Mutual Diffusion Coefficients Research Articles

Fick diffusion coefficients via molecular dynamics: An alternative approach in the Fourier domain

Mutual diffusion coefficient data are required for several systems of scientific and engineering interest to properly describe mass transport phenomena over a wide range of pressures, temperatures, and compositions. In this work, we calculated Fick diffusion coefficients for some CO2 and n-alkane mixtures at high pressures using a new method, which we derived by introducing modifications to the Fourier Correlation Method (FCM) originally proposed by Nichols and Wheeler [I&EC Research, 54, 12,156–12,164 (2015)]. The modified FCM (mFCM) results were validated through comparisons with experimental data and with Fick coefficients calculated by employing well-established Molecular Dynamics methodologies. The new approach has some interesting advantages, such as providing Fick coefficients for molecular systems directly through a single equilibrium calculation, in contrast to traditional methods in which an extra calculation is needed to obtain the so-called thermodynamic factor. It is shown that the new approach considerably reduces the finite-size effect of the simulation box on the calculated diffusion coefficients, which are thus obtained in the thermodynamic limit.

Temperature-Dependent Mixing behaviours of Bi -Mg Liquid Alloys

ABSTRACT Bi – Mg is a strongly interacting system (the free energy of mixing > 3 RT at equiatomic composition), the compositional dependence of the thermodynamic properties (free energy of mixing, heat of mixing and entropy of mixing) exhibits asymmetric behaviour about equiatomic composition and are in well agreement with experimental data literature. Such an interesting feature is explained here through complex formation model on the basis that a complex of the form Bi2Mg3 exists in the bulk phase. Its energetics is used to investigate the structural properties (concentration fluctuation in long wavelength limit and chemical short-range order parameter) and the transport property (ratio of mutual diffusion coefficient to intrinsic diffusion coefficient). The mixing behaviour of Bi – Mg system is further explored through the study of coefficient of viscosity, surface composition and surface tension. Our study indicates that the surface is enormously rich with Bismuth concentrations throughout the composition of the alloys.

Effect of sodium chloride on the behaviour of the lactose in aqueous solution studied from diffusion experiments and molecular dynamics simulations

Ternary mutual diffusion coefficients (D11, D22, D12 and D21) measured by the Taylor dispersion method are reported for aqueous solutions of (NaCl + lactose) at 298.15 K and NaCl concentrations up to 1.00 mol dm−3. The coupled diffusion of NaCl (1) and lactose (2) is significant, as indicated by the large negative cross-diffusion coefficients. In this sense, from the values of these cross-diffusion coefficients a counter-transport of 0.4 mol of NaCl per mol of diffusing lactose is inferred, whereas only 0.02 mol of lactose could be counter-transported by one diffusing mole of NaCl. The main diffusion coefficient data are compared with the binary ones of both pure solutes in water and discussed on the basis of Onsager-Fuoss and Pikal models. From these data and by performing molecular dynamics simulations, it is possible to obtain a better understanding of the effect of sodium chloride on the transport of lactose in aqueous solutions, as well as to assume the importance of the Na+-lactose short-range interaction, competing with the coulomb long-range interaction between the sodium and chloride ions, especially at low concentration of NaCl.

Impact of intermolecular attraction and repulsion on molecular diffusion and virial coefficients of spheroidal and rod-shaped proteins

Recognition of protein intermolecular interactions is a key factor for the study and manipulation of protein activity in living systems and biotechnology formulations. Experimental parameter that is sensitive to intermolecular interactions is molecular diffusion. This work presents an extension of an earlier work where we proposed the complementary use of pulsed field gradient nuclear magnetic resonance (PFG NMR) and dynamic light scattering (DLS) to study the specific features of intermolecular interactions via protein translational diffusion. PFG NMR methodology characterizes the thermal motion of protein by means of the self-diffusion coefficient and friction formalism. DLS experiments provide the protein collective (or mutual) diffusion coefficient, which evaluates the direct, non-specific intermolecular interactions of proteins by means of virial coefficients. Theoretical analysis of obtained experimental diffusion data is based on the combination of the friction formalism of nonequilibrium thermodynamics (Vink approach) with the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. To evaluate the electrostatic potential of proteins with different shape - spheroidal alfa-chymotrypsin (ChTr) and the rod-shaped fibrinogen (Fg) we applied the model of “porous” colloid particles. Our analysis has shown that the atypical local decrease of collective diffusion relative to self-diffusion is a consequence of the dominance of van der Waals attraction over electrostatic repulsion for the rod-shaped Fg.

The study of Si/Ge interdiffusion using molecular dynamics simulation

The coefficients of mutual diffusion of silicon into germanium (and vice-versa) at temperatures of 900-1300K were found based on molecular dynamics simulation. For the characteristic temperature Tc=1100 K, which is close to the melting point of Ge, we determined the thickness of the diffusing layer for each type of atom. It is shown that the depth of diffusing significantly depends on the sintering time, and silicon atoms penetrate 1.5 times deeper into bulk germanium than germanium into silicon.

Inverse Rheological Methods for the Determination of Polymer Structures, Diffusion of Small Molecules and Nanofiber Lengths

This paper presents so-called inverse rheology methods to determine various parameters that are essential to go further in terms of modelling and/or simulation in the field of polymer processing. The following systems from our previous works are presented: i) Determination of the molecular structure of a poly(∊-caprolactone) polymerized in-situ by ring-opening; ii) Measurement of the mutual diffusion coefficient: two cases are considered, namely the diffusion of a plasticizer and the diffusion of an organic peroxide in a polymer melt and iii) Determination of the average length of polymer nanofibers in suspension and study of the universal behavior of nanofibers of different natures in dilute and semi-dilute suspensions. The application of these different studies in the field of reactive extrusion, blending and multi-scale structuring are presented and discussed.

Inverse Rheological Methods for the Determination of Polymer Structures, Diffusion of Small Molecules and Nanofiber Lengths

Abstract This paper presents so-called inverse rheology methods to determine various parameters that are essential to go further in terms of modelling and/or simulation in the field of polymer processing. The following systems from our previous works are presented: i) Determination of the molecular structure of a poly(e-caprolactone) polymerized in-situ by ring-opening; ii) Measurement of the mutual diffusion coefficient: two cases are considered, namely the diffusion of a plasticizer and the diffusion of an organic peroxide in a polymer melt and iii) Determination of the average length of polymer nanofibers in suspension and study of the universal behavior of nanofibers of different natures in dilute and semi-dilute suspensions. The application of these different studies in the field of reactive extrusion, blending and multi-scale structuring are presented and discussed.

Evaluating diffusion and the thermodynamic factor for binary ionic mixtures

Molecular dynamics (MD) simulations are a powerful tool for the calculation of transport properties in mixtures. Not only are MD simulations capable of treating multicomponent systems, they are also applicable over a wide range of temperatures and densities. In plasma physics, this is particularly important for applications such as inertial confinement fusion. While many studies have focused on the effect of plasma coupling on transport properties, here we focus on the effects of mixing. We compute the thermodynamic factor, a measure of ideal/non-ideal mixing, for three binary ionic mixtures. We consider mixtures of hydrogen and carbon, hydrogen and argon, and argon and carbon, each at 500 randomly generated state points in the warm dense matter and plasma regimes. The calculated thermodynamic factors indicate different mixing behavior across phase space, which can significantly affect the corresponding mutual diffusion coefficients. As MD simulations are still computationally expensive, we apply modern data science tools to predict the thermodynamic factor over a large phase space. Further, we propose a more accurate approximation to the mutual diffusion coefficient than the commonly applied Darken relation.

Investigation of atomic diffusion behavior of Mo/Au interface

The atomic diffusion behavior of Mo/Au interface was investigated by using molecular dynamics (MD) simulations which combines classical diffusion theory and molecular dynamics simulation, mutual diffusion coefficient and radial distribution function of Mo atoms and Au atoms were obtained. The results indicate that Au atoms can diffuse into Mo layer, while Mo atoms diffuse onto the surface of Au layer extremely difficult. The mutual diffusion coefficients and degree of atomic disorder (Mo and Au atoms) increase with the increase of diffusion temperature. The results were verified by scanning electron microscope (SEM) and X-ray photoelectron spectroscopy (XPS) analysis. The Mo 3d characteristic peaks can not be detected on the surface of Mo/Au film at annealing temperature below 673 K, which indicates that Mo atoms can not reach the surfaces of Au layers through the atomic diffusion behavior. The experimental results agree well with the simulation results. However, Mo/Au film structure has been destroyed due to aggregated Au grains at annealing temperature 973 K. Therefore, the experimental results should be taken into account in MD simulations.

Interactions between glycyl-L-phenylalanine and β-cyclodextrin from diffusion, spectroscopic and computational studies

The transport and association of the dipeptide glycyl-L-phenylalanine (Gly-L-Phen) in solutions containing cyclodextrins are of prime importance given its relevance in different areas, from biochemistry to wastewater treatment. We have investigated the interaction between aqueous Gly-L-Phen and β-cyclodextrin (β-CD) by NMR, DFT calculations in parallel with UV/visible absorption, luminescence spectral measurements and diffusion experiments. Ternary mutual diffusion coefficients of aqueous {Gly-L-Phen + β-CD} solutions have been measured by using the Taylor dispersion technique. The results show that the association of Gly-L-Phen and β-CD has a significant effect on the diffusion coefficients, consistent with an association constant of about 50 to 100, assuming a 1:1 (Gly-L-Phen):(β-CD) stoichiometry. This stoichiometry has been assessed by the continuous variation (Job's plot) method and the association constant was determined by using the Hildebrand-Benesi equation modified for NMR applications. The association constant was estimated to be equal to 40. This association constant is in close agreement with that obtained by fluorescence measurements (K = 43). Additionally, from NMR, detailed structural information on the complex has been obtained. This has been complemented by DFT and TD-DFT studies.

Special modes of diffusion mass transfer in isothermal triple gas mixtures

In isothermal three-component gas mixtures in quasi-stationary conditions the procedure of numerical solution of Stefan-Maxwell diffusion equations using the software package “MathCad” is considered. It is shown that one of the specific features of multicomponent diffusion is the appearance of nonlinear concentration distributions of components in vertical channels. Due to the difference in the coefficients of mutual diffusion of gases in some systems under certain conditions, nonlinear distributions of component concentrations lead to a non-monotonic distribution of the density of the gas mixture. By the example of hydrogen – nitrogen – methane and methane – n-butane – nitrogen systems at a constant temperature T = 298 K, the influence of the content of the component with the highest molecular weight in the triple gas mixture on the degree of nonlinearity of the density distribution in the diffusion channel is analyzed. It is suggested that the inversion of the density distribution of the mixture may be the cause of convective instability in triple gas systems. The results of calculations are compared with experimental data.

Mutual diffusion coefficient of concentrated trehalose aqueous solutions including supercooled regions measured by the Soret forced Rayleigh scattering method

We measured the binary mutual diffusion (interdiffusion) coefficient of trehalose aqueous solutions D in the concentration range from 0.1 to 0.8 mass fraction and the temperature range from 25 to 50 °C including supercooled regions under atmospheric pressure. The experimental apparatus was based on the Soret forced Rayleigh scattering (SFRS) technique, which uses the Soret effect to create a periodic spatial concentration modulation (Δw <10−5) of micrometer-order fringe spacing in a disaccharide aqueous solution due to the absorption of an optical interference grating generated by two crossing pulsed excitation laser beams (ΔT <10−2 °C). The decay of the mass diffusion process is monitored by the diffraction intensity of a probing laser beam within a few milliseconds. These characteristics of SFRS enabled us to measure highly viscous disaccharide aqueous solutions under supercooled states. The uncertainties of the experimental results were estimated to be within ±3% for low concentration and ±9% for high concentration (w > 0.55). The experimental results demonstrated that the rate of decrease in the mutual diffusion coefficient with the increasing concentration is more pronounced in supercooled regions than in dilute normal regions. We also measured the mutual diffusion coefficient of sucrose aqueous solutions at 30 °C in the supercooled regions to compare the results with those obtained from trehalose. We observed that the mutual diffusion coefficient of the trehalose aqueous solutions were smaller than those of sucrose with the increasing concentration, the ratio of Dtrehalose to Dsucrose showed an almost linear concentration-dependence towards the values that were less than half. Our findings suggest that trehalose can be more effective than sucrose in terms of the relaxation of the composition near their glass transitions.

Generalized Form for Finite-Size Corrections in Mutual Diffusion Coefficients of Multicomponent Mixtures Obtained from Equilibrium Molecular Dynamics Simulation.

The system-size dependence of computed mutual diffusion coefficients of multicomponent mixtures is investigated, and a generalized correction term is derived. The generalized finite-size correction term was validated for the ternary molecular mixture chloroform/acetone/methanol as well as 28 ternary LJ systems. It is shown that only the diagonal elements of the Fick matrix show system-size dependency. The finite-size effects of these elements can be corrected by adding the term derived by Yeh and Hummer (J. Phys. Chem. B2004, 108, 15873–15879). By performing an eigenvalue analysis of the finite-size effects of the matrix of Fick diffusivities we show that the eigenvector matrix of Fick diffusivities does not depend on the size of the simulation box. Only eigenvalues, which describe the speed of diffusion, depend on the size of the system. An analytic relation for finite-size effects of the matrix of Maxwell–Stefan diffusivities was developed. All Maxwell–Stefan diffusivities depend on the system size, and the required correction depends on the matrix of thermodynamic factors.

Lithium Salt Diffusion in Diblock Copolymer Electrolyte Using Fourier Transform Infrared Spectroscopy

Diffusion of a lithium salt through a diblock copolymer electrolyte was studied using vibrational spectroscopy. Lithium bis-trifluoromethylsulfonimide (LiTFSI) was dissolved in a lamellar-structured, high-molecular-weight polystyrene-poly(ethylene oxide) diblock copolymer at various concentrations (0 - 4.51 molLiTFSI/kgPEO). The diffusion coefficient of LiTFSI was determined from time-resolved Fourier Transform infrared spectroscopy attenuated total reflectance (FTIR-ATR) as a function of the salt concentration. By applying the Beer-Lambert law, FTIR-ATR was used to detect concentration changes. Mutual diffusion was driven by putting in contact two polymer electrolyte membranes with different salt concentrations. Thus, mutual diffusion coefficients were obtained without the influence of electric fields or electrode interfaces. The accuracy of the simple experimental approach and straightforward analysis were validated by comparison to diffusion coefficients reported from measurements in electrochemical cells. Both methods yield mutual diffusion coefficients of lithium salt that are only weakly (and non-monotonically) dependent on salt concentration. There is some indication in the spectra that there exist two populations of salt with different dissociation states. This could explain the observed non-monotonic concentration dependence of the mutual diffusion coefficient of the salt. This hypothesis will be examined quantitatively with complementary measurements in future work.

Mutual diffusion coefficients of ethanol + n-heptane and diethyl carbonate + n-heptane from 288.15 K to 318.15 K

The mutual diffusion coefficients of ethanol + n-heptane and diethyl carbonate (DEC) + n-heptane binary solutions were measured over the mass fraction from 0.05 to 0.95 at the pressure of 0.101 MPa, and at temperatures T = 288.15 K, 298.15 K, 308.15 K and 318.15 K. The expanded relative uncertainty (k = 2) of the Mach-Zehnder digital holographic interferometry employed in the measurements was estimated to be less than 2.4% with the confidence level of 0.95. A semi-empirical correlation was used to fit the mutual diffusion coefficients as a function of concentration and temperature, which represents the experimental values with the absolute average relative deviations being 0.94% for ethanol + n-heptane and 0.90% for DEC + n-heptane. The temperature and concentration dependences of the mutual diffusion coefficients were investigated. The strongest non-ideal thermodynamic behaviors appear when the mass fraction of ethanol is within the limits of 0.45 to 0.65 or that of DEC is within the limits of 0.45 to 0.65. Besides, the mutual diffusion coefficients of ethanol + n-heptane and DEC + n-heptane binary solutions are found to be extremely sensitive to the solute concentration over the mass fraction of ethanol and DEC from 0.00 to 0.05, respectively.

Determination of the Diffusion Coefficient of Supercritical CO2 in Low-Permeability Formation Cores

CO₂ diffusion in the oil phase in the presence of porous media is of great importance to forecast the performance of enhanced oil recovery and carbon dioxide capture and storage. When CO₂ is brought into contact with an oil phase, diffusion occurs. The indirect pressure-decay methodology has been applied successfully to determine the mutual diffusion coefficients of supercritical CO₂ and crude oil at temperature of 65 °C. Theoretically, a one-dimensional double-way mass transfer model incorporating the capillary and adsorption effects of porous media has been constructed to quantify the mutual dynamic diffusion coefficients. The crude oil has been characterized into five pseudo-components for the accurate description of the phase behavior of CO₂ gas and oil phases. An optimization method along with the PR equation of state is employed to determine each component’s diffusion coefficients in the gas and oil phases for the purpose of minimization of the difference between the experimental data and calculated results. Satisfactory agreements are obtained with a merely 0.97% pressure difference when a variable diffusion coefficient is implemented. The short-time experimental test and a long-time-duration calculation are recommended for further diffusion investigation. The capillary analysis gave a regressed fractal dimension of 2.7049 with the average absolute deviation of 0.602%. The adsorption phenomenon can be greatly influenced by the existence of heavy components. The heavier the components, the greater their impact on adsorption. Furthermore, a faster and enhanced diffusion process is observed at high pressure and temperature. The combination of several complex mechanisms leads to the initial gradual increase of the diffusion coefficient with time, and then, it arrives at a plateau, which is slightly different from the previous diffusion coefficient changing tendency mentioned in the literature. In the presence of a low-permeability formation core, the determined diffusion coefficients of CO₂ in the gas and liquid phases are increased from 4.38 × 10–⁹ to 6.21 × 10–⁹ and 6.16 × 10–¹⁰ to 9.21 × 10–¹⁰ m²/s when the system pressure is decreased from 18.2 to 12.11 MPa, respectively. In addition, the capillary effect can lead to a reduction of the diffusion coefficient in the oil phase but has little effect on the diffusion coefficient in the gas phase.

Dynamic Light Scattering for Studying Mutual Diffusion Coefficients in Electrolyte Systems Comprised Entirely of Ions

This study demonstrates the applicability of heterodyne dynamic light scattering (DLS) for the investigation of molecular diffusive mass transport in electrolyte systems by the determination of mutual diffusion coefficients at macroscopic thermodynamic equilibrium. For four binary model mixtures composed entirely of ions, it could be evidenced that the obtained experimental signals are associated with hydrodynamic modes. In the range from (293 to 353) K, the influence of temperature on the mutual diffusion coefficient and its relation to other thermophysical properties are discussed for the selected systems. These systems are based on three different ionic liquids (ILs) and a salt and always share a common ion in the mixture. A non-ideal behavior is observed for one study on the concentration dependence of the mutual diffusion coefficient for one of the binary IL systems in the mole fraction range between 0.1 and 0.9. For the four systems studied in this work, expanded uncertainties of the mutual diffusion coefficient go down to 3.0% and are 8.0% on average.

Знаходження та аналіз парціальних коефіцієнтів взаємодифузії для бінарних розчинів з хлороформом на основі комплексно-асоціативної моделі

In the article within the complex-associative model of liquid systems the nonlinear diffusion for a number of binary solutions, such as acetone-chloroform, tetrachlorethane-chloroform, diethyl ether-chloroform and benzene-chloroform, is considered: Real binary solutions are replaced by ideal three-component ones, which consist of averaged two associates of substance and solvent and an effective averaged complex, which is the result of quasi-chemical reactions of molecular solutions. The coefficient of mutual diffusion, which nonmonotonically depends on the concentration of the solvent, is represented as a matrix of partial coefficients of mutual diffusion, which are constant values and represent the material parameters of the considered solutions. The method of analytical calculation of numerical values of such quantities when considering the simplest type of one averaged complex is developed. It is shown that the partial coefficients are constant values and the analysis of their values for the considered solutions depending on the structure of the molecules of the substance, enthalpy and temperature is carried out. Based on the proposed approach, the deviation of the calculated «Fick’s» coefficient of mutual diffusion through the matrix of partial coefficients in comparison with experimental data is less than 2.5%.

Diffusion coefficients of carbon dioxide—ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) system at temperatures of 313 K and 323 K and pressures of 5 MPa and 8 MPa

This work reports the mutual diffusion coefficients of carbon dioxide - 1-Butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) system at different temperatures (313.15 and 323.15 K) and pressures (5 and 8 MPa). We have determined the time-dependent solubility of carbon dioxide in the ionic liquid and then, fit a computational fluid dynamics (CFD) model to the experimental data to obtain the diffusion coefficients. The increase in the molar density and the expansion of the liquid phase during the dissolution of carbon dioxide are taken into account in the transport model. The results show that the mutual diffusion coefficients increase with carbon dioxide mole fraction and the values obtained at thermodynamic phase equilibrium compare well with those calculated using different correlations.

Experimental determination and predictive modelling of the mutual diffusion coefficients of water and ionic liquid 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate

Mutual diffusion coefficients of a binary mixture of water + ionic liquid 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate have been investigated by means of experimental and predictive approaches. Optical digital interferometry has been employed to determine the mutual diffusion coefficients over the full ionic liquid mass fraction range and at four temperatures between 298.15 and 313.15 K. Moreover, the prediction ability of four different models has been tested. The influence of using different excess Gibbs energy (gE) models to calculate the relevant thermodynamics properties was also addressed. The mutual diffusion coefficient has a strong dependence on concentration and varies from 2 × 10−10 to 1.27 × 10−9 m2 s−1. The concentration and temperature dependencies of the present experimental diffusion coefficients were correlated using empirical and predictive equations. The use of binary interaction parameter regressed from diffusion data instead of vapor-liquid equilibria improves considerably the prediction ability of the employed predictive models. Among the studied predictive models, the modified group contribution model provides the best results with an absolute relative deviation of 2.1%. Throughout the paper, thermodynamic and kinetic behavior of the mixture are analyzed for establishing an appropriate criterion for the screening of ionic liquids as working fluids for absorption refrigeration systems.