Mutual Diffusion Coefficients Research Articles

Transport Properties in Multicomponent Systems Containing Cyclodextrins and Nickel Ions.

In this work, we propose a comprehensive experimental study of the diffusion of nickel ions in combination with different cyclodextrins as carrier molecules for enhanced solubility and facilitated transport. For this, ternary mutual diffusion coefficients measured by Taylor dispersion method are reported for aqueous solutions containing nickel salts and different cyclodextrins (that is, α-CD, β-CD, and γ-CD) at 298.15 K. A combination of Taylor dispersion and other methods, such as UV-vis spectroscopy, will be used to obtain complementary information on these systems. The determination of the physicochemical properties of these salts with CDs in aqueous solution provides information that allows us to understand solute-solvent interactions, and gives a significant contribution to understanding the mechanisms underlying diffusional transport in aqueous solutions, and, consequently, to mitigating the potential toxicity associated with these metal ions. For example, using mutual diffusion data, it is possible to estimate the number of moles of each ion transported per mole of the cyclodextrin driven by its own concentration gradient.

Effect of Caffeine in the Diffusion Behaviour of Analgesic Drugs in Aqueous Solutions

The aim of the study was to examine the effect of caffeine on the diffusion of two pain-relieving drugs, namely paracetamol and sodium salicylate, in aqueous solutions at a temperature of 25.00ºC, using the Taylor dispersion method to determine the mutual diffusion coefficients for these ternary aqueous solutions. Ternary mutual diffusion coefficients are reported for aqueous solutions of paracetamol + caffeine, and sodium salicylate + caffeine, at 25.00ºC, and concentrations up to 0.050mol·dm-3. The data indicate that the presence of caffeine affects the diffusion of analgesic drugs. For example, a coupled diffusion of these drugs with caffeine was observed through the non-zero values of the cross-diffusion coefficients. Support for this came from the good agreement between our data and the predicted by a model of the diffusion that includes 1:1 complex, being obtained the association constants for systems [(caffeine and paracetamol) and (caffeine and salicylate sodium)], K=70mol-1·dm3 and K=80, respectively. These data provide us with a better understanding of the mechanisms of mass transport through diffusion in biological systems, as well as the structure of these systems.

Effect of a 0.05% Nickel Addition to Zinc Melt on the Mutual Diffusion Coefficient of Iron and Zinc in the Formation of a Zinc Coating

Effect of a 0.05% Nickel Addition to Zinc Melt on the Mutual Diffusion Coefficient of Iron and Zinc in the Formation of a Zinc Coating

A novel measurement method for measuring the concentration-dependent mutual diffusion coefficients based on finite volume method

This paper presents a novel measurement method based on the finite volume method (FVM), which can be used for measuring the concentration-dependent mutual diffusion coefficient D(C) in binary solution. The measurement principle of D was derived by integrating the Fick’s second law in the control volume and establishing discretization equation. By simulating the diffusion process of binary solution, discussed the feasibility of this method. This new method can be used by an experimental system that can monitor changes in concentration distribution, such as optical interferometry. A set of 20 binary mixtures was tested to verify the method. The experimental results showed good agreement with and the literature, which verifies the accuracy of the method. The relative expanded combined uncertainty for the proposed method is estimated to 2.2 %. In addition, D(C) of LiTSFI aqueous solution was measured by the new method based on the digital holographic interferometry system at 288.15 K, 298.15 K and 308.15 K over the mass fraction range of 0 ∼ 0.447 (0 ∼ 2 mol/L). The temperature and concentration influences of D were discussed and a semi-empirical correlation was built.

Computer modeling of thermotransport in a uniform binary liquid solution with equimolar n-alkane mixtures

By means of molecular dynamics (MD), two novel methods, a thermal mean-path that may outline temperature profiles effectively in the MD system and a modified coarse-grained force field potential (the MCG-FFP) that may depict inter/intra-molecular interactions fairly well among n-alkane species, are employed to simulate a thermotransport process in a uniform liquid solution with two equimolar n-pentane (nC-5) and n-decane (nC-10) mixtures. In addition, all the MD simulations are running under two constraints: a weak thermal gradient exerting on the MD system from its hot through cold boundary sides and the standard-state acting on the MD system from its outer environment. During the whole MD simulations, coefficients of thermal diffusion and mass mutual diffusion, and the Soret coefficient (SC) for the MD system are calculated by using the MCG-FFP. As a result, the MD simulations indicate that nC-5 species with light molar-mass would migrate toward the hot boundary region, while nC-10 species with heavy molar-mass would migrate toward the cold one. Coefficients calculated from the MCG-FFP are found to meet relevant experimental outputs fairly well. Furthermore, an empirical formula developed by means of relevant continuum methods is used for calculating coefficients of mass mutual diffusion in solutions mixing with multimolar nC-5 and nC-10 species. Its one output is found to corroborate pretty well with that from the MD simulations. This may expect that such the formula would perform universally when characterizing properties of mass mutual diffusion in binary liquid solutions with other multimolar alkane mixtures in the petroleum engineering.

Molecular Modeling of Supercritical Processes and the Lattice—Gas Model

The existing possibilities for modeling the kinetics of supercritical processes at the molecular level are considered from the point of view that the Second Law of thermodynamics must be fulfilled. The only approach that ensures the fulfillment of the Second Law of thermodynamics is the molecular theory based on the discrete–continuous lattice gas model. Expressions for the rates of the elementary stage on its basis give a self-consistent description of the equilibrium states of the mixtures under consideration. The common usage today of ideal kinetic models in SC processes in modeling industrial chemistry contradicts the non-ideal equation of states. The used molecular theory is the theory of absolute reaction rates for non-ideal reaction systems, which takes into account intermolecular interactions that change the effective activation energies of elementary stages. This allows the theory to describe the rates of elementary stages of chemical transformations and molecular transport at arbitrary temperatures and reagent densities in different phases. The application of this theory in a wide range of state parameters (pressure and temperature) is considered when calculating the rates of elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependencies are calculated within the framework of the law of the corresponding states for the coefficients of compressibility, shear viscosity, and thermal conductivity of pure substances, and for the coefficients of compressibility, self- and mutual diffusion, and shear viscosity of binary mixtures. The effect of density and temperature on the rates of elementary stages under supercritical conditions has been demonstrated for a reaction’s effective energies of activation, diffusion and share viscosity coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described.

Role of Mutual Diffusion in the Dissolution Behavior of One Primary Bulk Gas Nanobubble in Liquid: A Molecular Dynamics Study.

Dissolution of one primary bulk gas nanobubble in an undersaturated liquid constitutes one of the underlying issues of the exceptional stability of bulk gas nanobubble population. In this paper, the mutual diffusion coefficient at the gas-liquid interface of one primary bulk gas nanobubble is investigated via all-atom molecular dynamics simulation, and the applicability of the Epstein-Plesset theory is verified. The mutual diffusion coefficient, different from the self-diffusion coefficient in bulk gas or bulk liquid, is essentially determined by the chemical potential due to its driving role in the mass transfer across the interface. We could ascribe the low-rate dissolution of one primary bulk gas nanobubble in an undersaturated liquid to the slight attenuation of the mutual diffusion coefficient at the interface. The results show that the dissolution process of one primary bulk gas nanobubble in an undersaturated liquid fundamentally obeys the Epstein-Plesset theory and that the macroscopic dissolution rate is intrinsically determined by the gas mutual diffusion coefficient at the interface rather than the self-diffusion coefficient in the bulk phase. The mass transfer viewpoint from the present study might actively promote subsequent studies on the super-stability of bulk gas nanobubble population in liquid.

Mutual diffusion coefficients of three alkanes (n-heptane, n-octane and isooctane) in cyclohexane from 288.15 K to 308.15 K

Mutual diffusion coefficients of three alkanes (n-heptane, n-octane and isooctane) in cyclohexane were measured by digital holographic interferometry under atmospheric pressure. The measured temperature points were 288.15 K, 298.15 K and 308.15 K, respectively and the mass fraction of the measured solution range was from 0.05 to 0.95. The extended relative uncertainty of the measurement system was estimated to be less than 2.4%. The dependence of mutual diffusion coefficient on temperature and solution concentration was studied. The mutual diffusion coefficients of these three binary mixtures increase with the increase of temperature and have a nearly linear relationship with the solution concentration. And the image processing process of holographic interference image is introduced in detail. Zhang et al.’s model, Darken model and Vignes model were used to predict the mutual diffusion coefficients of the three binary mixtures, the absolute average of relative deviations (AARDs) are 2.97%, 3.89% and 6.18%, respectively and Zhang et al.’s model is the one with the best agreement among the three models.

Diffusion coefficients and phase equilibria of carbon dioxide–ionic liquid, 1‐butyl‐3‐methylimidazolium hexafluorophosphate ([bmim][PF6]) system

AbstractThis article presents the mutual diffusion coefficients of a carbon dioxide–ionic liquid, [bmim][PF6], system at temperatures of 313.15 and 323.15 K and pressures of 5 and 8 MPa. In order to estimate the diffusion coefficients, we have carried out experiments to find time‐dependent carbon dioxide solubilities in the ionic liquid and then fit a transport model to the data. In a system containing high pressure carbon dioxide and ionic liquid, carbon dioxide dissolves in the liquid until its equilibrium mole fraction is reached. During this process, the position of the liquid–vapour interface and the density of the liquid phase change. To account for the variation in liquid density, an equation fit to the experimental density data is included in the transport model. To track the moving interface, the volume‐of‐fluid method is used. The diffusivities at dilute concentration and at thermodynamic phase equilibrium are determined and compared with the literature values and those obtained from correlations.

Interactions of Sodium Salicylate with β-Cyclodextrin and an Anionic Resorcin[4]arene: Mutual Diffusion Coefficients and Computational Study.

The interaction between sodium salicylate (NaSal) and the two macrocycles 5,11,17,23-tetrakissulfonatomethylene-2,8,14,20-tetra(ethyl)resorcinarene (Na4EtRA) and β-cyclodextrin (β-CD) has been studied by the determination of ternary mutual diffusion coefficients, and spectroscopic and computational techniques. The results obtained by the Job method suggest that the complex formation is given in a 1:1 ratio for all systems. The mutual diffusion coefficients and the computational experiments have shown that the β-CD-NaSal system presents an inclusion process, whereas the Na4EtRA-NaSal system forms an outer-side complex. This fact is also in line with the results obtained from the computational experiments, where the calculated solvation free energy has been found to be more negative for the Na4EtRA-NaSal complex because of the partial entry of the drug inside the Na4EtRA cavity.

Influence of dispersive long-range interactions on transport and excess properties of simple mixtures

The influence of dispersive long-range interactions on liquid bulk phase transport and excess properties of six binary Lennard–Jones (LJ) mixtures was studied by molecular dynamics simulation and equation of state modelling. For the transport properties, the self-diffusion coefficients, mutual diffusion coefficients, shear viscosity, and thermal conductivity were considered. For the excess properties, the excess energy, volume, Gibbs energy, and entropy were studied. Moreover, the thermodynamic factor was studied. The two components had the same size parameter in all cases, but different dispersion energies and different cross-interaction parameters. Thereby, the six resulting mixtures show three types of phase behaviour: ideal, high- and low-boiling azeotrope. For studying the influence of the dispersive long-range interactions, the results of the full LJ potential were compared to the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the self-diffusion and the mutual diffusion coefficients, whereas the shear viscosity and the thermal conductivity are hardly affected. For all investigated properties, the dispersive long-range interactions have practically no influence on the composition dependency.

Simultaneous Measurement of Thermal and Mutual Diffusion Coefficients by Dynamic Light Scattering

Simultaneous Measurement of Thermal and Mutual Diffusion Coefficients by Dynamic Light Scattering

Measuring mutual diffusion coefficients in aqueous binary mixtures with unidimensional drying cells.

Chemical diffusion is a mass transport process caused by thermally generated motions of species. In a binary mixture, the diffusion of one species in one direction involves the diffusion of another species in the opposite direction, which corresponds to a single mutual diffusion coefficient. Here, we report a simple and general method to measure such coefficients in binary liquid mixtures, using the PNIPAM/water system as a study case. Experimentally, we show how a simple unidirectional drying cell coupled with a spatially-resolved characterization method such as Raman microscopy can yield concentration gradients developing in between two boundaries of known and constant chemical potential. Acquiring such gradients over time leads to a time-set that is shown to collapse to a single master curve using a change of variable. Such a scaling law offers a self-checking frame for solving analytically the diffusion-advection equation. As a result, we show that a simple analytical formula relates the measured concentration gradient with the concentration-dependent mutual diffusion coefficient. In the PNIPAM/water system, the mutual diffusion coefficient sharply decreases at low water content. Our work thus highlights the importance of considering the concentration-dependence of the mutual diffusion coefficient in complex aqueous solutions and provides a method to measure it.

Diffusion-driven rotation in cholesteric liquid crystals studied using molecular dynamics simulation of a mixture of the Gay-Berne fluid and the Lennard-Jones fluid.

Diffusion-driven rotation in cholesteric liquid crystals has been studied using molecular dynamics simulation. Then a chemical potential gradient parallel to the cholesteric axis induces a torque that rotates the director at a constant rate around this axis, besides driving a mass current. An equimolar mixture of Gay-Berne ellipsoids and Lennard-Jones spheres was used as the molecular model. In order to keep the system homogeneous, the color conductivity algorithm was used to apply a color field instead of a chemical potential gradient to drive a mass current. Then the particles are given a color charge that interacts with a color field in the same way as with an electric field, but these charges do not interact with each other. This algorithm is often used to calculate the mutual diffusion coefficient. In the above liquid crystal model, it was found that the color field induces a torque that rotates the director at a constant rate around the cholesteric axis in addition to driving a mass current. The phenomenon was quantified by calculating the cross-coupling coefficient between the color field and the director angular velocity. The results were cross-checked by using a director rotation algorithm to exert a torque to rotate the director at a constant rate. Besides rotation of the director, this resulted in a mass current parallel to the cholesteric axis. The cross-coupling coefficient between the torque and the mass current was equal to the cross-coupling coefficient between the color field and the director rotation rate within a statistical uncertainty of 10 percent, thus fulfilling the Onsager reciprocity relations. As a further cross-check, these cross-coupling coupling coefficients, the color conductivity, and the twist viscosity were calculated by evaluating the corresponding Green-Kubo relations. Finally, it was noted that the orientation of the cholesteric axis parallel to the color field is the one that minimizes the irreversible energy dissipation rate. This is in accordance with a theorem stating that this quantity is minimal in the linear regime of a nonequilibrium steady state.

Formation of glassy skins in drying polymer solutions: approximate analytical solutions.

We study the formation of a glassy skin at the air interface of drying polymer solutions. We introduce a simple approximation, which is valid for most diffusion problems, and which allows us to derive analytical relationships for the polymer concentration as a function of time. We show that the approximate results differ by less than 15% from those obtained by numerically solving the diffusion equation. We use the approximation to study skin formation in evaporating solutions. We focus on the influence of variations of the mutual diffusion coefficient with concentration, when the latter decreases sharply at high concentrations, as observed in the vicinity of the glass transition. We show that the skin thickness depends very strongly on the exponent characterising the decrease of the diffusion coefficient, in contrast to the polymer volume fraction at the interface, which varies only slightly with the exponent.

Effect of potassium dihydrogen citrate on the diffusion behaviour of citric acid

Ternary mutual diffusion coefficients (D11, D22, D12, and D21) in aqueous solutions of citric acid (H3Cit) (component 1) plus potassium dihydrogen citrate (KH2Cit) (component 2) at 298.15 K and concentrations up to 0.040 mol dm−3 were measured using a Taylor scattering method. The obtaining of the negative values for D12 and D21 cross coefficients, mainly in dilute solutions and for the first ones, indicates that there is a strongly coupled diffusion of these components. In fact, the concentration gradients of KH2Cit drive substantial counter current coupled flows of H3Cit citric acid, indicating that each mol of diffusing potassium dihydrogen citrate can counteract the transport of up to 0.74 mol of citric acid, approximately. A better interpretation of the electrostatic mechanism for the coupled diffusion of KH2Cit and H3Cit was achieved based on the values predicted by the Nernst-Planck equations, having been verified as a good agreement between them and experimental data.

On the diffusion of ketoprofen and ibuprofen in water: An experimental and theoretical approach

In view of its importance for the development of dispersion and distribution models in the environment and also for the design of removal methods from wastewaters, the mobility and solute-solvent interaction in aqueous solutions of two non-steroidal anti-inflammatory drugs (ketoprofen and ibuprofen) were studied by measuring mutual diffusion coefficients of each pharmaceutical in water at infinitesimal concentration as a function of temperature, using the Taylor dispersion method. Intra-diffusion coefficients of the same solutes in water at the same temperature range were also calculated by Molecular Dynamics simulations. The analysis of the simulation trajectories allowed the study of the structure of the solvent molecules around the solute and their mutual interaction, which was also addressed by quantum mechanical (DFT) calculations. Ibuprofen presents a higher mutual diffusion coefficient in water than ketoprofen and molecular dynamics simulations are able to predict the experimental values for two solutes. Besides the solute molecular weight and molecular dimensions, the diffusion coefficients of these two pharmaceuticals are influenced by the solute-solvent interactions, which seem to be stronger in the case of ketoprofen. The solvation free energy obtained via DFT calculations confirms that hypothesis.

Processes of charge, mass and heat transfer in FeNi composite

The paper presents a study of the processes of mutual diffusion in the binary system Fe - Ni (obtained by the electrocondensation of nickel and iron powders) by the method of X-ray energy dispersive spectroscopy, as well as the processes of thermal and electrical conductivity in the temperature range of 5-300 K. Well-separated regions of almost pure iron and nickel were revealed . The nickel content, estimated by the concentration dependence of the mutual diffusion coefficient, which determines the kinetics of the process of homogenization of the electroconsolidated sample of the Fe - Ni composite, was ~ 70 at. %. The value of the mutual diffusion coefficient of the electroconsolidated Fe - Ni composite is significantly higher than that of an alloy of a similar composition, which is probably the result of the influence of SPS technology (pressure and current in one direction during consolidation), as well as a significant contribution of grain boundary diffusion mass transfer in the composite. It was established that the electrical and thermal conductivity of the electroconsolidated sample is significantly higher than that of samples of the same composition obtained by melting. It was found that the temperature dependence of the electrical resistance of the electroconsolidated sample in the studied interval of 5-300 K is due to the scattering of electrons on defects and on phonons, and the scattering of electrons on phonons can be approximated with high accuracy by the Bloch-Gruneisen-Wilson ratio. The paper shows that the experimental data on the temperature dependence of the effective electrical resistance and thermal conductivity in the range 4.2-300 K of the electroconsolidated Fe0.50Ni0.50 composite are within the Hashin-Shtrikman limits for the conductivities of a three-phase system. The components of the system are pure Fe and Ni, and the intergranular medium in the form of an alloy with an average composition close to Fe0.50Ni0.50 is considered as the third phase.

Mass transfer kinetics inside bio-(aero)gels during solvent exchange and supercritical drying: On the relevance of advection, gel-porosity and a peculiarity regarding the tortuosity

Spatially and temporally resolved composition profiles were measured inside biopolymer gels during solvent exchange and supercritical (sc) drying using one-dimensional Raman spectroscopy. The effective diffusion coefficients of solvent exchange and sc drying were obtained by fitting modelled composition profiles to the experimentally obtained ones. We considered one purely diffusional model, which excludes advection, and one convective model, which regards the superposition of diffusion and advection inside the pore system. The tortuosity was obtained by relating the obtained effective diffusion coefficients in porous media with the mutual diffusion coefficients. When considering the solvent exchange experiments the derived tortuosities for agar gels are about 1.1 and are in good agreement with literature data. When considering the sc drying experiments, the derived tortuosities are about 3.2, which is again in good agreement with literature data, but in contradiction to the tortuosities derived for the same agar gels from the solvent exchange experiments before.

Transport properties of binary Lennard-Jones mixtures: Insights from entropy scaling and conformal solution theory

The relation of transport properties and the molecular interactions in binary mixtures was studied. The self-diffusion coefficient, Maxwell–Stefan as well as Fickian mutual diffusion coefficient, shear viscosity, and thermal conductivity of liquid binary simple mixtures were therefore sampled using molecular dynamics simulations. The mixtures were described by the Lennard-Jones potential. The molecular interaction parameters were chosen such that a large variety of mixture behavior was covered. The two components had the same size parameter in all cases, but different dispersion energies. Moreover, the cross-interaction parameter used in the modified Lorentz-Berthelot combination rule was varied such that the resulting mixtures showed different types of phase behavior: ideal, high- and low-boiling azeotrope. The results are discussed using conformal solution theory as a link between the molecular interactions in the mixtures and the macroscopic properties. Moreover, the applicability of Rosenfeld’s entropy scaling is tested. Despite the important differences of the studied mixtures regarding their molecular interactions and the large pressure, temperature, and composition range considered, a practically monovariate relation of these properties with respect to the configurational entropy is observed. Yet, the quality of the approximation differs for the studied properties.