Phase Diffusion Coefficient Research Articles

Group superballistic diffusion: Bimodal velocity inducing coexistence of two states in a corrugated plane

We consider anomalous diffusion of a particle moving in a tilted periodic potential in the presence of Lévy noise and nonlinear friction. Using Monte Carlo simulations, we have found some interesting characteristics of diffusion in such a nonlinear system: when the noise intensity is weak and the external force is close to the critical value at which local minima of the potential just vanish, the nonmonotonic behavior of the effective diffusion index and the superballistic diffusion are observed. This is due to the bimodal nature of the velocity distribution, and thus the test particles exist in either a running state or a long-tailed behind state in the spatial coordinate; the latter is disintegrated into small pieces of the probability peaks. We provide a relation between the group diffusion coefficient and the phase diffusion coefficient. It is shown that the distance between the above two-state centers increasing with time plays the definitive role in the superballistic group diffusion.

Alternative analytical analysis for improved Loschmidt diffusion cell

To measure gas phase diffusion coefficients across porous media, an apparatus called a Loschmidt diffusion cell is often utilized. In previous studies with such an apparatus, an infinite-length assumption is used to simplify the analytical solution. Experimentally, cell lengths must be quite long and measurement time is very brief to fulfill this assumption. In this study, Fick’s second law is applied, and separation of variables with shifted homogeneity technique is performed for data analysis to enable design of a more compact experimental apparatus with extended measurement times and improved precision. The analytical solution is proved by both the inverse-matrix method and finite-volume discretization. Finally, using the new analytical solution obtained, the effective diffusion coefficient is determined for porous media used in fuel cell applications.

Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation

Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale L increases with time. The so-called coarsening exponent n characterizes the time dependence of the scale of the pattern, L(t)≈t(n), and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of D(λ), the phase diffusion coefficient, as a function of the wavelength λ of the base steady state u(0)(x). D carries all information about coarsening dynamics and, through the relation |D(L)|=/~L(2)/t, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a orward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved.

Phase diagram of carbon-oxygen plasma mixtures in white dwarf stars

The liquid-solid phase-diagram of dense carbon-oxygen plasma mixtures found in white dwarf stars interiors is determined from molecular dynamics (MD) simulations. Our MD simulations consist of boxes with 55296 ions with different carbon to oxygen ratios. Finite size effects are estimated comparing the new MD simulations results to previous smaller simulations. We use bond angle metric to identify whether an ion is in the solid, liquid or interface and study non-equilibrium effects by obtaining the diffusion coefficients in the different phases. Our phase diagram agrees with predictions from Medin and Cumming obtained by an independent method.

Fluorescence recovery after photo-bleaching as a method to determine local diffusion coefficient in the stratum corneum

Fluorescence recovery after photo-bleaching experiments were performed in human stratum corneum in vitro. Fluorescence multiphoton tomography was used, which allowed the dimensions of the photobleached volume to be at the micron scale and located fully within the lipid phase of the stratum corneum. Analysis of the fluorescence recovery data with simplified mathematical models yielded the diffusion coefficient of small molecular weight organic fluorescent dye Rhodamine B in the stratum corneum lipid phase of about (3–6)×10−9cm2s−1. It was concluded that the presented method can be used for detailed analysis of localised diffusion coefficients in the stratum corneum phases for various fluorescent probes.

The convective drying of liquid films on slender wires

We solve numerically the balance equations of mass and thermal energy for drying liquid films of binary solutions on cylindrical substrates to simulate the drying process of liquid coatings on round metal wires, which are used for electrical insulation in magnet wire technology. The liquid phase diffusion coefficient and the solvent activity are treated as concentration and temperature dependent. The evaporation rate of the solvent across the shrinking liquid–gas interface is determined using the film theory, accounting for the thermodynamic state of the ambient medium and the convective flow situation. The quality of the coatings is assessed by the temporal evolution of radial profiles of the solute mass fraction and by detecting boiling, which leads to the formation of vapour bubbles in the liquid films and is undesired. A guideline for uniform drying at various drying conditions is presented. The simulation model is applied to the test system PVA-water.

Deterministic characterization of phase noise in biomolecular oscillators

On top of the many external perturbations, cellular oscillators also face intrinsic perturbations due the randomness of chemical kinetics. Biomolecular oscillators, distinct in their parameter sets or distinct in their architecture, show different resilience with respect to such intrinsic perturbations. Assessing this resilience can be done by ensemble stochastic simulations. These are computationally costly and do not permit further insights into the mechanistic cause of the observed resilience. For reaction systems operating at a steady state, the linear noise approximation (LNA) can be used to determine the effect of molecular noise. Here we show that methods based on LNA fail for oscillatory systems and we propose an alternative ansatz. It yields an asymptotic expression for the phase diffusion coefficient of stochastic oscillators. Moreover, it allows us to single out the noise contribution of every reaction in an oscillatory system. We test the approach on the one-loop model of the Drosophila circadian clock. Our results are consistent with those obtained through stochastic simulations with a gain in computational efficiency of about three orders of magnitude.

Gas uptake and chemical aging of semisolid organic aerosol particles.

Organic substances can adopt an amorphous solid or semisolid state, influencing the rate of heterogeneous reactions and multiphase processes in atmospheric aerosols. Here we demonstrate how molecular diffusion in the condensed phase affects the gas uptake and chemical transformation of semisolid organic particles. Flow tube experiments show that the ozone uptake and oxidative aging of amorphous protein is kinetically limited by bulk diffusion. The reactive gas uptake exhibits a pronounced increase with relative humidity, which can be explained by a decrease of viscosity and increase of diffusivity due to hygroscopic water uptake transforming the amorphous organic matrix from a glassy to a semisolid state (moisture-induced phase transition). The reaction rate depends on the condensed phase diffusion coefficients of both the oxidant and the organic reactant molecules, which can be described by a kinetic multilayer flux model but not by the traditional resistor model approach of multiphase chemistry. The chemical lifetime of reactive compounds in atmospheric particles can increase from seconds to days as the rate of diffusion in semisolid phases can decrease by multiple orders of magnitude in response to low temperature or low relative humidity. The findings demonstrate that the occurrence and properties of amorphous semisolid phases challenge traditional views and require advanced formalisms for the description of organic particle formation and transformation in atmospheric models of aerosol effects on air quality, public health, and climate.

Phase synchronization of three locally coupled chaotic electrochemical oscillators: Enhanced phase diffusion and identification of indirect coupling

Experiments are carried out with three locally coupled phase coherent chaotic electrochemical oscillators (A-B-C) in nickel dissolution in sulfuric acid. As the interaction strength is increased among the electrodes, an onset of synchronization is observed where the frequencies become identical and the phase differences are bounded. The precision of the period of the oscillators is characterized by phase diffusion coefficients from phases and phase differences. The transition to synchronization with increase of coupling strength was found to be accompanied by enhanced phase fluctuations that cause the precision of the oscillations to deteriorate. A parallel synchrony analysis showed that the direct (between A and B and B and C) and the indirect (between A and C) couplings can be correctly identified with the use of a partial phase synchrony index; therefore, the network topology can be deduced from dynamical measurements. Numerical simulations with a locally coupled model for electrochemical chaos confirm the presence of enhanced phase fluctuations close to the transition to synchronization and the usefulness of the partial phase synchrony index for differentiation of direct from indirect interactions in a small network of oscillators.

Liquid phase diffusion of branched alkanes in silicalite

AbstractThis work provides a new mass transfer model based on the Maxwell–Stefan theory, especially adapted to represent adsorbed phase multicomponent diffusion at high‐adsorbent loading. In our model—contrarily to the well‐known model developed by Krishna et al. (Chem Eng Sci. 1990;45:7:1779–1791; Gas Sep Purif. 1993;7:91–104; J Phys Chem B. 2005;109:6386–6396)—the hypothesis that the micropores are saturated does not imply a dependency between the adsorbed phase diffusion coefficients. Experimental liquid phase breakthrough curves of 2‐methylpentane (2MP), 3‐methylpentane (3MP), 2,3‐dimethylbutane (23DMB), and 2,2‐dimethylbutane (22DMB) were measured at 458 K in silicalite. The self‐diffusion coefficients and Langmuir parameters of the different species were determined using binary exchange breakthrough curves. The Maxwell–Stefan diffusion coefficients obtained for the different isomers are in the order D3MP,nc+1 > D2MP,nc+1 ≫ D23DMB,nc+1, and vary between 4 × 10−15 m2 s−1 for 3MP to 6 × 10−16 m2 s−1 for 23DMB. The 22DMB diffusion coefficient is so low that it could not be estimated (the quantity of 22DMB entering silicalite during the experiment is not significant). The model was then validated by comparing experimental breakthrough curves at different feed concentrations and simulations using the independently estimated parameters. Even though the diffusion coefficients of the different isomers vary by one order of magnitude, the agreement between simulated and experimental curves is very satisfactory, showing the good predictive power of our model. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior

The single-particle model presented by Santhanagopalan et al. [ J. Power Sources , 156 , 620 (2006)] is extended to include an energy balance. The temperature dependence of the solid phase diffusion coefficient of the lithium in the intercalation particles, the electrochemical reaction rate constants, and the open circuit potentials (OCPs) of the positive and negative electrodes are included in the model. The solution phase polarization is approximated using a nonlinear resistance, which is a function of current and temperature. The model is used to predict the temperature and voltage profiles in a lithium-ion cell during galvanostatic operations. The single-particle thermal model is validated by comparing the simulated voltage and temperature profiles to the results obtained using a distributed porous electrode model. The simulation results from the single-particle thermal model also show good agreement with experimental voltage data obtained from lithium-ion pouch cells under different discharge rates (C/33, C/2 and C) at different temperatures (15, 25, 35, and ).

Short Time Scale Dynamics and a Second Correlation between Liquid and Gas Phase Chemical Rates: Diffusion Processes in Noble Gas Fluids

A theoretical formula for single-atom diffusion rates that predicts an isothermal correlation relation between the liquid (l) and gas (g) phase diffusion coefficients, D(T, ρl) and D(T, ρg) is developed. This formula is based on a molecular level expression for the atom’s diffusion coefficient, D(T, ρ), and on numerical results for 1715 thermodynamic states of 25 rare gas fluids. These numerical results show that at fixed temperature, T, the decay time, τDIF, which governs the shortest time decay of an appropriate force autocorrelation function, F(t) F0, is density (ρ)-independent. This independence holds since τDIF arises from the ρ-independent shortest time inertial motions of the solvent. The ρ independence implies the following l−g diffusion coefficient correlation equation: D−1(T, ρl) = (ρl/ρg) D−1(T, ρg) [ρl−1F0,l2/ρg−1F0,g2]. This relation is identical in form to the familiar (isolated binary-collision-like) empirical correlation formula for vibrational energy relaxation rate constants. This is because both correlation relations arise from inertial dynamics. Inertial dynamics always determines short-time fluid motions, so it is likely that similar correlation relations occur for all liquid phase chemical processes. These correlation relations will be most valuable for phenomena dominated by short time scale dynamics.

Effect of temperature on precision of chaotic oscillations in nickel electrodissolution

We investigate the effects of temperature on complexity features of chaotic electrochemical oscillations using the anodic electrodissolution of nickel in sulfuric acid. The precision of the "period" of chaotic oscillation is characterized by phase diffusion coefficient (D). It is shown that reduced phase diffusion coefficient (D/frequency) exhibits Arrhenius-type dependency on temperature with apparent activation energy of 108 kJ/mol. The reduced Lyapunov exponent of the attractor exhibits no considerable dependency on temperature. These results suggest that the precision of electrochemical oscillations deteriorates with increase in temperature and the variation of phase diffusion coefficient does not necessarily correlate with that of Lyapunov exponent. Modeling studies qualitatively simulate the behavior observed in the experiments: the precision of oscillations in the chaotic Ni dissolution model can be tuned by changes of a time scale parameter of an essential variable, which is responsible for the development of chaotic behavior.

Coefficients of Evaporation and Gas Phase Diffusion of Low-Volatility Organic Solvents in Nitrogen from Interferometric Study of Evaporating Droplets

Evaporation of motionless, levitating droplets of pure, low-volatility liquids was studied with interferometric methods. Experiments were conducted on charged droplets in the electrodynamic trap in nitrogen at atmospheric pressure at 298 K. Mono-, di-, tri-, and tetra(ethylene glycols) and 1,3-dimethyl-2-imidazolidinone were studied. The influence of minute impurities (<0.1%) upon the process of droplet evaporation was observed and discussed. The gas phase diffusion and evaporation coefficients were found from droplet radii evolution under the assumption of known vapor pressure. Diffusion coefficients were compared with independent measurements and calculations (in air). Good agreement was found for mono- and di(ethylene glycols), and for 1,3-dimethyl-2-imidazolidinone, which confirmed the used vapor pressure values. The value of equilibrium vapor pressure for tri(ethylene glycol) was proposed to be 0.044 +/- 0.008 Pa. The evaporation coefficient was found to increase from 0.035 to 0.16 versus the molecular mass of the compound.

Electrochemical intercalation kinetics of lithium ions for spinel LiNi0.5Mn1.5O4 cathode material

The crystal structure and electrochemical intercalation kinetics of spinel LiNi0.5Mn1.5O4 such as the resistance of a solid electrolyte interphase (SEI) film, charge transfer resistance (Rct), surface layer capacitance, exchange current density (i0), and chemical diffusion coefficient are evaluated by Fourier transform infrared (FT-IR) and electrochemical impedance spectroscopy (EIS), respectively. FT-IR shows that LiNi0.5Mn1.5O4 thus obtained has a cubic spinel structure, which can be indexed in a space group of Fd3m with a disordering distribution of Ni. EIS indicates that Rs is almost a constant at different states of charge. The thickness of SEI film increases with increasing of the cell voltage. Rct values evidently decreases when lithium ions deintercalated from the cathode in the voltage range from OCV to 4.6 V, and Rct value increases with increasing potential of deintercalation over 4.7 V. i0 varies between 0.2 and 1.6 mA cm−2, and the solid phase diffusion coefficient of Li+ changed depending on the electrode potential in the range of 10−11–10−9 cm2 s−1.

Modelling the coupled transfer of mass and thermal energy in the vapour–liquid region of a nitrogen–oxygen mixture

Current non-equilibrium distillation models do not explicitly include the coupling between thermal and mass fluxes. We present a calculation model for the coupled transfer of mass and thermal energy in the vapour–liquid region of a binary mixture. The region is modelled as a vapour–liquid interface in between two homogeneous films. The entropy production in the vapour–liquid region can be calculated using both irreversible thermodynamics and the entropy balance. The film thickness ratio is found by requiring the entropy production calculated with the two methods to be equal, while keeping the vapour film thickness fixed. Using a nitrogen–oxygen mixture as example, we show that neglecting the coupling between thermal and mass fluxes can have a large impact on the magnitude and direction of the theoretical (net) fluxes. The size of the impact depends on the vapour film thickness, but it is significant for all thicknesses. By increasing the number of control volumes that is used to represent the liquid and vapour films, we also show that the fluxes depend highly on the resistivity profiles in the films. They depend slightly on the interface resistance. A sensitivity analysis of the transport properties shows that accurate values of the Maxwell–Stefan diffusion coefficients in both homogeneous phases and of the liquid phase heat of transfer are most important. Especially the measurable heat flux at the liquid boundary of the system is sensitive to neglect of coupling, to neglect of the interface resistance and to uncertainties in the transfer properties.

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

AbstractDiffusion of gases in polymers below the glass transition temperature, Tg, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [13C]O2 diffusion in polymer films at 298 K are performed. Data obtained in polymers with Tg above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below Tg is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below Tg requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010

Phase instability and coarsening in two dimensions

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent length scale or coarsening (increase in the length scale with time) are the two major alternatives. When and under which conditions one dynamics prevails over the other is a long-standing problem, particularly beyond one dimension. It is shown that the challenge can be defied in two dimensions, using the concept of phase diffusion equation. We find that coarsening is related to the lambda dependence of a suitable phase diffusion coefficient, D11(lambda) , depending on lattice symmetry and conservation laws. These results are exemplified analytically on prototypical nonlinear equations.

Diffusion at a planar interface using continuous distribution of sources

Many investigations of films grown on planar substrates at higher temperatures are accompanied by interdiffusion of atomic species across the planar interface from the substrate into the film and from the film into the substrate. In the present work, a new analysis is presented so that the concentration profiles of the diffusing species with different diffusion coefficients are determined. The analysis is carried out using the mathematical method of continuous distribution of diffusing sources in the two phases. The two boundary conditions in the form of continuity of flux and concentration at the interface are used to solve for the two distribution functions. These results are used to solve for the concentration profiles resulting from the mass diffusion in the two-phase medium. Application of the solution to a bilayer system with a planar interface and different diffusion coefficients in the adjoining phases is provided to illustrate the use of this method to several situations.

Electrochemical ion transfer across liquid/liquid interfaces confined within solid-state micropore arrays – simulations and experiments

Miniaturised liquid/liquid interfaces provide benefits for bioanalytical detection with electrochemical methods. In this work, microporous silicon membranes which can be used for interface miniaturisation were characterized by simulations and experiments. The microporous membranes possessed hexagonal arrays of pores with radii between 10 and 25 microm, a pore depth of 100 microm and pore centre-to-centre separations between 99 and 986 microm. Cyclic voltammetry was used to monitor ion transfer across arrays of micro-interfaces between two immiscible electrolyte solutions (microITIES) formed at these membranes, with the organic phase present as an organogel. The results were compared to computational simulations taking into account mass transport by diffusion and encompassing diffusion to recessed interfaces and overlapped diffusion zones. The simulation and experimental data were both consistent with the situation where the location of the liquid/liquid (l/l) interface was on the aqueous side of the silicon membrane and the pores were filled with the organic phase. While the current for the forward potential scan (transfer of the ion from the aqueous phase to the organic phase) was strongly dependent on the location of the l/l interface, the current peak during the reverse scan (transfer of the ion from the organic phase to the aqueous phase) was influenced by the ratio of the transferring ion's diffusion coefficients in both phases. The diffusion coefficient of the transferring ion in the gelified organic phase was ca. nine times smaller than in the aqueous phase. Asymmetric cyclic voltammogram shapes were caused by the combined effect of non-symmetrical diffusion (spherical and linear) and by the inequality of the diffusion coefficient in both phases. Overlapping diffusion zones were responsible for the observation of current peaks instead of steady-state currents during the forward scan. The characterisation of the diffusion behaviour is an important requirement for application of these silicon membranes in electroanalytical chemistry.