diffusion equation. The approximate analytical solution for the substrate concentration and mediator concentration and the current for the small experimental kinetic values and diffusion coefficients are presented. We additionally determine the problem’s numerical solution using the MATLAB tool. A satisfactory agreement can be seen when the numerical outcomes verify with the analytical findings.

Numerical study of concentration polarization of reverse osmosis film via the lattice Boltzmann method

The concentration polarization is the main factor affecting the water production rate of reverse osmosis. This article proposes a new numerical model based on the lattice Boltzmann method for simulating concentration polarization that can easily handle the computational instability caused by small diffusion coefficient. Based on this model, the concentration polarization in empty channel and unilateral spacer channel are simulated, respectively. The results show that the thickness of the CPL is generally about one tenth of the channel height. Increasing the Re can weaken concentration polarization, reduce the thickness of the CPL, and thereby increase permeate flux. Increasing the TMP can increase permeation flux, but it also accelerates the accumulation of solute increases the solute concentration within the CPL, and accelerates fouling. The spacer can effectively weaken the concentration polarization and increase permeate flux. But the unilateral spacer can cause uneven performance of the upper and bottom membranes.

Sensitive organic/inorganic polarized photodetectors enhanced by charge transfer with image sensing capacity.

Organic photodetectors (OPDs) have attracted increasing attention in the future wearable sensing and real-time health monitoring, due to their intrinsic features including the mechanical flexibility, low-cost processing and cooling-free operations; while their performances are lagging as the results of inferior carrier mobility and small exciton diffusion coefficient of organic molecules. Graphene exhibits the great photoresponse with wide spectral bandwidth and high response speed. However, weak light absorption and the absence of a gain mechanism have limited its photoresponsivity. Here, we report a sensitive organic/inorganic phototransistor with fast response speed by coupling PTCDA organic single crystal with the monolayer graphene. The long range exciton diffusion in highly ordered π-conjugated molecules, efficient exciton dissociation and charge transfer at the PTCDA/graphene heterointerfaces, and the high mobility of graphene enable a high responsivity (8 × 104A/W), short response time (220 µs) and excellent specific detectivity (>1011 Jones), which is higher than the level of commercial on-chip device. This interfacial photogating effect is verified by the high-resolution spatial photocurrent mapping experiment. In addition, the high sensitivity to polarization is clear and the ultrahigh photoconductive gain enables a near-infrared (NIR) response for 980 and 1550 nm. Finally, high-speed visible and NIR imaging applications are successfully demonstrated. This work suggests that high quality organic single crystal/graphene is a promising platform for future high performance optoelectronic systems and imaging applications.

Phosphorus Sources and Transport Pathways in the North Chaohu Lake Catchment of China

To understand the cause of the high content of phosphorus in the North Chaohu Lake Catchment of China, the distribution of the total phosphorus in groundwater and the dissolution of rock phosphorus near Chaohu Lake were investigated, and a few interesting findings have been revealed. Firstly, four main processes affecting the groundwater quality in North Chaohu Lake Catchment were identified with the results of factor analysis, including anthropogenic activities and the dissolution of carbonate rocks, phosphorus, and fluorine-bearing minerals. Secondly, the dissolution of rock phosphorus can be well described using the one-dimensional diffusion equation, with a semi-infinite boundary condition, and the Langmuir kinetic equation. A relatively low ambient temperature (less than 25 °C) was probably responsible for the small diffusion coefficient compared to that of the previous studies. Thirdly, the high-potential maximum dissolution of rock phosphorus (Cmax) indicated that the dissolution of rock phosphorus could pose a risk to the ambient water body, and Cmax was found to be independent of the total rock phosphorus content.

Large deviations for trajectory observables of diffusion processes in dimension d > 1 in the double limit of large time and small diffusion coefficient

For diffusion processes in dimension d > 1, the statistics of trajectory observables over the time-window [0,T] can be studied via the Feynman–Kac deformations of the Fokker–Planck generator, which can be interpreted as Euclidean non-Hermitian electromagnetic quantum Hamiltonians. It is interesting to compare the four regimes corresponding to the time T, either finite or large, and to the diffusion coefficient D, either finite or small. (1) For finite T and finite D, one needs to consider the full time-dependent quantum problem that involves the full spectrum of the Hamiltonian. (2) For large time T→+∞ and finite D, one only needs to consider the ground-state properties of the quantum Hamiltonian to obtain the generating function of rescaled cumulants and to construct the corresponding canonical conditioned processes. (3) For finite T and D → 0, one only needs to consider the dominant classical trajectory and its action satisfying the Hamilton–Jacobi equation, as in the semi-classical Wentzel–Kramers–Brillouin (WKB) approximation of quantum mechanics. (4) In the double limit T→+∞ and D → 0, the simplifications in the large deviations in TD of trajectory observables can be analyzed via the two orders of limits, i.e. either from the limit D → 0 of the ground-state properties of the quantum Hamiltonians of (2), or from the limit of long classical trajectories T→+∞ in the semi-classical WKB approximation of (3). This general framework is illustrated in dimension d = 2 with rotational invariance.

Traveling waves and their spectral instability in volume–filling chemotaxis model

In this paper, I consider a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By the geometric singular perturbation theory together with the center-stable and center unstable manifolds, one gets the existence of a positive traveling wave connecting the two constant steady states (0,0) and (b,αbβ) with a small wave speed ϵc. In addition, the traveling wave is monotone for b≥1 and is not monotone for 0<b<1. Moreover, by the spectral analysis it shows that the above traveling wave is spectrally unstable in some exponentially weighted spaces.

Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion

Abstract We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.

Role of imperfections in transfer of organic micro-pollutants through RO/NF membranes: Numerical study

Due to relatively low diffusivities, the rejection of organic micro-pollutants in pressure-driven membrane processes is more affected by Concentration Polarization (CP) than that of typical inorganic ions. On the other hand, it can be more sensitive to various membrane imperfections because the rejection of these solutes by intact membranes can be expected to be quite high. This makes necessary simultaneous accounting for membrane imperfections and Concentration Polarization in Reverse Osmosis and/or Nanofiltration of organic micro-pollutants. This study, for the first time, explores this problem numerically for the model of a single circular opening in a selective layer (the porous support is assumed to remain undamaged). The solute accumulated due to the CP close to the surrounding intact active layer “spills over” to the imperfection, which leads to an enhanced transmembrane solute passage as compared to the classical solution-diffusion-imperfection model assuming this passage to be controlled by the feed concentration. Our analysis reveals that the extent of this “spill-over” depends primarily on the size of imperfection (we studied the range between 0.2 μm and 20 μm) as well as on the ratio of hydraulic resistances of selective and support layers. Smaller imperfections in active layers of membranes with less permeable porous supports have larger impact. The extent of CP away from the imperfection is also important. Contrary to the trend expected for imperfection-free membranes (a better rejection of larger solutes due to a stronger steric exclusion and hindrance), the solute passage through imperfections is demonstrated to be larger for solutes with smaller diffusion coefficients, so in future experiments this can be considered a signature feature of a noticeable impact of imperfections. Quantifying their impact is important for understanding membrane aging, rational selection of membrane cleaning procedures as well as development of better membranes.

Impact of Spatial Memory on a Predator–Prey System with Allee Effect

Recently, spatial memory and Allee effect have been widely investigated in population models, independently. This paper introduces these two aspects to a predator–prey system, and studies the interaction of two species. Allee effect causes bistability, and the predator-free steady-state is always locally stable. Prey-taxis can play a stable role in positive constant steady-state, and spatial memory delay generates the inhomogeneous Hopf bifurcation and even stability switching. In the absence of spatial memory delay, the stronger the predator is subject to the Allee effect, the larger the prey-taxis coefficient is required to keep two species coexist in a stable spatially homogenous form. With the same prey-taxis coefficient, the critical threshold of spatial memory delay corresponding to large predator diffusion coefficient is distinctly bigger than the one corresponding to small predator diffusion coefficient. Moreover, the amplitudes of spatial patterns, which reflect the degree of inhomogeneity, oscillate as spatial memory delay varies.

PH-depended behaviors of electrolytes in nanofluidic salinity gradient energy harvesting

Transmembrane ion transportation in the nanofluidic salinity gradient energy conversion process is significantly regulated by the ion characteristics and concentration-depended physical and chemical properties of the electrolyte solution. In this paper, considering the Born and dielectrophoretic forces and nonhomogeneous electrolyte solution, impacts of various electrolytes on the nanofluidic energy conversion performance are systematically investigated under various solution pHs. When the solution pH is less than the isoelectric point (IEP), with BeCl2 solution employed, where the anion diffusion and concentration coefficient are much larger than those of the anion, significant transmembrane anion diffusion exists, leading to the highest osmotic current and maximum power output, even when the solution pH > IEP where the nanochannel is negatively charged, the ion selectivity is still not altered. At pH < IEP, 2:1 electrolytes, where the cation has small ion diffusion coefficient and the anion has larger diffusion coefficient and hydrated radius could result in upgraded energy conversion performance; At pH > IEP, 1:1 electrolytes where the cation has large ion diffusion coefficient and the anion has small diffusion coefficient and large hydrated radius are more appealing. In addition, the relationships between ion characteristics, power extracted, and energy conversion efficiency are further obtained via machine learning.

Defect deferred correction method for two domain natural convection problem

This paper concerns defect deferred correction method used to resolve interactions between the atmosphere and ocean for applications like climate research, hurricane modelling and regional weather forecasting. The defect deferred correction method is obtained by combining the defect correction method and the deferred correction method. There are two advantages of using the defect deferred correction method to solve a two domain natural convection problem, namely, reaching the second-order time accuracy and solving small viscosity or diffusion coefficient problems. Finally, we will verify the conclusion from both theoretical analysis and numerical experiments.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability.

Asymptotic behavior of the principal eigenvalue and basic reproduction ratio for time-periodic reaction-diffusion systems with time delay

This paper is devoted to asymptotic behavior of the basic reproduction ratio for time-periodic and delay reaction-diffusion systems in the cases of small and large diffusion coefficients. First, we employ the generalized Kerin-Rutman theorem to establish the existence of the principal eigenvalue for periodic and cooperative reaction-diffusion systems with delay. Then, motivated by Kerin-Rutman theorem, we provide a method to estimate the upper and lower bounds of principal eigenvalues so as to obtain the asymptotic behavior of the principal eigenvalue. In view of the relationship between the basic reproduction ratio and the principal eigenvalue, we obtain the limiting profile of the basic reproduction ratio according to the asymptotic behavior of the principal eigenvalue.