Limiting Diffusion Coefficients Research Articles

Experimental Study on Methane Diffusion Characteristics of Different Metamorphic Deformed Coals Based on the Counter Diffusion Method

The diffusion coefficient (D) is a key parameter that characterizes the gas transport occurring in coal seams. Typically, D is calculated using the desorption curve of particle coal. However, this method cannot accurately reflect the diffusion characteristics under the stress constraint conditions of in situ coal seams. In this study, different metamorphic deformed coals of medium and high coal rank were considered based on Fick’s law of counter diffusion. The change laws of D under different confining pressures, gas pressures, and temperature conditions were tested and analyzed, and the influencing mechanisms on D are discussed. The results showed that D of different metamorphic deformed coals exponentially decreased with an increase in confining pressures, and exponentially increased with increases in gas pressures and temperature. There is a limit diffusion coefficient. The influence of the confining pressure on D can essentially be determined by changes in the effective stress, and D negatively affects the effective stress, similar to permeability. The effect of gas pressure on D involves two mechanisms: mechanical and adsorption effects, which are jointly restricted by the effective stress and the shrinkage and expansion deformation of coal particles. Temperature mainly affects D by changing the root-mean-square speed and average free path of the gas molecules. Under the same temperature and pressure conditions, D first increased and then decreased with an increase in the degree of deformation. D of the fragmented coal was the largest. Under similar deformation conditions, D of the high-rank anthracite was larger than that of the medium-rank fat coal. Porosity is a key factor affecting the change in D in different metamorphic deformed coals.

Interactions between Sodium Hyaluronate and β-Cyclodextrin as Seen by Transport Properties.

Knowledge of mass transport parameters, diffusion, and viscosity of hyaluronic acid (HA) in the presence of cyclodextrins is of considerable importance for areas such as food packaging and drug delivery, among others. Despite a number of studies investigating the functionalization of HA or the corresponding sodium salt by cyclodextrins, only a few studies have reported the effect of cyclodextrins on the mass transport of HA in the presence of these oligosaccharides. Here, we report the tracer binary and ternary interdiffusion coefficients of sodium hyaluronate (NaHy) in water and aqueous β-cyclodextrin solutions. The diffusion behavior of sodium hyaluronate was dependent on the reduced viscosity of NaHy, which, in turn, presented a concave dependence on concentration, with a minimum at approximately 2.5 g dm-3. The significant decrease in the limiting diffusion coefficient of NaHy (at most 45%) at NaHy concentrations below 1 g dm-3 in the presence of β-cyclodextrin, taking water as the reference, allowed us to conclude that NaHy strongly interacted with the cyclodextrin.

Lateral diffusion in the presence of obstacles, reexamined.

In transient anomalous subdiffusion, diffusion is anomalous at short times, crossing over to normal at long times. This behavior is well-known for obstructed diffusion with obstacle concentrations below the percolation threshold, and is characterized by the anomalous exponent alpha, the limiting diffusion coefficient D(inf), and the crossover time t(cross), all functions of the obstacle concentration. In my work [Biophys J 66 (1994) 394], the anomalous and normal regions are chosen by eye in a log-log plot of D(t) = RSQ/t versus time t. Straight lines are found for each region by a least-squares fit, and t(cross) is defined as the intersection of these lines. Ellery et al. [J Chem Phys 144 (2016) 171104] criticized this approach and presented a method based on eigenvalues of the transition matrix. Their crossover times were significantly different from mine, and Ellery et al. claimed that their method provides a simpler and more objective evaluation of t(cross). I examine an alternative interpretation, that their method is an elegant measurement of a different characteristic time of the random walk. To test this, I compare results of the eigenvalue method with results of standard Monte Carlo calculations for various characteristic times, including distinct sites visited as a function of time, the number of visits per site (yielding the cover time and the blanket time), and the first passage time from the center of the lattice to the boundary of the region without periodic boundary conditions. The calculations are done for random walks on a square lattice with random obstacles and periodic boundary conditions. Importantly, I examine the dependence of the results on system size, and include percolation analysis so that higher obstacle concentrations can be included in some calculations. The so-called lazy random walk algorithm is also examined.

Abraham Solvation Parameter Model: Calculation of L Solute Descriptors for Large C11 to C42 Methylated Alkanes from Measured Gas–Liquid Chromatographic Retention Data

Abraham model L solute descriptors have been determined for 149 additional C11 to C42 monomethylated and polymethylated alkanes based on published Kovat’s retention indices based upon gas–liquid chromatographic measurements. The calculated solute descriptors, in combination with previously published Abraham model correlations, can be used to predict a number of very important chemical and thermodynamic properties including partition coefficients, molar solubility ratios, gas–liquid chromatographic and HPLC retention data, infinite dilution activity coefficients, molar enthalpies of solvation, standard molar vaporization and sublimation at 298 K, vapor pressures, and limiting diffusion coefficients. The predictive computations are illustrated by estimating both the standard molar enthalpies of sublimation and the enthalpies of solvation in benzene for the monomethylated and polymethylated alkanes considered in the current study.

On the transport and dynamics of disaccharides: H-bonding effect in sucrose and sucralose

Sucrose and sucralose are ubiquitous in foods and, as a consequence, they play a relevant role in our diet, with a significant impact on health. Due to their chemical similarities, these disaccharides are also relevant by fundamental issues, including the dynamic and structure in aqueous solutions. Despite their relevance for food industry, information about the effect of salts on the diffusion of both sucralose and sucrose is scarce. Moreover, studies aiming to explain how the substitution of hydrogens (in sucrose) by chlorines (in sucralose) affects the dynamics and the hydration of these compounds are missing in the literature. By using diffusion measurements and molecular dynamic (MD) simulations, we contribute to a better understanding of the H-bonds between the disaccharides and water molecules and, thus, of their solubility differences and sweetness perception. The effect of sodium chloride, and therefore of the ionic strength, on the dynamics and diffusion of both disaccharides was also evaluated.The limiting diffusion coefficient of sucralose is higher than that found for sucrose, thus indicating a lower hydration shell of the former, as well as a less affinity towards water molecules. In the presence of NaCl, the coupled diffusion shows that the interaction between the electrolyte and sucrose is stronger, highlighting the role of hydroxyl groups on the interaction with sodium ion, as it is confirmed by MD simulations.

Run-and-Tumble Motion: The Role of Reversibility

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

Coupled mutual diffusion in aqueous (ammonium monovanadate + butyl-substituted sulfonated resorcinarene) solutions: An experimental and theoretical approach

Binary mutual diffusion coefficients (D) of aqueous solutions of the macrocyclic salt tetrasodium 5,11,17,23-tetrakissulfonatemethylen-2,8,14,20-tetra(butyl)resorcin[4]arene (Na4BRA) have been measured at 298.15 K by the Taylor dispersion method. The limiting diffusion coefficient of Na4BRA obtained by extrapolation of the data is used to evaluate the limiting conductivity and hydrodynamic radius of the BRA4− ion. The change in the hydrodynamic radius of sulfonated resorcinarenes with increasing the length of alkyl substituents is analysed. In the second part of this work, the effect of ammonium monovanadate on the diffusion of aqueous Na4BRA was investigated by measuring apparent ternary mutual diffusion coefficients for aqueous NH4VO3(1) + Na4BRA(2) solutions. In binary aqueous Na4BRA solutions (no added NH4VO3), the BRA4− ions diffuse at the same speed as the smaller and relatively mobile Na+ counterions to maintain electroneutrality. As the NH4VO3 concentration is raised, the main diffusion coefficient of NH4BRA drops to the tracer diffusion coefficients of BRA4− ions in supporting NH4VO3 solutions. Coupled diffusion of NH4VO3 and Na4BRA is significant. In particular, Na4BRA concentration gradients produce significant counter-current coupled flows of NH4VO3. Nernst equations are used to provide an electrostatic interpretation of the strongly coupled diffusion of Na4BRA and NH4VO3.

Effect of Hofmeister Ions on Transport Properties of Aqueous Solutions of Sodium Hyaluronate.

Tracer diffusion coefficients obtained from the Taylor dispersion technique at 25.0 °C were measured to study the influence of sodium, ammonium and magnesium salts at 0.01 and 0.1 mol dm−3 on the transport behavior of sodium hyaluronate (NaHy, 0.1%). The selection of these salts was based on their position in Hofmeister series, which describe the specific influence of different ions (cations and anions) on some physicochemical properties of a system that can be interpreted as a salting-in or salting-out effect. In our case, in general, an increase in the ionic strength (i.e., concentrations at 0.01 mol dm−3) led to a significant decrease in the limiting diffusion coefficient of the NaHy 0.1%, indicating, in those circumstances, the presence of salting-in effects. However, the opposite effect (salting-out) was verified with the increase in concentration of some salts, mainly for NH4SCN at 0.1 mol dm−3. In this particular salt, the cation is weakly hydrated and, consequently, its presence does not favor interactions between NaHy and water molecules, promoting, in those circumstances, less resistance to the movement of NaHy and thus to the increase of its diffusion (19%). These data, complemented by viscosity measurements, permit us to have a better understanding about the effect of these salts on the transport behaviour of NaHy.

Fast Determination of the Limiting Ionic Diffusion Coefficient in Lithium Metal Polymer Batteries

The energy conversion and its storage is a tremendous challenge for our society. Despite the great progress of the Lithium (Li)-ion technology based on flammable liquid electrolyte, their intrinsic instability is a strong safety issue for large-scale applications. The use of solid polymer electrolytes (SPEs) is an adequate solution in terms of safety and energy density thanks to their stability towards Li metal.[1] Moreover, as for conventional liquid electrolyte, the cationic transference number of poly(ethylene oxide) based SPE is typically below 0.2 which limits their power performance due to the formation of concentration gradient throughout the electrodes.[2] In such Li metal battery, the SPE acts as both separator and functionalized cathode binder ensuring ionic transport all over the battery. To increase the battery energy density a simple way is to use thicker cathode. Indeed, for a given electrode formulation, the energy density is directly linked to the active material loading.[3]The goal of this study is to propose a quick and efficient methodology to optimize the thickness of the SPE and of the cathode based on charge transport parameters, which allows to determine the effective limiting Li+ diffusion coefficient. Revisiting a protocol by Doyle et al.[4] the battery power performance is rapidly established, at least 8 time faster than conventional cycling (charge-discharge steps) with a similar accuracy as depicted in Figure 1.[5] Then, by using an approach based on the Sand equation a limiting current density is determined. A unique mother curve of the capacity as a function of the limiting current density is obtained whatever the electrode and electrolyte thicknesses. Finally, the effective limiting diffusion coefficient is estimated which in turn allows to design the best electrode depending on electrolyte thickness.

Effect of Electrode and Electrolyte Thicknesses on All-Solid-State Battery Performance Analyzed With the Sand Equation

The energy conversion and storage are great challenges for our society. Despite the progress accomplished by the Lithium(Li)-ion technology based on flammable liquid electrolyte, their intrinsic instability is the strong safety issue for large scale applications. The use of solid polymer electrolytes (SPEs) is an adequate solution in terms of safety and energy density. To increase the energy density (resp. specific energy) of the batteries, the positive electrode thickness must be augmented. However, as for Li-ion liquid electrolyte, the cationic transference number of SPEs is low, typically below 0.2, which limits their power performance because of the formation of strong gradient of concentration throughout the battery. Thus, for a given battery system a compromise between the energy density and the power has to be found in a rapid manner. The goal of this study is to propose a simple efficient methodology to optimize the thickness of the SPE and the positive electrode based on charge transport parameters, which allows to determine the effective limiting Li+ diffusion coefficient. First, we rapidly establish the battery power performance thanks to a specific discharge protocol. Then, by using an approach based on the Sand equation a limiting current density is determined. A unique mother curve of the capacity as a function of the limiting current density is obtained whatever the electrode and electrolyte thicknesses. Finally, the effective limiting diffusion coefficient is estimated which in turn allows to design the best electrode depending on electrolyte thickness.

Limiting diffusion coefficients of glufosinate ammonium, cymoxanil and imidacloprid in aqueous solutions

We have measured the limiting diffusion coefficients of three different pesticides in aqueous solutions: glufosinate ammonium, cymoxanil and imidacloprid, highly used for tomato production. The experiments were carried in aqueous solutions, at 25 °C, at concentrations below 3 mmol dm−3 (depending on the solubility of pesticides). Mutual diffusion coefficients (D) obtained by using the Taylor dispersion technique, and by using pure water and different solutions of concentration c, as carrier stream and injection solutions, respectively, show that the systems can be analyzed as binary ones. The hydrodynamic radii and the respective limiting diffusion coefficients of the glufosinate anion, cymoxanil and imidacloprid have also been estimated. For the electrolyte glufosinate ammonium, by using the Nernst equation, it is also possible to estimate the limiting molar conductivity of the glufosinate anion.In order to mimic field conditions, we have measured the tracer diffusion coefficients of glufosinate ammonium in aqueous solutions of ammonium nitrate at different concentrations, permitting us to analysis the salting-in effects on the diffusion of this pesticide.From these measurements useful information on the thermodynamic, transport and structural parameters can be obtained, allowing a better understanding of the behaviour of these compounds in aqueous solution.These studies have been complemented with 1H and 31P NMR spectroscopy in order to obtain more additional structural information on the interaction of ammonium nitrate with glufosinate-ammonium in aqueous solution. The results obtained support the hypothesis of salting-in effects on the diffusion of this pesticide in aqueous solution.

Limiting diffusion coefficients of [Formula: see text],[Formula: see text]-amino acids in water and in sodium chloride aqueous solutions at 298.15 K.

Transport properties of model compounds in aqueous solutions such as amino acids can provide valuable information in order to understand the complex interactions in aqueous solutions as well as the protein stability in water and the relevant factors involved. Informations about the diffusion of amino acids in water and in aqueous solutions of sodium chloride are very scarce, especially for the 5-aminopentanoic acid and 6-aminohexanoic acid. In this study, limiting binary mutual diffusion coefficients at 298.15 K of 5-aminopentanoic and 6-aminohexanoic acids in aqueous solutions of NaCl 0.15 mol kg-1, using the Taylor dispersion technique, were determined and the results compared with the limiting binary mutual diffusion coefficients for 2-aminopentanoic acid, and 2-aminohexanoic acid, obtained in the same experimental conditions. The discussion of the properties of the selected amino acids is centered on the positions of the ionic groups in the hydrocarbon chain and, in addition, we have discussed the effects of NaCl on their structures and properties. The data on diffusion properties are supported by 1H, 13C and 23Na NMR experiments, which we have obtained for 5-aminopentanoic and 6-aminohexanoic acids, in aqueous solution, also in the presence of NaCl.

Limiting Diffusion Coefficients for Ions and Nonelectrolytes in Solvents Water, Methanol, Ethanol, Propan-1-ol, Butan-1-ol, Octan-1-ol, Propanone and Acetonitrile at 298\xa0K, Analyzed Using Abraham Descriptors

We have used literature data on the conductivity of single ions to obtain limiting diffusion coefficients (Do) of ions in water, alcohols, propanone and acetonitrile. We then used literature data on limiting diffusion coefficients of nonelectrolytes in order to set up linear free energy relationships that combine data for ions and nonelectrolytes, as log10 (Do) in the same equation, all values being at 298 K. These equations are for solvents water (N = 377, SD = 0.0474), methanol (N = 96, SD = 0.0332), ethanol (N = 96, SD = 0.0666), propan-1-ol (N = 71, SD = 0.0487), butan-1-ol (N = 53, SD = 0.0600), octan-1-ol (N = 61, SD = 0.0684), propanone (N = 86, SD = 0.0366) and acetonitrile (N = 74, SD = 0.0438) where N is the number of data points, that is ions plus nonelectrolytes, and SD is the standard deviation in log10 (Do). It is shown that solute hydrogen bond acidity, solute hydrogen bond basicity and solute volume all lower the diffusion constants of ions and nonelectrolytes in the various solvents studied.

The structure and diffusion behaviour of the 1:1 copper(II) complex of ethambutol in aqueous solution

Ethambutol (as its dihydrochloride) is a bacteriostatic drug, which is widely used as part of the Tuberculosis treatment protocol. It can also act as a ligand for various metal ions, such as copper(II), leading to complexes with potentially interesting applications in medicinal and analytical chemistry. The structure of such complexes is relevant to the question of the coordination geometry of the copper(II) ion in aqueous solution. We report a structural study of the 1:1 complex formed between ethambutol (Emb) and copper(II), using visible absorption, multinuclear NMR (1H and 13C), and EPR spectroscopies, and density functional theory (DFT) calculations. These all support a pentacoordinate structure with a distorted square pyramidal geometry involving a central Cu(II) ion coordinated by a tetradentate Emb ligand and one water molecule. The diffusion behaviour of this complex has been studied, and is compared with that of the free ligand by measuring limiting mutual diffusion coefficients for aqueous systems at 25 °C using the Taylor dispersion method. From these results, we have estimated the tracer diffusion coefficient of ethambutol in supporting solutions of copper nitrate and the limiting diffusion coefficients of the 1:1 complex formed between ethambutol and copper ion. By using the Stokes-Einstein equation, the limiting hydrodynamic radii of this complex, Rh, have also been estimated and are compared with the free Emb.

Gravity-assisted synthesis of micro/nano-structured polypyrrole for supercapacitors

A highly electroactive polypyrrole film (GA-hPPy) with micro/nano-structured horn-like arrays is synthesized by a pulse potentiostatic method with the assistance of gravity. Compared with the conventional cauliflower-like PPy (cPPy) that is synthesized without gravity assistance, GA-hPPy exhibits horn-like morphology in good ordering and uniform size, which leads to remarkably high ionic and electronic conductivity, as confirmed by apparent diffusion coefficient and limit diffusion coefficient. It presents great specific capacitance up to 360Fg−1 at the scanning rate of 10mVs−1 and ultrafast charging/discharging capability, with a specific capacitance of 208Fg−1 at the scanning rate of 1000mVs−1. Its cycling performance is validated to be stable as 88.2% of capacitance held after 10,000 continual cycles. With these distinguishing properties, GA-hPPy is promising to be an excellent active material for supercapacitors.

Optimization of Taylor Dispersion Technique for Measurement of Mutual Diffusion in Benchmark Mixtures

The Taylor dispersion technique has been used for measuring binary mutual diffusion coefficients for mixtures of 1,2,3,4-tetrahydronaphthalene (THN), isobutylbenzene (IBB) and dodecane (C12H26) at 0.5:0.5 mass fraction symmetric points, and for 0.9:0.1 mass fraction in IBB- C12H26. From the Stokes–Einstein equation and our experimental results, the limiting diffusion coefficients, D0, and the equivalent solvated radii, Rs, have been estimated at infinitesimal concentration of these species (TNH, IBB and C12H26). The measured diffusion coefficients are used to estimate activity coefficients of the components in the mixture, contributing to a better understanding of the structure of such systems and of their thermodynamic behaviour at different concentrations. We have also investigated the diffusion properties for a ternary system containing equal mass fractions of all the components (0.33THN: 0.33IBB: 0.33C12H26) and at 298.15 K.

Limiting diffusion coefficients of sodium octanoate, and octanoic acid in aqueous solutions without and with α-cyclodextrin

The Taylor dispersion technique has been used for measuring limiting binary mutual diffusion coefficients of octanoic acid and sodium octanoate at T=298.15K (D0), respectively, using water as carrier solution, and different injections solutions from (0.75 to 100)·10−3mol⋅dm−3. These D0 values, together with the Stokes–Einstein equation, were used to determine the equivalent hydrodynamic radii, Rh, at infinitesimal concentration of these species (octanoic acid and sodium octanoate). In addition, the limiting diffusion coefficients of the molecular (D0m) and dissociated (D0±) forms of the octanoic acid were estimated.We have also investigated the diffusion properties for a system containing octanoic acid, α-cyclodextrin (α-CD) and water. From these results, we have estimated the percentages of free (C7COOH) and associated forms of octanoic acid (α-CD/C7COOH) and the equilibrium constant, K, for a supramolecular host–guest complex between octanoic acid and α-CD.

Determination of binary diffusion coefficients of hydrocarbon mixtures using MLP and ANFIS networks based on QSPR method

In this article, at first, a quantitative structure–property relationship (QSPR) model for estimation of limiting diffusion coefficients of hydrocarbon liquids, DAB0, is developed. Particle swarm optimization variable selection (PSOvs) method, together with multi-linear regression (MLR) model, selects suitable descriptors from a pool of 1124 predefined descriptors. The MLR model is trained based on a data bank of 345 experimental binary diffusivities of hydrocarbons in infinite dilution solutions. The objective function of the optimizer for descriptor selection is the multi-variant RQK function. In addition, an artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) are developed as two nonlinear black-box estimators of DAB0 based on the descriptors obtained from PSOvs algorithm. The estimation results of these three QSPR models (PSO-MLR, ANN and ANFIS) are compared with five semi-empirical correlations. Furthermore, using 402 experimental binary diffusion coefficient data at different concentrations and temperatures, another multi-layer perceptron network (MLPN) is constructed to predict the diffusion coefficients of binary hydrocarbon liquid systems at various concentrations and temperatures. The input variables of this network are DAB0, DBA0, and mole fraction of the component A. Average absolute relative deviations (AARD) of the developed MLP-QSPR model for training, test, and whole data are respectively, 5.86%, 7.79%, and 6.32%. Indeed this model has less than 5% AARD for more than 50% of the data points. Also, the results of the MLP model designed to estimate the binary diffusivities of concentrated hydrocarbon mixtures show that the average absolute relative error for the whole of test and training data is 6.3%. The comparison of the developed MLP model with experimental data and some of semi-empirical correlations indicates that the suggested modeling scheme based on QSPR and MLP method has very good accuracies for estimation/prediction of liquid hydrocarbon diffusivity not only in infinite dilution but also at concentrated solutions.

Proton exchange membranes from sulfonated polyetheretherketone and sulfonated polyethersulfone-cardo blends: Conductivity, water sorption and permeation properties

Five blend membranes were prepared by solvent evaporation from solutions of the synthesized sulfonated polyetheretherketone (SPEEK) and sulfonated polyethersulfone-cardo (SPESc). Their ion exchange capacity and degree of sulfonation determined by acid–base titration and by thermogravimetric analysis were consistent. The blends glass transition behavior obtained by differential scanning calorimetry suggests that the two sulfonated polymers are compatible in the whole composition range. The values of the activation energy for proton transport determined by conductivity measurements on the SPEEK-based blend membranes were in the range of 13–34kJmol−1, which suggest a mixed transport mechanism that involves both proton jumps on ionic sites and water of hydration and diffusion of proton–water complex in hydrophilic domains.The water vapor sorption in the membranes exhibits sigmoid-shape isotherms which were well fitted by the “new dual mode sorption” model, and the fitted parameters values were successfully used to model the change in the water permeation flux with the upstream water activity using the first Fick's diffusion equation. The fast increase in the permeation flux beyond a critical value of activity (0.5) was owing to the exponential concentration-dependent diffusion coefficient. These modelings allowed us to show a strong increase in the limit diffusion coefficient of water and a decrease in the water-diffusion plasticization coefficient with the SPEEK content in the polymer blends.

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.