Diffusion Coefficients In Systems Research Articles

Expanding the applicability of multiphoton fluorescence recovery after photobleaching by incorporating shear stress in laminar flow.

Multi-photon fluorescence recovery after photobleaching (MPFRAP) is a nonlinear microscopy technique used to measure the diffusion coefficient of fluorescently tagged molecules in solution. Previous MPFRAP fitting models calculate the diffusion coefficient in systems with diffusion or diffusion in laminar flow. We propose an MPFRAP fitting model that accounts for shear stress in laminar flow, making it a more applicable technique for in vitro and in vivo studies involving diffusion. Fluorescence recovery curves are generated using high-throughput molecular dynamics simulations and then fit to all three models (diffusion, diffusion and flow, and diffusion and shear flow) to define the limits within which accurate diffusion coefficients are produced. Diffusion is simulated as a random walk with a variable horizontal bias to account for shear flow. Contour maps of the accuracy of the fitted diffusion coefficient as a function of scaled velocity and scaled shear rate show the parameter space within which each model produces accurate diffusion coefficients; the shear-flow model covers a larger area than the previous models. The shear-flow model allows MPFRAP to be a viable optical tool for studying more biophysical systems than previous models.

Electrochemical Reduction of Iron Oxide - Produced from Iron Combustion - for the Valorization of Iron Fuel Cycle

Iron is a prospective candidate for energy carriers in the energy transition era with high energy density. In this concept, energy is released by the combustion of iron powder whilst the solid product - iron oxide - can be collected and reduced back to metallic iron, forming a recyclable iron fuel cycle. The electrochemical technique is considered to be a suitable reduction method as it has attractive aspects including low electric energy consumption, low temperature, direct usage of renewable energy, and a short process chain. In this study, the performance of iron electrodeposition is investigated using an electrolysis cell containing a suspension of micron-sized combusted iron powder in aqueous NaOH (50%wt, 18 M) at a temperature of 110°C. The parallel plate electrolyzer used in these experiments consists of a stainless-steel plate (cathode) and a nickel gauze (anode). The effects imposed by varying current density, iron oxide composition, and iron oxide particle diameter on Faradaic efficiency and reduced iron yield are evaluated. Additional experiments using a rotating disc electrode (RDE) are also conducted to determine the system's diffusion coefficient under different operating conditions. Generally, cathodic deposition of metallic iron is successfully achieved and the morphology of the deposited iron depends on the operation conditions including the current density and heterogeneity of the flow system. The obtained results open new perspectives for efficient and cost-effective iron production/regeneration. Figure 1

Diffusion Coefficients in Systems Related to Reservoir Fluids: Available Data and Evaluation of Correlations

Molecular diffusion determines the time to reach local equilibrium in a reservoir. It can be a main production mechanism in scenarios such as production from fractured reservoirs or tight formation. However, there is a lack of high-pressure diffusion coefficients for reservoir fluids and its related systems. Many correlations exist, but there is no consensus on their accuracy for these systems. We provide a systematic review of the available data for systems related to reservoir fluids, as well as a comprehensive comparison of five commonly used correlations for hydrocarbon mixtures, including the extended Sigmund, Riazi-Whitson, Leahy-Dios-Firoozabadi, Wilke–Chang, and the Hayduk–Minhas correlations. We collected extensive data of diffusion coefficients in binary mixtures related to petroleum fluids and established a database of over 80 binaries and 1600 data points. We also collected the data for gas diffusion in different oils and reservoir fluids, but the data in high-pressure live oils are extremely scarce. The five correlations were evaluated using the binary database, and a few selected correlations using the oil database. None of the correlations show consistent and dominant superiority for all the binary mixtures, although some are better for particular groups/regions. For oils and reservoir fluids, the composition information is often incomplete. Only a few sets allow a comparison between different correlations. Although some trends can be identified from the correlation evaluation, no conclusive recommendation is made for a particular model, due to the data scarcity. The findings underscore the need for more accurate measurement and modeling of gas diffusion in mixtures that are more representative of reservoir fluids at high pressures.

Measuring the Hydrodynamic Radius of Colloidal Quantum Dots by Fluorescence Correlation Spectroscopy.

Colloidal quantum dots (QDs), due to their versatile optoelectronic properties, have been used in life science applications, especially in fluorescence-based techniques, for over two decades. A great variety of QD syntheses and conjugations are available, and tailoring these for the desired application requires a refined structural characterization. Life science applications rely on the interaction of QDs with biostructures; hence, the knowledge of the QD actual size (i.e., its hydrodynamic radius in the medium the experiment is being carried) and the size of their conjugates is paramount. Fluorescence correlation spectroscopy (FCS) is an optical technique that uses fluorophore light emission to measure its hydrodynamic radius, instead of relying on particle light scattering or crystalline structure, making it ideal for studying bioconjugated QDs in suspension. From the fluorescence intensity autocorrelation, FCS measures the diffusion coefficient of systems in a diluted sample and, by obtaining the diffusion coefficient, it is possible to calculate its hydrodynamic radius. In this chapter we describe the main aspects of the FCS technique and how to use it to calculate the hydrodynamic radius of QDs.

Control the relaxation properties of the diffuse bistable potential

The purpose of this work is to investigate procedures to control the population dynamics in a bistable potential. We use the solutions of the Fokker–Planck equation for the distribution function corresponding to a bistable potential under action of an external electric field. The control is performed with a piecewise protocol with time independent potentials. This protocol provides to be adequate for this problem, controlling the time necessary to balance of system probabilities. Some trajectories were controlled and the limits of procedure clarified. Nevertheless, with the application of the control protocol we clarify some simple phenomena of the system, associating the application of the external field with the system diffusion coefficient.

An innovative method for determining the diffusion coefficient of product nuclide

Abstract Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN_1 → RN_2 → RN_3) and a parallel reaction (RN_1 → RN_2A + RN_2B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.

Characterization of Gas Flow Ability and Contribution of Diffusion to Total Mass Flux in the Shale

The aim of this study is to search a parameter which characterize the flow ability and analyze the contribution of diffusion to total mass flux of gas flow in pore of shale whose size is as low as nanoscale. The diffusion coefficient of the flow region which was determined by Kundsen number was taken as the diffusion coefficient of system, then it was substituted into the equation which describes gas diffusive and flow in nano- porous media, the apparent permeability and mass flux were calculated and the impacts of the pore radius and gas type were analyzed finally. The result showed that the diffusion of gas in shale was mainly in the transition diffusion or Fick diffusion region; The ratio of the apparent permeability of considering the diffusion and slippage effect to Darcy permeability and the ratio of diffusion mass flux to total mass flux increased with the decreasing of the pore radius; The diffusion ability of the methane was stronger than ethane's. The present study implied that the calculated results of the diffusion coefficient which considers three kind of diffusion was less than that one considering Knudsen diffusion only; Considering diffusion and slippage effect, the apparent permeability of nanoscale pore of shale was 10 -6 μm 2 level, not 10 -9 μm 2 level in general temperature and pressure of shale reservoir.

Mutual diffusion coefficients in systems containing the nickel ion

Mutual diffusion coefficients of nickel chloride in water have been measured at 293.15 K and 303.15 K and at concentrations between 0.020 mol dm−3 and 0.100 mol dm−3, using a conductimetric cell. The experimental mutual diffusion coefficients are discussed on the basis of the Onsager–Fuoss model. The equivalent conductances at infinitesimal concentration of the nickel ion in these solutions at those temperatures have been estimated using these results.In addition, from these data, we have estimated some transport and structural parameters, such as limiting diffusion coefficient, ionic conductance at infinitesimal concentration, hydrodynamic radii and activation energy, contributing this way to a better understanding of the structure of these systems and of their thermodynamic behavior in aqueous solution at different concentrations.

Melting and superionic transition of Gd-doped ceria nanocrystals: Molecular dynamics study

Molecular dynamics program for simulation of nanocrystals in vacuum, with ionic model approximation, was developed. The use of graphics processor allows us to speed up calculation by two orders of magnitude in comparison with CPU realization. For Ce1−XGdXO2−X/2 system by fitting to experimental data pair interaction potentials were obtained, comparison with existing potential set was carried out. Melting temperature of CeO2 nanocrystal depends on its octahedron diagonal size as Тm(L,nm)=Тm(∞)−(5534±153)⋅L−2.Structural disorder of Ce1−XGdXO2−X/2 nanocrystals (X=0–0.3) in superionic transition and melting regimes was investigated. Dependences of melting temperature and specific volume change at melting from gadolinium dopant quantity have downward trend. It is shown, that oxygen sublattice disorder (“melting”) in crystallites takes place at about 0.7Tm. The contribution of intrinsic disorder to anion diffusion coefficient in systems with gadolinium dopant was extracted and the presence of superionic transition is shown. Comparison with high-temperature ionic conductivity data was carried out.

How Is Charge Transport Different in Ionic Liquids and Electrolyte Solutions?

In this article we show that, analyzed in a barycentric reference frame, the deviation in conductivity measured directly from impedance experiments with respect to that estimated indirectly from NMR diffusion experiments has different origins in electrolyte solutions and pure salts. In the case of electrolyte solutions, the momentum conservation law is satisfied by solvent + ions. Instead, in a molten salt or ionic liquid momentum conservation must be satisfied solely by the ions. This has significant implications. While positively correlated motion of ions of opposite charge is a well justified explanation for the reduction in impedance conductivity in the case of electrolyte solutions, it is not so in the case of ionic liquids and molten salts. This work presents a set of equations that in the case of ionic liquids and molten salts can be used to obtain from direct measurements of impedance and NMR the distinct part of the diffusion coefficient matrix in the barycentric reference frame. In other words, by using experimentally measurable quantities, these equations allow us to access the motional coupling between ions for which there is no single direct experimental measurement technique. While equations of this type have been proposed before, the ones presented here can be easily derived from the momentum conservation law and linear response theory. Our results indicate that the decrease in the impedance conductivity with respect to NMR conductivity in ionic liquids and molten salts is due to anticorrelated motion of ions of same charge. This scenario is different in electrolyte solutions, where the positively correlated motion of ions of opposite charge makes a significant contribution to the decrease in the impedance conductivity. In contrast, in a system comprising a single binary salt (a room temperature ionic liquid or a molten salt), the cation-anion distinct diffusion coefficient is negative definite and opposes the contribution from the cation-cation and anion-anion distinct diffusion coefficients. This property of the cation-anion distinct diffusion coefficient in systems comprising just two ion-constituents holds true not just in the barycentric reference frame but also in any of the internal reference frames of nonequilibrium thermodynamics.

Measuring diffusion using the differential form of Fick's law and magnetic resonance imaging

Diffusion is an important process in many biological and industrial processes. Diffusion coefficients are traditionally measured using integrated solutions of Fick's law for systems with well-defined boundary conditions. We report a simple method for measuring diffusion coefficients in processes without well-defined boundary conditions or without a simple integrated solution using the differential form of Fick's law. Magnetic resonance imaging (MRI) was used to obtain spatially and time-resolved profiles of the diffusion of H2O from an agarose gel to a neighboring D2O reservoir. The differential form of Fick's second law was used to solve for the diffusion coefficient, D=1.3×10−9 m2 s−1. MRI is well suited to this type of analysis as it naturally generates time- and space-resolved images. This analytical method allows for the determination of diffusion coefficients in systems that lack an integral solution to the diffusion equation.

충전재 변화에 따른 Chip Scale Package(CSP)용 액상 에폭시 수지 성형물 (Epoxy Molding Compound)의 흡습특성

반도체의 경박단소화, 고밀도화에 따라 향후 반도체 패키지의 주 형태는 CSP(Chip Scale Package)가 될 것이다. 이러한 CSP에 사용되는 에폭시 수지 시스템의 흡습특성을 조사하기 위하여 에폭시 수지 및 충전재 변화에 따른 확산계수와 흡습율 변화를 조사하였다. 본 연구에 사용된 에폭시 수지로는 RE-304S, RE-310S, 및 HP-4032D를, 경화제로는 Kayahard MCD를, 경화촉매로는 2-methyl imidazole을 사용하였다. 충전재 크기 변화에 따른 에폭시 수지 성형물의 흡습특성을 조사하기 위하여 충전재로는 마이크로 크기 수준 및 나노 크기 수준의 구형 용융 실리카를 사용하였다. 이러한 에폭시 수지 성형물의 유리전이온도는 시차주사열량계를 이용하여 측정하였으며, 시간에 따른 흡습특성은 <TEX>$85^{\circ}C$</TEX> and 85% 상대습도 조건하에서 항온항습기를 사용하여 측정하였다. 에폭시 수지 성형물의 확산계수는 Ficks의 법칙에 기초한 변형된 Crank 방정식을 사용하여 계산 하였다. 충전재를 사용하지 않은 에폭시 수지 시스템의 경우, 유리전이온도가 증가함에 따라 확산계수와 포화흡습율이 증가 하였으며 이는 유리전이온도 증가에 따른 에폭시 수지 성형물의 자유부피 증가로 설명하였다. 충전재를 사용한 경우, 충전재의 함량 증가에 따라 유리전이온도와 포화흡습율은 거의 변화가 없었으나, 확산계수는 충전재의 입자 크기에 따라 많은 변화를 보여주었다. 마이크로 크기 수준의 충전재를 사용한 경우 확산은 자유부피를 통하여 주로 이루어지나, 나노 크기 수준의 충전재를 사용한 에폭시 수지 성형물에서는 충전재의 표면적 증가에 따른, 수분 흡착의 상호작용을 통한 확산이 지배적으로 이루어진다고 판단된다. Since the requirement of the high density integration and thin package technique of semiconductor have been increasing, the main package type of semiconductor will be a chip scale package (CSP). The changes of diffusion coefficient and moisture content ratio of epoxy resin systems according to the change of liquid type epoxy resin and fillers for CSP applications were investigated. The epoxy resins used in this study are RE-304S, RE310S, and HP-4032D, and Kayahard MCD as hardener and 2-methylimidazole as catalyst were used in these epoxy resin systems. The micro-sized and nano-sized spherical type fused silica as filler were used in order to study the moisture absorption properties of these epoxy molding compound (EMC) according to the change of filler size. The temperature of glass transition (Tg) of these EMC was measured using Dynamic Scanning Calorimeter (DSC), and the moisture absorption properties of these EMC according to the change of time were observed at <TEX>$85^{\circ}C$</TEX> and 85% relative humidity condition using a thermo-hygrostat. The diffusion coefficients in these EMC were calculated in terms of modified Crank equation based on Ficks' law. An increase of diffusion coefficient and maximum moisture absorption ratio with Tg in these systems without filler can be observed, which are attributed to the increase of free volume with Tg. In the EMC with filler, the changes of Tg and maximum moisture absorption ratio with the filler content can be hardly observed, however, the diffusion coefficients of these systems with filler content show the outstanding changes according to the filler size. The diffusion via free volume is dominant in the EMC with micro-sized filler; however, the diffusion with the interaction of absorption according the increase of the filler surface area is dominant in the EMC with nano-sized filler.

A High Diffusive Model for Nanomaterials.

Considerable attention is today devoted to the engineering of films widely used in photocatalytic, solar energy converters, photochemical and photoelectrochemical cells, dye-sensitized solar cells (DSSCs), to optimize electronic time response following photogeneration. However, the precise nature of transport processes in these systems has remained unresolved. To investigate such aspects of carrier dynamics, we have suggested a model for the calculation of correlation functions, expressed as the Fourier transform of the frequency-dependent complex conductivity σ(ω). Results are presented for the velocity correlation functions, the mean square deviation of position and the diffusion coefficient in systems, like TiO2 and doped Si, of large interest in present devices. Fast diffusion occurs in short time intervals of the order of few collision times. Consequences for efficiency of this fast response are discussed in relation to nanostructured devices.

Dimensional Analysis of Chronoamperometry: Proof and Verification of Cottrellian Behavior of Systems with Composition-Dependent Diffusion Coefficients

Chronoamperometry with a Dirichlet boundary condition and semi-infinite linear diffusion exhibits Cottrellian behavior, that is, the product it1/2 is constant as a function of time as long as the system is initially homogeneous, a conclusion that can be reached using only dimensional analysis; no detailed mathematical analysis is required. The generality of this result is known to include purely diffusional systems and systems in which transport also involves migration. In the present work, it is shown that Cottrellian behavior obtains, even when the system diffusion coefficients are a function of system composition, regardless of the exact form of that function. These conclusions are confirmed by simulations of examples for purely diffusional systems as well as for systems with migration. Some experimental examples from the literature are cited.

Collective diffusion in an interacting one-dimensional lattice gas: Arbitrary interactions, activation energy, and nonequilibrium diffusion

Collective diffusion is investigated within the kinetic lattice gas model for a system of interacting particles in one dimension. Analytic relations between the collective diffusion coefficient, diffusion activation energy, the attempt frequency pre-exponential factor, vs the particle density for both attractive and repulsive particleparticle interactions of an arbitrary strength are derived using the recently proposed Phys. Rev. B 70, 125431 2004 variational method. The analytic results agree with results of Monte Carlo simulations within a broad range of temperatures. At low coverages for strongly repulsive interactions the activation energy is roughly equal to its value for the noninteracting system but around = 0.5 it decreases rapidly by more than strictly accounted for by adparticle-adparticle interactions. Only at significantly higher coverages it increases reaching the expected limiting value. Peaks in the coverage dependence of the effective attempt frequency for both the repulsive and the attractive interactions are interpreted to reflect peaks in the total number of microscopic configurations accessible to the system at a given coverage and temperature. It is argued that the method used in this work allows for making meaningful estimates of the diffusion coefficient for systems far from thermal equilibrium.

Electrochemical modeling of intercalation processes with phase field models

In this paper, we apply phase field models to move beyond Fick’s law in describing Li diffusion in secondary battery electrodes. Phase field models are potentially more accurate and allow simpler tracking of phase boundaries than Fick’s equation. The phase field models are implemented using the highly accurate but fast Chebyshev-spectral method. Using the phase field we investigate to what extent non-Fickian behavior can affect results from experimental techniques for measuring diffusion coefficients, such as Galvanostatic Intermittent Titration Technique (GITT) and Potentiostatic Intermittent Titration Technique (PITT). We show that GITT and PITT can still accurately measure the diffusion coefficient in systems described by phase field models even when significant gradient energy terms are present.

Combining PGSE NMR with Homonuclear Dipolar Decoupling

A new robust approach for combining multiple-pulse homonuclear decoupling and PGSE NMR is introduced for accurately measuring molecular diffusion coefficients in systems with nonvanishing static homonuclear dipolar couplings. Homonuclear decoupling suppresses dipolar dephasing during the gradient pulses but its efficiency and scaling factor for the effective gradient vary across the sample because of the large variation of the frequency offset caused by the gradient. The resulting artifacts are reduced by introducing a slice selection scheme. The method is demonstrated by (19)F PGSE NMR experiments in a lyotropic liquid crystal.

13C PGSE NMR Experiment with Heteronuclear Dipolar Decoupling to Measure Diffusion in Liquid Crystals and Solids

A new PGSE NMR experiment, designed to measure molecular diffusion coefficients in systems with nonvanishing static dipolar coupling, is described. The fast static dipolar dephasing of the single-quantum 13C coherences is removed by multiple-pulse heteronuclear decoupling. The resulting slow dephasing of the 13C coherences allows for inserting appropriate gradient pulses into the pulse sequence. The presence of the large magnetic field gradient reduces the efficiency of the decoupling sequences which is compensated for by introducing a scheme of sequential slice selection across the sample. The method is demonstrated by 19F-decoupled 13C PGSE NMR experiments in a lyotropic nematic and lamellar liquid crystal.

High-temperature wall-tube cell Design, characterization and results of mass transport phenomena

A high-temperature wall-tube electrode cell (WTE) for electrochemical studies in hydrothermal systems is described. The cell contains a jet impinging on a wall (electrode) where the hydrodynamics in the stagnation region is well defined and the WTE has uniform accessibility and is equivalent to a rotating disc electrode (RDE). The construction and testing of the high-temperature WTE is described and its performance tested using different redox couples such as hexacyanoferrate(II/III) and quinone/hydroquinone. Diffusion coefficients of iron(II)/iron(III) are reported at temperatures up to 142 °C in sulfate solutions and are analysed taking into account the speciation in the solution. The application of the Stokes–Einstein equation to describe the temperature dependence of the diffusion coefficients in systems with strong ionic association is discussed for iron(II)/iron(III) and other species.

Determination of diffusion coefficients in volume-changing systems—Application in the case of potato drying

This work was based on a modified Crank approach in order to determine the diffusion coefficient in systems where volume changes occur during dyring. The modified model was applied to the case of potato drying, for both raw and blanched potatoes, at two temperatures: 60 and 80°C. The degree of volume change (shrinkage) was different for raw and blanched potatoes, but only small differences have been observed for the diffusion coefficient of reference, which was evaluated at 2·25 (± 0·13) × 10 −10 m 2/s for raw potatoes and 2·48 (± 0·28) × 10 −10 m 2/s for blanched potatoes.