Determination Of Diffusion Coefficients Research Articles

Determination of diffusion coefficients in agarose and polyacrylamide gels for 112 organic chemicals for passive sampling by organic Diffusive Gradients in Thin films (o-DGT).

The diffusive gradient in thin film technique was recently adapted to organic compounds. The diffusional coefficient (D) is a key parameter needed to calculate the time-weighted average concentration. In this study, two methods are used for D measurement in two gels (agarose and polyacrylamide): the diffusion cell method (Dcell) and the slice stacking method (Dstack). Thus, D were discussed and compared for 112 organic compounds, including pesticides, hormones, and pharmaceuticals. Dstack tends to be higher than Dcell. It could be explained by the presence of a non-negligible diffusive boundary layer thickness in diffusion cell. Consequently, the use of sampling rates (RS) should be more adequate to determine water concentration, for a given bulk flow velocity. Dstack also corresponds to the diffusion in gel only, allowing the determination of the maximal RS, and would be considered as a reference value that can be adjusted to in situ conditions, by applying the appropriate DBL thickness. The range and variability of D values found in the literature and obtained in this work were discussed. Relationships between D and compound physicochemical properties (molecular mass, log Dow, polar surface area, van der Waals volume) were investigated. We did not find clear and robust correlation between D and any single physicochemical property, for the set of compounds tested.

Hydrogen Diffusivity in Different Microstructures of 42CrMo4 Steel

It is well known that the presence of hydrogen decreases the mechanical properties of ferritic steels, giving rise to the phenomenon known as hydrogen embrittlement (HE). The sensitivity to HE increases with the strength of the steel due to the increase of its microstructural defects (hydrogen traps), which eventually increase hydrogen solubility and decrease hydrogen diffusivity in the steel. The aim of this work is to study hydrogen diffusivity in a 42CrMo4 steel submitted to different heat treatments—annealing, normalizing and quench and tempering—to obtain different microstructures, with a broad range of hardness levels. Electrochemical hydrogen permeation tests were performed in a modified Devanathan and Stachursky double-cell. The build-up transient methodology allowed the determination of the apparent hydrogen diffusion coefficient, Dapp, and assessment of its evolution during the progressive filling of the microstructural hydrogen traps. Consequently, the lattice hydrogen diffusion coefficient, DL, was determined. Optical and scanning electron microscopy (SEM) were employed to examine the steel microstructures in order to understand their interaction with hydrogen atoms. In general, the results show that the permeation parameters are strongly related to the steel hardness, being less affected by the type of microstructure.

Carbon dioxide adsorption and interaction with formation fluids of Jordanian unconventional reservoirs

Shales are mostly unexploited energy resources. However, the extraction and production of their hydrocarbons require innovative methods. Applications involving carbon dioxide in shales could combine its potential use in oil recovery with its storage in view of its impact on global climate. The success of these approaches highly depends on various mechanisms taking place in the rock pores simultaneously. In this work, properties governing these mechanisms are presented at technically relevant conditions. The pendant and sessile drop methods are utilized to measure interfacial tension and wettability, respectively. The gravimetric method is used to quantify CO2 adsorption capacity of shale and gas adsorption kinetics is evaluated to determine diffusion coefficients. It is found that interfacial properties are strongly affected by the operating pressure. The oil-CO2 interfacial tension shows a decrease from approx. 21 mN/m at 0.1 MPa to around 3 mN/m at 20 MPa. A similar trend is observed in brine-CO2 systems. The diffusion coefficient is observed to slightly increase with pressure at supercritical conditions. Finally, the contact angle is found to be directly related to the gas adsorption at the rock surface: Up to 3.8 wt% of CO2 is adsorbed on the shale surface at 20 MPa and 60 °C where a maximum in contact angle is also found. To the best of the author’s knowledge, the affinity of calcite-rich surfaces toward CO2 adsorption is linked experimentally to the wetting behavior for the first time. The results are discussed in terms of CO2 storage scenarios occurring optimally at 20 MPa.

Effect of Osmotic Pretreatment Combined with Vacuum Impregnation or High Pressure on the Water Diffusion Coefficients of Convection Drying: Case Study on Apples.

The paper presents water diffusion coefficients as providing a significant contribution to the creation of a comprehensive database and knowledge of weight variation during the drying process of raw plant materials that is used for modelling the technological process and designing innovative products. Dehydration is one of the most widely used methods for improving the stability and durability of fruit and vegetables because it reduces water activity and microbial activity, and minimises the physical and chemical changes during storage. The considerable impact of pressure on heat exchange and weight during the convection drying process of osmotically pretreated apples is demonstrated. The course of the drying curves and the drying rate is determined by the use of pressures of 0.02 and 500 MPa. Varied pressure applied during osmotic impregnation significantly influences the value of the diffusion coefficient: the average determined for the entire course of the drying curve and the average determined in the intervals of the reduced water content. The lowest values of the average water diffusion coefficient are obtained for apples preboiled under overpressure conditions and, at the same time, the determined diffusion coefficients in the water content are characterised on the drying curve by a clearly decreasing course until the reduced water content reaches approximately 0.2.

Insights from molecular dynamics on CO2 diffusion coefficient in saline water over a wide range of temperatures, pressures, and salinity: CO2 geological storage implications

Successful design and execution of CO2 sequestration in saline aquifers requires a comprehensive understanding of CO2 transport properties. CO2 diffusion coefficient affects CO2 dissolution behavior in water/brine and controls phenomena such as shape of viscous fingers and onset of instabilities. Experimental determination of CO2 diffusion coefficient is a technically and economically challenging task. In this research work, we used Molecular Dynamics (MD) simulation to compute CO2 diffusion coefficient in various NaCl saline water concentrations (1–6 mol NaCl/kg water) under a broad range of temperatures (294–423 K) and pressures (10–30 MPa) to acquire a data set for CO2 diffusion coefficient in different conditions. According to the results, NaCl concentration increase gives rise to a decrease in CO2 diffusion coefficient by 15%, 29%, 49%, and 64% at 1 M, 2 M, 4 M, and 6 M solutions, respectively, compared to pure water. Presence of more cations due to salinity increase forms further hydration shells act as a barrier for CO2 diffusion. In addition, the rise in CO2 diffusion at elevated temperatures can be explained by the cation's hydration shell size reduction with temperature increment due to intensifying repulsive forces among water molecules. We proposed a new precise correlation for estimation of CO2 diffusion coefficients over temperatures and salinity ranges of this study. Regarding the pressure variation effects, no tangible changes were observed with pressure increase, validating a negligible influence on diffusion coefficient. Furthermore, the CO2 diffusion coefficient variability in presence of other salts, namely MgCl2, CaCl2, KCl, and Na2SO4, were computed separately. Comparing the influence of various salts, CaCl2 and KCl have the highest and lowest effect on the CO2 diffusion coefficient, respectively. Finally, a set of direct numerical simulations were conducted to study the impact of CO2 diffusion coefficient on CO2 dissolution process. The results obtained from this research work shed light on the importance of CO2 diffusion coefficient changes in saline water for prediction of dissolution process behavior.

Intercomparison of determining diffusion coefficients of I− in compacted bentonite using various mathematical models of through-diffusion experiments in the laboratory

Intercomparison of determining diffusion coefficients of I− in compacted bentonite using various mathematical models of through-diffusion experiments in the laboratory

Quantitative theory for the diffusive dynamics of liquid condensates.

Key processes of biological condensates are diffusion and material exchange with their environment. Experimentally, diffusive dynamics are typically probed via fluorescent labels. However, to date, a physics-based, quantitative framework for the dynamics of labeled condensate components is lacking. Here, we derive the corresponding dynamic equations, building on the physics of phase separation, and quantitatively validate the related framework via experiments. We show that by using our framework, we can precisely determine diffusion coefficients inside liquid condensates via a spatio-temporal analysis of fluorescence recovery after photobleaching (FRAP) experiments. We showcase the accuracy and precision of our approach by considering space- and time-resolved data of protein condensates and two different polyelectrolyte-coacervate systems. Interestingly, our theory can also be used to determine a relationship between the diffusion coefficient in the dilute phase and the partition coefficient, without relying on fluorescence measurements in the dilute phase. This enables us to investigate the effect of salt addition on partitioning and bypasses recently described quenching artifacts in the dense phase. Our approach opens new avenues for theoretically describing molecule dynamics in condensates, measuring concentrations based on the dynamics of fluorescence intensities, and quantifying rates of biochemical reactions in liquid condensates.

Homogenization of Continuum-Scale Transport Properties from Molecular Dynamics Simulations: An Application to Aqueous-Phase Methane Diffusion in Silicate Channels.

Silica-based materials including zeolites are commonly used for wide-ranging applications including separations and catalysis. Substrate transport rates in these materials can significantly influence the efficiency of such applications. Two factors that contribute to transport rates include (1) the porosity of the silicate matrix and (2) nonbonding interactions between the diffusing species and the silicate surface. These contributions generally emerge from disparate length scales, namely, "microscopic" (roughly nanometer-scale) and "macroscopic" (roughly micron-scale), respectively. Here, we develop a simulation framework to estimate the simultaneous impact of these factors on methane mass transport in silicate channels. Specifically, we develop a model of methane transport using homogenization theory to obtain transport parameters valid at length scales of hundreds to thousands of nanometers. These parameters implicitly reflect interactions taking place at fractions of a nanometer. The inputs to the homogenization analysis are data from extensive molecular dynamics simulations that incorporate atomistic-scale interactions, processed to yield local diffusion coefficients and mean force potentials. With this model, we demonstrate how nuances in silicate hydration and silica/methane interactions impact methane diffusion rates in silicate materials, including the effects of silicate surface chemistry such as the presence of silanol groups. The molecular dynamics simulations indicate that methane diffusivity at the silica surface is lower than the bulk-like rates observed at the center of channels of sufficient width. However, potentials of mean force generally evidence attractive methane/silica interactions that enhance diffusion overall. By simultaneously accounting for both of these effects, we show that the effective diffusion coefficient for the nanoporous silicate can be approximately double the value of estimates assuming fully bulk-like behavior in the channel. This study therefore demonstrates the importance of determining diffusion coefficients and potentials of mean force at an atomistic level when estimating transport properties in bulk materials. Importantly, we provide a simple homogenization framework to incorporate these molecular-scale attributes into bulk material transport estimates. This hybrid homogenization/molecular dynamics approach will be of general use for describing small-molecule transport in materials with detailed molecular interactions.

Influence of non-linear chloride binding on the determination of apparent chloride diffusion coefficient for cement paste with mineral additives

The determination of apparent chloride diffusion coefficients (Da) in standard codes employs the linear chloride binding assumption. However, this assumption is too simplified as chloride binding is actually non-linear. This paper intends to investigate the influence of non-linear chloride binding on the determination of Da values in the bulk diffusion test. To achieve this aim, a semi-analytical method for the semi-infinite diffusion problem was firstly established. This method can be used in data fitting to obtain the Da values considering non-linear chloride binding. Then, bulk diffusion test and mercury intrusion porosimetry were conducted on four different cement pastes with fly ash and blast furnace slag. Based on chloride profiles, the chloride binding isotherms were obtained through data fitting. Meanwhile, the Da values considering the linear and non-linear chloride binding assumption were calculated respectively and compared. The results show that the chloride binding isotherms in the bulk diffusion test fit well with the Freundlich isotherm but are not so non-linear as expected. The proposed method can calculate the effective diffusion coefficient which cannot be obtained in standard codes. Da values will vary along the chloride ion diffusion direction rather than be a constant once the non-linear chloride binding is considered. The comparison between different cement paste mixtures indicates that both the apparent diffusion coefficient calculated from free chloride profiles or total chloride profiles can only be regarded as a qualitative description of resistance to chloride diffusion for a certain mixture. The comparison between different mixtures based on these values is not reliable.

Interactions between PAMAM-NH2 and 6-Mercaptopurine: Qualitative and Quantitative NMR studies.

Despite being used as an anti-leukemic drug, the poor solubility of 6-mercaptopurine (6-MP) limits its use in topical and parenteral applications. Dendrimers are commonly used as drug carriers to improve their solubility in aqueous solution. In this work, the interactions between 6-MP and the amine-terminated poly(amidoamine) dendrimers (PAMAM-NH2 ) were investigated by various NMR technology. The chemical shift titrations disclosed that the 6-MP interacted with the surface of PAMAM-NH2 mainly through electrostatics. The determination of diffusion coefficient and relaxation measurements further confirmed the presence of interactions in 6-MP/PAMAM-NH2 complexes. In addition, the encapsulation of 6-MP within the cavity of PAMAM-NH2 was revealed through nuclear Overhauser effect spectroscopy and Saturation Transfer Double Difference analysis. Finally, the binding strength (H-8 is 100% and H-2 is 70%) of 6-MP to PAMAM-NH2 was quantitatively expressed using epitope maps. This study provides a systematic methodology for qualitative and quantitative studies of the interactions between dendrimers and drug molecules in general.

Determining diffusion coefficients of coal particles by solving the inverse problem based on the data of methane desorption measurements

The diffusion coefficient is the key parameter been used to evaluate the methane diffusion behavior. Generally, the diffusion coefficient is determined by analytical solutions, including the unipore diffusion model and the bidisperse diffusion model. However, the essential assumptions limit the applicability and accuracy of analytical solutions. Inverse modeling has been proved to be useful in a variety of disparate fields. In this work, the detailed process and principles of using inverse modeling in gas diffusion are introduced. The effectiveness and accuracy of MMA, SNOPT and LM algorithms in determining the diffusion coefficient are analyzed. Results show that the inverse problem is a feasible method and the LM algorithm takes the shortest time and is recommended. The analytical solution (diffusion coefficient) of particles whose sizes are 0.074–0.2 mm, 0.25–0.5 mm and 0.5–1 mm are 13.8% times, 5.0% times and 1.6% times larger than that of the numerical solution, respectively. The numerical method has higher computing accuracy of small coal particles. As the current work is the first to present efficient techniques for the solution of diffusion coefficient-related inverse problems in COMSOL, the applicability of inverse modeling in complicated gas diffusion problems has also been prospected.

Ion dynamics in fluoride-containing polyatomic anion cathodes by muon spectroscopy

Polyatomic anion insertion electrodes present compositional and morphological variety, as well as the ability to tune operational voltages by influencing the nature of metal-oxygen bonding. Realizing the application of these compounds as electrodes in Li- and Na-ion batteries requires a detailed understanding of ion dynamics in these systems. Here is presented the microscopic Li-ion and Na-ion diffusion properties in LiFeSO4F and Na2FePO4F, respectively, using muon spin relaxation (μ +SR) spectroscopy for the first time. Li-ion diffusion processes in the tavorite LiFeSO4F phase are found to proceed with an activation energy (E a) of 48(4) meV and a diffusion coefficient of 1.71 × 10−9 cm2 s−1, while Na-ion mobility in Na2FePO4F has a calculated diffusion coefficient of 3.47 × 10−10cm2 s−1 and a higher energy barrier to ion diffusion at 96(8) meV. This is the first such examination of fluoride-containing polyatomic cathodes using μ +SR, where the presence of the highly electronegative fluoride species was thought to preclude activation energy and diffusion coefficient determination due to strong μ +-F− interactions. These insights open up the possibility of studying a myriad of fluoride-containing electrode materials using the μ +SR technique.

A novel model for determination of apparent diffusion coefficient of gaseous solvent mixture-heavy oil system with consideration of swelling effect and density variation

A reliable estimation of the apparent diffusion coefficient (D) of gaseous solvent mixtures (GSMs) in heavy oil (HO) is necessary for the design of GSM-based recovery techniques. In this study, diffusion measurements of GSM-HO systems were carried out at various temperatures (25°C to 54.2°C) and pressures (5 to 10 MPa). Then, a novel mathematical model was proposed to describe the diffusion process of GSMs in HO considering the oil swelling effect and density variation. The oil swelling effect was described with a newly developed density model of GSM-HO systems. Finally, the developed model was solved via a numerical method to determine the D of GSMs in HO and the dynamic processes of HO swelling under varied temperature and pressure conditions. The results indicated that the D values at the measured temperatures and pressures ranged from 3.81-22.62×10−10 m2•s−1. The average D value of the GSMs increased with temperature and pressure. The GSM concentration in HO, the height of the GSM-HO interface, and the swelling velocity of HO rapidly increased at the early stage and then slowly increased over time. The maximum GSM concentration was observed at the GSM-HO interface.

Numerical modeling of the diffusional transport of nitrogen in multi-phase solid titanium and its application to determine diffusion coefficients

As part of a program to understand the dissolution of nitrogen-rich titanium solids in liquid titanium, this manuscript presents a numerical study of nitrogen transport in titanium at elevated temperatures. A Landau transformation was applied to the equations governing mass transport which were used as the basis for the numerical model. The numerical model was used initially to simulate nitrogen transport in a planar geometry and the predicted nitrogen concentration profiles and displacement of Ti–N phase boundaries showed good agreement with analytically derived solutions. The numerical model was then used to simulate nitrogen transport in commercially pure titanium cylinders. The model results were shown to be sensitive to the diffusion coefficients of Ti–N phases present in the system. Based on the sensitivity analysis, diffusion coefficients at 1650 °C of 4.3 × 10 − 11 m 2 s − 1 , 1.6 × 10 − 11 m 2 s − 1 and 1.7 × 10 − 12 m 2 s − 1 for β-Ti, α-Ti and TiN phases, respectively, were back calculated using the model. The model predictions, using the new diffusion coefficients, showed good agreement with previously published data in terms of both the nitrogen concentration profiles and displacements of Ti–N phase boundaries under the conditions examined in the study. The comparison indicates the presented model is capable of accurately approximating the transport of nitrogen in titanium at elevated temperatures.

Development of optical digital interferometry for visualizing and modelling the mass diffusion of ammonia in water in an absorption process

This study reports the development and implementation of Optical Digital Interferometry for visualizing and modelling mass diffusion in the absorption process of ammonia in water. Absorption experiments were performed at infinite dilution of ammonia and at 293 K, 303 K, and 313 K. The method developed makes it possible to visualize the development of the mass diffusion layer and determine the evolution of concentration profiles in the ammonia/water mixture, providing new spatio-temporal data on the absorption process. A non-equilibrium model based on Fick’s Second Law was used to describe the mass diffusion process. It was found that the model can successfully reproduce the experimental profiles of the ammonia concentration. The method developed also allows the simultaneous determination of mass diffusivity and mass transfer coefficients from a single experimental test. The values obtained for the mass diffusivity of ammonia in water vary from 1.54 × 10-9 m2 s−1 at 293.1 K to 2.50 × 10-9 m2 s−1 at 313.1 K. The relative deviations between the experimental mass diffusivity and literature values did not exceed 6.0%. The mass transfer coefficient ranges from 2.12 × 10-5 m s−1 at 293.1 K to 4.19 × 10-5 m s−1 at 313.1 K. The results show the potential of Optical Digital Interferometry for the development and validation of heat and mass transfer models used to design components in absorption refrigeration systems.

Modification and Patterning of Self‐Assembled Monolayers Using Electrogenerated Etchants and Homogeneous Scavenging Reactions in a Scanning Electrochemical Microscope

AbstractSelf‐assembled monolayers (SAMs) of oligoethylene glycol (OEG)‐terminated alkanethiolates on gold, which are used to control protein adsorption and cell adhesion, were patterned by reaction with Br2/HOBr electrogenerated at a microelectrode of a scanning electrochemical microscope (SECM). The spreading of the Br2 diffusion layers was limited by a homogeneous reaction with cystamine or L‐cystine as scavengers. The influence of process parameters on the patterning process was explored by simulation and combinatorial experiments. The experimental determination of pattern sizes from SECM feedback images was verified by scanning force microscopy. The simulation considered the local Br2 formation as well as Br2 consumption in the reaction with the OEG SAM, by reduction at the gold substrate, and by the homogeneous scavenging reaction. It used experimentally determined diffusion coefficients and rate constants of the scavenging reaction. and Experiments and simulation confirmed the existence of regions in the parameter space, in which the patterning process is robust against small variation of the parameters working distance, pulse time and scavenger excess.

Evaluation of canonical choline chloride based deep eutectic solvents as dye-sensitized solar cell electrolytes.

Deep eutectic solvents (DESs) are beginning to attract interest as electrolyte alternatives to conventional organic solvents and ionic liquids within dye-sensitized solar cells (DSSCs). The precise roles played by DES components and whether they simply represent a benign medium for mobilizing charge carriers or present beneficial functionality that impacts device performance remain unclear. To begin to address this deficiency in understanding, we performed a comprehensive characterization of the three "canonical" choline chloride-based DESs (i.e., reline, ethaline, and glyceline) as DSSC electrolytes hosting the iodide-triiodide (I-/I3 -) redox couple. The measurement of electrolyte viscosities, determination of triiodide diffusion coefficients, and photovoltaic performances assessed for water contents up to 40 wt. % allow the emergence of several important insights. A comparison to the observed photovoltaic performance arising from the individual components aids in further clarifying the impact of DES chemistry and solution viscosity on photovoltaic and charge carrier diffusion characteristics. Finally, we introduce the DES guaniline-consisting of a 1:1 molar ratio mixture of choline chloride with guanidinium thiocyanate-demonstrating it to be a superior DSSC electrolyte over those formulated from the three most widely studied canonical DESs at all water contents investigated.

Determination of Optimal Diffusion Coefficients in Lake Zirahuén through a Local Inverse Problem

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated by an ellipse, finding the optimal major and minor axes. The inverse problem was implemented by comparing these observational data with the concentration obtained numerically from the 2D advection–diffusion equation, varying the diffusion tensor. When the tensor was isotropic, values of K11=K22≈0.003 m2/s were found; when nonequal coefficients were considered, it was found that K11≈0.005 m2/s and K22≈0.002 m2/s, and the cross-term K12 influenced the results of the orientation of the ellipse. It is important to mention that, with this simple technique, the parameter estimation had consequences of great importance as the value for the diffusion coefficient was bounded significantly under particular conditions for this site of study.

Numerical Simulations of Gas Sorption Experiments in Polymers: Influence of Aspect Ratio and Pressure Increase Rate on the Determination of Diffusion Coefficient

AbstractDiffusion and sorption phenomena of gases in polymers are of relevance for a number of technological applications, e.g., polymer foaming and membrane technology. The diffusion coefficient and the solubility, which depend on temperature and applied gas pressure, can be determined using the buoyancy method. In this work, the influence of two important parameters are investigated, i.e., the dimensions of the polymer sample and the pressure increase rate, on the accuracy of the determination of the diffusion coefficient D using gas sorption measurements. Numerical simulations on effectively two‐dimensional diffusion phenomena in polymers are performed in order to obtain “ideal” experimental data. This set of “ideal” experimental data for polymer samples with specified geometrical dimensions is used for determination of the diffusion coefficient based on the analytical solution of Fickian diffusion in one spatial dimension. Different fitting procedures for determination of the diffusion coefficient are compared. Because of the finite time, which is necessary for pressure increase in a sorption experiment, the influence of pressure increase rate is also studied. This analysis reveals that an aspect ratio larger than 32 and a time for pressure increase smaller than approximately 3 × 10−9 m2D−1 is necessary for a reliable determination of diffusion coefficient D.

Diffusion of strontium implanted in glassy carbon

Glassy carbon has properties making it attractive as a containment material for radioactive waste. In this study, the diffusivity of the radiological important fission product, strontium, is measured. Two hundred kiloelectronvolt strontium ions were implanted at room temperature. The implanted samples were either annealed isochronally for 1 h up to 900°C or by increasing the temperature linearly up to 648°C. The Sr profiles were determined by Rutherford backscattering spectrometry (RBS). The isochronally annealed samples showed Fickian diffusion at 300°C ( D = 6.7 × 10 −19 m 2 s −1 ) with segregation occurring at the higher temperatures. Raman spectroscopy indicated a link between damage annealing and the onset of segregation. During increasing temperature, the system is dynamic with diffusion taking place. An equation to determine diffusion coefficients for ramped heating was derived. Fickian diffusion occurred with an activation energy of 1.97 eV for 414–454°C, and from 458 to 558°C, it was 0.184 eV. At higher temperatures, a segregation of the strontium towards the surface was observed. A calculation of the heat of segregation of Sr in carbon supports this segregation. The results show that the in situ RBS measurements with a linear increase in temperature give additional information compared with the conventional isochronal annealing.