Calculation of diffusion coefficients for carbon dioxide + solute system near the critical conditions by non-equilibrium molecular dynamics simulation

A non-equilibrium molecular dynamics simulation was adopted to calculate the diffusion coefficients for a pseudo-binary system of carbon dioxide and for a carbon dioxide + solute system at 308.2 and 318.2 K. The calculated results were compared with the self- and tracer diffusion coefficients calculated by an equilibrium molecular dynamics simulation. The simulated results for the pseudo-binary system of carbon dioxide by the non-equilibrium molecular dynamics simulation are in good agreement with the results of self diffusion coefficients for pure carbon dioxide by the equilibrium molecular dynamics simulation. The simulated results of mutual diffusion coefficients for the carbon dioxide + solute system by the non-equilibrium molecular dynamics simulation are slightly lower than the results of the tracer diffusion coefficients by the equilibrium molecular dynamics simulation. The anomalous behavior of diffusion coefficients near the critical concentration was represented by the results of the non-equilibrium molecular dynamics simulation.     

Correlation of diffusion coefficients for naphthalene and dimethylnaphthalene isomers in supercritical carbon dioxide

An equation proposed by Darken, including the thermodynamic factor and tracer diffusion coefficients of solvent and solute, was adopted to correlate the diffusion coefficients for naphthalene and dimethylnaphthalene (DMN) isomers in supercritical carbon dioxide and the correlated results were compared with the experimental data. IML equation of state with mixing rules and combining rules containing two adjustable interaction parameters were used for calculation of the thermodynamic factor. By using the interaction parameters adjusted to the solubility data, the concentration dependence of diffusion coefficients and their anomaly near the critical point of carbon dioxide can be quantitatively represented. In order to improve the reliability of experimental results, some re-measured diffusion coefficient data for naphthalene, 2,6- and 2,7-DMN at 308.2 K, and new data for naphthalene at 318.2 K and for 2,3-DMN at 308.2 K are presented.     

Tracer and self-diffusion of rosebengal sodium131I in 1% agar gel medium

Tracer and self-diffusion coefficients for Rosebengal labelled with¹³¹I are determined in agar gel medium at different temperatures and the activation energies for the two processes are determined by zone diffusion technique. The slight difference in tracer and self-diffusion values observed is small enough to be consistent with Hertz's recent theory of linear response of tracer diffusion coefficients in electrolyte and non-electrolyte systems.     

Accurate tracer diffusion coefficients of Na+ and Cl− ions in dilute aqueous sodium chloride solutions measured with the closed capillary method

A simple and absolute closed capillary method is introduced for measuring tracer diffusion coefficients in liquids with both - and -active tracers. In this method a narrow capillary is partially filled with a labelled solution and an unlabelled solution is used to fill the rest of the capillary. The diffusion coefficient is obtained from the time dependence of the monitored activity when the length of the capillary is known. The method has been tested by remeasuring the tracer diffusion coefficients of²²NaCl and Na³⁶Cl for solutions covering a wide range of total NaCl concentration. The average precision of the measurements was about 0.3%. The results obtained for Na³⁶Cl tracer diffusion are in good agreement with the data found in literature. The²²NaCl tracer diffusion coefficients that were measured in dilute solutions agree well with those obtained using the continuous open-ended capillary method but differ from results for solutions between 0.1 and 1M obtained with the diaphragm cell method.     

The effect of riboflavin-photoinduced degradation of alginate matrices on the diffusion of poly(oxyethylene) probes in the polymer network

The effect of irradiation, in the wavelength range of 310-800 nm, on the tracer diffusion of poly(oxyethylene) (POE) of different molecular weights embedded in various alginate matrices with the photosensitizer riboflavin (RF) present, has been investigated with the aid of pulsed field gradient spin-echo NMR (PGSE-NMR). Both alginate solutions of different polymer concentration were studied as well as corresponding acid gels of alginate produced by introduction of different amount of glucono-δ-lactone (GDL). In 2 wt.% alginate solutions, the values of the tracer diffusion coefficient suggest a strong obstruction effect as the probe molecular weight increases. Faster probe diffusion was observed for the irradiated samples, which indicates a photochemical scission of the polymer chains and the formation of a fragmented polymer network that facilitates the migration of the tracer chains. A semidilute alginate/RF solution was transformed into a gel by adding sufficient amount of GDL. GDL lowers the pH of the solution under the pK_a of alginate, favouring intermolecular associations and the evolution of a less homogeneous network with more open structure. Therefore, the POE chains were shown to diffuse faster in the acid gel matrix than in the corresponding more homogeneous alginate solutions. The photochemically induced cleavage again promoted faster migration of the probe chains in the irradiated samples. The probe diffusion of the eight-arm star-shaped POE sample revealed an augmented obstruction effect with increasing alginate concentration and higher values of the diffusion coefficient were found in gels. The evolution of a tighter network inhibits the diffusion of the probe molecules. At lower alginate concentrations the values of the tracer diffusion coefficients are higher for the irradiated samples than for the non-exposed systems.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Molecular dynamics simulation study of friction and diffusion of a tracer in a Lennard–Jones solvent

The friction and diffusion coefficients of a tracer in a Lennard–Jones (LJ) solvent are evaluated by equilibrium molecular dynamics simulations in a microcanonical ensemble. The solvent molecules interact through a repulsive LJ force each other and the tracer of diameter σ₂ interacts with the solvent molecules through the same repulsive LJ force with a different LJ parameter σ. Positive deviation of the diffusion coefficient D of the tracer from a Stokes–Einstein behavior is observed and the plot of 1/D versus σ₂ shows a linear behavior. It is also observed that the friction coefficient ζ of the tracer varies linearly with σ₂ in accord with the prediction of the Stokes formula but shows a smaller slope than the Stokes prediction. When the values of ratios of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation D = k _B T/ζ, from which the tracer is considered as a Brownian particle.     

Tracer diffusion properties of core–shell latex films studied by photoinduced grating relaxation

This article reports the application of the Photo‐Induced Grating Relaxation technique (also known as Forced Rayleigh Scattering) to investigate the dynamics of films prepared from structured core–shell latex particles via the transport property of the photochromic tracer molecule Aberchrome 540®. The core–shell particles were prepared with a fluoropolymer core (immiscible and impenetrable to the tracer) and a poly(butyl methacrylate) shell. The incompletely dried films (with residual water) manifest their spatial heterogeneity via non‐Fickian behavior (spatial scale‐ dependent apparent diffusion coefficient). The diffusion data was interpreted using the two‐state diffusion model, previously developed to describe the tracer diffusion in latex films without any core–shell structure. In contrast to dry latex films made from homogeneous particles, where one observes Fickian diffusion indicative of a homogeneous polymer film, we find that the lattice of fluoropolymer cores leads to a length scale dependent diffusion coefficient for the tracer. This effect can be interpreted as microscopic evidence for a strain hardening effect due to the presence of a hardened layer of matrix polymer (= shell) surrounding the core, which act as nanofillers. This strain hardening effect could be quantified within the two‐state diffusion model in terms of tracer diffusion coefficients and root mean squared displacements. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2823–2834, 2007     

Tracer diffusion in fluctuating block copolymer melts

We present a theoretical investigation of the tracer diffusion of diblock copolymers and homopolymers in a thermally fluctuating block copolymer melt above the order-disorder transition (ODT) temperature. Entanglement effects and differences in monomeric friction coefficients are ignored; hence, the theory should be most applicable to short copolymers with rheologically similar blocks. Overall, we find that the diffusion rates of both tracer block copolymers and homopolymers in a block copolymer melt are suppressed when compared with diffusivities in a strictly homogeneous medium with the same average composition. This mobility suppression is due to thermally excited composition fluctuations in block copolymer melts near the ODT; the latter result in transient potential barriers to diffusion. We explore the dependence of the tracer diffusion coefficient on molecular weights and compositions of both matrix and tracer, as well as temperature. A comparison of our theoretical predictions to recent experiments by T. Lodge and coworkers shows qualitative agreement. © 1996 John Wiley & Sons, Inc.     

Determination of lattice and grain boundary diffusion coefficients in protective alumina scales on high temperature alloys using SEM,TEM and SIMS

Grain and grain boundary diffusion coefficients in alumina scales on FeCrAl-based ODS alloys have been determined. The boundary diffusion-coefficients have been derived by combining gravimetrically determined growth rate data with SEM and TEM analyses of the oxide scale microstructure. The diffusion coefficients determined have been used as input parameters for a computer model describing the oxygen isotope exchange between grain and grain boundary in the alumina scale which forms during a two-stage oxidation using (18)O-tracers. This comparison of the calculated tracer profiles with profiles determined experimentally by SIMS allows the estimation of the lattice diffusion coefficient of oxygen in the alumina scale.     

THE DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DEFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUIDCHROMATOGRAPHY TECHNIQUE

1INTRODUCTIONTheseparationprocessoflarge-scaleliquidchromatographyisaunstabletransferprocess.Theseparationefficiencyisaffecteddirectlybytheadsorptionisotherms,themasstransferresistancewithinsolidadsorbentparticleandtheoperationparametersinthesystem.Therefore,thedeterminationoftheisothermsandisnecessaryfordesigningandoptimizingthechromatographicprocess.Thereareseveralmethodstodeterminekineticparameters.Carl(1992)carriedoutthekineticexperimentoftheadsorptioninacontinuousstirredtankadsorberl…     

Molecular dynamics simulation of solution structure and dynamics of aqueous sodium chloride solutions from dilute to supersaturated concentration

Constant-temperature and constant-pressure (NpT) molecular dynamics simulations were performed to study the effects of salt concentration ranging from dilute to supersaturated concentrations on solution structure and dynamical properties of aqueous sodium chloride solutions at 298 K. The rigid SPC/E model was used for water molecules, and sodium and chloride ions were modeled as charged Lennard–Jones particles. Na⁺–Cl⁻ radial distribution functions showed the presence of contact ion pairs and solvent separated ion pairs. The coordination numbers of Na⁺–Cl⁻ ion pairs increased with salt concentration up to saturated concentration, although the number of contact ion pairs was almost constant in supersaturated regions. The tracer diffusion coefficients of both ions decreased with salt concentration up to saturated concentration, while that of sodium ion was almost constant in supersaturated regions. The tracer diffusion coefficients of both ions were therefore quite close to each other. The constant number of the contact ion pairs and the almost equality of the tracer diffusion coefficients of both ions would lead to the formation of clusters in supersaturated solutions.     

Determination of lattice and grain boundary diffusion coefficients in protective alumina scales on high temperature alloys using SEM, TEM and SIMS

Grain and grain boundary diffusion coefficients in alumina scales on FeCrAl-based ODS alloys have been determined. The boundary diffusion-coefficients have been derived by combining gravimetrically determined growth rate data with SEM and TEM analyses of the oxide scale microstructure. The diffusion coefficients determined have been used as input parameters for a computer model describing the oxygen isotope exchange between grain and grain boundary in the alumina scale which forms during a two-stage oxidation using ¹⁸O-tracers. This comparison of the calculated tracer profiles with profiles determined experimentally by SIMS allows the estimation of the lattice diffusion coefficient of oxygen in the alumina scale.     

THE DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DIFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUID CHROMATOGRAPHY TECHNIQUE

The parameter identification model is proposed for determining the linear adsorption isotherms and the solid diffusion coefficients by using adsorption chromatorgaphy.Axial dispersion coefficients is firstly determined by pulse-respond experiment technique with an inert substance as tracer,then the elution curves of chromatography separating the isomer mannitol and sorbitol are determined by the chromatographic measuring technique,and pinally the adsorption isotherms and the solid diffusion coefficients of mannitol and sorbitol on Ca^2+ resins are estimated by using this model.The results show that the axial dispersion coefficients increase with fluid velocity increasing,The adsorption equilibrium constants decrease with temperature rising;and the solid diffusion coefficients increase with temperature rising.The theoretical elution curves are good agreement with the experimental elution curves of the liquid adsorption chromatography separating the mannitol and the sorbitol.The model provides a simple and reliable procedure to estimate the kinetic and thermodynamic parmeters of the adsorption.     

The “fast” and “slow” mode theories of interdiffusion in polymer mixtures: Resolution of a controversy

The theory of interdiffusion of a pair of components in multicomponent polymer mixtures is reviewed from a statistical point of view, and the foundation of the “fast” and “slow” mode theories, as well as the more recent “ANK” theory of interdiffusion is critically examined. The ANK theory reproduces the results of the slow and fast mode theories as the two limits when the vacancy concentration is varied from zero to a large value, and shows that the interdiffusion coefficient in a binary compressible mixture at finite vacancy concentrations can not in general be expressed only in terms of the tracer diffusion coefficients of the components, but it involves in addition the cooperative diffusion coefficient which characterizes the relaxation of total density fluctuations. The predictions of the ANK expression for the molecular dependence of the kinetic factor is compared with recent scattering experiments.     

Spatial scale-dependent tracer diffusion in bulk polycarbonate studied by holographic relaxation

The diffusion of a photochromic dye tracer in polycarbonate was studied by a holographic relaxation technique (forced Rayleigh scattering) at temperatures close to the glass transition temperature. By varying the holographic grating period the results could be interpreted via the spatial scale dependence of apparent diffusion coefficients within a two-state diffusion model. This indicates inhomogeneities on the scale of a few micrometers in the polymer glass.     

Limiting diffusion coefficients of ionic liquids in water and methanol: a combined experimental and molecular dynamics study

Mutual diffusion coefficients D(12) of the ionic liquids 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C(2)MIM][NTf(2)]) and [C(4)MIM][NTf(2)] in highly diluted solutions of water and methanol have been measured at different temperatures between 288 K and 313 K using the Taylor dispersion technique. Tracer diffusion coefficients of the two cations [C(2)MIM](+) and [C(4)MIM](+) as well as the anion [NTf(2)](-) in these solutions have been obtained by molecular dynamics (MD) simulations. For our simulations we used well established force fields for the solvents water and methanol and a recently developed force field for imidazolium-based ionic liquid [C(n)MIM][NTf(2)]. Mutual diffusion coefficients D(12) have been calculated from the tracer diffusion coefficients using the Nernst-Hartley equation strictly valid only at low ionic concentration. The agreement between the diffusion coefficients reported in the literature, the experimental data obtained in this work and the MD results is excellent.     

Relation between amorphous structure of polymers and penetrant diffusion: A molecular dynamics simulation

Molecular dynamics simulation has been performed for studying the relation between amorphous structure of polymers and penetrant diffusion. The self-diffusion coefficients of O₂ and He in various polymer models, which differ from each other in view of the amorphous structure, were calculated above their glass transition temperatures. The amorphous structure was characterized by considering the percolation of the unoccupied volume. A good correlation was found between the self-diffusion coefficients and the number of clusters in the unoccupied volume at the critical point of the percolation. Based on the simulated cluster size distribution at the critical point, we defined a parameter into which effects of both the amorphous structure and the penetrant size are well incorporated. It was confirmed that the penetrant diffusion is intimately associated with the amorphous structure of polymers.     

Chemical self diffusion in CdTe

The diffusion constant determining the rate of the variation in the stoichiometric composition of CdTe for a change in cadmium pressure is measured for indium doped crystals. The results for doped as well as undoped crystals are expressed in terms of previously determined equiconcentration tracer diffusion constants using a detailed point defect model. Factors responsible for asymmetrical behavior are discussed.     

Diffusion of camphorquinone in uniaxially drawn polycarbonate films

Employing the laser-induced holographic grating relaxation technique, we have measured tracer diffusion coefficients of a phtochromous dye, camphorquinone, in uniaxially drawn polycarbonate films as a function of stretch ratio. Anisotropy in the tracer diffusion coefficient has been observed with D_∥ greater than D_⟂ by at least a factor of 4 for the film stretched to the stretch ratio δ = 2.3. The diffusion coefficient along the direction of stretch D_∥ increases significantly with increasing δ, whereas D_⟂ decreases slightly with increasing δ. The stretch ratio dependence of D_∥ and D_⟂ is interpreted according to a modified free volume theory. The strain rate and stretch temperature dependence of the anisotropic tracer diffusion coefficient has also been investigated. © 1992 John Wiley & Sons, Inc.